Finite Group Databasebeta

← #28349043

Subgroups — #28349043

Order 13696.

374 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293345C211yesmaximal, characteristic, complemented
2#20293277C211yesmaximal, characteristic
3#20293031C211yesmaximal, characteristic, complemented
4#20292964C211yesmaximal, characteristic, complemented
5#20292963C211yesmaximal, characteristic, complemented
6#20292949C211yesmaximal, characteristic, complemented
7#20292911C211yesmaximal, characteristic, complemented
8#20292905C211yesmaximal, characteristic, complemented
9#20292872C211yesmaximal, characteristic, complemented
10#20292871C211yesmaximal, characteristic, complemented
11#20292718C211yesmaximal, characteristic, complemented
12#20292702C211yesmaximal, characteristic, complemented
13#20292670C211yesmaximal, characteristic, complemented
14#20292666C211yesmaximal, characteristic, complemented
15#482×C107C211yesmaximal, characteristic, complemented
16C2×#13133817—21no—
17C2×#13133806C2211yescharacteristic
18C2×#13133802C2211yescharacteristic
19C2×#13133801C2211yescharacteristic
20#16812108C2211yescharacteristic
21#16812108C2211yescharacteristic
22#16812103—21no—
23#16812102—21no—
24#16812095—21no—
25#16812091—21no—
26#16812090—21no—
27#16812089C2211yescharacteristic
28#16812088C2211yescharacteristic
29#16812086—21no—
30#16812080C2211yescharacteristic
31C4×Dic214—21no—
32#16812074C2211yescharacteristic
33D4×Dic107C2211yescharacteristic
34C4×C22⋊D107C2211yescharacteristic
35#16812067C2211yescharacteristic
36C2×C4⋊Dic107C2211yescharacteristic
37C4⋊C4×D107C2211yescharacteristic
38#16812043C2211yescharacteristic
39#16812043C2211yescharacteristic
40#16812042C2211yescharacteristic
41#16812042C2211yescharacteristic
42#16812042C2211yescharacteristic
43#16812040C2211yescharacteristic
44#16812040C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812032C2211yescharacteristic
49#16812030C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52#121×C107C2211yescharacteristic
53#117×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59#13133817—44no—
60C2×Dic214—21no—
61C2×Dic214—21no—
62C2×Dic214C2311yescharacteristic
63C2×C22⋊D107—21no—
64C2×C22⋊D107D411yescharacteristic
65C22×Dic107—21no—
66C22×Dic107—21no—
67C2×C4×D107—21no—
68C2×C4×D107C2311yescharacteristic
69#13133806—22no—
70#13133802—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⋊C4D411yescharacteristic
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87C22⋊Dic107—21no—
88C22⋊Dic107D411yescharacteristic
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4D411yescharacteristic
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107C2311yescharacteristic
95C2×D4×C107—21no—
96C2×D4×C107C2311yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C4⋊C4×C107C2311yescharacteristic
101C4⋊C4×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C22⋊C4×C107—21no—
104C22⋊C4×C107—21no—
105C42×C107—21no—
106C23×C107—21no—
107C23×C107C2×D411yescharacteristic
108C22×D107C2×D411yescharacteristic
109D4×C107—21no—
110D4×C107—21no—
111D4×C107—42no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107C2×D411yescharacteristic
118C2×C4×C107C2411yescharacteristic
119C22⋊D107—22no—
120C22⋊D107—42no—
121C2×Dic107—21no—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—42no—
126C2×Dic107—42no—
127C2×Dic107C2×D411yescharacteristic
128C2×Dic107C2×D411yescharacteristic
129C2×Dic107C2×D411yescharacteristic
130C4×D107—21no—
131C4×D107—21no—
132C4×D107—42no—
133Dic214—21no—
134Dic214—21no—
135Dic214—42no—
136Dic214—42no—
137C8×C107—21no—
138C8×C107—21no—
139C107⋊C8—21no—
140C107⋊C8#4112yescomplemented
141C22×C107—21no—
142C22×C107—21no—
143C22×C107—21no—
144C22×C107—41no—
145C22×C107—41no—
146C22×C107—41no—
147C22×C107C22×D411yescharacteristic
148C2×D107—21no—
149C2×D107—21no—
150C2×D107—21no—
151C4×C107—21no—
152C4×C107—41no—
153C4×C107—41no—
154C4×C107—41no—
155C4×C107C2×#4111yescharacteristic
156C4×C1072−1+411yescharacteristic
157Dic107—21no—
158Dic107—21no—
159Dic107—41no—
160Dic107—41no—
161Dic107—41no—
162Dic107—41no—
163Dic107AGL(1,ℤ/8)12yes—
164C2×C107—41no—
165C2×C107—81no—
166C2×C107#54711yescharacteristic
