Finite Group Databasebeta

← #15676215

Subgroups — #15676215

Order 2944.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D23C211yesmaximal, characteristic
2C2×C4×C22⋊D23C211yesmaximal, characteristic, complemented
3C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic, complemented
4C22×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D23C211yesmaximal, characteristic, complemented
6#13092317C211yesmaximal, characteristic, complemented
7#13092317C211yesmaximal, characteristic, complemented
8#13092297C211yesmaximal, characteristic, complemented
9#13092295C211yesmaximal, characteristic, complemented
10#13092295C211yesmaximal, characteristic, complemented
11#13092276C211yesmaximal, characteristic, complemented
12#13092272C211yesmaximal, characteristic, complemented
13#13092272C211yesmaximal, characteristic, complemented
14#13092264C211yesmaximal, characteristic, complemented
15C23×#386C211yesmaximal, characteristic, complemented
16C24×D23C2211yescharacteristic
17C24×D23C2211yescharacteristic
18C22×D4×C23C2211yescharacteristic
19C23×C4×C23C2211yescharacteristic, complemented
20C22×C22⋊D23C2211yescharacteristic
21C22×C22⋊D23C2211yescharacteristic
22C23×Dic23C2211yescharacteristic, complemented
23C2×D4×D23—24no—
24C2×D4×D23—24no—
25C2×D4×D23C418yescomplemented
26C22×D92C2211yescharacteristic
27C22×C4×D23C2211yescharacteristic
28C22×C4×D23C2211yescharacteristic, complemented
29C22×C4×D23C2211yescharacteristic, complemented
30C2×C22⋊C4×C23C2211yescharacteristic, complemented
31C2×C22⋊C4×C23C2211yescharacteristic, complemented
32C2×C22⋊C4×C23C2211yescharacteristic, complemented
33C2×C22⋊Dic23C2211yescharacteristic, complemented
34C2×C22⋊Dic23C2211yescharacteristic, complemented
35C2×C22⋊Dic23C2211yescharacteristic, complemented
36C4×C22⋊D23—24no—
37C2×(C2×D23)⋊C4—24no—
38C2×(C2×D23)⋊C4C2211yescharacteristic
39C2×(C2×D23)⋊C4C2211yescharacteristic
40C2×(C2×D23)⋊C4C2211yescharacteristic
41C2×(C2×D23)⋊C4C2211yescharacteristic
42C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
48C2×Dic23⋊C4C2211yescharacteristic, complemented
49C2×Dic23⋊C4C2211yescharacteristic, complemented
50C2×C4×Dic23C2211yescharacteristic, complemented
51C2×C4×Dic23C2211yescharacteristic, complemented
52(C22⋊D23)⋊C4—24no—
53C22⋊C4×D23—24no—
54C23×#95C2211yescharacteristic, complemented
55C23×#95C2211yescharacteristic, complemented
56C23⋊#95C2211yescharacteristic, complemented
57C23⋊#95C2211yescharacteristic, complemented
58C24×C23C2311yescharacteristic
59C24×C23C2311yescharacteristic
60C23×D23—22no—
61C23×D23—22no—
62C23×D23—22no—
63C23×D23—22no—
64C23×D23—22no—
65C23×D23—22no—
66C23×D23—22no—
67C23×D23—22no—
68C23×D23—41no—
69C23×D23—41no—
70C23×D23—41no—
71C23×D23—41no—
72C23×D23C2×C414yescomplemented
73C23×D23C2×C414yescomplemented
74C23×D23C2311yescharacteristic
75C23×D23C2311yescharacteristic
