Finite Group Databasebeta

← #17198676

Subgroups — #17198676

Order 4352.

2290 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531970C211yesmaximal, characteristic, complemented
2#14531941C211yesmaximal, characteristic, complemented
3#14531941C211yesmaximal, characteristic, complemented
4#14531932C211yesmaximal, characteristic, complemented
5#14531920C211yesmaximal, characteristic, complemented
6#14531890C211yesmaximal, characteristic, complemented
7#14531836C211yesmaximal, characteristic, complemented
8#14531836C211yesmaximal, characteristic, complemented
9#14531826C211yesmaximal, characteristic, complemented
10#14531804C211yesmaximal, characteristic, complemented
11#14531780C211yesmaximal, characteristic, complemented
12#14531780C211yesmaximal, characteristic, complemented
13#14531724C211yesmaximal, characteristic, complemented
14#14531713C211yesmaximal, characteristic, complemented
15#14531669C211yesmaximal, characteristic, complemented
16#14531644C211yesmaximal, characteristic, complemented
17#14531578C211yesmaximal, characteristic, complemented
18#14531578C211yesmaximal, characteristic, complemented
19#14531551C211yesmaximal, characteristic, complemented
20#14531551C211yesmaximal, characteristic, complemented
21#14531510C211yesmaximal, characteristic, complemented
22#14531510C211yesmaximal, characteristic, complemented
23#14531489C211yesmaximal, characteristic, complemented
24#14531489C211yesmaximal, characteristic, complemented
25#14531479C211yesmaximal, characteristic, complemented
26#14531456C211yesmaximal, characteristic, complemented
27#14531417C211yesmaximal, characteristic, complemented
28#123×Dic17C211yesmaximal, characteristic, complemented
29#121×Dic17C211yesmaximal, characteristic, complemented
30#14531229C211yesmaximal, characteristic, complemented
31C2×C17×#540C211yesmaximal, 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×#10587612C2211yescharacteristic
41C2×#10587612C2211yescharacteristic
42C22×C4⋊Dic17C2211yescharacteristic
43C22×C4×Dic17C2211yescharacteristic
44#11762712C2211yescharacteristic
45#11762712C2211yescharacteristic
46#11762712C2211yescharacteristic
47#11762712C2211yescharacteristic
48#11762712C2211yescharacteristic
49#11762712C2211yescharacteristic
50#11762712C2211yescharacteristic
51#11762712C2211yescharacteristic
52#11762708C2211yescharacteristic
53#11762708C2211yescharacteristic
54#11762708C2211yescharacteristic
55#11762708C2211yescharacteristic
56#11762708C2211yescharacteristic
57#11762708C2211yescharacteristic
58#11762702C2211yescharacteristic
59#11762702C2211yescharacteristic
60#11762702C2211yescharacteristic
61#11762702C2211yescharacteristic
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#11762695C2211yescharacteristic
79#11762695C2211yescharacteristic
80#11762695C2211yescharacteristic
81#11762695C2211yescharacteristic
82#11762695C2211yescharacteristic
83#11762695C2211yescharacteristic
84#11762695C2211yescharacteristic
85#11762695C2211yescharacteristic
86#11762695C2211yescharacteristic
87#11762695C2211yescharacteristic
88#11762695C2211yescharacteristic
89#11762695C2211yescharacteristic
90#11762695C2211yescharacteristic
91#11762695C2211yescharacteristic
92#11762695C2211yescharacteristic
93#11762695C2211yescharacteristic
94#11762695C2211yescharacteristic
95#11762695C2211yescharacteristic
