Finite Group Databasebeta

← #28345117

Subgroups — #28345117

Order 13696.

402 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
1#117×D107C211yesmaximal, characteristic
2#20292688C211yesmaximal, characteristic, complemented
3#20292685C211yesmaximal, characteristic, complemented
4#20292685C211yesmaximal, characteristic, complemented
5#20292683C211yesmaximal, characteristic, complemented
6#20292682C211yesmaximal, characteristic, complemented
7#20292679C211yesmaximal, characteristic, complemented
8#20292678C211yesmaximal, characteristic, complemented
9#20292652C211yesmaximal, characteristic, complemented
10#20292652C211yesmaximal, characteristic, complemented
11#20292589C211yesmaximal, characteristic
12C22⋊C8×D107C211yesmaximal, characteristic
13#20292584C211yesmaximal, characteristic, complemented
14#20292581C211yesmaximal, characteristic, complemented
15#433×C107C211yesmaximal, characteristic, complemented
16C22×C4×D107C2211yescharacteristic
17C2×#13133801C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21#16812068C2211yescharacteristic
22#16812067C411yescharacteristic
23#16812067C411yescharacteristic
24#16812066C2211yescharacteristic
25#16812066C2211yescharacteristic
26#16812065C411yescharacteristic
27#16812065C411yescharacteristic
28C4⋊C4×D107C411yescharacteristic
29C4⋊C4×D107C411yescharacteristic
30C22⋊C4×D107C411yescharacteristic
31C22⋊C4×D107C411yescharacteristic
32C42×D107C2211yescharacteristic
33C42×D107C2211yescharacteristic
34C4⋊(C107⋊C8)C2211yescharacteristic, complemented
35C4⋊(C107⋊C8)C2211yescharacteristic, complemented
36Dic107⋊C8C2211yescharacteristic, complemented
37Dic107⋊C8C2211yescharacteristic, complemented
38Dic107⋊C8C2211yescharacteristic, complemented
39Dic107⋊C8C2211yescharacteristic, complemented
40C22⋊(C107⋊C8)C2211yescharacteristic
41C22⋊(C107⋊C8)C2211yescharacteristic
42(C2×D107)⋊C8C2211yescharacteristic
43(C2×D107)⋊C8C2211yescharacteristic
44(C2×D107)⋊C8C2211yescharacteristic
45(C2×D107)⋊C8C2211yescharacteristic
46#16812020C2211yescharacteristic, complemented
47#16812019C2211yescharacteristic, complemented
48#16812019C2211yescharacteristic, complemented
49C4×C107⋊C8C2211yescharacteristic, complemented
50C8×Dic107C2211yescharacteristic, complemented
51C8×Dic107C2211yescharacteristic, 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×D107C2×C411yescharacteristic
60C22×Dic107C2×C411yescharacteristic
61C2×C4×D107—22no—
62C2×C4×D107—22no—
63C2×C4×D107C2×C411yescharacteristic
64C2×C4×D107C2×C411yescharacteristic
65C2×C4×D107C2×C411yescharacteristic
66C2×C4×D107C2×C411yescharacteristic
67C2×C4×D107C2×C411yescharacteristic
68C2×C4×D107C2×C411yescharacteristic
69C2×C4×D107C2311yescharacteristic
70C2×C4×D107C2311yescharacteristic
71#13133801—22no—
72#13133801—22no—
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C2×C107⋊C8C2311yescharacteristic
76C2×C107⋊C8C2311yescharacteristic
77C8×D107—22no—
78C8×D107—22no—
79C4⋊Dic107C2×C411yescharacteristic
80C4⋊Dic107C2×C411yescharacteristic
81Dic107⋊C4C2×C411yescharacteristic
82Dic107⋊C4C2×C411yescharacteristic
83Dic107⋊C4C2×C411yescharacteristic
84Dic107⋊C4C2×C411yescharacteristic
85C22⋊Dic107C2×C411yescharacteristic
86C22⋊Dic107C2×C411yescharacteristic
87(C2×D107)⋊C4C2×C411yescharacteristic
88(C2×D107)⋊C4C2×C411yescharacteristic
89(C2×D107)⋊C4C2×C411yescharacteristic
90(C2×D107)⋊C4C2×C411yescharacteristic
91C4×Dic107C2×C411yescharacteristic
92C4×Dic107C2×C411yescharacteristic
