Finite Group Databasebeta

← #17200280

Subgroups — #17200280

Order 4352.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531941C211yesmaximal, characteristic, complemented
2#14531941C211yesmaximal, characteristic, complemented
3#14531932C211yesmaximal, characteristic, complemented
4#14531908C211yesmaximal, characteristic, complemented
5#14531908C211yesmaximal, characteristic, complemented
6#14531849C211yesmaximal, characteristic, complemented
7#14531836C211yesmaximal, characteristic, complemented
8#14531836C211yesmaximal, characteristic, complemented
9#14531826C211yesmaximal, characteristic, complemented
10#14531826C211yesmaximal, characteristic, complemented
11#14531780C211yesmaximal, characteristic, complemented
12#14531780C211yesmaximal, characteristic, complemented
13#14531768C211yesmaximal, characteristic, complemented
14#14531768C211yesmaximal, characteristic, complemented
15#14531768C211yesmaximal, characteristic, complemented
16#14531578C211yesmaximal, characteristic, complemented
17#14531578C211yesmaximal, characteristic, complemented
18#14531563C211yesmaximal, characteristic, complemented
19#14531563C211yesmaximal, characteristic, complemented
20#14531510C211yesmaximal, characteristic, complemented
21#14531489C211yesmaximal, characteristic, complemented
22#14531489C211yesmaximal, characteristic, complemented
23#14531479C211yesmaximal, characteristic, complemented
24#14531479C211yesmaximal, characteristic, complemented
25#14531445C211yesmaximal, characteristic, complemented
26#14531445C211yesmaximal, characteristic, complemented
27#14531445C211yesmaximal, characteristic, complemented
28#123×Dic17C211yesmaximal, characteristic, complemented
29#121×Dic17C211yesmaximal, characteristic, complemented
30#121×Dic17C211yesmaximal, characteristic, complemented
31C2×C17×#560C211yesmaximal, characteristic
32C2×D4×Dic17C2211yescharacteristic
33C2×D4×Dic17C2211yescharacteristic
34C2×D4×Dic17C2211yescharacteristic
35C2×D4×Dic17C2211yescharacteristic
36C2×D4×Dic17C2211yescharacteristic
37C2×D4×Dic17C2211yescharacteristic
38C2×D4×Dic17C2211yescharacteristic
39C2×D4×Dic17C2211yescharacteristic
40C2×D4×Dic17C2211yescharacteristic
41C2×D4×Dic17C2211yescharacteristic, complemented
42C2×D4×Dic17C2211yescharacteristic, complemented
43C2×D4×Dic17C2211yescharacteristic, complemented
44C2×#10587612C2211yescharacteristic, complemented
45C2×#10587612C2211yescharacteristic, complemented
46C22×C22⋊Dic17C2211yescharacteristic
47C22×C22⋊Dic17C2211yescharacteristic
48C22×C22⋊Dic17C2211yescharacteristic
49C22×C4×Dic17C2211yescharacteristic, complemented
50#11762712C2211yescharacteristic
51#11762712C2211yescharacteristic
52#11762712C2211yescharacteristic
53#11762712C2211yescharacteristic
54#11762712C2211yescharacteristic
55#11762712C2211yescharacteristic
56#11762712C2211yescharacteristic
57#11762712C2211yescharacteristic
58#11762712C2211yescharacteristic
59#11762712C2211yescharacteristic, complemented
60#11762712C2211yescharacteristic, complemented
61#11762712C2211yescharacteristic, complemented
62#11762708C2211yescharacteristic, complemented
63#11762708C2211yescharacteristic, complemented
64#11762708C2211yescharacteristic, complemented
65#11762708C2211yescharacteristic, complemented
66#11762708C2211yescharacteristic, complemented
67#11762708C2211yescharacteristic, complemented
68#11762702C2211yescharacteristic
69#11762702C2211yescharacteristic
70#11762702C2211yescharacteristic
71#11762702C2211yescharacteristic
72#11762702C2211yescharacteristic
73#11762702C2211yescharacteristic
74#11762702C2211yescharacteristic
75#11762702C2211yescharacteristic
76#11762702C2211yescharacteristic
77#11762702C2211yescharacteristic
78#11762702C2211yescharacteristic
79#11762702C2211yescharacteristic
80#11762702C2211yescharacteristic
81#11762702C2211yescharacteristic
82#11762702C2211yescharacteristic
83#11762702C2211yescharacteristic
84#11762702C2211yescharacteristic
85#11762702C2211yescharacteristic