167C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C107#57811yescharacteristic
169D107—41no—
170#3353—1071nomaximal, Sylow
171C107#335311yescharacteristic, complemented, Sylow
172#556—1071no—
173#547—1071no—
174#500—1071no—
175#484—1071no—
176#484—1071no—
177#482—1071no—
178#482D10711yescharacteristic, complemented
179#475—1071no—
180#474—1071no—
181#468—1071no—
182#468—1071no—
183C4×SD16—1071no—
184#436—1071no—
185#428—1071no—
186#428—1071no—
187C2×#41—2141no—
188C2×SD16—1071no—
189C2×M16—1071no—
190C2×M16—1071no—
191C4⋊Q8—1071no—
192C4⋊Q8—1071no—
193#126—2141no—
194#126—2141no—
195#124—2141no—
196#123—2141no—
197#123—2141no—
198C22⋊Q8—1071no—
199C22⋊Q8—1071no—
200C22⋊Q8—2141no—
201#121—1071no—
202#121C2×D10711yescharacteristic
203C4×Q8—1071no—
204C4×Q8—2141no—
205C4×D4—1071no—
206C4×D4—1071no—
207#117—1071no—
208#117C2×D10711yescharacteristic
209C2×C4⋊C4—1071no—
210C2×C4⋊C4—1071no—
211#107—1071no—
212#107—1071no—
213#107—1071no—
214#107—1071no—
215#107—1071no—
216#107C2×D10711yescharacteristic
217#106—1071no—
218#106—1071no—
219#106C2×D10711yescharacteristic
220C4⋊C8—1071no—
221#103—1071no—
222#103—1071no—
223#103—1071no—
224#102—1071no—
225#102C2×D10711yescharacteristic
226#102C2×D10711yescharacteristic
227C22⋊C8—1071no—
228C22⋊C8C2×D10711yescharacteristic
229C4×C8—1071no—
230#41—4284no—
231C2×Q8—1071no—
232C2×Q8—2141no—
233C2×Q8—2141no—
234C2×D4—21no—
235C2×D4—1071no—
236C2×D4—2141no—
237C2×D4C22×D10711yescharacteristic
238C22×C4—1071no—
239C22×C4—2141no—
240C22×C4—2141no—
241C22×C4—2141no—
242C22×C4C22×D10711yescharacteristic
243SD16—2142no—
244M16—2142no—
245M16—2142no—
246C2×C8—1071no—
247C2×C8—1071no—
248C2×C8C22×D10711yescharacteristic
249C2×C8C22×D10711yescharacteristic
250C4⋊C4—1071no—
251C4⋊C4—1071no—
252C4⋊C4—1071no—
253C4⋊C4—1071no—
254C4⋊C4—2141no—
255C4⋊C4—2141no—
256C4⋊C4—2141no—
257C4⋊C4—2141no—
258C4⋊C4—2141no—
259C4⋊C4—2141no—
260C4⋊C4—2141no—
261C4⋊C4C22×D10711yescharacteristic
262C4⋊C4C22×D10711yescharacteristic
263C4⋊C4C22×D10711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—1071no—
267C22⋊C4—1071no—
268C22⋊C4—2141no—
269C22⋊C4—2141no—
270C22⋊C4—2141no—
271C22⋊C4—2141no—
272C22⋊C4—2141no—
273C42—21no—
274C42—1071no—
275C42—2141no—
276C42—2141no—
277C23—21no—
278C23—1071no—
279C23D4×D10711yescharacteristic
280Q8—4282no—
281Q8—4282no—
282Q8—2141no—
283Q8—2141no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—4282no—
288D4—2142no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—1071no—
295C2×C4—1071no—
296C2×C4—1071no—
297C2×C4—4282no—
298C2×C4—4282no—
299C2×C4—4282no—
300C2×C4—2141no—
301C2×C4—2141no—
302C2×C4—2141no—
303C2×C4—2141no—
304C2×C4—2141no—
305C2×C4—2141no—
306C2×C4D4×D10711yescharacteristic
307C2×C4C23×D10711yescharacteristic
308C8—21no—
309C8—21no—
310C8—1072no—
311C8—2141no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—2141no—
319C22—2141no—
320C22—2141no—
321C22C2×D4×D10711yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—1072no—
327C4—4281no—
328C4—4281no—
329C4—4281no—
330C4—4281no—
331C4—2141no—
332C4—2141no—
333C4#41×D10711yescharacteristic
334C4#1681215611yescharacteristic
335C2—41no—
336C2—81no—
337C2—4281no—
338C2#2029327511yescharacteristic
339C2AGL(1,ℤ/8)×D10711yescharacteristic
340C2#2029344111yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#482×C107C2
socleC22×C107C22×D4
prime radical#20293277C2
hypercenter#482D107
hypocenterC107#3353
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20293345C2semidirect
3. #20293031C2semidirect
4. #20292964C2semidirect
5. #20292963C2semidirect
6. #20292949C2semidirect
7. #20292911C2semidirect
8. #20292905C2semidirect
9. #20292872C2semidirect
10. #20292871C2semidirect
11. #20292718C2semidirect
12. #20292702C2semidirect
13. #20292670C2semidirect
14. #20292666C2semidirect
15. #482×C107C2semidirect
140. C107⋊C8#41semidirect
171. C107#3353semidirect
178. #482D107semidirect

Maximal subgroups

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

subgroupindex
#202933452
#202932772
#202930312
#202929642
#202929632
#202929492
#202929112
#202929052
#202928722
#202928712
#202927182
#202927022
#202926702
#202926662
#482×C1072
#3353107