Finite Group Databasebeta

← #28346389

Subgroups — #28346389

Order 13696.

414 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293137C211yesmaximal, characteristic
2#117×D107C211yesmaximal, characteristic, complemented
3#20292971C211yesmaximal, characteristic, complemented
4#20292970C211yesmaximal, characteristic, complemented
5#20292969C211yesmaximal, characteristic, complemented
6#20292968C211yesmaximal, characteristic, complemented
7#20292950C211yesmaximal, characteristic, complemented
8#20292949C211yesmaximal, characteristic, complemented
9#20292948C211yesmaximal, characteristic, complemented
10#20292668C211yesmaximal, characteristic, complemented
11#20292666C211yesmaximal, characteristic, complemented
12#20292625C211yesmaximal, characteristic, complemented
13#20292625C211yesmaximal, characteristic, complemented
14#20292589C211yesmaximal, characteristic, complemented
15#482×C107C211yesmaximal, characteristic, complemented
16C2×#13133817C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×#13133801C2211yescharacteristic
20#16812091—21no—
21#16812089C2211yescharacteristic
22#16812088C2211yescharacteristic
23#16812080C2211yescharacteristic
24#16812077—21no—
25D4×Dic107—21no—
26(C22⋊D107)⋊C4—21no—
27#16812068C2211yescharacteristic
28#16812067C2211yescharacteristic
29#16812067C2211yescharacteristic
30#16812067C2211yescharacteristic
31#16812066—21no—
32#16812065—21no—
33C4⋊C4×D107C2211yescharacteristic
34C4⋊C4×D107C2211yescharacteristic
35C22⋊C4×D107—21no—
36C42×D107—21no—
37#16812043C2211yescharacteristic, complemented
38#16812042C2211yescharacteristic, complemented
39#16812042C2211yescharacteristic, complemented
40#16812041C2211yescharacteristic, complemented
41#16812040C2211yescharacteristic, complemented
42#16812040C2211yescharacteristic, complemented
43#16812034C2211yescharacteristic, complemented
44#16812034C2211yescharacteristic, complemented
45#16812032C2211yescharacteristic, complemented
46#16812032C2211yescharacteristic, complemented
47#16812030C2211yescharacteristic, complemented
48#16812030C2211yescharacteristic, complemented
49C22⋊(C107⋊C8)C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51(C2×D107)⋊C8C2211yescharacteristic
52#121×C107C2211yescharacteristic
53#117×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic, complemented
55#106×C107C2211yescharacteristic, complemented
56#102×C107C2211yescharacteristic, complemented
57#102×C107C2211yescharacteristic, complemented
58C22⋊C8×C107C2211yescharacteristic
59C23×D107D411yescharacteristic
60#13133817—22no—
61#13133817—22no—
62C2×Dic214C2311yescharacteristic
63C2×C22⋊D107—21no—
64C2×C22⋊D107—21no—
65C22×Dic107—21no—
66C22×Dic107D411yescharacteristic
67C2×C4×D107—22no—
68C2×C4×D107—22no—
69C2×C4×D107—21no—
70C2×C4×D107—21no—
71C2×C4×D107D411yescharacteristic
72C2×C4×D107D411yescharacteristic
73C2×C4×D107C2311yescharacteristic
74C2×C4×D107C2311yescharacteristic
75#13133801—22no—
76#13133801—22no—
77C2×C107⋊C8C2311yescharacteristic
78C2×C107⋊C8C2311yescharacteristic
79C4⋊Dic107—21no—
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86C22⋊Dic107—21no—
87C22⋊Dic107—21no—
88C22⋊Dic107—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—
97C2×D4×C107—21no—
98C2×D4×C107C2311yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107C2311yescharacteristic
103C4⋊C4×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C22⋊C4×C107—21no—
106C22⋊C4×C107—21no—
107C42×C107—21no—
108C23×C107—21no—
109C23×C107C2×D411yescharacteristic
110C22×D107—22no—
111C22×D107—41no—
112C22×D107—41no—
113C22×D107C2×D411yescharacteristic
114C22×D107C2×D411yescharacteristic
115D4×C107—21no—
116D4×C107—21no—
117D4×C107—42no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2411yescharacteristic
125C22⋊D107—42no—
126C22⋊D107—42no—
127C2×Dic107—22no—
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—42no—
133C2×Dic107C2×D411yescharacteristic
134C2×Dic107C2×D411yescharacteristic
135C4×D107—22no—
136C4×D107—21no—
137C4×D107—21no—
138C4×D107—22no—
139C4×D107—42no—
140C4×D107—42no—
141C4×D107#4112yes—
142C4×D107#4112yes—
143Dic214—21no—
144Dic214—21no—
145C8×C107—21no—
146C8×C107—21no—
147C107⋊C8—21no—
148C107⋊C8—21no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107—21no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107C22×D411yescharacteristic
156C2×D107—21no—
157C2×D107—21no—
158C2×D107—21no—
159C2×D107—21no—
160C2×D107—21no—
161C2×D107—44no—
162C2×D107#12312yes—
163C4×C107—21no—
164C4×C107—41no—
165C4×C107—41no—
166C4×C107—41no—
167C4×C107C2×#4111yescharacteristic
168C4×C107C2×#4111yescharacteristic
169Dic107—21no—
170Dic107—41no—
171Dic107—41no—
172Dic107—41no—
173Dic107—41no—
174Dic107#12312yes—
175C2×C107—41no—
176C2×C107—81no—
177C2×C107C2×#12311yescharacteristic
