Finite Group Databasebeta

← #17198707

Subgroups — #17198707

Order 4352.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531976C211yesmaximal, characteristic, complemented
2#14531950C211yesmaximal, characteristic, complemented
3#14531932C211yesmaximal, characteristic, complemented
4#14531925C211yesmaximal, characteristic, complemented
5#14531908C211yesmaximal, characteristic, complemented
6#14531908C211yesmaximal, characteristic, complemented
7#14531908C211yesmaximal, characteristic, complemented
8#14531896C211yesmaximal, characteristic, complemented
9#14531859C211yesmaximal, characteristic, complemented
10#14531815C211yesmaximal, characteristic, complemented
11#14531780C211yesmaximal, characteristic, complemented
12#14531768C211yesmaximal, characteristic, complemented
13#14531733C211yesmaximal, characteristic, complemented
14#14531724C211yesmaximal, characteristic, complemented
15#14531633C211yesmaximal, characteristic, complemented
16#14531633C211yesmaximal, characteristic, complemented
17#14531599C211yesmaximal, characteristic, complemented
18#14531578C211yesmaximal, characteristic, complemented
19#14531551C211yesmaximal, characteristic, complemented
20#14531551C211yesmaximal, characteristic, complemented
21#14531497C211yesmaximal, characteristic, complemented
22#14531489C211yesmaximal, characteristic, complemented
23#14531479C211yesmaximal, characteristic, complemented
24#14531479C211yesmaximal, characteristic, complemented
25#14531445C211yesmaximal, characteristic, complemented
26#14531445C211yesmaximal, characteristic, complemented
27#14531427C211yesmaximal, characteristic, complemented
28#123×Dic17C211yesmaximal, characteristic, complemented
29#121×Dic17C211yesmaximal, characteristic, complemented
30#14531229C211yesmaximal, characteristic, complemented
31C2×C17×#538C211yesmaximal, characteristic
32C2×Q8×Dic17C2211yescharacteristic, complemented
33C2×D4×Dic17C2211yescharacteristic
34C2×D4×Dic17C2211yescharacteristic
35C2×D4×Dic17C2211yescharacteristic
36C2×D4×Dic17C2211yescharacteristic
37C2×D4×Dic17C2211yescharacteristic, complemented
38C2×#10587612C2211yescharacteristic
39C2×#10587612C2211yescharacteristic
40C2×#10587612C2211yescharacteristic, complemented
41C22×C22⋊Dic17C2211yescharacteristic
42C22×C22⋊Dic17C2211yescharacteristic
43C22×C4×Dic17C2211yescharacteristic, complemented
44#11762716C2211yescharacteristic, complemented
45#11762716C2211yescharacteristic, complemented
46#11762716C2211yescharacteristic, complemented
47#11762712C2211yescharacteristic
48#11762712C2211yescharacteristic
49#11762712C2211yescharacteristic
50#11762712C2211yescharacteristic
51#11762712C2211yescharacteristic
52#11762712C2211yescharacteristic
53#11762712C2211yescharacteristic
54#11762712C2211yescharacteristic
55#11762712C2211yescharacteristic, complemented
56#11762708C2211yescharacteristic, complemented
57#11762708C2211yescharacteristic, complemented
58#11762708C2211yescharacteristic, complemented
59#11762708C2211yescharacteristic, complemented
60#11762708C2211yescharacteristic, complemented
61#11762708C2211yescharacteristic, complemented
62#11762702C2211yescharacteristic
63#11762702C2211yescharacteristic
64#11762702C2211yescharacteristic
65#11762702C2211yescharacteristic
66#11762702C2211yescharacteristic
67#11762702C2211yescharacteristic
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#11762702C2211yescharacteristic, complemented
93#11762702C2211yescharacteristic, 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#11762695C2211yescharacteristic, complemented
105#11762695C2211yescharacteristic, complemented
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, complemented
