Finite Group Databasebeta

← #81239

Subgroups — #81239

Order 384.

328 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5688C211yesmaximal, characteristic, complemented
2#5580C211yesmaximal, characteristic
3C3×#479C211yesmaximal, characteristic, complemented
4#5066C211yesmaximal, characteristic, complemented
5#5022C211yesmaximal, characteristic, complemented
6#4885C211yesmaximal, characteristic
7#4876C211yesmaximal, characteristic, complemented
8#4866C211yesmaximal, characteristic
9#4856C211yesmaximal, characteristic, complemented
10#4847C211yesmaximal, characteristic, complemented
11#4835C211yesmaximal, characteristic, complemented
12#4815C211yesmaximal, characteristic, complemented
13#4814C211yesmaximal, characteristic, complemented
14#4794C211yesmaximal, characteristic, complemented
15#4794C211yesmaximal, characteristic, complemented
16#3240—31nomaximal, Sylow
17C3×#125C2211yescharacteristic
18C3×C4×Q8C2211yescharacteristic
19#947C2211yescharacteristic
20#946C2211yescharacteristic
21#898—21no—
22#896—21no—
23#896—21no—
24#895C2211yescharacteristic
25#894—21no—
26#892C2211yescharacteristic
27#892C2211yescharacteristic
28#890C2211yescharacteristic
29#888C2211yescharacteristic
30#888C2211yescharacteristic
31#887—21no—
32#887—21no—
33C4×D12—21no—
34C4×D12C2211yescharacteristic
35#872—21no—
36C42×D3C2211yescharacteristic
37#870C2211yescharacteristic
38C3×#107C2211yescharacteristic
39C3×#106C2211yescharacteristic
40C3×C4⋊C8C2211yescharacteristic
41C3×#103C2211yescharacteristic
42C3×#103C2211yescharacteristic
43#835C2211yescharacteristic
44#835C2211yescharacteristic
45#821C2211yescharacteristic
46#821C2211yescharacteristic
47(C2×D3)⋊C8C2211yescharacteristic
48(C2×D3)⋊C8C2211yescharacteristic
49#818C2211yescharacteristic
50#817C2211yescharacteristic
51#815C2211yescharacteristic
52#815C2211yescharacteristic
53#809C2211yescharacteristic
54#809C2211yescharacteristic
55#808C2211yescharacteristic
56#808C2211yescharacteristic
57#807C2211yescharacteristic
58#807C2211yescharacteristic
59C4⋊(C3⋊C8)C2211yescharacteristic
60#533—31no—
61#529—31no—
62#501—31no—
63#501—31no—
64#489—31no—
65#489—31no—
66#485—31no—
67#485—31no—
68#482—31no—
69#482—31no—
70#479—31no—
71#479D311yescharacteristic, complemented
72#478—31no—
73#478—31no—
74#432—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×D12—21no—
77C2×D12C2311yescharacteristic
78C2×C4×D3—21no—
79C2×C4×D3D411yescharacteristic
80C2×C4×D3D411yescharacteristic
81C2×C4×D3C2311yescharacteristic
82C2×Dic6—21no—
83C2×Dic6—21no—
84C2×C3×C8C2311yescharacteristic
85C2×C3×C8C2311yescharacteristic
86C3×C4⋊C4—21no—
87C3×C4⋊C4—21no—
88C3×C4⋊C4—21no—
89C3×C4⋊C4C2311yescharacteristic
90C3×C4⋊C4C2311yescharacteristic
91C3×C4⋊C4C2311yescharacteristic
92C3×C42—21no—
93C3×C42C2311yescharacteristic
94(C2×D3)⋊C4—21no—
95(C2×D3)⋊C4—21no—
96(C2×D3)⋊C4—21no—
97(C2×D3)⋊C4—21no—
98(C2×D3)⋊C4—21no—
99(C2×D3)⋊C4—21no—
100(C2×D3)⋊C4—21no—
101C4⋊Dic3—21no—
102C4⋊Dic3C2311yescharacteristic
103C4⋊Dic3C2311yescharacteristic
104C4⋊Dic3C2311yescharacteristic
105Dic3⋊C4—21no—
106Dic3⋊C4—21no—
107Dic3⋊C4—21no—
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4—21no—
111C4×Dic3—21no—
112C4×Dic3—21no—
113C4×Dic3D411yescharacteristic
114C4×Dic3D411yescharacteristic
115C4×Dic3C2311yescharacteristic
116C2×C3⋊C8C2311yescharacteristic
117C2×C3⋊C8C2311yescharacteristic
118C4⋊Q8—31no—
119C4⋊Q8—31no—
120#126—61no—
121#125—31no—
122#125—31no—
123#125C2×D311yescharacteristic
124#124—31no—
125#123—61no—
126C22⋊Q8—31no—
127C22⋊Q8—61no—
128C22⋊Q8—61no—
129#121—31no—
130C4×Q8—61no—
131C4×Q8—61no—
132C4×Q8C2×D311yescharacteristic
133C4×D4—31no—
134C4×D4—61no—
135#117—31no—
136#117—31no—
137#117—61no—
138C2×C42—31no—
139#107—31no—
140#107—31no—
