Finite Group Databasebeta

← #15676714

Subgroups — #15676714

Order 2944.

1056 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67288C211yesmaximal, characteristic, complemented
2C2×#10625053C211yesmaximal, characteristic, complemented
3C2×#10625108C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D23C211yesmaximal, characteristic, complemented
5#13092330C211yesmaximal, characteristic, complemented
6#13092329C211yesmaximal, characteristic, complemented
7#13092326C211yesmaximal, characteristic, complemented
8#13092325C211yesmaximal, characteristic, complemented
9#13092296C211yesmaximal, characteristic, complemented
10#13092295C211yesmaximal, characteristic, complemented
11#13092295C211yesmaximal, characteristic, complemented
12#13092293C211yesmaximal, characteristic, complemented
13#13092293C211yesmaximal, characteristic, complemented
14#13092279C211yesmaximal, characteristic, complemented
15C23×#386C211yesmaximal, characteristic, complemented
16C24×D23C2211yescharacteristic
17C22×D4×C23C2211yescharacteristic
18C23×C4×C23C2211yescharacteristic, complemented
19C22×C22⋊D23C2211yescharacteristic
20C22×C22⋊D23C2211yescharacteristic
21C22×C22⋊D23C2211yescharacteristic
22C22×C22⋊D23C2211yescharacteristic, complemented
23C2×#67288—24no—
24C2×#67288—24no—
25C2×#67288—24no—
26C22×D92C2211yescharacteristic
27C22×D92C2211yescharacteristic
28C22×C4×D23C2211yescharacteristic
29C22×C4×D23C2211yescharacteristic
30C22×C4×D23C2211yescharacteristic, complemented
31C22×Dic46C2211yescharacteristic, complemented
32C2×C22⋊C4×C23C2211yescharacteristic
33C2×C22⋊C4×C23C2211yescharacteristic
34C2×C22⋊C4×C23C2211yescharacteristic, complemented
35C2×C22⋊Dic23C2211yescharacteristic
36C2×C22⋊Dic23C2211yescharacteristic
37C2×C22⋊Dic23C2211yescharacteristic, complemented
38#10625108—24no—
39C2×(C2×D23)⋊C4C2211yescharacteristic
40C2×(C2×D23)⋊C4C2211yescharacteristic
41C2×(C2×D23)⋊C4C2211yescharacteristic
42C2×(C2×D23)⋊C4C2211yescharacteristic
43C2×(C2×D23)⋊C4C2211yescharacteristic
44C2×(C2×D23)⋊C4C2211yescharacteristic
45C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
47#10625053—24no—
48C22⋊C4×D23—24no—
49C23×#95C2211yescharacteristic, complemented
50C23×#95C2211yescharacteristic, complemented
51C23⋊#95C2211yescharacteristic, complemented
52C23⋊#95C2211yescharacteristic, complemented
53C23⋊#95C2211yescharacteristic, complemented
54C23⋊#95C2211yescharacteristic, complemented
55C23⋊#95C2211yescharacteristic, complemented
56C23⋊#95C2211yescharacteristic, complemented
57C24×C23C2311yescharacteristic
58C24×C23C2311yescharacteristic
59C23×D23—22no—
60C23×D23—22no—
61C23×D23—22no—
62C23×D23—22no—
63C23×D23—22no—
64C23×D23—41no—
65C23×D23—41no—
66C23×D23C2311yescharacteristic
67C23×D23C2311yescharacteristic
68C23×D23C2311yescharacteristic
69C2×D4×C23—22no—
70C2×D4×C23—22no—
71C2×D4×C23—41no—
72C22×C4×C23—22no—
73C22×C4×C23—22no—
74C22×C4×C23—22no—
75C22×C4×C23C2311yescharacteristic
76C22×C4×C23C2311yescharacteristic
77C22×C4×C23C2311yescharacteristic
78C22×C4×C23C2311yescharacteristic
79C22×C4×C23C2311yescharacteristic
80C2×C22⋊D23—22no—
81C2×C22⋊D23—22no—
82C2×C22⋊D23—22no—
83C2×C22⋊D23—22no—
84C2×C22⋊D23—22no—
85C2×C22⋊D23—22no—
86C2×C22⋊D23—22no—
87C2×C22⋊D23—22no—
88C2×C22⋊D23—22no—
89C2×C22⋊D23—41no—
90C2×C22⋊D23—41no—
91C2×C22⋊D23D414yescomplemented
