Finite Group Databasebeta

← #21447509

Subgroups — #21447509

Order 7808.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840330C211yesmaximal, characteristic
2#16839745C212yesmaximal, complemented
3#16839559C211yesmaximal, characteristic, complemented
4#16839558C212yesmaximal, complemented
5C61×#355C211yesmaximal, characteristic, complemented
6C2×#11758226C2211yescharacteristic
7C2×D4×D61C411yescharacteristic
8M16×D61—22no—
9#14519774C411yescharacteristic
10#14519773C411yescharacteristic
11#14519766C2211yescharacteristic
12#14519750—22no—
13#14519747—22no—
14#14519734C411yescharacteristic
15#14519696C2212yescomplemented
16#14519693—22no—
17#124×C61C2211yescharacteristic
18#101×C61C2212yescomplemented
19C23×D61—21no—
20C2×Q8×C61C2311yescharacteristic
21C2×D4×C61C2×C411yescharacteristic
22C2×C22⋊D61—22no—
23C2×C22⋊D61—21no—
24#11758226—42no—
25D4×D61—42no—
26C2×D244—22no—
27C2×D244C2×C411yescharacteristic
28C2×D244C2×C411yescharacteristic
29C2×D244D412yes—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D412yes—
32M16×C61—22no—
33C22⋊C4×C61—22no—
34C42×C61C2×C411yescharacteristic
35#11758198—21no—
36#11758198—22no—
37#11758196—21no—
38C4×Dic61C2×C411yescharacteristic
39#11758194—22no—
40#11758189—42no—
41C8×D61—42no—
42C23×C61—21no—
43C22×D61—21no—
44C22×D61—42no—
45C22×D61—82no—
46C22×D61C22⋊C411yescharacteristic
47C22×D61C22⋊C412yes—
48Q8×C61—41no—
49D4×C61—41no—
50C2×C4×C61—21no—
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D412yes—
53C22⋊D61—42no—
54C22⋊D61—82no—
55C2×Dic61—21no—
56C2×Dic61C22⋊C411yescharacteristic
57D244—41no—
58D244—42no—
59D244—41no—
60D244—82no—
61C4×D61—22no—
62C4×D61—22no—
63C4×D61—22no—
64C8×C61—42no—
65#92418—42no—
66C22×C61—42no—
67C22×C61—41no—
68C22×C61C2×C22⋊C411yescharacteristic
69C2×D61—21no—
70C2×D61—22no—
71C2×D61—42no—
72C2×D61—41no—
73C2×D61—42no—
74C2×D61—41no—
75C2×D61—84no—
76C4×C61—22no—
77C4×C61—21no—
78C4×C61—41no—
79Dic61—41no—
80Dic61#9912yes—
81#2134—611nomaximal, Sylow
82C2×C61—21no—
83C2×C61—81no—
84C2×C61C2×#9911yescharacteristic
85D61—42no—
86D61—41no—
87D61—81no—
88#535—611no—
89#413—612no—
90#355—611no—
91#355—612no—
92#355D6111yescharacteristic, complemented
93C61#213411yescharacteristic, complemented, Sylow
94C2×#41—611no—
95C22×D4—611no—
96C2×M16—1222no—
97#127—611no—
98#127—611no—
99#124—611no—
100#124C2×D6111yescharacteristic
101#121—1222no—
102#120—1222no—
103#117—611no—
104#101—612no—
105#101C2×D6112yescomplemented
106#100—1222no—
107C24—1221no—
108#41—2442no—
109C2×Q8C22×D6111yescharacteristic
110C2×D4—611no—
111C2×D4—611no—
112C2×D4—612no—
113C2×D4—1222no—
114C2×D4—1221no—
115C2×D4—1222no—
116C2×D4—2442no—
117C2×D4C4×D6111yescharacteristic
118C22×C4—611no—
119C22×C4—612no—
120M16—22no—
121M16—1222no—
122M16—2442no—
123C2×C8—2442no—
124C4⋊C4—1221no—
125C22⋊C4—22no—
126C22⋊C4—1221no—
127C22⋊C4—1222no—
128C42—611no—
129C42C4×D6111yescharacteristic
130C23—21no—
131C23—611no—
132C23—612no—
133C23—1221no—
134C23—4882no—
135C23—2442no—
136Q8—41no—
137D4—41no—
138D4—4882no—
139D4—4882no—
140D4—2442no—
141D4—2441no—
142D4—2441no—
143D4—2442no—
144C2×C4—21no—
145C2×C4—611no—
146C2×C4—1222no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—1221no—
150C2×C4C2×C4×D6111yescharacteristic
151C2×C4D4×D6112yes—
152C8—42no—
153C8—2442no—
154C22—42no—
155C22—41no—
156C22—1222no—
157C22—1221no—
158C22—4884no—
159C22—2442no—
160C22—2442no—
161C22—2441no—
162C22—2441no—
163C22C22⋊C4×D6111yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—612no—
168C4—2441no—
169C2—21no—
170C2—81no—
171C2—4881no—
172C2—2441no—
173C2—2442no—
174C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#355C2
socleC2×C61C2×#99
hypercenter#355D61
hypocenterC61#2134
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #16839745C2semidirect
3. #16839559C2semidirect
4. #16839558C2semidirect
5. C61×#355C2semidirect
15. #14519696C22semidirect
18. #101×C61C22semidirect
92. #355D61semidirect
93. C61#2134semidirect
105. #101C2×D61semidirect