Finite Group Databasebeta

← #21445898

Subgroups — #21445898

Order 7808.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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×C4⋊C4×D61C211yesmaximal, characteristic
2#16839725C212yesmaximal
3#16839531C211yesmaximal, characteristic, complemented
4#16839530C212yesmaximal, complemented
5C61×#343C211yesmaximal, characteristic, complemented
6C22×C4×D61C412yes—
7C22×C4×D61C2211yescharacteristic
8C2×#11758194C2212yes—
9C2×C4⋊Dic61C2211yescharacteristic
10C2×#11758196C412yes—
11C4⋊C4×D61—22no—
12C4⋊C4×D61—22no—
13#14519689—22no—
14#14519689—22no—
15C2×M16×C61C2212yes—
16C2×C4⋊C4×C61C2211yescharacteristic
17C23×D61C2×C411yescharacteristic
18C22×C4×C61C2×C412yes—
19C22×C4×C61C2311yescharacteristic
20C22×Dic61C2×C411yescharacteristic
21C22×Dic61C2×C412yes—
22C2×C4×D61—22no—
23C2×C4×D61—21no—
24C2×C4×D61—21no—
25C2×C4×D61—22no—
26C2×C4×D61—22no—
27C2×C4×D61—44no—
28C2×C4×D61D412yes—
29C2×C4×D61D412yes—
30M16×C61—22no—
31M16×C61—22no—
32C2×C8×C61—22no—
33C4⋊C4×C61—22no—
34C4⋊Dic61—22no—
35#11758196—24no—
36#11758194—22no—
37#11758194—22no—
38C2×#92418—22no—
39C23×C61C22×C411yescharacteristic
40C22×D61—21no—
41C22×D61—21no—
42C22×D61—22no—
43C22×D61—22no—
44C22×D61C22⋊C411yescharacteristic
45C22×D61C22⋊C411yescharacteristic
46C2×C4×C61—22no—
47C2×C4×C61—42no—
48C2×C4×C61C2×D412yes—
49C2×C4×C61#4112yes—
50C2×C4×C61#4111yescharacteristic
51C2×C4×C61#4111yescharacteristic
52C2×Dic61—21no—
53C2×Dic61—21no—
54C2×Dic61—22no—
55C2×Dic61—42no—
56C2×Dic61C22⋊C412yes—
57C4×D61—22no—
58C4×D61—22no—
59C4×D61—22no—
60C4×D61—22no—
61C4×D61—44no—
62C4×D61—44no—
63C8×C61—42no—
64#92418—42no—
65C22×C61—21no—
66C22×C61—21no—
67C22×C61C2×C22⋊C411yescharacteristic
68C22×C61#11711yescharacteristic
69C22×C61#11711yescharacteristic
70C2×D61—24no—
71C2×D61—24no—
72C2×D61—21no—
73C2×D61—21no—
74C2×D61—21no—
75C2×D61—21no—
76C2×D61#10012yes—
77C2×D61#10112yes—
78C4×C61—42no—
79C4×C61#12312yes—
80C4×C61#12312yes—
81Dic61—22no—
82Dic61—42no—
83#1821—611nomaximal, Sylow
84C2×C61—21no—
85C2×C61—21no—
86C2×C61#38111yescharacteristic
87C2×C61C2×#10011yescharacteristic
88C2×C61C2×#10111yescharacteristic
89D61—22no—
90D61—22no—
91C22×C4⋊C4—611no—
92#407—612no—
93#343—612no—
94#343—611no—
95#343D6111yescharacteristic, complemented
96C61#182111yescharacteristic, complemented, Sylow
97C23×C4—611no—
98C23×C4—612no—
99C2×M16—612no—
100C2×M16C2×D6112yes—
101C2×C4⋊C4—612no—
102C2×C4⋊C4—611no—
103C2×C4⋊C4—1222no—
104C2×C4⋊C4—1222no—
105C2×C4⋊C4C2×D6111yescharacteristic
106C22⋊C8—1222no—
107C22⋊C8—1222no—
108C24—611no—
109C22×C4—611no—
110C22×C4—612no—
111C22×C4—612no—
112C22×C4—612no—
113C22×C4—1222no—
114C22×C4—1222no—
115C22×C4—1222no—
116C22×C4—1221no—
117C22×C4—1221no—
118C22×C4—2444no—
119C22×C4C4×D6112yes—
120C22×C4C22×D6111yescharacteristic
121M16—22no—
122M16—22no—
123M16—1222no—
124M16—1222no—
125C2×C8—22no—
126C2×C8—1222no—
127C4⋊C4—22no—
128C4⋊C4—1224no—
129C4⋊C4—1222no—
130C23—611no—
131C23—611no—
132C23—1222no—
133C23—1222no—
134C23—1221no—
135C23—1221no—
136C23C2×C4×D6111yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—612no—
140C2×C4—1221no—
141C2×C4—1221no—
142C2×C4—1222no—
143C2×C4—1222no—
144C2×C4—1222no—
145C2×C4—1222no—
146C2×C4—1222no—
147C2×C4—2444no—
148C2×C4—2444no—
149C2×C4—2442no—
150C2×C4#1175822212yes—
151C2×C4D4×D6112yes—
152C2×C4#1175822411yescharacteristic
153C2×C4#1175822611yescharacteristic
154C8—42no—
155C8—2442no—
156C22—21no—
157C22—21no—
158C22—612no—
159C22—612no—
160C22—1224no—
161C22—1224no—
162C22—1221no—
163C22—1221no—
164C22—1221no—
165C22—1221no—
166C22C22⋊C4×D6111yescharacteristic
167C22#1451973411yescharacteristic
168C22#1451973511yescharacteristic
169C4—42no—
170C4—1222no—
171C4—2442no—
172C4#1451975912yes—
173C4#1451976212yes—
174C2—21no—
175C2—21no—
176C2—1222no—
177C2—1222no—
178C2#1683962411yescharacteristic
179C2#100×D6111yescharacteristic
180C2#101×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61C2×C22⋊C4
hypercenter#343D61
hypocenterC61#1821
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #16839531C2semidirect
4. #16839530C2semidirect
5. C61×#343C2semidirect
95. #343D61semidirect
96. C61#1821semidirect