92C22×Dic23C2311yescharacteristic
93C22×Dic23C2311yescharacteristic
94C22×Dic23C2311yescharacteristic
95C22×Dic23C2311yescharacteristic
96C22×Dic23C2311yescharacteristic
97#67288—232no—
98C2×D92—22no—
99C2×D92—22no—
100C2×D92—22no—
101C2×D92—22no—
102C2×D92—41no—
103C2×D92D414yescomplemented
104C2×C4×D23—22no—
105C2×C4×D23—22no—
106C2×C4×D23—22no—
107C2×C4×D23—22no—
108C2×C4×D23—22no—
109C2×C4×D23—22no—
110C2×C4×D23—41no—
111C2×C4×D23—41no—
112C2×C4×D23D414yescomplemented
113C2×Dic46—22no—
114C2×Dic46—22no—
115C2×Dic46—22no—
116C22⋊C4×C23—22no—
117C22⋊C4×C23—22no—
118C22⋊C4×C23—41no—
119C22⋊Dic23—22no—
120C22⋊Dic23—22no—
121C22⋊Dic23—41no—
122(C2×D23)⋊C4—22no—
123(C2×D23)⋊C4—22no—
124(C2×D23)⋊C4—22no—
125(C2×D23)⋊C4—22no—
126(C2×D23)⋊C4—22no—
127(C2×D23)⋊C4—22no—
128(C2×D23)⋊C4—41no—
129(C2×D23)⋊C4—41no—
130C23×C23—21no—
131C23×C23—21no—
132C23×C23—21no—
133C23×C23—21no—
134C23×C23—21no—
135C23×C23—21no—
136C23×C23—21no—
137C23×C23—21no—
138C23×C23—21no—
139C23×C23—21no—
140C23×C23—21no—
141C23×C23—21no—
142C23×C23C2×D412yes—
143C23×C23#4112yescomplemented
144C23×C23C2411yescharacteristic
145C22×D23—21no—
146C22×D23—21no—
147C22×D23—21no—
148C22×D23—21no—
149C22×D23—28no—
150C22×D23—21no—
151C22×D23—21no—
152C22×D23—21no—
153C22×D23—21no—
154C22×D23—21no—
155C22×D23—21no—
156C22×D23—21no—
157C22×D23—21no—
158C22×D23—21no—
159C22×D23—21no—
160C22×D23—21no—
161C22×D23—21no—
162C22×D23—44no—
163C22×D23—44no—
164C22×D23—44no—
165C22×D23—44no—
166C22×D23—44no—
167C22×D23—44no—
168C22×D23C2×D412yes—
169C22×D23C2×D412yes—
170C22×D23C2×D412yes—
171C22×D23C2×D412yes—
172C22×D23#4112yescomplemented
173D4×C23—44no—
174C2×C4×C23—28no—
175C2×C4×C23—21no—
176C2×C4×C23—21no—
177C2×C4×C23—21no—
178C2×C4×C23—21no—
179C2×C4×C23—21no—
180C2×C4×C23—21no—
181C2×C4×C23—21no—
182C2×C4×C23—21no—
183C2×C4×C23—21no—
184C2×C4×C23—21no—
185C2×C4×C23—21no—
186C2×C4×C23—21no—
187C2×C4×C23—21no—
188C2×C4×C23C2×D412yes—
189C2×C4×C23C2×D412yes—
190C22⋊D23—28no—
191C22⋊D23—28no—
192C22⋊D23—44no—
193C22⋊D23—44no—
194C2×Dic23—21no—
195C2×Dic23—21no—
196C2×Dic23—21no—
197C2×Dic23—21no—
198C2×Dic23—21no—
199C2×Dic23—21no—
200C2×Dic23—21no—
201C2×Dic23—21no—
202C2×Dic23—21no—
203C2×Dic23—21no—
204C2×Dic23—21no—
205C2×Dic23—21no—
206C2×Dic23—21no—
207C2×Dic23C2×D412yes—
208C2×Dic23C2×D412yes—
209D92—28no—
210D92—44no—
211C4×D23—28no—
212C4×D23—28no—
213C4×D23—44no—
214Dic46—28no—
215#2404—231nomaximal, Sylow
216C22×C23—22no—
217C22×C23—22no—
218C22×C23—22no—
219C22×C23—22no—
220C22×C23—22no—
221C22×C23—22no—
222C22×C23—41no—
223C22×C23—41no—
224C22×C23—41no—
225C22×C23—41no—
226C22×C23—41no—
227C22×C23—41no—
228C22×C23—41no—
229C22×C23—41no—
230C22×C23C22×D411yescharacteristic
231C22×C23C22×D411yescharacteristic
232C22×C23C22×D411yescharacteristic
233C22×C23C2×#4111yescharacteristic
234C22×C23C2×#4111yescharacteristic
235C22×C23H(5,𝔽2)11yescharacteristic
236C22×C23H(5,𝔽2)11yescharacteristic
237C2×D23—22no—
238C2×D23—22no—
239C2×D23—22no—
240C2×D23—22no—
241C2×D23—22no—
242C2×D23—22no—
243C2×D23—22no—
244C2×D23—22no—
245C2×D23—22no—
246C2×D23—22no—
247C2×D23—22no—
248C2×D23—22no—
249C2×D23—416no—
250C2×D23—41no—
251C2×D23—41no—
252C2×D23—41no—
253C2×D23—41no—
254C2×D23—41no—
255C2×D23—41no—
256C2×D23—41no—
257C2×D23—41no—
258C2×D23#12014yes—
259C4×C23—22no—