119#11762689C2211yescharacteristic, complemented
120#11762684C2211yescharacteristic
121#11762684C2211yescharacteristic
122#11762684C2211yescharacteristic
123#11762684C2211yescharacteristic
124#11762684C2211yescharacteristic
125#11762684C2211yescharacteristic
126#11762684C2211yescharacteristic
127#11762684C2211yescharacteristic
128#11762684C2211yescharacteristic, complemented
129#11762684C2211yescharacteristic, complemented
130#11762684C2211yescharacteristic, complemented
131#11762684C2211yescharacteristic, complemented
132#11762679C2211yescharacteristic, complemented
133#11762677C2211yescharacteristic, complemented
134#11762672C2211yescharacteristic
135#11762672C2211yescharacteristic
136#11762672C2211yescharacteristic, complemented
137#11762669C2211yescharacteristic
138#11762669C2211yescharacteristic
139#11762669C2211yescharacteristic, complemented
140#11762669C2211yescharacteristic, complemented
141#11762669C2211yescharacteristic, complemented
142#11762665C2211yescharacteristic
143#11762665C2211yescharacteristic
144C4⋊C4×Dic17C2211yescharacteristic, complemented
145C4⋊C4×Dic17C2211yescharacteristic, complemented
146C4⋊C4×Dic17C2211yescharacteristic, complemented
147C4⋊C4×Dic17C2211yescharacteristic, complemented
148C4⋊C4×Dic17C2211yescharacteristic, complemented
149C4⋊C4×Dic17C2211yescharacteristic, complemented
150C4×C4⋊Dic17C2211yescharacteristic, complemented
151C4×C4⋊Dic17C2211yescharacteristic, complemented
152C4×C4⋊Dic17C2211yescharacteristic, complemented
153C22⋊C4×Dic17C2211yescharacteristic
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C22⋊C4×Dic17C2211yescharacteristic, complemented
163C22⋊C4×Dic17C2211yescharacteristic, complemented
164C22⋊C4×Dic17C2211yescharacteristic, complemented
165C4×C22⋊Dic17C2211yescharacteristic
166C4×C22⋊Dic17C2211yescharacteristic
167C4×C22⋊Dic17C2211yescharacteristic, complemented
168#11762655C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170#11762655C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172C17×#538C4116yescomplemented
173C2×C17×#126C2211yescharacteristic
174C2×C17×#126C2211yescharacteristic
175C2×C17×#124C2211yescharacteristic
176C2×C17×#124C2211yescharacteristic
177C2×C17×#123C2211yescharacteristic
178C2×C17×#123C2211yescharacteristic
179C2×C17×C22⋊Q8C2211yescharacteristic
180C2×C17×#121C2211yescharacteristic
181C2×C17×#121C2211yescharacteristic
182C2×C17×#121C2211yescharacteristic
183C2×C17×#120C2211yescharacteristic
184C2×C17×#120C2211yescharacteristic
185C2×C4×D4×C17C2211yescharacteristic
186C2×C4×D4×C17C2211yescharacteristic
187C22×C22⋊C4×C17C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×Q8×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C17×#126C2×C418yescomplemented
210C17×#126C2×C418yescomplemented
211C17×#124C2×C418yescomplemented
212C17×#124C2×C418yescomplemented
213C17×#123C2×C418yescomplemented
214C17×#123C2×C418yescomplemented
215C17×C22⋊Q8C2×C418yescomplemented
216C17×#121C2×C418yescomplemented
217C17×#121C2×C418yescomplemented
218C17×#121C2×C418yescomplemented
219C17×#120C2×C418yescomplemented
220C17×#120C2×C418yescomplemented
221C4×D4×C17C2×C418yescomplemented
222C4×D4×C17C2×C418yescomplemented
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2×C418yescomplemented
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊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×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246C2×C22⋊Dic17—42no—
247C2×C22⋊Dic17—42no—
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
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
280Q8×Dic17—42no—
281D4×Dic17—42no—
282D4×Dic17—42no—
