Finite Group Databasebeta

← #28346481

Subgroups — #28346481

Order 13696.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293161C211yesmaximal, characteristic, complemented
2C4×#13133818C211yesmaximal, characteristic, complemented
3#20292969C211yesmaximal, characteristic, complemented
4#20292952C211yesmaximal, characteristic, complemented
5#20292935C211yesmaximal, characteristic, complemented
6#20292928C211yesmaximal, characteristic, complemented
7#20292850C211yesmaximal, characteristic, complemented
8#20292843C211yesmaximal, characteristic, complemented
9#20292791C211yesmaximal, characteristic, complemented
10#20292774C211yesmaximal, characteristic
11C4×Dic428C211yesmaximal, characteristic, complemented
12C4×#13133807C211yesmaximal, characteristic, complemented
13C4×#13133807C211yesmaximal, characteristic, complemented
14C4×D856C211yesmaximal, characteristic, complemented
15#431×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×Dic428C2211yescharacteristic
18C2×#13133807C2211yescharacteristic
19C2×#13133807C2211yescharacteristic
20C2×D856C2211yescharacteristic
21#16812103—21no—
22#16812101C2211yescharacteristic
23#16812097C2211yescharacteristic
24#16812092—21no—
25#16812088C2211yescharacteristic
26#16812083C2211yescharacteristic
27C4×Dic214C2211yescharacteristic
28C4×Dic214C2211yescharacteristic
29C4×Dic214C2211yescharacteristic
30C4×D428C2211yescharacteristic
31C4×D428C2211yescharacteristic
32C4×D428C2211yescharacteristic
33C4×C22⋊D107—21no—
34C4×C22⋊D107—21no—
35C4×C22⋊D107—21no—
36#16812068C2211yescharacteristic
37#16812066—21no—
38#16812066—21no—
39C42×D107—21no—
40#16812043C2211yescharacteristic
41#16812043C2211yescharacteristic
42#16812041C2211yescharacteristic
43#16812041C2211yescharacteristic
44#16812034C2211yescharacteristic
45#16812034C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812031C2211yescharacteristic
50#16812031C2211yescharacteristic
51#16812031C2211yescharacteristic
52C2×C42×C107C2211yescharacteristic
53C4⋊C8×C107C2211yescharacteristic
54C4⋊C8×C107C2211yescharacteristic
55C22⋊C8×C107C2211yescharacteristic
56C22⋊C8×C107C2211yescharacteristic
57C4×C8×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59#13133818—22no—
60#13133818—22no—
61C2×Dic214C2311yescharacteristic
62C2×Dic214C2311yescharacteristic
63C2×D428C2311yescharacteristic
64C2×D428C2311yescharacteristic
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C4×D107—21no—
68C2×C4×D107—21no—
69C2×C4×D107—21no—
70C2×C4×D107—21no—
71Dic428—22no—
72#13133807—22no—
73#13133807—22no—
74D856—22no—
75C4⋊Dic107C2311yescharacteristic
76C4⋊Dic107C2311yescharacteristic
77C4⋊Dic107C2311yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93C4×Dic107—21no—
94C4×Dic107—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C22×C4×C107D411yescharacteristic
98C22×C4×C107D411yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C2×C8×C107C2311yescharacteristic
103C2×C8×C107C2311yescharacteristic
104C42×C107D411yescharacteristic
105C42×C107D411yescharacteristic
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C23×C107C2×D411yescharacteristic
109C22×D107—21no—
110C22×D107—21no—
111C2×C4×C107—22no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—41no—
115C2×C4×C107C2×D411yescharacteristic
116C2×C4×C107C2×D411yescharacteristic
117C2×C4×C107C2×D411yescharacteristic
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2411yescharacteristic
121C22⋊D107—24no—
122C22⋊D107—42no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129D428—21no—
130D428—21no—
131D428—21no—
132D428#4112yes—
133C4×D107—24no—
134C4×D107—42no—
135C4×D107—42no—
136C4×D107—42no—
137Dic214—21no—
138Dic214—21no—
139Dic214—21no—
140Dic214#4112yes—
141C8×C107—21no—
142C8×C107—21no—
143C8×C107—21no—
144C8×C107—21no—
145C22×C107—21no—
146C22×C107—21no—
147C22×C107—21no—
148C22×C107C22×D411yescharacteristic
149C2×D107—22no—
150C2×D107—41no—
151C2×D107—41no—
152C2×D107—41no—
153C2×D107—41no—
154C2×D107—41no—
155C4×C107—21no—
156C4×C107—21no—
157C4×C107—21no—
158C4×C107—21no—
159C4×C107#13512yes—
160C4×C107C2×#4111yescharacteristic
161C4×C107C2×#4111yescharacteristic
162Dic107—22no—
163Dic107—41no—
164Dic107—41no—
165Dic107—41no—
166Dic107—41no—
167Dic107—41no—
168C2×C107—41no—
169C2×C107#52511yescharacteristic
170C2×C107C2×#13511yescharacteristic
171C2×C107#57511yescharacteristic