76C23×D23C2311yescharacteristic
77C2×D4×C23—22no—
78C2×D4×C23—22no—
79C2×D4×C23C2×C414yescomplemented
80C22×C4×C23—22no—
81C22×C4×C23—22no—
82C22×C4×C23—41no—
83C22×C4×C23C2311yescharacteristic
84C22×C4×C23C2311yescharacteristic
85C22×C4×C23C2311yescharacteristic
86C22×C4×C23C2311yescharacteristic
87C22×C4×C23C2311yescharacteristic
88C2×C22⋊D23—22no—
89C2×C22⋊D23—22no—
90C2×C22⋊D23C2×C414yes—
91C2×C22⋊D23C2×C414yescomplemented
92C2×C22⋊D23D414yes—
93C2×C22⋊D23D414yes—
94C22×Dic23—22no—
95C22×Dic23—22no—
96C22×Dic23—41no—
97C22×Dic23C2311yescharacteristic
98C22×Dic23C2311yescharacteristic
99C22×Dic23C2311yescharacteristic
100C22×Dic23C2311yescharacteristic
101C22×Dic23C2311yescharacteristic
102D4×D23—232no—
103C2×D92—22no—
104C2×D92—22no—
105C2×D92C2×C414yescomplemented
106C2×C4×D23—22no—
107C2×C4×D23—22no—
108C2×C4×D23—22no—
109C2×C4×D23—22no—
110C2×C4×D23—22no—
111C2×C4×D23—22no—
112C2×C4×D23—41no—
113C2×C4×D23—41no—
114C2×C4×D23C2×C414yescomplemented
115C22⋊C4×C23—22no—
116C22⋊C4×C23—22no—
117C22⋊C4×C23—41no—
118C22⋊Dic23—22no—
119C22⋊Dic23—22no—
120C22⋊Dic23—41no—
121(C2×D23)⋊C4—22no—
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—
130(C2×D23)⋊C4D414yescomplemented
131Dic23⋊C4—22no—
132Dic23⋊C4—22no—
133C4×Dic23—22no—
134C4×Dic23—22no—
135C23×C23—21no—
136C23×C23—21no—
137C23×C23—21no—
138C23×C23—21no—
139C23×C23—21no—
140C23×C23—21no—
141C23×C23—21no—
142C23×C23—21no—
143C23×C23—21no—
144C23×C23—21no—
145C23×C23C22×C412yes—
146C23×C23C22×C412yes—
147C23×C23C2×D412yes—
148C23×C23C2×D412yes—
149C23×C23C2411yescharacteristic
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—28no—
159C22×D23—21no—
160C22×D23—21no—
161C22×D23—21no—
162C22×D23—21no—
163C22×D23—21no—
164C22×D23—21no—
165C22×D23—28no—
166C22×D23—28no—
167C22×D23—28no—
168C22×D23—44no—
169C22×D23—44no—
170C22×D23—44no—
171C22×D23—44no—
172C22×D23—44no—
173C22×D23—44no—
174C22×D23—44no—
175C22×D23—44no—
176C22×D23—44no—
177C22×D23—44no—
178C22×D23C22×C412yes—
179C22×D23C22×C412yes—
180C22×D23C22×C412yes—
181C22×D23C2×D412yes—
182C22×D23C2×D412yes—
183C22×D23C2×D412yes—
184C22×D23#4112yes—
185D4×C23—28no—
186C2×C4×C23—21no—
187C2×C4×C23—21no—
188C2×C4×C23—21no—
189C2×C4×C23—21no—
190C2×C4×C23—21no—
191C2×C4×C23—21no—
192C2×C4×C23—21no—
193C2×C4×C23—21no—
194C2×C4×C23—21no—
195C2×C4×C23—21no—
196C2×C4×C23—21no—
197C2×C4×C23—21no—
198C2×C4×C23—21no—
199C2×C4×C23—44no—
200C2×C4×C23C22×C412yes—
201C2×C4×C23C2×D412yescomplemented
202C22⋊D23—28no—
203C22⋊D23C22⋊C4116yescomplemented
204C2×Dic23—21no—
205C2×Dic23—21no—
206C2×Dic23—21no—
207C2×Dic23—21no—
208C2×Dic23—21no—
209C2×Dic23—21no—
210C2×Dic23—21no—
211C2×Dic23—21no—
212C2×Dic23—21no—
213C2×Dic23—21no—
214C2×Dic23—21no—
215C2×Dic23—44no—
216C2×Dic23C22×C412yes—
217C2×Dic23C2×D412yes—
218C2×Dic23C2×D412yes—
219C2×Dic23C2×D412yescomplemented
220D92—28no—
