Finite Group Databasebeta

← #79649

Subgroups — #79649

Order 384.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×SD16C211yesmaximal, characteristic
2#5572C211yesmaximal, characteristic, complemented
3#5545C211yesmaximal, characteristic
4C3×C4×SD16C211yesmaximal, characteristic, complemented
5Dic3×SD16C211yesmaximal, characteristic, complemented
6#5026C211yesmaximal, characteristic, complemented
7#5018C211yesmaximal, characteristic, complemented
8#4860C211yesmaximal, characteristic, complemented
9#4852C211yesmaximal, characteristic, complemented
10#4817C211yesmaximal, characteristic, complemented
11#4802C211yesmaximal, characteristic, complemented
12#4770C211yesmaximal, characteristic
13#4757C211yesmaximal, characteristic, complemented
14C4×#204C211yesmaximal, characteristic, complemented
15#4689C211yesmaximal, characteristic, complemented
16#2949—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×D3×D4C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic, complemented
21C3×C4×D4C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic, complemented
23C2×#215C2211yescharacteristic
24D4×Dic3C2211yescharacteristic
25C2×#214C2211yescharacteristic
26C4×#67—21no—
27C2×(C2×D3)⋊C4—21no—
28D3×SD16C418yescomplemented
29C2×#204C2211yescharacteristic
30C2×ΓL(1,𝔽25)C2211yescharacteristic
31C2×D3×C8C2211yescharacteristic
32#893C2211yescharacteristic
33#892—21no—
34#892C2211yescharacteristic
35#892C2211yescharacteristic
36#887—21no—
37#887C2211yescharacteristic, complemented
38#67⋊C4—21no—
39D3×C22⋊C4—21no—
40C4×D12C2211yescharacteristic
41#872—21no—
42#872C2211yescharacteristic
43C4×Dic6—21no—
44C4×Dic6C2211yescharacteristic, complemented
45C3×#106C2211yescharacteristic, complemented
46C3×#103C2211yescharacteristic, complemented
47C3×#102C2211yescharacteristic
48C3×C4×C8C2211yescharacteristic, complemented
49#835C2211yescharacteristic, complemented
50#832C2211yescharacteristic
51#821C2211yescharacteristic
52#817C2211yescharacteristic, complemented
53#816C2211yescharacteristic, complemented
54#815C2211yescharacteristic, complemented
55C8×Dic3C2211yescharacteristic, complemented
56#810C2211yescharacteristic, complemented
57#809C2211yescharacteristic
58#807C2211yescharacteristic, complemented
59#807C2211yescharacteristic, complemented
60#803C2211yescharacteristic, complemented
61C22×SD16—31no—
62#519—31no—
63#518—31no—
64#440—31no—
65#440—31no—
66#440—31no—
67#440—31no—
68C4×SD16—31no—
69C4×SD16—31no—
70C4×SD16—31no—
71C4×SD16D311yescharacteristic, complemented
72#427—31no—
73#419—31no—
74#418—31no—
75#405—31no—
76C23×D3—21no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4—21no—
80C2×#67—21no—
81C22×Dic3—21no—
82D3×Q8—22no—
83D3×Q8C2×C414yescomplemented
84D3×D4—22no—
85D3×D4C2×C414yes—
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×C4×D3C2311yescharacteristic
91C2×Dic6—21no—
92C2×Dic6C2311yescharacteristic
93C3×SD16C2×C414yescomplemented
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C3×C4⋊C4—21no—
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100C3×C42—21no—
101C3×C42C2311yescharacteristic
102#217—21no—
103#215C2×C414yescomplemented
104#214C2×C414yescomplemented
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4D411yescharacteristic
110(C2×D3)⋊C4D411yescharacteristic
111C4⋊Dic3—21no—
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114Dic3⋊C4—21no—
115Dic3⋊C4—21no—
116Dic3⋊C4D411yescharacteristic
117Dic3⋊C4D411yescharacteristic
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3—21no—
121C4×Dic3—21no—
122C4×Dic3—21no—
123C4×Dic3C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126#204C2×C414yescomplemented
127ΓL(1,𝔽25)—22no—
128D3×C8C2×C414yescomplemented
129C22×Q8—31no—
130C22×D4—31no—
131C2×SD16—31no—
132C2×SD16—31no—
133C2×SD16—38no—
134C2×SD16—31no—
135C2×SD16C2×D311yescharacteristic
136C2×M16—31no—
137C22×C8—31no—
138C4×Q8—31no—
139C4×Q8—31no—
140C4×Q8—31no—
141C4×Q8—61no—
142C4×Q8—61no—
143C4×Q8C2×D311yescharacteristic, complemented
144C4×D4—31no—
145C4×D4—31no—
146C4×D4—31no—
147C4×D4—61no—
148C4×D4—61no—
149C4×D4C2×D311yescharacteristic
150#117—31no—
151#117—31no—
152#117—31no—
153#117—61no—
154#117—61no—
155C2×C22⋊C4—61no—
156C2×C22⋊C4—61no—
157#107—31no—
158#107—31no—
159#106—31no—
160#106C2×D311yescharacteristic, complemented
161#103—31no—
162#103—31no—
163#103—31no—
164#103C2×D311yescharacteristic, complemented
165#102—31no—
166#102—31no—
167#102—31no—
168#102C2×D311yescharacteristic
169#97—31no—
170#97—31no—
171C4×C8—31no—
172C4×C8C2×D311yescharacteristic, complemented
173C23×C3—21no—
174C22×D3—21no—
175C22×D3—24no—
176C22×D3—81no—
177C22×D3—81no—
178C22×D3C2×D411yescharacteristic