178C2×C107#57511yescharacteristic
179C2×C107#57511yescharacteristic
180D107—22no—
181D107—41no—
182#3093—1071nomaximal, Sylow
183C107#309311yescharacteristic, complemented, Sylow
184#525—1071no—
185C2×#117—1071no—
186#485—1071no—
187#485—1071no—
188#485—1071no—
189#485—1071no—
190#482—1071no—
191#482—1071no—
192#482—1071no—
193#482D10711yescharacteristic, complemented
194#428—1071no—
195#428—1071no—
196#417—1071no—
197#417—1071no—
198#407—1071no—
199C2×#41—1071no—
200C23×C4—1071no—
201C2×M16—1071no—
202C2×M16—1071no—
203#123—2141no—
204C22⋊Q8—1071no—
205C22⋊Q8—1071no—
206#121—1071no—
207#121C2×D10711yescharacteristic
208#120—2141no—
209C4×D4—2141no—
210C4×D4—2141no—
211#117—1071no—
212#117—1071no—
213#117—1071no—
214#117—1071no—
215#117—2141no—
216#117—2141no—
217#117C2×D10711yescharacteristic
218C2×C4⋊C4—1071no—
219C2×C4⋊C4—1071no—
220C2×C22⋊C4—2141no—
221C2×C42—2141no—
222#107—1071no—
223#107—1071no—
224#107—1071no—
225#107C2×D10711yescharacteristic, complemented
226#106—1071no—
227#106—1071no—
228#106—1071no—
229#106C2×D10711yescharacteristic, complemented
230#103—1071no—
231#103—1071no—
232#103—1071no—
233#103—1071no—
234#102—1071no—
235#102—1071no—
236#102C2×D10711yescharacteristic, complemented
237#102C2×D10711yescharacteristic, complemented
238C22⋊C8—1071no—
239C22⋊C8—1071no—
240C22⋊C8—1071no—
241C22⋊C8C2×D10711yescharacteristic
242C24—1071no—
243#41—2142no—
244#41—2142no—
245C2×Q8—1071no—
246C2×D4—21no—
247C2×D4—2141no—
248C2×D4—2141no—
249C2×D4C22×D10711yescharacteristic
250C22×C4—1071no—
251C22×C4—1071no—
252C22×C4—1071no—
253C22×C4—1071no—
254C22×C4—1071no—
255C22×C4—2142no—
256C22×C4—2142no—
257C22×C4—2141no—
258C22×C4—2141no—
259C22×C4—2141no—
260C22×C4C22×D10711yescharacteristic
261M16—2142no—
262M16—2142no—
263C2×C8—1071no—
264C2×C8—1071no—
265C2×C8C22×D10711yescharacteristic
266C2×C8C22×D10711yescharacteristic
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—1071no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4—2141no—
274C4⋊C4C22×D10711yescharacteristic
275C4⋊C4C22×D10711yescharacteristic
276C4⋊C4C22×D10711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C22⋊C4—2141no—
285C22⋊C4—2141no—
286C42—21no—
287C42—2141no—
288C42—2141no—
289C42—2141no—
290C42—2141no—
291C23—21no—
292C23—1071no—
293C23—1071no—
294C23—4281no—
295C23—4281no—
296C23—2142no—
297C23D4×D10711yescharacteristic
298Q8—2141no—
299Q8—2141no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—4282no—
304D4—4282no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—1071no—
311C2×C4—1072no—
312C2×C4—1072no—
313C2×C4—1071no—
314C2×C4—4282no—
315C2×C4—4282no—
316C2×C4—4282no—
317C2×C4—2142no—
318C2×C4—2142no—
319C2×C4—2142no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4—2141no—
325C2×C4—2141no—
326C2×C4D4×D10711yescharacteristic
327C2×C4C23×D10711yescharacteristic
328C8—21no—
329C8—21no—
330C8—2141no—
331C8—2141no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1072no—
339C22—4284no—
340C22—2141no—
341C22—2141no—
342C22—2141no—
343C22—2141no—
344C22—2141no—
345C22C2×D4×D10711yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—1072no—
351C4—4281no—
352C4—4281no—
353C4—4281no—
354C4—4281no—
355C4—2141no—
356C4#41×D10711yescharacteristic
357C4#41×D10711yescharacteristic
358C2—41no—
359C2—81no—
360C2—4281no—
361C2—2142no—
362C2#123×D10711yescharacteristic
363C2#2029342311yescharacteristic
364C2#2029342411yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#482×C107C2
socleC22×C107C22×D4
prime radical#20293137C2
hypercenter#482D107
hypocenterC107#3093
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
2. #117×D107C2semidirect
3. #20292971C2semidirect
4. #20292970C2semidirect
5. #20292969C2semidirect
6. #20292968C2semidirect
7. #20292950C2semidirect
8. #20292949C2semidirect
9. #20292948C2semidirect
10. #20292668C2semidirect
11. #20292666C2semidirect
12. #20292625C2semidirect
13. #20292625C2semidirect
14. #20292589C2semidirect
15. #482×C107C2semidirect
37. #16812043C22semidirect
38. #16812042C22semidirect
39. #16812042C22semidirect
40. #16812041C22semidirect
41. #16812040C22semidirect
42. #16812040C22semidirect
43. #16812034C22semidirect
44. #16812034C22semidirect
45. #16812032C22semidirect
46. #16812032C22semidirect
47. #16812030C22semidirect
48. #16812030C22semidirect
54. #107×C107C22semidirect
55. #106×C107C22semidirect
56. #102×C107C22semidirect
57. #102×C107C22semidirect
183. C107#3093semidirect
193. #482D107semidirect
225. #107C2×D107semidirect
229. #106C2×D107semidirect
236. #102C2×D107semidirect
237. #102C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202931372
#117×D1072
#202929712
#202929702
#202929692
#202929682
#202929502
#202929492
#202929482
#202926682
#202926662
#202926252
#202925892
#482×C1072
#3093107