Finite Group Databasebeta

← #21461150

Subgroups — #21461150

Order 7808.

246 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840783C211yesmaximal, characteristic, complemented
2#16840779C211yesmaximal, characteristic, complemented
3Q8⋊#92420C212yesmaximal, complemented
4D4⋊#92420C212yesmaximal, complemented
5#41×Dic61C211yesmaximal, characteristic
6#14519844—21no—
7C4⋊#92420C2212yes—
8C22⋊#92420—21no—
9C22⋊#92420—21no—
10#14519832—21no—
11C4×#92420C2212yes—
12Q8×Dic61C411yescharacteristic
13Q8×Dic61C2211yescharacteristic
14D4×Dic61—21no—
15D4×Dic61—21no—
16D4×Dic61C411yescharacteristic
17D4×Dic61C2211yescharacteristic
18#14519736—21no—
19#14519736C411yescharacteristic
20C2×C4×Dic61—21no—
21C2×C4×Dic61C2211yescharacteristic
22C2×#41×C61C411yescharacteristic
23#41×C61—22no—
24#41×C61—22no—
25C2×Q8×C61C2×C411yescharacteristic
26C2×D4×C61—21no—
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C2×C411yescharacteristic
30C22×Dic61—21no—
31C22×Dic61—21no—
32C22×Dic61D411yescharacteristic
33C22×Dic61D411yescharacteristic
34C2×#92420—22no—
35C2×#92420—22no—
36C22⋊Dic61—21no—
37C22⋊Dic61—21no—
38C22⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43C4×Dic61—21no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61—21no—
51C23×C61C22⋊C411yescharacteristic
52Q8×C61—21no—
53Q8×C61M1612yes—
54D4×C61—24no—
55D4×C61—21no—
56D4×C61M1612yes—
57C2×C4×C61—24no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C2×Dic61—22no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—41no—
67C2×Dic61—42no—
68C2×Dic61—42no—
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C2×D411yescharacteristic
72C2×Dic61C2×D411yescharacteristic
73#92420—42no—
74#92420—42no—
75C22×C61—21no—
76C22×C61—22no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C4×C61—21no—
83C4×C61—22no—
84C4×C61C2×M1611yescharacteristic
85C4×C61C2×M1611yescharacteristic
86Dic61—21no—
87Dic61—21no—
88Dic61—21no—
89Dic61—41no—
90Dic61—41no—
91Dic61#13512yes—
92#1488—611nomaximal, Sylow
93C2×C61—41no—
94C2×C61—42no—
95C2×C61#40711yescharacteristic
96C2×C61#41611yescharacteristic
97C2×C61#42111yescharacteristic
98C4×#41—611no—
99#432—611no—
100#431—611no—
101Q8⋊C8—612no—
102D4⋊C8—612no—
103C61#148811yescharacteristic, complemented, Sylow
104C2×#41#692311yescharacteristic
105C4×Q8—611no—
106C4×Q8—611no—
107C4×D4—611no—
108C4×D4—611no—
109C4×D4—1221no—
110C4×D4—1221no—
111#117—611no—
112#117—1221no—
113C2×C42—611no—
114C2×C42—1221no—
115C4⋊C8—612no—
116C4⋊C8—1221no—
117C22⋊C8—1221no—
118C22⋊C8—1221no—
119#97—1221no—
120C4×C8—612no—
121#41—22no—
122#41—22no—
123C2×Q8C2×#692311yescharacteristic
124C2×D4—21no—
125C2×D4C2×#692311yescharacteristic
126C22×C4—21no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—1221no—
130C22×C4—1221no—
131C22×C4C2×#692311yescharacteristic
132C2×C8—1222no—
133C2×C8—1222no—
134C4⋊C4—611no—
135C4⋊C4—611no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C42—611no—
142C42—611no—
143C42—611no—
144C42—611no—
145C42—1221no—
146C42—1221no—
147C42—1221no—
148C23—21no—
149C23C22⋊#692311yescharacteristic
150Q8—21no—
151Q8#1175821712yes—
152D4—24no—
153D4—21no—
154D4#1175821712yes—
155C2×C4—24no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—1222no—
164C2×C4—1221no—
165C2×C4—1221no—
166C2×C4—2442no—
167C2×C4—2441no—
168C2×C4—2442no—
169C2×C4C22⋊#692311yescharacteristic
170C2×C4C22×#692311yescharacteristic
171C8—2442no—
172C8—2442no—
173C22—21no—
174C22—22no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22C2×C22⋊#692311yescharacteristic
180C4—21no—
181C4—22no—
182C4—612no—
183C4—1221no—
184C4—1221no—
185C4—1221no—
186C4—2441no—
187C4—2441no—
188C4C2×#1175821711yescharacteristic
189C4C2×#1175821711yescharacteristic
190C2—41no—
191C2—42no—
192C2#1684073211yescharacteristic
193C2#1684075211yescharacteristic
194C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×#41×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×#41#6923
hypocenterC61#1488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #16840783C2semidirect
2. #16840779C2semidirect
3. Q8⋊#92420C2semidirect
4. D4⋊#92420C2semidirect
103. C61#1488semidirect