Finite Group Databasebeta

← #17050817

Subgroups — #17050817

Order 4352.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#63223C211yesmaximal, characteristic, complemented
2#14531229C211yesmaximal, characteristic, complemented
3#14529766C211yesmaximal, characteristic, complemented
4#14529729C211yesmaximal, characteristic, complemented
5#14529233C211yesmaximal, characteristic, complemented
6#14529228C211yesmaximal, characteristic, complemented
7#14529087C211yesmaximal, characteristic, complemented
8#14529087C211yesmaximal, characteristic, complemented
9#14528883C211yesmaximal, characteristic, complemented
10#14528883C211yesmaximal, characteristic, complemented
11#14528804C211yesmaximal, characteristic, complemented
12#14528594C211yesmaximal, characteristic, complemented
13#14528493C211yesmaximal, characteristic, complemented
14C2×#11762568C211yesmaximal, characteristic, complemented
15C17×#3475C211yesmaximal, characteristic
16C22×#63223C2211yescharacteristic
17C22×#63223C2211yescharacteristic
18C2×#10587612C2211yescharacteristic
19C22×C4×Dic17C2211yescharacteristic
20#11762887—21no—
21#11762881—21no—
22#11762881—21no—
23D4×#3622—21no—
24#11762833C2211yescharacteristic
25C2×#10587508C2211yescharacteristic
26C2×#10587508C2211yescharacteristic
27C2×#10587508C2211yescharacteristic
28C2×#10587508C2211yescharacteristic
29#11762773C2211yescharacteristic
30#11762773C2211yescharacteristic
31C4×#63223C2211yescharacteristic
32#11762702—21no—
33#11762695—21no—
34#11762689—21no—
35#11762684—21no—
36C4×C4⋊Dic17C2211yescharacteristic
37C4×C22⋊Dic17C2211yescharacteristic
38C4×C22⋊Dic17C2211yescharacteristic
39#11762655C2211yescharacteristic
40#11762568C2211yescharacteristic
41#11762568C2211yescharacteristic
42#11762568C2211yescharacteristic
43#11762568C2211yescharacteristic
44#11762568C2211yescharacteristic
45#11762568C2211yescharacteristic
46#11762568C2211yescharacteristic
47#11762568C2211yescharacteristic
48#11762568C2211yescharacteristic
49#11762568C2211yescharacteristic
50#11762568C2211yescharacteristic
51#11762568C2211yescharacteristic
52C17×#556C411yescharacteristic, complemented
53C17×#555C411yescharacteristic, complemented
54C17×#554C411yescharacteristic, complemented
55C17×#553C411yescharacteristic, complemented
56C17×#553C411yescharacteristic, complemented
57C17×#552—21no—
58C17×#552C411yescharacteristic, complemented
59C17×#552C411yescharacteristic, complemented
60C17×#551—21no—
61C17×#551—21no—
62C17×#547C411yescharacteristic, complemented
63C17×#546—21no—
64C17×#533C2211yescharacteristic
65C17×#529—21no—
66C17×#529—21no—
67C17×#529—21no—
68C17×#525C2211yescharacteristic
69C17×#525C2211yescharacteristic
70C4×#41×C17—21no—
71C4×#41×C17C2211yescharacteristic
72C2×C4×D4×C17C2211yescharacteristic
73C2×C17×#117C2211yescharacteristic
74C2×C17×#117C2211yescharacteristic
75C2×#41×C17—21no—
76C2×#41×C17C2311yescharacteristic
77C22×D4×C17D411yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×Dic17—21no—
81C17×C4⋊Q8C2×C411yescharacteristic, complemented
82C17×C4⋊Q8C2×C411yescharacteristic, complemented
83C17×#126—21no—
84C17×#126—21no—
85C17×#126—21no—
