Finite Group Databasebeta

← #74910

Subgroups — #74910

Order 384.

816 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#938C211yesmaximal, characteristic, complemented
2C2×#937C211yesmaximal, characteristic, complemented
3C2×#930C211yesmaximal, characteristic, complemented
4C2×#882C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6#5213C211yesmaximal, characteristic, complemented
7#4961C211yesmaximal, characteristic, complemented
8#4961C211yesmaximal, characteristic, complemented
9#4960C211yesmaximal, characteristic, complemented
10#4955C211yesmaximal, characteristic, complemented
11#4953C211yesmaximal, characteristic, complemented
12#4677C211yesmaximal, characteristic, complemented
13#4674C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2668—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic, complemented
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic, complemented
24C22×D12C2211yescharacteristic
25C22×D12C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic, complemented
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic, complemented
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic, complemented
33#938—24no—
34#937—24no—
35#930—24no—
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
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C4⋊Dic3C2211yescharacteristic, complemented
47C2×C4⋊Dic3C2211yescharacteristic, complemented
48C2×C4⋊Dic3C2211yescharacteristic, complemented
49#882—24no—
50C3×#95C2211yescharacteristic, complemented
51C3×#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C2×#121—31no—
57C2×#121—31no—
58C2×#120—31no—
59C2×#120—31no—
60#399—31no—
61#397—31no—
62#397—31no—
63#394—31no—
64#394—31no—
65#392—31no—
66#386—31no—
67#386—31no—
68#386—31no—
69#386D311yescharacteristic, complemented
70#379—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—41no—
77C23×D3—41no—
78C23×D3—41no—
79C23×D3—41no—
80C23×D3C2311yescharacteristic
81C23×D3C2311yescharacteristic
82C23×D3C2311yescharacteristic
83C2×C3×D4—41no—
84C2×C3×D4—41no—
85C2×C3×D4D414yescomplemented
86C22×C3×C4—22no—
87C22×C3×C4—41no—
88C22×C3×C4—41no—
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—22no—
98C2×#67—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—22no—
102C2×#67—41no—
103C2×#67—41no—
104C2×#67—41no—
105C2×#67—41no—
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C2×D12—22no—
112C2×D12—22no—
113C2×D12—41no—
114C2×D12—41no—
115C2×D12—41no—
116C2×D12D414yescomplemented
117C2×C4×D3—22no—
118C2×C4×D3—41no—
119C2×C4×D3—41no—
120C3×C22⋊C4—22no—
121C3×C22⋊C4—41no—
122C3×C22⋊C4—41no—
123#217—22no—
124#217—22no—
125#217—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—22no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—41no—
133(C2×D3)⋊C4—41no—
134(C2×D3)⋊C4—41no—
135(C2×D3)⋊C4—41no—
136C4⋊Dic3—22no—
137C4⋊Dic3—22no—
138C4⋊Dic3—41no—
139C25—31no—
140C22×D4—31no—
141C22×D4—31no—
142C22×D4—31no—
143C22×D4—31no—
144C22×D4—31no—
145C22×D4—31no—
146C22×D4C2×D311yescharacteristic
147C23×C4—31no—
148C23×C4C2×D311yescharacteristic, complemented
149#121—64no—
150#121—64no—
151#120—64no—
152#120—64no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4—31no—
155C2×C4⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4—31no—
160C2×C22⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4—31no—
163C2×C22⋊C4—31no—
164C2×C22⋊C4—31no—
165C2×C22⋊C4—31no—
166C2×C22⋊C4—31no—
167C2×C22⋊C4—31no—
168C2×C22⋊C4—31no—
169C2×C22⋊C4C2×D311yescharacteristic
170C2×C22⋊C4C2×D311yescharacteristic
171C2×C22⋊C4C2×D311yescharacteristic, complemented
172#95—31no—
173#95—31no—
174#95—31no—
175#95—31no—
176#95C2×D311yescharacteristic, complemented
177#95C2×D311yescharacteristic, complemented
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3C2×D412yes—
191C23×C3C2×D412yes—
192C23×C3C2411yescharacteristic
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
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—44no—
212C22×D3—44no—
213C22×D3—44no—
214C22×D3—44no—
215C22×D3—44no—
216C22×D3—44no—
217C22×D3—44no—
218C22×D3C2×D412yes—
219C22×D3C2×D412yes—
220C22×D3#4112yes—
221C3×D4—44no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—44no—
236C2×C3×C4C2×D412yes—
237C2×C3×C4C2×D412yes—
238#67—44no—
239#67—44no—
240#67—44no—
241#67—44no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257D12—44no—
258D12—44no—
259C4×D3—44no—
260C24—31no—
261C24—31no—
262C24—31no—
263C24—62no—
264C24—62no—
265C24—62no—
266C24—121no—
267C24—121no—
268C24—121no—
269C24—121no—
270C24C22×D311yescharacteristic
271C24C22×D311yescharacteristic
272C2×D4—34no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—62no—
276C2×D4—62no—
277C2×D4—62no—
278C2×D4—62no—
279C2×D4—62no—
280C2×D4—62no—
281C2×D4—62no—