96#11762695C2211yescharacteristic
97#11762695C2211yescharacteristic
98#11762689C2211yescharacteristic
99#11762689C2211yescharacteristic
100#11762689C2211yescharacteristic
101#11762689C2211yescharacteristic
102#11762689C2211yescharacteristic
103#11762689C2211yescharacteristic
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#11762684C2211yescharacteristic
123#11762684C2211yescharacteristic
124#11762684C2211yescharacteristic
125#11762684C2211yescharacteristic
126#11762684C2211yescharacteristic
127#11762684C2211yescharacteristic
128#11762684C2211yescharacteristic
129#11762684C2211yescharacteristic
130#11762684C2211yescharacteristic
131#11762684C2211yescharacteristic
132#11762677C2211yescharacteristic
133#11762675C2211yescharacteristic
134#11762675C2211yescharacteristic
135#11762675C2211yescharacteristic
136#11762672C2211yescharacteristic
137#11762672C2211yescharacteristic
138#11762672C2211yescharacteristic
139#11762669C2211yescharacteristic
140#11762669C2211yescharacteristic
141#11762669C2211yescharacteristic
142#11762669C2211yescharacteristic
143#11762669C2211yescharacteristic
144C4⋊C4×Dic17C2211yescharacteristic
145C4⋊C4×Dic17C2211yescharacteristic
146C4⋊C4×Dic17C2211yescharacteristic
147C4⋊C4×Dic17C2211yescharacteristic
148C4⋊C4×Dic17C2211yescharacteristic
149C4⋊C4×Dic17C2211yescharacteristic
150C4×C4⋊Dic17C2211yescharacteristic
151C22⋊C4×Dic17C2211yescharacteristic
152C22⋊C4×Dic17C2211yescharacteristic
153C22⋊C4×Dic17C2211yescharacteristic
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C4×C22⋊Dic17C2211yescharacteristic
162C4×C22⋊Dic17C2211yescharacteristic
163C4×C22⋊Dic17C2211yescharacteristic
164C4×C22⋊Dic17C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic
166#11762655C2211yescharacteristic
167#11762655C2211yescharacteristic
168#11762655C2211yescharacteristic
169C2×#10587502C2211yescharacteristic
170C2×#10587502C2211yescharacteristic
171C2×#10587502C2211yescharacteristic
172C17×#540C4116yescomplemented
173C2×C17×#127C2211yescharacteristic
174C2×C17×#125C2211yescharacteristic
175C2×C17×#123C2211yescharacteristic
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×C4×D4×C17C2211yescharacteristic
186C2×C4×D4×C17C2211yescharacteristic
187C2×C17×#117C2211yescharacteristic
188C22×D4×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
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C23×C4×C17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C17×#127C2×C418yescomplemented
214C17×#125C2×C418yescomplemented
215C17×#123C2×C418yescomplemented
216C17×#123C2×C418yescomplemented
217C17×#123C2×C418yescomplemented
218C17×#123C2×C418yescomplemented
219C17×#121C2×C418yescomplemented
220C17×#121C2×C418yescomplemented
221C17×#121C2×C418yescomplemented
222C17×#121C2×C418yescomplemented
223C17×#121C2×C418yescomplemented
224C17×#121C2×C418yescomplemented
225C4×D4×C17C2×C418yescomplemented
226C4×D4×C17C2×C418yescomplemented
227C17×#117C2×C418yescomplemented
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊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×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C42×C17C2311yescharacteristic
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
278D4×Dic17—42no—
279D4×Dic17—42no—
280D4×Dic17—42no—
281D4×Dic17—42no—
282D4×Dic17—42no—
283D4×Dic17—42no—
284D4×Dic17—42no—
285D4×Dic17—42no—
