Finite Group Databasebeta

← #21451518

Subgroups — #21451518

Order 7808.

476 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14519768C211yesmaximal, characteristic, complemented
2C2×#14519733C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic, complemented
4#16839698C211yesmaximal, characteristic
5#16839693C211yesmaximal, characteristic, complemented
6#16839659C212yesmaximal, complemented
7#16839655C212yesmaximal
8#16839644C212yesmaximal, complemented
9#16839634C212yesmaximal
10#16839607C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic
12C23×Dic61C2211yescharacteristic
13#14519768—24no—
14#14519733—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C4×Dic61C2211yescharacteristic
25C2×C4×Dic61C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61—22no—
43C22×Dic61—22no—
44C22×Dic61—22no—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C4⋊C4×C61—22no—
52C22⋊C4×C61—24no—
53C22⋊C4×C61—22no—
54C22⋊Dic61—22no—
55C22⋊Dic61—24no—
56C4⋊Dic61—22no—
57C4⋊Dic61—24no—
58#11758196—22no—
59#11758196—22no—
60#11758196—24no—
61#11758196—24no—
62#11758196—24no—
63C4×Dic61—22no—
64C4×Dic61—24no—
65C4×Dic61D414yes—
66C23×C61—21no—
67C23×C61—22no—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61#4112yes—
71C23×C61C2411yescharacteristic
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×Dic61—28no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61C2×D412yes—
96C2×Dic61C2×D412yes—
97C2×Dic61#4114yes—
98C2×Dic61#4112yes—
99C22×C61—22no—
100C22×C61—24no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—42no—
104C22×C61C22×D411yescharacteristic
105C22×C61C2×#4111yescharacteristic
106C22×C61C2×#4112yes—
107C22×C61C2×#4111yescharacteristic
108C22×C612−1+412yes—
109C4×C61—22no—
110C4×C61—42no—
111C4×C61—41no—
112C4×C61—42no—
113Dic61—22no—
114Dic61—22no—
115Dic61—22no—
116Dic61—24no—
117Dic61—42no—
118Dic61—41no—
119#2611—611nomaximal, Sylow
120C2×C61—42no—
121C2×C61#52511yescharacteristic
122C2×C61#53211yescharacteristic
123C2×C61#53611yescharacteristic
124C2×C61#55212yes—
125C2×C61#55212yes—
126C2×#125—611no—
127C2×#117—611no—
128#400—611no—
129#399—611no—
130#398—611no—
131#397D6111yescharacteristic
132#389—612no—
133#388—612no—
134#387—612no—
135#385—612no—
136#376—611no—
137C61#261111yescharacteristic, complemented, Sylow
138C23×C4—611no—
139#125—1224no—
140#117—1224no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—611no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C22⋊C4—611no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4C2×D6111yescharacteristic
152C2×C22⋊C4C2×D6112yes—
153C2×C42—611no—
154C2×C42—611no—
155C2×C42—612no—
156#95—612no—
157#95—611no—
158#95—612no—
159#95—612no—
160#95—612no—
161#95C2×D6111yescharacteristic
162#95C2×D6112yes—
163C24C22×D6111yescharacteristic
164C22×C4—612no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—612no—
170C22×C4—1222no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4C22×D6112yes—
174C22×C4C22×D6112yes—
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—1224no—
179C4⋊C4—1224no—
180C4⋊C4—1222no—
181C4⋊C4—1224no—
182C4⋊C4—1224no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C22⋊C4—24no—
186C22⋊C4—22no—
187C22⋊C4—1222no—
188C22⋊C4—1224no—
189C42—614no—
190C42—1224no—
191C42—1222no—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—22no—
196C23#1175822412yes—
197C23C23×D6111yescharacteristic
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—612no—
208C2×C4—612no—
209C2×C4—614no—
210C2×C4—612no—
211C2×C4—1228no—
212C2×C4—1221no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4D4×D6112yes—
225C22—24no—
226C22—22no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22C2×D4×D6111yescharacteristic
231C22#41×D6111yescharacteristic
232C22#41×D6112yes—
233C22C2×#1175822411yescharacteristic
234C22#1451982412yes—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—1224no—
240C4—1222no—
241C4—1222no—
242C4—1222no—
243C4—2442no—
244C4—2441no—
245C2—42no—
246C2#1684027211yescharacteristic
247C2#1684031111yescharacteristic
248C2#1684033411yescharacteristic
249C2#1684044812yes—
250C2#1684044912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2611
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519768C2semidirect
3. #16839702C2semidirect
5. #16839693C2semidirect
6. #16839659C2semidirect
8. #16839644C2semidirect
10. #16839607C2semidirect
137. C61#2611semidirect