Finite Group Databasebeta

← #21450771

Subgroups — #21450771

Order 7808.

676 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 177 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×#14519776C211yesmaximal, characteristic, complemented
2C2×#14519755C214yesmaximal, complemented
3C2×#14519739C211yesmaximal, characteristic
4#16839697C214yesmaximal, complemented
5#16839664C211yesmaximal, characteristic
6#16839663C211yesmaximal, characteristic
7#16839631C211yesmaximal, characteristic, complemented
8C4×#11758196C211yesmaximal, characteristic, complemented
9C61×#384C211yesmaximal, characteristic, complemented
10C22×Dic122C2212yes—
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519776—24no—
14#14519755—216no—
15#14519739—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2214yes—
19C2×#11758196C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2214yes—
22C2×#11758198C2214yes—
23C2×C4×Dic61C2211yescharacteristic
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26C2×C4⋊C4×C61C2214yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30C23×D61C2312yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61C2312yes—
36C22×Dic61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2311yescharacteristic
39C2×D244—22no—
40C2×D244—22no—
41C2×D244Q814yescomplemented
42C2×C4×D61—24no—
43C2×C4×D61—28no—
44C2×Dic122—28no—
45C2×Dic122—24no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61—28no—
48C4⋊C4×C61—22no—
49C42×C61—22no—
50#11758198—28no—
51#11758198—24no—
52#11758198—28no—
53C4⋊Dic61—22no—
54#11758196—28no—
55#11758196—24no—
56#11758196D418yescomplemented
57C4×Dic61—22no—
58C4×Dic61D414yes—
59C23×C61C2411yescharacteristic
60C22×D61—24no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—24no—
64C22×D61C2×Q814yes—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—24no—
69C2×C4×C61—24no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D414yes—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×Q812yes—
74C2×C4×C61#4112yes—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—24no—
80C2×Dic61C2×D412yes—
81C2×Dic61C2×D414yes—
82C2×Dic61C2×D412yes—
83C2×Dic61C2×D414yes—
84D244—28no—
85C4×D61—48no—
86Dic122—48no—
87C22×C61C22×D411yescharacteristic
88C22×C61C22×D412yes—
89C22×C61C22×Q811yescharacteristic
90C22×C61C2×#4111yescharacteristic
91C22×C612−1+412yes—
92C2×D61—24no—
93C2×D61—28no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—44no—
97C4×C61—24no—
98C4×C61—42no—
99C4×C61—42no—
100C4×C61C22⋊Q814yescomplemented
101Dic61—22no—
102Dic61—24no—
103Dic61—42no—
104Dic61#12714yes—
105#2542—611nomaximal, Sylow
106C2×C61C2×C22⋊Q811yescharacteristic
107C2×C61C2×#12711yescharacteristic
108C2×C61#53611yescharacteristic
109C2×C61#54712yes—
110C2×C61D4×Q812yes—
111D61—44no—
112C2×C4⋊Q8—611no—
113C2×C22⋊Q8—614no—
114C2×C4×D4—611no—
115#399—614no—
116#390—611no—
117#390—611no—
118#384—611no—
119#384D6111yescharacteristic, complemented
120C4×C4⋊C4—611no—
121C61#254211yescharacteristic, complemented, Sylow
122C22×Q8—612no—
123C22×D4—611no—
124C23×C4—612no—
125C4⋊Q8—1224no—
126C22⋊Q8—12216no—
127C4×D4—1224no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4—614no—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C4⋊C4C2×D6114yes—
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C22⋊C4—612no—
136C2×C22⋊C4—614no—
137C2×C22⋊C4—614no—
138C2×C42—611no—
139C2×C42—611no—
140C2×C42C2×D6111yescharacteristic
141#95—612no—
142C24—612no—
143C2×Q8—1228no—
144C2×Q8—1224no—
145C2×D4—614no—
146C2×D4—1222no—
147C2×D4—1222no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—1224no—
153C22×C4—1228no—
154C22×C4C22×D6112yes—
155C22×C4C22×D6112yes—
156C22×C4C22×D6112yes—
157C22×C4C22×D6111yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—28no—
160C4⋊C4—22no—
161C4⋊C4—618no—
162C4⋊C4—1228no—
163C4⋊C4—1224no—
164C4⋊C4—1222no—
165C22⋊C4—1224no—
166C22⋊C4—1228no—
167C22⋊C4—1228no—
168C42—22no—
169C42—614no—
170C42—1222no—
171C23—614no—
172C23—1224no—
173C23—1222no—
174C23—1222no—
175C23—1224no—
176C23C23×D6111yescharacteristic
177Q8—2448no—
178D4—1228no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—22no—
185C2×C4—612no—
186C2×C4—614no—
187C2×C4—612no—
188C2×C4—614no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1224no—
193C2×C4—1222no—
194C2×C4—2448no—
195C2×C4#1175822212yes—
196C2×C4D4×D6114yes—
197C2×C4D4×D6112yes—
198C2×C4Q8×D6112yes—
199C22—1224no—
200C22—1228no—
201C22—2442no—
202C22—2442no—
203C22—2444no—
204C22C2×D4×D6111yescharacteristic
205C22C2×D4×D6112yes—
206C22C2×Q8×D6111yescharacteristic
207C22C2×#1175822211yescharacteristic
208C22#1451982512yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—614no—
213C4—1222no—
214C4—1224no—
215C4—2442no—
216C4#1451975514yescomplemented
217C2—2444no—
218C2C2×#1451975511yescharacteristic
219C2#127×D6111yescharacteristic
220C2#1684033711yescharacteristic
221C2#1684041312yes—
222C2#1684042712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#384C2
hypercenter#384D61
hypocenterC61#2542
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
2. C2×#14519755C2semidirect
4. #16839697C2semidirect
7. #16839631C2semidirect
8. C4×#11758196C2semidirect
9. C61×#384C2semidirect
41. C2×D244Q8semidirect
56. #11758196D4semidirect
100. C4×C61C22⋊Q8semidirect
119. #384D61semidirect
121. C61#2542semidirect
216. C4#14519755semidirect