Finite Group Databasebeta

← #75912

Subgroups — #75912

Order 384.

932 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#895C211yesmaximal, characteristic, complemented
2C2×#884C211yesmaximal, characteristic, complemented
3C2×#882C211yesmaximal, characteristic, complemented
4C2×#882C211yesmaximal, characteristic, complemented
5C2×#882C211yesmaximal, characteristic, complemented
6C2×#874C211yesmaximal, characteristic, complemented
7C3×#388C211yesmaximal, characteristic, complemented
8#4991C211yesmaximal, characteristic, complemented
9#4960C211yesmaximal, characteristic, complemented
10#4960C211yesmaximal, characteristic, complemented
11#4940C211yesmaximal, characteristic, complemented
12#4672C211yesmaximal, characteristic, complemented
13#4671C211yesmaximal, characteristic, complemented
14#4671C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2669—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×D12C2211yescharacteristic
25C22×D12C2211yescharacteristic
26C22×D12C2211yescharacteristic
27C22×D12C2211yescharacteristic, complemented
28C22×D12C2211yescharacteristic, complemented
29C22×D12C2211yescharacteristic, complemented
30C22×C4×D3C2211yescharacteristic, complemented
31C2×C3×C4⋊C4C2211yescharacteristic, complemented
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35C2×C3×C42C2211yescharacteristic, complemented
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×Dic3⋊C4C2211yescharacteristic, complemented
48#895—24no—
49#884—24no—
50#882—24no—
51#882—24no—
52#882—24no—
53#874—24no—
54C3×#95C2211yescharacteristic, complemented
55C3×#95C2211yescharacteristic, complemented
56C3⋊#95C2211yescharacteristic, complemented
57C3⋊#95C2211yescharacteristic, complemented
58C2×#127—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#120—31no—
62C2×#120—31no—
63C2×#120—31no—
64#394—31no—
65#394—31no—
66#392—31no—
67#392—31no—
68#392—31no—
69#392—31no—
70#388—31no—
71#388D311yescharacteristic, complemented
72#386—31no—
73C24×C3C2311yescharacteristic
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—41no—
78C23×D3—41no—
79C23×D3—41no—
80C23×D3—41no—
81C23×D3C2311yescharacteristic
82C23×D3C2311yescharacteristic
83C23×D3C2311yescharacteristic
84C23×D3C2311yescharacteristic
85C23×D3C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C2×#67—22no—
93C2×#67—22no—
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—41no—
98C2×#67—41no—
99C2×#67—41no—
100C2×#67—41no—
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C2×D12—22no—
105C2×D12—22no—
106C2×D12—22no—
107C2×D12—22no—
108C2×D12—22no—
109C2×D12—22no—
110C2×D12—22no—
111C2×D12—22no—
112C2×D12—22no—
113C2×D12—22no—
114C2×D12—22no—
115C2×D12—22no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—41no—
119C2×D12—41no—
120C2×D12—41no—
121C2×D12—41no—
122C2×D12—41no—
123C2×D12—41no—
124C2×D12—41no—
125C2×D12—41no—
126C2×D12—41no—
127C2×D12—41no—
128C2×D12—41no—
129C2×D12—41no—
130C2×D12D414yescomplemented
131C2×C4×D3—22no—
132C2×C4×D3—22no—
133C2×C4×D3—41no—
134C3×C4⋊C4—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137C3×C22⋊C4D414yescomplemented
138C3×C42—22no—
139(C2×D3)⋊C4—22no—
140(C2×D3)⋊C4—22no—
141(C2×D3)⋊C4—22no—
142(C2×D3)⋊C4—22no—
143(C2×D3)⋊C4—22no—
144(C2×D3)⋊C4—22no—
145(C2×D3)⋊C4—22no—
146(C2×D3)⋊C4—41no—
147(C2×D3)⋊C4—41no—
148(C2×D3)⋊C4—41no—
149(C2×D3)⋊C4D414yescomplemented
150Dic3⋊C4—22no—
151C25—31no—
152C22×D4—31no—
153C22×D4—31no—
154C22×D4—31no—
155C22×D4—31no—
156C22×D4—31no—
157C22×D4—31no—
158C22×D4—31no—
159C22×D4—31no—
160C22×D4—31no—
161C22×D4—31no—
162C22×D4—31no—
163C22×D4—31no—
164C23×C4—31no—
165#127—64no—
166#121—64no—
167#121—64no—
168#120—64no—
169#120—64no—
170#120—64no—
171C2×C4⋊C4—31no—
172C2×C4⋊C4C2×D311yescharacteristic, complemented
173C2×C22⋊C4—31no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—31no—
176C2×C22⋊C4—31no—
