Finite Group Databasebeta

← #21449004

Subgroups — #21449004

Order 7808.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14519769C211yesmaximal, characteristic
2#16839659C212yesmaximal
3#16839657C212yesmaximal
4#16839649C212yesmaximal
5#16839647C212yesmaximal
6#16839645C212yesmaximal
7#16839643C212yesmaximal
8#16839628C211yesmaximal, characteristic
9C61×#382C211yesmaximal, characteristic
10#14519769C418yescomplemented
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C4×Dic61C2212yes—
20C2×C4×Dic61C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2212yes—
31#95×C61C2212yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C4⋊C4×C61—41no—
42C4⋊C4×C61—41no—
43C42×C61C2×C414yes—
44C4⋊Dic61—41no—
45C4⋊Dic61—41no—
46C4⋊Dic61C2×C414yes—
47C4⋊Dic61C2×C414yes—
48#11758196—42no—
49#11758196—42no—
50#11758196C2×C418yes—
51#11758196C2×C418yes—
52C4×Dic61—42no—
53C4×Dic61—42no—
54C23×C61C2411yescharacteristic
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61C22×C412yes—
68C2×C4×C61C22×C412yes—
69C2×C4×C61C22×C412yes—
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×Dic61C22×C414yes—
81C2×Dic61C22×C414yes—
82C22×C61C23×C411yescharacteristic
83C22×C61H(5,𝔽2)11yescharacteristic
84C22×C61H(5,𝔽2)11yescharacteristic
85C22×C612−1+411yescharacteristic
86C22×C612−1+411yescharacteristic
87C22×C612−1+411yescharacteristic
88C22×C612−1+411yescharacteristic
89C4×C61—22no—
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—42no—
93C4×C61—42no—
94Dic61—24no—
95Dic61—24no—
96Dic61—42no—
97Dic61—42no—
98#2382—611nomaximal, Sylow
99C2×C61#51911yescharacteristic
100C2×C61#52011yescharacteristic
101C2×C61#52011yescharacteristic
102C2×C61#56211yescharacteristic
103C2×C61#56311yescharacteristic
104C2×C61#56311yescharacteristic
105C2×C61#56411yescharacteristic
106C2×#125—611no—
107#389—612no—
108#389—612no—
109#387—612no—
110#387—612no—
111#387—612no—
112#387—612no—
113#382—611no—
114#382D6111yescharacteristic
115C61#238211yescharacteristic, complemented, Sylow
116#125—618no—
117C2×C4⋊C4—611no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—612no—
120C2×C4⋊C4—612no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—612no—
125C2×C4⋊C4C2×D6111yescharacteristic
126C2×C4⋊C4C2×D6111yescharacteristic
127C2×C42—612no—
128C2×C42—612no—
129C2×C42C2×D6111yescharacteristic
130#95—612no—
131#95—612no—
132#95—612no—
133#95—612no—
134#95—612no—
135#95—612no—
136#95C2×D6112yes—
137#95C2×D6112yes—
138C22×C4—612no—
139C22×C4—612no—
140C22×C4—612no—
141C22×C4—612no—
142C22×C4C22×D6112yes—
143C22×C4C22×D6112yes—
144C22×C4C22×D6111yescharacteristic
145C22×C4C22×D6111yescharacteristic
146C22×C4C22×D6111yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—618no—
150C4⋊C4—618no—
151C4⋊C4—614no—
152C4⋊C4—614no—
153C4⋊C4—2442no—
154C4⋊C4—2442no—
155C4⋊C4—2441no—
156C4⋊C4—2441no—
157C42—2442no—
158C42—2442no—
159C42C4×D6114yes—
160C23C23×D6111yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—614no—
174C2×C4—614no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4C2×C4×D6112yes—
186C2×C4C2×C4×D6112yes—
187C2×C4C2×C4×D6112yes—
188C22C22×C4×D6111yescharacteristic
189C22#1451982211yescharacteristic
190C22#1451982311yescharacteristic
191C22#1451982411yescharacteristic
192C22#1451982411yescharacteristic
193C22#1451982411yescharacteristic
194C22#1451982511yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—1224no—
201C4—1224no—
202C4—2442no—
203C4—2442no—
204C2#1684023911yescharacteristic
205C2#1684024211yescharacteristic
206C2#1684024311yescharacteristic
207C2#1684050611yescharacteristic
208C2#1684051211yescharacteristic
209C2#1684051611yescharacteristic
210C2C61⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#382C2
socleC23×C61C24
hypercenter#382D61
hypocenterC61#2382
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #14519769C4semidirect
115. C61#2382semidirect