Finite Group Databasebeta

← #75826

Subgroups — #75826

Order 384.

808 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#893C211yesmaximal, characteristic, complemented
2C2×#882C211yesmaximal, characteristic
3C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×#388C211yesmaximal, characteristic, complemented
5#4990C211yesmaximal, characteristic, complemented
6#4957C211yesmaximal, characteristic, complemented
7#4956C211yesmaximal, characteristic, complemented
8#4955C211yesmaximal, characteristic, complemented
9#4951C211yesmaximal, characteristic, complemented
10#4939C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#4669C211yesmaximal, characteristic, complemented
13#4668C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2321—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×D12C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×C4×D3C2211yescharacteristic
22C22×C4×D3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic, complemented
24C2×C3×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C42C2211yescharacteristic, complemented
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
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, complemented
40C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C4⋊Dic3C2211yescharacteristic, complemented
43C2×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic3C2211yescharacteristic, complemented
45C2×C4×Dic3C2211yescharacteristic, complemented
46#893—24no—
47#882C418yescomplemented
48D3×C22⋊C4—24no—
49C3×#95C2211yescharacteristic, complemented
50C3×#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C2×#120—31no—
56C2×C4×D4—31no—
57C22×C22⋊C4—31no—
58#390—31no—
59#390—31no—
60#388—31no—
61#388—31no—
62#388—31no—
63#388D311yescharacteristic, complemented
64#386—31no—
65#386—31no—
66#386—31no—
67#385—31no—
68#379—31no—
69C4×C22⋊C4—31no—
70C24×C3C2311yescharacteristic
71C23×D3—22no—
72C23×D3—22no—
73C23×D3—41no—
74C23×D3—41no—
75C23×D3—41no—
76C23×D3—41no—
77C23×D3C2×C414yescomplemented
78C23×D3C2311yescharacteristic
79C23×D3C2311yescharacteristic
80C23×D3C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C2×#67—41no—
88C2×#67—41no—
89C2×#67C2×C414yescomplemented
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C2×D12—22no—
96C2×D12—22no—
97C2×D12—41no—
98C2×D12—41no—
99C2×D12C2×C414yes—
100C2×D12C2×C414yescomplemented
101C2×C4×D3—22no—
102C2×C4×D3—22no—
103C2×C4×D3—41no—
104C2×C4×D3—41no—
105C2×C4×D3—41no—
106C2×C4×D3—41no—
107C2×C4×D3—41no—
108C2×C4×D3—41no—
109C2×C4×D3D414yescomplemented
110C3×C4⋊C4—22no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4—41no—
113C3×C22⋊C4C2×C414yescomplemented
114C3×C42—41no—
115#217—22no—
116#217—41no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—41no—
123(C2×D3)⋊C4—41no—
124(C2×D3)⋊C4—41no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4C2×C414yescomplemented
127(C2×D3)⋊C4C2×C414yescomplemented
128C4⋊Dic3—41no—
129Dic3⋊C4—41no—
130C4×Dic3—22no—
131C4×Dic3—41no—
132C25—31no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C23×C4—31no—
137C23×C4—31no—
138C23×C4—31no—
139#120—38no—
140C4×D4—64no—
141C2×C4⋊C4—31no—
142C2×C4⋊C4—31no—
143C2×C4⋊C4C2×D311yescharacteristic, complemented
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—64no—
158C2×C22⋊C4C2×D311yescharacteristic
159C2×C22⋊C4C2×D311yescharacteristic
160C2×C22⋊C4C2×D311yescharacteristic
161C2×C42—31no—
162C2×C42—31no—
163C2×C42C2×D311yescharacteristic, complemented
164#95—31no—
165#95—31no—
166#95—31no—
167#95—31no—
168#95C2×D311yescharacteristic, complemented
169#95C2×D311yescharacteristic, complemented
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3C22×C412yes—
177C23×C3C2411yescharacteristic
178C22×D3—21no—
179C22×D3—21no—
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
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—28no—
195C22×D3—44no—
196C22×D3—44no—
197C22×D3—44no—
198C22×D3—44no—
199C22×D3—44no—
200C22×D3—44no—
201C22×D3C22×C412yes—
202C22×D3C22×C412yes—
203C22×D3C22×C412yes—
204C22×D3C2×D412yes—
205C22×D3#4112yes—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4C22×C412yes—
222C2×C3×C4C22×C412yes—
223C2×C3×C4C2×D412yes—
224#67—44no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3C22×C412yes—
239C2×Dic3C2×D412yes—
240D12—28no—
241D12—44no—
242C4×D3—44no—
243C4×D3—44no—
244C4×D3—44no—
245C24—31no—
246C24—31no—
247C24—31no—
248C24—34no—
249C24—62no—
250C24—62no—
251C24—121no—
252C24—121no—
253C24—121no—
254C24—121no—
255C24C22×D311yescharacteristic
256C2×D4—34no—
257C2×D4—34no—
258C2×D4—34no—
259C2×D4—62no—
260C2×D4—62no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—34no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—62no—
