Finite Group Databasebeta

← #28347913

Subgroups — #28347913

Order 13696.

322 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293238C211yesmaximal, characteristic
2#20293235C211yesmaximal, characteristic
3#20292936C211yesmaximal, characteristic, complemented
4#20292935C211yesmaximal, characteristic, complemented
5#20292934C211yesmaximal, characteristic, complemented
6#20292932C211yesmaximal, characteristic, complemented
7#20292884C211yesmaximal, characteristic
8#20292882C211yesmaximal, characteristic
9#20292867C211yesmaximal, characteristic
10#20292865C211yesmaximal, characteristic
11#20292835C211yesmaximal, characteristic, complemented
12#20292835C211yesmaximal, characteristic, complemented
13#20292834C211yesmaximal, characteristic, complemented
14#20292652C211yesmaximal, characteristic
15#462×C107C211yesmaximal, characteristic, complemented
16C2×#13133808C2211yescharacteristic
17C2×#13133808C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812107C2211yescharacteristic
21#16812104—21no—
22#16812104—21no—
23#16812104—21no—
24#16812103—21no—
25#16812101—21no—
26#16812101C2211yescharacteristic
27#16812100C2211yescharacteristic
28#16812099—21no—
29#16812099—21no—
30#16812099—21no—
31#16812089C2211yescharacteristic
32#16812085C2211yescharacteristic
33#16812085C2211yescharacteristic
34#16812085C2211yescharacteristic
35Q8×Dic107C2211yescharacteristic
36Q8×Dic107C2211yescharacteristic
37C4×Dic214C2211yescharacteristic
38#16812066C2211yescharacteristic
39#16812043C2211yescharacteristic
40#16812042C2211yescharacteristic
41#16812041C2211yescharacteristic
42#16812040C2211yescharacteristic
43C4⋊(C107⋊C8)C2211yescharacteristic
44Dic107⋊C8C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812033C2211yescharacteristic
49#16812033C2211yescharacteristic
50#16812033C2211yescharacteristic
51#16812033C2211yescharacteristic
52C2×Q16×C107C2211yescharacteristic
53C2×Q16×C107C2211yescharacteristic
54C4⋊Q8×C107C2211yescharacteristic
55C4×Q8×C107C2211yescharacteristic
56C4⋊C8×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58#103×C107C2211yescharacteristic
59C2×Dic214C2311yescharacteristic
60C2×C4×D107C2311yescharacteristic
61#13133808—41no—
62#13133808—41no—
63#13133801—41no—
64C2×C107⋊C8C2311yescharacteristic
65C2×C107⋊C8C2311yescharacteristic
66C8×D107—41no—
67C4⋊Dic107—21no—
68C4⋊Dic107—21no—
69C4⋊Dic107—21no—
70C4⋊Dic107—21no—
71C4⋊Dic107C2311yescharacteristic
72C4⋊Dic107C2311yescharacteristic
73C4⋊Dic107C2311yescharacteristic
74Dic107⋊C4—21no—
75Dic107⋊C4—21no—
76Dic107⋊C4—21no—
77Dic107⋊C4—21no—
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4D411yescharacteristic
84Dic107⋊C4D411yescharacteristic
85(C2×D107)⋊C4—21no—
86(C2×D107)⋊C4—21no—
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4D411yescharacteristic
90(C2×D107)⋊C4D411yescharacteristic
91C4×Dic107—21no—
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107C2311yescharacteristic
95C2×Q8×C107C2311yescharacteristic
96C2×Q8×C107C2311yescharacteristic
97C2×Q8×C107C2311yescharacteristic
98Q16×C107—41no—
99Q16×C107—41no—
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107—21no—
103C4⋊C4×C107—21no—
104C4⋊C4×C107—21no—
105C4⋊C4×C107C2311yescharacteristic
106C42×C107—21no—
107C42×C107C2311yescharacteristic
108C22×D107C2×D411yescharacteristic
109Q8×C107—21no—
110Q8×C107—21no—
111Q8×C107—21no—
112Q8×C107—21no—
113Q8×C107—21no—
114Q8×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2411yescharacteristic
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107C2×D411yescharacteristic
127C2×Dic107C2×D411yescharacteristic
128C2×Dic107C2×D411yescharacteristic
129C4×D107—21no—
130C4×D107—21no—
131Dic214—21no—
132Dic214—21no—
133C8×C107—21no—
134C8×C107—21no—
135C107⋊C8—21no—
136C107⋊C8—21no—
137C22×C107C22×D411yescharacteristic
138C2×D107—21no—
139C2×D107—21no—
140C2×D107—21no—
141C4×C107—21no—
142C4×C107—21no—
143C4×C107—41no—
144C4×C107—41no—
145C4×C107—41no—
146C4×C107—41no—