221C4×D23—28no—
222C4×D23—44no—
223C4×D23—44no—
224D4×C22⋊C4—231nomaximal, Sylow
225C22×C23—22no—
226C22×C23—22no—
227C22×C23—22no—
228C22×C23—22no—
229C22×C23—22no—
230C22×C23—22no—
231C22×C23—22no—
232C22×C23—22no—
233C22×C23—22no—
234C22×C23—41no—
235C22×C23—41no—
236C22×C23—41no—
237C22×C23—41no—
238C22×C23C2×C22⋊C414yescomplemented
239C22×C23C23×C411yescharacteristic
240C22×C23C22×D411yescharacteristic
241C22×C23C22×D411yescharacteristic
242C22×C23C22×D411yescharacteristic
243C22×C23C2×#4111yescharacteristic
244C22×C23H(5,𝔽2)11yescharacteristic
245C22×C23H(5,𝔽2)11yescharacteristic
246C2×D23—22no—
247C2×D23—22no—
248C2×D23—22no—
249C2×D23—22no—
250C2×D23—22no—
251C2×D23—22no—
252C2×D23—22no—
253C2×D23—22no—
254C2×D23—22no—
255C2×D23—22no—
256C2×D23—22no—
257C2×D23—22no—
258C2×D23—22no—
259C2×D23—22no—
260C2×D23—22no—
261C2×D23—416no—
262C2×D23—416no—
263C2×D23—41no—
264C2×D23—41no—
265C2×D23—41no—
266C2×D23—41no—
267C2×D23C2×C22⋊C414yescomplemented
268C2×D23C4×D414yescomplemented
269C4×C23—22no—
270C4×C23—22no—
271C4×C23—41no—
272C4×C23—41no—
273C4×C23—41no—
274Dic23—22no—
275Dic23—41no—
276Dic23—41no—
277Dic23—41no—
278Dic23C2×C22⋊C414yescomplemented
279C23×D4—231no—
280C2×C4×D4—231no—
281C2×C4×D4—231no—
282C22×C22⋊C4—231no—
283C22×C22⋊C4—231no—
284#390—231no—
285#390—231no—
286#386—231no—
287#386—231no—
288#386—231no—
289#386D2311yescharacteristic, complemented
290#380—231no—
291#379—231no—
292#379—231no—
293C4×C22⋊C4—231no—
294C2×C23—24no—
295C2×C23—42no—
296C2×C23C22×C22⋊C411yescharacteristic
297C2×C23C2×C4×D411yescharacteristic
298C2×C23#51811yescharacteristic
299C2×C23D4211yescharacteristic
300C2×C23D4211yescharacteristic
301C2×C23#54611yescharacteristic
302C2×C23#54611yescharacteristic
303D23—24no—
304D23—24no—
305D23—42no—
306C25—231no—
307C25—231no—
308C22×D4—231no—
309C22×D4—231no—
310C22×D4—238no—
311C22×D4—231no—
312C22×D4—464no—
313C22×D4—464no—
314C22×D4C2×D2311yescharacteristic
315C23×C4—231no—
316C23×C4—231no—
317C23×C4—231no—
318C23×C4—231no—
319C23×C4C2×D2311yescharacteristic, complemented
320C4×D4—464no—
321C4×D4—464no—
322C2×C4⋊C4—231no—
323C2×C4⋊C4—231no—
324C2×C22⋊C4—231no—
325C2×C22⋊C4—231no—
326C2×C22⋊C4—231no—
327C2×C22⋊C4—231no—
328C2×C22⋊C4—231no—
329C2×C22⋊C4—231no—
330C2×C22⋊C4—231no—
331C2×C22⋊C4—231no—
332C2×C22⋊C4—231no—
333C2×C22⋊C4—231no—
334C2×C22⋊C4—231no—
335C2×C22⋊C4—231no—
336C2×C22⋊C4—231no—
337C2×C22⋊C4—464no—
338C2×C22⋊C4—464no—
339C2×C22⋊C4C2×D2311yescharacteristic, complemented
340C2×C22⋊C4C2×D2311yescharacteristic, complemented
341C2×C22⋊C4C2×D2311yescharacteristic, complemented
342C2×C42—231no—
343C2×C42—231no—
344#95—231no—
345#95—231no—
346#95C2×D2311yescharacteristic, complemented
347#95C2×D2311yescharacteristic, complemented
348C23D4×C22⋊C411yescharacteristic, complemented, Sylow
349C24—231no—
350C24—231no—
351C24—231no—
352C24—234no—
