Finite Group Databasebeta

← #21461791

Subgroups — #21461791

Order 7808.

260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840840C211yesmaximal, characteristic
2#16840768C212yesmaximal, complemented
3#16840735C211yesmaximal, characteristic
4#16840643C212yesmaximal, complemented
5#16839734C211yesmaximal, characteristic
6#14519864—22no—
7#14519864—22no—
8D61⋊M16—21no—
9C2×#11758217—21no—
10C2×#11758217C2211yescharacteristic
11C2×#11758217C2212yes—
12C22×#92420C2211yescharacteristic
13#14519844—22no—
14C4⋊#92420—22no—
15#14519834—21no—
16C22⋊#92420—21no—
17C2×#11758224C2211yescharacteristic
18#14519733C2212yes—
19#14519692C411yescharacteristic
20#14519691C412yes—
21#99×C61C411yescharacteristic
22C2×D4×C61C2×C411yescharacteristic
23C2×C22⋊D61C2×C411yescharacteristic
24C2×C22⋊D61Q811yescharacteristic
25C22×Dic61D411yescharacteristic
26C22×Dic61C2311yescharacteristic
27#11758224—22no—
28#11758224—22no—
29C2×C4×D61D411yescharacteristic
30C2×Dic122Q811yescharacteristic
31#11758217—22no—
32#11758217—22no—
33#11758217—22no—
34#11758217—22no—
35C2×#92420—21no—
36C2×#92420—21no—
37C2×#92420—21no—
38C2×#92420—21no—
39C2×#92420—22no—
40C2×#92420D412yes—
41C2×#92420D412yes—
42#11758213—21no—
43#11758213—21no—
44D61⋊C8—22no—
45C22⋊C4×C61C2×C412yes—
46C22⋊Dic61C2×C412yes—
47#11758196—22no—
48C4×Dic61—22no—
49C23×C61C4⋊C411yescharacteristic
50C23×C61C22×C411yescharacteristic
51C22×D61C4⋊C411yescharacteristic
52D4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61C4⋊C411yescharacteristic
55C22⋊D61—22no—
56C22⋊D61—22no—
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—22no—
60C2×Dic61C4⋊C411yescharacteristic
61C2×Dic61C2×D412yes—
62C2×Dic61C2×D411yescharacteristic
63C2×Dic61C2×Q811yescharacteristic
64C2×Dic61#4112yes—
65C4×D61—21no—
66C4×D61—21no—
67Dic122—22no—
68#92420—22no—
69#92420—22no—
70#92420—41no—
71#92420—41no—
72C22×C61—21no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61C2×C4⋊C411yescharacteristic
76C22×C61C4×D412yes—
77C2×D61—21no—
78C2×D61—41no—
79C4×C61—21no—
80C4×C61—42no—
81Dic61—21no—
82Dic61—42no—
83Dic61#12011yescharacteristic
84Dic61C22⋊Q812yes—
85Dic61#12311yescharacteristic
86#1868—611nomaximal, Sylow
87C2×C61—22no—
88C2×C61—21no—
89C2×C61—41no—
90C2×C61#38511yescharacteristic
91D61—41no—
92#568—611no—
93#424—612no—
94#410—611no—
95#408—611no—
96#344—612no—
97C61#186811yescharacteristic, complemented, Sylow
98C2×#41—611no—
99#131—1222no—
100#131—1222no—
101C2×M16—612no—
102C2×M16—611no—
103C2×M16—1221no—
104C2×M16—1221no—
105C22×C8—611no—
106#117—612no—
107C4⋊C8—1222no—
108C4⋊C8—1222no—
109#99—611no—
110#99—612no—
111#99#692311yescharacteristic
112C22⋊C8—1221no—
113C22⋊C8—1221no—
114#41—1222no—
115#41—1222no—
116C2×Q8—611no—
117C2×D4—611no—
118C2×D4—611no—
119C2×D4C2×#692311yescharacteristic
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—611no—
123M16—1222no—
124M16—1222no—
125M16—1221no—
126M16—1221no—
127M16—1222no—
128M16—1222no—
129C2×C8—612no—
130C2×C8—612no—
131C2×C8—1222no—
132C2×C8—1221no—
133C2×C8—1221no—
134C2×C8—1221no—
135C2×C8—1221no—
136C2×C8—1222no—
137C4⋊C4—1222no—
138C22⋊C4—612no—
139C22⋊C4C2×#692312yes—
140C42—1222no—
141C23—611no—
142C23C4⋊#692311yescharacteristic
143C23C22×#692311yescharacteristic
144Q8—1222no—
145D4—22no—
146D4—1222no—
147D4—1222no—
148C2×C4—22no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—612no—
152C2×C4—612no—
153C2×C4—611no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—1222no—
159C2×C4C4⋊#692311yescharacteristic
160C8—1222no—
161C8—1222no—
162C8—2441no—
163C8—2441no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—1221no—
168C22—2441no—
169C22C2×C4⋊#692311yescharacteristic
170C22D4×#692312yes—
171C4—21no—
172C4—42no—
173C4—611no—
174C4—612no—
175C4—611no—
176C4—1221no—
177C4—2442no—
178C2—22no—
179C2—21no—
180C2—41no—
181C2—2441no—
182C2#1684070911yescharacteristic
subgroupG/H
centerC2#16840709
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#99×C61C4
socleC2×C61#385
hypercenter#99#6923
hypocenterC61#1868
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #16840768C2semidirect
4. #16840643C2semidirect
97. C61#1868semidirect