86#11762702C2211yescharacteristic, complemented
87#11762702C2211yescharacteristic, complemented
88#11762702C2211yescharacteristic, complemented
89#11762702C2211yescharacteristic, complemented
90#11762702C2211yescharacteristic, complemented
91#11762702C2211yescharacteristic, complemented
92#11762695C2211yescharacteristic, complemented
93#11762695C2211yescharacteristic, complemented
94#11762695C2211yescharacteristic, complemented
95#11762695C2211yescharacteristic, complemented
96#11762695C2211yescharacteristic, complemented
97#11762695C2211yescharacteristic, complemented
98#11762695C2211yescharacteristic, complemented
99#11762695C2211yescharacteristic, complemented
100#11762695C2211yescharacteristic, complemented
101#11762695C2211yescharacteristic, complemented
102#11762695C2211yescharacteristic, complemented
103#11762695C2211yescharacteristic, complemented
104#11762689C2211yescharacteristic
105#11762689C2211yescharacteristic
106#11762689C2211yescharacteristic
107#11762689C2211yescharacteristic
108#11762689C2211yescharacteristic
109#11762689C2211yescharacteristic
110#11762689C2211yescharacteristic
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762689C2211yescharacteristic
114#11762689C2211yescharacteristic
115#11762689C2211yescharacteristic
116#11762689C2211yescharacteristic
117#11762689C2211yescharacteristic
118#11762689C2211yescharacteristic
119#11762689C2211yescharacteristic
120#11762689C2211yescharacteristic
121#11762689C2211yescharacteristic
122#11762689C2211yescharacteristic, complemented
123#11762689C2211yescharacteristic, complemented
124#11762689C2211yescharacteristic, complemented
125#11762689C2211yescharacteristic, complemented
126#11762689C2211yescharacteristic, complemented
127#11762689C2211yescharacteristic, complemented
128#11762684C2211yescharacteristic
129#11762684C2211yescharacteristic
130#11762684C2211yescharacteristic
131#11762684C2211yescharacteristic
132#11762684C2211yescharacteristic
133#11762684C2211yescharacteristic
134#11762684C2211yescharacteristic
135#11762684C2211yescharacteristic
136#11762684C2211yescharacteristic
137#11762684C2211yescharacteristic, complemented
138#11762684C2211yescharacteristic, complemented
139#11762684C2211yescharacteristic, complemented
140#11762675C2211yescharacteristic, complemented
141#11762672C2211yescharacteristic, complemented
142#11762669C2211yescharacteristic, complemented
143#11762669C2211yescharacteristic, complemented
144#11762669C2211yescharacteristic, complemented
145#11762669C2211yescharacteristic, complemented
146#11762665C2211yescharacteristic
147C4⋊C4×Dic17C2211yescharacteristic, complemented
148C4⋊C4×Dic17C2211yescharacteristic, complemented
149C4⋊C4×Dic17C2211yescharacteristic, complemented
150C4⋊C4×Dic17C2211yescharacteristic, complemented
151C4⋊C4×Dic17C2211yescharacteristic, complemented
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4×C4⋊Dic17C2211yescharacteristic, complemented
154C4×C4⋊Dic17C2211yescharacteristic, complemented
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic
164C22⋊C4×Dic17C2211yescharacteristic, complemented
165C22⋊C4×Dic17C2211yescharacteristic, complemented
166C22⋊C4×Dic17C2211yescharacteristic, complemented
167C4×C22⋊Dic17C2211yescharacteristic, complemented
168C4×C22⋊Dic17C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172C17×#560C4116yescomplemented
173C2×C17×#127C2211yescharacteristic
174C2×C17×#126C2211yescharacteristic
175C2×C17×#126C2211yescharacteristic
176C2×C17×#123C2211yescharacteristic
177C2×C17×#123C2211yescharacteristic
178C2×C17×#123C2211yescharacteristic
179C2×C17×#121C2211yescharacteristic
180C2×C17×#121C2211yescharacteristic
181C2×C17×#121C2211yescharacteristic
182C2×C17×#121C2211yescharacteristic
183C2×C17×#121C2211yescharacteristic
184C2×C17×#121C2211yescharacteristic
185C2×C17×#120C2211yescharacteristic
186C2×C17×#120C2211yescharacteristic
187C2×C17×#120C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×D4×C17C2311yescharacteristic