283D4×Dic17—42no—
284D4×Dic17—42no—
285D4×Dic17—42no—
286#10587612—42no—
287#10587612—42no—
288#10587612—42no—
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4×Dic17—42no—
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×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
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
370C24×C17—41no—
371C24×C17—41no—
372C24×C17—41no—
373C24×C17—41no—
374C24×C17—41no—
375C24×C17—41no—
376C24×C17C22×C414yes—
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C24×C17C2411yescharacteristic
380C24×C17C2411yescharacteristic
381C24×C17C2411yescharacteristic
382C2×Q8×C17—41no—
383C2×Q8×C17—41no—
384C2×Q8×C17C22×C414yes—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17—41no—
388C2×D4×C17—41no—
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×C17C22×C414yes—
400C2×D4×C17C22×C414yes—
401C2×D4×C17C22×C414yes—
402C2×D4×C17C22×C414yes—
403C2×D4×C17C22×C414yes—
404C2×D4×C17C22×C414yes—
405C2×D4×C17C22×C414yes—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17—41no—
414C22×C4×C17C22×C414yes—
415C22×C4×C17C22×C414yes—
416C22×C4×C17C22×C414yes—
417C22×C4×C17C22×C414yes—
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×Dic17—22no—
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—22no—
432C22×Dic17—22no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17—41no—
437C22×Dic17—41no—
438C22×Dic17—41no—
439C22×Dic17—41no—
440C22×Dic17—41no—
441C22×Dic17—41no—
442C22×Dic17—41no—
443C22×Dic17—41no—
444C22×Dic17—41no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17—41no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C4⋊C4×C17C22×C414yes—
469C4⋊C4×C17C22×C414yes—
470C4⋊C4×C17C22×C414yes—
471C4⋊C4×C17C22×C414yes—
472C4⋊C4×C17C22×C414yes—
473C4⋊C4×C17C22×C414yes—
474C22⋊C4×C17C22×C414yes—
475C22⋊C4×C17C22×C414yes—
476C22⋊C4×C17C22×C414yes—
477C22⋊C4×C17C22×C414yes—
478C22⋊C4×C17C22×C414yes—
479C22⋊C4×C17C22×C414yes—
480C22⋊C4×C17C22×C414yes—
481C22⋊C4×C17C22×C414yes—
482C22⋊C4×C17C22×C414yes—
483C22⋊C4×C17C22×C414yes—
484C22⋊C4×C17C22×C414yes—
485C22⋊C4×C17C22×C414yes—
486C22⋊C4×C17C22×C414yes—
487C22⋊C4×C17C22×C414yes—
488C42×C17C22×C414yes—
489C42×C17C22×C414yes—
490C22⋊Dic17—22no—
491C22⋊Dic17—22no—
492C22⋊Dic17—22no—
493C22⋊Dic17—22no—
494C22⋊Dic17—22no—
495C22⋊Dic17—41no—
496C22⋊Dic17—41no—
497C22⋊Dic17—41no—
498C22⋊Dic17—41no—
499C22⋊Dic17—41no—
500C22⋊Dic17—41no—
501C22⋊Dic17—41no—
502C22⋊Dic17—41no—
503C22⋊Dic17—41no—
504C22⋊Dic17—41no—
505C22⋊Dic17—41no—
506C22⋊Dic17—41no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509C22⋊Dic17—41no—
510C22⋊Dic17—41no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17—41no—
519C22⋊Dic17—41no—
520C22⋊Dic17—41no—
521C22⋊Dic17—41no—
522C4⋊Dic17—22no—
523C4⋊Dic17—22no—
524C4⋊Dic17—22no—
525C4⋊Dic17—41no—
526C4⋊Dic17—41no—
527C4⋊Dic17—41no—
528C4⋊Dic17—41no—
529C4⋊Dic17—41no—
530C4⋊Dic17—41no—
531C4⋊Dic17—41no—
532C4⋊Dic17—41no—
533C4⋊Dic17—41no—
534C4⋊Dic17—41no—
535C4⋊Dic17—41no—
536C4⋊Dic17—41no—
537C4⋊Dic17—41no—
538C4⋊Dic17—41no—
539C4⋊Dic17—41no—
540C4⋊Dic17—41no—
541C4⋊Dic17—41no—
542C4×Dic17—22no—
543C4×Dic17—22no—
544C4×Dic17—22no—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—41no—
548C4×Dic17—41no—
549C4×Dic17—41no—
550C4×Dic17—41no—
551C4×Dic17—41no—
552C4×Dic17—41no—
553C4×Dic17—41no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17—41no—
561C4×Dic17—41no—
562#34451—171nomaximal, Sylow
563C23×C17—21no—
564C23×C17—21no—
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—44no—
594C23×C17—44no—
595C23×C17—44no—
596C23×C17—82no—
597C23×C17—82no—
598C23×C17—82no—
599C23×C17—82no—
600C23×C17C23×C412yes—
601C23×C17C23×C412yes—
