Finite Group Databasebeta

← #28345471

Subgroups — #28345471

Order 13696.

406 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13133817C211yesmaximal, characteristic
2#20292756C211yesmaximal, characteristic, complemented
3#20292755C211yesmaximal, characteristic, complemented
4#20292701C211yesmaximal, characteristic, complemented
5#20292699C211yesmaximal, characteristic, complemented
6#20292696C211yesmaximal, characteristic, complemented
7C8×C22⋊D107C211yesmaximal, characteristic, complemented
8(C22⋊D107)⋊C8C211yesmaximal, characteristic, complemented
9#20292683C211yesmaximal, characteristic, complemented
10#20292681C211yesmaximal, characteristic, complemented
11#20292681C211yesmaximal, characteristic, complemented
12M16×Dic107C211yesmaximal, characteristic, complemented
13C2×#16812019C211yesmaximal, characteristic, complemented
14#97×D107C211yesmaximal, characteristic, complemented
15#435×C107C211yesmaximal, characteristic, complemented
16C2×#13133817C411yescharacteristic
17C2×#13133802C2211yescharacteristic
18C22×C107⋊C8C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21C4×Dic214C2211yescharacteristic
22#16812074C411yescharacteristic
23D4×Dic107C411yescharacteristic
24C4×C22⋊D107C2211yescharacteristic
25C4×C22⋊D107C2211yescharacteristic
26(C22⋊D107)⋊C4C411yescharacteristic
27(C22⋊D107)⋊C4C411yescharacteristic
28#16812067C411yescharacteristic
29#16812065C411yescharacteristic
30#16812065C411yescharacteristic
31C2×C4×Dic107C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C42×D107C2211yescharacteristic
34C4⋊(C107⋊C8)C2211yescharacteristic
35Dic107⋊C8C2211yescharacteristic
36Dic107⋊C8C2211yescharacteristic
37Dic107⋊C8C2211yescharacteristic
38Dic107⋊C8C2211yescharacteristic
39C22⋊(C107⋊C8)C2211yescharacteristic
40C22⋊(C107⋊C8)C2211yescharacteristic
41(C2×D107)⋊C8C2211yescharacteristic
42(C2×D107)⋊C8C2211yescharacteristic
43#16812020C2211yescharacteristic
44#16812019C2211yescharacteristic
45#16812019C2211yescharacteristic
46#16812019C2211yescharacteristic
47#16812019C2211yescharacteristic
48#16812019C2211yescharacteristic
49#16812019C2211yescharacteristic
50C8×Dic107C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×M16×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55C4⋊C8×C107C2211yescharacteristic
56C22⋊C8×C107C2211yescharacteristic
57C22⋊C8×C107C2211yescharacteristic
58#97×C107C2211yescharacteristic
59#13133817—24no—
60C2×Dic214C2×C411yescharacteristic
61C2×C22⋊D107C2×C411yescharacteristic
62C2×C22⋊D107C2×C411yescharacteristic
63C22×Dic107C2×C411yescharacteristic
64C22×Dic107C2×C411yescharacteristic
65C22×Dic107C2×C411yescharacteristic
66C22×Dic107C2×C411yescharacteristic
67C2×C4×D107C2×C411yescharacteristic
68C2×C4×D107C2×C411yescharacteristic
69C2×C4×D107C2311yescharacteristic
70#13133802—22no—
71C2×C107⋊C8—22no—
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C2×C107⋊C8C2311yescharacteristic
76C8×D107—22no—
77C8×D107—22no—
78C4⋊Dic107C2×C411yescharacteristic
79Dic107⋊C4C2×C411yescharacteristic
80Dic107⋊C4C2×C411yescharacteristic
81Dic107⋊C4C2×C411yescharacteristic
82Dic107⋊C4C2×C411yescharacteristic
83C22⋊Dic107C2×C411yescharacteristic
84C22⋊Dic107C2×C411yescharacteristic
85(C2×D107)⋊C4C2×C411yescharacteristic
86(C2×D107)⋊C4C2×C411yescharacteristic
87C4×Dic107C2×C411yescharacteristic
88C4×Dic107C2×C411yescharacteristic
