Finite Group Databasebeta

← #79829

Subgroups — #79829

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×#918C211yesmaximal, characteristic
2C4×#239C211yesmaximal, characteristic
3C4×D3×Q8C211yesmaximal, characteristic, complemented
4C3×#441C211yesmaximal, characteristic, complemented
5Dic3×Q16C211yesmaximal, characteristic, complemented
6#5030C211yesmaximal, characteristic, complemented
7#5026C211yesmaximal, characteristic, complemented
8#4861C211yesmaximal, characteristic, complemented
9#4852C211yesmaximal, characteristic, complemented
10#4803C211yesmaximal, characteristic
11#4802C211yesmaximal, characteristic, complemented
12#4790C211yesmaximal, characteristic, complemented
13#4788C211yesmaximal, characteristic, complemented
14#4710C211yesmaximal, characteristic, complemented
15#4707C211yesmaximal, characteristic, complemented
16C4×#137—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×C3×Q16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic
21C3×C4×Q8C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23Q8×Dic3C2211yescharacteristic
24C2×#216C2211yescharacteristic
25C2×#215C2211yescharacteristic
26#918C418yescomplemented
27C2×#204C2211yescharacteristic
28C2×ΓL(1,𝔽25)C2211yescharacteristic
29C2×ΓL(1,𝔽25)C2211yescharacteristic
30#893—21no—
31#893C2211yescharacteristic
32#892—21no—
33#892C2211yescharacteristic
34D3×C4⋊C4—21no—
35D3×C4⋊C4C2211yescharacteristic
36#887—21no—
37#887C2211yescharacteristic
38C4×D12—21no—
39C4×D12C2211yescharacteristic
40C42×D3—21no—
41C42×D3—21no—
42C42×D3C2211yescharacteristic
43C4×Dic6—21no—
44C4×Dic6C2211yescharacteristic
45C3×#106C2211yescharacteristic
46C3×#103C2211yescharacteristic
47C3×#103C2211yescharacteristic
48C3×#97C2211yescharacteristic
49#835C2211yescharacteristic
50#835C2211yescharacteristic
51#821C2211yescharacteristic
52#818C2211yescharacteristic
53#816C2211yescharacteristic
54C8×Dic3C2211yescharacteristic
55C8×Dic3C2211yescharacteristic
56#810C2211yescharacteristic
57#809C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60#803C2211yescharacteristic
61C2×#137—31no—
62C4×#41—31no—
63C2×C4×Q8—31no—
64#441—31no—
65#441D311yescharacteristic, complemented
66#440—31no—
67#440—31no—
68C4×Q16—31no—
69C4×Q16—31no—
70C4×SD16—31no—
71C4×SD16—31no—
72#428—31no—
73#419—31no—
74#417—31no—
75C4×M16—31no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×Q8C2311yescharacteristic
78#239—22no—
79#239C2×C414yes—
80D3×Q8—22no—
81D3×Q8C2×C414yescomplemented
82C2×D12—21no—
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3D411yescharacteristic
90C2×C4×D3D411yescharacteristic
91C2×C4×D3C2311yescharacteristic
92C2×Dic6—21no—
93C2×Dic6C2311yescharacteristic
94C3×Q16C2×C414yescomplemented
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4—21no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C42—21no—
102C3×C42—21no—
103C3×C42C2311yescharacteristic
104#216C2×C414yescomplemented
105#215C2×C414yescomplemented
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3C2311yescharacteristic
112C4⋊Dic3C2311yescharacteristic
113Dic3⋊C4—21no—
114Dic3⋊C4—21no—
115Dic3⋊C4—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
126#204C2×C414yescomplemented
127ΓL(1,𝔽25)—22no—
128ΓL(1,𝔽25)C2×C414yescomplemented
129C2×#41—31no—
130C22×Q8—31no—
131#137—38no—
132C2×Q16—31no—
133C2×Q16C2×D311yescharacteristic
134C2×SD16—31no—
135C2×SD16—31no—
136C2×M16—31no—
137C2×M16—31no—
138C4×Q8—31no—
139C4×Q8—31no—
140C4×Q8—31no—
141C4×Q8—31no—
142C4×Q8—61no—
143C4×Q8—61no—
144C4×Q8C2×D311yescharacteristic
145C4×Q8C2×D311yescharacteristic
146C4×D4—31no—
147C4×D4—31no—
148C4×D4—61no—
149C4×D4—61no—
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#103C2×D311yescharacteristic
166#103C2×D311yescharacteristic
167#102—31no—
168#102—31no—
169#97—31no—
170#97C2×D311yescharacteristic