172D107—42no—
173D107—81no—
174#3102—1071nomaximal, Sylow
175C107#310211yescharacteristic, complemented, Sylow
176#529—1071no—
177C4×#41—1071no—
178#485—1071no—
179#482—1071no—
180#479—1071no—
181#478—1071no—
182#464—1071no—
183#463—1071no—
184#452—1071no—
185#449—1071no—
186C4×Q16—1071no—
187C4×SD16—1071no—
188C4×SD16—1071no—
189C4×D8—1071no—
190#431D10711yescharacteristic, complemented
191C2×#41—1071no—
192C2×Q16—1071no—
193C2×SD16—1071no—
194C2×SD16—1071no—
195C2×D8—1071no—
196#126—2141no—
197#125—1071no—
198#124—1071no—
199#123—2141no—
200C22⋊Q8—1071no—
201#121—1071no—
202C4×Q8—1071no—
203C4×Q8—1071no—
204C4×Q8—1071no—
205C4×D4—1071no—
206C4×D4—1071no—
207C4×D4—1071no—
208C4×D4—2141no—
209C4×D4—2141no—
210C4×D4—2141no—
211#117—1071no—
212#117—2141no—
213#117—2141no—
214C2×C42—2141no—
215C2×C42C2×D10711yescharacteristic
216#107—1071no—
217#107—1071no—
218#106—1071no—
219#106—1071no—
220C4⋊C8C2×D10711yescharacteristic
221C4⋊C8C2×D10711yescharacteristic
222#103—1071no—
223#103—1071no—
224#103—1071no—
225#103—1071no—
226#102—1071no—
227#102—1071no—
228#102—1071no—
229#102—1071no—
230C22⋊C8C2×D10711yescharacteristic
231C22⋊C8C2×D10711yescharacteristic
232C4×C8C2×D10711yescharacteristic
233C4×C8C2×D10711yescharacteristic
234#41—2142no—
235#41—2142no—
236C2×Q8—1071no—
237C2×Q8—1071no—
238C2×D4—1071no—
239C2×D4—1071no—
240C2×D4—2141no—
241C2×D4—2141no—
242C22×C4—2141no—
243C22×C4—2141no—
244C22×C4—2141no—
245C22×C4—2141no—
246C22×C4D42811yescharacteristic
247C22×C4D42811yescharacteristic
248C22×C4C22×D10711yescharacteristic
249Q16—2142no—
250SD16—2142no—
251SD16—2142no—
252D8—2142no—
253C2×C8C22×D10711yescharacteristic
254C2×C8C22×D10711yescharacteristic
255C2×C8C22×D10711yescharacteristic
256C2×C8C22×D10711yescharacteristic
257C4⋊C4—1071no—
258C4⋊C4—1071no—
259C4⋊C4—1071no—
260C4⋊C4—1071no—
261C4⋊C4—2141no—
262C4⋊C4—2141no—
263C4⋊C4—2141no—
264C4⋊C4—2141no—
265C4⋊C4—2141no—
266C4⋊C4—2141no—
267C22⋊C4—2141no—
268C22⋊C4—2141no—
269C22⋊C4—2141no—
270C22⋊C4—2141no—
271C22⋊C4—2141no—
272C22⋊C4—2141no—
273C22⋊C4—2141no—
274C22⋊C4—2141no—
275C42—2141no—
276C42—2141no—
277C42—2141no—
278C42—2141no—
279C42D42811yescharacteristic
280C42D42811yescharacteristic
281C42C22×D10711yescharacteristic
282C42C22×D10711yescharacteristic
283C23—2141no—
284C23—2141no—
285C23C2×D42811yescharacteristic
286Q8—1072no—
287Q8—2141no—
288Q8—2141no—
289Q8—2141no—
290D4—1072no—
291D4—4282no—
292D4—2144no—
293D4—2141no—
294D4—2141no—
295D4—2141no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—4282no—
301C2×C4—4282no—
302C2×C4—4282no—
303C2×C4—2144no—
304C2×C4—2141no—
305C2×C4—2141no—
306C2×C4—2141no—
307C2×C4—2141no—
308C2×C4—2141no—
309C2×C4—2141no—
310C2×C4C2×D42811yescharacteristic
311C2×C4C2×D42811yescharacteristic
312C2×C4C2×D42811yescharacteristic
313C2×C4C2×D42811yescharacteristic
314C2×C4C2×D42811yescharacteristic
315C2×C4C23×D10711yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—4281no—
324C22—4281no—
325C22—4281no—
326C22—4281no—
327C22—4281no—
328C22—2142no—
329C22C22×D42811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—4281no—
335C4—4281no—
336C4—4281no—
337C4—4281no—
338C4—4281no—
339C4—2142no—
340C4#1681213112yes—
341C4#41×D10711yescharacteristic
342C4#41×D10711yescharacteristic
343C2—41no—
344C2—8561no—
345C2—4282no—
346C2#2029313911yescharacteristic
347C2C2×#1681213111yescharacteristic
348C2#2029342711yescharacteristic
subgroupG/H
centerC2×C4C2×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#431×C107C2
socleC22×C107C22×D4
prime radical#20292774C2
hypercenter#431D107
hypocenterC107#3102
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #20293161C2semidirect
2. C4×#13133818C2semidirect
3. #20292969C2semidirect
4. #20292952C2semidirect
5. #20292935C2semidirect
6. #20292928C2semidirect
7. #20292850C2semidirect
8. #20292843C2semidirect
9. #20292791C2semidirect
11. C4×Dic428C2semidirect
12. C4×#13133807C2semidirect
13. C4×#13133807C2semidirect
14. C4×D856C2semidirect
15. #431×C107C2semidirect
175. C107#3102semidirect
190. #431D107semidirect

Maximal subgroups

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

subgroupindex
#202931612
C4×#131338182
#202929692
#202929522
#202929352
#202929282
#202928502
#202928432
#202927912
#202927742
C4×Dic4282
C4×#131338072
C4×D8562
#431×C1072
#3102107