89C4×Dic107C2×C411yescharacteristic
90C4×Dic107C2×C411yescharacteristic
91C4×Dic107C2×C411yescharacteristic
92C4×Dic107C2×C411yescharacteristic
93C4×Dic107C2311yescharacteristic
94C4×Dic107C2311yescharacteristic
95C4×Dic107C2311yescharacteristic
96C2×D4×C107C2×C411yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99M16×C107—22no—
100C2×C8×C107—22no—
101C2×C8×C107C2311yescharacteristic
102C2×C8×C107C2311yescharacteristic
103C2×C8×C107C2311yescharacteristic
104C2×C8×C107C2311yescharacteristic
105C4⋊C4×C107C2×C411yescharacteristic
106C22⋊C4×C107C2×C411yescharacteristic
107C22⋊C4×C107C2×C411yescharacteristic
108C42×C107C2311yescharacteristic
109C23×C107C22×C411yescharacteristic
110C23×C107C22×C411yescharacteristic
111C22×D107C22×C411yescharacteristic
112D4×C107—22no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107C22×C411yescharacteristic
118C2×C4×C107C22×C411yescharacteristic
119C2×C4×C107C22×C411yescharacteristic
120C2×C4×C107C22×C411yescharacteristic
121C2×C4×C107C2411yescharacteristic
122C22⋊D107—22no—
123C22⋊D107M1614yescomplemented
124C2×Dic107—22no—
125C2×Dic107—22no—
126C2×Dic107—41no—
127C2×Dic107—41no—
128C2×Dic107C22×C411yescharacteristic
129C2×Dic107C22×C411yescharacteristic
130C2×Dic107C22×C411yescharacteristic
131C2×Dic107C22×C411yescharacteristic
132C2×Dic107C22×C411yescharacteristic
133C2×Dic107C22×C411yescharacteristic
134C2×Dic107C22×C411yescharacteristic
135C4×D107—22no—
136C4×D107—21no—
137C4×D107—21no—
138C4×D107—41no—
139Dic214—22no—
140C8×C107—21no—
141C8×C107—21no—
142C8×C107—21no—
143C8×C107#4112yescomplemented
144C107⋊C8—21no—
145C107⋊C8—21no—
146C107⋊C8—21no—
147C107⋊C8#4112yescomplemented
148C22×C107—21no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107—21no—
152C22×C107—21no—
153C22×C107C2×M1612yes—
154C22×C107C23×C411yescharacteristic
155C2×D107—21no—
156C2×D107—21no—
157C2×D107C2×M1612yes—
158C4×C107—21no—
159C4×C107—21no—
160C4×C107—21no—
161C4×C107—21no—
162C4×C107C2×#4111yescharacteristic
163C4×C107C2×#4111yescharacteristic
164Dic107—21no—
165Dic107—21no—
166Dic107—21no—
167Dic107—21no—
168Dic107—21no—
169Dic107—21no—
170Dic107C2×M1612yes—
171C2×C107—22no—
172C2×C107—41no—
173C2×C107C4×#4111yescharacteristic
174C2×C107C22×M1611yescharacteristic
175C2×C107#56811yescharacteristic
176D107—22no—
177#2970—1071nomaximal, Sylow
178C107#297011yescharacteristic, complemented, Sylow
179C4×#41—1071no—
180#446—1071no—
181#446—1071no—
182#435—1071no—
183#435—1071no—
184#435—1071no—
185#435D10711yescharacteristic, complemented
186C8×D4—1071no—
187C8×D4—1071no—
188#432—1071no—
189#432—1071no—
190#432—1071no—
191C4×M16—1071no—
192C2×#97—1071no—
193C2×#97—1071no—
194C2×#41—1071no—
195C2×M16—1071no—
196C2×M16C2×D10711yescharacteristic
197C22×C8—1071no—
198C22×C8—1071no—
199C22×C8—1071no—
200C22×C8C2×D10711yescharacteristic
201C4×Q8—1071no—
202C4×Q8—1071no—
203C4×D4—1071no—
204C4×D4—1071no—
205C4×D4—1071no—
206C4×D4—1071no—
207C4×D4—1071no—
208C4×D4C2×D10711yescharacteristic
209#117—1071no—
210#117—1071no—
211#117—1071no—
212C2×C42—1071no—
213C2×C42—1071no—
214C2×C42—1071no—
215C4⋊C8—1071no—
216C4⋊C8—1071no—
217C4⋊C8—1071no—
218C4⋊C8—1071no—
219C4⋊C8—1071no—
220C4⋊C8C2×D10711yescharacteristic
221C22⋊C8—1071no—
222C22⋊C8—1071no—
223C22⋊C8—1071no—
224C22⋊C8—1071no—
225C22⋊C8C2×D10711yescharacteristic