199C22×D4×C17C2311yescharacteristic
200C22×D4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C23×C4×C17C2311yescharacteristic
203C23×C4×C17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C17×#127C2×C418yescomplemented
217C17×#126C2×C418yescomplemented
218C17×#126C2×C418yescomplemented
219C17×#123C2×C418yescomplemented
220C17×#123C2×C418yescomplemented
221C17×#123C2×C418yescomplemented
222C17×#121C2×C418yescomplemented
223C17×#121C2×C418yescomplemented
224C17×#121C2×C418yescomplemented
225C17×#121C2×C418yescomplemented
226C17×#121C2×C418yescomplemented
227C17×#121C2×C418yescomplemented
228C17×#120C2×C418yescomplemented
229C17×#120C2×C418yescomplemented
230C17×#120C2×C418yescomplemented
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C42×C17C2311yescharacteristic
250C2×C22⋊Dic17—42no—
251C2×C22⋊Dic17—42no—
252C2×C22⋊Dic17—42no—
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277C2×C22⋊Dic17C2311yescharacteristic
278C2×C22⋊Dic17C2311yescharacteristic
279C2×C22⋊Dic17C2311yescharacteristic
280C2×C22⋊Dic17C2311yescharacteristic
281C2×C22⋊Dic17C2311yescharacteristic
282C2×C22⋊Dic17C2311yescharacteristic
283C2×C22⋊Dic17C2311yescharacteristic
284C2×C22⋊Dic17C2311yescharacteristic
285C2×C22⋊Dic17C2311yescharacteristic
286C2×C22⋊Dic17C2311yescharacteristic
287C2×C22⋊Dic17C2311yescharacteristic
288C2×C22⋊Dic17C2311yescharacteristic
289D4×Dic17—42no—
290D4×Dic17—42no—
291D4×Dic17—42no—
292D4×Dic17—42no—
293D4×Dic17—42no—
294D4×Dic17—42no—
295D4×Dic17—42no—
296D4×Dic17—42no—
297D4×Dic17—42no—
298D4×Dic17—42no—
299D4×Dic17—42no—
300D4×Dic17—42no—
301#10587612—42no—
302#10587612—42no—
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4⋊Dic17C2311yescharacteristic
310C2×C4⋊Dic17C2311yescharacteristic
311C2×C4⋊Dic17C2311yescharacteristic
312C2×C4⋊Dic17C2311yescharacteristic
313C2×C4⋊Dic17C2311yescharacteristic
314C2×C4⋊Dic17C2311yescharacteristic
315C2×C4⋊Dic17C2311yescharacteristic
316C2×C4⋊Dic17C2311yescharacteristic
317C2×C4⋊Dic17C2311yescharacteristic
318C2×C4⋊Dic17C2311yescharacteristic
319C2×C4⋊Dic17C2311yescharacteristic
320C2×C4⋊Dic17C2311yescharacteristic
321C2×C4×Dic17—42no—
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335C2×C4×Dic17C2311yescharacteristic
336C2×C4×Dic17C2311yescharacteristic
337C2×C4×Dic17C2311yescharacteristic
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17—41no—
377C24×C17—41no—
378C24×C17—41no—
379C24×C17—41no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17C22×C414yes—
383C24×C17C2411yescharacteristic
384C24×C17C2411yescharacteristic
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C24×C17C2411yescharacteristic
388C24×C17C2411yescharacteristic
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17—41no—
394C2×D4×C17—41no—
395C2×D4×C17—41no—
396C2×D4×C17—41no—
397C2×D4×C17—41no—
398C2×D4×C17—41no—
399C2×D4×C17—41no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17—41no—
403C2×D4×C17—41no—
404C2×D4×C17—41no—
405C2×D4×C17—41no—
406C2×D4×C17—41no—
407C2×D4×C17—41no—
408C2×D4×C17—41no—
409C2×D4×C17—41no—
410C2×D4×C17—41no—
411C2×D4×C17—41no—
412C2×D4×C17—41no—
413C2×D4×C17C22×C414yes—
414C2×D4×C17C22×C414yes—
415C2×D4×C17C22×C414yes—
416C2×D4×C17C22×C414yes—
417C2×D4×C17C22×C414yes—
418C2×D4×C17C22×C414yes—
419C2×D4×C17C22×C414yes—
420C2×D4×C17C22×C414yes—
421C2×D4×C17C22×C414yes—
422C2×D4×C17C22×C414yes—
423C2×D4×C17C22×C414yes—
424C2×D4×C17C22×C414yes—
425C22×C4×C17—41no—
426C22×C4×C17—41no—
427C22×C4×C17—41no—
428C22×C4×C17—41no—
429C22×C4×C17—41no—
430C22×C4×C17—41no—
431C22×C4×C17C22×C414yes—
432C22×C4×C17C22×C414yes—
433C22×C4×C17C22×C414yes—
434C22×C4×C17C2411yescharacteristic
435C22×C4×C17C2411yescharacteristic
436C22×C4×C17C2411yescharacteristic
437C22×C4×C17C2411yescharacteristic
438C22×C4×C17C2411yescharacteristic
439C22×C4×C17C2411yescharacteristic
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×Dic17—22no—
444C22×Dic17—22no—
445C22×Dic17—22no—
446C22×Dic17—22no—
447C22×Dic17—22no—