171C4×C8—31no—
172C4×C8—31no—
173C22×D3—21no—
174C22×D3C2×D411yescharacteristic
175C3×Q8—21no—
176C3×Q8—21no—
177C3×Q8C22×C412yes—
178C3×Q8C22×C412yes—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2411yescharacteristic
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3C2×D411yescharacteristic
190C2×Dic3C2×D411yescharacteristic
191C2×Dic3C2×D411yescharacteristic
192D12—24no—
193D12—21no—
194D12C22×C412yes—
195C4×D3—24no—
196C4×D3—24no—
197C4×D3—22no—
198C4×D3—41no—
199C4×D3—42no—
200C4×D3—42no—
201C4×D3—42no—
202C4×D3C22×C412yes—
203C4×D3#4112yes—
204Dic6—21no—
205Dic6—24no—
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—61no—
216C2×Q8—62no—
217C2×Q8C22×D311yescharacteristic
218C2×Q8C22×D311yescharacteristic
219C2×D4—31no—
220C2×D4—61no—
221C22×C4—31no—
222C22×C4—31no—
223C22×C4—31no—
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229Q16—34no—
230Q16C4×D314yescomplemented
231SD16—34no—
232SD16—34no—
233M16—34no—
234M16—62no—
235C2×C8—31no—
236C2×C8—31no—
237C2×C8C22×D311yescharacteristic
238C2×C8C22×D311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
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—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C42—21no—
254C42—21no—
255C42—31no—
256C42—31no—
257C42—31no—
258C42—61no—
259C42—61no—
260C42—61no—
261C42—61no—
262C42—61no—
263C42C22×D311yescharacteristic
264C22×C3C22×D411yescharacteristic
265C2×D3—21no—
266C2×D3—21no—
267C2×D3—22no—
268C2×D3—41no—
269C2×D3—41no—
270C2×D3C4×D412yes—
271C3×C4—22no—
272C3×C4—22no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4C23×C411yescharacteristic
278C3×C4C2×#4111yescharacteristic
279Dic3—22no—
280Dic3—21no—
281Dic3—41no—
282Dic3—41no—
283Dic3C4×D412yes—
284Dic3#13712yescomplemented
285C23—31no—
286C23—61no—
287Q8—21no—
288Q8—21no—
289Q8—32no—
290Q8—64no—
291Q8—61no—
292Q8C2×C4×D312yes—
293Q8C2×C4×D312yes—
294D4—32no—
295D4—64no—
296D4—61no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—31no—
302C2×C4—31no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—31no—
306C2×C4—62no—
307C2×C4—64no—
308C2×C4—64no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—121no—
313C2×C4—122no—
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×C3C2×C4×D411yescharacteristic
324C2×C3C2×#13711yescharacteristic
325C2×C3#57511yescharacteristic
326D3—22no—
327D3—42no—
328C22—32no—
329C22—61no—
330C22—61no—
331C22—62no—
332C22—121no—
333C22—121no—
334C22C2×D3×D411yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—32no—
340C4—32no—
341C4—41no—
342C4—41no—
343C4—61no—
344C4—62no—
345C4—121no—
346C4—121no—
347C4C22×C4×D311yescharacteristic
348C4D3×#4111yescharacteristic
349C3C4×#13711yescharacteristic, complemented, Sylow
350C2—62no—
351C2—122no—
352C2C4×D3×D411yescharacteristic
353C2D3×#13711yescharacteristic
354C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutatorC3×C4C23×C4
FrattiniC2×C4C23×D3
FittingC3×#441C2
socleC22×C3C22×D4
prime radicalC2×#239C22
cosocleC2×C3×C4C24
hypercenter#441D3
hypocenterC3C4×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C4×D3×Q8C2semidirect
4. C3×#441C2semidirect
5. Dic3×Q16C2semidirect
6. #5030C2semidirect
7. #5026C2semidirect
8. #4861C2semidirect
9. #4852C2semidirect
11. #4802C2semidirect
12. #4790C2semidirect
13. #4788C2semidirect
14. #4710C2semidirect
15. #4707C2semidirect
26. #918C4semidirect
65. #441D3semidirect
81. D3×Q8C2×C4semidirect
94. C3×Q16C2×C4semidirect
104. #216C2×C4semidirect
105. #215C2×C4semidirect
126. #204C2×C4semidirect
128. ΓL(1,𝔽25)C2×C4semidirect
230. Q16C4×D3semidirect
284. Dic3#137semidirect
349. C3C4×#137semidirect

Maximal subgroups

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

subgroupindex
C2×#9182
C4×#2392
C4×D3×Q82
C3×#4412
Dic3×Q162
#50302
#50262
#48612
#48522
#48032
#48022
#47902
#47882
#47102
#47072
C4×#1373