Finite Group Databasebeta

← #21451625

Subgroups — #21451625

Order 7808.

668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519757C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D61C211yesmaximal, characteristic
3#16839697C211yesmaximal, characteristic, complemented
4#16839685C212yesmaximal, complemented
5#16839684C212yesmaximal, complemented
6#16839675C211yesmaximal, characteristic, complemented
7#16839674C211yesmaximal, characteristic, complemented
8#16839633C212yesmaximal, complemented
9#16839621C211yesmaximal, characteristic, complemented
10#16839617C212yesmaximal
11C61×#399C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C22×Dic122C2211yescharacteristic, complemented
14C22×C4×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519757—24no—
17C2×C4⋊Dic61C2212yescomplemented
18C2×#11758196C2212yescomplemented
19C2×#11758196C2212yescomplemented
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C22⋊C4×D61—24no—
29#14519684C2212yescomplemented
30#14519684C2212yescomplemented
31#14519684C2211yescharacteristic, complemented
32C2×C4⋊C4×C61C2211yescharacteristic, complemented
33C2×C4⋊C4×C61C2212yescomplemented
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic, complemented
37C24×C61C2311yescharacteristic
38C23×D61—22no—
39C23×D61—22no—
40C23×D61—42no—
41C23×D61—42no—
42C23×D61Q814yescomplemented
43C23×D61C2311yescharacteristic
44C23×D61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C22×C4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C22×Dic61C2312yes—
52C22×Dic61C2311yescharacteristic
53C2×C4×D61—22no—
54C2×C4×D61—42no—
55C2×C4×D61—42no—
56C2×C4×D61D414yes—
57C2×Dic122—22no—
58C2×Dic122—42no—
59C4⋊C4×C61—22no—
60C4⋊C4×C61—42no—
61C22⋊C4×C61—22no—
62C22⋊C4×C61—42no—
63C22⋊Dic61—22no—
64C22⋊Dic61—42no—
65#11758198—24no—
66#11758198—24no—
67#11758198—22no—
68#11758198—22no—
69#11758198—42no—
70#11758198—42no—
71C4⋊Dic61—24no—
72#11758196—42no—
73#11758196—42no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61C2×Q812yes—
79C23×C61C2411yescharacteristic
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—28no—
87C22×D61—48no—
88C22×D61—44no—
89C22×D61—44no—
90C22×D61—48no—
91C22×D61C2×D412yes—
92C22×D61C2×Q812yes—
93C22×D61C2×Q812yes—
94C22×D61#4112yes—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61C2×D412yes—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61C2×D412yes—
115C4×D61—44no—
116C4×D61—44no—
117Dic122—44no—
118C22×C61—22no—
119C22×C61—24no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—42no—
123C22×C61C22×D411yescharacteristic
124C22×C61C22×Q811yescharacteristic
125C22×C61C2×#4111yescharacteristic
126C22×C61H(5,𝔽2)12yes—
127C22×C61H(5,𝔽2)12yes—
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—24no—
131C2×D61—24no—
132C2×D61—22no—
133C2×D61—24no—
134C2×D61—416no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—42no—
138C2×D61C22⋊Q814yes—
139C4×C61—22no—
140C4×C61—41no—
141C4×C61—42no—
142C4×C61—42no—
143Dic61—22no—
144Dic61—42no—
145Dic61—41no—
146Dic61—42no—
147#2626—611nomaximal, Sylow
148C2×C61—42no—
149C2×C61C2×C22⋊Q811yescharacteristic
150C2×C61#53411yescharacteristic
151C2×C61#53511yescharacteristic
152C2×C61#53812yes—
153C2×C61#54312yes—
154D61—24no—
155D61—42no—
156C2×C22⋊Q8—611no—
157C22×C22⋊C4—611no—
158#399—611no—
159#399D6111yescharacteristic, complemented