286#10587612—42no—
287#10587612—42no—
288C2×C4⋊Dic17—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×Dic17—42no—
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×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
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×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C24×C17C2411yescharacteristic
373C24×C17C2411yescharacteristic
374C24×C17C2411yescharacteristic
375C2×D4×C17—41no—
376C2×D4×C17—41no—
377C2×D4×C17—41no—
378C2×D4×C17—41no—
379C2×D4×C17—41no—
380C2×D4×C17—41no—
381C2×D4×C17—41no—
382C2×D4×C17—41no—
383C2×D4×C17—41no—
384C2×D4×C17—41no—
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×C17C22×C414yes—
396C2×D4×C17C22×C414yes—
397C2×D4×C17C22×C414yes—
398C2×D4×C17C22×C414yes—
399C2×D4×C17C22×C414yes—
400C2×D4×C17C22×C414yes—
401C2×D4×C17C22×C414yes—
402C2×D4×C17C22×C414yes—
403C2×D4×C17C22×C414yes—
404C2×D4×C17C22×C414yes—
405C22×C4×C17—41no—
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×C17—41no—
415C22×C4×C17C22×C414yes—
416C22×C4×C17C22×C414yes—
417C22×C4×C17C22×C414yes—
418C22×C4×C17C22×C414yes—
419C22×C4×C17C22×C414yes—
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×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×Dic17—22no—
431C22×Dic17—22no—
432C22×Dic17—22no—
433C22×Dic17—22no—
434C22×Dic17—22no—
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×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C22×Dic17C2411yescharacteristic
475C22×Dic17C2411yescharacteristic
476C4⋊C4×C17C22×C414yes—
477C4⋊C4×C17C22×C414yes—
478C4⋊C4×C17C22×C414yes—
479C4⋊C4×C17C22×C414yes—
480C4⋊C4×C17C22×C414yes—
481C4⋊C4×C17C22×C414yes—
482C4⋊C4×C17C22×C414yes—
483C4⋊C4×C17C22×C414yes—
484C22⋊C4×C17C22×C414yes—
485C22⋊C4×C17C22×C414yes—
486C22⋊C4×C17C22×C414yes—
487C22⋊C4×C17C22×C414yes—
488C22⋊C4×C17C22×C414yes—
489C22⋊C4×C17C22×C414yes—
490C22⋊C4×C17C22×C414yes—
491C22⋊C4×C17C22×C414yes—
492C22⋊C4×C17C22×C414yes—
493C22⋊C4×C17C22×C414yes—
494C42×C17C22×C414yes—
495C42×C17C22×C414yes—
496C22⋊Dic17—22no—
497C22⋊Dic17—22no—
498C22⋊Dic17—22no—
499C22⋊Dic17—22no—
500C22⋊Dic17—22no—
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—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C4⋊Dic17—22no—
527C4⋊Dic17—22no—
528C4⋊Dic17—22no—
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—41no—
543C4⋊Dic17—41no—
544C4×Dic17—22no—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—22no—
548C4×Dic17—22no—
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#34450—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×C17C23×C412yes—
594C23×C17C23×C412yes—
595C23×C17C23×C412yes—
596C23×C17C23×C412yes—
597C23×C17C23×C412yes—
598C23×C17C2511yescharacteristic
599D4×C17—44no—
600D4×C17—44no—
601D4×C17—44no—
602D4×C17—44no—
603D4×C17—44no—
604D4×C17—44no—
605D4×C17—44no—
606D4×C17—44no—
607D4×C17—44no—
608D4×C17—44no—
609C2×C4×C17—21no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
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—44no—
630C2×C4×C17—44no—
631C2×C4×C17—44no—
632C2×C4×C17—44no—
633C2×C4×C17—44no—
634C2×C4×C17C23×C412yes—
635C2×C4×C17C23×C412yes—
636C2×C4×C17C23×C412yes—
637C2×C4×C17C23×C412yes—
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×Dic17—21no—
645C2×Dic17—21no—
646C2×Dic17—21no—
647C2×Dic17—21no—
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—44no—