448C22×Dic17—22no—
449C22×Dic17—22no—
450C22×Dic17—22no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17—41no—
463C22×Dic17—41no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17—41no—
467C22×Dic17—41no—
468C22×Dic17—41no—
469C22×Dic17—41no—
470C22×Dic17—41no—
471C22×Dic17—41no—
472C22×Dic17—41no—
473C22×Dic17—41no—
474C22×Dic17—41no—
475C22×Dic17—41no—
476C22×Dic17—41no—
477C22×Dic17—41no—
478C22×Dic17—41no—
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490C22×Dic17C2411yescharacteristic
491C22×Dic17C2411yescharacteristic
492C22×Dic17C2411yescharacteristic
493C22×Dic17C2411yescharacteristic
494C22×Dic17C2411yescharacteristic
495C4⋊C4×C17C22×C414yes—
496C4⋊C4×C17C22×C414yes—
497C4⋊C4×C17C22×C414yes—
498C4⋊C4×C17C22×C414yes—
499C4⋊C4×C17C22×C414yes—
500C4⋊C4×C17C22×C414yes—
501C22⋊C4×C17C22×C414yes—
502C22⋊C4×C17C22×C414yes—
503C22⋊C4×C17C22×C414yes—
504C22⋊C4×C17C22×C414yes—
505C22⋊C4×C17C22×C414yes—
506C22⋊C4×C17C22×C414yes—
507C22⋊C4×C17C22×C414yes—
508C22⋊C4×C17C22×C414yes—
509C22⋊C4×C17C22×C414yes—
510C22⋊C4×C17C22×C414yes—
511C22⋊C4×C17C22×C414yes—
512C22⋊C4×C17C22×C414yes—
513C42×C17C22×C414yes—
514C22⋊Dic17—22no—
515C22⋊Dic17—22no—
516C22⋊Dic17—22no—
517C22⋊Dic17—22no—
518C22⋊Dic17—22no—
519C22⋊Dic17—22no—
520C22⋊Dic17—22no—
521C22⋊Dic17—22no—
522C22⋊Dic17—22no—
523C22⋊Dic17—22no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17—41no—
527C22⋊Dic17—41no—
528C22⋊Dic17—41no—
529C22⋊Dic17—41no—
530C22⋊Dic17—41no—
531C22⋊Dic17—41no—
532C22⋊Dic17—41no—
533C22⋊Dic17—41no—
534C22⋊Dic17—41no—
535C22⋊Dic17—41no—
536C22⋊Dic17—41no—
537C22⋊Dic17—41no—
538C22⋊Dic17—41no—
539C22⋊Dic17—41no—
540C22⋊Dic17—41no—
541C22⋊Dic17—41no—
542C22⋊Dic17—41no—
543C22⋊Dic17—41no—
544C22⋊Dic17—41no—
545C22⋊Dic17—41no—
546C22⋊Dic17—41no—
547C22⋊Dic17—41no—
548C22⋊Dic17—41no—
549C22⋊Dic17—41no—
550C4⋊Dic17—22no—
551C4⋊Dic17—22no—
552C4⋊Dic17—22no—
553C4⋊Dic17—22no—
554C4⋊Dic17—41no—
555C4⋊Dic17—41no—
556C4⋊Dic17—41no—
557C4⋊Dic17—41no—
558C4⋊Dic17—41no—
559C4⋊Dic17—41no—
560C4⋊Dic17—41no—
561C4⋊Dic17—41no—
562C4⋊Dic17—41no—
563C4⋊Dic17—41no—
564C4⋊Dic17—41no—
565C4⋊Dic17—41no—
566C4⋊Dic17—41no—
567C4⋊Dic17—41no—
568C4×Dic17—22no—
569C4×Dic17—22no—
570C4×Dic17—22no—
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17—41no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583C4×Dic17—41no—
584C4×Dic17—41no—
585C4×Dic17—41no—
586#34517—171nomaximal, Sylow
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—44no—
624C23×C17—44no—
625C23×C17—44no—
626C23×C17—82no—
627C23×C17—82no—
628C23×C17—82no—
629C23×C17—82no—
630C23×C17C23×C412yes—
631C23×C17C23×C412yes—
632C23×C17C23×C412yes—
633C23×C17C23×C412yes—
634C23×C17C23×C412yes—
635C23×C17C23×C412yes—
636C23×C17C2511yescharacteristic
637D4×C17—44no—
638D4×C17—44no—
639D4×C17—44no—
640D4×C17—44no—
641D4×C17—44no—
642D4×C17—44no—
643D4×C17—44no—
644D4×C17—44no—
645D4×C17—44no—
646D4×C17—44no—
647D4×C17—44no—
648D4×C17—44no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—44no—
668C2×C4×C17—44no—
669C2×C4×C17—44no—
670C2×C4×C17C23×C412yes—
671C2×C4×C17C23×C412yes—
672C2×C4×C17C23×C412yes—
673C2×C4×C17C23×C412yes—
674C2×C4×C17C23×C412yes—
675C2×C4×C17C23×C412yes—
676C2×C4×C17C23×C412yes—
677C2×C4×C17C23×C412yes—
678C2×C4×C17C23×C412yes—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—44no—
725C2×Dic17—44no—
726C2×Dic17—82no—
727C2×Dic17—82no—
728C2×Dic17—82no—
729C2×Dic17—82no—
730C2×Dic17—82no—
731C2×Dic17—82no—
732C2×Dic17—82no—
733C2×Dic17—82no—
734C2×Dic17—82no—
735C2×Dic17—82no—
736C2×Dic17H(5,𝔽2)12yes—
737C2×Dic17H(5,𝔽2)12yes—
738C2×Dic17H(5,𝔽2)12yes—
739C2×#560D1711yescharacteristic
740#2377—171no—
741#2377—171no—
742#2376—171no—
743#2373—171no—
744#2373—171no—
745#2366—171no—
746#2364—171no—
747#2364—171no—
748#2363—171no—
749#2363—171no—
750#2359—171no—
751#2359—171no—
752#2358—171no—
753#2358—171no—
754#2358—171no—
755#2335—171no—
756#2335—171no—
757#2334—171no—
758#2334—171no—
759#2328—171no—