86C17×#126—21no—
87C17×#126—21no—
88C17×#126—21no—
89C17×#125—21no—
90C17×#125—21no—
91C17×#125—21no—
92C17×#125C2×C411yescharacteristic, complemented
93C17×#125C2×C411yescharacteristic, complemented
94C17×#124—21no—
95C17×#124—21no—
96C17×#124—21no—
97C17×#123—21no—
98C17×#123—21no—
99C17×#123—21no—
100C17×#123—21no—
101C17×#123—21no—
102C17×#123—21no—
103C17×#123—21no—
104C17×#123—21no—
105C17×C22⋊Q8—21no—
106C17×C22⋊Q8—21no—
107C17×C22⋊Q8—21no—
108C17×C22⋊Q8—21no—
109C17×C22⋊Q8—21no—
110C17×C22⋊Q8C2×C411yescharacteristic
111C17×C22⋊Q8C2×C411yescharacteristic
112C17×C22⋊Q8C2×C411yescharacteristic, complemented
113C17×C22⋊Q8C2×C411yescharacteristic, complemented
114C17×#121—21no—
115C17×#121—21no—
116C17×#121—21no—
117C17×#121C2×C411yescharacteristic
118C17×#121C2×C411yescharacteristic
119C17×#121C2×C411yescharacteristic, complemented
120C17×#121C2×C411yescharacteristic, complemented
121C17×#120—21no—
122C17×#120—21no—
123C4×Q8×C17—21no—
124C4×Q8×C17—21no—
125C4×Q8×C17—21no—
126C4×Q8×C17C2×C411yescharacteristic, complemented
127C4×Q8×C17C2×C411yescharacteristic, complemented
128C4×D4×C17—21no—
129C4×D4×C17—21no—
130C4×D4×C17—21no—
131C4×D4×C17—21no—
132C4×D4×C17—21no—
133C4×D4×C17—21no—
134C4×D4×C17—21no—
135C4×D4×C17—21no—
136C4×D4×C17—21no—
137C4×D4×C17C2×C411yescharacteristic
138C4×D4×C17C2×C411yescharacteristic
139C4×D4×C17C2×C411yescharacteristic
140C4×D4×C17C2×C411yescharacteristic
141C4×D4×C17C2×C411yescharacteristic, complemented
142C4×D4×C17C2×C411yescharacteristic, complemented
143C4×D4×C17D411yescharacteristic
144C4×D4×C17D411yescharacteristic
145C4×D4×C17D411yescharacteristic
146C4×D4×C17D411yescharacteristic
147C17×#117—21no—
148C17×#117—21no—
149C17×#117—21no—
150C17×#117—21no—
151C17×#117—21no—
152C17×#117—21no—
153C17×#117—21no—
154C17×#117—21no—
155C17×#117C2×C411yescharacteristic
156C17×#117C2×C411yescharacteristic
157C17×#117C2×C411yescharacteristic, complemented
158C17×#117C2×C411yescharacteristic, complemented
159C17×#117C2311yescharacteristic
160C17×#117C2311yescharacteristic
161C17×#117C2311yescharacteristic
162C2×C4⋊C4×C17C2×C411yescharacteristic
163C2×C4⋊C4×C17C2×C411yescharacteristic
164C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
165C2×C4⋊C4×C17C2×C411yescharacteristic, complemented
166C2×C4⋊C4×C17D411yescharacteristic
167C2×C22⋊C4×C17—21no—
168C2×C22⋊C4×C17—21no—
169C2×C22⋊C4×C17D411yescharacteristic
170C2×C22⋊C4×C17D411yescharacteristic
171C2×C42×C17—21no—
172C2×C42×C17—21no—
173C2×C42×C17—21no—
174C2×C42×C17C2311yescharacteristic
175C2×C22⋊Dic17—21no—
176C2×C22⋊Dic17—21no—
177C2×C22⋊Dic17—21no—
178#10587612—22no—
179#10587612—41no—
180C2×C4⋊Dic17—21no—
181C2×C4⋊Dic17—21no—
182C2×C4×Dic17—21no—
183C2×C4×Dic17—22no—
184C2×C4×Dic17—41no—
185C2×C4×Dic17C2311yescharacteristic
186C2×C4×Dic17C2311yescharacteristic
187C2×C4×Dic17C2311yescharacteristic
188C2×C4×Dic17C2311yescharacteristic
189C2×#63223—22no—
190C2×#63223—22no—
191C2×#63223—21no—
192C2×#63223—21no—
193C2×#63223—41no—
194C2×#63223—41no—
195C2×#63223C2311yescharacteristic
196C2×#63223C2311yescharacteristic
197C2×#63223C2311yescharacteristic
