Finite Group Databasebeta

← #21451639

Subgroups — #21451639

Order 7808.

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

normal subgroups only

This group has 488 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×#14519775C211yesmaximal, characteristic, complemented
2C2×#14519733C211yesmaximal, characteristic
3#16839703C212yesmaximal, complemented
4#16839698C212yesmaximal
5#16839683C211yesmaximal, characteristic, complemented
6#16839681C211yesmaximal, characteristic, complemented
7#16839674C211yesmaximal, characteristic
8#16839659C212yesmaximal, complemented
9#16839626C211yesmaximal, characteristic, complemented
10#16839620C212yesmaximal
11C61×#393C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14#14519775—24no—
15#14519733—24no—
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C2×Q8×C61—22no—
39C2×Q8×C61—42no—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×Dic61—22no—
45C22×Dic61—22no—
46C22×Dic61Q814yescomplemented
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C2×Dic122—22no—
54C2×Dic122—42no—
55C22⋊C4×C61—22no—
56C22⋊C4×C61—42no—
57C22⋊Dic61—22no—
58C22⋊Dic61—42no—
59C4⋊Dic61—42no—
60#11758196—22no—
61#11758196—22no—
62#11758196—24no—
63#11758196—24no—
64#11758196—24no—
65#11758196—42no—
66C4×Dic61—22no—
67C4×Dic61D414yes—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61C2×Q812yes—
73C23×C61C2411yescharacteristic
74Q8×C61—44no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D412yes—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—28no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61C2×D412yes—
98C2×Dic61C2×D412yes—
99C2×Dic61C2×Q812yes—
100C2×Dic61C2×Q812yes—
101C2×Dic61#4112yes—
102Dic122—44no—
103C22×C61—22no—
104C22×C61—24no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61C22×D411yescharacteristic
109C22×C61C22×Q811yescharacteristic
110C22×C61C2×#4111yescharacteristic
111C22×C61H(5,𝔽2)12yes—
112C22×C612−1+412yes—
113C4×C61—22no—
114C4×C61—42no—
115C4×C61—41no—
116C4×C61—42no—
117Dic61—22no—
118Dic61—22no—
119Dic61—42no—
120Dic61—41no—
121Dic61—42no—
122Dic61C22⋊Q814yes—
123#2628—611nomaximal, Sylow
124C2×C61—42no—
125C2×C61C2×C22⋊Q811yescharacteristic
126C2×C61#53511yescharacteristic
127C2×C61#53611yescharacteristic
128C2×C61#54212yes—
129C2×C61#54412yes—
130C2×C4⋊Q8—611no—
131C2×#117—611no—
132#400—612no—
133#399—612no—
134#395—611no—
135#395—611no—
136#393—611no—
137#393D6111yescharacteristic
138#389—612no—
139#382—611no—
140#380—612no—
141C61#262811yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C22×Q8C2×D6111yescharacteristic
144C23×C4—611no—
145C4⋊Q8—1224no—
146#117—1224no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—612no—
154C2×C22⋊C4—611no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4C2×D6111yescharacteristic
157C2×C22⋊C4C2×D6112yes—
158C2×C42—611no—
159C2×C42—611no—
160#95—612no—
161#95—612no—
162#95—611no—
163#95—612no—
164#95—612no—
165#95C2×D6111yescharacteristic
166#95C2×D6112yes—
167C24C22×D6111yescharacteristic
168C2×Q8—22no—
169C2×Q8—42no—
170C2×Q8—1222no—
171C2×Q8—2442no—
172C22×C4—611no—
173C22×C4—614no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—612no—
177C22×C4—612no—
178C22×C4—611no—
179C22×C4—1222no—
180C22×C4—1222no—
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6112yes—
183C22×C4C22×D6112yes—
184C22×C4C22×D6111yescharacteristic
185C4⋊C4—1224no—
186C4⋊C4—1222no—
187C4⋊C4—1224no—
188C4⋊C4—1224no—
189C4⋊C4—1222no—
190C4⋊C4—2442no—
191C4⋊C4—2442no—
192C22⋊C4—22no—
193C22⋊C4—42no—
194C22⋊C4—1222no—
195C22⋊C4—2442no—
196C42—614no—
197C42—1222no—
198C23—21no—
199C23—21no—
200C23—22no—
201C23—22no—
202C23Q8×D6112yes—
203C23C23×D6111yescharacteristic
204Q8—44no—
205Q8—2444no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—612no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—612no—
219C2×C4—612no—
220C2×C4—1228no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4D4×D6112yes—
233C22—22no—
234C22—24no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22C2×D4×D6111yescharacteristic
239C22C2×Q8×D6111yescharacteristic
240C22#41×D6111yescharacteristic
241C22#1451982212yes—
242C22#1451982412yes—
243C4—22no—
244C4—42no—
245C4—41no—
246C4—42no—
247C4—614no—
248C4—1222no—
249C4—1222no—
250C4—2441no—
251C4—2442no—
252C4—2442no—
253C2—42no—
254C2C22⋊Q8×D6111yescharacteristic
255C2#1684032711yescharacteristic
256C2#1684033211yescharacteristic
257C2#1684037612yes—
258C2#1684039112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2628
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
3. #16839703C2semidirect
5. #16839683C2semidirect
6. #16839681C2semidirect
8. #16839659C2semidirect
9. #16839626C2semidirect
46. C22×Dic61Q8semidirect
141. C61#2628semidirect