Finite Group Databasebeta

← #77114

Subgroups — #77114

Order 384.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#939C211yesmaximal, characteristic, complemented
2C2×#937C211yesmaximal, characteristic, complemented
3C2×#884C211yesmaximal, characteristic, complemented
4C2×#882C211yesmaximal, characteristic, complemented
5C2×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#394C211yesmaximal, characteristic, complemented
8#4989C211yesmaximal, characteristic, complemented
9#4988C211yesmaximal, characteristic, complemented
10#4960C211yesmaximal, characteristic, complemented
11#4959C211yesmaximal, characteristic, complemented
12#4958C211yesmaximal, characteristic, complemented
13#4944C211yesmaximal, characteristic, complemented
14#4676C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2424—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic, complemented
23C23×Dic3C2211yescharacteristic, complemented
24C22×D12C2211yescharacteristic
25C22×D12C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic
27C22×C4×D3C2211yescharacteristic
28C2×C3×C4⋊C4C2211yescharacteristic, complemented
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C22⋊C4C2211yescharacteristic, complemented
32C2×C3×C22⋊C4C2211yescharacteristic, complemented
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35#939—24no—
36#937—24no—
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×Dic3⋊C4C2211yescharacteristic, complemented
47C2×Dic3⋊C4C2211yescharacteristic, complemented
48C2×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C4×Dic3C2211yescharacteristic, complemented
50#884—24no—
51#882—24no—
52#67⋊C4—24no—
53D3×C22⋊C4—24no—
54C3×#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C3⋊#95C2211yescharacteristic, complemented
57C3⋊#95C2211yescharacteristic, complemented
58C2×#121—31no—
59C2×#121—31no—
60C2×#120—31no—
61C2×#120—31no—
62C2×C4×D4—31no—
63C22×C22⋊C4—31no—
64#396—31no—
65#394—31no—
66#394D311yescharacteristic, complemented
67#392—31no—
68#390—31no—
69#388—31no—
70#386—31no—
71#386—31no—
72#385—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—22no—
79C23×D3—22no—
80C23×D3—41no—
81C23×D3—41no—
82C23×D3C2311yescharacteristic
83C23×D3C2311yescharacteristic
84C23×D3C2311yescharacteristic
85C2×C3×D4—22no—
86C2×C3×D4—22no—
87C2×C3×D4—41no—
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C2×#67—22no—
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—22no—
98C2×#67—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—41no—
102C2×#67—41no—
103C2×#67—41no—
104C2×#67D414yescomplemented
105C22×Dic3—22no—
106C22×Dic3—22no—
107C22×Dic3—41no—
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C22×Dic3C2311yescharacteristic
112C22×Dic3C2311yescharacteristic
113C2×D12—22no—
114C2×D12—22no—
115C2×D12—22no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—41no—
119C2×C4×D3—22no—
120C2×C4×D3—22no—
121C2×C4×D3—22no—
122C2×C4×D3—22no—
123C2×C4×D3—41no—
124C2×C4×D3—41no—
125C3×C4⋊C4—41no—
126C3×C22⋊C4—22no—
127C3×C22⋊C4—22no—
128C3×C22⋊C4—22no—
129C3×C22⋊C4—22no—
130#217—22no—
131#217D414yescomplemented
132(C2×D3)⋊C4—22no—
133(C2×D3)⋊C4—22no—
134(C2×D3)⋊C4—22no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—41no—
140(C2×D3)⋊C4D414yescomplemented
141Dic3⋊C4—22no—
142Dic3⋊C4—22no—
143Dic3⋊C4—22no—
144C4×Dic3—22no—
145C25—31no—
146C22×D4—31no—
147C22×D4—31no—
148C22×D4—31no—
149C22×D4—31no—
150C22×D4—31no—
151C22×D4—31no—
