Finite Group Databasebeta

← #28346647

Subgroups — #28346647

Order 13696.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293248C211yesmaximal, characteristic, complemented
2#20293101C211yesmaximal, characteristic, complemented
3#20292969C211yesmaximal, characteristic, complemented
4#20292952C211yesmaximal, characteristic, complemented
5#20292918C211yesmaximal, characteristic, complemented
6#20292908C211yesmaximal, characteristic, complemented
7#20292843C211yesmaximal, characteristic, complemented
8#20292843C211yesmaximal, characteristic, complemented
9#20292780C211yesmaximal, characteristic, complemented
10#20292763C211yesmaximal, characteristic
11#20292740C211yesmaximal, characteristic, complemented
12#20292729C211yesmaximal, characteristic, complemented
13C4×#13133807C211yesmaximal, characteristic, complemented
14C4×D856C211yesmaximal, characteristic, complemented
15#433×C107C211yesmaximal, characteristic, complemented
16C22×D428C2211yescharacteristic
17C2×#13133807C2211yescharacteristic
18C2×#13133807C2211yescharacteristic
19C2×D856C2211yescharacteristic
20C2×D856C2211yescharacteristic
21#16812109C2211yescharacteristic, complemented
22#16812104—21no—
23#16812097C2211yescharacteristic, complemented
24#16812095—21no—
25#16812091—21no—
26#16812088C2211yescharacteristic
27#16812087—21no—
28#16812083C2211yescharacteristic
29C4×Dic214C2211yescharacteristic, complemented
30C4×D428C2211yescharacteristic
31C4×D428C2211yescharacteristic
32C4×D428C2211yescharacteristic
33C4×D428C2211yescharacteristic
34C4×D428C2211yescharacteristic, complemented
35#16812071—21no—
36#16812071—21no—
37#16812068C2211yescharacteristic
38C22⋊C4×D107—21no—
39C22⋊C4×D107—21no—
40#16812043C2211yescharacteristic, complemented
41#16812043C2211yescharacteristic, complemented
42#16812041C2211yescharacteristic, complemented
43#16812041C2211yescharacteristic, complemented
44#16812034C2211yescharacteristic, complemented
45#16812034C2211yescharacteristic, complemented
46#16812031C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812031C2211yescharacteristic
50#16812031C2211yescharacteristic, complemented
51#16812031C2211yescharacteristic, complemented
52#117×C107C2211yescharacteristic
53C4⋊C8×C107C2211yescharacteristic, complemented
54C4⋊C8×C107C2211yescharacteristic, complemented
55C22⋊C8×C107C2211yescharacteristic
56C22⋊C8×C107C2211yescharacteristic
57#97×C107C2211yescharacteristic, complemented
58C4×C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60C2×Dic214—21no—
61C2×Dic214C2311yescharacteristic
62C2×D428—21no—
63C2×D428—22no—
64C2×D428—22no—
65C2×D428C2311yescharacteristic
66C2×D428C2311yescharacteristic
67C2×D428C2311yescharacteristic
68C2×C22⋊D107—21no—
69C2×C4×D107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74#13133807—22no—
75#13133807—22no—
76D856—22no—
77D856—22no—
78C4⋊Dic107—21no—
79C4⋊Dic107C2311yescharacteristic
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
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—
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C22×C4×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107D411yescharacteristic
103C4⋊C4×C107D411yescharacteristic
104C22⋊C4×C107D411yescharacteristic
105C22⋊C4×C107D411yescharacteristic
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C23×C107C2×D411yescharacteristic
109C22×D107—21no—
110C22×D107—21no—
111C22×D107—24no—
112C22×D107—21no—
113C22×D107—81no—
114C22×D107—81no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107C2×D411yescharacteristic
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2411yescharacteristic
123C22⋊D107—81no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129D428—24no—
130D428—21no—
131D428—21no—
132D428—21no—
133D428—21no—
134D428#4112yes—
135D428#4112yes—
136C4×D107—81no—
137C4×D107—81no—
138C4×D107—81no—
139C4×D107—81no—
140C4×D107—81no—
141Dic214—21no—
142Dic214—21no—
143Dic214—81no—
144C8×C107—21no—
145C8×C107—21no—
146C8×C107—21no—
147C8×C107—21no—
148C22×C107—21no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107C22×D411yescharacteristic
152C2×D107—22no—
153C2×D107—22no—
154C2×D107—41no—
155C2×D107—41no—
156C2×D107—41no—
157C2×D107—41no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C2×D107—84no—
162C4×C107—21no—
163C4×C107—21no—
164C4×C107—21no—
165C4×C107—21no—
166C4×C107—21no—
167C4×C107C2×#4111yescharacteristic
168C4×C107C2×#4111yescharacteristic
169Dic107—41no—
170Dic107—41no—
171Dic107—41no—
172Dic107—41no—
173Dic107—41no—
174C2×C107—41no—
175C2×C107#52511yescharacteristic
176C2×C107#57611yescharacteristic
177C2×C107#57711yescharacteristic
178D107—42no—
179D107—42no—
180D107—81no—
181#3118—1071nomaximal, Sylow
182C107#311811yescharacteristic, complemented, Sylow
183#542—1071no—
