Finite Group Databasebeta

← #80924

Subgroups — #80924

Order 384.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5639C211yesmaximal, characteristic, complemented
2#5630C211yesmaximal, characteristic
3C3×#470C211yesmaximal, characteristic, complemented
4#5187C211yesmaximal, characteristic, complemented
5#5185C211yesmaximal, characteristic, complemented
6#5131C211yesmaximal, characteristic, complemented
7#5128C211yesmaximal, characteristic, complemented
8#5046C211yesmaximal, characteristic, complemented
9#5045C211yesmaximal, characteristic, complemented
10#4871C211yesmaximal, characteristic, complemented
11#4863C211yesmaximal, characteristic, complemented
12#4812C211yesmaximal, characteristic, complemented
13#4803C211yesmaximal, characteristic, complemented
14#4800C211yesmaximal, characteristic, complemented
15#4788C211yesmaximal, characteristic, complemented
16#3323—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C22×D12C2211yescharacteristic
19C2×C3×Q16C2211yescharacteristic, complemented
20C2×C3×M16C2211yescharacteristic
21C3×C22⋊Q8C2211yescharacteristic
22C3×C22⋊Q8C2211yescharacteristic
23#947C2211yescharacteristic
24#946C2211yescharacteristic, complemented
25Q8×Dic3C2211yescharacteristic, complemented
26C2×#215C2211yescharacteristic
27C2×#215C2211yescharacteristic
28C4×#67C2211yescharacteristic
29#926C2211yescharacteristic
30C2×ΓL(1,𝔽25)C2211yescharacteristic, complemented
31#895—21no—
32#895C2211yescharacteristic
33#894—21no—
34#893C2211yescharacteristic
35#892—21no—
36D3×C4⋊C4C2211yescharacteristic, complemented
37#890C2211yescharacteristic, complemented
38#889—21no—
39#883—21no—
40#882—21no—
41D3×C22⋊C4—21no—
42#879—21no—
43C3×#106C2211yescharacteristic, complemented
44C3×#103C2211yescharacteristic, complemented
45C3×#103C2211yescharacteristic, complemented
46#835C2211yescharacteristic, complemented
47#835C2211yescharacteristic, complemented
48#830C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#821C2211yescharacteristic
53(C2×D3)⋊C8C2211yescharacteristic, complemented
54Dic3⋊C8C2211yescharacteristic, complemented
55C8×Dic3C2211yescharacteristic, complemented
56#809C2211yescharacteristic
57#809C2211yescharacteristic
58#808C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60#552—31no—
61#546—31no—
62#488—31no—
63#485—31no—
64#481—31no—
65#478—31no—
66#470D311yescharacteristic, complemented
67#468—31no—
68#464—31no—
69#452—31no—
70#450—31no—
71C4×SD16—31no—
72#436—31no—
73#418—31no—
74#417—31no—
75C23×D3—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×Q8C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C2×#67D411yescharacteristic
80#239—22no—
81#239—41no—
82C2×D12—22no—
83C2×D12—21no—
84C2×D12—21no—
85C2×D12—21no—
86C2×D12—41no—
87C2×D12C2311yescharacteristic
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3C2311yescharacteristic
93C3×Q16—41no—
94C3×M16—41no—
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4—21no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C22⋊C4—21no—
102C3×C22⋊C4—21no—
103#217—21no—
104#217D411yescharacteristic
105#215—22no—
106#215—41no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4D411yescharacteristic
113C4⋊Dic3—21no—
114C4⋊Dic3—21no—
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120Dic3⋊C4D411yescharacteristic
121C4×Dic3—21no—
122C4×Dic3—21no—
123C4×Dic3C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126ΓL(1,𝔽25)—41no—
127C2×#41—31no—
128C22×D4—31no—
129C2×Q16C2×D311yescharacteristic, complemented
130C2×SD16—31no—
131C2×SD16—31no—
132C2×M16—31no—
133C2×M16C2×D311yescharacteristic
134#126—61no—
135#125—31no—
136#125—61no—
137#124—31no—
138#123—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8C2×D311yescharacteristic
142C22⋊Q8C2×D311yescharacteristic
143#121—31no—
144#121—61no—
145#120—61no—
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4—31no—
149#117—31no—
150#117—61no—
151C2×C4⋊C4—31no—
152C2×C22⋊C4—61no—
153#107—31no—
154#106—31no—
155#106C2×D311yescharacteristic, complemented
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103C2×D311yescharacteristic, complemented
160#103C2×D311yescharacteristic, complemented
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167C22⋊C8—31no—
168C22⋊C8—31no—
169C4×C8—31no—
170C23×C3C2×D411yescharacteristic
171C22×D3—21no—
172C22×D3—21no—