272C22×C4—62no—
273C22×C4—121no—
274C22×C4—121no—
275C22×C4—121no—
276C22×C4—121no—
277C22×C4—121no—
278C22×C4—121no—
279C22×C4C22×D311yescharacteristic
280C22×C4C22×D311yescharacteristic
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—121no—
287C4⋊C4—121no—
288C22⋊C4—22no—
289C22⋊C4—34no—
290C22⋊C4—34no—
291C22⋊C4—41no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—121no—
299C22⋊C4—121no—
300C22⋊C4—121no—
301C22⋊C4—121no—
302C22⋊C4—121no—
303C22⋊C4C4×D314yescomplemented
304C42—41no—
305C42—62no—
306C42—121no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3C23×C411yescharacteristic
315C22×C3C22×D411yescharacteristic
316C22×C3C2×#4111yescharacteristic
317C22×C3H(5,𝔽2)11yescharacteristic
318C22×C3H(5,𝔽2)11yescharacteristic
319C22×C3H(5,𝔽2)11yescharacteristic
320C22×C3H(5,𝔽2)11yescharacteristic
321C2×D3—22no—
322C2×D3—22no—
323C2×D3—22no—
324C2×D3—22no—
325C2×D3—22no—
326C2×D3—22no—
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—22no—
330C2×D3—22no—
331C2×D3—22no—
332C2×D3—22no—
333C2×D3—416no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3C4×D414yes—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349Dic3—22no—
350Dic3—22no—
351Dic3—41no—
352Dic3—41no—
353Dic3—41no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—32no—
361C23—32no—
362C23—32no—
363C23—32no—
364C23—32no—
365C23—68no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—124no—
383C23—124no—
384C23—124no—
385C23—124no—
386C23—124no—
387C23—124no—
388C23C2×C4×D312yes—
389C23C23×D311yescharacteristic
390D4—68no—
391D4—124no—
392D4—124no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—32no—
409C2×C4—32no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—124no—
424C2×C4—124no—
425C2×C4—124no—
426C2×C4C2×C4×D312yes—
427C2×C4C2×C4×D312yes—
428C2×C4D3×D412yes—
429C2×C3—42no—
430C2×C3C2×C4×D411yescharacteristic
431C2×C3#51811yescharacteristic
432C2×C3#51811yescharacteristic
433C2×C3#53411yescharacteristic
434C2×C3#53511yescharacteristic
435C2×C3#53811yescharacteristic
436C2×C3#53811yescharacteristic
437D3—24no—
438D3—42no—
439D3—42no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—34no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—62no—
452C22—62no—
453C22—62no—
454C22—62no—
455C22—62no—
456C22—62no—
457C22—62no—
458C22—62no—
459C22—62no—
460C22—1216no—
461C22—121no—
462C22—121no—
463C22—121no—
464C22—121no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22C22×C4×D311yescharacteristic
470C22C2×D3×D411yescharacteristic
471C22#100411yescharacteristic
472C22D3×#4111yescharacteristic
473C22#100911yescharacteristic
474C22#100911yescharacteristic
475C22#100911yescharacteristic
476C4—22no—
477C4—22no—
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—62no—
483C4—62no—
484C4—121no—
485C4—121no—
486C4—121no—
487C3#232111yescharacteristic, complemented, Sylow
488C2—42no—
489C2—64no—
490C2—122no—
491C2—122no—
492C2#552111yescharacteristic
493C2C4×D3×D411yescharacteristic
494C2#554511yescharacteristic
495C2#560511yescharacteristic
496C2#565711yescharacteristic
497C2#567411yescharacteristic
498C2#570411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#388C2
socle, cosocleC23×C3C24
prime radicalC2×#882C2
hypercenter#388D3
hypocenterC3#2321
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#893C2semidirect
3. C2×D3×C22⋊C4C2semidirect
4. C3×#388C2semidirect
5. #4990C2semidirect
6. #4957C2semidirect
7. #4956C2semidirect
8. #4955C2semidirect
9. #4951C2semidirect
10. #4939C2semidirect
11. C4×(C2×D3)⋊C4C2semidirect
12. #4669C2semidirect
13. #4668C2semidirect
14. #4665C2semidirect
15. #4665C2semidirect
23. C22×C4×D3C22semidirect
24. C2×C3×C4⋊C4C22semidirect
28. C2×C3×C42C22semidirect
39. C2×(C2×D3)⋊C4C22semidirect
40. C2×(C2×D3)⋊C4C22semidirect
41. C2×(C2×D3)⋊C4C22semidirect
42. C2×C4⋊Dic3C22semidirect
43. C2×Dic3⋊C4C22semidirect
44. C2×C4×Dic3C22semidirect
45. C2×C4×Dic3C22semidirect
47. #882C4semidirect
49. C3×#95C22semidirect
50. C3×#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
63. #388D3semidirect
77. C23×D3C2×C4semidirect
89. C2×#67C2×C4semidirect
100. C2×D12C2×C4semidirect
109. C2×C4×D3D4semidirect
113. C3×C22⋊C4C2×C4semidirect
126. (C2×D3)⋊C4C2×C4semidirect
127. (C2×D3)⋊C4C2×C4semidirect
143. C2×C4⋊C4C2×D3semidirect
163. C2×C42C2×D3semidirect
168. #95C2×D3semidirect
169. #95C2×D3semidirect
303. C22⋊C4C4×D3semidirect
487. C3#2321semidirect

Maximal subgroups

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

subgroupindex
C2×#8932
C2×#8822
C2×D3×C22⋊C42
C3×#3882
#49902
#49572
#49562
#49552
#49512
#49392
C4×(C2×D3)⋊C42
#46692
#46682
#46652
#23213