260C4×C23—22no—
261C4×C23—41no—
262C4×C23—41no—
263C4×C23—41no—
264Dic23—22no—
265Dic23—22no—
266Dic23—41no—
267Dic23—41no—
268Dic23—41no—
269C22×#41—231no—
270C2×#120—231no—
271C2×#120—231no—
272C22×C22⋊C4—231no—
273#393—231no—
274#393—231no—
275#392—231no—
276#392—231no—
277#386—231no—
278#386—231no—
279#386—231no—
280#386—231no—
281#386—231no—
282#386D2311yescharacteristic, complemented
283#381—231no—
284C2×C23—42no—
285C2×C23—42no—
286C2×C23C2×#12011yescharacteristic
287C2×C23#52511yescharacteristic
288C2×C23#53511yescharacteristic
289C2×C23#54611yescharacteristic
290C2×C23#54611yescharacteristic
291C2×C23#54611yescharacteristic
292C2×C23#54611yescharacteristic
293D23—24no—
294D23—42no—
295D23—42no—
296C25—231no—
297C2×#41—464no—
298C2×#41—464no—
299C2×#41—464no—
300C22×Q8—231no—
301C22×D4—231no—
302C22×D4—231no—
303C22×D4—231no—
304C22×D4—231no—
305C22×D4—231no—
306C22×D4—231no—
307C22×D4C2×D2311yescharacteristic
308C23×C4—231no—
309C23×C4—231no—
310C23×C4—231no—
311C23×C4C2×D2311yescharacteristic, complemented
312#120—464no—
313#120—464no—
314C2×C22⋊C4—231no—
315C2×C22⋊C4—231no—
316C2×C22⋊C4—231no—
317C2×C22⋊C4—231no—
318C2×C22⋊C4—231no—
319C2×C22⋊C4—231no—
320C2×C22⋊C4—231no—
321C2×C22⋊C4—231no—
322C2×C22⋊C4—231no—
323C2×C22⋊C4—231no—
324C2×C22⋊C4—231no—
325C2×C22⋊C4—464no—
326C2×C22⋊C4C2×D2311yescharacteristic
327C2×C22⋊C4C2×D2311yescharacteristic
328C2×C22⋊C4C2×D2311yescharacteristic, complemented
329#95—231no—
330#95—231no—
331#95—231no—
332#95—231no—
333#95—231no—
334#95—231no—
335#95C2×D2311yescharacteristic, complemented
336#95C2×D2311yescharacteristic, complemented
337C23#240411yescharacteristic, complemented, Sylow
338C24—231no—
339C24—231no—
340C24—231no—
341C24—462no—
342C24—462no—
343C24—462no—
344C24—462no—
345C24—462no—
346C24—921no—
347C24—921no—
348C24C22×D2311yescharacteristic
349C24C22×D2311yescharacteristic
350#41—4632no—
351C2×Q8—462no—
352C2×Q8—462no—
353C2×Q8—462no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—41no—
357C2×D4—234no—
358C2×D4—234no—
359C2×D4—462no—
360C2×D4—462no—
361C2×D4—462no—
362C2×D4—462no—
363C2×D4—462no—
364C2×D4—462no—
365C2×D4—462no—
366C2×D4—462no—
367C2×D4—462no—
368C2×D4—462no—
369C2×D4—462no—
370C2×D4—462no—
371C2×D4—462no—
372C2×D4—921no—
373C2×D4—921no—
374C2×D4—921no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—231no—
379C22×C4—231no—
380C22×C4—234no—
381C22×C4—231no—
382C22×C4—231no—
383C22×C4—231no—
384C22×C4—462no—
385C22×C4—462no—
386C22×C4—462no—
387C22×C4—462no—
388C22×C4—462no—
389C22×C4—462no—
390C22×C4—921no—
391C22×C4—921no—
392C22×C4C22×D2311yescharacteristic
393C22×C4C22×D2311yescharacteristic
394C22×C4C22×D2311yescharacteristic
395C22×C4C22×D2311yescharacteristic
396C22×C4C22×D2311yescharacteristic
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—41no—
400C22⋊C4—462no—
401C22⋊C4—462no—
402C22⋊C4—462no—
403C22⋊C4—462no—
404C22⋊C4—462no—
405C22⋊C4—462no—
406C22⋊C4—462no—
407C22⋊C4—462no—
408C22⋊C4—921no—
409C22⋊C4—921no—
410C22⋊C4—921no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—232no—
424C23—232no—
425C23—232no—
426C23—232no—
427C23—232no—
428C23—468no—
429C23—461no—
430C23—461no—
431C23—461no—
432C23—461no—
433C23—461no—
434C23—461no—
435C23—461no—
436C23—461no—
437C23—461no—
438C23—461no—
439C23—461no—
440C23—461no—
441C23—461no—