173C22×D3—42no—
174C22×D3—42no—
175C22×D3—81no—
176C22×D3C2×D411yescharacteristic
177C3×Q8—21no—
178C3×Q8—21no—
179C3×Q8—21no—
180C3×Q8—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2411yescharacteristic
189#67—41no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3C2×D411yescharacteristic
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195D12—21no—
196D12—21no—
197D12—21no—
198D12—42no—
199D12—42no—
200D12—81no—
201D12#4112yes—
202C4×D3—21no—
203C4×D3—21no—
204C4×D3—42no—
205C4×D3—42no—
206C4×D3—81no—
207C3×C8—21no—
208C3×C8—21no—
209C3⋊C8—21no—
210C3⋊C8—21no—
211C24—61no—
212#41—62no—
213#41—121no—
214C2×Q8C22×D311yescharacteristic
215C2×Q8C22×D311yescharacteristic
216C2×D4—31no—
217C2×D4—31no—
218C2×D4—31no—
219C2×D4—62no—
220C2×D4—61no—
221C2×D4—61no—
222C2×D4—61no—
223C2×D4—121no—
224C22×C4—31no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4C22×D311yescharacteristic
229Q16—41no—
230SD16—62no—
231SD16—121no—
232M16—41no—
233M16—121no—
234C2×C8—31no—
235C2×C8—31no—
236C2×C8C22×D311yescharacteristic
237C2×C8C22×D311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—31no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4C22×D311yescharacteristic
249C4⋊C4C22×D311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—31no—
253C22⋊C4—31no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C42—31no—
261C42—61no—
262C42—61no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3C22×D411yescharacteristic
267C2×D3—21no—
268C2×D3—22no—
269C2×D3—21no—
270C2×D3—21no—
271C2×D3—41no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C2×D3—84no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4C2×#4111yescharacteristic
283C3×C4H(5,𝔽2)11yescharacteristic
284Dic3—21no—
285Dic3—21no—
286Dic3—21no—
287Dic3—41no—
288Dic3—41no—
289C23—31no—
290C23—61no—
291C23—61no—
292C23—122no—
293C23—122no—
294C23—241no—
295C23D3×D411yescharacteristic
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300D4—32no—
301D4—61no—
302D4—61no—
303D4—61no—
304D4—122no—
305D4—122no—
306D4—121no—
307D4—241no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—31no—
315C2×C4—31no—
316C2×C4—31no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—122no—
322C2×C4—122no—
323C2×C4—241no—
324C2×C4D3×D411yescharacteristic
325C2×C4C23×D311yescharacteristic
326C8—21no—
327C8—21no—
328C8—61no—
329C8—61no—
330C2×C3—41no—
331C2×C3#54611yescharacteristic
332C2×C3#57511yescharacteristic
333C2×C3#57711yescharacteristic
334D3—41no—
335D3—42no—
336D3—81no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—61no—
341C22—61no—
342C22—61no—
343C22—62no—
344C22—121no—
345C22—121no—
346C22—121no—
347C22—121no—
348C22—121no—
349C22—244no—
350C22C2×D3×D411yescharacteristic
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—61no—
357C4—61no—
358C4—61no—
359C4—121no—
360C4—121no—
361C4#100411yescharacteristic
362C4D3×#4111yescharacteristic
363C3#332311yescharacteristic, complemented, Sylow
364C2—41no—
365C2—121no—
366C2—122no—
367C2—241no—
368C2#561011yescharacteristic
369C2#577711yescharacteristic
370C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#470C2
socleC22×C3C22×D4
prime radical#5630C2
hypercenter#470D3
hypocenterC3#3323
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #5639C2semidirect
3. C3×#470C2semidirect
4. #5187C2semidirect
5. #5185C2semidirect
6. #5131C2semidirect
7. #5128C2semidirect
8. #5046C2semidirect
9. #5045C2semidirect
10. #4871C2semidirect
11. #4863C2semidirect
12. #4812C2semidirect
13. #4803C2semidirect
14. #4800C2semidirect
15. #4788C2semidirect
19. C2×C3×Q16C22semidirect
24. #946C22semidirect
25. Q8×Dic3C22semidirect
30. C2×ΓL(1,𝔽25)C22semidirect
36. D3×C4⋊C4C22semidirect
37. #890C22semidirect
43. C3×#106C22semidirect
44. C3×#103C22semidirect
45. C3×#103C22semidirect
46. #835C22semidirect
47. #835C22semidirect
53. (C2×D3)⋊C8C22semidirect
54. Dic3⋊C8C22semidirect
55. C8×Dic3C22semidirect
58. #808C22semidirect
59. #807C22semidirect
66. #470D3semidirect
129. C2×Q16C2×D3semidirect
155. #106C2×D3semidirect
159. #103C2×D3semidirect
160. #103C2×D3semidirect
363. C3#3323semidirect

Maximal subgroups

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

subgroupindex
#56392
#56302
C3×#4702
#51872
#51852
#51312
#51282
#50462
#50452
#48712
#48632
#48122
#48032
#48002
#47882
#33233