760#2325—171no—
761#2325—171no—
762#2324—171no—
763#2324—171no—
764#2321—171no—
765#2321—171no—
766#2321—171no—
767C4×#123—171no—
768C4×#121—171no—
769C4×#121—171no—
770C22×C17—22no—
771C22×C17—22no—
772C22×C17—22no—
773C22×C17—22no—
774C22×C17—22no—
775C22×C17—22no—
776C22×C17—22no—
777C22×C17—22no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
785C22×C17—22no—
786C22×C17—22no—
787C22×C17—22no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—41no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—88no—
813C22×C17C24×C411yescharacteristic
814C22×C17C2×H(5,𝔽2)11yescharacteristic
815C22×C17C2×H(5,𝔽2)11yescharacteristic
816C22×C17C2×H(5,𝔽2)11yescharacteristic
817C22×C17#58511yescharacteristic
818C22×C17#58511yescharacteristic
819C22×C17#58511yescharacteristic
820C4×C17—22no—
821C4×C17—22no—
822C4×C17—22no—
823C4×C17—22no—
824C4×C17—22no—
825C4×C17—22no—
826C4×C17—22no—
827C4×C17—22no—
828C4×C17—22no—
829Dic17—22no—
830Dic17—22no—
831Dic17—22no—
832Dic17—41no—
833Dic17—41no—
834Dic17—41no—
835Dic17—41no—
836Dic17—41no—
837Dic17—41no—
838Dic17—41no—
839Dic17—41no—
840Dic17—41no—
841Dic17—41no—
842Dic17—41no—
843Dic17—41no—
844Dic17—41no—
845#560Dic17116yescomplemented
846C2×#127C2×D1711yescharacteristic
847C2×#126C2×D1711yescharacteristic
848C2×#126C2×D1711yescharacteristic
849C2×#123C2×D1711yescharacteristic
850C2×#123C2×D1711yescharacteristic
851C2×#123C2×D1711yescharacteristic
852C2×#121C2×D1711yescharacteristic
853C2×#121C2×D1711yescharacteristic
854C2×#121C2×D1711yescharacteristic
855C2×#121C2×D1711yescharacteristic
856C2×#121C2×D1711yescharacteristic
857C2×#121C2×D1711yescharacteristic
858C2×#120C2×D1711yescharacteristic
859C2×#120C2×D1711yescharacteristic
860C2×#120C2×D1711yescharacteristic
861C2×C4×D4—171no—
862C2×C4×D4—171no—
863C2×C4×D4—171no—
864C2×C4×D4—171no—
865C2×C4×D4—171no—
866C2×C4×D4—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×C4×D4—171no—
870C2×C4×D4—171no—
871C2×C4×D4—171no—
872C2×C4×D4—171no—
873C2×#117—171no—
874C2×#117—171no—
875C22×C22⋊C4—171no—
876C22×C22⋊C4—171no—
877C22×C22⋊C4—171no—
878C22×C42—171no—
879#390—171no—
880#390—171no—
881#390—171no—
882#390—171no—
883#390—171no—
884#390—171no—
885#390—171no—
886#390—171no—
887#390—171no—
888#390—171no—
889#390—171no—
890#390—171no—
891#389—171no—
892#389—171no—
893#389—171no—
894#389—171no—
895#389—171no—
896#389—171no—
897#388—171no—
898#388—171no—
899#388—171no—
900#388—171no—
901#388—171no—
902#388—171no—
903#388—171no—
904#388—171no—
905#388—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388—171no—
921#387—171no—
922#387—171no—
923#387—171no—
924#387—171no—
925#387—171no—
926#387—171no—
927#387—171no—
928#387—171no—
929#387—171no—
930#387—171no—
931#387—171no—
932#387—171no—
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386—171no—
954#386—171no—
955#386—171no—
956#386—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#385—171no—
969#382—171no—
970#381—171no—
971#380—171no—
972#380—171no—
973#380—171no—
974#380—171no—
975#379—171no—
976C4×C4⋊C4—171no—
977C4×C4⋊C4—171no—
978C4×C4⋊C4—171no—
979C4×C4⋊C4—171no—
980C4×C4⋊C4—171no—
981C4×C4⋊C4—171no—
982C4×C4⋊C4—171no—
983C4×C4⋊C4—171no—
984C4×C22⋊C4—171no—
985C4×C22⋊C4—171no—
986C4×C22⋊C4—171no—
987C4×C22⋊C4—171no—
988C4×C22⋊C4—171no—
989C4×C22⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992C4×C22⋊C4—171no—
993C4×C22⋊C4—171no—
994C4×C22⋊C4—171no—
995C4×C22⋊C4—171no—
996C4×C22⋊C4—171no—
997C4×C22⋊C4—171no—
998#376—171no—
999C2×#95—171no—
1000C2×#95—171no—
1001C2×C17—42no—
1002C2×C17—42no—
1003C2×C17—42no—
1004C2×C17—42no—
1005C2×C17—42no—
1006C2×C17—42no—
1007C2×C17C4×H(5,𝔽2)11yescharacteristic
1008C2×C17C4×H(5,𝔽2)11yescharacteristic
1009C2×C17C4×H(5,𝔽2)11yescharacteristic
1010C2×C17#353411yescharacteristic
1011C2×C17#354211yescharacteristic
1012C2×C17#354611yescharacteristic
1013C2×C17#356611yescharacteristic
1014C25C22×D1711yescharacteristic
1015C22×D4C22×D1711yescharacteristic
1016C22×D4C22×D1711yescharacteristic