442C23—461no—
443C23—461no—
444C23—461no—
445C23—924no—
446C23—924no—
447C23—924no—
448C23—924no—
449C23—924no—
450C23—924no—
451C23#6728812yescomplemented
452C23D4×D2312yes—
453C23C23×D2311yescharacteristic
454Q8—468no—
455D4—44no—
456D4—468no—
457D4—468no—
458D4—468no—
459D4—924no—
460D4—924no—
461D4—924no—
462C2×C4—28no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—232no—
477C2×C4—232no—
478C2×C4—468no—
479C2×C4—468no—
480C2×C4—461no—
481C2×C4—461no—
482C2×C4—461no—
483C2×C4—461no—
484C2×C4—461no—
485C2×C4—461no—
486C2×C4—461no—
487C2×C4—461no—
488C2×C4—461no—
489C2×C4—461no—
490C2×C4—461no—
491C2×C4—461no—
492C2×C4—461no—
493C2×C4—924no—
494C2×C4D4×D2312yes—
495C2×C4D4×D2312yes—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—234no—
511C22—462no—
512C22—462no—
513C22—462no—
514C22—462no—
515C22—462no—
516C22—462no—
517C22—462no—
518C22—462no—
519C22—462no—
520C22—462no—
521C22—462no—
522C22—462no—
523C22—9216no—
524C22—921no—
525C22—921no—
526C22—921no—
527C22—921no—
528C22—921no—
529C22—921no—
530C22—921no—
531C22—921no—
532C22C2×#6728811yescharacteristic
533C22C2×D4×D2311yescharacteristic
534C22C2×D4×D2311yescharacteristic
535C22C2×D4×D2311yescharacteristic
536C22#1062515511yescharacteristic
537C22#41×D2311yescharacteristic
538C22#1062516011yescharacteristic
539C4—22no—
540C4—22no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—462no—
545C4—462no—
546C4—921no—
547C4—921no—
548C4—921no—
549C2—42no—
550C2—42no—
551C2—464no—
552C2—922no—
553C2—922no—
554C2#120×D2311yescharacteristic
555C2#1309292611yescharacteristic
556C2#1309298311yescharacteristic
557C2#1309305711yescharacteristic
558C2#1309305911yescharacteristic
559C2#1309306311yescharacteristic
560C2#1309306411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutator, socle, cosocleC23×C23C24
FittingC23×#386C2
hypercenter#386D23
hypocenterC23#2404
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#67288C2semidirect
2. C2×#10625053C2semidirect
3. C2×#10625108C2semidirect
4. C2×C22⋊C4×D23C2semidirect
5. #13092330C2semidirect
6. #13092329C2semidirect
7. #13092326C2semidirect
8. #13092325C2semidirect
9. #13092296C2semidirect
10. #13092295C2semidirect
11. #13092295C2semidirect
12. #13092293C2semidirect
13. #13092293C2semidirect
14. #13092279C2semidirect
15. C23×#386C2semidirect
18. C23×C4×C23C22semidirect
22. C22×C22⋊D23C22semidirect
30. C22×C4×D23C22semidirect
31. C22×Dic46C22semidirect
34. C2×C22⋊C4×C23C22semidirect
37. C2×C22⋊Dic23C22semidirect
45. C2×(C2×D23)⋊C4C22semidirect
46. C2×(C2×D23)⋊C4C22semidirect
49. C23×#95C22semidirect
50. C23×#95C22semidirect
51. C23⋊#95C22semidirect
52. C23⋊#95C22semidirect
53. C23⋊#95C22semidirect
54. C23⋊#95C22semidirect
55. C23⋊#95C22semidirect
56. C23⋊#95C22semidirect
91. C2×C22⋊D23D4semidirect
103. C2×D92D4semidirect
112. C2×C4×D23D4semidirect
143. C23×C23#41semidirect
172. C22×D23#41semidirect
282. #386D23semidirect
311. C23×C4C2×D23semidirect
328. C2×C22⋊C4C2×D23semidirect
335. #95C2×D23semidirect
336. #95C2×D23semidirect
337. C23#2404semidirect
451. C23#67288semidirect

Maximal subgroups

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

subgroupindex
C22×#672882
C2×#106250532
C2×#106251082
C2×C22⋊C4×D232
#130923302
#130923292
#130923262
#130923252
#130922962
#130922952
#130922932
#130922792
C23×#3862
#240423