198C2×#63223C2311yescharacteristic
199C22×#3622—21no—
200C22×#3622—21no—
201#10587508—22no—
202#10587508—22no—
203#10587508—41no—
204#10587508—41no—
205#10587502—21no—
206#10587502—21no—
207#10587502—21no—
208#10587502—21no—
209#10587502—21no—
210C22⋊#3622—21no—
211C22⋊#3622—21no—
212C22⋊#3622—21no—
213C22⋊#3622—21no—
214C4⋊#3622—21no—
215C4⋊#3622—21no—
216#10587474—21no—
217C4×#3622—21no—
218C24×C17C2×D411yescharacteristic
219C24×C17C2×D411yescharacteristic
220#41×C17—21no—
221#41×C17—21no—
222#41×C17—21no—
223#41×C17—21no—
224#41×C17—44no—
225C2×Q8×C17—21no—
226C2×Q8×C17—21no—
227C2×Q8×C17C22×C411yescharacteristic
228C2×D4×C17—21no—
229C2×D4×C17—21no—
230C2×D4×C17—21no—
231C2×D4×C17—21no—
232C2×D4×C17—21no—
233C2×D4×C17—42no—
234C2×D4×C17C22⋊C411yescharacteristic
235C2×D4×C17C22⋊C411yescharacteristic
236C2×D4×C17C22⋊C411yescharacteristic
237C2×D4×C17C22⋊C411yescharacteristic
238C2×D4×C17C22×C411yescharacteristic
239C22×C4×C17—21no—
240C22×C4×C17—21no—
241C22×C4×C17—21no—
242C22×C4×C17—21no—
243C22×C4×C17—21no—
244C22×C4×C17—21no—
245C22×C4×C17—21no—
246C22×C4×C17—21no—
247C22×C4×C17—21no—
248C22×C4×C17—21no—
249C22×C4×C17—21no—
250C22×C4×C17—21no—
251C22×C4×C17—21no—
252C22×C4×C17—21no—
253C22×C4×C17—21no—
254C22×C4×C17C22×C411yescharacteristic
255C22×C4×C17C22×C411yescharacteristic
256C22×C4×C17C22×C411yescharacteristic
257C22×C4×C17C22×C411yescharacteristic
258C22×C4×C17C2×D411yescharacteristic
259C22×C4×C17C2×D411yescharacteristic
260C22×C4×C17C2×D411yescharacteristic
261C22×C4×C17C2×D411yescharacteristic
262C22×C4×C17C2×D411yescharacteristic
263C22×C4×C17C2×D411yescharacteristic
264C22×C4×C17C2×D411yescharacteristic
265C22×C4×C17C2×D411yescharacteristic
266C22×C4×C17C2411yescharacteristic
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—42no—
272C22×Dic17—42no—
273C22×Dic17—42no—
274C4⋊C4×C17—21no—
275C4⋊C4×C17—21no—
276C4⋊C4×C17—21no—
277C4⋊C4×C17—21no—
278C4⋊C4×C17—21no—
279C4⋊C4×C17—21no—
280C4⋊C4×C17—21no—
281C4⋊C4×C17—21no—
282C4⋊C4×C17—21no—
283C4⋊C4×C17—21no—
284C4⋊C4×C17—21no—
285C4⋊C4×C17—21no—
286C4⋊C4×C17—21no—
287C4⋊C4×C17—21no—
288C4⋊C4×C17—21no—
289C4⋊C4×C17—21no—
290C4⋊C4×C17C22⋊C411yescharacteristic
291C4⋊C4×C17C22⋊C411yescharacteristic
292C4⋊C4×C17C22⋊C411yescharacteristic
293C4⋊C4×C17C22⋊C411yescharacteristic
294C4⋊C4×C17C22×C411yescharacteristic
295C4⋊C4×C17C22×C411yescharacteristic
296C4⋊C4×C17C22×C411yescharacteristic
297C4⋊C4×C17C22×C411yescharacteristic
298C4⋊C4×C17C22×C411yescharacteristic
299C4⋊C4×C17C22×C411yescharacteristic
300C22⋊C4×C17—21no—
301C22⋊C4×C17—21no—
302C22⋊C4×C17—21no—
303C22⋊C4×C17—21no—
304C22⋊C4×C17—21no—
305C22⋊C4×C17—21no—
306C22⋊C4×C17—21no—
307C22⋊C4×C17—21no—
308C22⋊C4×C17—21no—
309C22⋊C4×C17—21no—
310C22⋊C4×C17—21no—
311C22⋊C4×C17—21no—
312C22⋊C4×C17—21no—
313C22⋊C4×C17—21no—
314C22⋊C4×C17—21no—
315C22⋊C4×C17—21no—
316C22⋊C4×C17—21no—
317C22⋊C4×C17C22⋊C411yescharacteristic
318C22⋊C4×C17C22⋊C411yescharacteristic
319C22⋊C4×C17C22⋊C411yescharacteristic
320C22⋊C4×C17C22⋊C411yescharacteristic
321C22⋊C4×C17C22⋊C411yescharacteristic
322C22⋊C4×C17C22⋊C411yescharacteristic
323C22⋊C4×C17C22⋊C411yescharacteristic