282C2×D4—62no—
283C2×D4—62no—
284C2×D4—62no—
285C2×D4—121no—
286C2×D4—121no—
287C2×D4—121no—
288C2×D4—121no—
289C2×D4—121no—
290C2×D4—121no—
291C2×D4—121no—
292C2×D4D1214yescomplemented
293C22×C4—22no—
294C22×C4—31no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—31no—
298C22×C4—31no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—62no—
302C22×C4—121no—
303C22×C4—121no—
304C22×C4C22×D311yescharacteristic
305C22×C4C22×D311yescharacteristic
306C22×C4C22×D311yescharacteristic
307C22×C4C22×D311yescharacteristic
308C22×C4C22×D311yescharacteristic
309C4⋊C4—62no—
310C4⋊C4—62no—
311C4⋊C4—121no—
312C22⋊C4—22no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—62no—
316C22⋊C4—62no—
317C22⋊C4—62no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C22⋊C4—62no—
322C22⋊C4—62no—
323C22⋊C4—62no—
324C22⋊C4—121no—
325C22⋊C4—121no—
326C22⋊C4—121no—
327C22⋊C4—121no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3C22×D411yescharacteristic
343C22×C3C22×D411yescharacteristic
344C22×C3C2×#4111yescharacteristic
345C22×C3H(5,𝔽2)11yescharacteristic
346C22×C3H(5,𝔽2)11yescharacteristic
347C22×C3H(5,𝔽2)11yescharacteristic
348C22×C3H(5,𝔽2)11yescharacteristic
349C2×D3—22no—
350C2×D3—22no—
351C2×D3—22no—
352C2×D3—22no—
353C2×D3—22no—
354C2×D3—22no—
355C2×D3—22no—
356C2×D3—22no—
357C2×D3—22no—
358C2×D3—416no—
359C2×D3—41no—
360C2×D3—41no—
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C2×D3—41no—
365C2×D3—41no—
366C2×D3—41no—
367C2×D3—41no—
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376Dic3—41no—
377Dic3—41no—
378Dic3—41no—
379Dic3—41no—
380Dic3—41no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—32no—
394C23—32no—
395C23—32no—
396C23—61no—
397C23—61no—
398C23—61no—
399C23—61no—
400C23—61no—
401C23—61no—
402C23—61no—
403C23—61no—
404C23—61no—
405C23—61no—
406C23—61no—
407C23—61no—
408C23—61no—
409C23—61no—
410C23—61no—
411C23—61no—
412C23—61no—
413C23—61no—
414C23—124no—
415C23—124no—
416C23—124no—
417C23—124no—
418C23—124no—
419C23—124no—
420C23—124no—
421C23C2×D1212yes—
422C23C2×D1212yes—
423C23C23×D311yescharacteristic
424D4—44no—
425D4—124no—
426D4—124no—
427D4—124no—
428D4—124no—
429D4—124no—
430D4—124no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—44no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—124no—
461C2×C4C2×D1212yes—
462C2×C4D3×D412yes—
463C2×C3—42no—
464C2×C3—42no—
465C2×C3#53411yescharacteristic
466C2×C3#53411yescharacteristic
467C2×C3#53811yescharacteristic
468C2×C3D4211yescharacteristic
469C2×C3#54611yescharacteristic
470C2×C3#54611yescharacteristic
471C2×C3#56011yescharacteristic
472D3—42no—
473D3—42no—
474D3—42no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—62no—
490C22—62no—
491C22—62no—
492C22—62no—
493C22—62no—
494C22—62no—
495C22—62no—
496C22—62no—
497C22—62no—
498C22—1216no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22C22×D1211yescharacteristic
512C22C2×D3×D411yescharacteristic
513C22#100411yescharacteristic
514C22#100411yescharacteristic
515C22#100411yescharacteristic
516C22D3×#4111yescharacteristic
517C22#100911yescharacteristic
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—121no—
524C4—121no—
525C4—121no—
526C4—121no—
527C4—121no—
528C3#266811yescharacteristic, complemented, Sylow
529C2—42no—
530C2—42no—
531C2—122no—
532C2—122no—
533C2—122no—
534C2#549311yescharacteristic
535C2D4×D1211yescharacteristic
536C2#555411yescharacteristic
537C2#558911yescharacteristic
538C2#561211yescharacteristic
539C2#562011yescharacteristic
540C2#565711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2668
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#938C2semidirect
2. C2×#937C2semidirect
3. C2×#930C2semidirect
4. C2×#882C2semidirect
5. C3×#386C2semidirect
6. #5213C2semidirect
7. #4961C2semidirect
8. #4961C2semidirect
9. #4960C2semidirect
10. #4955C2semidirect
11. #4953C2semidirect
12. #4677C2semidirect
13. #4674C2semidirect
14. #4665C2semidirect
15. #4665C2semidirect
19. C23×C3×C4C22semidirect
23. C22×#67C22semidirect
26. C22×C4×D3C22semidirect
29. C2×C3×C22⋊C4C22semidirect
32. C2×#217C22semidirect
44. C2×(C2×D3)⋊C4C22semidirect
45. C2×(C2×D3)⋊C4C22semidirect
46. C2×C4⋊Dic3C22semidirect
47. C2×C4⋊Dic3C22semidirect
48. C2×C4⋊Dic3C22semidirect
50. C3×#95C22semidirect
51. C3×#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
69. #386D3semidirect
85. C2×C3×D4D4semidirect
116. C2×D12D4semidirect
148. C23×C4C2×D3semidirect
171. C2×C22⋊C4C2×D3semidirect
176. #95C2×D3semidirect
177. #95C2×D3semidirect
292. C2×D4D12semidirect
528. C3#2668semidirect

Maximal subgroups

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

subgroupindex
C2×#9382
C2×#9372
C2×#9302
C2×#8822
C3×#3862
#52132
#49612
#49602
#49552
#49532
#46772
#46742
#46652
#26683