226C22⋊C8C2×D10711yescharacteristic
227#97—1071no—
228#97—1071no—
229#97—1071no—
230#97—1071no—
231#97—1071no—
232#97—1071no—
233#97—1071no—
234#97C2×D10711yescharacteristic
235C4×C8—1071no—
236C4×C8—1071no—
237#41—2144no—
238C2×Q8—1071no—
239C2×D4—1071no—
240C2×D4—1071no—
241C2×D4C4×D10711yescharacteristic
242C22×C4—1071no—
243C22×C4—1071no—
244C22×C4—1071no—
245C22×C4—1071no—
246C22×C4—1071no—
247C22×C4—1071no—
248C22×C4—1071no—
249C22×C4C22×D10711yescharacteristic
250C22×C4C22×D10711yescharacteristic
251M16—22no—
252M16—2142no—
253C2×C8—22no—
254C2×C8—1071no—
255C2×C8—1071no—
256C2×C8—1071no—
257C2×C8—1071no—
258C2×C8—2142no—
259C2×C8—2142no—
260C2×C8—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—1071no—
270C4⋊C4C4×D10711yescharacteristic
271C22⋊C4—1071no—
272C22⋊C4—1071no—
273C22⋊C4—1071no—
274C22⋊C4—1071no—
275C22⋊C4C4×D10711yescharacteristic
276C22⋊C4C4×D10711yescharacteristic
277C42—1071no—
278C42—1071no—
279C42—1071no—
280C42—1071no—
281C42—1071no—
282C42—1071no—
283C42—1071no—
284C42—1071no—
285C42—1071no—
286C42C22×D10711yescharacteristic
287C23—1071no—
288C23C2×C4×D10711yescharacteristic
289C23C2×C4×D10711yescharacteristic
290Q8—2142no—
291D4—22no—
292D4—1074no—
293D4—2142no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—1071no—
299C2×C4—1071no—
300C2×C4—1071no—
301C2×C4—1071no—
302C2×C4—1071no—
303C2×C4—1071no—
304C2×C4—1071no—
305C2×C4—4281no—
306C2×C4—4281no—
307C2×C4—4281no—
308C2×C4—2142no—
309C2×C4—2142no—
310C2×C4—2142no—
311C2×C4—2141no—
312C2×C4—2141no—
313C2×C4C2×C4×D10711yescharacteristic
314C2×C4C2×C4×D10711yescharacteristic
315C2×C4C2×C4×D10711yescharacteristic
316C2×C4C2×C4×D10711yescharacteristic
317C2×C4C23×D10711yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—1072no—
322C8—2141no—
323C8—2141no—
324C8—2141no—
325C8#1313381712yescomplemented
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—1072no—
332C22—2141no—
333C22—2141no—
334C22M16×D10712yes—
335C22C22×C4×D10711yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—1072no—
341C4—2141no—
342C4—2141no—
343C4—2141no—
344C4—2141no—
345C4—2141no—
346C4—2141no—
347C4#41×D10711yescharacteristic
348C4C2×#1313381711yescharacteristic
349C2—22no—
350C2—41no—
351C2—2142no—
352C2C4×#1313381711yescharacteristic
353C2C2×M16×D10711yescharacteristic
354C2#2029339211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
Fitting#435×C107C2
prime radicalC2×#13133817C4
cosocleC2×C4×C107C24
hypercenter#435D107
hypocenterC107#2970
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #20292756C2semidirect
3. #20292755C2semidirect
4. #20292701C2semidirect
5. #20292699C2semidirect
6. #20292696C2semidirect
7. C8×C22⋊D107C2semidirect
8. (C22⋊D107)⋊C8C2semidirect
9. #20292683C2semidirect
10. #20292681C2semidirect
11. #20292681C2semidirect
12. M16×Dic107C2semidirect
13. C2×#16812019C2semidirect
14. #97×D107C2semidirect
15. #435×C107C2semidirect
123. C22⋊D107M16semidirect
143. C8×C107#41semidirect
147. C107⋊C8#41semidirect
178. C107#2970semidirect
185. #435D107semidirect
325. C8#13133817semidirect

Maximal subgroups

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

subgroupindex
C4×#131338172
#202927562
#202927552
#202927012
#202926992
#202926962
C8×C22⋊D1072
(C22⋊D107)⋊C82
#202926832
#202926812
M16×Dic1072
C2×#168120192
#97×D1072
#435×C1072
#2970107