Finite Group Databasebeta

← #21461863

Subgroups — #21461863

Order 7808.

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

normal subgroups only

This group has 344 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#16840842C211yesmaximal, characteristic, complemented
2#16840754C212yesmaximal, complemented
3#16840743C211yesmaximal, characteristic, complemented
4#16840629C212yesmaximal, complemented
5#16840330C211yesmaximal, characteristic
6#14519865—24no—
7D61⋊M16—22no—
8D61⋊M16C2212yes—
9#14519856C2212yes—
10#14519839—24no—
11#14519836—22no—
12C2×#11758226C2211yescharacteristic
13C2×D4×D61C2211yescharacteristic
14#14519774C411yescharacteristic, complemented
15#14519773C411yescharacteristic, complemented
16#14519766C411yescharacteristic, complemented
17#14519750—22no—
18#14519747—22no—
19#14519734C2211yescharacteristic
20#124×C61C411yescharacteristic, complemented
21C23×D61—21no—
22C2×Q8×C61C2×C411yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C2×C22⋊D61—22no—
25C2×C22⋊D61—21no—
26#11758226—22no—
27#11758226—22no—
28D4×D61—22no—
29D4×D61—22no—
30C2×D244—22no—
31C2×D244C2×C411yescharacteristic
32C2×D244C2×C411yescharacteristic
33C2×D244D412yes—
34C2×C4×D61D412yes—
35C2×C4×D61C2311yescharacteristic
36C22⋊#6923—22no—
37#11758217—22no—
38C4⋊#6923—22no—
39C4×#6923—22no—
40#11758213—24no—
41#11758213—22no—
42D61⋊C8—24no—
43D61⋊C8D414yescomplemented
44C22⋊C4×C61—22no—
45C42×C61C2×C411yescharacteristic
46#11758198—21no—
47#11758198—22no—
48#11758196—21no—
49C4×Dic61C2×C411yescharacteristic
50C23×C61—21no—
51C22×D61—21no—
52C22×D61—42no—
53C22×D61—82no—
54C22×D61C22⋊C412yes—
55C22×D61C2×D411yescharacteristic
56C2×#6923—42no—
57Q8×C61—22no—
58D4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61C22⋊C412yes—
61C2×C4×C61C22×C411yescharacteristic
62C22⋊D61—41no—
63C22⋊D61—41no—
64C22⋊D61—82no—
65C2×Dic61—21no—
66C2×Dic61C2×D411yescharacteristic
67D244—24no—
68D244—22no—
69D244—22no—
70D244—82no—
71C4×D61—22no—
72C4×D61—22no—
73C4×D61C2×D412yes—
74C4×D61#4112yes—
75#92420—24no—
76C22×C61—42no—
77C22×C61—41no—
78C22×C61C2×C22⋊C411yescharacteristic
79C2×D61—22no—
80C2×D61—41no—
81C2×D61—42no—
82C2×D61—42no—
83C2×D61—41no—
84C2×D61—84no—
85C2×D61#12112yes—
86#6923—82no—
87C4×C61—22no—
88C4×C61—41no—
89C4×C61C4×D412yes—
90Dic61—41no—
91Dic61#12011yescharacteristic
92Dic61#12311yescharacteristic
93#1910—611nomaximal, Sylow
94C2×C61—21no—
95C2×C61—81no—
96C2×C61#38611yescharacteristic
97D61—22no—
98D61—42no—
99D61—81no—
100#568—611no—
101#535—611no—
102#418—612no—
103#410—611no—
104H(3,ℤ/4)—612no—
105C61#191011yescharacteristic, complemented, Sylow
106C2×#41—611no—
107C22×D4—611no—
108#131—1224no—
109C2×M16—612no—
110C2×M16—1222no—
111#127—611no—
112#127—611no—
113#124—611no—
114#124#692311yescharacteristic, complemented
115#121—1222no—
116#120—1222no—
117#117—611no—
118#117—612no—
119#102—1224no—
120#99—1222no—
121C24—1221no—
122#41—1222no—
123#41—1222no—
124C2×Q8C2×#692311yescharacteristic
125C2×D4—612no—
126C2×D4—611no—
127C2×D4—611no—
128C2×D4—1222no—
129C2×D4—1222no—
130C2×D4—1222no—
131C2×D4—1221no—
132C2×D4—1222no—
133C2×D4C2×#692311yescharacteristic
134C22×C4—611no—
135C22×C4—612no—
136M16—1222no—
137M16—1222no—
138M16—1224no—
139C2×C8—614no—
140C2×C8—1224no—
141C4⋊C4—1221no—
142C4⋊C4—1222no—
143C22⋊C4—22no—
144C22⋊C4—1221no—
145C22⋊C4—1222no—
146C22⋊C4—1222no—
147C42—611no—
148C42—1222no—
149C42C2×#692311yescharacteristic
150C23—21no—
151C23—611no—
152C23—612no—
153C23—1221no—
154C23—4882no—
155C23—2442no—
156Q8—22no—
157D4—22no—
158D4—1224no—
159D4—1222no—
160D4—1222no—
161D4—4882no—
162D4—4882no—
163D4—2441no—
164D4—2441no—
165C2×C4—21no—
166C2×C4—611no—
167C2×C4—612no—
168C2×C4—612no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1221no—
172C2×C4—2442no—
173C2×C4C22⋊#692312yes—
174C2×C4C22×#692311yescharacteristic
175C8—1224no—
176C22—42no—
177C22—41no—
178C22—612no—
179C22—1222no—
180C22—4884no—
181C22—2441no—
182C22—2442no—
183C22—2442no—
184C22—2441no—
185C22C2×C22⋊#692311yescharacteristic
186C4—22no—
187C4—41no—
188C4—611no—
189C4—611no—
190C4—4882no—
191C4—2441no—
192C4D4×#692312yes—
193C2—21no—
194C2—81no—
195C2—1222no—
196C2—4881no—
197C2—2442no—
198C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61#386
hypercenter#124#6923
hypocenterC61#1910
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840842C2semidirect
2. #16840754C2semidirect
3. #16840743C2semidirect
4. #16840629C2semidirect
14. #14519774C4semidirect
15. #14519773C4semidirect
16. #14519766C4semidirect
20. #124×C61C4semidirect
43. D61⋊C8D4semidirect
105. C61#1910semidirect
114. #124#6923semidirect