691C2×Dic17—44no—
692C2×Dic17—82no—
693C2×Dic17—82no—
694C2×Dic17—82no—
695C2×Dic17—82no—
696C2×Dic17—82no—
697C2×Dic17—82no—
698C2×Dic17—82no—
699C2×Dic17—82no—
700C2×Dic17H(5,𝔽2)12yes—
701C2×Dic17H(5,𝔽2)12yes—
702C2×#540D1711yescharacteristic
703#2382—171no—
704#2377—171no—
705#2377—171no—
706#2376—171no—
707#2374—171no—
708#2371—171no—
709#2364—171no—
710#2364—171no—
711#2363—171no—
712#2361—171no—
713#2359—171no—
714#2359—171no—
715#2353—171no—
716#2352—171no—
717#2346—171no—
718#2343—171no—
719#2335—171no—
720#2335—171no—
721#2333—171no—
722#2333—171no—
723#2328—171no—
724#2328—171no—
725#2325—171no—
726#2325—171no—
727#2324—171no—
728#2322—171no—
729#2318—171no—
730C4×#123—171no—
731C4×#121—171no—
732#2290—171no—
733C22×C17—22no—
734C22×C17—22no—
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—41no—
749C22×C17—41no—
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×C17C24×C411yescharacteristic
769C22×C17C2×H(5,𝔽2)11yescharacteristic
770C22×C17C2×H(5,𝔽2)11yescharacteristic
771C22×C17#58511yescharacteristic
772C22×C17#58511yescharacteristic
773C22×C17#58511yescharacteristic
774C22×C17#58511yescharacteristic
775C4×C17—22no—
776C4×C17—22no—
777C4×C17—22no—
778C4×C17—22no—
779C4×C17—22no—
780C4×C17—22no—
781C4×C17—22no—
782C4×C17—22no—
783C4×C17—22no—
784C4×C17—22no—
785Dic17—22no—
786Dic17—22no—
787Dic17—41no—
788Dic17—41no—
789Dic17—41no—
790Dic17—41no—
791Dic17—41no—
792Dic17—41no—
793Dic17—41no—
794Dic17—41no—
795Dic17—41no—
796Dic17—41no—
797Dic17—41no—
798Dic17—41no—
799Dic17—41no—
800Dic17—41no—
801#540Dic17116yescomplemented
802C2×#127C2×D1711yescharacteristic
803C2×#125C2×D1711yescharacteristic
804C2×#123C2×D1711yescharacteristic
805C2×#123C2×D1711yescharacteristic
806C2×#123C2×D1711yescharacteristic
807C2×#123C2×D1711yescharacteristic
808C2×#121C2×D1711yescharacteristic
809C2×#121C2×D1711yescharacteristic
810C2×#121C2×D1711yescharacteristic
811C2×#121C2×D1711yescharacteristic
812C2×#121C2×D1711yescharacteristic
813C2×#121C2×D1711yescharacteristic
814C2×C4×D4—171no—
815C2×C4×D4—171no—
816C2×C4×D4—171no—
817C2×C4×D4—171no—
818C2×C4×D4—171no—
819C2×C4×D4—171no—
820C2×C4×D4—171no—
821C2×C4×D4—171no—
822C2×C4×D4C2×D1711yescharacteristic
823C2×C4×D4C2×D1711yescharacteristic
824C2×#117—171no—
825C2×#117—171no—
826C2×#117C2×D1711yescharacteristic
827C22×C4⋊C4—171no—
828C22×C42—171no—
829#390—171no—
830#390—171no—
831#390—171no—
832#390—171no—
833#390—171no—
834#390—171no—
835#390—171no—
836#390—171no—
837#389—171no—
838#389—171no—
839#389—171no—
840#389—171no—
841#389—171no—
842#389—171no—
843#388—171no—
844#388—171no—
845#388—171no—
846#388—171no—
847#388—171no—
848#388—171no—
849#388—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#387—171no—
864#387—171no—
865#387—171no—
866#387—171no—
867#387—171no—
868#387—171no—
869#387—171no—
870#387—171no—
871#387—171no—
872#387—171no—
873#387—171no—
874#387—171no—
875#387—171no—
876#387—171no—
877#387—171no—
878#387—171no—
879#387—171no—
880#387—171no—
881#387—171no—
882#387—171no—
883#386—171no—
884#386—171no—
885#386—171no—
886#386—171no—
887#386—171no—
888#386—171no—
889#386—171no—
890#386—171no—
891#386—171no—
892#386—171no—
893#386—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#385—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#383—171no—
918#382—171no—
