Finite Group Databasebeta

← #21451180

Subgroups — #21451180

Order 7808.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×Q8×Dic61C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic
4#16839701C211yesmaximal, characteristic
5#16839681C211yesmaximal, characteristic
6#16839666C212yesmaximal
7#16839657C212yesmaximal
8#16839649C212yesmaximal
9#16839648C212yesmaximal
10#16839626C211yesmaximal, characteristic
11C61×#395C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13Q8×Dic61—24no—
14#14519742—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2211yescharacteristic
23C2×C4×Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C2×Q8×C61—22no—
38C2×Q8×C61—24no—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C2×Dic122—22no—
51C2×Dic122—22no—
52C2×Dic122Q814yescomplemented
53C4⋊C4×C61—22no—
54C4⋊C4×C61—24no—
55C4⋊Dic61—22no—
56C4⋊Dic61—24no—
57#11758196—22no—
58#11758196—24no—
59#11758196—22no—
60#11758196—24no—
61C4×Dic61—22no—
62C4×Dic61—22no—
63C4×Dic61—24no—
64C4×Dic61D414yes—
65C23×C61C2411yescharacteristic
66Q8×C61—28no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×Q812yes—
79C2×C4×C61#4114yes—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—24no—
89C2×Dic61—22no—
90C2×Dic61C2×D412yes—
91C2×Dic61C2×D412yes—
92C2×Dic61C2×Q812yes—
93C2×Dic61C2×Q812yes—
94C2×Dic61#4112yes—
95Dic122—28no—
96C22×C61C22×D411yescharacteristic
97C22×C61C22×Q811yescharacteristic
98C22×C61C2×#4111yescharacteristic
99C22×C61C2×#4112yes—
100C22×C612−1+412yes—
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—24no—
104C4×C61—41no—
105C4×C61—42no—
106Dic61—22no—
107Dic61—22no—
108Dic61—41no—
109Dic61—42no—
110Dic61—42no—
111Dic61C22⋊Q814yes—
112#2581—611nomaximal, Sylow
113C2×C61C2×C22⋊Q811yescharacteristic
114C2×C61#52511yescharacteristic
115C2×C61#53611yescharacteristic
116C2×C61#55612yes—
117C2×C61#55712yes—
118C2×C4×Q8—611no—
119C2×C4×Q8—611no—
120#400—611no—
121#400—611no—
122#395—611no—
123#395D6111yescharacteristic
124#391—612no—
125#389—612no—
126#387—612no—
127#387—612no—
128#382—611no—
129C61#258111yescharacteristic, complemented, Sylow
130C22×Q8—611no—
131C22×Q8C2×D6111yescharacteristic
132C4×Q8—1224no—
133C4×Q8—1224no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4C2×D6111yescharacteristic
141C2×C4⋊C4C2×D6112yes—
142C2×C42—611no—
143C2×C42—611no—
144C2×C42—611no—
145C2×C42—612no—
146#95—612no—
147#95—611no—
148#95—612no—
149#95—612no—
150#95—612no—
151#95—612no—
152#95—612no—
153#95C2×D6111yescharacteristic
154#95C2×D6112yes—
155C2×Q8—22no—
156C2×Q8—24no—
157C2×Q8—614no—
158C2×Q8—1222no—
159C2×Q8—1222no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—612no—
164C22×C4—612no—
165C22×C4—611no—
166C22×C4C22×D6112yes—
167C22×C4C22×D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169C22×C4C22×D6112yes—
170C22×C4C22×D6111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—24no—
173C4⋊C4—1224no—
174C4⋊C4—1222no—
175C4⋊C4—1224no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1224no—
179C42—614no—
180C42—1222no—
181C42—1224no—
182C42—1222no—
183C23C23×D6111yescharacteristic
184Q8—28no—
185Q8—1228no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—612no—
197C2×C4—612no—
198C2×C4—612no—
199C2×C4—612no—
200C2×C4—612no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1222no—
204C2×C4—1221no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1224no—
211C2×C4D4×D6112yes—
212C2×C4#1175822414yes—
213C2×C4Q8×D6112yes—
214C22C2×D4×D6111yescharacteristic
215C22C2×Q8×D6111yescharacteristic
216C22#41×D6111yescharacteristic
217C22C2×#1175822412yes—
218C22#1451982512yes—
219C4—22no—
220C4—22no—
221C4—24no—
222C4—42no—
223C4—41no—
224C4—614no—
225C4—1222no—
226C4—1222no—
227C4—2442no—
228C4—2441no—
229C4—2442no—
230C2C22⋊Q8×D6111yescharacteristic
231C2#1684026811yescharacteristic
232C2#1684033711yescharacteristic
233C2#1684048312yes—
234C2#1684048712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2581
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
52. C2×Dic122Q8semidirect
129. C61#2581semidirect