179C3×Q8—21no—
180C3×Q8C22×C412yes—
181C3×D4—21no—
182C3×D4C22×C412yes—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—81no—
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2×D411yescharacteristic
189C2×C3×C4C2411yescharacteristic
190#67—24no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—81no—
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197C2×Dic3C2×D411yescharacteristic
198D12—21no—
199D12C22×C412yes—
200C4×D3—24no—
201C4×D3—81no—
202C4×D3—81no—
203C4×D3C22×C412yes—
204C4×D3#4112yes—
205Dic6—21no—
206Dic6—24no—
207Dic6C22×C412yes—
208C3×C8—21no—
209C3×C8C22×C412yes—
210C3⋊C8—21no—
211C3⋊C8C22×C412yes—
212C24—61no—
213C2×Q8—34no—
214C2×Q8—31no—
215C2×Q8—61no—
216C2×Q8—62no—
217C2×Q8C22×D311yescharacteristic
218C2×D4—34no—
219C2×D4—31no—
220C2×D4—62no—
221C2×D4—61no—
222C2×D4C22×D311yescharacteristic
223C22×C4—21no—
224C22×C4—31no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229SD16—34no—
230SD16—34no—
231SD16—34no—
232SD16C4×D314yescomplemented
233M16—62no—
234C2×C8—31no—
235C2×C8—34no—
236C2×C8—31no—
237C2×C8C22×D311yescharacteristic
238C2×C8C22×D311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—31no—
243C4⋊C4—31no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4C22×D311yescharacteristic
248C4⋊C4C22×D311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—31no—
251C22⋊C4—31no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C42—21no—
258C42—31no—
259C42—61no—
260C42—61no—
261C42—61no—
262C42—61no—
263C42—61no—
264C42C22×D311yescharacteristic
265C22×C3—22no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3C22×D411yescharacteristic
269C2×D3—21no—
270C2×D3—21no—
271C2×D3—22no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—84no—
275C2×D3C4×D412yes—
276C3×C4—22no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4C23×C411yescharacteristic
282C3×C4C2×#4111yescharacteristic
283Dic3—22no—
284Dic3—21no—
285Dic3—21no—
286Dic3—41no—
287Dic3—41no—
288Dic3C4×D412yes—
289C23—21no—
290C23—31no—
291C23—64no—
292C23—61no—
293C23—241no—
294C23—241no—
295Q8—21no—
296Q8—32no—
297Q8—64no—
298Q8—61no—
299Q8C2×C4×D312yes—
300D4—21no—
301D4—32no—
302D4—64no—
303D4—61no—
304D4C2×C4×D312yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—31no—
309C2×C4—32no—
310C2×C4—32no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—64no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—81no—
318C2×C4—241no—
319C2×C4—241no—
320C2×C4—241no—
321C2×C4D3×D411yescharacteristic
322C2×C4D3×D411yescharacteristic
323C2×C4C23×D311yescharacteristic
324C8—21no—
325C8—32no—
326C8—61no—
327C8C2×C4×D312yes—
328C2×C3—42no—
329C2×C3C2×C4×D411yescharacteristic
330C2×C3#57711yescharacteristic
331C2×C3#57711yescharacteristic
332D3—22no—
333D3—42no—
334C22—22no—
335C22—32no—
336C22—41no—
337C22—41no—
338C22—61no—
339C22—61no—
340C22—62no—
341C22—121no—
342C22—121no—
343C22—244no—
344C22C2×D3×D411yescharacteristic
345C4—21no—
346C4—21no—
347C4—22no—
348C4—32no—
349C4—41no—
350C4—41no—
351C4—61no—
352C4—61no—
353C4—62no—
354C4—121no—
355C4—121no—
356C4C22×C4×D311yescharacteristic
357C4D3×#4111yescharacteristic
358C3#294911yescharacteristic, complemented, Sylow
359C2—42no—
360C2—62no—
361C2—122no—
362C2C4×D3×D411yescharacteristic
363C2#576211yescharacteristic
364C2#577011yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radicalC2×D3×D4C22
cosocleC2×C3×C4C24
hypercenterC4×SD16D3
hypocenterC3#2949
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #5572C2semidirect
4. C3×C4×SD16C2semidirect
5. Dic3×SD16C2semidirect
6. #5026C2semidirect
7. #5018C2semidirect
8. #4860C2semidirect
9. #4852C2semidirect
10. #4817C2semidirect
11. #4802C2semidirect
13. #4757C2semidirect
14. C4×#204C2semidirect
15. #4689C2semidirect
20. C3×C4×Q8C22semidirect
22. Q8×Dic3C22semidirect
28. D3×SD16C4semidirect
37. #887C22semidirect
44. C4×Dic6C22semidirect
45. C3×#106C22semidirect
46. C3×#103C22semidirect
48. C3×C4×C8C22semidirect
49. #835C22semidirect
52. #817C22semidirect
53. #816C22semidirect
54. #815C22semidirect
55. C8×Dic3C22semidirect
56. #810C22semidirect
58. #807C22semidirect
59. #807C22semidirect
60. #803C22semidirect
71. C4×SD16D3semidirect
83. D3×Q8C2×C4semidirect
93. C3×SD16C2×C4semidirect
103. #215C2×C4semidirect
104. #214C2×C4semidirect
126. #204C2×C4semidirect
128. D3×C8C2×C4semidirect
143. C4×Q8C2×D3semidirect
160. #106C2×D3semidirect
164. #103C2×D3semidirect
172. C4×C8C2×D3semidirect
232. SD16C4×D3semidirect
358. C3#2949semidirect

Maximal subgroups

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

subgroupindex
C2×D3×SD162
#55722
#55452
C3×C4×SD162
Dic3×SD162
#50262
#50182
#48602
#48522
#48172
#48022
#47702
#47572
C4×#2042
#46892
#29493