602C23×C17C23×C412yes—
603C23×C17C23×C412yes—
604C23×C17C23×C412yes—
605C23×C17C2511yescharacteristic
606Q8×C17—44no—
607D4×C17—44no—
608D4×C17—44no—
609D4×C17—44no—
610D4×C17—44no—
611D4×C17—44no—
612D4×C17—44no—
613D4×C17—44no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—44no—
635C2×C4×C17—44no—
636C2×C4×C17—44no—
637C2×C4×C17—44no—
638C2×C4×C17C23×C412yes—
639C2×C4×C17C23×C412yes—
640C2×C4×C17C23×C412yes—
641C2×C4×C17C23×C412yes—
642C2×C4×C17C23×C412yes—
643C2×C4×C17C23×C412yes—
644C2×C4×C17C23×C412yes—
645C2×C4×C17C23×C412yes—
646C2×C4×C17C23×C412yes—
647C2×C4×C17C23×C412yes—
648C2×Dic17—21no—
649C2×Dic17—21no—
650C2×Dic17—21no—
651C2×Dic17—21no—
652C2×Dic17—21no—
653C2×Dic17—21no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
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—44no—
695C2×Dic17—44no—
696C2×Dic17—82no—
697C2×Dic17—82no—
698C2×Dic17—82no—
699C2×Dic17—82no—
700C2×Dic17—82no—
701C2×Dic17—82no—
702C2×Dic17H(5,𝔽2)12yes—
703C2×Dic17H(5,𝔽2)12yes—
704C2×#538D1711yescharacteristic
705#2383—171no—
706#2378—171no—
707#2376—171no—
708#2375—171no—
709#2373—171no—
710#2373—171no—
711#2373—171no—
712#2372—171no—
713#2367—171no—
714#2362—171no—
715#2359—171no—
716#2358—171no—
717#2354—171no—
718#2353—171no—
719#2342—171no—
720#2342—171no—
721#2337—171no—
722#2335—171no—
723#2333—171no—
724#2333—171no—
725#2326—171no—
726#2325—171no—
727#2324—171no—
728#2324—171no—
729#2321—171no—
730#2321—171no—
731#2319—171no—
732C4×#123—171no—
733C4×#121—171no—
734#2290—171no—
735C22×C17—22no—
736C22×C17—22no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—22no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—22no—
748C22×C17—22no—
749C22×C17—22no—
750C22×C17—41no—
751C22×C17—41no—
752C22×C17—41no—
753C22×C17—41no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17—41no—
757C22×C17—41no—
758C22×C17—41no—
759C22×C17—41no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—88no—
771C22×C17C24×C411yescharacteristic
772C22×C17C2×H(5,𝔽2)11yescharacteristic
773C22×C17C2×H(5,𝔽2)11yescharacteristic
774C22×C17#58511yescharacteristic
775C22×C17#58511yescharacteristic
776C22×C17#58511yescharacteristic
777C22×C17#58511yescharacteristic
778C4×C17—22no—
779C4×C17—22no—
780C4×C17—22no—
781C4×C17—22no—
782C4×C17—22no—
783C4×C17—22no—
784C4×C17—22no—
785C4×C17—22no—
786C4×C17—22no—
787C4×C17—22no—
788Dic17—22no—
789Dic17—22no—
790Dic17—41no—
791Dic17—41no—
792Dic17—41no—
793Dic17—41no—
794Dic17—41no—
795Dic17—41no—
796Dic17—41no—
797Dic17—41no—
798Dic17—41no—
799Dic17—41no—
800Dic17—41no—
801Dic17—41no—
802Dic17—41no—
803Dic17—41no—
804#538Dic17116yescomplemented
805C2×#126C2×D1711yescharacteristic
806C2×#126C2×D1711yescharacteristic
807C2×#124C2×D1711yescharacteristic
808C2×#124C2×D1711yescharacteristic
809C2×#123C2×D1711yescharacteristic
810C2×#123C2×D1711yescharacteristic
811C2×C22⋊Q8C2×D1711yescharacteristic
812C2×#121C2×D1711yescharacteristic
813C2×#121C2×D1711yescharacteristic
814C2×#121C2×D1711yescharacteristic
815C2×#120C2×D1711yescharacteristic
816C2×#120C2×D1711yescharacteristic
817C2×C4×Q8—171no—
818C2×C4×D4—171no—
819C2×C4×D4—171no—
820C2×C4×D4—171no—
821C2×C4×D4—171no—
822C2×C4×D4—171no—
823C2×C4×D4C2×D1711yescharacteristic
824C2×C4×D4C2×D1711yescharacteristic
825C2×#117—171no—
826C2×#117—171no—
827C2×#117—171no—
828C22×C22⋊C4—171no—
829C22×C22⋊C4—171no—
830C22×C22⋊C4C2×D1711yescharacteristic
831C22×C42—171no—
832#391—171no—
833#391—171no—
834#391—171no—
835#390—171no—
836#390—171no—
837#390—171no—
838#390—171no—
839#390—171no—
840#390—171no—
841#390—171no—
842#390—171no—
843#390—171no—
844#389—171no—
845#389—171no—
846#389—171no—
