Finite Group Databasebeta

← #21462090

Subgroups — #21462090

Order 7808.

258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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#16840741C212yesmaximal, complemented
2#16840668C212yesmaximal, complemented
3#16840666C212yesmaximal, complemented
4#16840308C211yesmaximal, characteristic
5#14519856—22no—
6#14519836C2214yes—
7#14519835—22no—
8C2×#11758222C2211yescharacteristic
9#14519775C411yescharacteristic, complemented
10#14519773C2211yescharacteristic
11#14519766C2211yescharacteristic
12#14519764C411yescharacteristic, complemented
13#14519749—22no—
14C4×C22⋊D61—22no—
15C2×C4×Dic61C411yescharacteristic, complemented
16C2×#41×C61C411yescharacteristic, complemented
17#41×C61—41no—
18#41×C61—41no—
19C2×Q8×C61C2×C411yescharacteristic
20C2×D4×C61—21no—
21C2×D4×C61C2×C411yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61C2×C411yescharacteristic
24C2×C22⋊D61—22no—
25C2×C22⋊D61D412yes—
26C22×Dic61—21no—
27#11758222—41no—
28#11758222—41no—
29C2×D244C2311yescharacteristic
30C2×C4×D61D412yes—
31C2×Dic122C2×C411yescharacteristic
32C22⋊#6923—24no—
33C4⋊#6923—42no—
34C4×#6923—42no—
35C22⋊Dic61—22no—
36#11758198—22no—
37#11758196—22no—
38C4×Dic61—21no—
39C4×Dic61C2×C411yescharacteristic
40C4×Dic61C2×C411yescharacteristic
41C23×C61—21no—
42C23×C61C22⋊C411yescharacteristic
43C22×D61C2×D412yes—
44C2×#6923—44no—
45Q8×C61—41no—
46D4×C61—41no—
47D4×C61—42no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22×C411yescharacteristic
55C22⋊D61—42no—
56C22⋊D61—44no—
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—42no—
60C2×Dic61C22⋊C412yes—
61D244—41no—
62C4×D61—22no—
63C4×D61—22no—
64Dic122—41no—
65C22×C61—21no—
66C22×C61—41no—
67C22×C61—42no—
68C22×C61—41no—
69C22×C61C2×C22⋊C411yescharacteristic
70C2×D61—22no—
71C2×D61—42no—
72#6923—84no—
73C4×C61—21no—
74C4×C61—41no—
75C4×C61#9911yescharacteristic
76C4×C61#9911yescharacteristic
77Dic61—22no—
78Dic61—22no—
79Dic61—41no—
80#2126—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—41no—
83C2×C61—81no—
84C2×C61C2×#9911yescharacteristic
85D61—42no—
86#532—611no—
87#410—612no—
88#354—612no—
89#353—612no—
90C61#212611yescharacteristic, complemented, Sylow
91C2×#41—611no—
92C2×#41#692311yescharacteristic, complemented
93C4⋊Q8—611no—
94#127—611no—
95#124—611no—
96#124—611no—
97#121—1222no—
98C4×D4—1222no—
99#117—1222no—
100C2×C42—611no—
101#99—614no—
102#99—1222no—
103#41—41no—
104#41—41no—
105#41—2441no—
106#41—2441no—
107C2×Q8—611no—
108C2×Q8C2×#692311yescharacteristic
109C2×D4—21no—
110C2×D4—612no—
111C2×D4—611no—
112C2×D4—1222no—
113C2×D4C2×#692311yescharacteristic
114C22×C4—21no—
115C22×C4—612no—
116C22×C4—1221no—
117C22×C4C2×#692311yescharacteristic
118C4⋊C4—1222no—
119C4⋊C4—2442no—
120C22⋊C4—1222no—
121C22⋊C4—1222no—
122C22⋊C4—1224no—
123C42—611no—
124C42—611no—
125C42—1221no—
126C42—2442no—
127C23—21no—
128C23—612no—
129C23C22⋊#692311yescharacteristic
130Q8—41no—
131Q8—2441no—
132D4—41no—
133D4—42no—
134D4—2441no—
135D4—2442no—
136D4—2444no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—612no—
143C2×C4—1221no—
144C2×C4—1222no—
145C2×C4—1222no—
146C2×C4—1221no—
147C2×C4—2442no—
148C2×C4—2444no—
149C2×C4C22⋊#692311yescharacteristic
150C2×C4C22×#692311yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—1222no—
156C22—2442no—
157C22C2×C22⋊#692311yescharacteristic
158C4—21no—
159C4—41no—
160C4—1222no—
161C4—1222no—
162C4—4884no—
163C4—2441no—
164C4#1451983511yescharacteristic
165C4#1451983511yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—2442no—
170C2C2×#1451983511yescharacteristic
subgroupG/H
centerC4#14519835
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×#41×C61C4
socleC2×C61C2×#99
hypercenterC2×#41#6923
hypocenterC61#2126
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #16840741C2semidirect
2. #16840668C2semidirect
3. #16840666C2semidirect
9. #14519775C4semidirect
12. #14519764C4semidirect
15. C2×C4×Dic61C4semidirect
16. C2×#41×C61C4semidirect
90. C61#2126semidirect
92. C2×#41#6923semidirect