Finite Group Databasebeta

← #77689

Subgroups — #77689

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×#895C211yesmaximal, characteristic, complemented
2C2×#884C211yesmaximal, characteristic, complemented
3C2×#882C211yesmaximal, characteristic, complemented
4C2×#882C211yesmaximal, characteristic, complemented
5C3×#397C211yesmaximal, characteristic, complemented
6#4993C211yesmaximal, characteristic, complemented
7#4959C211yesmaximal, characteristic, complemented
8#4956C211yesmaximal, characteristic, complemented
9#4955C211yesmaximal, characteristic, complemented
10#4675C211yesmaximal, characteristic, complemented
11#4672C211yesmaximal, characteristic, complemented
12#4671C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2668—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×D12C2211yescharacteristic, complemented
25C22×C4×D3C2211yescharacteristic, complemented
26C22×C4×D3C2211yescharacteristic, complemented
27C2×C3×C4⋊C4C2211yescharacteristic, complemented
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46#895—24no—
47#884—24no—
48#882—24no—
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#397D311yescharacteristic, complemented
63#394—31no—
64#394—31no—
65#392—31no—
66#386—31no—
67#386—31no—
68#386—31no—
69#386—31no—
70#379—31no—
71C24×C3C2311yescharacteristic
72C23×D3—22no—
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—41no—
76C23×D3—41no—
77C23×D3—41no—
78C23×D3—41no—
79C23×D3C2311yescharacteristic
80C23×D3C2311yescharacteristic
81C23×D3C2311yescharacteristic
82C23×D3C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—41no—
92C2×#67—41no—
93C2×#67—41no—
94C2×#67D414yescomplemented
95C22×Dic3C2311yescharacteristic
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C2×D12—22no—
100C2×D12—22no—
101C2×D12—22no—
102C2×D12—22no—
103C2×D12—22no—
104C2×D12—22no—
105C2×D12—22no—
106C2×D12—22no—
107C2×D12—41no—
108C2×D12—41no—
109C2×D12—41no—
110C2×D12—41no—
111C2×D12—41no—
112C2×D12—41no—
113C2×D12D414yescomplemented
114C2×C4×D3—22no—
115C2×C4×D3—22no—
116C2×C4×D3—41no—
117C2×C4×D3—41no—
118C2×C4×D3—41no—
119C2×C4×D3—41no—
120C3×C4⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—22no—
123C3×C22⋊C4—22no—
124#217—41no—
125(C2×D3)⋊C4—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—
136(C2×D3)⋊C4—41no—
137Dic3⋊C4—22no—
138Dic3⋊C4—41no—
139C25—31no—
140C22×D4—31no—
141C22×D4—31no—
142C22×D4—31no—
143C22×D4—31no—
144C22×D4—31no—
145C22×D4—31no—
146C22×D4—31no—
147C23×C4—31no—
148C23×C4—31no—
149#121—64no—
150#121—64no—
151#120—64no—
152#120—64no—
153C2×C4⋊C4—31no—
154C2×C4⋊C4—31no—
155C2×C4⋊C4C2×D311yescharacteristic, complemented
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
172#95—31no—
173#95—31no—
174#95—31no—
175#95C2×D311yescharacteristic, complemented
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×C3C2×D412yes—
185C23×C3C2411yescharacteristic
186C22×D3—21no—
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—21no—
192C22×D3—21no—
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—44no—
211C22×D3—44no—
212C22×D3—44no—
213C22×D3—44no—
214C22×D3—44no—
215C22×D3—44no—
216C22×D3—44no—
217C22×D3C2×D412yes—
218C22×D3C2×D412yes—
219C22×D3C2×D412yes—
220C22×D3#4112yes—
221C2×C3×C4—21no—
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—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4C2×D412yes—
239#67—44no—
240#67—44no—
241C2×Dic3—21no—
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×Dic3C2×D412yes—
253D12—44no—
254D12—44no—
255D12—44no—
256D12—44no—
257D12—44no—
258C4×D3—44no—
259C4×D3—44no—
260C24—31no—
261C24—31no—
262C24—31no—
263C24—31no—
264C24—62no—
265C24—62no—
266C24—62no—
267C24—121no—
268C24—121no—
269C24—121no—
270C24—121no—
271C24C22×D311yescharacteristic
272C2×D4—34no—
273C2×D4—34no—
274C2×D4—62no—
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—121no—
285C2×D4—121no—
286C2×D4—121no—
287C2×D4—121no—
288C2×D4—121no—
289C2×D4—121no—
290C2×D4—121no—
291C2×D4—121no—
292C2×D4—121no—
293C22×C4—31no—
294C22×C4—31no—
295C22×C4—31no—
296C22×C4—31no—
297C22×C4—62no—
298C22×C4—62no—
299C22×C4—121no—
300C22×C4—121no—
301C22×C4—121no—
302C22×C4—121no—
303C22×C4C22×D311yescharacteristic
