Finite Group Databasebeta

← #21453519

Subgroups — #21453519

Order 7808.

472 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 129 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#16839684C212yesmaximal, complemented
2#16839682C211yesmaximal, characteristic, complemented
3#16839675C212yesmaximal, complemented
4#16839663C211yesmaximal, characteristic
5#16839645C212yesmaximal, complemented
6#16839640C212yesmaximal
7#16839636C212yesmaximal, complemented
8#16839621C212yesmaximal, complemented
9C61×#400C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13C2×C4⋊Dic61C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#95×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2212yes—
31C23×D61C2312yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C2×D244—41no—
41C2×D244—41no—
42C2×D244Q814yescomplemented
43C2×C4×D61—24no—
44C2×C4×D61—42no—
45C2×C4×D61—42no—
46C2×Dic122—42no—
47C2×Dic122—41no—
48C4⋊C4×C61—41no—
49C4⋊C4×C61—41no—
50#11758198—24no—
51#11758198—42no—
52#11758198—42no—
53#11758198—42no—
54#11758198—42no—
55C4⋊Dic61—24no—
56#11758196—42no—
57#11758196—42no—
58C4×Dic61—41no—
59C23×C61C2411yescharacteristic
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61C2×Q814yes—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61C2×Q812yes—
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#4114yes—
89D244—44no—
90C4×D61—48no—
91Dic122—44no—
92C22×C61C22×Q811yescharacteristic
93C22×C61C2×#4112yes—
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C61H(5,𝔽2)11yescharacteristic
96C22×C61H(5,𝔽2)12yes—
97C2×D61—24no—
98C2×D61—24no—
99C2×D61—24no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C4×C61—22no—
105C4×C61—42no—
106C4×C61—42no—
107C4×C61—41no—
108C4×C61—41no—
109Dic61—24no—
110Dic61—42no—
111Dic61—42no—
112#2784—611nomaximal, Sylow
113C2×C61#53812yes—
114C2×C61#54311yescharacteristic
115C2×C61#55412yes—
116C2×C61#55511yescharacteristic
117C2×C61#56011yescharacteristic
118D61—44no—
119#400D6111yescharacteristic, complemented
120#396—612no—
121#395—611no—
122#393—612no—
123#390—611no—
124#387—612no—
125#386—612no—
126#385—612no—
127#380—612no—
128C61#278411yescharacteristic, complemented, Sylow
129C22×Q8—611no—
130C22×D4—611no—
131C23×C4—612no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4C2×D6111yescharacteristic
136C2×C4⋊C4C2×D6111yescharacteristic
137C2×C22⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C22⋊C4—612no—
140C2×C22⋊C4—612no—
141C2×C22⋊C4—612no—
142C2×C42—611no—
143#95—612no—
144#95—611no—
145#95—612no—
146#95—612no—
147#95C2×D6111yescharacteristic
148#95C2×D6112yes—
149#95C2×D6112yes—
150C24—612no—
151C2×Q8—2441no—
152C2×Q8—2442no—
153C2×D4—614no—
154C2×D4—2441no—
155C2×D4—2441no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—612no—
159C22×C4—1224no—
160C22×C4—2442no—
161C22×C4—2442no—
162C22×C4C22×D6112yes—
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C22×C4C22×D6111yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—1224no—
170C4⋊C4—2442no—
171C4⋊C4—2442no—
172C22⋊C4—1224no—
173C22⋊C4—2442no—
174C22⋊C4—2442no—
175C22⋊C4—2442no—
176C22⋊C4—2442no—
177C42—2441no—
178C23—614no—
179C23—1222no—
180C23—1222no—
181C23—1222no—
182C23—1222no—
183C23—1222no—
184C23—1222no—
185C23C23×D6111yescharacteristic
186Q8—2444no—
187D4—2444no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—614no—
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×C4Q8×D6112yes—
211C22—1224no—
212C22—1224no—
213C22—1224no—
214C22—2442no—
215C22—2442no—
216C22—2442no—
217C22—2442no—
218C22C2×Q8×D6111yescharacteristic
219C22#41×D6112yes—
220C22#1451982211yescharacteristic
221C22#1451982312yes—
222C22#1451982311yescharacteristic
223C4—22no—
224C4—42no—
225C4—41no—
226C4—41no—
227C4—42no—
228C4—1224no—
229C4—2442no—
230C4—2442no—
231C2—2444no—
232C2#1684035112yes—
233C2#1684038711yescharacteristic
234C2#1684046812yes—
235C2#1684047411yescharacteristic
236C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2784
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #16839684C2semidirect
2. #16839682C2semidirect
3. #16839675C2semidirect
5. #16839645C2semidirect
7. #16839636C2semidirect
8. #16839621C2semidirect
9. C61×#400C2semidirect
42. C2×D244Q8semidirect
119. #400D61semidirect
128. C61#2784semidirect