Finite Group Databasebeta

← #21450801

Subgroups — #21450801

Order 7808.

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

normal subgroups only

This group has 576 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×#14519777C211yesmaximal, characteristic, complemented
2C2×#14519764C211yesmaximal, characteristic
3C2×#14519764C211yesmaximal, characteristic
4C2×#14519742C211yesmaximal, characteristic, complemented
5#16839685C214yesmaximal, complemented
6#16839667C211yesmaximal, characteristic, complemented
7#16839655C214yesmaximal, complemented
8C4×#11758196C211yesmaximal, characteristic, complemented
9C61×#390C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12#14519777—24no—
13#14519764—24no—
14#14519764—24no—
15#14519742—24no—
16C2×C4⋊Dic61C2214yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2214yes—
21C2×C22⋊Dic61C2212yes—
22C2×C4×Dic61C2212yes—
23C2×C4×Dic61C2211yescharacteristic
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2214yes—
26#14519684C2212yes—
27C22×D4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2214yes—
30C2×C42×C61C2211yescharacteristic
31C24×C61C2312yes—
32C2×D4×C61—22no—
33C2×D4×C61—22no—
34C2×D4×C61—22no—
35C22×C4×C61C2312yes—
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2311yescharacteristic
43C2×Dic122—22no—
44C2×Dic122—22no—
45C2×Dic122—22no—
46C2×Dic122—22no—
47C2×Dic122—22no—
48C2×Dic122D414yes—
49C4⋊C4×C61—22no—
50C22⋊C4×C61—28no—
51C42×C61—22no—
52C22⋊Dic61—28no—
53C22⋊Dic61—24no—
54C22⋊Dic61—24no—
55C4⋊Dic61—28no—
56#11758196—24no—
57#11758196—24no—
58C4×Dic61—22no—
59C4×Dic61—24no—
60C4×Dic61D414yes—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—24no—
64C23×C61—22no—
65C23×C61—24no—
66C23×C61C2411yescharacteristic
67D4×C61—44no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—24no—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×D412yes—
74C2×C4×C61#4114yes—
75C2×C4×C61#4112yes—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
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×Dic61C2×D414yes—
89Dic122—28no—
90Dic122—44no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—44no—
95C22×C61—44no—
96C22×C61C22×D411yescharacteristic
97C22×C61C22×D411yescharacteristic
98C22×C61C2×#4112yes—
99C22×C61C2×#4111yescharacteristic
100C22×C612−1+412yes—
101C4×C61—24no—
102C4×C61—42no—
103C4×C61#12114yes—
104Dic61—24no—
105Dic61—22no—
106Dic61—22no—
107Dic61—42no—
108Dic61—42no—
109#2545—611nomaximal, Sylow
110C2×C61—82no—
111C2×C61C2×#12111yescharacteristic
112C2×C61#53211yescharacteristic
113C2×C61#53611yescharacteristic
114C2×C61#54812yes—
115C2×C61#55612yes—
116C2×C4⋊Q8—611no—
117C2×#124—611no—
118C2×#124—611no—
119C2×C4×Q8—611no—
120#396—614no—
121#391—611no—
122#390D6111yescharacteristic
123#388—614no—
124C4×C4⋊C4—611no—
125C61#254511yescharacteristic, complemented, Sylow
126C22×Q8—611no—
127C22×Q8—611no—
128C22×D4C2×D6111yescharacteristic
129C4⋊Q8—1224no—
130#124—1224no—
131#124—1224no—
132C4×Q8—1224no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—614no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4C2×D6111yescharacteristic
137C2×C22⋊C4—612no—
138C2×C22⋊C4—614no—
139C2×C22⋊C4—612no—
140C2×C22⋊C4C2×D6114yes—
141C2×C42—611no—
142C2×C42—612no—
143C2×C42—611no—
144C2×C42C2×D6111yescharacteristic
145#95—612no—
146#95—614no—
147C24C22×D6112yes—
148C2×Q8—614no—
149C2×Q8—1222no—
150C2×Q8—1222no—
151C2×Q8—1222no—
152C2×Q8—1222no—
153C2×Q8—1222no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—22no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—612no—
160C22×C4—612no—
161C22×C4—612no—
162C22×C4C22×D6112yes—
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—1224no—
167C4⋊C4—1228no—
168C4⋊C4—1224no—
169C22⋊C4—28no—
170C22⋊C4—1224no—
171C22⋊C4—1224no—
172C22⋊C4—1228no—
173C42—22no—
174C42—614no—
175C42—1224no—
176C42—1222no—
177C23—22no—
178C23—22no—
179C23—24no—
180C23—22no—
181C23—24no—
182C23C23×D6111yescharacteristic
183Q8—1228no—
184Q8—2444no—
185D4—44no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—612no—
191C2×C4—612no—
192C2×C4—614no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4#1175822212yes—
204C2×C4D4×D6112yes—
205C2×C4D4×D6112yes—
206C2×C4#1175822414yes—
207C22—44no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—44no—
212C22C2×D4×D6111yescharacteristic
213C22C2×D4×D6111yescharacteristic
214C22C2×#1175822412yes—
215C22C2×#1175822211yescharacteristic
216C22#1451982412yes—
217C4—24no—
218C4—42no—
219C4—1224no—
220C4—1222no—
221C4—1222no—
222C4—2442no—
223C4—2442no—
224C4#1451975014yes—
225C2—82no—
226C2C2×#1451975011yescharacteristic
227C2#1684031011yescharacteristic
228C2#1684033211yescharacteristic
229C2#1684041812yes—
230C2#1684048212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2545
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519777C2semidirect
4. C2×#14519742C2semidirect
5. #16839685C2semidirect
6. #16839667C2semidirect
7. #16839655C2semidirect
8. C4×#11758196C2semidirect
125. C61#2545semidirect