141#107—31no—
142#107C2×D311yescharacteristic
143#106—31no—
144#106—31no—
145#106—31no—
146#106C2×D311yescharacteristic
147C4⋊C8—31no—
148C4⋊C8C2×D311yescharacteristic
149#103—31no—
150#103—31no—
151#103C2×D311yescharacteristic
152#103C2×D311yescharacteristic
153#102—31no—
154#102—31no—
155#102—31no—
156#102—31no—
157C22⋊C8—31no—
158C22⋊C8—31no—
159#97—31no—
160#97—31no—
161C22×D3—21no—
162C22×D3C2×D411yescharacteristic
163C3×Q8—21no—
164C3×Q8—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4C2×D411yescharacteristic
170C2×C3×C4C2×D411yescharacteristic
171C2×C3×C4C2411yescharacteristic
172C2×Dic3—21no—
173C2×Dic3—21no—
174C2×Dic3—21no—
175C2×Dic3C2×D411yescharacteristic
176C2×Dic3C2×D411yescharacteristic
177C2×Dic3C2×D411yescharacteristic
178D12—21no—
179D12—21no—
180D12—42no—
181C4×D3—21no—
182C4×D3—21no—
183C4×D3—41no—
184C4×D3—41no—
185C4×D3—42no—
186Dic6—42no—
187Dic6—42no—
188C3×C8—21no—
189C3×C8—21no—
190C3⋊C8—21no—
191C3⋊C8—21no—
192C2×Q8—61no—
193C2×Q8—61no—
194C2×Q8C22×D311yescharacteristic
195C2×D4—31no—
196C2×D4—61no—
197C22×C4—31no—
198C22×C4—31no—
199C22×C4—31no—
200C22×C4—61no—
201C2×C8—31no—
202C2×C8—31no—
203C2×C8C22×D311yescharacteristic
204C2×C8C22×D311yescharacteristic
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—31no—
209C4⋊C4—31no—
210C4⋊C4—31no—
211C4⋊C4—61no—
212C4⋊C4—61no—
213C4⋊C4—61no—
214C4⋊C4—61no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C4⋊C4C22×D311yescharacteristic
219C4⋊C4C22×D311yescharacteristic
220C4⋊C4C22×D311yescharacteristic
221C22⋊C4—61no—
222C22⋊C4—61no—
223C22⋊C4—61no—
224C22⋊C4—61no—
225C22⋊C4—61no—
226C22⋊C4—61no—
227C22⋊C4—61no—
228C42—21no—
229C42—31no—
230C42—31no—
231C42—31no—
232C42—61no—
233C42—61no—
234C42C22×D311yescharacteristic
235C22×C3C22×D411yescharacteristic
236C2×D3—21no—
237C2×D3—21no—
238C2×D3—21no—
239C2×D3—41no—
240C2×D3—41no—
241C2×D3—41no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—41no—
248C3×C42−1+411yescharacteristic
249C3×C42−1+411yescharacteristic
250Dic3—21no—
251Dic3—21no—
252Dic3—21no—
253Dic3—41no—
254Dic3—41no—
255Dic3—41no—
256C23—31no—
257C23—61no—
258Q8—21no—
259Q8—21no—
260Q8—122no—
261Q8—122no—
262D4—61no—
263D4—61no—
264D4—122no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—61no—
275C2×C4—61no—
276C2×C4—61no—
277C2×C4—121no—
278C2×C4—121no—
279C2×C4—122no—
280C2×C4D3×D411yescharacteristic
281C2×C4D3×D411yescharacteristic
282C2×C4C23×D311yescharacteristic
283C8—21no—
284C8—21no—
285C8—61no—
286C8—61no—
287C2×C3#53611yescharacteristic
288C2×C3#57511yescharacteristic
289C2×C3#57511yescharacteristic
290D3—41no—
291D3—81no—
292C22—61no—
293C22—61no—
294C22—61no—
295C22—121no—
296C22—121no—
297C22—121no—
298C22C2×D3×D411yescharacteristic
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—61no—
306C4—61no—
307C4—61no—
308C4—121no—
309C4—121no—
310C4—121no—
311C4#100711yescharacteristic
312C4#101011yescharacteristic
313C3#324011yescharacteristic, complemented, Sylow
314C2—121no—
315C2—241no—
316C2#562811yescharacteristic
317C2#576811yescharacteristic
318C2#577711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#479C2
socleC22×C3C22×D4
prime radical#895C22
hypercenter#479D3
hypocenterC3#3240
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #5688C2semidirect
3. C3×#479C2semidirect
4. #5066C2semidirect
5. #5022C2semidirect
7. #4876C2semidirect
9. #4856C2semidirect
10. #4847C2semidirect
11. #4835C2semidirect
12. #4815C2semidirect
13. #4814C2semidirect
14. #4794C2semidirect
15. #4794C2semidirect
71. #479D3semidirect
313. C3#3240semidirect

Maximal subgroups

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

subgroupindex
#56882
#55802
C3×#4792
#50662
#50222
#48852
#48762
#48662
#48562
#48472
#48352
#48152
#48142
#47942
#32403