919#382—171no—
920#382—171no—
921#381—171no—
922#381—171no—
923#381—171no—
924#380—171no—
925#380—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929C4×C4⋊C4—171no—
930C4×C4⋊C4—171no—
931C4×C4⋊C4—171no—
932C4×C4⋊C4—171no—
933C4×C4⋊C4—171no—
934C4×C4⋊C4—171no—
935C4×C4⋊C4—171no—
936C4×C22⋊C4—171no—
937C4×C22⋊C4—171no—
938C4×C22⋊C4—171no—
939C4×C22⋊C4—171no—
940C4×C22⋊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—
951#376—171no—
952#376—171no—
953#376—171no—
954C2×#95—171no—
955C2×#95—171no—
956C2×#95—171no—
957C2×C17—42no—
958C2×C17—42no—
959C2×C17—42no—
960C2×C17—42no—
961C2×C17—42no—
962C2×C17#342811yescharacteristic
963C2×C17C4×H(5,𝔽2)11yescharacteristic
964C2×C17C4×H(5,𝔽2)11yescharacteristic
965C2×C17#353311yescharacteristic
966C2×C17#354211yescharacteristic
967C2×C17#355111yescharacteristic
968C2×C17#356711yescharacteristic
969C22×D4C22×D1711yescharacteristic
970C22×D4C22×D1711yescharacteristic
971C22×D4C22×D1711yescharacteristic
972C22×D4C22×D1711yescharacteristic
973C22×D4C22×D1711yescharacteristic
974C22×D4C22×D1711yescharacteristic
975C22×D4C22×D1711yescharacteristic
976C22×D4C22×D1711yescharacteristic
977C22×D4C22×D1711yescharacteristic
978C22×D4C22×D1711yescharacteristic
979C23×C4—171no—
980C23×C4—171no—
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
993C23×C4C22×D1711yescharacteristic
994#127C2×Dic1718yescomplemented
995#125C2×Dic1718yescomplemented
996#123C2×Dic1718yescomplemented
997#123C2×Dic1718yescomplemented
998#123C2×Dic1718yescomplemented
999#123C2×Dic1718yescomplemented
1000#121C2×Dic1718yescomplemented
1001#121C2×Dic1718yescomplemented
1002#121C2×Dic1718yescomplemented
1003#121C2×Dic1718yescomplemented
1004#121C2×Dic1718yescomplemented
1005#121C2×Dic1718yescomplemented
1006C4×D4—682no—
1007C4×D4—682no—
1008C4×D4—682no—
1009C4×D4—682no—
1010C4×D4—682no—
1011C4×D4—682no—
1012C4×D4—682no—
1013C4×D4—682no—
1014C4×D4C2×Dic1718yescomplemented
1015C4×D4C2×Dic1718yescomplemented
1016#117—682no—
1017#117—682no—
1018#117C2×Dic1718yescomplemented
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⋊C4—171no—
1037C2×C4⋊C4—682no—
1038C2×C4⋊C4C22×D1711yescharacteristic
1039C2×C4⋊C4C22×D1711yescharacteristic
1040C2×C4⋊C4C22×D1711yescharacteristic
1041C2×C4⋊C4C22×D1711yescharacteristic
1042C2×C4⋊C4C22×D1711yescharacteristic
1043C2×C4⋊C4C22×D1711yescharacteristic
1044C2×C4⋊C4C22×D1711yescharacteristic
1045C2×C4⋊C4C22×D1711yescharacteristic
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—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4C22×D1711yescharacteristic
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×C42—171no—
1087C2×C42—171no—
1088C2×C42—171no—
1089C2×C42—171no—
1090C2×C42—171no—
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—682no—
1105C2×C42C22×D1711yescharacteristic
1106C2×C42C22×D1711yescharacteristic
1107#95—171no—
1108#95—171no—
1109#95—171no—
1110#95—171no—
1111#95—171no—
1112#95—171no—
1113#95—171no—
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—
1151C17#3445011yescharacteristic, complemented, Sylow
1152C24C23×D1711yescharacteristic
1153C24C23×D1711yescharacteristic
1154C24C23×D1711yescharacteristic
1155C24C23×D1711yescharacteristic
1156C24C23×D1711yescharacteristic
1157C2×D4—41no—
1158C2×D4—41no—
1159C2×D4—41no—
1160C2×D4—41no—
1161C2×D4—41no—
