Finite Group Databasebeta

← #28348371

Subgroups — #28348371

Order 13696.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293348C211yesmaximal, characteristic, complemented
2#20293276C211yesmaximal, characteristic
3#20292976C211yesmaximal, characteristic, complemented
4#20292969C211yesmaximal, characteristic, complemented
5#20292966C211yesmaximal, characteristic, complemented
6#20292905C211yesmaximal, characteristic, complemented
7#20292866C211yesmaximal, characteristic, complemented
8#20292865C211yesmaximal, characteristic, complemented
9#20292835C211yesmaximal, characteristic, complemented
10#20292786C211yesmaximal, characteristic, complemented
11SD16×Dic107C211yesmaximal, characteristic, complemented
12(C22⋊D107)⋊C8C211yesmaximal, characteristic, complemented
13#20292623C211yesmaximal, characteristic, complemented
14#20292620C211yesmaximal, characteristic, complemented
15#452×C107C211yesmaximal, characteristic, complemented
16C2×#13133817C2211yescharacteristic
17C2×#13133808C2211yescharacteristic
18C22×C107⋊C8C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812108C2211yescharacteristic
21#16812107C2211yescharacteristic
22#16812104—21no—
23#16812102—21no—
24#16812095—21no—
25#16812092—21no—
26#16812090—21no—
27#16812088C2211yescharacteristic
28#16812085C2211yescharacteristic
29#16812085C2211yescharacteristic
30#16812081—21no—
31Q8×Dic107C2211yescharacteristic
32#16812074—21no—
33D4×Dic107C2211yescharacteristic
34C4×C22⋊D107C2211yescharacteristic
35#16812068C2211yescharacteristic
36#16812067C2211yescharacteristic
37C2×Dic107⋊C4—21no—
38#16812043C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812041C2211yescharacteristic
41Dic107⋊C8C2211yescharacteristic
42#16812034C2211yescharacteristic
43#16812034C2211yescharacteristic
44#16812033C2211yescharacteristic
45#16812033C2211yescharacteristic
46#16812033C2211yescharacteristic
47#16812032C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812030C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×#41×C107C2211yescharacteristic
53C2×Q16×C107C2211yescharacteristic
54C2×SD16×C107C2211yescharacteristic
55C22⋊Q8×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59#13133817—22no—
60#13133817—41no—
61C2×Dic214—21no—
62C2×Dic214C2311yescharacteristic
63C2×C22⋊D107—21no—
64C2×C22⋊D107D411yescharacteristic
65C22×Dic107—21no—
66C22×Dic107—21no—
67C2×C4×D107C2311yescharacteristic
68#13133808—41no—
69C2×C107⋊C8—41no—
70C2×C107⋊C8C2311yescharacteristic
71C2×C107⋊C8C2311yescharacteristic
72C8×D107—41no—
73C4⋊Dic107—21no—
74C4⋊Dic107C2311yescharacteristic
75C4⋊Dic107C2311yescharacteristic
76C4⋊Dic107C2311yescharacteristic
77Dic107⋊C4—21no—
78Dic107⋊C4—21no—
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4D411yescharacteristic
84C22⋊Dic107—21no—
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87C22⋊Dic107D411yescharacteristic
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4D411yescharacteristic
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107—21no—
95C4×Dic107C2311yescharacteristic
96#41×C107—22no—
97#41×C107—41no—
98C2×Q8×C107C2311yescharacteristic
99C2×Q8×C107C2311yescharacteristic
100C2×D4×C107—21no—
101C2×D4×C107C2311yescharacteristic
102C22×C4×C107—21no—
103C22×C4×C107C2311yescharacteristic
104Q16×C107—41no—
105SD16×C107—22no—
106C2×C8×C107C2311yescharacteristic
107C2×C8×C107C2311yescharacteristic
108C4⋊C4×C107—21no—
109C4⋊C4×C107C2311yescharacteristic
110C22⋊C4×C107—21no—
111C23×C107—21no—
112C23×C107C2×D411yescharacteristic
113C22×D107C2×D411yescharacteristic
114Q8×C107—21no—
115Q8×C107—21no—
116Q8×C107—21no—
117Q8×C107—21no—
118D4×C107—21no—
119D4×C107—42no—
120D4×C107#4112yes—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—42no—
127C2×C4×C107C2×D411yescharacteristic
128C2×C4×C107C2411yescharacteristic
129C22⋊D107—22no—
130C22⋊D107—42no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—42no—
136C2×Dic107—42no—
137C2×Dic107C2×D411yescharacteristic
138C2×Dic107C2×D411yescharacteristic
139C2×Dic107C2×D411yescharacteristic
140C4×D107—21no—
141C4×D107—21no—
142Dic214—21no—
143Dic214—21no—
144Dic214—42no—
145C8×C107—21no—
146C8×C107—21no—
147C107⋊C8—21no—
148C107⋊C8—21no—
149C22×C107—22no—
150C22×C107—21no—
151C22×C107—21no—
152C22×C107—21no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107C22×D411yescharacteristic
156C2×D107—21no—
157C2×D107—21no—
158C2×D107—21no—
159C4×C107—21no—
160C4×C107—41no—
161C4×C107—41no—