1017C22×D4C22×D1711yescharacteristic
1018C22×D4C22×D1711yescharacteristic
1019C22×D4C22×D1711yescharacteristic
1020C22×D4C22×D1711yescharacteristic
1021C22×D4C22×D1711yescharacteristic
1022C22×D4C22×D1711yescharacteristic
1023C22×D4C22×D1711yescharacteristic
1024C22×D4C22×D1711yescharacteristic
1025C22×D4C22×D1711yescharacteristic
1026C22×D4C22×D1711yescharacteristic
1027C23×C4—171no—
1028C23×C4—171no—
1029C23×C4—171no—
1030C23×C4—171no—
1031C23×C4—171no—
1032C23×C4—171no—
1033C23×C4—171no—
1034C23×C4—171no—
1035C23×C4—171no—
1036C23×C4—171no—
1037C23×C4—171no—
1038C23×C4—171no—
1039C23×C4C22×D1711yescharacteristic
1040C23×C4C22×D1711yescharacteristic
1041C23×C4C22×D1711yescharacteristic
1042#127C2×Dic1718yescomplemented
1043#126C2×Dic1718yescomplemented
1044#126C2×Dic1718yescomplemented
1045#123C2×Dic1718yescomplemented
1046#123C2×Dic1718yescomplemented
1047#123C2×Dic1718yescomplemented
1048#121C2×Dic1718yescomplemented
1049#121C2×Dic1718yescomplemented
1050#121C2×Dic1718yescomplemented
1051#121C2×Dic1718yescomplemented
1052#121C2×Dic1718yescomplemented
1053#121C2×Dic1718yescomplemented
1054#120C2×Dic1718yescomplemented
1055#120C2×Dic1718yescomplemented
1056#120C2×Dic1718yescomplemented
1057C4×D4—682no—
1058C4×D4—682no—
1059C4×D4—682no—
1060C4×D4—682no—
1061C4×D4—682no—
1062C4×D4—682no—
1063C4×D4—682no—
1064C4×D4—682no—
1065C4×D4—682no—
1066C4×D4—682no—
1067C4×D4—682no—
1068C4×D4—682no—
1069#117—682no—
1070#117—682no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4C22×D1711yescharacteristic
1090C2×C4⋊C4C22×D1711yescharacteristic
1091C2×C4⋊C4C22×D1711yescharacteristic
1092C2×C4⋊C4C22×D1711yescharacteristic
1093C2×C4⋊C4C22×D1711yescharacteristic
1094C2×C4⋊C4C22×D1711yescharacteristic
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—682no—
1132C2×C22⋊C4—682no—
1133C2×C22⋊C4—682no—
1134C2×C22⋊C4C22×D1711yescharacteristic
1135C2×C22⋊C4C22×D1711yescharacteristic
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C42—171no—
1147C2×C42—171no—
1148C2×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—171no—
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—171no—
1162C2×C42—171no—
1163C2×C42—171no—
1164C2×C42—682no—
1165C2×C42C22×D1711yescharacteristic
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202C17#3451711yescharacteristic, complemented, Sylow
1203C24—41no—
1204C24—41no—
1205C24—41no—
1206C24—41no—
1207C24—41no—
1208C24—41no—
1209C24C22×Dic1714yes—
1210C24C23×D1711yescharacteristic
1211C24C23×D1711yescharacteristic
1212C24C23×D1711yescharacteristic
1213C24C23×D1711yescharacteristic
1214C24C23×D1711yescharacteristic
1215C24C23×D1711yescharacteristic
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—41no—
1224C2×D4—41no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—41no—
1231C2×D4—41no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4C22×Dic1714yes—
1241C2×D4C22×Dic1714yes—
1242C2×D4C22×Dic1714yes—
1243C2×D4C22×Dic1714yes—
1244C2×D4C22×Dic1714yes—
1245C2×D4C22×Dic1714yes—
1246C2×D4C22×Dic1714yes—
1247C2×D4C22×Dic1714yes—
1248C2×D4C22×Dic1714yes—
1249C2×D4C22×Dic1714yes—
1250C2×D4C22×Dic1714yes—
1251C2×D4C22×Dic1714yes—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—171no—
1259C22×C4—171no—
1260C22×C4—171no—
1261C22×C4—171no—
1262C22×C4—171no—
1263C22×C4—171no—
1264C22×C4—171no—
1265C22×C4—171no—
1266C22×C4—171no—
1267C22×C4—171no—
1268C22×C4—171no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—342no—
1275C22×C4—342no—
1276C22×C4—342no—
1277C22×C4—342no—
1278C22×C4—342no—
1279C22×C4—342no—
1280C22×C4—342no—
1281C22×C4—342no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—681no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4—681no—
1294C22×C4—681no—
1295C22×C4—681no—
1296C22×C4—681no—
1297C22×C4—681no—
1298C22×C4—681no—
1299C22×C4—681no—
1300C22×C4—681no—
1301C22×C4—681no—
1302C22×C4—681no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4—681no—
1309C22×C4—681no—
1310C22×C4C22×Dic1714yes—