184#518—1071no—
185#485—1071no—
186#482—1071no—
187#476—1071no—
188#474—1071no—
189#463—1071no—
190#463—1071no—
191#450—1071no—
192#447—1071no—
193#442—1071no—
194#440—1071no—
195C4×SD16—1071no—
196C4×D8—1071no—
197#433D10711yescharacteristic, complemented
198C22×D4—1071no—
199C2×SD16—1071no—
200C2×SD16—1071no—
201C2×D8—1071no—
202C2×D8—1071no—
203C4⋊Q8—1071no—
204#126—2141no—
205#124—1071no—
206#124—2141no—
207#123—2141no—
208C22⋊Q8—1071no—
209C22⋊Q8—2141no—
210#121—1071no—
211C4×Q8—1071no—
212C4×D4—1071no—
213C4×D4—1071no—
214C4×D4—1071no—
215C4×D4—1071no—
216C4×D4—1071no—
217C4×D4—2141no—
218C4×D4—2141no—
219#117—1071no—
220#117C2×D10711yescharacteristic
221C2×C22⋊C4—2141no—
222C2×C22⋊C4—2141no—
223#107—1071no—
224#107—1071no—
225#106—1071no—
226#106—1071no—
227C4⋊C8C2×D10711yescharacteristic, complemented
228C4⋊C8C2×D10711yescharacteristic, complemented
229#103—1071no—
230#103—1071no—
231#102—1071no—
232#102—1071no—
233#102—1071no—
234#102—1071no—
235#102—1071no—
236#102—1071no—
237C22⋊C8C2×D10711yescharacteristic
238C22⋊C8C2×D10711yescharacteristic
239#97C2×D10711yescharacteristic, complemented
240C4×C8C2×D10711yescharacteristic, complemented
241C24—2141no—
242C2×Q8—1071no—
243C2×Q8—2141no—
244C2×D4—1071no—
245C2×D4—1071no—
246C2×D4—1071no—
247C2×D4—2142no—
248C2×D4—2142no—
249C2×D4—2141no—
250C2×D4—2141no—
251C22×C4—2141no—
252C22×C4—2141no—
253C22×C4—2141no—
254C22×C4—2141no—
255C22×C4—2141no—
256C22×C4C22×D10711yescharacteristic
257SD16—2142no—
258SD16—2142no—
259D8—2142no—
260D8—2142no—
261C2×C8C22×D10711yescharacteristic
262C2×C8C22×D10711yescharacteristic
263C2×C8C22×D10711yescharacteristic
264C2×C8C22×D10711yescharacteristic
265C4⋊C4—1071no—
266C4⋊C4—1071no—
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—2141no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4D42811yescharacteristic
273C4⋊C4D42811yescharacteristic
274C22⋊C4—2141no—
275C22⋊C4—2141no—
276C22⋊C4—2141no—
277C22⋊C4—2141no—
278C22⋊C4—2141no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C22⋊C4D42811yescharacteristic
285C22⋊C4D42811yescharacteristic
286C42—2141no—
287C42—2141no—
288C42C22×D10711yescharacteristic
289C42C22×D10711yescharacteristic
290C23—8561no—
291C23—8561no—
292C23—2144no—
293C23—2141no—
294C23—2141no—
295C23—2141no—
296C23C2×D42811yescharacteristic
297Q8—8561no—
298Q8—2141no—
299Q8—2141no—
300D4—8561no—
301D4—1072no—
302D4—1072no—
303D4—2144no—
304D4—2141no—
305D4—2141no—
306D4—2141no—
307D4—2141no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—8561no—
311C2×C4—8561no—
312C2×C4—8561no—
313C2×C4—8561no—
314C2×C4—8561no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4C2×D42811yescharacteristic
321C2×C4C2×D42811yescharacteristic
322C2×C4C2×D42811yescharacteristic
323C2×C4C2×D42811yescharacteristic
324C2×C4C2×D42811yescharacteristic
325C2×C4C23×D10711yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—8564no—
334C22—4281no—
335C22—4281no—
336C22—4281no—
337C22—4281no—
338C22—4281no—
339C22—4281no—
340C22—4281no—
341C22—2142no—
342C22—2142no—
343C22C22×D42811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—4281no—
350C4—4281no—
351C4—4281no—
352C4—4281no—
353C4—4281no—
354C4#41×D10711yescharacteristic
355C4#41×D10711yescharacteristic
356C2—41no—
357C2—8561no—
358C2—4282no—
359C2—4282no—
360C2#2029313911yescharacteristic
361C2#2029343211yescharacteristic
362C2#2029343911yescharacteristic
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#433×C107C2
socleC22×C107C22×D4
prime radical#20292763C2
hypercenter#433D107
hypocenterC107#3118
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20293248C2semidirect
2. #20293101C2semidirect
3. #20292969C2semidirect
4. #20292952C2semidirect
5. #20292918C2semidirect
6. #20292908C2semidirect
7. #20292843C2semidirect
8. #20292843C2semidirect
9. #20292780C2semidirect
11. #20292740C2semidirect
12. #20292729C2semidirect
13. C4×#13133807C2semidirect
14. C4×D856C2semidirect
15. #433×C107C2semidirect
21. #16812109C22semidirect
23. #16812097C22semidirect
29. C4×Dic214C22semidirect
34. C4×D428C22semidirect
40. #16812043C22semidirect
41. #16812043C22semidirect
42. #16812041C22semidirect
43. #16812041C22semidirect
44. #16812034C22semidirect
45. #16812034C22semidirect
50. #16812031C22semidirect
51. #16812031C22semidirect
53. C4⋊C8×C107C22semidirect
54. C4⋊C8×C107C22semidirect
57. #97×C107C22semidirect
58. C4×C8×C107C22semidirect
182. C107#3118semidirect
197. #433D107semidirect
227. C4⋊C8C2×D107semidirect
228. C4⋊C8C2×D107semidirect
239. #97C2×D107semidirect
240. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202932482
#202931012
#202929692
#202929522
#202929182
#202929082
#202928432
#202927802
#202927632
#202927402
#202927292
C4×#131338072
C4×D8562
#433×C1072
#3118107