353C24—234no—
354C24—462no—
355C24—462no—
356C24—462no—
357C24—462no—
358C24—462no—
359C24—462no—
360C24—462no—
361C24—462no—
362C24—921no—
363C24—921no—
364C24—921no—
365C24—921no—
366C24C22×D2311yescharacteristic
367C24C22×D2311yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—234no—
371C2×D4—234no—
372C2×D4—234no—
373C2×D4—234no—
374C2×D4—234no—
375C2×D4—462no—
376C2×D4—462no—
377C2×D4—462no—
378C2×D4—462no—
379C2×D4—4632no—
380C2×D4C4×D2314yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—231no—
385C22×C4—231no—
386C22×C4—234no—
387C22×C4—231no—
388C22×C4—231no—
389C22×C4—231no—
390C22×C4—462no—
391C22×C4—462no—
392C22×C4—462no—
393C22×C4—462no—
394C22×C4—462no—
395C22×C4—462no—
396C22×C4—462no—
397C22×C4—462no—
398C22×C4—921no—
399C22×C4—921no—
400C22×C4—921no—
401C22×C4C22×D2311yescharacteristic
402C22×C4C22×D2311yescharacteristic
403C22×C4C22×D2311yescharacteristic
404C22×C4C22×D2311yescharacteristic
405C22×C4C22×D2311yescharacteristic
406C4⋊C4—462no—
407C4⋊C4—462no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—234no—
412C22⋊C4—462no—
413C22⋊C4—462no—
414C22⋊C4—462no—
415C22⋊C4—462no—
416C22⋊C4—462no—
417C22⋊C4—462no—
418C22⋊C4—462no—
419C22⋊C4—462no—
420C22⋊C4—462no—
421C22⋊C4—921no—
422C22⋊C4—921no—
423C22⋊C4—921no—
424C42—462no—
425C42—462no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—232no—
437C23—232no—
438C23—232no—
439C23—232no—
440C23—232no—
441C23—232no—
442C23—232no—
443C23—468no—
444C23—468no—
445C23—468no—
446C23—461no—
447C23—461no—
448C23—461no—
449C23—461no—
450C23—461no—
451C23—461no—
452C23—461no—
453C23—461no—
454C23—468no—
455C23—461no—
456C23—461no—
457C23—461no—
458C23—461no—
459C23—461no—
460C23—461no—
461C23—924no—
462C23—924no—
463C23—924no—
464C23—924no—
465C23—924no—
466C23—924no—
467C23—924no—
468C23—924no—
469C23—924no—
470C23—924no—
471C23C2×C4×D2312yes—
472C23C2×C4×D2312yes—
473C23D4×D2312yes—
474C23D4×D2312yes—
475C23C23×D2311yescharacteristic
476D4—28no—
477D4—2316no—
478D4—468no—
479D4—468no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—44no—
494C2×C4—232no—
495C2×C4—232no—
496C2×C4—232no—
497C2×C4—232no—
498C2×C4—468no—
499C2×C4—461no—
500C2×C4—461no—
501C2×C4—461no—
502C2×C4—461no—
503C2×C4—461no—
504C2×C4—461no—
505C2×C4—461no—
506C2×C4—461no—
507C2×C4—461no—
508C2×C4—461no—
509C2×C4—461no—
510C2×C4—924no—
511C2×C4—924no—
512C2×C4—924no—
513C2×C4C2×C4×D2312yes—
514C2×C4D4×D2312yescomplemented
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—234no—
529C22—234no—
530C22—462no—
531C22—462no—
532C22—462no—
533C22—462no—
534C22—462no—
535C22—462no—
536C22—462no—
537C22—462no—
538C22—462no—
539C22—462no—
540C22—462no—
541C22—462no—
542C22—462no—
543C22—462no—
544C22—462no—
545C22—9216no—
546C22—9216no—
547C22—921no—
548C22—921no—
549C22—921no—
550C22—921no—
551C22C22⋊C4×D2314yescomplemented