160#396—612no—
161#396—612no—
162#393—611no—
163#393—611no—
164#385—612no—
165#380—611no—
166#379—612no—
167C61#262611yescharacteristic, complemented, Sylow
168C25—611no—
169C22×Q8—611no—
170C23×C4—611no—
171C23×C4—611no—
172C22⋊Q8—1224no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4—612no—
175C2×C4⋊C4—612no—
176C2×C4⋊C4C2×D6111yescharacteristic, complemented
177C2×C4⋊C4C2×D6112yescomplemented
178C2×C22⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—611no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—1224no—
187C2×C22⋊C4C2×D6111yescharacteristic
188C2×C22⋊C4C2×D6112yes—
189#95—611no—
190#95—612no—
191#95—612no—
192#95C2×D6111yescharacteristic, complemented
193C24—611no—
194C24—611no—
195C24—614no—
196C24—1222no—
197C24—1222no—
198C24—2442no—
199C24—2442no—
200C24C22×D6111yescharacteristic
201C2×Q8—1222no—
202C2×Q8—2442no—
203C22×C4—611no—
204C22×C4—614no—
205C22×C4—612no—
206C22×C4—612no—
207C22×C4—611no—
208C22×C4—1222no—
209C22×C4—2442no—
210C22×C4—2442no—
211C22×C4C22×D6111yescharacteristic
212C22×C4C22×D6112yes—
213C22×C4C22×D6112yes—
214C22×C4C22×D6111yescharacteristic
215C4⋊C4—22no—
216C4⋊C4—42no—
217C4⋊C4—1224no—
218C4⋊C4—2442no—
219C4⋊C4—2442no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—1222no—
223C22⋊C4—1224no—
224C22⋊C4—1224no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C22⋊C4—2442no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—22no—
234C23—612no—
235C23—612no—
236C23—612no—
237C23—612no—
238C23—1228no—
239C23—1222no—
240C23—1222no—
241C23—1221no—
242C23—1221no—
243C23—1222no—
244C23—1222no—
245C23—2448no—
246C23—2444no—
247C23—2444no—
248C23—2448no—
249C23Q8×D6112yes—
250C23C23×D6111yescharacteristic
251Q8—2444no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—612no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—2444no—
272C2×C4—2444no—
273C2×C4D4×D6112yes—
274C22—22no—
275C22—24no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—614no—
280C22—1222no—
281C22—1222no—
282C22—1224no—
283C22—1224no—
284C22—1222no—
285C22—1224no—
286C22—24416no—
287C22—2441no—
288C22—2441no—
289C22—2442no—
290C22C2×D4×D6111yescharacteristic
291C22C2×Q8×D6111yescharacteristic
292C22#41×D6111yescharacteristic
293C22#1451982212yes—
294C22#1451982312yes—
295C4—22no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—1222no—
300C4—2442no—
301C4—2441no—
302C4—2442no—
303C2—42no—
304C2—1224no—
305C2—2442no—
306C2C22⋊Q8×D6111yescharacteristic
307C2#1684032311yescharacteristic
308C2#1684032511yescharacteristic
309C2#1684034812yes—
310C2#1684038712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2626
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519757C2semidirect
3. #16839697C2semidirect
4. #16839685C2semidirect
5. #16839684C2semidirect
6. #16839675C2semidirect
7. #16839674C2semidirect
8. #16839633C2semidirect
9. #16839621C2semidirect
11. C61×#399C2semidirect
13. C22×Dic122C22semidirect
17. C2×C4⋊Dic61C22semidirect
18. C2×#11758196C22semidirect
19. C2×#11758196C22semidirect
29. #14519684C22semidirect
30. #14519684C22semidirect
31. #14519684C22semidirect
32. C2×C4⋊C4×C61C22semidirect
33. C2×C4⋊C4×C61C22semidirect
36. #95×C61C22semidirect
42. C23×D61Q8semidirect
159. #399D61semidirect
167. C61#2626semidirect
176. C2×C4⋊C4C2×D61semidirect
177. C2×C4⋊C4C2×D61semidirect
192. #95C2×D61semidirect