Finite Group Databasebeta

← #28346278

Subgroups — #28346278

Order 13696.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D107C211yesmaximal, characteristic, complemented
2C4×#13133817C211yesmaximal, characteristic
3#20292937C211yesmaximal, characteristic, complemented
4#20292935C211yesmaximal, characteristic, complemented
5#20292933C211yesmaximal, characteristic, complemented
6#20292931C211yesmaximal, characteristic, complemented
7#20292929C211yesmaximal, characteristic, complemented
8#20292927C211yesmaximal, characteristic, complemented
9#20292925C211yesmaximal, characteristic, complemented
10#20292668C211yesmaximal, characteristic, complemented
11#20292666C211yesmaximal, characteristic, complemented
12#20292649C211yesmaximal, characteristic, complemented
13#20292625C211yesmaximal, characteristic
14#20292625C211yesmaximal, characteristic
15#478×C107C211yesmaximal, characteristic, complemented
16C2×#13133817C2211yescharacteristic
17C2×#13133801C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19#16812101C2211yescharacteristic
20#16812100C2211yescharacteristic
21#16812100C2211yescharacteristic
22#16812099—21no—
23#16812099—21no—
24C4×Dic214C2211yescharacteristic
25#16812074C2211yescharacteristic
26D4×Dic107C2211yescharacteristic
27C4×C22⋊D107—21no—
28(C22⋊D107)⋊C4—21no—
29#16812067C2211yescharacteristic
30#16812065—21no—
31C4⋊C4×D107—21no—
32C4⋊C4×D107—21no—
33C4⋊C4×D107C2211yescharacteristic
34C4⋊C4×D107C2211yescharacteristic
35C2×C4×Dic107—21no—
36C42×D107C2211yescharacteristic
37#16812043C2211yescharacteristic
38#16812042C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812041C2211yescharacteristic
41#16812040C2211yescharacteristic
42#16812040C2211yescharacteristic
43C4⋊(C107⋊C8)C2211yescharacteristic
44Dic107⋊C8C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812032C2211yescharacteristic
49#16812032C2211yescharacteristic
50#16812030C2211yescharacteristic
51#16812030C2211yescharacteristic
52#125×C107C2211yescharacteristic
53C4×D4×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56C4⋊C8×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58#102×C107C2211yescharacteristic
59#13133817—22no—
60#13133817Q814yes—
61C2×Dic214C2311yescharacteristic
62C2×C22⋊D107—21no—
63C22×Dic107—21no—
64C22×Dic107—21no—
65C2×C4×D107—21no—
66C2×C4×D107—21no—
67C2×C4×D107D411yescharacteristic
68C2×C4×D107D411yescharacteristic
69C2×C4×D107C2311yescharacteristic
70#13133801—22no—
71#13133801—22no—
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C4⋊Dic107—21no—
75C4⋊Dic107—21no—
76C4⋊Dic107C2311yescharacteristic
77C4⋊Dic107C2311yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87C22⋊Dic107—21no—
88(C2×D107)⋊C4—21no—
89C4×Dic107—21no—
90C4×Dic107—21no—
91C4×Dic107—21no—
92C4×Dic107D411yescharacteristic
93C4×Dic107D411yescharacteristic
94C4×Dic107C2311yescharacteristic
95C2×D4×C107C2311yescharacteristic
96C22×C4×C107—21no—
97C2×C8×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C4⋊C4×C107—21no—
100C4⋊C4×C107—21no—
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C22⋊C4×C107—21no—
105C42×C107C2311yescharacteristic
106C23×C107—21no—
107C22×D107C2×D411yescharacteristic
108D4×C107—21no—
109D4×C107C2×Q812yes—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—42no—
114C2×C4×C107C2×D411yescharacteristic
115C2×C4×C107C2×D411yescharacteristic
116C2×C4×C107C2411yescharacteristic
117C22⋊D107—24no—
118C2×Dic107—21no—
119C2×Dic107—24no—
120C2×Dic107—21no—
121C2×Dic107—21no—
122C2×Dic107—21no—
123C2×Dic107—42no—
124C2×Dic107C2×D411yescharacteristic
125C2×Dic107C2×D411yescharacteristic
126C2×Dic107C2×D411yescharacteristic
127C4×D107—41no—
128C4×D107—41no—
129C4×D107—42no—
130C4×D107—42no—
131C4×D107C2×Q812yes—
132C4×D107#4112yes—
133Dic214—21no—
134Dic214C2×Q812yes—
135C8×C107—21no—
136C8×C107—21no—
137C107⋊C8—21no—
138C107⋊C8—21no—
139C22×C107—22no—
140C22×C107—41no—
141C22×C107—41no—
142C22×C107C22×D411yescharacteristic
143C2×D107—21no—
144C2×D107—21no—
145C2×D107C22⋊Q812yes—
146C4×C107—21no—
147C4×C107—21no—
148C4×C107—41no—
149C4×C107—41no—
150C4×C107—41no—
151C4×C107C22×Q811yescharacteristic
152C4×C107C2×#4111yescharacteristic
153Dic107—22no—
154Dic107—21no—