177C2×C22⋊C4—31no—
178C2×C22⋊C4—31no—
179C2×C22⋊C4—31no—
180C2×C22⋊C4—31no—
181C2×C22⋊C4—31no—
182C2×C22⋊C4—31no—
183C2×C22⋊C4—31no—
184C2×C22⋊C4C2×D311yescharacteristic
185C2×C22⋊C4C2×D311yescharacteristic
186C2×C22⋊C4C2×D311yescharacteristic
187C2×C42C2×D311yescharacteristic, complemented
188#95—31no—
189#95—31no—
190#95C2×D311yescharacteristic, complemented
191#95C2×D311yescharacteristic, complemented
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3C2×D412yes—
199C23×C3C2411yescharacteristic
200C22×D3—21no—
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—21no—
206C22×D3—21no—
207C22×D3—21no—
208C22×D3—21no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—21no—
216C22×D3—21no—
217C22×D3—21no—
218C22×D3—21no—
219C22×D3—21no—
220C22×D3—21no—
221C22×D3—21no—
222C22×D3—21no—
223C22×D3—21no—
224C22×D3—21no—
225C22×D3—21no—
226C22×D3—21no—
227C22×D3—21no—
228C22×D3—21no—
229C22×D3—21no—
230C22×D3—21no—
231C22×D3—21no—
232C22×D3—44no—
233C22×D3—44no—
234C22×D3—44no—
235C22×D3—44no—
236C22×D3—44no—
237C22×D3—44no—
238C22×D3—44no—
239C22×D3C2×D412yes—
240C22×D3C2×D412yes—
241C22×D3C2×D412yes—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4C2×D412yes—
257C2×C3×C4C2×D412yes—
258C2×C3×C4C2×D412yes—
259C2×C3×C4C2×D412yes—
260#67—44no—
261#67—44no—
262#67—44no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3C2×D412yes—
272D12—44no—
273D12—44no—
274D12—44no—
275D12—44no—
276D12—44no—
277D12—44no—
278D12—44no—
279D12—44no—
280D12—44no—
281C4×D3—44no—
282C24—31no—
283C24—31no—
284C24—31no—
285C24—31no—
286C24—31no—
287C24—62no—
288C24—62no—
289C24—62no—
290C24—121no—
291C24—121no—
292C24—121no—
293C24—121no—
294C24C22×D311yescharacteristic
295C2×D4—34no—
296C2×D4—62no—
297C2×D4—62no—
298C2×D4—62no—
299C2×D4—62no—
300C2×D4—62no—
301C2×D4—62no—
302C2×D4—62no—
303C2×D4—62no—
304C2×D4—62no—
305C2×D4—62no—
306C2×D4—62no—
307C2×D4—62no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4—62no—
311C2×D4—62no—
312C2×D4—62no—
313C2×D4—62no—
314C2×D4—62no—
315C2×D4—121no—
316C2×D4—121no—
317C2×D4—121no—
318C2×D4—121no—
319C2×D4—121no—
320C2×D4—121no—
321C2×D4—121no—
322C2×D4—121no—
323C2×D4—121no—
324C2×D4—121no—
325C2×D4—121no—
326C2×D4—121no—
327C2×D4—121no—
328C2×D4—121no—
329C2×D4—121no—
330C2×D4—121no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—62no—
335C22×C4—62no—
336C22×C4—121no—
337C22×C4C22×D311yescharacteristic
338C22×C4C22×D311yescharacteristic
339C22×C4C22×D311yescharacteristic
340C22×C4C22×D311yescharacteristic
341C22×C4C22×D311yescharacteristic
342C22×C4C22×D311yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—62no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—34no—
348C22⋊C4—62no—
349C22⋊C4—62no—
350C22⋊C4—62no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22⋊C4—62no—
354C22⋊C4—62no—
355C22⋊C4—121no—
356C22⋊C4—121no—
357C22⋊C4—121no—
358C22⋊C4D1214yescomplemented
359C42—22no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3C22×D411yescharacteristic
368C22×C3C22×D411yescharacteristic
369C22×C3C22×D411yescharacteristic
370C22×C3H(5,𝔽2)11yescharacteristic
371C22×C3H(5,𝔽2)11yescharacteristic
372C22×C3H(5,𝔽2)11yescharacteristic
373C22×C3H(5,𝔽2)11yescharacteristic
374C2×D3—22no—
375C2×D3—22no—
376C2×D3—22no—
377C2×D3—22no—
378C2×D3—22no—
379C2×D3—22no—
380C2×D3—22no—
381C2×D3—22no—
382C2×D3—22no—
383C2×D3—416no—
384C2×D3—41no—
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—41no—
391C2×D3—41no—
392C2×D3—41no—
393C2×D3—41no—
394C2×D3—41no—
395C2×D3—41no—
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C2×D3—41no—
401C2×D3—41no—
402C2×D3—41no—
403C2×D3—41no—
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C2×D3—41no—
408C2×D3—41no—
409C2×D3—41no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—41no—
415C3×C4—41no—
416Dic3—22no—
417Dic3—41no—
418Dic3—41no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—32no—
