Finite Group Databasebeta

← #21461342

Subgroups — #21461342

Order 7808.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840785C211yesmaximal, characteristic, complemented
2#16840780C211yesmaximal, characteristic, complemented
3#16840621C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840309C211yesmaximal, characteristic
6#14519844C2212yes—
7#14519844C2212yes—
8#14519834—21no—
9#14519834—21no—
10#14519832—21no—
11C4×#92420—21no—
12C2×#11758222—21no—
13#14519776C2211yescharacteristic
14#14519773C2211yescharacteristic
15#14519763—21no—
16#14519752C411yescharacteristic
17#14519750—21no—
18#14519748C411yescharacteristic
19C4×D244C411yescharacteristic
20C4×C22⋊D61—21no—
21C42×D61C2211yescharacteristic
22C4×D4×C61C411yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C2×C22⋊D61—21no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28#11758222—44no—
29C2×D244—21no—
30C2×D244C2×C411yescharacteristic
31C2×C4×D61—21no—
32C2×C4×D61C2×C411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×Dic122—21no—
36C2×#92420—22no—
37C2×#92420—22no—
38C4⋊C4×C61C2×C411yescharacteristic
39C22⋊C4×C61—21no—
40C42×C61C2×C411yescharacteristic
41C22⋊Dic61—21no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61C2×C411yescharacteristic
45#11758196—21no—
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C23×C61—21no—
50C22×D61—21no—
51C22×D61C22⋊C411yescharacteristic
52D4×C61—41no—
53C2×C4×C61—21no—
54C2×C4×C61—42no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C22⋊D61—42no—
59C22⋊D61—42no—
60C22⋊D61—42no—
61C2×Dic61—21no—
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C2×Dic61C2×D411yescharacteristic
65D244—41no—
66D244—42no—
67C4×D61—22no—
68C4×D61—22no—
69C4×D61—41no—
70C4×D61—42no—
71Dic122—42no—
72#92420—42no—
73#92420—42no—
74C22×C61—41no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61C2×C22⋊C411yescharacteristic
78C2×D61—21no—
79C2×D61—21no—
80C2×D61—21no—
81C2×D61—41no—
82C2×D61—41no—
83C2×D61—41no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—41no—
88Dic61—21no—
89Dic61—41no—
90Dic61#13512yes—
91Dic61AGL(1,ℤ/8)12yes—
92#1553—611nomaximal, Sylow
93C2×C61—81no—
94C2×C61#41311yescharacteristic
95C2×C61#41611yescharacteristic
96C2×C61#41811yescharacteristic
97D61—41no—
98D61—81no—
99#532—611no—
100#432—611no—
101#431—611no—
102#332—612no—
103#331—612no—
104C61#155311yescharacteristic, complemented, Sylow
105C2×#41—1221no—
106C4⋊Q8—611no—
107#127—611no—
108#124—1221no—
109#121—611no—
110#121—611no—
111#121—1221no—
112C4×D4—611no—
113C4×D4—1221no—
114C4×D4#692311yescharacteristic
115C2×C42—611no—
116C4⋊C8—612no—
117C4⋊C8—612no—
118C22⋊C8—1221no—
119C22⋊C8—1221no—
120#97—1221no—
121C4×C8—1221no—
122#41—2444no—
123C2×Q8—1221no—
124C2×D4—611no—
125C2×D4—1221no—
126C2×D4—1221no—
127C2×D4—1221no—
128C2×D4—1221no—
129C2×D4C2×#692311yescharacteristic
130C22×C4—21no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—1221no—
135C2×C8—1222no—
136C2×C8—1222no—
137C4⋊C4—611no—
138C4⋊C4—1221no—
139C4⋊C4C2×#692311yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—1221no—
142C22⋊C4—1221no—
143C22⋊C4—1221no—
144C42—611no—
145C42—611no—
146C42—611no—
147C42C2×#692311yescharacteristic
148C23—21no—
149C23—611no—
150C23—1221no—
151Q8—2442no—
152D4—41no—
153D4—2441no—
154D4—2442no—
155D4—2442no—
156D4—2442no—
157D4—2442no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—1221no—
166C2×C4—2441no—
167C2×C4—2442no—
168C2×C4C22⋊#692311yescharacteristic
169C2×C4C22⋊#692311yescharacteristic
170C2×C4C22×#692311yescharacteristic
171C8—2442no—
172C8—2442no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—1221no—
177C22—1221no—
178C22—1221no—
179C22—2441no—
180C22—2441no—
181C22—2441no—
182C22C2×C22⋊#692311yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—612no—
188C4—612no—
189C4—1221no—
190C4—2441no—
191C2—81no—
192C2—4881no—
193C2—2441no—
194C2#1684074811yescharacteristic
195C2#1684075211yescharacteristic
196C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1553
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #16840785C2semidirect
2. #16840780C2semidirect
3. #16840621C2semidirect
4. #16840620C2semidirect
104. C61#1553semidirect