847#389—171no—
848#389—171no—
849#389—171no—
850#388—171no—
851#388—171no—
852#388—171no—
853#388—171no—
854#388—171no—
855#388—171no—
856#388—171no—
857#388—171no—
858#388—171no—
859#388—171no—
860#388—171no—
861#388—171no—
862#388—171no—
863#388—171no—
864#388—171no—
865#388—171no—
866#388—171no—
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#387—171no—
883#387—171no—
884#387—171no—
885#387—171no—
886#387—171no—
887#387—171no—
888#387—171no—
889#387—171no—
890#387—171no—
891#387—171no—
892#387—171no—
893#387—171no—
894#386—171no—
895#386—171no—
896#386—171no—
897#386—171no—
898#386—171no—
899#386—171no—
900#386—171no—
901#386—171no—
902#386—171no—
903#386—171no—
904#386—171no—
905#386—171no—
906#386—171no—
907#386—171no—
908#385—171no—
909#385—171no—
910#385—171no—
911#385—171no—
912#385—171no—
913#385—171no—
914#385—171no—
915#385—171no—
916#385—171no—
917#385—171no—
918#385—171no—
919#385—171no—
920#384—171no—
921#383—171no—
922#381—171no—
923#381—171no—
924#381—171no—
925#380—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929#380—171no—
930#379—171no—
931#379—171no—
932C4×C4⋊C4—171no—
933C4×C4⋊C4—171no—
934C4×C4⋊C4—171no—
935C4×C4⋊C4—171no—
936C4×C4⋊C4—171no—
937C4×C4⋊C4—171no—
938C4×C4⋊C4—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C22⋊C4—171no—
942C4×C22⋊C4—171no—
943C4×C22⋊C4—171no—
944C4×C22⋊C4—171no—
945C4×C22⋊C4—171no—
946C4×C22⋊C4—171no—
947C4×C22⋊C4—171no—
948C4×C22⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4—171no—
955C4×C22⋊C4—171no—
956#376—171no—
957#376—171no—
958#376—171no—
959C2×#95—171no—
960C2×C17—42no—
961C2×C17—42no—
962C2×C17—42no—
963C2×C17—42no—
964C2×C17—42no—
965C2×C17#342811yescharacteristic
966C2×C17C4×H(5,𝔽2)11yescharacteristic
967C2×C17C4×H(5,𝔽2)11yescharacteristic
968C2×C17#353311yescharacteristic
969C2×C17#354211yescharacteristic
970C2×C17#355111yescharacteristic
971C2×C17#356811yescharacteristic
972C25C22×D1711yescharacteristic
973C22×Q8C22×D1711yescharacteristic
974C22×D4C22×D1711yescharacteristic
975C22×D4C22×D1711yescharacteristic
976C22×D4C22×D1711yescharacteristic
977C22×D4C22×D1711yescharacteristic
978C22×D4C22×D1711yescharacteristic
979C22×D4C22×D1711yescharacteristic
980C22×D4C22×D1711yescharacteristic
981C23×C4—171no—
982C23×C4—171no—
983C23×C4—171no—
984C23×C4—171no—
985C23×C4—171no—
986C23×C4—171no—
987C23×C4—171no—
988C23×C4—171no—
989C23×C4C22×D1711yescharacteristic
990C23×C4C22×D1711yescharacteristic
991C23×C4C22×D1711yescharacteristic
992C23×C4C22×D1711yescharacteristic
993#126C2×Dic1718yescomplemented
994#126C2×Dic1718yescomplemented
995#124C2×Dic1718yescomplemented
996#124C2×Dic1718yescomplemented
997#123C2×Dic1718yescomplemented
998#123C2×Dic1718yescomplemented
999C22⋊Q8C2×Dic1718yescomplemented
1000#121C2×Dic1718yescomplemented
1001#121C2×Dic1718yescomplemented
1002#121C2×Dic1718yescomplemented
1003#120C2×Dic1718yescomplemented
1004#120C2×Dic1718yescomplemented
1005C4×Q8—682no—
1006C4×D4—682no—
1007C4×D4—682no—
1008C4×D4—682no—
1009C4×D4—682no—
1010C4×D4—682no—
1011C4×D4C2×Dic1718yescomplemented
1012C4×D4C2×Dic1718yescomplemented
1013#117—682no—
1014#117—682no—
1015#117—682no—
1016C2×C4⋊C4—171no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—171no—
1020C2×C4⋊C4—171no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4C22×D1711yescharacteristic
1037C2×C4⋊C4C22×D1711yescharacteristic
1038C2×C4⋊C4C22×D1711yescharacteristic
1039C2×C4⋊C4C22×D1711yescharacteristic
1040C2×C4⋊C4C22×D1711yescharacteristic
1041C2×C4⋊C4C22×D1711yescharacteristic
1042C2×C22⋊C4—171no—
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—171no—
1045C2×C22⋊C4—171no—
1046C2×C22⋊C4—171no—
