Finite Group Databasebeta

← #21450816

Subgroups — #21450816

Order 7808.

604 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519766C211yesmaximal, characteristic
3C2×#14519765C211yesmaximal, characteristic
4C2×#14519739C211yesmaximal, characteristic
5#16839691C214yesmaximal, complemented
6#16839667C211yesmaximal, characteristic, complemented
7#16839621C214yesmaximal, complemented
8C4×#11758196C211yesmaximal, characteristic, complemented
9C61×#391C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519775—24no—
14#14519766—24no—
15#14519765—24no—
16#14519739—24no—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2214yes—
22C2×#11758198C2214yes—
23C2×C4×Dic61C2211yescharacteristic
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2214yes—
27C22×Q8×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2214yes—
31C23×D61C2312yes—
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×Dic61C2311yescharacteristic
43C2×D244—22no—
44C2×D244—22no—
45C2×D244D414yes—
46C2×C4×D61—24no—
47C2×C4×D61—28no—
48C2×Dic122—22no—
49C2×Dic122—22no—
50C2×Dic122—22no—
51C4⋊C4×C61—22no—
52C42×C61—22no—
53#11758198—28no—
54#11758198—28no—
55#11758198—24no—
56#11758196—24no—
57#11758196—24no—
58#11758196—24no—
59C4×Dic61—22no—
60C4×Dic61D414yes—
61C23×C61C2411yescharacteristic
62C22×D61—22no—
63C22×D61—24no—
64C22×D61—22no—
65C22×D61—24no—
66C22×D61C2×D414yes—
67Q8×C61—44no—
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×C61—22no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61#4112yes—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88C2×Dic61#4114yes—
89D244—28no—
90C4×D61—48no—
91Dic122—44no—
92C22×C61C22×D411yescharacteristic
93C22×C61C22×D411yescharacteristic
94C22×C61C2×#4112yes—
95C22×C61C2×#4111yescharacteristic
96C22×C612−1+412yes—
97C2×D61—24no—
98C2×D61—28no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—44no—
102C4×C61—42no—
103C4×C61—42no—
104C4×C61—42no—
105C4×C61#12114yes—
106Dic61—22no—
107Dic61—42no—
108Dic61—42no—
109Dic61#12414yescomplemented
110#2547—611nomaximal, Sylow
111C2×C61C2×#12111yescharacteristic
112C2×C61C2×#12411yescharacteristic
113C2×C61#53611yescharacteristic
114C2×C61#54712yes—
115C2×C61#55612yes—
116D61—44no—
117C2×C4⋊Q8—611no—
118C2×#124—611no—
119C2×#124—611no—
120C2×C4×D4—611no—
121#397—614no—
122#391—611no—
123#391D6111yescharacteristic, complemented
124#380—614no—
125C4×C4⋊C4—611no—
126C61#254711yescharacteristic, complemented, Sylow
127C22×Q8—611no—
128C22×Q8C2×D6111yescharacteristic
129C22×D4—611no—
130C23×C4—612no—
131C4⋊Q8—1224no—
132#124—1224no—
133#124—1224no—
134C4×D4—1224no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4—612no—
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C22⋊C4—612no—
140C2×C22⋊C4—614no—
141C2×C22⋊C4—614no—
142C2×C42—611no—
143C2×C42—611no—
144C2×C42C2×D6111yescharacteristic
145#95—612no—
146#95—614no—
147#95C2×D6114yes—
148C24—612no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—1222no—
153C2×Q8—1222no—
154C2×Q8—1222no—
155C2×D4—614no—
156C2×D4—1222no—
157C2×D4—1222no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—612no—
161C22×C4—612no—
162C22×C4—1224no—
163C22×C4—1228no—
164C22×C4C22×D6112yes—
165C22×C4C22×D6112yes—
166C22×C4C22×D6112yes—
167C22×C4C22×D6111yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—1224no—
170C4⋊C4—1224no—
171C4⋊C4—1224no—
172C22⋊C4—1224no—
173C22⋊C4—1228no—
174C22⋊C4—1228no—
175C42—22no—
176C42—614no—
177C42—1222no—
178C23—614no—
179C23—1222no—
180C23—1224no—
181C23—1222no—
182C23—1224no—
183C23C23×D6111yescharacteristic
184Q8—44no—
185Q8—2444no—
186D4—1228no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—612no—
196C2×C4—614no—
197C2×C4—612no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—2448no—
206C2×C4#1175822212yes—
207C2×C4D4×D6112yes—
208C2×C4D4×D6112yes—
209C22—1224no—
210C22—1228no—
211C22—2444no—
212C22—2442no—
213C22—2442no—
214C22C2×D4×D6111yescharacteristic
215C22C2×D4×D6111yescharacteristic
216C22#41×D6112yes—
217C22C2×#1175822211yescharacteristic
218C22#1451982512yes—
219C4—42no—
220C4—42no—
221C4—42no—
222C4—614no—
223C4—1222no—
224C4—2442no—
225C4—2442no—
226C4#1451975014yes—
227C2—2444no—
228C2C2×#1451975011yescharacteristic
229C2#124×D6111yescharacteristic
230C2#1684033711yescharacteristic
231C2#1684041412yes—
232C2#1684048412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2547
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. #16839691C2semidirect
6. #16839667C2semidirect
7. #16839621C2semidirect
8. C4×#11758196C2semidirect
9. C61×#391C2semidirect
109. Dic61#124semidirect
123. #391D61semidirect
126. C61#2547semidirect