Finite Group Databasebeta

← #21462113

Subgroups — #21462113

Order 7808.

250 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 52 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#16840749C212yesmaximal, complemented
2#16840672C212yesmaximal, complemented
3#16840671C212yesmaximal, complemented
4#16840311C211yesmaximal, characteristic
5C2×#11758217—22no—
6#14519838C2214yes—
7#14519837—22no—
8C2×#11758226C411yescharacteristic
9C2×#11758224C2211yescharacteristic
10#14519775C2211yescharacteristic
11#14519773C411yescharacteristic
12#14519765C2211yescharacteristic
13#14519750—22no—
14#14519737—22no—
15C42×D61C411yescharacteristic
16#124×C61C411yescharacteristic
17C2×Q8×C61C2×C411yescharacteristic
18C2×D4×C61C2×C411yescharacteristic
19C2×C22⋊D61—22no—
20C2×C22⋊D61D412yes—
21C22×Dic61D412yes—
22#11758226—41no—
23#11758226—41no—
24#11758224—41no—
25#11758224—41no—
26C2×D244—21no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61C2×C411yescharacteristic
31C2×Dic122C2311yescharacteristic
32#11758217—24no—
33#11758217—42no—
34C2×#92420—42no—
35C22⋊C4×C61—22no—
36C42×C61C2×C411yescharacteristic
37#11758198—22no—
38#11758196—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic
41C23×C61C22⋊C412yes—
42C22×D61—21no—
43C22×D61C22⋊C411yescharacteristic
44Q8×C61—41no—
45D4×C61—41no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61C22×C411yescharacteristic
49C22⋊D61—42no—
50C22⋊D61—44no—
51C2×Dic61—21no—
52C2×Dic61—22no—
53C2×Dic61—22no—
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61C2×D412yes—
56D244—41no—
57D244—42no—
58C4×D61—21no—
59C4×D61—21no—
60C4×D61—42no—
61C4×D61—41no—
62C4×D61—41no—
63Dic122—41no—
64#92420—44no—
65C22×C61—22no—
66C22×C61—42no—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—21no—
69C2×D61—41no—
70C2×D61—42no—
71C2×D61—41no—
72C4×C61—21no—
73C4×C61—41no—
74C4×C61—41no—
75Dic61—22no—
76Dic61—22no—
77Dic61#9911yescharacteristic
78Dic61#9911yescharacteristic
79#2132—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—42no—
82C2×C61C2×#9911yescharacteristic
83D61—41no—
84D61—81no—
85#532—611no—
86#413—612no—
87#356—612no—
88#355—612no—
89C61#213211yescharacteristic, complemented, Sylow
90C2×#41—611no—
91C2×#41—611no—
92C2×M16—1222no—
93C4⋊Q8—611no—
94#127—611no—
95#124—611no—
96#124#692311yescharacteristic
97#121—1222no—
98C4×D4—1222no—
99C2×C42—611no—
100#101—614no—
101#100—1222no—
102#41—2441no—
103#41—2441no—
104#41—2441no—
105#41—2441no—
106C2×Q8—611no—
107C2×Q8C2×#692311yescharacteristic
108C2×D4—612no—
109C2×D4—611no—
110C2×D4—1221no—
111C2×D4—1222no—
112C2×D4C2×#692311yescharacteristic
113C22×C4—612no—
114C22×C4—611no—
115C22×C4—1221no—
116C22×C4—1221no—
117M16—1224no—
118M16—2442no—
119C2×C8—2442no—
120C4⋊C4—1222no—
121C22⋊C4—22no—
122C22⋊C4—1222no—
123C42—611no—
124C42—1221no—
125C42C2×#692311yescharacteristic
126C23—611no—
127C23—1221no—
128C23C22⋊#692312yes—
129Q8—41no—
130Q8—2441no—
131D4—41no—
132D4—2441no—
133D4—2442no—
134D4—2442no—
135D4—2444no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—611no—
139C2×C4—612no—
140C2×C4—1221no—
141C2×C4—1221no—
142C2×C4—1222no—
143C2×C4—1222no—
144C2×C4—1221no—
145C2×C4—2441no—
146C2×C4—2441no—
147C2×C4—2442no—
148C2×C4C22×#692311yescharacteristic
149C8—2444no—
150C22—22no—
151C22—42no—
152C22—1221no—
153C22—2442no—
154C22—2441no—
155C22—2441no—
156C22C2×C22⋊#692311yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—611no—
161C4—611no—
162C4—1222no—
163C4—1222no—
164C2—21no—
165C2—42no—
166C2—4881no—
167C2—2441no—
168C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61C2×#99
hypercenter#124#6923
hypocenterC61#2132
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840749C2semidirect
2. #16840672C2semidirect
3. #16840671C2semidirect
89. C61#2132semidirect