147C4×C107H(5,𝔽2)11yescharacteristic
148C4×C1072−1+411yescharacteristic
149Dic107—21no—
150Dic107—21no—
151Dic107—21no—
152Dic107—41no—
153Dic107—41no—
154Dic107—41no—
155Dic107—41no—
156C2×C107#53711yescharacteristic
157C2×C107#57811yescharacteristic
158C2×C107#57811yescharacteristic
159D107—41no—
160#3261—1071nomaximal, Sylow
161C107#326111yescharacteristic, complemented, Sylow
162#541—1071no—
163#541—1071no—
164#479—1071no—
165#479—1071no—
166#479—1071no—
167#479—1071no—
168#470—1071no—
169#470—1071no—
170#467—1071no—
171#467—1071no—
172#462—1071no—
173#462—1071no—
174#462—1071no—
175#462D10711yescharacteristic, complemented
176#424—1071no—
177C2×Q16—1071no—
178C2×Q16—1071no—
179C2×Q16C2×D10711yescharacteristic
180C2×Q16C2×D10711yescharacteristic
181C2×M16—1071no—
182C22×C8—1071no—
183C4⋊Q8—1071no—
184C4⋊Q8C2×D10711yescharacteristic
185#126—2141no—
186#126—2141no—
187#126—2141no—
188#126—2141no—
189#125—1071no—
190#125—1071no—
191#125—2141no—
192#125—2141no—
193#125—2141no—
194#125—2141no—
195C22⋊Q8—1071no—
196C22⋊Q8—1071no—
197C22⋊Q8—1071no—
198C22⋊Q8—1071no—
199C4×Q8—1071no—
200C4×Q8—1071no—
201C4×Q8—1071no—
202C4×Q8C2×D10711yescharacteristic
203#117—1071no—
204#107—1071no—
205#107—1071no—
206#106—1071no—
207#106—1071no—
208C4⋊C8—1071no—
209C4⋊C8—1071no—
210C4⋊C8—1071no—
211C4⋊C8C2×D10711yescharacteristic
212#103—1071no—
213#103—1071no—
214#103—1071no—
215#103—1071no—
216#103—1071no—
217#103—1071no—
218#103C2×D10711yescharacteristic
219#103C2×D10711yescharacteristic
220C2×Q8—1071no—
221C2×Q8C22×D10711yescharacteristic
222C2×Q8C22×D10711yescharacteristic
223C2×Q8C22×D10711yescharacteristic
224C22×C4—1071no—
225Q16—41no—
226Q16—41no—
227Q16—4281no—
228Q16—4281no—
229M16—4281no—
230C2×C8—1071no—
231C2×C8—1071no—
232C2×C8—4281no—
233C2×C8C22×D10711yescharacteristic
234C2×C8C22×D10711yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—1071no—
239C4⋊C4—1071no—
240C4⋊C4—1071no—
241C4⋊C4—1071no—
242C4⋊C4—1071no—
243C4⋊C4—2141no—
244C4⋊C4—2141no—
245C4⋊C4—2141no—
246C4⋊C4—2141no—
247C4⋊C4—2141no—
248C4⋊C4—2141no—
249C4⋊C4—2141no—
250C4⋊C4—2141no—
251C4⋊C4—2141no—
252C4⋊C4—2141no—
253C4⋊C4—2141no—
254C4⋊C4—2141no—
255C4⋊C4—2141no—
256C4⋊C4C22×D10711yescharacteristic
257C22⋊C4—1071no—
258C22⋊C4—1071no—
259C22⋊C4—2141no—
260C22⋊C4—2141no—
261C22⋊C4—2141no—
262C22⋊C4—2141no—
263C42—21no—
264C42—1071no—
265C42—2141no—
266C42—2141no—
267C42—2141no—
268C42C22×D10711yescharacteristic
269C23—1071no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—2141no—
277Q8—2141no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—1071no—
283C2×C4—1071no—
284C2×C4—1071no—
285C2×C4—2141no—
286C2×C4—2141no—
287C2×C4—2141no—
288C2×C4—2141no—
289C2×C4—2141no—
290C2×C4—2141no—
291C2×C4D4×D10711yescharacteristic
292C2×C4D4×D10711yescharacteristic
293C2×C4C23×D10711yescharacteristic
294C8—21no—
295C8—21no—
296C8—2141no—
297C8—2141no—
298C22—2141no—
299C22—2141no—
300C22—2141no—
301C22C2×D4×D10711yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—4281no—
309C4—4281no—
310C4—4281no—
311C4—4281no—
312C4—2141no—
313C4—2141no—
314C4—2141no—
315C4#1681215411yescharacteristic
316C4#1681215611yescharacteristic
317C2—4281no—
318C2#2029320611yescharacteristic
319C2#2029344011yescharacteristic
320C2#2029344311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#462×C107C2
socleC22×C107C22×D4
prime radicalC22×D107C2×D4
hypercenter#462D107
hypocenterC107#3261
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #20292936C2semidirect
4. #20292935C2semidirect
5. #20292934C2semidirect
6. #20292932C2semidirect
11. #20292835C2semidirect
12. #20292835C2semidirect
13. #20292834C2semidirect
15. #462×C107C2semidirect
161. C107#3261semidirect
175. #462D107semidirect

Maximal subgroups

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

subgroupindex
#202932382
#202932352
#202929362
#202929352
#202929342
#202929322
#202928842
#202928822
#202928672
#202928652
#202928352
#202928342
#202926522
#462×C1072
#3261107