Finite Group Databasebeta

← C4×#915 #79646

Subgroups — C4×#915 #79646

Order 384.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#915C211yesmaximal, characteristic
2C4×D3×Q8C211yesmaximal, characteristic, complemented
3C4×#237C211yesmaximal, characteristic
4C3×C4×SD16C211yesmaximal, characteristic, complemented
5#5164C211yesmaximal, characteristic, complemented
6C4×#216C211yesmaximal, characteristic, complemented
7C4×#214C211yesmaximal, characteristic, complemented
8#4861C211yesmaximal, characteristic, complemented
9#4853C211yesmaximal, characteristic, complemented
10#4802C211yesmaximal, characteristic, complemented
11#4789C211yesmaximal, characteristic, complemented
12#4771C211yesmaximal, characteristic
13#4757C211yesmaximal, characteristic, complemented
14C4×Dic12C211yesmaximal, characteristic, complemented
15C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16C4×#137—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×#237C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23C2×#216C2211yescharacteristic
24D4×Dic3C2211yescharacteristic
25C2×#214C2211yescharacteristic
26C4×#67—21no—
27C2×C4×Dic3—21no—
28#915C418yesdirect product factor
29C2×Dic12C2211yescharacteristic
30C2×ΓL(1,𝔽25)C2211yescharacteristic
31C2×ΓL(1,𝔽25)C2211yescharacteristic
32#892C2211yescharacteristic
33D3×C4⋊C4—21no—
34D3×C4⋊C4C2211yescharacteristic
35#887—21no—
36#887C2211yescharacteristic
37#887C2211yescharacteristic
38#67⋊C4—21no—
39#877—21no—
40C42×D3—21no—
41C42×D3C2211yescharacteristic
42C4×Dic6—21no—
43C4×Dic6C2211yescharacteristic
44C4×Dic6C2211yescharacteristic
45C3×#106C2211yescharacteristic
46C3×#103C2211yescharacteristic
47C3×#102C2211yescharacteristic
48C3×C4×C8C2211yescharacteristic
49#835C2211yescharacteristic
50#832C2211yescharacteristic
51#818C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#815C2211yescharacteristic
55#815C2211yescharacteristic
56#810C2211yescharacteristic
57#810C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60C4×C3⋊C8C2211yescharacteristic
61C2×#137—31no—
62C4×#41—31no—
63C2×C4×Q8—31no—
64#441—31no—
65#441—31no—
66#440—31no—
67#440—31no—
68C4×Q16—31no—
69C4×Q16—31no—
70C4×SD16—31no—
71C4×SD16D311yescharacteristic, complemented
72#428—31no—
73#419—31no—
74#417—31no—
75C4×M16—31no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C2×#67—21no—
80C22×Dic3—21no—
81C22×Dic3—21no—
82D3×Q8—22no—
83D3×Q8C2×C414yescomplemented
84#237—22no—
85#237C2×C414yes—
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3D411yescharacteristic
89C2×C4×D3D411yescharacteristic
90C2×C4×D3C2311yescharacteristic
91C2×Dic6—21no—
92C2×Dic6C2311yescharacteristic
93C2×Dic6C2311yescharacteristic
94C3×SD16C2×C414yescomplemented
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4—21no—
98C3×C4⋊C4C2311yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C22⋊C4—21no—
101C3×C42—21no—
102C3×C42C2311yescharacteristic
103#217—21no—
104#216C2×C414yescomplemented
105#214C2×C414yescomplemented
106(C2×D3)⋊C4—21no—
107C4⋊Dic3—21no—
108C4⋊Dic3C2311yescharacteristic
109C4⋊Dic3C2311yescharacteristic
110Dic3⋊C4—21no—
111Dic3⋊C4—21no—
112Dic3⋊C4—21no—
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115C4×Dic3—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3—21no—
121C4×Dic3D411yescharacteristic
122C4×Dic3D411yescharacteristic
123C4×Dic3C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126Dic12C2×C414yescomplemented
127ΓL(1,𝔽25)—22no—
128ΓL(1,𝔽25)C2×C414yescomplemented
129C2×#41—31no—
130C22×Q8—31no—
131#137—38no—
132C2×Q16—31no—
133C2×Q16—31no—
134C2×SD16—31no—
135C2×SD16C2×D311yescharacteristic
136C2×M16—31no—
137C2×M16—31no—
138C4×Q8—31no—
139C4×Q8—31no—
140C4×Q8—31no—
141C4×Q8—31no—
142C4×Q8—31no—
143C4×Q8—61no—
144C4×Q8—61no—
145C4×Q8C2×D311yescharacteristic
146C4×D4—31no—
147C4×D4—61no—
148C4×D4—61no—
149C4×D4C2×D311yescharacteristic
150#117—31no—
151#117—61no—
152C2×C4⋊C4—31no—
153C2×C4⋊C4—61no—
154C2×C42—31no—
155C2×C42—61no—
156C2×C42—61no—
157#107—31no—
158#107—31no—
159#106—31no—
160#106C2×D311yescharacteristic
161#103—31no—
162#103—31no—
163#103—31no—
164#103—31no—
165#103—31no—
166#103C2×D311yescharacteristic
167#102—31no—
168#102C2×D311yescharacteristic
169#97—31no—
170#97—31no—
171C4×C8—31no—
172C4×C8C2×D311yescharacteristic