1047C2×C22⋊C4—171no—
1048C2×C22⋊C4—171no—
1049C2×C22⋊C4—171no—
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—682no—
1075C2×C22⋊C4—682no—
1076C2×C22⋊C4C2×Dic1718yescomplemented
1077C2×C22⋊C4C22×D1711yescharacteristic
1078C2×C22⋊C4C22×D1711yescharacteristic
1079C2×C22⋊C4C22×D1711yescharacteristic
1080C2×C22⋊C4C22×D1711yescharacteristic
1081C2×C22⋊C4C22×D1711yescharacteristic
1082C2×C22⋊C4C22×D1711yescharacteristic
1083C2×C22⋊C4C22×D1711yescharacteristic
1084C2×C22⋊C4C22×D1711yescharacteristic
1085C2×C22⋊C4C22×D1711yescharacteristic
1086C2×C22⋊C4C22×D1711yescharacteristic
1087C2×C22⋊C4C22×D1711yescharacteristic
1088C2×C22⋊C4C22×D1711yescharacteristic
1089C2×C22⋊C4C22×D1711yescharacteristic
1090C2×C22⋊C4C22×D1711yescharacteristic
1091C2×C42—171no—
1092C2×C42—171no—
1093C2×C42—171no—
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—171no—
1102C2×C42—171no—
1103C2×C42—171no—
1104C2×C42—171no—
1105C2×C42—171no—
1106C2×C42—171no—
1107C2×C42—171no—
1108C2×C42—171no—
1109C2×C42—171no—
1110C2×C42—171no—
1111C2×C42—682no—
1112C2×C42C22×D1711yescharacteristic
1113C2×C42C22×D1711yescharacteristic
1114#95—171no—
1115#95—171no—
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154C17#3445111yescharacteristic, complemented, Sylow
1155C24—41no—
1156C24—41no—
1157C24—41no—
1158C24—41no—
1159C24—41no—
1160C24—41no—
1161C24C22×Dic1714yes—
1162C24C23×D1711yescharacteristic
1163C24C23×D1711yescharacteristic
1164C24C23×D1711yescharacteristic
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C2×Q8—41no—
1168C2×Q8—41no—
1169C2×Q8C22×Dic1714yes—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—41no—
1177C2×D4—41no—
1178C2×D4—41no—
1179C2×D4—41no—
1180C2×D4—41no—
1181C2×D4—41no—
1182C2×D4—41no—
1183C2×D4—41no—
1184C2×D4C22×Dic1714yes—
1185C2×D4C22×Dic1714yes—
1186C2×D4C22×Dic1714yes—
1187C2×D4C22×Dic1714yes—
1188C2×D4C22×Dic1714yes—
1189C2×D4C22×Dic1714yes—
1190C2×D4C22×Dic1714yes—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—171no—
1200C22×C4—171no—
1201C22×C4—171no—
1202C22×C4—171no—
1203C22×C4—171no—
1204C22×C4—171no—
1205C22×C4—171no—
1206C22×C4—171no—
1207C22×C4—171no—
1208C22×C4—171no—
1209C22×C4—171no—
1210C22×C4—171no—
1211C22×C4—171no—
1212C22×C4—171no—
1213C22×C4—171no—
1214C22×C4—171no—
1215C22×C4—342no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—342no—
1219C22×C4—342no—
1220C22×C4—681no—
1221C22×C4—681no—
1222C22×C4—681no—
1223C22×C4—681no—
1224C22×C4—681no—
1225C22×C4—681no—
1226C22×C4—681no—
1227C22×C4—681no—
1228C22×C4—681no—
1229C22×C4—681no—
1230C22×C4—681no—
1231C22×C4—681no—
1232C22×C4—681no—
1233C22×C4—681no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4C22×Dic1714yes—
1240C22×C4C22×Dic1714yes—
1241C22×C4C22×Dic1714yes—
1242C22×C4C22×Dic1714yes—
1243C22×C4C23×D1711yescharacteristic
1244C22×C4C23×D1711yescharacteristic
1245C22×C4C23×D1711yescharacteristic
1246C22×C4C23×D1711yescharacteristic
1247C22×C4C23×D1711yescharacteristic
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C4⋊C4—342no—
1254C4⋊C4—342no—
1255C4⋊C4—342no—
1256C4⋊C4—681no—
1257C4⋊C4—681no—
1258C4⋊C4—681no—
1259C4⋊C4—681no—
1260C4⋊C4—681no—
1261C4⋊C4—681no—
1262C4⋊C4—681no—
1263C4⋊C4—681no—
1264C4⋊C4—681no—
1265C4⋊C4—681no—
1266C4⋊C4—681no—
1267C4⋊C4—681no—
1268C4⋊C4—681no—
1269C4⋊C4—681no—
1270C4⋊C4—681no—
1271C4⋊C4—681no—
1272C4⋊C4—681no—
1273C4⋊C4C22×Dic1714yes—
1274C4⋊C4C22×Dic1714yes—
1275C4⋊C4C22×Dic1714yes—
1276C4⋊C4C22×Dic1714yes—
1277C4⋊C4C22×Dic1714yes—
1278C4⋊C4C22×Dic1714yes—
1279C22⋊C4—342no—
1280C22⋊C4—342no—
1281C22⋊C4—342no—
1282C22⋊C4—342no—
1283C22⋊C4—342no—
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⋊C4—681no—