162C4×C107—41no—
163C4×C107C2×#4111yescharacteristic
164C4×C107H(5,𝔽2)11yescharacteristic
165Dic107—21no—
166Dic107—21no—
167Dic107—41no—
168Dic107—41no—
169Dic107—41no—
170Dic107—41no—
171Dic107#13512yes—
172C2×C107—41no—
173C2×C107—42no—
174C2×C107#54611yescharacteristic
175C2×C107C2×#13511yescharacteristic
176C2×C107#57811yescharacteristic
177D107—41no—
178#3302—1071nomaximal, Sylow
179C107#330211yescharacteristic, complemented, Sylow
180#556—1071no—
181#547—1071no—
182#487—1071no—
183#485—1071no—
184#485—1071no—
185#474—1071no—
186#467—1071no—
187#467—1071no—
188#462—1071no—
189#452—1071no—
190#452D10711yescharacteristic, complemented
191C4×SD16—1071no—
192C8×D4—1071no—
193#416—1071no—
194#416—1071no—
195C2×#41—1071no—
196C2×#41C2×D10711yescharacteristic
197C2×Q16—1071no—
198C2×Q16C2×D10711yescharacteristic
199C2×SD16C2×D10711yescharacteristic
200C22×C8—1071no—
201C22×C8—1071no—
202C4⋊Q8—1071no—
203C4⋊Q8—1071no—
204#126—2141no—
205#126—2141no—
206#124—2141no—
207#123—2141no—
208#123—2141no—
209C22⋊Q8—1071no—
210C22⋊Q8—1071no—
211C22⋊Q8—1071no—
212C22⋊Q8C2×D10711yescharacteristic
213#121—2141no—
214C4×Q8—1071no—
215C4×Q8—2141no—
216C4×D4—1071no—
217C4×D4—1071no—
218#117—1071no—
219#117—1071no—
220C2×C4⋊C4—2141no—
221#107—1071no—
222#107—1071no—
223#106—1071no—
224C4⋊C8—1071no—
225#103—1071no—
226#103—1071no—
227#103—1071no—
228#103—1071no—
229#103—1071no—
230#103—1071no—
231#103C2×D10711yescharacteristic
232#102—1071no—
233#102—1071no—
234#102C2×D10711yescharacteristic
235C22⋊C8—1071no—
236C22⋊C8C2×D10711yescharacteristic
237C4×C8—1071no—
238#41—22no—
239#41—41no—
240#41—4281no—
241#41—2142no—
242C2×Q8—1071no—
243C2×Q8—2141no—
244C2×Q8C22×D10711yescharacteristic
245C2×Q8C22×D10711yescharacteristic
246C2×D4—21no—
247C2×D4—1071no—
248C2×D4—2141no—
249C2×D4C22×D10711yescharacteristic
250C22×C4—21no—
251C22×C4—1071no—
252C22×C4—2141no—
253C22×C4—2141no—
254C22×C4C22×D10711yescharacteristic
255Q16—41no—
256Q16—4281no—
257SD16—22no—
258C2×C8—1071no—
259C2×C8—1071no—
260C2×C8—4281no—
261C2×C8—4281no—
262C2×C8C22×D10711yescharacteristic
263C2×C8C22×D10711yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—1071no—
266C4⋊C4—1071no—
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—2141no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4—2141no—
274C4⋊C4—2141no—
275C4⋊C4—2141no—
276C4⋊C4C22×D10711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1071no—
279C22⋊C4—1071no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C22⋊C4—2141no—
285C22⋊C4—2141no—
286C42—1071no—
287C42—2141no—
288C42—2141no—
289C42—2141no—
290C23—21no—
291C23—1071no—
292C23D4×D10711yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—4282no—
298Q8—2141no—
299Q8—2141no—
300D4—21no—
301D4—42no—
302D4—4282no—
303D4—2142no—
304D4#1313381712yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—1071no—
312C2×C4—1071no—
313C2×C4—1071no—
314C2×C4—4282no—
315C2×C4—4282no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4D4×D10711yescharacteristic
323C2×C4C23×D10711yescharacteristic
324C8—21no—
325C8—21no—
326C8—2141no—
327C8—2141no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—2141no—
335C22—2141no—
336C22—2141no—
337C22C2×D4×D10711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—1072no—
343C4—4281no—
344C4—4281no—
345C4—4281no—
346C4—4281no—
347C4—2141no—
348C4—2141no—
349C4C2×#1313381711yescharacteristic
350C4#1681215411yescharacteristic
351C2—41no—
352C2—42no—
353C2—4281no—
354C2#2029326411yescharacteristic
355C2#135×D10711yescharacteristic
356C2#2029344311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#452×C107C2
socleC22×C107C22×D4
prime radical#20293276C2
hypercenter#452D107
hypocenterC107#3302
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #20293348C2semidirect
3. #20292976C2semidirect
4. #20292969C2semidirect
5. #20292966C2semidirect
6. #20292905C2semidirect
7. #20292866C2semidirect
8. #20292865C2semidirect
9. #20292835C2semidirect
10. #20292786C2semidirect
11. SD16×Dic107C2semidirect
12. (C22⋊D107)⋊C8C2semidirect
13. #20292623C2semidirect
14. #20292620C2semidirect
15. #452×C107C2semidirect
179. C107#3302semidirect
190. #452D107semidirect

Maximal subgroups

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

subgroupindex
#202933482
#202932762
#202929762
#202929692
#202929662
#202929052
#202928662
#202928652
#202928352
#202927862
SD16×Dic1072
(C22⋊D107)⋊C82
#202926232
#202926202
#452×C1072
#3302107