152C22×D4C2×D311yescharacteristic
153C23×C4—31no—
154C23×C4—31no—
155C23×C4—31no—
156#121—64no—
157#121—64no—
158#120—64no—
159#120—64no—
160C4×D4—64no—
161C2×C4⋊C4—31no—
162C2×C4⋊C4—31no—
163C2×C4⋊C4—31no—
164C2×C4⋊C4C2×D311yescharacteristic, complemented
165C2×C22⋊C4—31no—
166C2×C22⋊C4—31no—
167C2×C22⋊C4—31no—
168C2×C22⋊C4—31no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—31no—
172C2×C22⋊C4—31no—
173C2×C22⋊C4—31no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—31no—
176C2×C22⋊C4—64no—
177C2×C22⋊C4C2×D311yescharacteristic
178C2×C22⋊C4C2×D311yescharacteristic
179C2×C22⋊C4C2×D311yescharacteristic, complemented
180C2×C22⋊C4C2×D311yescharacteristic, complemented
181C2×C42—31no—
182#95—31no—
183#95—31no—
184#95—31no—
185#95C2×D311yescharacteristic, complemented
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3C2×D412yes—
199C23×C3C2×D412yes—
200C23×C3C2411yescharacteristic
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—28no—
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—44no—
220C22×D3—44no—
221C22×D3—44no—
222C22×D3—44no—
223C22×D3—44no—
224C22×D3—44no—
225C22×D3C2×D412yes—
226C22×D3C2×D412yes—
227C22×D3#4112yes—
228C22×D3#4112yes—
229C3×D4—44no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4C2×D412yes—
245#67—28no—
246#67—44no—
247#67—44no—
248#67—44no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—44no—
261C2×Dic3C2×D412yes—
262C2×Dic3C2×D412yes—
263C2×Dic3C2×D412yes—
264C2×Dic3C2×D412yes—
265D12—44no—
266D12—44no—
267C4×D3—44no—
268C4×D3—44no—
269C24—31no—
270C24—31no—
271C24—31no—
272C24—62no—
273C24—62no—
274C24—62no—
275C24—62no—
276C24—62no—
277C24—121no—
278C24—121no—
279C24C22×D311yescharacteristic
280C24C22×D311yescharacteristic
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—34no—
284C2×D4—41no—
285C2×D4—62no—
286C2×D4—62no—
287C2×D4—62no—
288C2×D4—62no—
289C2×D4—62no—
290C2×D4—62no—
291C2×D4—62no—
292C2×D4—62no—
293C2×D4—62no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—62no—
297C2×D4—62no—
298C2×D4—121no—
299C2×D4—121no—
300C2×D4—121no—
301C2×D4—121no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—62no—
308C22×C4—62no—
309C22×C4—62no—
310C22×C4—62no—
311C22×C4—62no—
312C22×C4—62no—
313C22×C4—121no—
314C22×C4—121no—
315C22×C4—121no—
316C22×C4C22×D311yescharacteristic
317C22×C4C22×D311yescharacteristic
318C22×C4C22×D311yescharacteristic
319C22×C4C22×D311yescharacteristic
320C22×C4C22×D311yescharacteristic
321C4⋊C4—41no—
322C4⋊C4—62no—
323C4⋊C4—62no—
324C4⋊C4—62no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—34no—
330C22⋊C4—34no—
331C22⋊C4—62no—
332C22⋊C4—62no—
333C22⋊C4—62no—
334C22⋊C4—62no—
335C22⋊C4—62no—
336C22⋊C4—62no—
337C22⋊C4—62no—
338C22⋊C4—62no—
339C22⋊C4—121no—
340C42—62no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3C22×D411yescharacteristic
356C22×C3C22×D411yescharacteristic
357C22×C3C22×D411yescharacteristic
358C22×C3C2×#4111yescharacteristic
359C22×C3C2×#4111yescharacteristic
360C22×C3H(5,𝔽2)11yescharacteristic
361C22×C3H(5,𝔽2)11yescharacteristic
362C2×D3—22no—
363C2×D3—22no—
364C2×D3—22no—
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—22no—
368C2×D3—22no—
369C2×D3—22no—
370C2×D3—22no—
371C2×D3—416no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—41no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—41no—
381C2×D3—41no—
382C2×D3—41no—
383C2×D3#12114yescomplemented
384C3×C4—22no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—41no—