304C22×C4C22×D311yescharacteristic
305C22×C4C22×D311yescharacteristic
306C22×C4C22×D311yescharacteristic
307C22×C4C22×D311yescharacteristic
308C22×C4C22×D311yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—62no—
311C4⋊C4—121no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—62no—
316C22⋊C4—62no—
317C22⋊C4—62no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C22⋊C4—62no—
322C22⋊C4—121no—
323C22⋊C4—121no—
324C22⋊C4—121no—
325C22⋊C4—121no—
326C22⋊C4—121no—
327C22⋊C4—121no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3C22×D411yescharacteristic
336C22×C3C22×D411yescharacteristic
337C22×C3C2×#4111yescharacteristic
338C22×C3H(5,𝔽2)11yescharacteristic
339C22×C3H(5,𝔽2)11yescharacteristic
340C22×C3H(5,𝔽2)11yescharacteristic
341C22×C3H(5,𝔽2)11yescharacteristic
342C2×D3—22no—
343C2×D3—22no—
344C2×D3—22no—
345C2×D3—22no—
346C2×D3—22no—
347C2×D3—22no—
348C2×D3—22no—
349C2×D3—22no—
350C2×D3—22no—
351C2×D3—22no—
352C2×D3—22no—
353C2×D3—22no—
354C2×D3—416no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—41no—
358C2×D3—41no—
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—41no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—41no—
377Dic3—22no—
378Dic3—41no—
379Dic3—41no—
380Dic3—41no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—32no—
388C23—32no—
389C23—32no—
390C23—32no—
391C23—61no—
392C23—61no—
393C23—61no—
394C23—61no—
395C23—61no—
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—61no—
415C23—124no—
416C23—124no—
417C23—124no—
418C23—124no—
419C23—124no—
420C23—124no—
421C23—124no—
422C23D3×D412yes—
423C23C23×D311yescharacteristic
424D4—124no—
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—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—32no—
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×C4—124no—
462C2×C4D3×D412yes—
463C2×C3—42no—
464C2×C3#53411yescharacteristic
465C2×C3#53411yescharacteristic
466C2×C3#53811yescharacteristic
467C2×C3D4211yescharacteristic
468C2×C3#54611yescharacteristic
469C2×C3#54611yescharacteristic
470C2×C3#56011yescharacteristic
471D3—42no—
472D3—42no—
473D3—42no—
474D3—42no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—62no—
483C22—62no—
484C22—62no—
485C22—62no—
486C22—62no—
487C22—62no—
488C22—62no—
489C22—62no—
490C22—62no—
491C22—62no—
492C22—62no—
493C22—62no—
494C22—1216no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22C2×D3×D411yescharacteristic
512C22C2×D3×D411yescharacteristic
513C22D3×#4111yescharacteristic
514C22#100911yescharacteristic
515C22#100911yescharacteristic
516C22#100911yescharacteristic
517C22#100911yescharacteristic
518C4—22no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—62no—
525C4—121no—
526C4—121no—
527C4—121no—
528C3#266811yescharacteristic, complemented, Sylow
529C2—42no—
530C2—122no—
531C2—122no—
532C2—122no—
533C2—122no—
534C2#560911yescharacteristic
535C2#565311yescharacteristic
536C2#565311yescharacteristic
537C2#565411yescharacteristic
538C2#567611yescharacteristic
539C2#570411yescharacteristic
540C2#571111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#397C2
hypercenter#397D3
hypocenterC3#2668
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #397

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. C3×#397C2semidirect
6. #4993C2semidirect
7. #4959C2semidirect
8. #4956C2semidirect
9. #4955C2semidirect
10. #4675C2semidirect
11. #4672C2semidirect
12. #4671C2semidirect
13. #4665C2semidirect
14. #4665C2semidirect
15. #4665C2semidirect
24. C22×D12C22semidirect
25. C22×C4×D3C22semidirect
26. C22×C4×D3C22semidirect
27. C2×C3×C4⋊C4C22semidirect
40. C2×(C2×D3)⋊C4C22semidirect
41. C2×(C2×D3)⋊C4C22semidirect
42. C2×(C2×D3)⋊C4C22semidirect
43. C2×(C2×D3)⋊C4C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
50. C3×#95C22semidirect
51. C3×#95C22semidirect
52. C3×#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
62. #397D3semidirect
94. C2×#67D4semidirect
113. C2×D12D4semidirect
155. C2×C4⋊C4C2×D3semidirect
175. #95C2×D3semidirect
176. #95C2×D3semidirect
177. #95C2×D3semidirect
528. C3#2668semidirect

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
C3×#3972
#49932
#49592
#49562
#49552
#46752
#46722
#46712
#46652
#26683