324C22⋊C4×C17C22⋊C411yescharacteristic
325C42×C17—21no—
326C42×C17—21no—
327C42×C17—21no—
328C42×C17—21no—
329C42×C17—21no—
330C42×C17—21no—
331C42×C17—21no—
332C42×C17—21no—
333C42×C17—21no—
334C42×C17C22×C411yescharacteristic
335C42×C17C22×C411yescharacteristic
336C42×C17C2×D411yescharacteristic
337C42×C17C2×D411yescharacteristic
338C22⋊Dic17—42no—
339C22⋊Dic17—42no—
340C22⋊Dic17—42no—
341C4⋊Dic17—42no—
342C4⋊Dic17—42no—
343C4×Dic17—21no—
344C4×Dic17—21no—
345C4×Dic17—21no—
346C4×Dic17—21no—
347C4×Dic17—21no—
348C4×Dic17—21no—
349C4×Dic17—21no—
350C4×Dic17—42no—
351C4×Dic17#4112yescomplemented
352#63223—21no—
353#63223—21no—
354#63223—21no—
355#63223—21no—
356#63223—21no—
357#63223—21no—
358#63223—21no—
359#63223—42no—
360#63223—42no—
361#63223#4112yescomplemented
362C2×#3622—21no—
363C2×#3622—21no—
364C2×#3622—21no—
365C2×#3622—21no—
366C2×#3622—42no—
367C2×#3622—42no—
368#22506—171nomaximal, Sylow
369C23×C17—21no—
370C23×C17—21no—
371C23×C17—22no—
372C23×C17—21no—
373C23×C17—21no—
374C23×C17—21no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17C2×C22⋊C411yescharacteristic
379C23×C17C2×C22⋊C411yescharacteristic
380C23×C17C2×C22⋊C411yescharacteristic
381C23×C17C2×C22⋊C411yescharacteristic
382C23×C17C22×D411yescharacteristic
383Q8×C17—21no—
384Q8×C17—21no—
385Q8×C17—42no—
386Q8×C17—81no—
387D4×C17—22no—
388D4×C17—22no—
389D4×C17—21no—
390D4×C17—21no—
391D4×C17—41no—
392D4×C17—41no—
393D4×C17—42no—
394D4×C17—41no—
395D4×C17—41no—
396D4×C17—42no—
397D4×C17—81no—
398D4×C17—81no—
399C2×C4×C17—21no—
400C2×C4×C17—21no—
401C2×C4×C17—21no—
402C2×C4×C17—21no—
403C2×C4×C17—21no—
404C2×C4×C17—21no—
405C2×C4×C17—21no—
406C2×C4×C17—21no—
407C2×C4×C17—21no—
408C2×C4×C17—21no—
409C2×C4×C17—21no—
410C2×C4×C17—21no—
411C2×C4×C17—21no—
412C2×C4×C17—21no—
413C2×C4×C17—21no—
414C2×C4×C17—21no—
415C2×C4×C17—21no—
416C2×C4×C17—21no—
417C2×C4×C17—21no—
418C2×C4×C17—21no—
419C2×C4×C17—21no—
420C2×C4×C17—21no—
421C2×C4×C17—21no—
422C2×C4×C17—21no—
423C2×C4×C17—21no—
424C2×C4×C17—21no—
425C2×C4×C17—21no—
426C2×C4×C17—41no—
427C2×C4×C17—41no—
428C2×C4×C17—42no—
429C2×C4×C17—42no—
430C2×C4×C17—42no—
431C2×C4×C17—41no—
432C2×C4×C17—41no—
433C2×C4×C17—81no—
434C2×C4×C17—81no—
435C2×C4×C17—81no—
436C2×C4×C17C2×C22⋊C411yescharacteristic
437C2×C4×C17C2×C22⋊C411yescharacteristic
438C2×C4×C17C2×C22⋊C411yescharacteristic
439C2×C4×C17C2×C22⋊C411yescharacteristic
440C2×C4×C17C2×C22⋊C411yescharacteristic
441C2×C4×C17C2×C22⋊C411yescharacteristic
442C2×C4×C17C2×C22⋊C411yescharacteristic
443C2×C4×C17C2×C22⋊C411yescharacteristic
444C2×C4×C17C23×C411yescharacteristic
445C2×C4×C17C22×D411yescharacteristic
446C2×C4×C17C2×#4111yescharacteristic
447C2×C4×C17C2×#4111yescharacteristic
448C2×C4×C17H(5,𝔽2)11yescharacteristic
449C2×C4×C172−1+411yescharacteristic
450C2×Dic17—22no—
451C2×Dic17—22no—
452C2×Dic17—41no—
453C2×Dic17—41no—
454C2×Dic17—41no—
455C2×Dic17—48no—
456C2×Dic17—41no—
457C2×Dic17—41no—
458C2×Dic17—41no—
459C2×Dic17—41no—
460C2×Dic17—41no—
461C2×Dic17—41no—
462C2×Dic17—41no—
463#3622—22no—
464#3622—41no—
465#3622—41no—
466#3622—41no—
467#3475D1711yescharacteristic