552C22C22×C4×D2311yescharacteristic
553C22C2×D4×D2311yescharacteristic
554C22C2×D4×D2311yescharacteristic
555C22C2×D4×D2311yescharacteristic
556C22#1062515511yescharacteristic
557C22#41×D2311yescharacteristic
558C22#1062516011yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—234no—
565C4—462no—
566C4—921no—
567C4—921no—
568C4—921no—
569C2—24no—
570C2—42no—
571C2—464no—
572C2—464no—
573C2—922no—
574C2C2×C22⋊C4×D2311yescharacteristic
575C2C4×D4×D2311yescharacteristic
576C2#1309288911yescharacteristic
577C2#1309304911yescharacteristic
578C2#1309305111yescharacteristic
579C2#1309305611yescharacteristic
580C2#1309305911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#386C2
socle, cosocleC23×C23C24
prime radicalC22×D4×D23C2
hypercenter#386D23
hypocenterC23D4×C22⋊C4
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D23C2semidirect
3. C2×(C22⋊D23)⋊C4C2semidirect
4. C22×(C2×D23)⋊C4C2semidirect
5. C2×C22⋊C4×D23C2semidirect
6. #13092317C2semidirect
7. #13092317C2semidirect
8. #13092297C2semidirect
9. #13092295C2semidirect
10. #13092295C2semidirect
11. #13092276C2semidirect
12. #13092272C2semidirect
13. #13092272C2semidirect
14. #13092264C2semidirect
15. C23×#386C2semidirect
19. C23×C4×C23C22semidirect
22. C23×Dic23C22semidirect
25. C2×D4×D23C4semidirect
28. C22×C4×D23C22semidirect
29. C22×C4×D23C22semidirect
30. C2×C22⋊C4×C23C22semidirect
31. C2×C22⋊C4×C23C22semidirect
32. C2×C22⋊C4×C23C22semidirect
33. C2×C22⋊Dic23C22semidirect
34. C2×C22⋊Dic23C22semidirect
35. C2×C22⋊Dic23C22semidirect
42. C2×(C2×D23)⋊C4C22semidirect
43. C2×(C2×D23)⋊C4C22semidirect
44. C2×(C2×D23)⋊C4C22semidirect
45. C2×(C2×D23)⋊C4C22semidirect
46. C2×(C2×D23)⋊C4C22semidirect
47. C2×(C2×D23)⋊C4C22semidirect
48. C2×Dic23⋊C4C22semidirect
49. C2×Dic23⋊C4C22semidirect
50. C2×C4×Dic23C22semidirect
51. C2×C4×Dic23C22semidirect
54. C23×#95C22semidirect
55. C23×#95C22semidirect
56. C23⋊#95C22semidirect
57. C23⋊#95C22semidirect
72. C23×D23C2×C4semidirect
73. C23×D23C2×C4semidirect
79. C2×D4×C23C2×C4semidirect
91. C2×C22⋊D23C2×C4semidirect
105. C2×D92C2×C4semidirect
114. C2×C4×D23C2×C4semidirect
130. (C2×D23)⋊C4D4semidirect
201. C2×C4×C23C2×D4semidirect
203. C22⋊D23C22⋊C4semidirect
219. C2×Dic23C2×D4semidirect
238. C22×C23C2×C22⋊C4semidirect
267. C2×D23C2×C22⋊C4semidirect
268. C2×D23C4×D4semidirect
278. Dic23C2×C22⋊C4semidirect
289. #386D23semidirect
319. C23×C4C2×D23semidirect
339. C2×C22⋊C4C2×D23semidirect
340. C2×C22⋊C4C2×D23semidirect
341. C2×C22⋊C4C2×D23semidirect
346. #95C2×D23semidirect
347. #95C2×D23semidirect
348. C23D4×C22⋊C4semidirect
380. C2×D4C4×D23semidirect
514. C2×C4D4×D23semidirect
551. C22C22⋊C4×D23semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D232
C2×C4×C22⋊D232
C2×(C22⋊D23)⋊C42
C22×(C2×D23)⋊C42
C2×C22⋊C4×D232
#130923172
#130922972
#130922952
#130922762
#130922722
#130922642
C23×#3862
D4×C22⋊C423