Finite Group Databasebeta

← #21453520

Subgroups — #21453520

Order 7808.

472 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#16839701C211yesmaximal, characteristic, complemented
2#16839685C212yesmaximal, complemented
3#16839682C211yesmaximal, characteristic, complemented
4#16839674C212yesmaximal, complemented
5#16839646C212yesmaximal, complemented
6#16839642C212yesmaximal
7#16839634C212yesmaximal, complemented
8#16839620C212yesmaximal, complemented
9C61×#390C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C23×Dic61C2212yes—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19#14519684C2211yescharacteristic
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×D4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2212yes—
30C2×C42×C61C2211yescharacteristic
31C24×C61C2312yes—
32C2×D4×C61—41no—
33C2×D4×C61—41no—
34C2×D4×C61Q814yescomplemented
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—24no—
40C22×Dic61—42no—
41C22×Dic61—42no—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C2×Dic122—42no—
47C2×Dic122—41no—
48C4⋊C4×C61—41no—
49C22⋊C4×C61—42no—
50C22⋊C4×C61—42no—
51C42×C61—41no—
52C22⋊Dic61—24no—
53C22⋊Dic61—42no—
54C22⋊Dic61—42no—
55C4⋊Dic61—41no—
56#11758196—24no—
57#11758196—42no—
58#11758196—42no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61C2×Q814yes—
66C23×C61C2411yescharacteristic
67D4×C61—44no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61C2×Q812yes—
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×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—48no—
90C2×Dic61#4114yes—
91Dic122—44no—
92C22×C61—24no—
93C22×C61—24no—
94C22×C61—24no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61C22×Q811yescharacteristic
100C22×C61C2×#4112yes—
101C22×C61H(5,𝔽2)11yescharacteristic
102C22×C61H(5,𝔽2)12yes—
103C22×C61H(5,𝔽2)11yescharacteristic
104C4×C61—22no—
105C4×C61—42no—
106C4×C61—41no—
107C4×C61—41no—
108Dic61—24no—
109Dic61—42no—
110Dic61—42no—
111Dic61—42no—
112#2784—611nomaximal, Sylow
113C2×C61—44no—
114C2×C61#53812yes—
115C2×C61#54311yescharacteristic
116C2×C61#55412yes—
117C2×C61#55511yescharacteristic
118C2×C61#56011yescharacteristic
119#400—611no—
120#396—612no—
121#395—611no—
122#393—612no—
123#390D6111yescharacteristic
124#387—612no—
125#386—612no—
126#385—612no—
127#380—612no—
128C61#278411yescharacteristic, complemented, Sylow
129C22×Q8—611no—
130C22×D4C2×D6111yescharacteristic
131C23×C4—612no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4C2×D6111yescharacteristic
137C2×C22⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C22⋊C4—612no—
140C2×C22⋊C4C2×D6112yes—
141C2×C22⋊C4C2×D6112yes—
142C2×C42C2×D6111yescharacteristic
143#95—611no—
144#95—612no—
145#95—611no—
146#95—612no—
147#95—612no—
148#95—612no—
149#95—612no—
150C24C22×D6112yes—
151C2×Q8—2442no—
152C2×Q8—2441no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4Dic12214yescomplemented
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—612no—
159C22×C4—612no—
160C22×C4—1224no—
161C22×C4—2442no—
162C22×C4—2442no—
163C22×C4C22×D6111yescharacteristic
164C22×C4C22×D6112yes—
165C22×C4C22×D6111yescharacteristic
166C22×C4C22×D6111yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—1224no—
169C4⋊C4—2442no—
170C4⋊C4—2442no—
171C4⋊C4—2441no—
172C22⋊C4—42no—
173C22⋊C4—42no—
174C22⋊C4—1224no—
175C22⋊C4—2442no—
176C22⋊C4—2442no—
177C42—41no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23C2×Dic12214yes—
185C23C23×D6111yescharacteristic
186Q8—2444no—
187D4—44no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—614no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—2448no—
210C2×C4C2×Dic12212yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22C22×Dic12211yescharacteristic
219C22#41×D6112yes—
220C22#1451982212yes—
221C22#1451982211yescharacteristic
222C22#1451982211yescharacteristic
223C4—22no—
224C4—41no—
225C4—41no—
226C4—42no—
227C4—1224no—
228C4—2442no—
229C4—2442no—
230C4—2442no—
231C2—44no—
232C2#1684034412yes—
233C2#1684038811yescharacteristic
234C2#1684047112yes—
235C2#1684047411yescharacteristic
236C2#1684049911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2784
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #16839701C2semidirect
2. #16839685C2semidirect
3. #16839682C2semidirect
4. #16839674C2semidirect
5. #16839646C2semidirect
7. #16839634C2semidirect
8. #16839620C2semidirect
34. C2×D4×C61Q8semidirect
128. C61#2784semidirect
155. C2×D4Dic122semidirect