155Dic107—21no—
156Dic107—41no—
157Dic107—41no—
158Dic107—41no—
159Dic107C22⋊Q812yes—
160C2×C107—42no—
161C2×C107C2×C22⋊Q811yescharacteristic
162C2×C107#57511yescharacteristic
163C2×C107#57511yescharacteristic
164D107—22no—
165#3080—1071nomaximal, Sylow
166C107#308011yescharacteristic, complemented, Sylow
167C2×#125—1071no—
168C4×#41—1071no—
169#479—1071no—
170#479—1071no—
171#479—1071no—
172#479—1071no—
173#478—1071no—
174#478—1071no—
175#478—1071no—
176#478D10711yescharacteristic, complemented
177#428—1071no—
178#428—1071no—
179#423—1071no—
180#417—1071no—
181#417—1071no—
182C2×#41—1071no—
183C2×M16—1071no—
184C2×M16—1071no—
185#125—1071no—
186#125—1071no—
187#125—1071no—
188#125—2141no—
189#125—2141no—
190#125C2×D10711yescharacteristic
191C4×Q8—1071no—
192C4×Q8—1071no—
193C4×D4—1071no—
194C4×D4—2141no—
195C4×D4—2141no—
196C4×D4C2×D10711yescharacteristic
197#117—1071no—
198#117—2141no—
199C2×C4⋊C4—1071no—
200C2×C4⋊C4—1071no—
201C2×C4⋊C4—2141no—
202C2×C4⋊C4—2141no—
203C2×C42—1071no—
204C2×C42—2141no—
205#107—1071no—
206#107—1071no—
207#107—1071no—
208#107C2×D10711yescharacteristic
209#106—1071no—
210#106—1071no—
211#106—1071no—
212#106C2×D10711yescharacteristic
213C4⋊C8—1071no—
214C4⋊C8—1071no—
215C4⋊C8—1071no—
216C4⋊C8C2×D10711yescharacteristic
217#103—1071no—
218#103—1071no—
219#103—1071no—
220#103—1071no—
221#102—1071no—
222#102—1071no—
223#102C2×D10711yescharacteristic
224#102C2×D10711yescharacteristic
225#41—1074no—
226#41—2142no—
227C2×Q8—1071no—
228C2×D4—2141no—
229C2×D4C22×D10711yescharacteristic
230C22×C4—21no—
231C22×C4—1071no—
232C22×C4—1071no—
233C22×C4—1071no—
234C22×C4—2141no—
235C22×C4—2141no—
236C22×C4—2141no—
237C22×C4—2141no—
238M16—2142no—
239M16—2142no—
240C2×C8—1071no—
241C2×C8—1071no—
242C2×C8C22×D10711yescharacteristic
243C2×C8C22×D10711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—1071no—
247C4⋊C4—1071no—
248C4⋊C4—1071no—
249C4⋊C4—2141no—
250C4⋊C4—2141no—
251C4⋊C4—2141no—
252C4⋊C4—2141no—
253C4⋊C4—2141no—
254C4⋊C4—2141no—
255C4⋊C4—2141no—
256C4⋊C4—2141no—
257C4⋊C4—2141no—
258C4⋊C4—2141no—
259C4⋊C4C22×D10711yescharacteristic
260C4⋊C4C22×D10711yescharacteristic
261C4⋊C4C22×D10711yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—2141no—
264C22⋊C4—2141no—
265C42—1071no—
266C42—1071no—
267C42—1071no—
268C42—2141no—
269C42—2141no—
270C42—2141no—
271C42C22×D10711yescharacteristic
272C23—21no—
273C23—1071no—
274Q8—1072no—
275Q8—2141no—
276D4—21no—
277D4—2144no—
278D4Q8×D10712yes—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—1071no—
284C2×C4—1072no—
285C2×C4—1072no—
286C2×C4—1071no—
287C2×C4—1071no—
288C2×C4—4281no—
289C2×C4—4281no—
290C2×C4—4282no—
291C2×C4—4282no—
292C2×C4—4282no—
293C2×C4—2144no—
294C2×C4—2141no—
295C2×C4—2141no—
296C2×C4—2141no—
297C2×C4—2141no—
298C2×C4D4×D10711yescharacteristic
299C2×C4D4×D10711yescharacteristic
300C2×C4C23×D10711yescharacteristic
301C8—21no—
302C8—21no—
303C8—2141no—
304C8—2141no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—1072no—
309C22—2141no—
310C22—2141no—
311C22C2×D4×D10711yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—1072no—
318C4—4281no—
319C4—4281no—
320C4—4281no—
321C4—2142no—
322C4—2141no—
323C4—2141no—
324C4C2×Q8×D10711yescharacteristic
325C4#41×D10711yescharacteristic
326C2—42no—
327C2—2142no—
328C2C22⋊Q8×D10711yescharacteristic
329C2#2029342311yescharacteristic
330C2#2029342411yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#478×C107C2
socleC22×C107C22×D4
prime radicalC2×#13133817C22
hypercenter#478D107
hypocenterC107#3080
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #125×D107C2semidirect
3. #20292937C2semidirect
4. #20292935C2semidirect
5. #20292933C2semidirect
6. #20292931C2semidirect
7. #20292929C2semidirect
8. #20292927C2semidirect
9. #20292925C2semidirect
10. #20292668C2semidirect
11. #20292666C2semidirect
12. #20292649C2semidirect
15. #478×C107C2semidirect
166. C107#3080semidirect
176. #478D107semidirect

Maximal subgroups

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

subgroupindex
#125×D1072
C4×#131338172
#202929372
#202929352
#202929332
#202929312
#202929292
#202929272
#202929252
#202926682
#202926662
#202926492
#202926252
#478×C1072
#3080107