426C23—32no—
427C23—32no—
428C23—61no—
429C23—61no—
430C23—61no—
431C23—61no—
432C23—61no—
433C23—61no—
434C23—61no—
435C23—61no—
436C23—61no—
437C23—61no—
438C23—61no—
439C23—61no—
440C23—61no—
441C23—61no—
442C23—61no—
443C23—61no—
444C23—61no—
445C23—61no—
446C23—61no—
447C23—61no—
448C23—61no—
449C23—61no—
450C23—61no—
451C23—61no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23—61no—
459C23—61no—
460C23—124no—
461C23—124no—
462C23—124no—
463C23—124no—
464C23—124no—
465C23—124no—
466C23—124no—
467C23C2×D1212yes—
468C23C23×D311yescharacteristic
469D4—124no—
470D4—124no—
471D4—124no—
472D4—124no—
473D4—124no—
474D4—124no—
475D4—124no—
476D4—124no—
477D4—124no—
478D4—124no—
479D4—124no—
480D4—124no—
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—21no—
494C2×C4—21no—
495C2×C4—32no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—124no—
505C2×C4C2×D1212yes—
506C2×C4C2×D1212yes—
507C2×C4D3×D412yes—
508C2×C4D3×D412yes—
509C2×C3—42no—
510C2×C3#53411yescharacteristic
511C2×C3#53511yescharacteristic
512C2×C3#53511yescharacteristic
513C2×C3D4211yescharacteristic
514C2×C3D4211yescharacteristic
515C2×C3D4211yescharacteristic
516C2×C3#56011yescharacteristic
517D3—42no—
518D3—42no—
519D3—42no—
520D3—81no—
521D3—81no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—62no—
530C22—62no—
531C22—62no—
532C22—62no—
533C22—62no—
534C22—62no—
535C22—62no—
536C22—62no—
537C22—62no—
538C22—1216no—
539C22—121no—
540C22—121no—
541C22—121no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22—121no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22—121no—
551C22—121no—
552C22—121no—
553C22—121no—
554C22—121no—
555C22—121no—
556C22—121no—
557C22—121no—
558C22—121no—
559C22—121no—
560C22—121no—
561C22—121no—
562C22—121no—
563C22—121no—
564C22—121no—
565C22C22×D1211yescharacteristic
566C22C2×D3×D411yescharacteristic
567C22C2×D3×D411yescharacteristic
568C22#100911yescharacteristic
569C22#100911yescharacteristic
570C22#100911yescharacteristic
571C22#100911yescharacteristic
572C4—22no—
573C4—22no—
574C4—22no—
575C4—22no—
576C4—41no—
577C4—41no—
578C4—62no—
579C4—121no—
580C4—121no—
581C3#266911yescharacteristic, complemented, Sylow
582C2—42no—
583C2—122no—
584C2—122no—
585C2—122no—
586C2—241no—
587C2—241no—
588C2#552511yescharacteristic
589C2D4×D1211yescharacteristic
590C2D4×D1211yescharacteristic
591C2#560911yescharacteristic
592C2#565311yescharacteristic
593C2#567411yescharacteristic
594C2#571111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
hypercenter#388D3
hypocenterC3#2669
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#895C2semidirect
2. C2×#884C2semidirect
3. C2×#882C2semidirect
4. C2×#882C2semidirect
5. C2×#882C2semidirect
6. C2×#874C2semidirect
7. C3×#388C2semidirect
8. #4991C2semidirect
9. #4960C2semidirect
10. #4960C2semidirect
11. #4940C2semidirect
12. #4672C2semidirect
13. #4671C2semidirect
14. #4671C2semidirect
15. #4665C2semidirect
27. C22×D12C22semidirect
28. C22×D12C22semidirect
29. C22×D12C22semidirect
30. C22×C4×D3C22semidirect
31. C2×C3×C4⋊C4C22semidirect
35. C2×C3×C42C22semidirect
42. C2×(C2×D3)⋊C4C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. C2×(C2×D3)⋊C4C22semidirect
45. C2×(C2×D3)⋊C4C22semidirect
46. C2×(C2×D3)⋊C4C22semidirect
47. C2×Dic3⋊C4C22semidirect
54. C3×#95C22semidirect
55. C3×#95C22semidirect
56. C3⋊#95C22semidirect
57. C3⋊#95C22semidirect
71. #388D3semidirect
130. C2×D12D4semidirect
137. C3×C22⋊C4D4semidirect
149. (C2×D3)⋊C4D4semidirect
172. C2×C4⋊C4C2×D3semidirect
187. C2×C42C2×D3semidirect
190. #95C2×D3semidirect
191. #95C2×D3semidirect
358. C22⋊C4D12semidirect
581. C3#2669semidirect

Maximal subgroups

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

subgroupindex
C2×#8952
C2×#8842
C2×#8822
C2×#8742
C3×#3882
#49912
#49602
#49402
#46722
#46712
#46652
#26693