Finite Group Databasebeta

← #21450552

Subgroups — #21450552

Order 7808.

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

normal subgroups only

This group has 420 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#16839687C212yesmaximal
2#16839687C211yesmaximal, characteristic
3#16839669C212yesmaximal, complemented
4#16839649C212yesmaximal, complemented
5#16839645C212yesmaximal, complemented
6#16839634C211yesmaximal, characteristic
7#16839629C212yesmaximal, complemented
8C22⋊C4×Dic61C212yesmaximal
9C61×#393C211yesmaximal, characteristic
10C23×Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2211yescharacteristic
16C2×C4×Dic61C2212yes—
17C2×C4×Dic61C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C2×Q8×C61—24no—
33C2×Q8×C61—41no—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×Dic61—24no—
39C22×Dic61—41no—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2312yes—
44C22⋊C4×C61—24no—
45C22⋊C4×C61—41no—
46C22⋊Dic61—24no—
47C22⋊Dic61—22no—
48C4⋊Dic61—24no—
49C4⋊Dic61—41no—
50#11758196—24no—
51C4×Dic61—24no—
52C4×Dic61—42no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—21no—
56C23×C61—21no—
57C23×C61#4112yes—
58C23×C61C2411yescharacteristic
59Q8×C61—44no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61#4114yes—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—44no—
82C2×Dic61#4114yes—
83C22×C61—24no—
84C22×C61—22no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61—42no—
88C22×C61C2×#4112yes—
89C22×C61C2×#4112yes—
90C22×C61C2×#4111yescharacteristic
91C22×C61H(5,𝔽2)11yescharacteristic
92C22×C612−1+411yescharacteristic
93C4×C61—24no—
94C4×C61—41no—
95C4×C61—41no—
96C4×C61—42no—
97Dic61—24no—
98Dic61—42no—
99Dic61—42no—
100Dic61—42no—
101#2523—611nomaximal, Sylow
102C2×C61—42no—
103C2×C61#52912yes—
104C2×C61#53911yescharacteristic
105C2×C61#55111yescharacteristic
106C2×C61#55111yescharacteristic
107C2×C61#55612yes—
108#397—612no—
109#397—611no—
110#393D6111yescharacteristic
111#391—612no—
112#387—612no—
113#387—612no—
114#385—611no—
115#383—612no—
116C4×C22⋊C4—612no—
117C61#252311yescharacteristic, complemented, Sylow
118C22×Q8C2×D6111yescharacteristic
119C23×C4—611no—
120C2×C4⋊C4—612no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—611no—
123C2×C22⋊C4—612no—
124C2×C22⋊C4—611no—
125C2×C22⋊C4C2×D6112yes—
126C2×C22⋊C4C2×D6111yescharacteristic
127C2×C42—612no—
128C2×C42—612no—
129#95—612no—
130#95—612no—
131#95—612no—
132#95—612no—
133#95—612no—
134#95—612no—
135#95—611no—
136#95—612no—
137#95C2×D6111yescharacteristic
138#95C2×D6112yes—
139C24C22×D6111yescharacteristic
140C2×Q8—24no—
141C2×Q8—41no—
142C22×C4—612no—
143C22×C4—612no—
144C22×C4—612no—
145C22×C4—612no—
146C22×C4—1224no—
147C22×C4—2441no—
148C22×C4C22×D6111yescharacteristic
149C22×C4C22×D6112yes—
150C22×C4C22×D6111yescharacteristic
151C22×C4C22×D6112yes—
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C4⋊C4—2441no—
155C22⋊C4—24no—
156C22⋊C4—41no—
157C22⋊C4—1224no—
158C22⋊C4—1222no—
159C42—1224no—
160C42—2442no—
161C23—22no—
162C23—22no—
163C23—21no—
164C23—21no—
165C23#1175822612yes—
166C23C23×D6111yescharacteristic
167Q8—44no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—614no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—2444no—
190C2×C4#1175822414yes—
191C22—24no—
192C22—22no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22#41×D6112yes—
197C22C2×#1175822412yes—
198C22C2×#1175822611yescharacteristic
199C22#1451982211yescharacteristic
200C22#1451982411yescharacteristic
201C4—24no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—1224no—
206C4—2442no—
207C4—2442no—
208C4—2442no—
209C2—42no—
210C2#1684029812yes—
211C2#1684036111yescharacteristic
212C2#1684044211yescharacteristic
213C2#1684044311yescharacteristic
214C2#1684048112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2523
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
3. #16839669C2semidirect
4. #16839649C2semidirect
5. #16839645C2semidirect
7. #16839629C2semidirect
117. C61#2523semidirect