1162C2×D4—41no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C2×D4—41no—
1167C2×D4—41no—
1168C2×D4—41no—
1169C2×D4—41no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—41no—
1177C2×D4C22×Dic1714yes—
1178C2×D4C22×Dic1714yes—
1179C2×D4C22×Dic1714yes—
1180C2×D4C22×Dic1714yes—
1181C2×D4C22×Dic1714yes—
1182C2×D4C22×Dic1714yes—
1183C2×D4C22×Dic1714yes—
1184C2×D4C22×Dic1714yes—
1185C2×D4C22×Dic1714yes—
1186C2×D4C22×Dic1714yes—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—41no—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—171no—
1198C22×C4—171no—
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—342no—
1214C22×C4—342no—
1215C22×C4—342no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—681no—
1219C22×C4—681no—
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×C4—681no—
1240C22×C4—681no—
1241C22×C4—681no—
1242C22×C4—681no—
1243C22×C4C22×Dic1714yes—
1244C22×C4C22×Dic1714yes—
1245C22×C4C22×Dic1714yes—
1246C22×C4C22×Dic1714yes—
1247C22×C4C22×Dic1714yes—
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C22×C4C23×D1711yescharacteristic
1254C22×C4C23×D1711yescharacteristic
1255C22×C4C23×D1711yescharacteristic
1256C22×C4C23×D1711yescharacteristic
1257C22×C4C23×D1711yescharacteristic
1258C4⋊C4—342no—
1259C4⋊C4—342no—
1260C4⋊C4—342no—
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⋊C4—681no—
1274C4⋊C4—681no—
1275C4⋊C4—681no—
1276C4⋊C4C22×Dic1714yes—
1277C4⋊C4C22×Dic1714yes—
1278C4⋊C4C22×Dic1714yes—
1279C4⋊C4C22×Dic1714yes—
1280C4⋊C4C22×Dic1714yes—
1281C4⋊C4C22×Dic1714yes—
1282C4⋊C4C22×Dic1714yes—
1283C4⋊C4C22×Dic1714yes—
1284C22⋊C4—342no—
1285C22⋊C4—342no—
1286C22⋊C4—342no—
1287C22⋊C4—342no—
1288C22⋊C4—342no—
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⋊C4—681no—
1312C22⋊C4—681no—
1313C22⋊C4—681no—
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—
1324C42—342no—
1325C42—342no—
1326C42—342no—
1327C42—342no—
1328C42—342no—
1329C42—681no—
1330C42—681no—
1331C42—681no—
1332C42—681no—
1333C42—681no—
1334C42—681no—
1335C42—681no—
1336C42—681no—
1337C42—681no—
1338C42—681no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42C22×Dic1714yes—
1343C42C22×Dic1714yes—
1344C23—21no—
1345C23—21no—
1346C23—21no—
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—
1374C23C23×Dic1712yes—
1375C23C23×Dic1712yes—
1376C23C23×Dic1712yes—
1377C23C23×Dic1712yes—
1378C23C23×Dic1712yes—
1379C23C24×D1711yescharacteristic
1380D4—44no—
1381D4—44no—
1382D4—44no—
1383D4—44no—
1384D4—44no—
1385D4—44no—
1386D4—44no—
1387D4—44no—
1388D4—44no—
1389D4—44no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
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—44no—
1411C2×C4—44no—
1412C2×C4—44no—
1413C2×C4—44no—
1414C2×C4—44no—
1415C2×C4—172no—
1416C2×C4—172no—
1417C2×C4—341no—
1418C2×C4—341no—
1419C2×C4—341no—
1420C2×C4—341no—
1421C2×C4—341no—
1422C2×C4—341no—
1423C2×C4—341no—
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—684no—
1464C2×C4—684no—
1465C2×C4—1362no—
1466C2×C4—1362no—
1467C2×C4—1362no—
1468C2×C4—1362no—
1469C2×C4—1362no—
1470C2×C4—1362no—
1471C2×C4—1362no—
1472C2×C4—1362no—
1473C2×C4C23×Dic1712yes—
1474C2×C4C23×Dic1712yes—
1475C2×C4C23×Dic1712yes—
1476C2×C4C23×Dic1712yes—
1477C2×C4C23×Dic1712yes—
1478C2×C4C23×Dic1712yes—
1479C2×C4C23×Dic1712yes—
1480C2×C4C23×Dic1712yes—
1481C2×C4C23×Dic1712yes—
1482C2×C4C23×Dic1712yes—
1483C22—22no—