93C4×Dic107C2×C411yescharacteristic
94C4×Dic107C2×C411yescharacteristic
95C4×Dic107C2311yescharacteristic
96C4×Dic107C2311yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107C2×C411yescharacteristic
103C4⋊C4×C107C2×C411yescharacteristic
104C22⋊C4×C107C2×C411yescharacteristic
105C22⋊C4×C107C2×C411yescharacteristic
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C23×C107C22×C411yescharacteristic
109C22×D107—22no—
110C22×D107—22no—
111C22×D107—41no—
112C22×D107C22×C411yescharacteristic
113C22×D107C22×C411yescharacteristic
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107C22×C411yescharacteristic
117C2×C4×C107C22×C411yescharacteristic
118C2×C4×C107C22×C411yescharacteristic
119C2×C4×C107C22×C411yescharacteristic
120C2×C4×C107C22×C411yescharacteristic
121C2×C4×C107C2411yescharacteristic
122C2×Dic107—22no—
123C2×Dic107C22×C411yescharacteristic
124C2×Dic107C22×C411yescharacteristic
125C2×Dic107C22×C411yescharacteristic
126C2×Dic107C22×C411yescharacteristic
127C2×Dic107C22×C411yescharacteristic
128C2×Dic107C22×C411yescharacteristic
129C4×D107—22no—
130C4×D107—22no—
131C4×D107—22no—
132C4×D107—21no—
133C4×D107—21no—
134C4×D107—22no—
135C4×D107—41no—
136C4×D107—41no—
137C4×D107#4112yes—
138C4×D107#4112yes—
139C8×C107—21no—
140C8×C107—21no—
141C8×C107—21no—
142C8×C107—21no—
143C107⋊C8—21no—
144C107⋊C8—21no—
145C107⋊C8—21no—
146C107⋊C8—21no—
147C22×C107—21no—
148C22×C107—21no—
149C22×C107—21no—
150C22×C107C23×C411yescharacteristic
151C2×D107—21no—
152C2×D107—21no—
153C2×D107—21no—
154C2×D107—21no—
155C2×D107—44no—
156C2×D107#11712yes—
157C2×D107#13112yes—
158C4×C107—21no—
159C4×C107—21no—
160C4×C107—21no—
161C4×C107—21no—
162C4×C107—21no—
163C4×C107C2×#4111yescharacteristic
164C4×C107C2×#4111yescharacteristic
165Dic107—21no—
166Dic107—21no—
167Dic107—21no—
168Dic107—21no—
169Dic107—21no—
170Dic107#11712yes—
171C2×C107—41no—
172C2×C107C2×#11711yescharacteristic
173C2×C107C2×#13111yescharacteristic
174C2×C107#56811yescharacteristic
175D107—22no—
176D107—22no—
177#2924—1071nomaximal, Sylow
178C107#292411yescharacteristic, complemented, Sylow
179C2×#117—1071no—
180#433—1071no—
181#433—1071no—
182#433—1071no—
183#433D10711yescharacteristic, complemented
184#432—1071no—
185#432—1071no—
186#431—1071no—
187#431—1071no—
188#424—1071no—
189#424—1071no—
190#407—1071no—
191C2×C22⋊C8—1071no—
192#405—1071no—
193#405—1071no—
194C23×C4—1071no—
195C2×M16—1071no—
196C2×M16—1071no—
197C22×C8—1071no—
198C22×C8—1071no—
199#117—1071no—
200#117—1071no—
201#117—1071no—
202#117—1071no—
203#117—1071no—
204#117—1071no—
205#117—1071no—
206#117C2×D10711yescharacteristic
207C2×C4⋊C4—1071no—
208C2×C4⋊C4—1071no—
209C2×C22⋊C4—1071no—
210C2×C22⋊C4—1071no—
211C2×C42—1071no—
212C2×C42—1071no—
213C4⋊C8—1071no—
214C4⋊C8—1071no—
215C4⋊C8—1071no—
216C4⋊C8—1071no—
217C4⋊C8—1071no—
218C4⋊C8—1071no—
219C4⋊C8C2×D10711yescharacteristic, complemented
220C4⋊C8C2×D10711yescharacteristic, complemented
221C22⋊C8—1071no—
222C22⋊C8—1071no—
223C22⋊C8—1071no—
224C22⋊C8—1071no—
225C22⋊C8—1071no—
226C22⋊C8—1071no—
227C22⋊C8C2×D10711yescharacteristic
228C22⋊C8C2×D10711yescharacteristic
229#97—1071no—
230#97—1071no—
231#97—1071no—
232#97C2×D10711yescharacteristic, complemented
233C4×C8—1071no—
234C4×C8—1071no—
235C4×C8—1071no—
236C4×C8C2×D10711yescharacteristic, complemented
237C24—1071no—
238C22×C4—1071no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—1071no—
242C22×C4—1071no—
243C22×C4—1071no—
244C22×C4—1071no—
