Finite Group Databasebeta

← #81422

Subgroups — #81422

Order 384.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5625C211yesmaximal, characteristic
2#5500C211yesmaximal, characteristic
3C3×#483C211yesmaximal, characteristic
4#5045C211yesmaximal, characteristic
5#4970C211yesmaximal, characteristic
6#4858C211yesmaximal, characteristic, complemented
7#4857C211yesmaximal, characteristic, complemented
8#4856C211yesmaximal, characteristic, complemented
9#4854C211yesmaximal, characteristic, complemented
10#4799C211yesmaximal, characteristic, complemented
11#4797C211yesmaximal, characteristic, complemented
12#4793C211yesmaximal, characteristic, complemented
13#4792C211yesmaximal, characteristic, complemented
14#4723C211yesmaximal, characteristic
15#4720C211yesmaximal, characteristic
16#3242—31nomaximal, Sylow
17C3×C22⋊Q8C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19Q8×Dic3C2211yescharacteristic
20#944C2211yescharacteristic
21#926C2211yescharacteristic
22#926C2211yescharacteristic
23#924—21no—
24#924—21no—
25#924C2211yescharacteristic
26#890—21no—
27#890—21no—
28#890C2211yescharacteristic
29#890C2211yescharacteristic
30#890C2211yescharacteristic
31#889—21no—
32#888—21no—
33#888C2211yescharacteristic
34#888C2211yescharacteristic
35#887C2211yescharacteristic
36#879—21no—
37#879—21no—
38C3×#106C2211yescharacteristic
39C3×#106C2211yescharacteristic
40C3×#103C2211yescharacteristic
41C3×#103C2211yescharacteristic
42C3×C22⋊C8C2211yescharacteristic
43#835C2211yescharacteristic
44#835C2211yescharacteristic
45#830C2211yescharacteristic
46#818C2211yescharacteristic
47#817C2211yescharacteristic
48#816C2211yescharacteristic
49#816C2211yescharacteristic
50#815C2211yescharacteristic
51Dic3⋊C8C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#808C2211yescharacteristic
57#807C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#544—31no—
61#541—31no—
62#501—31no—
63#499—31no—
64#491—31no—
65#487—31no—
66#485—31no—
67#485—31no—
68#484—31no—
69#483D311yescharacteristic
70#479—31no—
71#479—31no—
72#477—31no—
73#475—31no—
74#433—31no—
75C2×C3×Q8C2311yescharacteristic
76C22×C3×C4—21no—
77C22×C3×C4C2311yescharacteristic
78C2×Dic6—21no—
79C2×Dic6—21no—
80C2×Dic6C2311yescharacteristic
81C2×C3×C8C2311yescharacteristic
82C2×C3×C8C2311yescharacteristic
83C3×C4⋊C4—21no—
84C3×C4⋊C4—21no—
85C3×C4⋊C4C2311yescharacteristic
86C3×C4⋊C4C2311yescharacteristic
87C3×C4⋊C4C2311yescharacteristic
88C3×C22⋊C4—21no—
89#217—21no—
90#217—21no—
91#217D411yescharacteristic
92#217D411yescharacteristic
93C4⋊Dic3—21no—
94C4⋊Dic3—21no—
95C4⋊Dic3—21no—
96C4⋊Dic3—21no—
97C4⋊Dic3D411yescharacteristic
98C4⋊Dic3D411yescharacteristic
99C4⋊Dic3C2311yescharacteristic
100C4⋊Dic3C2311yescharacteristic
101C4⋊Dic3C2311yescharacteristic
102Dic3⋊C4—21no—
103Dic3⋊C4—21no—
104Dic3⋊C4—21no—
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×Dic3—21no—
114C4×Dic3C2311yescharacteristic
115C4×Dic3C2311yescharacteristic
116C2×C3⋊C8C2311yescharacteristic
117C2×C3⋊C8C2311yescharacteristic
118C4⋊Q8—31no—
119C4⋊Q8—31no—
120C4⋊Q8—31no—
121C4⋊Q8—61no—
122#126—61no—
123#126—61no—
124#125—31no—
125#125—31no—
126#125—31no—
127#125—61no—
128#125—61no—
129#125—61no—
130C22⋊Q8—31no—
131C22⋊Q8—61no—
132C22⋊Q8—61no—
133C22⋊Q8C2×D311yescharacteristic
134C4×Q8—31no—
135C4×Q8—31no—
136#117—31no—
137#117—31no—
138C2×C4⋊C4C2×D311yescharacteristic
139#107—31no—
140#107—31no—
141#107—31no—
142#107—31no—
143#106—31no—
144#106—31no—