173C23×C3—21no—
174C22×D3C2×D411yescharacteristic
175C3×Q8—21no—
176C3×Q8C22×C412yes—
177C3×D4—21no—
178C3×D4C22×C412yes—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—42no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2411yescharacteristic
186#67—24no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—24no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—42no—
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196C4×D3—24no—
197C4×D3—22no—
198C4×D3—41no—
199C4×D3—42no—
200C4×D3C22×C412yes—
201C4×D3#4112yes—
202Dic6—21no—
203Dic6—21no—
204Dic6—24no—
205Dic6C22×C412yes—
206Dic6C22×C412yes—
207C3×C8—21no—
208C3×C8C22×C412yes—
209C3⋊C8—21no—
210C3⋊C8C22×C412yes—
211#41—34no—
212#41—62no—
213C2×Q8—34no—
214C2×Q8—31no—
215C2×Q8—31no—
216C2×Q8—61no—
217C2×Q8—62no—
218C2×Q8C22×D311yescharacteristic
219C2×D4—61no—
220C2×D4C22×D311yescharacteristic
221C22×C4—21no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—31no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229Q16—34no—
230Q16—34no—
231SD16—34no—
232SD16C4×D314yescomplemented
233M16—34no—
234M16—62no—
235C2×C8—31no—
236C2×C8—31no—
237C2×C8C22×D311yescharacteristic
238C2×C8C22×D311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—61no—
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—61no—
252C22⋊C4—61no—
253C42—21no—
254C42—31no—
255C42—31no—
256C42—31no—
257C42—61no—
258C42—61no—
259C42—61no—
260C42—61no—
261C42—61no—
262C42—61no—
263C42C22×D311yescharacteristic
264C22×C3—22no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3C22×D411yescharacteristic
268C2×D3—21no—
269C2×D3—21no—
270C2×D3C4×D412yes—
271C3×C4—22no—
272C3×C4—21no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4#13712yescomplemented
276C3×C4C23×C411yescharacteristic
277C3×C4C2×#4111yescharacteristic
278Dic3—22no—
279Dic3—22no—
280Dic3—21no—
281Dic3—21no—
282Dic3—41no—
283Dic3—41no—
284Dic3C4×D412yes—
285C23—21no—
286C23—31no—
287Q8—21no—
288Q8—32no—
289Q8—32no—
290Q8—64no—
291Q8—61no—
292Q8—61no—
293Q8C2×C4×D312yes—
294D4—21no—
295D4—64no—
296D4C2×C4×D312yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—31no—
301C2×C4—32no—
302C2×C4—32no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—42no—
306C2×C4—64no—
307C2×C4—64no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—62no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—121no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4D3×D411yescharacteristic
317C2×C4D3×D411yescharacteristic
318C2×C4C23×D311yescharacteristic
319C8—21no—
320C8—32no—
321C8—61no—
322C8C2×C4×D312yes—
323C2×C3—42no—
324C2×C3C2×C4×D411yescharacteristic
325C2×C3C2×#13711yescharacteristic
326C2×C3#57511yescharacteristic
327D3—22no—
328C22—22no—
329C22—32no—
330C22—41no—
331C22—41no—
332C22—61no—
333C22—61no—
334C22C2×D3×D411yescharacteristic
335C4—21no—
336C4—22no—
337C4—32no—
338C4—41no—
339C4—41no—
340C4—61no—
341C4—61no—
342C4—62no—
343C4—62no—
344C4—121no—
345C4—121no—
346C4#91512yesdirect product factor
347C4C22×C4×D311yescharacteristic
348C4D3×#4111yescharacteristic
349C3C4×#13711yescharacteristic, complemented, Sylow
350C2—42no—
351C2—62no—
352C2C4×D3×D411yescharacteristic
353C2C2×#91511yescharacteristic
354C2#576811yescharacteristic
subgroupG/H
centerC2×C4D3×D4
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radicalC2×#237C22
cosocleC2×C3×C4C24
hypercenterC4×SD16D3
hypocenterC3C4×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×D3×Q8C2semidirect
4. C3×C4×SD16C2semidirect
5. #5164C2semidirect
6. C4×#216C2semidirect
7. C4×#214C2semidirect
8. #4861C2semidirect
9. #4853C2semidirect
10. #4802C2semidirect
11. #4789C2semidirect
13. #4757C2semidirect
14. C4×Dic12C2semidirect
15. C4×ΓL(1,𝔽25)C2semidirect
28. #915C4direct (N × H)
71. C4×SD16D3semidirect
83. D3×Q8C2×C4semidirect
94. C3×SD16C2×C4semidirect
104. #216C2×C4semidirect
105. #214C2×C4semidirect
126. Dic12C2×C4semidirect
128. ΓL(1,𝔽25)C2×C4semidirect
232. SD16C4×D3semidirect
275. C3×C4#137semidirect
346. C4#915direct (N × H)
349. C3C4×#137semidirect

Maximal subgroups

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

subgroupindex
C2×#9152
C4×D3×Q82
C4×#2372
C3×C4×SD162
#51642
C4×#2162
C4×#2142
#48612
#48532
#48022
#47892
#47712
#47572
C4×Dic122
C4×ΓL(1,𝔽25)2
C4×#1373