468D4×M16—171no—
469#2290—171no—
470#1995—171no—
471#1986—171no—
472#1897—171no—
473#1896—171no—
474#1871—171no—
475#1871—171no—
476#1826—171no—
477#1826—171no—
478#1806—171no—
479#1759—171no—
480#1733—171no—
481C2×#339—171no—
482C22×C17—21no—
483C22×C17—21no—
484C22×C17—21no—
485C22×C17—21no—
486C22×C17—21no—
487C22×C17—21no—
488C22×C17—21no—
489C22×C17—21no—
490C22×C17—21no—
491C22×C17—21no—
492C22×C17—21no—
493C22×C17—21no—
494C22×C17—21no—
495C22×C17—42no—
496C22×C17—42no—
497C22×C17—41no—
498C22×C17—41no—
499C22×C17—41no—
500C22×C17—81no—
501C22×C17—81no—
502C22×C17#42112yes—
503C22×C17C22×C22⋊C411yescharacteristic
504C22×C17#54611yescharacteristic
505C22×C17#54711yescharacteristic
506C4×C17—21no—
507C4×C17—21no—
508C4×C17—21no—
509C4×C17—21no—
510C4×C17—21no—
511C4×C17—21no—
512C4×C17—21no—
513C4×C17—21no—
514C4×C17—41no—
515C4×C17—41no—
516C4×C17—41no—
517C4×C17—41no—
518C4×C17—41no—
519C4×C17—41no—
520C4×C17—41no—
521C4×C17C4×#4111yescharacteristic
522C4×C17#52011yescharacteristic
523C4×C17#54611yescharacteristic
524C4×C17#54711yescharacteristic
525Dic17—42no—
526Dic17—42no—
527Dic17—81no—
528Dic17—81no—
529C22×M16—171no—
530C22×M16—171no—
531#556Dic1711yescharacteristic, complemented
532#555Dic1711yescharacteristic, complemented
533#554Dic1711yescharacteristic, complemented
534#553Dic1711yescharacteristic, complemented
535#553Dic1711yescharacteristic, complemented
536#552—21no—
537#552Dic1711yescharacteristic, complemented
538#552Dic1711yescharacteristic, complemented
539#551—21no—
540#551—21no—
541#547Dic1711yescharacteristic, complemented
542#546—21no—
543#533C2×D1711yescharacteristic
544#529—21no—
545#529—21no—
546#529—21no—
547#525C2×D1711yescharacteristic
548#525C2×D1711yescharacteristic
549C4×#41—21no—
550C4×#41C2×D1711yescharacteristic
551C2×C4×D4C2×D1711yescharacteristic
552C2×#117—171no—
553C2×#117C2×D1711yescharacteristic
554C2×#117C2×D1711yescharacteristic
555C22×C42—171no—
556#436—341no—
557#435—341no—
558#435—341no—
559C8×D4—341no—
560#423—171no—
561C2×#104—171no—
562C2×#104—171no—
563C2×#104—171no—
564C2×#104—171no—
565#407—171no—
566#407—171no—
567C4×M16—171no—
568#388—341no—
569#387—341no—
570#386—341no—
571#385—341no—
572C4×C4⋊C4—171no—
573C4×C22⋊C4—171no—
574C4×C22⋊C4—171no—
575#376—171no—
576#339—171no—
577#339—171no—
578#339—171no—
579#339—171no—
580#339—171no—
581#339—171no—
582#339—171no—
583#339—171no—
584#339—171no—
585#339—171no—
586#339—171no—
587#339—171no—
588C2×C17—21no—
589C2×C17—21no—
590C2×C17—22no—
591C2×C17—41no—
592C2×C17—41no—
593C2×C17—41no—
594C2×C17—81no—
595C2×C17#233911yescharacteristic
596C2×C17C2×#42111yescharacteristic
597C2×C17#290111yescharacteristic
598C2×#41—21no—
599C2×#41C22×D1711yescharacteristic
600C22×D4C22⋊D1711yescharacteristic
601C23×C4—341no—
602C23×C4C22×D1711yescharacteristic
603C23×C4C22×D1711yescharacteristic
604C2×M16—171no—
605C2×M16—171no—
606C2×M16—171no—
607C2×M16—171no—
608C2×M16—341no—
609C2×M16—341no—
610C2×M16—342no—
611C2×M16—342no—
612C2×M16—681no—
613C2×M16—681no—
614C22×C8—341no—
615C22×C8—341no—
616C4⋊Q8C2×Dic1711yescharacteristic, complemented