1311C22⋊C4C22×Dic1714yes—
1312C22⋊C4C22×Dic1714yes—
1313C22⋊C4C22×Dic1714yes—
1314C22⋊C4C22×Dic1714yes—
1315C22⋊C4C22×Dic1714yes—
1316C22⋊C4C22×Dic1714yes—
1317C22⋊C4C22×Dic1714yes—
1318C22⋊C4C22×Dic1714yes—
1319C22⋊C4C22×Dic1714yes—
1320C22⋊C4C22×Dic1714yes—
1321C22⋊C4C22×Dic1714yes—
1322C22⋊C4C22×Dic1714yes—
1323C22⋊C4C22×Dic1714yes—
1324C22⋊C4C22×Dic1714yes—
1325C42—342no—
1326C42—342no—
1327C42—342no—
1328C42—342no—
1329C42—342no—
1330C42—681no—
1331C42—681no—
1332C42—681no—
1333C42—681no—
1334C42—681no—
1335C42—681no—
1336C42—681no—
1337C42—681no—
1338C42—681no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42C22×Dic1714yes—
1346C42C22×Dic1714yes—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—21no—
1376C23—21no—
1377C23—44no—
1378C23—44no—
1379C23—44no—
1380C23—82no—
1381C23—82no—
1382C23—82no—
1383C23—82no—
1384C23C23×Dic1712yes—
1385C23C23×Dic1712yes—
1386C23C23×Dic1712yes—
1387C23C23×Dic1712yes—
1388C23C23×Dic1712yes—
1389C23C24×D1711yescharacteristic
1390Q8—44no—
1391D4—44no—
1392D4—44no—
1393D4—44no—
1394D4—44no—
1395D4—44no—
1396D4—44no—
1397D4—44no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—44no—
1419C2×C4—44no—
1420C2×C4—44no—
1421C2×C4—44no—
1422C2×C4—172no—
1423C2×C4—172no—
1424C2×C4—341no—
1425C2×C4—341no—
1426C2×C4—341no—
1427C2×C4—341no—
1428C2×C4—341no—
1429C2×C4—341no—
1430C2×C4—341no—
1431C2×C4—341no—
1432C2×C4—341no—
1433C2×C4—341no—
1434C2×C4—341no—
1435C2×C4—341no—
1436C2×C4—341no—
1437C2×C4—341no—
1438C2×C4—341no—
1439C2×C4—341no—
1440C2×C4—341no—
1441C2×C4—341no—
1442C2×C4—341no—
1443C2×C4—341no—
1444C2×C4—341no—
1445C2×C4—341no—
1446C2×C4—341no—
1447C2×C4—341no—
1448C2×C4—341no—
1449C2×C4—341no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—684no—
1471C2×C4—684no—
1472C2×C4—1362no—
1473C2×C4—1362no—
1474C2×C4—1362no—
1475C2×C4—1362no—
1476C2×C4—1362no—
1477C2×C4—1362no—
1478C2×C4C23×Dic1712yes—
1479C2×C4C23×Dic1712yes—
1480C2×C4C23×Dic1712yes—
1481C2×C4C23×Dic1712yes—
1482C2×C4C23×Dic1712yes—
1483C2×C4C23×Dic1712yes—
1484C2×C4C23×Dic1712yes—
1485C2×C4C23×Dic1712yes—
1486C2×C4C23×Dic1712yes—
1487C2×C4C23×Dic1712yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—22no—
1501C22—22no—
1502C22—22no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—88no—
1524C22C24×Dic1711yescharacteristic
1525C22H(5,𝔽2)×D1711yescharacteristic
1526C22H(5,𝔽2)×D1711yescharacteristic
1527C22#1176364411yescharacteristic
1528C22#1176364411yescharacteristic
1529C22#1176364511yescharacteristic
1530C22#1176364511yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—22no—
1538C4—22no—
1539C4—22no—
1540C4—22no—
1541C4—342no—
1542C4—342no—
1543C4—681no—
1544C4—681no—
1545C4—681no—
1546C4—681no—
1547C4—681no—
1548C4—681no—
1549C4—681no—
1550C4—681no—
1551C4—681no—
1552C4—681no—
1553C4—681no—
1554C4—681no—
1555C4—681no—
1556C4—681no—
1557C2—42no—
1558C2—42no—
1559C2—42no—
1560C2—42no—
1561C2—42no—
1562C2#1454198711yescharacteristic
1563C2H(5,𝔽2)×Dic1711yescharacteristic
1564C2H(5,𝔽2)×Dic1711yescharacteristic
1565C2#1454295111yescharacteristic
1566C2#1454309911yescharacteristic
1567C2#1454320111yescharacteristic
1568C2#1454347711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
Fitting, prime radicalC2×C17×#538C2
socle, cosocleC23×C17C25
hypercenterC2×#538D17
hypocenterC17#34451
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #14531976C2semidirect
2. #14531950C2semidirect
3. #14531932C2semidirect
4. #14531925C2semidirect
5. #14531908C2semidirect
6. #14531908C2semidirect
7. #14531908C2semidirect
8. #14531896C2semidirect
9. #14531859C2semidirect
10. #14531815C2semidirect
11. #14531780C2semidirect
12. #14531768C2semidirect