1484C22—22no—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
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—
1518C22C24×Dic1711yescharacteristic
1519C22H(5,𝔽2)×D1711yescharacteristic
1520C22H(5,𝔽2)×D1711yescharacteristic
1521C22#1176364411yescharacteristic
1522C22#1176364411yescharacteristic
1523C22#1176364511yescharacteristic
1524C22#1176364511yescharacteristic
1525C4—22no—
1526C4—22no—
1527C4—22no—
1528C4—22no—
1529C4—22no—
1530C4—22no—
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—342no—
1536C4—342no—
1537C4—681no—
1538C4—681no—
1539C4—681no—
1540C4—681no—
1541C4—681no—
1542C4—681no—
1543C4—681no—
1544C4—681no—
1545C4—681no—
1546C4—681no—
1547C4—681no—
1548C4—681no—
1549C4—681no—
1550C4—681no—
1551C2—42no—
1552C2—42no—
1553C2—42no—
1554C2—42no—
1555C2—42no—
1556C2#1454198711yescharacteristic
1557C2H(5,𝔽2)×Dic1711yescharacteristic
1558C2H(5,𝔽2)×Dic1711yescharacteristic
1559C2#1454294411yescharacteristic
1560C2#1454309111yescharacteristic
1561C2#1454320511yescharacteristic
1562C2#1454346911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
Fitting, prime radicalC2×C17×#540C2
socle, cosocleC23×C17C25
hypercenterC2×#540D17
hypocenterC17#34450
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #14531970C2semidirect
2. #14531941C2semidirect
3. #14531941C2semidirect
4. #14531932C2semidirect
5. #14531920C2semidirect
6. #14531890C2semidirect
7. #14531836C2semidirect
8. #14531836C2semidirect
9. #14531826C2semidirect
10. #14531804C2semidirect
11. #14531780C2semidirect
12. #14531780C2semidirect
13. #14531724C2semidirect
14. #14531713C2semidirect
15. #14531669C2semidirect
16. #14531644C2semidirect
17. #14531578C2semidirect
18. #14531578C2semidirect
19. #14531551C2semidirect
20. #14531551C2semidirect
21. #14531510C2semidirect
22. #14531510C2semidirect
23. #14531489C2semidirect
24. #14531489C2semidirect
25. #14531479C2semidirect
26. #14531456C2semidirect
27. #14531417C2semidirect
28. #123×Dic17C2semidirect
29. #121×Dic17C2semidirect
30. #14531229C2semidirect
172. C17×#540C4semidirect
213. C17×#127C2×C4semidirect
214. C17×#125C2×C4semidirect
215. C17×#123C2×C4semidirect
216. C17×#123C2×C4semidirect
217. C17×#123C2×C4semidirect
218. C17×#123C2×C4semidirect
219. C17×#121C2×C4semidirect
220. C17×#121C2×C4semidirect
221. C17×#121C2×C4semidirect
222. C17×#121C2×C4semidirect
223. C17×#121C2×C4semidirect
224. C17×#121C2×C4semidirect
225. C4×D4×C17C2×C4semidirect
226. C4×D4×C17C2×C4semidirect
227. C17×#117C2×C4semidirect
801. #540Dic17semidirect
994. #127C2×Dic17semidirect
995. #125C2×Dic17semidirect
996. #123C2×Dic17semidirect
997. #123C2×Dic17semidirect
998. #123C2×Dic17semidirect
999. #123C2×Dic17semidirect
1000. #121C2×Dic17semidirect
1001. #121C2×Dic17semidirect
1002. #121C2×Dic17semidirect
1003. #121C2×Dic17semidirect
1004. #121C2×Dic17semidirect
1005. #121C2×Dic17semidirect
1014. C4×D4C2×Dic17semidirect
1015. C4×D4C2×Dic17semidirect
1018. #117C2×Dic17semidirect
1151. C17#34450semidirect

Maximal subgroups

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

subgroupindex
#145319702
#145319412
#145319322
#145319202
#145318902
#145318362
#145318262
#145318042
#145317802
#145317242
#145317132
#145316692
#145316442
#145315782
#145315512
#145315102
#145314892
#145314792
#145314562
#145314172
#123×Dic172
#121×Dic172
#145312292
C2×C17×#5402
#3445017