617C4⋊Q8C2×Dic1711yescharacteristic, complemented
618#126—21no—
619#126—21no—
620#126—21no—
621#126—21no—
622#126—21no—
623#126—21no—
624#125—21no—
625#125—21no—
626#125—21no—
627#125C2×Dic1711yescharacteristic, complemented
628#125C2×Dic1711yescharacteristic, complemented
629#124—21no—
630#124—21no—
631#124—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—21no—
637#123—21no—
638#123—21no—
639#123—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8C2×Dic1711yescharacteristic
646C22⋊Q8C2×Dic1711yescharacteristic
647C22⋊Q8C2×Dic1711yescharacteristic, complemented
648C22⋊Q8C2×Dic1711yescharacteristic, complemented
649#121—21no—
650#121—21no—
651#121—21no—
652#121C2×Dic1711yescharacteristic
653#121C2×Dic1711yescharacteristic
654#121C2×Dic1711yescharacteristic, complemented
655#121C2×Dic1711yescharacteristic, complemented
656#120—21no—
657#120—21no—
658C4×Q8—21no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8C2×Dic1711yescharacteristic, complemented
662C4×Q8C2×Dic1711yescharacteristic, complemented
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4C2×Dic1711yescharacteristic
673C4×D4C2×Dic1711yescharacteristic
674C4×D4C2×Dic1711yescharacteristic
675C4×D4C2×Dic1711yescharacteristic
676C4×D4C2×Dic1711yescharacteristic, complemented
677C4×D4C2×Dic1711yescharacteristic, complemented
678C4×D4C22⋊D1711yescharacteristic
679C4×D4C22⋊D1711yescharacteristic
680C4×D4C22⋊D1711yescharacteristic
681C4×D4C22⋊D1711yescharacteristic
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117—21no—
688#117—21no—
689#117—21no—
690#117—342no—
691#117—681no—
692#117C2×Dic1711yescharacteristic
693#117C2×Dic1711yescharacteristic
694#117C2×Dic1711yescharacteristic, complemented
695#117C2×Dic1711yescharacteristic, complemented
696#117C22×D1711yescharacteristic
697#117C22×D1711yescharacteristic
698#117C22×D1711yescharacteristic
699C2×C4⋊C4—341no—
700C2×C4⋊C4—341no—
701C2×C4⋊C4C2×Dic1711yescharacteristic
702C2×C4⋊C4C2×Dic1711yescharacteristic
703C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
704C2×C4⋊C4C2×Dic1711yescharacteristic, complemented
705C2×C4⋊C4C22⋊D1711yescharacteristic
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—341no—
709C2×C22⋊C4—341no—
710C2×C22⋊C4—341no—
711C2×C22⋊C4C22⋊D1711yescharacteristic
712C2×C22⋊C4C22⋊D1711yescharacteristic
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—171no—
717C2×C42—171no—
718C2×C42—171no—
719C2×C42—171no—
720C2×C42—342no—
721C2×C42—341no—
722C2×C42—681no—
723C2×C42C22×D1711yescharacteristic
724C4⋊C8—341no—
725C4⋊C8—341no—
726#104—342no—
727#104—342no—
728#104—681no—
729#104—681no—
730C22⋊C8—341no—
731C22⋊C8—341no—
732C22⋊C8—341no—
733C22⋊C8—341no—
734#97—341no—
735C4×C8—341no—
736#95—341no—
737#95—341no—
738#95—341no—
739#95—341no—
740#95—341no—
741C17#2250611yescharacteristic, complemented, Sylow
742C24C2×C22⋊D1711yescharacteristic
743C24C2×C22⋊D1711yescharacteristic
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8C22×Dic1711yescharacteristic
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—42no—
758C2×D4C22⋊Dic1711yescharacteristic
759C2×D4C22⋊Dic1711yescharacteristic
760C2×D4C22⋊Dic1711yescharacteristic