1311C22×C4C22×Dic1714yes—
1312C22×C4C22×Dic1714yes—
1313C22×C4C23×D1711yescharacteristic
1314C22×C4C23×D1711yescharacteristic
1315C22×C4C23×D1711yescharacteristic
1316C22×C4C23×D1711yescharacteristic
1317C22×C4C23×D1711yescharacteristic
1318C22×C4C23×D1711yescharacteristic
1319C22×C4C23×D1711yescharacteristic
1320C22×C4C23×D1711yescharacteristic
1321C22×C4C23×D1711yescharacteristic
1322C4⋊C4—342no—
1323C4⋊C4—342no—
1324C4⋊C4—342no—
1325C4⋊C4—342no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4—681no—
1332C4⋊C4—681no—
1333C4⋊C4—681no—
1334C4⋊C4—681no—
1335C4⋊C4—681no—
1336C4⋊C4—681no—
1337C4⋊C4—681no—
1338C4⋊C4—681no—
1339C4⋊C4—681no—
1340C4⋊C4C22×Dic1714yes—
1341C4⋊C4C22×Dic1714yes—
1342C4⋊C4C22×Dic1714yes—
1343C4⋊C4C22×Dic1714yes—
1344C4⋊C4C22×Dic1714yes—
1345C4⋊C4C22×Dic1714yes—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4—681no—
1360C22⋊C4—681no—
1361C22⋊C4—681no—
1362C22⋊C4—681no—
1363C22⋊C4—681no—
1364C22⋊C4—681no—
1365C22⋊C4—681no—
1366C22⋊C4—681no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4C22×Dic1714yes—
1383C22⋊C4C22×Dic1714yes—
1384C22⋊C4C22×Dic1714yes—
1385C22⋊C4C22×Dic1714yes—
1386C22⋊C4C22×Dic1714yes—
1387C22⋊C4C22×Dic1714yes—
1388C22⋊C4C22×Dic1714yes—
1389C22⋊C4C22×Dic1714yes—
1390C22⋊C4C22×Dic1714yes—
1391C22⋊C4C22×Dic1714yes—
1392C22⋊C4C22×Dic1714yes—
1393C22⋊C4C22×Dic1714yes—
1394C42—342no—
1395C42—342no—
1396C42—342no—
1397C42—342no—
1398C42—342no—
1399C42—681no—
1400C42—681no—
1401C42—681no—
1402C42—681no—
1403C42—681no—
1404C42—681no—
1405C42—681no—
1406C42—681no—
1407C42—681no—
1408C42—681no—
1409C42—681no—
1410C42—681no—
1411C42—681no—
1412C42C22×Dic1714yes—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—44no—
1450C23—44no—
1451C23—44no—
1452C23—82no—
1453C23—82no—
1454C23—82no—
1455C23—82no—
1456C23C23×Dic1712yes—
1457C23C23×Dic1712yes—
1458C23C23×Dic1712yes—
1459C23C23×Dic1712yes—
1460C23C23×Dic1712yes—
1461C23C23×Dic1712yes—
1462C23C24×D1711yescharacteristic
1463D4—44no—
1464D4—44no—
1465D4—44no—
1466D4—44no—
1467D4—44no—
1468D4—44no—
1469D4—44no—
1470D4—44no—
1471D4—44no—
1472D4—44no—
1473D4—44no—
1474D4—44no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—44no—
1494C2×C4—44no—
1495C2×C4—44no—
1496C2×C4—172no—
1497C2×C4—172no—
1498C2×C4—172no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—684no—
1545C2×C4—684no—
1546C2×C4—1362no—
1547C2×C4—1362no—
1548C2×C4—1362no—
1549C2×C4—1362no—
1550C2×C4—1362no—
1551C2×C4—1362no—
1552C2×C4—1362no—
1553C2×C4—1362no—
1554C2×C4—1362no—
1555C2×C4—1362no—
1556C2×C4C23×Dic1712yes—
1557C2×C4C23×Dic1712yes—
1558C2×C4C23×Dic1712yes—
1559C2×C4C23×Dic1712yes—
1560C2×C4C23×Dic1712yes—
1561C2×C4C23×Dic1712yes—
1562C2×C4C23×Dic1712yes—
1563C2×C4C23×Dic1712yes—
1564C2×C4C23×Dic1712yes—
1565C22—22no—
1566C22—22no—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—22no—
1571C22—22no—
1572C22—22no—
1573C22—22no—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—88no—
1608C22C24×Dic1711yescharacteristic
1609C22H(5,𝔽2)×D1711yescharacteristic
1610C22H(5,𝔽2)×D1711yescharacteristic
1611C22H(5,𝔽2)×D1711yescharacteristic
1612C22#1176364411yescharacteristic
1613C22#1176364411yescharacteristic
1614C22#1176364411yescharacteristic
1615C4—22no—
1616C4—22no—
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—22no—
1621C4—22no—
1622C4—22no—
1623C4—22no—
1624C4—342no—
1625C4—342no—
1626C4—342no—
1627C4—681no—
1628C4—681no—
1629C4—681no—
1630C4—681no—
1631C4—681no—
1632C4—681no—
1633C4—681no—
1634C4—681no—
1635C4—681no—
1636C4—681no—
1637C4—681no—
1638C4—681no—
1639C4—681no—
1640C2—42no—
1641C2—42no—
1642C2—42no—
1643C2—42no—
1644C2—42no—
1645C2—42no—
1646C2H(5,𝔽2)×Dic1711yescharacteristic
1647C2H(5,𝔽2)×Dic1711yescharacteristic
1648C2H(5,𝔽2)×Dic1711yescharacteristic
1649C2#1454296511yescharacteristic
1650C2#1454308911yescharacteristic
1651C2#1454314711yescharacteristic
1652C2#1454344111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
Fitting, prime radicalC2×C17×#560C2
socle, cosocleC23×C17C25