13. #14531733C2semidirect
14. #14531724C2semidirect
15. #14531633C2semidirect
16. #14531633C2semidirect
17. #14531599C2semidirect
18. #14531578C2semidirect
19. #14531551C2semidirect
20. #14531551C2semidirect
21. #14531497C2semidirect
22. #14531489C2semidirect
23. #14531479C2semidirect
24. #14531479C2semidirect
25. #14531445C2semidirect
26. #14531445C2semidirect
27. #14531427C2semidirect
28. #123×Dic17C2semidirect
29. #121×Dic17C2semidirect
30. #14531229C2semidirect
32. C2×Q8×Dic17C22semidirect
37. C2×D4×Dic17C22semidirect
40. C2×#10587612C22semidirect
43. C22×C4×Dic17C22semidirect
44. #11762716C22semidirect
45. #11762716C22semidirect
46. #11762716C22semidirect
55. #11762712C22semidirect
56. #11762708C22semidirect
57. #11762708C22semidirect
58. #11762708C22semidirect
59. #11762708C22semidirect
60. #11762708C22semidirect
61. #11762708C22semidirect
86. #11762702C22semidirect
87. #11762702C22semidirect
88. #11762702C22semidirect
89. #11762702C22semidirect
90. #11762702C22semidirect
91. #11762702C22semidirect
92. #11762702C22semidirect
93. #11762702C22semidirect
94. #11762695C22semidirect
95. #11762695C22semidirect
96. #11762695C22semidirect
97. #11762695C22semidirect
98. #11762695C22semidirect
99. #11762695C22semidirect
100. #11762695C22semidirect
101. #11762695C22semidirect
102. #11762695C22semidirect
103. #11762695C22semidirect
104. #11762695C22semidirect
105. #11762695C22semidirect
118. #11762689C22semidirect
119. #11762689C22semidirect
128. #11762684C22semidirect
129. #11762684C22semidirect
130. #11762684C22semidirect
131. #11762684C22semidirect
132. #11762679C22semidirect
133. #11762677C22semidirect
136. #11762672C22semidirect
139. #11762669C22semidirect
140. #11762669C22semidirect
141. #11762669C22semidirect
144. C4⋊C4×Dic17C22semidirect
145. C4⋊C4×Dic17C22semidirect
146. C4⋊C4×Dic17C22semidirect
147. C4⋊C4×Dic17C22semidirect
148. C4⋊C4×Dic17C22semidirect
149. C4⋊C4×Dic17C22semidirect
150. C4×C4⋊Dic17C22semidirect
151. C4×C4⋊Dic17C22semidirect
152. C4×C4⋊Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
162. C22⋊C4×Dic17C22semidirect
163. C22⋊C4×Dic17C22semidirect
164. C22⋊C4×Dic17C22semidirect
167. C4×C22⋊Dic17C22semidirect
168. #11762655C22semidirect
169. #11762655C22semidirect
170. #11762655C22semidirect
171. C2×#10587502C22semidirect
172. C17×#538C4semidirect
209. C17×#126C2×C4semidirect
210. C17×#126C2×C4semidirect
211. C17×#124C2×C4semidirect
212. C17×#124C2×C4semidirect
213. C17×#123C2×C4semidirect
214. C17×#123C2×C4semidirect
215. C17×C22⋊Q8C2×C4semidirect
216. C17×#121C2×C4semidirect
217. C17×#121C2×C4semidirect
218. C17×#121C2×C4semidirect
219. C17×#120C2×C4semidirect
220. C17×#120C2×C4semidirect
221. C4×D4×C17C2×C4semidirect
222. C4×D4×C17C2×C4semidirect
229. C2×C22⋊C4×C17C2×C4semidirect
804. #538Dic17semidirect
993. #126C2×Dic17semidirect
994. #126C2×Dic17semidirect
995. #124C2×Dic17semidirect
996. #124C2×Dic17semidirect
997. #123C2×Dic17semidirect
998. #123C2×Dic17semidirect
999. C22⋊Q8C2×Dic17semidirect
1000. #121C2×Dic17semidirect
1001. #121C2×Dic17semidirect
1002. #121C2×Dic17semidirect
1003. #120C2×Dic17semidirect
1004. #120C2×Dic17semidirect
1011. C4×D4C2×Dic17semidirect
1012. C4×D4C2×Dic17semidirect
1076. C2×C22⋊C4C2×Dic17semidirect
1154. C17#34451semidirect

Maximal subgroups

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

subgroupindex
#145319762
#145319502
#145319322
#145319252
#145319082
#145318962
#145318592
#145318152
#145317802
#145317682
#145317332
#145317242
#145316332
#145315992
#145315782
#145315512
#145314972
#145314892
#145314792
#145314452
#145314272
#123×Dic172
#121×Dic172
#145312292
C2×C17×#5382
#3445117