Finite Group Databasebeta

← #81987

Subgroups — #81987

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#5729C211yesmaximal, characteristic
2#5698C211yesmaximal, characteristic
3C3×#501C211yesmaximal, characteristic, complemented
4#5093C211yesmaximal, characteristic, complemented
5#5065C211yesmaximal, characteristic, complemented
6#4888C211yesmaximal, characteristic
7#4884C211yesmaximal, characteristic
8#4877C211yesmaximal, characteristic, complemented
9#4875C211yesmaximal, characteristic, complemented
10#4868C211yesmaximal, characteristic
11#4862C211yesmaximal, characteristic
12#4857C211yesmaximal, characteristic, complemented
13#4854C211yesmaximal, characteristic, complemented
14#4709C211yesmaximal, characteristic
15#4703C211yesmaximal, characteristic, complemented
16#3242—31nomaximal, Sylow
17C3×C4⋊Q8C2211yescharacteristic
18C3×#125C2211yescharacteristic
19#946—21no—
20#944—21no—
21#898—21no—
22#898—21no—
23#897C2211yescharacteristic
24#897C2211yescharacteristic
25#896—21no—
26#892C2211yescharacteristic
27D3×C4⋊C4C2211yescharacteristic
28#890—21no—
29#890—21no—
30#890C2211yescharacteristic
31#889—21no—
32#888C2211yescharacteristic
33#887C2211yescharacteristic
34#887C2211yescharacteristic
35#872C2211yescharacteristic
36#870C2211yescharacteristic
37#869C2211yescharacteristic
38C3×#107C2211yescharacteristic
39C3×#107C2211yescharacteristic
40C3×#106C2211yescharacteristic
41C3×#106C2211yescharacteristic
42C3×#97C2211yescharacteristic
43(C2×D3)⋊C8C2211yescharacteristic
44(C2×D3)⋊C8C2211yescharacteristic
45#816C2211yescharacteristic
46#816C2211yescharacteristic
47#816C2211yescharacteristic
48#816C2211yescharacteristic
49Dic3⋊C8C2211yescharacteristic
50Dic3⋊C8C2211yescharacteristic
51#810C2211yescharacteristic
52#810C2211yescharacteristic
53#810C2211yescharacteristic
54#810C2211yescharacteristic
55#808C2211yescharacteristic
56#808C2211yescharacteristic
57#807C2211yescharacteristic
58#807C2211yescharacteristic
59C4×C3⋊C8C2211yescharacteristic
60#544—31no—
61#541—31no—
62#501D311yescharacteristic, complemented
63#499—31no—
64#491—31no—
65#487—31no—
66#485—31no—
67#485—31no—
68#484—31no—
69#483—31no—
70#479—31no—
71#479—31no—
72#477—31no—
73#475—31no—
74#433—31no—
75C2×C3×Q8—21no—
76C2×C4×D3—21no—
77C2×C4×D3C2311yescharacteristic
78C2×Dic6—21no—
79C2×Dic6C2311yescharacteristic
80C2×Dic6C2311yescharacteristic
81C2×C3×C8C2311yescharacteristic
82C2×C3×C8C2311yescharacteristic
83C3×C4⋊C4—21no—
84C3×C4⋊C4—21no—
85C3×C4⋊C4—21no—
86C3×C4⋊C4C2311yescharacteristic
87C3×C4⋊C4C2311yescharacteristic
88C3×C4⋊C4C2311yescharacteristic
89C3×C4⋊C4C2311yescharacteristic
90C3×C42C2311yescharacteristic
91(C2×D3)⋊C4—21no—
92(C2×D3)⋊C4—21no—
93(C2×D3)⋊C4—21no—
94(C2×D3)⋊C4D411yescharacteristic
95(C2×D3)⋊C4D411yescharacteristic
96C4⋊Dic3—21no—
97C4⋊Dic3—21no—
98C4⋊Dic3—21no—
99C4⋊Dic3—21no—
100C4⋊Dic3—21no—
101C4⋊Dic3C2311yescharacteristic
102C4⋊Dic3C2311yescharacteristic
103Dic3⋊C4—21no—
104Dic3⋊C4—21no—
105Dic3⋊C4—21no—
106Dic3⋊C4—21no—
107Dic3⋊C4—21no—
108Dic3⋊C4—21no—
109Dic3⋊C4—21no—
110Dic3⋊C4D411yescharacteristic
111Dic3⋊C4D411yescharacteristic
112C4×Dic3—21no—
113C4×Dic3—21no—
114C4×Dic3—21no—
115C4×Dic3C2311yescharacteristic
116C2×C3⋊C8C2311yescharacteristic
117C2×C3⋊C8C2311yescharacteristic
118C4⋊Q8—31no—
119C4⋊Q8—31no—
120C4⋊Q8—61no—
121C4⋊Q8C2×D311yescharacteristic
122#126—61no—
123#126—61no—
124#125—31no—
125#125—31no—
126#125—61no—
127#125—61no—
128#125—61no—
