Finite Group Databasebeta

← #21454090

Subgroups — #21454090

Order 7808.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#16839704C212yesmaximal
2#16839703C212yesmaximal
3#16839700C212yesmaximal
4#16839682C212yesmaximal
5#16839682C211yesmaximal, characteristic
6#16839681C212yesmaximal
7#16839627C211yesmaximal, characteristic
8#16839626C212yesmaximal
9C61×#395C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×C4×Dic61C2211yescharacteristic
17#14519684C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C2×Q8×C61—41no—
32C2×Q8×C61—42no—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×Dic122—41no—
43C2×Dic122—42no—
44C4⋊C4×C61—41no—
45C4⋊C4×C61—42no—
46C4⋊Dic61—41no—
47#11758196—42no—
48#11758196—42no—
49#11758196—42no—
50#11758196—42no—
51C4×Dic61Q814yescomplemented
52C23×C61C2411yescharacteristic
53Q8×C61—44no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61C2×Q812yes—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—24no—
77C2×Dic61C2×Q814yes—
78Dic122—44no—
79C22×C61C22×Q811yescharacteristic
80C22×C61H(5,𝔽2)11yescharacteristic
81C22×C61H(5,𝔽2)12yes—
82C22×C612−1+411yescharacteristic
83C22×C612−1+412yes—
84C4×C61—22no—
85C4×C61—41no—
86C4×C61—41no—
87C4×C61—42no—
88C4×C61—42no—
89Dic61—24no—
90Dic61—42no—
91Dic61—42no—
92Dic61—42no—
93#2844—611nomaximal, Sylow
94C2×C61#54412yes—
95C2×C61#54411yescharacteristic
96C2×C61H(3,𝔽4)11yescharacteristic
97C2×C61#56311yescharacteristic
98C2×C61#56312yes—
99#400—612no—
100#400—612no—
101#400—612no—
102#395—612no—
103#395—612no—
104#395—611no—
105#395D6111yescharacteristic
106#382—611no—
107#382—612no—
108C61#284411yescharacteristic, complemented, Sylow
109C22×Q8—611no—
110C22×Q8C2×D6111yescharacteristic
111C2×C4⋊C4—612no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4—612no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C4⋊C4C2×D6112yes—
118C2×C42—611no—
119#95—612no—
120#95—612no—
121#95—612no—
122#95—612no—
123#95—612no—
124#95—611no—
125#95—612no—
126#95—612no—
127#95—612no—
128#95C2×D6112yes—
129#95C2×D6111yescharacteristic
130C2×Q8—41no—
131C2×Q8—42no—
132C2×Q8—2441no—
133C2×Q8—2442no—
134C22×C4—612no—
135C22×C4—612no—
136C22×C4—612no—
137C22×C4—612no—
138C22×C4C22×D6112yes—
139C22×C4C22×D6111yescharacteristic
140C22×C4C22×D6111yescharacteristic
141C22×C4C22×D6112yes—
142C22×C4C22×D6111yescharacteristic
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—2442no—
146C4⋊C4—2442no—
147C4⋊C4—2442no—
148C4⋊C4—2442no—
149C4⋊C4—2441no—
150C42—614no—
151C23C23×D6111yescharacteristic
152Q8—44no—
153Q8—2444no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—614no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1224no—
176C2×C4—1222no—
177C2×C4Q8×D6112yes—
178C22C2×Q8×D6111yescharacteristic
179C22#1451982211yescharacteristic
180C22#1451982212yes—
181C22#1451982411yescharacteristic
182C22#1451982512yes—
183C4—22no—
184C4—41no—
185C4—42no—
186C4—41no—
187C4—42no—
188C4—1224no—
189C4—2442no—
190C4—2442no—
191C4—2442no—
192C2#1684038912yes—
193C2#1684039111yescharacteristic
194C2#1684050511yescharacteristic
195C2#1684051111yescharacteristic
196C2#1684051312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2844
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
51. C4×Dic61Q8semidirect
108. C61#2844semidirect