Finite Group Databasebeta

← #21451590

Subgroups — #21451590

Order 7808.

528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519757C211yesmaximal, characteristic
3C2×#14519753C211yesmaximal, characteristic
4C2×#14519734C211yesmaximal, characteristic
5#16839696C214yesmaximal, complemented
6#16839691C214yesmaximal
7#16839668C211yesmaximal, characteristic, complemented
8#16839627C211yesmaximal, characteristic, complemented
9C61×#391C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×C4×D61C2211yescharacteristic
12#14519775—24no—
13#14519757—24no—
14#14519753—24no—
15#14519734—24no—
16C2×C4⋊Dic61C2212yes—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196C2214yes—
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2214yes—
26#14519684C2214yes—
27C22×Q8×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2214yes—
31C23×D61C2311yescharacteristic
32C2×Q8×C61—22no—
33C2×Q8×C61—22no—
34C2×Q8×C61—22no—
35C22×C4×C61C2312yes—
36C22×C4×C61C2312yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2312yes—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61D414yes—
46C2×Dic122—22no—
47C2×Dic122—22no—
48C2×Dic122—22no—
49C4⋊C4×C61—22no—
50C42×C61—22no—
51#11758198—24no—
52#11758198—24no—
53#11758198—24no—
54C4⋊Dic61—22no—
55C4⋊Dic61—24no—
56#11758196—24no—
57#11758196—24no—
58#11758196—28no—
59C4×Dic61D414yes—
60C23×C61C2411yescharacteristic
61C22×D61—21no—
62C22×D61—21no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61C2×D412yes—
66Q8×C61—44no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—24no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×D412yes—
77C2×C4×C61#4112yes—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61C2×D414yes—
88C2×Dic61C2×D412yes—
89C4×D61—28no—
90Dic122—44no—
91C22×C61C22×D411yescharacteristic
92C22×C61C22×D411yescharacteristic
93C22×C61C2×#4111yescharacteristic
94C22×C612−1+412yes—
95C22×C612−1+412yes—
96C2×D61—22no—
97C2×D61—22no—
98C2×D61—22no—
99C2×D61—42no—
100C2×D61—42no—
101C4×C61—42no—
102C4×C61—42no—
103C4×C61—42no—
104C4×C61#12114yes—
105Dic61—22no—
106Dic61—24no—
107Dic61—42no—
108Dic61—42no—
109#2621—611nomaximal, Sylow
110C2×C61C2×#12111yescharacteristic
111C2×C61#53611yescharacteristic
112C2×C61#53612yes—
113C2×C61#53611yescharacteristic
114C2×C61#54112yes—
115D61—42no—
116C2×C4⋊Q8—611no—
117C2×C22⋊Q8—611no—
118C2×C22⋊Q8—611no—
119C2×#117—611no—
120#398—614no—
121#397—614no—
122#391—611no—
123#391D6111yescharacteristic, complemented
124#382—611no—
125C61#262111yescharacteristic, complemented, Sylow
126C22×Q8—611no—
127C22×Q8C2×D6111yescharacteristic
128C23×C4—611no—
129C4⋊Q8—1224no—
130C22⋊Q8—1224no—
131C22⋊Q8—1224no—
132#117—1224no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4—614no—
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C22⋊C4—612no—
140C2×C22⋊C4—612no—
141C2×C22⋊C4—612no—
142C2×C42—611no—
143C2×C42C2×D6111yescharacteristic
144#95—614no—
145#95—614no—
146#95C2×D6114yes—
147C24—611no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—1222no—
152C2×Q8—1222no—
153C2×Q8—1222no—
154C22×C4—612no—
155C22×C4—611no—
156C22×C4—614no—
157C22×C4—612no—
158C22×C4—612no—
159C22×C4—1222no—
160C22×C4—1222no—
161C22×C4C22×D6112yes—
162C22×C4C22×D6112yes—
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—1224no—
167C4⋊C4—1224no—
168C4⋊C4—1228no—
169C4⋊C4—1224no—
170C4⋊C4—1222no—
171C22⋊C4—1224no—
172C22⋊C4—1224no—
173C22⋊C4—1224no—
174C42—22no—
175C42—614no—
176C23—612no—
177C23—1221no—
178C23—1221no—
179C23—1222no—
180C23—1222no—
181C23C23×D6111yescharacteristic
182Q8—44no—
183Q8—2444no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—614no—
193C2×C4—612no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1228no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1224no—
204C2×C4#1175822212yes—
205C2×C4D4×D6112yes—
206C2×C4D4×D6112yes—
207C22—1222no—
208C22—1222no—
209C22—1222no—
210C22—2442no—
211C22—2442no—
212C22C2×D4×D6111yescharacteristic
213C22C2×D4×D6111yescharacteristic
214C22C2×#1175822211yescharacteristic
215C22#1451982412yes—
216C22#1451982512yes—
217C4—42no—
218C4—42no—
219C4—42no—
220C4—1222no—
221C4—1224no—
222C4—2442no—
223C4—2442no—
224C4#1451975014yes—
225C2—2442no—
226C2C2×#1451975011yescharacteristic
227C2#1684033211yescharacteristic
228C2#1684033512yes—
229C2#1684033711yescharacteristic
230C2#1684037012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2621
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
5. #16839696C2semidirect
7. #16839668C2semidirect
8. #16839627C2semidirect
9. C61×#391C2semidirect
123. #391D61semidirect
125. C61#2621semidirect