Finite Group Databasebeta

← #21451030

Subgroups — #21451030

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×#14519776C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic
4#16839701C211yesmaximal, characteristic
5#16839700C211yesmaximal, characteristic
6#16839666C212yesmaximal
7#16839666C212yesmaximal
8#16839666C212yesmaximal
9#16839626C212yesmaximal
10#16839613C211yesmaximal, characteristic
11C61×#400C211yesmaximal, characteristic
12C22×Dic122C2212yes—
13C22×Dic122C2211yescharacteristic
14#14519776—24no—
15#14519742—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
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—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2211yescharacteristic
35#95×C61C2212yes—
36#95×C61C2212yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×Dic122—22no—
49C2×Dic122—22no—
50C2×Dic122—24no—
51C2×Dic122—28no—
52C2×Dic122Q814yescomplemented
53C4⋊C4×C61—22no—
54C4⋊C4×C61—22no—
55C4⋊Dic61—22no—
56#11758196—22no—
57#11758196—22no—
58#11758196—24no—
59#11758196—24no—
60C4×Dic61—22no—
61C4×Dic61—22no—
62C4×Dic61—24no—
63C4×Dic61D414yes—
64C23×C61C2411yescharacteristic
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—24no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×Q812yes—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—24no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88C2×Dic61C2×Q812yes—
89C2×Dic61C2×Q812yes—
90C2×Dic61#4112yes—
91C2×Dic61#4114yes—
92Dic122—28no—
93Dic122—48no—
94C22×C61C22×D411yescharacteristic
95C22×C61C22×Q811yescharacteristic
96C22×C61C2×#4111yescharacteristic
97C22×C61C2×#4112yes—
98C22×C612−1+412yes—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—42no—
102C4×C61—41no—
103C4×C61—42no—
104Dic61—22no—
105Dic61—42no—
106Dic61—41no—
107Dic61—42no—
108Dic61C22⋊Q814yes—
109Dic61#12414yes—
110#2568—611nomaximal, Sylow
111C2×C61C2×C22⋊Q811yescharacteristic
112C2×C61C2×#12411yescharacteristic
113C2×C61#53611yescharacteristic
114C2×C61#55612yes—
115C2×C61#55712yes—
116C2×C4⋊Q8—611no—
117C2×C4×Q8—611no—
118#400—611no—
119#400—611no—
120#400—611no—
121#400D6111yescharacteristic
122#391—612no—
123#391—612no—
124#391—612no—
125#382—612no—
126C4×C4⋊C4—611no—
127C61#256811yescharacteristic, complemented, Sylow
128C22×Q8—611no—
129C22×Q8—612no—
130C4⋊Q8—1224no—
131C4×Q8—1224no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4C2×D6111yescharacteristic
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C42—611no—
140C2×C42—611no—
141C2×C42—611no—
142C2×C42—612no—
143#95—611no—
144#95—612no—
145#95—612no—
146#95—612no—
147#95—612no—
148#95—612no—
149#95—612no—
150#95C2×D6111yescharacteristic
151#95C2×D6112yes—
152#95C2×D6112yes—
153C2×Q8—614no—
154C2×Q8—1222no—
155C2×Q8—1222no—
156C2×Q8—1224no—
157C2×Q8—1228no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—612no—
162C22×C4—611no—
163C22×C4—612no—
164C22×C4C22×D6112yes—
165C22×C4C22×D6111yescharacteristic
166C22×C4C22×D6112yes—
167C22×C4C22×D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—1224no—
172C4⋊C4—1222no—
173C4⋊C4—1224no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C42—614no—
177C42—1224no—
178C42—1222no—
179C42—1222no—
180C23C23×D6111yescharacteristic
181Q8—1228no—
182Q8—2448no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—612no—
194C2×C4—612no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—614no—
198C2×C4—612no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1224no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4D4×D6112yes—
209C2×C4Q8×D6112yes—
210C22C2×D4×D6111yescharacteristic
211C22C2×Q8×D6111yescharacteristic
212C22#41×D6111yescharacteristic
213C22#41×D6112yes—
214C22#1451982412yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—42no—
219C4—41no—
220C4—614no—
221C4—614no—
222C4—1222no—
223C4—2442no—
224C4—2442no—
225C4—2441no—
226C2C22⋊Q8×D6111yescharacteristic
227C2#124×D6111yescharacteristic
228C2#1684033411yescharacteristic
229C2#1684047912yes—
230C2#1684048912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2568
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
52. C2×Dic122Q8semidirect
127. C61#2568semidirect