761C2×D4C22⋊Dic1711yescharacteristic
762C2×D4C22×Dic1711yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—341no—
779C22×C4—341no—
780C22×C4—341no—
781C22×C4—341no—
782C22×C4—682no—
783C22×C4—682no—
784C22×C4—682no—
785C22×C4C22×Dic1711yescharacteristic
786C22×C4C22×Dic1711yescharacteristic
787C22×C4C22×Dic1711yescharacteristic
788C22×C4C22×Dic1711yescharacteristic
789C22×C4C2×C22⋊D1711yescharacteristic
790C22×C4C2×C22⋊D1711yescharacteristic
791C22×C4C2×C22⋊D1711yescharacteristic
792C22×C4C2×C22⋊D1711yescharacteristic
793C22×C4C2×C22⋊D1711yescharacteristic
794C22×C4C2×C22⋊D1711yescharacteristic
795C22×C4C2×C22⋊D1711yescharacteristic
796C22×C4C2×C22⋊D1711yescharacteristic
797C22×C4C23×D1711yescharacteristic
798M16—172no—
799M16—341no—
800M16—341no—
801M16—341no—
802M16—341no—
803M16—341no—
804M16—341no—
805M16—341no—
806M16—682no—
807M16—682no—
808C2×C8—341no—
809C2×C8—341no—
810C2×C8—341no—
811C2×C8—341no—
812C2×C8—682no—
813C2×C8—682no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—682no—
831C4⋊C4—682no—
832C4⋊C4C22⋊Dic1711yescharacteristic
833C4⋊C4C22⋊Dic1711yescharacteristic
834C4⋊C4C22⋊Dic1711yescharacteristic
835C4⋊C4C22⋊Dic1711yescharacteristic
836C4⋊C4C22×Dic1711yescharacteristic
837C4⋊C4C22×Dic1711yescharacteristic
838C4⋊C4C22×Dic1711yescharacteristic
839C4⋊C4C22×Dic1711yescharacteristic
840C4⋊C4C22×Dic1711yescharacteristic
841C4⋊C4C22×Dic1711yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—682no—
860C22⋊C4—682no—
861C22⋊C4—682no—
862C22⋊C4C22⋊Dic1711yescharacteristic
863C22⋊C4C22⋊Dic1711yescharacteristic
864C22⋊C4C22⋊Dic1711yescharacteristic
865C22⋊C4C22⋊Dic1711yescharacteristic
866C22⋊C4C22⋊Dic1711yescharacteristic
867C22⋊C4C22⋊Dic1711yescharacteristic
868C22⋊C4C22⋊Dic1711yescharacteristic
869C22⋊C4C22⋊Dic1711yescharacteristic
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—172no—
880C42—341no—
881C42—341no—
882C42—341no—
883C42—341no—
884C42—341no—
885C42—341no—
886C42—341no—
887C42—682no—
888C42C22×Dic1711yescharacteristic
889C42C22×Dic1711yescharacteristic
890C42C2×C22⋊D1711yescharacteristic
891C42C2×C22⋊D1711yescharacteristic
892C23—21no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23C2×C22⋊Dic1711yescharacteristic
902C23C2×C22⋊Dic1711yescharacteristic
903C23C2×C22⋊Dic1711yescharacteristic
904C23C2×C22⋊Dic1711yescharacteristic
905C23C22×C22⋊D1711yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—81no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—41no—
915D4—41no—
916D4—42no—
917D4—41no—
918D4—42no—
919D4—41no—
920D4—81no—
921D4—81no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—342no—
960C2×C4—342no—
961C2×C4—681no—
962C2×C4—681no—
963C2×C4—681no—
964C2×C4—688no—
965C2×C4—681no—
966C2×C4—681no—
967C2×C4—681no—
968C2×C4—681no—
969C2×C4—681no—
970C2×C4—681no—
971C2×C4—681no—
972C2×C4C2×C22⋊Dic1711yescharacteristic
973C2×C4C2×C22⋊Dic1711yescharacteristic
974C2×C4C2×C22⋊Dic1711yescharacteristic
975C2×C4C2×C22⋊Dic1711yescharacteristic
976C2×C4C2×C22⋊Dic1711yescharacteristic
977C2×C4C2×C22⋊Dic1711yescharacteristic
978C2×C4C2×C22⋊Dic1711yescharacteristic
979C2×C4C2×C22⋊Dic1711yescharacteristic
