Finite Group Databasebeta

← #21451002

Subgroups — #21451002

Order 7808.

584 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14519739C211yesmaximal, characteristic
3#16839697C211yesmaximal, characteristic, complemented
4#16839682C211yesmaximal, characteristic, complemented
5#16839675C211yesmaximal, characteristic, complemented
6#16839649C212yesmaximal, complemented
7#16839640C212yesmaximal
8#16839636C212yesmaximal, complemented
9#16839621C212yesmaximal, complemented
10#95×D61C211yesmaximal, characteristic, complemented
11C61×#400C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C4×D61C2212yes—
15C22×C4×D61C2211yescharacteristic
16C22×C4×D61C2211yescharacteristic
17#14519757—24no—
18#14519739—24no—
19C2×C4⋊Dic61C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2211yescharacteristic
35#95×C61C2212yes—
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2312yes—
48C2×D244—22no—
49C2×D244—22no—
50C2×D244Q814yescomplemented
51C2×C4×D61—24no—
52C2×C4×D61—22no—
53C2×C4×D61—24no—
54C2×C4×D61—42no—
55C2×C4×D61—42no—
56C2×C4×D61—42no—
57C2×C4×D61D414yes—
58C2×Dic122—22no—
59C2×Dic122—42no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62#11758198—22no—
63#11758198—24no—
64#11758198—22no—
65#11758198—24no—
66#11758198—42no—
67C4⋊Dic61—24no—
68#11758196—24no—
69#11758196—42no—
70C4×Dic61—22no—
71C23×C61C2411yescharacteristic
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—21no—
77C22×D61—22no—
78C22×D61C2×D412yes—
79C22×D61C2×Q812yes—
80C22×D61C2×Q812yes—
81C22×D61#4112yes—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×Q812yes—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61C2×D412yes—
104C2×Dic61#4114yes—
105D244—28no—
106C4×D61—44no—
107C4×D61—48no—
108C4×D61—44no—
109Dic122—44no—
110C22×C61C22×D411yescharacteristic
111C22×C61C22×Q811yescharacteristic
112C22×C61C2×#4111yescharacteristic
113C22×C61C2×#4112yes—
114C22×C61H(5,𝔽2)12yes—
115C2×D61—22no—
116C2×D61—22no—
117C2×D61—24no—
118C2×D61—24no—
119C2×D61—22no—
120C2×D61—24no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—42no—
124C2×D61C22⋊Q814yes—
125C4×C61—22no—
126C4×C61—22no—
127C4×C61—42no—
128C4×C61—41no—
129C4×C61—42no—
130Dic61—22no—
131Dic61—24no—
132Dic61—41no—
133Dic61—42no—
134#2564—611nomaximal, Sylow
135C2×C61C2×C22⋊Q811yescharacteristic
136C2×C61#53211yescharacteristic
137C2×C61#53411yescharacteristic
138C2×C61#55112yes—
139C2×C61#55412yes—
140D61—24no—
141D61—42no—
142C2×C22⋊Q8—611no—
143C2×C4×D4—611no—
144#400D6111yescharacteristic, complemented
145#399—611no—
146#395—611no—
147#393—611no—
148#387—612no—
149#386—612no—
150#385—612no—
151#380—612no—
152C2×#95—611no—
153C61#256411yescharacteristic, complemented, Sylow
154C22×Q8—611no—
155C22×D4—611no—
156C23×C4—611no—
157C23×C4—612no—
158C23×C4—611no—
159C22⋊Q8—1224no—
160C4×D4—1224no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4C2×D6111yescharacteristic
165C2×C4⋊C4C2×D6111yescharacteristic
166C2×C22⋊C4—611no—
167C2×C22⋊C4—611no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4—612no—
170C2×C22⋊C4—612no—
171C2×C42—611no—
172#95—612no—
173#95—611no—
174#95—612no—
175#95—612no—
176#95C2×D6111yescharacteristic
177#95C2×D6112yes—
178#95C2×D6112yes—
179C24—611no—
180C24—611no—
181C2×Q8—1222no—
182C2×Q8—2442no—
183C2×D4—614no—
184C2×D4—1222no—
185C2×D4—1222no—
186C22×C4—612no—
187C22×C4—611no—
188C22×C4—614no—
189C22×C4—611no—
190C22×C4—612no—
191C22×C4—1222no—
192C22×C4—1224no—
193C22×C4—1224no—
194C22×C4—2442no—
195C22×C4—2442no—
196C22×C4—2442no—
197C22×C4C22×D6112yes—
198C22×C4C22×D6112yes—
199C22×C4C22×D6111yescharacteristic
200C22×C4C22×D6111yescharacteristic
201C22×C4C22×D6111yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—1224no—
205C4⋊C4—1224no—
206C4⋊C4—2442no—
207C22⋊C4—1224no—
208C22⋊C4—1222no—
209C22⋊C4—1224no—
210C22⋊C4—1222no—
211C22⋊C4—2442no—
212C42—1222no—
213C23—612no—
214C23—612no—
215C23—612no—
216C23—612no—
217C23—1222no—
218C23—1222no—
219C23—1221no—
220C23—1222no—
221C23—1221no—
222C23—1222no—
223C23C23×D6111yescharacteristic
224Q8—2444no—
225D4—1228no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—612no—
238C2×C4—614no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—2444no—
248C2×C4—2448no—
249C2×C4—2444no—
250C2×C4D4×D6112yes—
251C2×C4Q8×D6112yes—
252C22—614no—
253C22—1224no—
254C22—1222no—
255C22—1222no—
256C22—1224no—
257C22—1224no—
258C22—1222no—
259C22—2441no—
260C22—2441no—
261C22—2442no—
262C22C2×D4×D6111yescharacteristic
263C22C2×Q8×D6111yescharacteristic
264C22#41×D6112yes—
265C22#41×D6111yescharacteristic
266C22#1451982312yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—1222no—
273C4—1224no—
274C4—2441no—
275C4—2442no—
276C2—1224no—
277C2—2442no—
278C2C22⋊Q8×D6111yescharacteristic
279C2#1684031111yescharacteristic
280C2#1684032311yescharacteristic
281C2#1684043712yes—
282C2#1684046812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2564
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14519757C2semidirect
3. #16839697C2semidirect
4. #16839682C2semidirect
5. #16839675C2semidirect
6. #16839649C2semidirect
8. #16839636C2semidirect
9. #16839621C2semidirect
10. #95×D61C2semidirect
11. C61×#400C2semidirect
50. C2×D244Q8semidirect
144. #400D61semidirect
153. C61#2564semidirect