388C3×C4—41no—
389Dic3—22no—
390Dic3—22no—
391Dic3—22no—
392Dic3—22no—
393Dic3—41no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—32no—
407C23—32no—
408C23—32no—
409C23—32no—
410C23—68no—
411C23—61no—
412C23—61no—
413C23—61no—
414C23—61no—
415C23—61no—
416C23—61no—
417C23—61no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—61no—
422C23—61no—
423C23—61no—
424C23—61no—
425C23—61no—
426C23—61no—
427C23—61no—
428C23—124no—
429C23—124no—
430C23—124no—
431C23—124no—
432C23—124no—
433C23—124no—
434C23D3×D412yes—
435C23D3×D412yes—
436C23C23×D311yescharacteristic
437D4—44no—
438D4—68no—
439D4—124no—
440D4—124no—
441D4—124no—
442D4—124no—
443D4—124no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—124no—
474C2×C4—124no—
475C2×C4—124no—
476C2×C4D3×D412yes—
477C2×C3—42no—
478C2×C3—42no—
479C2×C3C2×#12111yescharacteristic
480C2×C3#52511yescharacteristic
481C2×C3#53811yescharacteristic
482C2×C3D4211yescharacteristic
483C2×C3D4211yescharacteristic
484C2×C3#54611yescharacteristic
485C2×C3#54611yescharacteristic
486D3—24no—
487D3—42no—
488D3—81no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—34no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—62no—
505C22—62no—
506C22—62no—
507C22—62no—
508C22—62no—
509C22—62no—
510C22—62no—
511C22—62no—
512C22—62no—
513C22—1216no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22—121no—
522C22—121no—
523C22—121no—
524C22—121no—
525C22C2×D3×D411yescharacteristic
526C22C2×D3×D411yescharacteristic
527C22C2×D3×D411yescharacteristic
528C22#100411yescharacteristic
529C22D3×#4111yescharacteristic
530C22D3×#4111yescharacteristic
531C22#100911yescharacteristic
532C4—22no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—62no—
538C4—62no—
539C4—62no—
540C4—62no—
541C4—121no—
542C3#242411yescharacteristic, complemented, Sylow
543C2—42no—
544C2—42no—
545C2—64no—
546C2—122no—
547C2—241no—
548C2#559011yescharacteristic
549C2D3×#12111yescharacteristic
550C2#560911yescharacteristic
551C2#561011yescharacteristic
552C2#565411yescharacteristic
553C2#565611yescharacteristic
554C2#567811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#394C2
hypercenter#394D3
hypocenterC3#2424
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#937C2semidirect
3. C2×#884C2semidirect
4. C2×#882C2semidirect
5. C2×#67⋊C4C2semidirect
6. C2×D3×C22⋊C4C2semidirect
7. C3×#394C2semidirect
8. #4989C2semidirect
9. #4988C2semidirect
10. #4960C2semidirect
11. #4959C2semidirect
12. #4958C2semidirect
13. #4944C2semidirect
14. #4676C2semidirect
15. #4665C2semidirect
22. C22×#67C22semidirect
23. C23×Dic3C22semidirect
28. C2×C3×C4⋊C4C22semidirect
31. C2×C3×C22⋊C4C22semidirect
32. C2×C3×C22⋊C4C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. C2×(C2×D3)⋊C4C22semidirect
45. C2×(C2×D3)⋊C4C22semidirect
46. C2×Dic3⋊C4C22semidirect
47. C2×Dic3⋊C4C22semidirect
48. C2×Dic3⋊C4C22semidirect
49. C2×C4×Dic3C22semidirect
54. C3×#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
57. C3⋊#95C22semidirect
66. #394D3semidirect
104. C2×#67D4semidirect
131. #217D4semidirect
140. (C2×D3)⋊C4D4semidirect
164. C2×C4⋊C4C2×D3semidirect
179. C2×C22⋊C4C2×D3semidirect
180. C2×C22⋊C4C2×D3semidirect
185. #95C2×D3semidirect
383. C2×D3#121semidirect
542. C3#2424semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#9372
C2×#8842
C2×#8822
C2×#67⋊C42
C2×D3×C22⋊C42
C3×#3942
#49892
#49882
#49602
#49592
#49582
#49442
#46762
#46652
#24243