980C2×C4#41×D1711yescharacteristic
981C2×C4#41×D1711yescharacteristic
982C2×C4#1058769611yescharacteristic
983C2×C4#1058769711yescharacteristic
984C2×C4C23×Dic1711yescharacteristic
985C2×C4C22×C22⋊D1711yescharacteristic
986C8—342no—
987C8—681no—
988C8—681no—
989C8—681no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22#1176282612yes—
1011C22C22×C22⋊Dic1711yescharacteristic
1012C22#1176344711yescharacteristic
1013C22#1176345811yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—41no—
1023C4—41no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—682no—
1030C4—682no—
1031C4—1361no—
1032C4—1361no—
1033C4#41×Dic1711yescharacteristic
1034C4#1176329211yescharacteristic
1035C4#1176344711yescharacteristic
1036C4#1176345811yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2#1453161411yescharacteristic
1045C2C2×#1176282611yescharacteristic
1046C2#1453733111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC17×#3475C2
socleC22×C17C22×C22⋊C4
cosocleC22×C4×C17C24
hypercenter#3475D17
hypocenterC17#22506
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. D4×#63223C2semidirect
2. #14531229C2semidirect
3. #14529766C2semidirect
4. #14529729C2semidirect
5. #14529233C2semidirect
6. #14529228C2semidirect
7. #14529087C2semidirect
8. #14529087C2semidirect
9. #14528883C2semidirect
10. #14528883C2semidirect
11. #14528804C2semidirect
12. #14528594C2semidirect
13. #14528493C2semidirect
14. C2×#11762568C2semidirect
52. C17×#556C4semidirect
53. C17×#555C4semidirect
54. C17×#554C4semidirect
55. C17×#553C4semidirect
56. C17×#553C4semidirect
58. C17×#552C4semidirect
59. C17×#552C4semidirect
62. C17×#547C4semidirect
81. C17×C4⋊Q8C2×C4semidirect
82. C17×C4⋊Q8C2×C4semidirect
92. C17×#125C2×C4semidirect
93. C17×#125C2×C4semidirect
112. C17×C22⋊Q8C2×C4semidirect
113. C17×C22⋊Q8C2×C4semidirect
119. C17×#121C2×C4semidirect
120. C17×#121C2×C4semidirect
126. C4×Q8×C17C2×C4semidirect
127. C4×Q8×C17C2×C4semidirect
141. C4×D4×C17C2×C4semidirect
142. C4×D4×C17C2×C4semidirect
157. C17×#117C2×C4semidirect
158. C17×#117C2×C4semidirect
164. C2×C4⋊C4×C17C2×C4semidirect
165. C2×C4⋊C4×C17C2×C4semidirect
351. C4×Dic17#41semidirect
361. #63223#41semidirect
531. #556Dic17semidirect
532. #555Dic17semidirect
533. #554Dic17semidirect
534. #553Dic17semidirect
535. #553Dic17semidirect
537. #552Dic17semidirect
538. #552Dic17semidirect
541. #547Dic17semidirect
616. C4⋊Q8C2×Dic17semidirect
617. C4⋊Q8C2×Dic17semidirect
627. #125C2×Dic17semidirect
628. #125C2×Dic17semidirect
647. C22⋊Q8C2×Dic17semidirect
648. C22⋊Q8C2×Dic17semidirect
654. #121C2×Dic17semidirect
655. #121C2×Dic17semidirect
661. C4×Q8C2×Dic17semidirect
662. C4×Q8C2×Dic17semidirect
676. C4×D4C2×Dic17semidirect
677. C4×D4C2×Dic17semidirect
694. #117C2×Dic17semidirect
695. #117C2×Dic17semidirect
703. C2×C4⋊C4C2×Dic17semidirect
704. C2×C4⋊C4C2×Dic17semidirect
741. C17#22506semidirect

Maximal subgroups

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

subgroupindex
D4×#632232
#145312292
#145297662
#145297292
#145292332
#145292282
#145290872
#145288832
#145288042
#145285942
#145284932
C2×#117625682
C17×#34752
#2250617