129#125C2×D311yescharacteristic
130C22⋊Q8—31no—
131C22⋊Q8—31no—
132C22⋊Q8—61no—
133C22⋊Q8—61no—
134C4×Q8—31no—
135C4×Q8—31no—
136#117—31no—
137#117—31no—
138C2×C4⋊C4—31no—
139#107—31no—
140#107—31no—
141#107C2×D311yescharacteristic
142#107C2×D311yescharacteristic
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#103—31no—
156#103—31no—
157C22⋊C8—31no—
158C22⋊C8—31no—
159#97C2×D311yescharacteristic
160C4×C8—31no—
161C22×D3C2×D411yescharacteristic
162C3×Q8—81no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4C2×D411yescharacteristic
168C2×C3×C4C2×D411yescharacteristic
169C2×C3×C4C2411yescharacteristic
170C2×Dic3—21no—
171C2×Dic3—21no—
172C2×Dic3—21no—
173C2×Dic3—21no—
174C2×Dic3C2×D411yescharacteristic
175C2×Dic3C2×D411yescharacteristic
176C2×Dic3C2×D411yescharacteristic
177C4×D3—21no—
178C4×D3—21no—
179C4×D3—81no—
180Dic6—21no—
181Dic6—21no—
182Dic6—21no—
183Dic6—21no—
184Dic6—81no—
185C3×C8—21no—
186C3×C8—21no—
187C3⋊C8—21no—
188C3⋊C8—21no—
189C2×Q8—21no—
190C2×Q8—31no—
191C2×Q8—31no—
192C2×Q8—61no—
193C22×C4—31no—
194C22×C4—61no—
195C2×C8—31no—
196C2×C8—31no—
197C2×C8C22×D311yescharacteristic
198C2×C8C22×D311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
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⋊C4C22×D311yescharacteristic
219C4⋊C4C22×D311yescharacteristic
220C4⋊C4C22×D311yescharacteristic
221C4⋊C4C22×D311yescharacteristic
222C22⋊C4—31no—
223C22⋊C4—31no—
224C22⋊C4—61no—
225C22⋊C4—61no—
226C22⋊C4—61no—
227C42—31no—
228C42—61no—
229C42—61no—
230C42—61no—
231C42C22×D311yescharacteristic
232C22×C3C22×D411yescharacteristic
233C2×D3—21no—
234C2×D3—21no—
235C2×D3—21no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—41no—
239C3×C4—41no—
240C3×C4—41no—
241C3×C4—41no—
242C3×C42−1+411yescharacteristic
243C3×C42−1+411yescharacteristic
244Dic3—21no—
245Dic3—21no—
246Dic3—21no—
247Dic3—41no—
248Dic3—41no—
249Dic3—41no—
250Dic3—41no—
251C23—31no—
252Q8—61no—
253Q8—61no—
254Q8—61no—
255Q8—61no—
256Q8—81no—
257Q8—241no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—31no—
263C2×C4—31no—
264C2×C4—31no—
265C2×C4—61no—
266C2×C4—61no—
267C2×C4—61no—
268C2×C4—61no—
269C2×C4—61no—
270C2×C4—61no—
271C2×C4—241no—
272C2×C4D3×D411yescharacteristic
273C2×C4D3×D411yescharacteristic
274C2×C4C23×D311yescharacteristic
275C8—21no—
276C8—21no—
277C8—61no—
278C8—61no—
279C2×C3#53611yescharacteristic
280C2×C3#57711yescharacteristic
281C2×C3#57811yescharacteristic
282D3—41no—
283C22—61no—
284C22—61no—
285C22—61no—
286C22C2×D3×D411yescharacteristic
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—61no—
294C4—61no—
295C4—61no—
296C4—121no—
297C4—121no—
298C4—121no—
299C4—121no—
300C4#100711yescharacteristic
301C4#100711yescharacteristic
302C3#324211yescharacteristic, complemented, Sylow
303C2—121no—
304C2#572411yescharacteristic
305C2#577511yescharacteristic
306C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#501C2
socleC22×C3C22×D4
prime radicalC22×D3C2×D4
hypercenter#501D3
hypocenterC3#3242
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. C3×#501C2semidirect
4. #5093C2semidirect
5. #5065C2semidirect
8. #4877C2semidirect
9. #4875C2semidirect
12. #4857C2semidirect
13. #4854C2semidirect
15. #4703C2semidirect
62. #501D3semidirect
302. C3#3242semidirect

Maximal subgroups

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

subgroupindex
#57292
#56982
C3×#5012
#50932
#50652
#48882
#48842
#48772
#48752
#48682
#48622
#48572
#48542
#47092
#47032
#32423