145#106C2×D311yescharacteristic
146#106C2×D311yescharacteristic
147C4⋊C8—31no—
148C4⋊C8—31no—
149#103—31no—
150#103—31no—
151#103—31no—
152#103—31no—
153#103—31no—
154#103—31no—
155#103C2×D311yescharacteristic
156#103C2×D311yescharacteristic
157C22⋊C8—31no—
158C22⋊C8C2×D311yescharacteristic
159#97—31no—
160C4×C8—31no—
161C23×C3C2×D411yescharacteristic
162C3×Q8—21no—
163C3×Q8—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—81no—
171C2×C3×C4C2×D411yescharacteristic
172C2×C3×C4C2411yescharacteristic
173C2×Dic3—21no—
174C2×Dic3—21no—
175C2×Dic3—21no—
176C2×Dic3—21no—
177C2×Dic3C2×D411yescharacteristic
178C2×Dic3C2×D411yescharacteristic
179C2×Dic3C2×D411yescharacteristic
180C2×Dic3C2×D411yescharacteristic
181Dic6—21no—
182Dic6—21no—
183Dic6—81no—
184Dic6—81no—
185C3×C8—21no—
186C3×C8—21no—
187C3⋊C8—21no—
188C3⋊C8—21no—
189C2×Q8—31no—
190C2×Q8—61no—
191C2×Q8—61no—
192C2×Q8C22×D311yescharacteristic
193C22×C4—21no—
194C22×C4C22×D311yescharacteristic
195C2×C8—31no—
196C2×C8—31no—
197C2×C8C22×D311yescharacteristic
198C2×C8C22×D311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—31no—
202C4⋊C4—31no—
203C4⋊C4—31no—
204C4⋊C4—31no—
205C4⋊C4—31no—
206C4⋊C4—61no—
207C4⋊C4—61no—
208C4⋊C4—61no—
209C4⋊C4—61no—
210C4⋊C4—61no—
211C4⋊C4—61no—
212C4⋊C4—61no—
213C4⋊C4—61no—
214C4⋊C4—61no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C4⋊C4—61no—
219C4⋊C4C22×D311yescharacteristic
220C4⋊C4C22×D311yescharacteristic
221C4⋊C4C22×D311yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—31no—
224C22⋊C4—31no—
225C22⋊C4—61no—
226C22⋊C4—61no—
227C42—31no—
228C42—31no—
229C42—61no—
230C42—61no—
231C42—61no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3C22×D411yescharacteristic
236C3×C4—21no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—41no—
240C3×C4—41no—
241C3×C42−1+411yescharacteristic
242C3×C42−1+411yescharacteristic
243Dic3—21no—
244Dic3—21no—
245Dic3—21no—
246Dic3—21no—
247Dic3—41no—
248Dic3—41no—
249Dic3—41no—
250Dic3—41no—
251C23D3×D411yescharacteristic
252Q8—21no—
253Q8—21no—
254Q8—61no—
255Q8—61no—
256Q8—241no—
257Q8—241no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—61no—
269C2×C4—61no—
270C2×C4—61no—
271C2×C4—61no—
272C2×C4—81no—
273C2×C4D3×D411yescharacteristic
274C2×C4C23×D311yescharacteristic
275C8—21no—
276C8—21no—
277C8—61no—
278C8—61no—
279C2×C3—41no—
280C2×C3#53611yescharacteristic
281C2×C3#57711yescharacteristic
282C2×C3#57811yescharacteristic
283C22—21no—
284C22—21no—
285C22—21no—
286C22C2×D3×D411yescharacteristic
287C4—21no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—61no—
293C4—61no—
294C4—61no—
295C4—61no—
296C4—121no—
297C4—121no—
298C4—121no—
299C4—121no—
300C4#101011yescharacteristic
301C4#101011yescharacteristic
302C3#324211yescharacteristic, complemented, Sylow
303C2—41no—
304C2#564811yescharacteristic
305C2#576211yescharacteristic
306C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#483C2
socleC22×C3C22×D4
prime radicalC23×C3C2×D4
hypercenter#483D3
hypocenterC3#3242
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
6. #4858C2semidirect
7. #4857C2semidirect
8. #4856C2semidirect
9. #4854C2semidirect
10. #4799C2semidirect
11. #4797C2semidirect
12. #4793C2semidirect
13. #4792C2semidirect
302. C3#3242semidirect

Maximal subgroups

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

subgroupindex
#56252
#55002
C3×#4832
#50452
#49702
#48582
#48572
#48562
#48542
#47992
#47972
#47932
#47922
#47232
#47202
#32423