245C22×C4—1071no—
246C22×C4—1071no—
247C22×C4—2142no—
248C22×C4—2142no—
249C22×C4C22×D10711yescharacteristic
250M16—2142no—
251M16—2142no—
252C2×C8—1071no—
253C2×C8—1071no—
254C2×C8—1071no—
255C2×C8—1071no—
256C2×C8—2142no—
257C2×C8—2142no—
258C2×C8C22×D10711yescharacteristic
259C2×C8C22×D10711yescharacteristic
260C2×C8C22×D10711yescharacteristic
261C2×C8C22×D10711yescharacteristic
262C4⋊C4—1071no—
263C4⋊C4—1071no—
264C4⋊C4—1071no—
265C4⋊C4—1071no—
266C4⋊C4—1071no—
267C4⋊C4—1071no—
268C4⋊C4C4×D10711yescharacteristic
269C4⋊C4C4×D10711yescharacteristic
270C22⋊C4—1071no—
271C22⋊C4—1071no—
272C22⋊C4—1071no—
273C22⋊C4—1071no—
274C22⋊C4—1071no—
275C22⋊C4—1071no—
276C22⋊C4C4×D10711yescharacteristic
277C22⋊C4C4×D10711yescharacteristic
278C42—1071no—
279C42—1071no—
280C42—1071no—
281C42—1071no—
282C42—1071no—
283C42—1071no—
284C42C22×D10711yescharacteristic
285C42C22×D10711yescharacteristic
286C23—1071no—
287C23—1071no—
288C23—4281no—
289C23—2142no—
290C23—2142no—
291C23C2×C4×D10711yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—1071no—
295C2×C4—1072no—
296C2×C4—1072no—
297C2×C4—1071no—
298C2×C4—1071no—
299C2×C4—1071no—
300C2×C4—1071no—
301C2×C4—1071no—
302C2×C4—4281no—
303C2×C4—4281no—
304C2×C4—2142no—
305C2×C4—2142no—
306C2×C4—2142no—
307C2×C4—2142no—
308C2×C4—2142no—
309C2×C4—2141no—
310C2×C4—2141no—
311C2×C4C2×C4×D10711yescharacteristic
312C2×C4C2×C4×D10711yescharacteristic
313C2×C4C2×C4×D10711yescharacteristic
314C2×C4C2×C4×D10711yescharacteristic
315C2×C4C2×C4×D10711yescharacteristic
316C2×C4C23×D10711yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—21no—
321C8—2141no—
322C8—2141no—
323C8—2141no—
324C8—2141no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—1072no—
329C22—1072no—
330C22—4284no—
331C22—2141no—
332C22—2141no—
333C22—2141no—
334C22—2141no—
335C22C22×C4×D10711yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—1072no—
342C4—2141no—
343C4—2141no—
344C4—2141no—
345C4—2141no—
346C4—2141no—
347C4#41×D10711yescharacteristic
348C4#41×D10711yescharacteristic
349C2—41no—
350C2—2142no—
351C2—2142no—
352C2#117×D10711yescharacteristic
353C2#131×D10711yescharacteristic
354C2#2029339211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
Fitting#433×C107C2
prime radicalC23×D107C2×C4
cosocleC2×C4×C107C24
hypercenter#433D107
hypocenterC107#2924
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #20292688C2semidirect
3. #20292685C2semidirect
4. #20292685C2semidirect
5. #20292683C2semidirect
6. #20292682C2semidirect
7. #20292679C2semidirect
8. #20292678C2semidirect
9. #20292652C2semidirect
10. #20292652C2semidirect
13. #20292584C2semidirect
14. #20292581C2semidirect
15. #433×C107C2semidirect
34. C4⋊(C107⋊C8)C22semidirect
35. C4⋊(C107⋊C8)C22semidirect
36. Dic107⋊C8C22semidirect
37. Dic107⋊C8C22semidirect
38. Dic107⋊C8C22semidirect
39. Dic107⋊C8C22semidirect
46. #16812020C22semidirect
47. #16812019C22semidirect
48. #16812019C22semidirect
49. C4×C107⋊C8C22semidirect
50. C8×Dic107C22semidirect
51. C8×Dic107C22semidirect
53. C4⋊C8×C107C22semidirect
54. C4⋊C8×C107C22semidirect
57. #97×C107C22semidirect
58. C4×C8×C107C22semidirect
178. C107#2924semidirect
183. #433D107semidirect
219. C4⋊C8C2×D107semidirect
220. C4⋊C8C2×D107semidirect
232. #97C2×D107semidirect
236. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#117×D1072
#202926882
#202926852
#202926832
#202926822
#202926792
#202926782
#202926522
#202925892
C22⋊C8×D1072
#202925842
#202925812
#433×C1072
#2924107