hypercenterC2×#560D17
hypocenterC17#34517
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#560

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14531941C2semidirect
2. #14531941C2semidirect
3. #14531932C2semidirect
4. #14531908C2semidirect
5. #14531908C2semidirect
6. #14531849C2semidirect
7. #14531836C2semidirect
8. #14531836C2semidirect
9. #14531826C2semidirect
10. #14531826C2semidirect
11. #14531780C2semidirect
12. #14531780C2semidirect
13. #14531768C2semidirect
14. #14531768C2semidirect
15. #14531768C2semidirect
16. #14531578C2semidirect
17. #14531578C2semidirect
18. #14531563C2semidirect
19. #14531563C2semidirect
20. #14531510C2semidirect
21. #14531489C2semidirect
22. #14531489C2semidirect
23. #14531479C2semidirect
24. #14531479C2semidirect
25. #14531445C2semidirect
26. #14531445C2semidirect
27. #14531445C2semidirect
28. #123×Dic17C2semidirect
29. #121×Dic17C2semidirect
30. #121×Dic17C2semidirect
41. C2×D4×Dic17C22semidirect
42. C2×D4×Dic17C22semidirect
43. C2×D4×Dic17C22semidirect
44. C2×#10587612C22semidirect
45. C2×#10587612C22semidirect
49. C22×C4×Dic17C22semidirect
59. #11762712C22semidirect
60. #11762712C22semidirect
61. #11762712C22semidirect
62. #11762708C22semidirect
63. #11762708C22semidirect
64. #11762708C22semidirect
65. #11762708C22semidirect
66. #11762708C22semidirect
67. #11762708C22semidirect
86. #11762702C22semidirect
87. #11762702C22semidirect
88. #11762702C22semidirect
89. #11762702C22semidirect
90. #11762702C22semidirect
91. #11762702C22semidirect
92. #11762695C22semidirect
93. #11762695C22semidirect
94. #11762695C22semidirect
95. #11762695C22semidirect
96. #11762695C22semidirect
97. #11762695C22semidirect
98. #11762695C22semidirect
99. #11762695C22semidirect
100. #11762695C22semidirect
101. #11762695C22semidirect
102. #11762695C22semidirect
103. #11762695C22semidirect
122. #11762689C22semidirect
123. #11762689C22semidirect
124. #11762689C22semidirect
125. #11762689C22semidirect
126. #11762689C22semidirect
127. #11762689C22semidirect
137. #11762684C22semidirect
138. #11762684C22semidirect
139. #11762684C22semidirect
140. #11762675C22semidirect
141. #11762672C22semidirect
142. #11762669C22semidirect
143. #11762669C22semidirect
144. #11762669C22semidirect
145. #11762669C22semidirect
147. C4⋊C4×Dic17C22semidirect
148. C4⋊C4×Dic17C22semidirect
149. C4⋊C4×Dic17C22semidirect
150. C4⋊C4×Dic17C22semidirect
151. C4⋊C4×Dic17C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4×C4⋊Dic17C22semidirect
154. C4×C4⋊Dic17C22semidirect
164. C22⋊C4×Dic17C22semidirect
165. C22⋊C4×Dic17C22semidirect
166. C22⋊C4×Dic17C22semidirect
167. C4×C22⋊Dic17C22semidirect
168. C4×C22⋊Dic17C22semidirect
169. #11762655C22semidirect
170. C2×#10587502C22semidirect
171. C2×#10587502C22semidirect
172. C17×#560C4semidirect
216. C17×#127C2×C4semidirect
217. C17×#126C2×C4semidirect
218. C17×#126C2×C4semidirect
219. C17×#123C2×C4semidirect
220. C17×#123C2×C4semidirect
221. C17×#123C2×C4semidirect
222. C17×#121C2×C4semidirect
223. C17×#121C2×C4semidirect
224. C17×#121C2×C4semidirect
225. C17×#121C2×C4semidirect
226. C17×#121C2×C4semidirect
227. C17×#121C2×C4semidirect
228. C17×#120C2×C4semidirect
229. C17×#120C2×C4semidirect
230. C17×#120C2×C4semidirect
845. #560Dic17semidirect
1042. #127C2×Dic17semidirect
1043. #126C2×Dic17semidirect
1044. #126C2×Dic17semidirect
1045. #123C2×Dic17semidirect
1046. #123C2×Dic17semidirect
1047. #123C2×Dic17semidirect
1048. #121C2×Dic17semidirect
1049. #121C2×Dic17semidirect
1050. #121C2×Dic17semidirect
1051. #121C2×Dic17semidirect
1052. #121C2×Dic17semidirect
1053. #121C2×Dic17semidirect
1054. #120C2×Dic17semidirect
1055. #120C2×Dic17semidirect
1056. #120C2×Dic17semidirect
1202. C17#34517semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145319412
#145319322
#145319082
#145318492
#145318362
#145318262
#145317802
#145317682
#145315782
#145315632
#145315102
#145314892
#145314792
#145314452
#123×Dic172
#121×Dic172
C2×C17×#5602
#3451717