Finite Group Databasebeta

← #21461824

Subgroups — #21461824

Order 7808.

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

normal subgroups only

This group has 360 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#16840829C211yesmaximal, characteristic
2#16840755C212yesmaximal, complemented
3D61⋊#100C211yesmaximal, characteristic
4#16840633C212yesmaximal, complemented
5#124×D61C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7D4×#6923—24no—
8#14519856C2212yes—
9C2×C22⋊#6923—22no—
10#14519840—24no—
11#14519837—22no—
12C2×Q8×D61C2211yescharacteristic
13C2×D4×D61C2211yescharacteristic
14#14519766C411yescharacteristic, complemented
15#14519765C411yescharacteristic, complemented
16#14519764C411yescharacteristic, complemented
17#14519763—22no—
18C22⋊C4×D61—22no—
19C42×D61C2211yescharacteristic
20#124×C61C411yescharacteristic, complemented
21C23×D61D412yes—
22C22×#6923—24no—
23C2×Q8×C61C2×C411yescharacteristic, complemented
24C2×D4×C61C2×C411yescharacteristic
25C2×C22⋊D61D412yes—
26Q8×D61—22no—
27Q8×D61—22no—
28D4×D61—22no—
29D4×D61—22no—
30C2×D244C2×C411yescharacteristic
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61C2311yescharacteristic
34C2×Dic122—21no—
35C2×Dic122C2×C411yescharacteristic, complemented
36C22⋊#6923—24no—
37C22⋊#6923—22no—
38#11758217—22no—
39C4⋊#6923D414yes—
40C4×#6923—22no—
41#11758213—22no—
42D61⋊C8—22no—
43C22⋊C4×C61—22no—
44C42×C61C2×C411yescharacteristic, complemented
45C22⋊Dic61—22no—
46#11758198—22no—
47#11758198—22no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic, complemented
50C23×C61C22⋊C412yes—
51C22×D61—22no—
52C22×D61—22no—
53C22×D61—44no—
54C22×D61C22⋊C412yes—
55C22×D61C2×D411yescharacteristic
56C2×#6923—24no—
57C2×#6923—84no—
58Q8×C61—22no—
59D4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61C22×C411yescharacteristic
63C22⋊D61—24no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61C2×D411yescharacteristic
67D244—22no—
68C4×D61—42no—
69C4×D61—41no—
70C4×D61—41no—
71C4×D61C2×D412yes—
72C4×D61#4112yes—
73Dic122—22no—
74Dic122—42no—
75#92420—42no—
76C22×C61—22no—
77C22×C61—42no—
78C22×C61C2×C22⋊C411yescharacteristic
79C2×D61—22no—
80C2×D61—22no—
81C2×D61—44no—
82C2×D61—42no—
83C2×D61—82no—
84C2×D61#12011yescharacteristic
85C2×D61#12311yescharacteristic
86#6923—44no—
87C4×C61—41no—
88C4×C61—41no—
89C4×C61C4×D412yes—
90Dic61—41no—
91Dic61—41no—
92Dic61#12112yes—
93#1885—611nomaximal, Sylow
94C2×C61—21no—
95C2×C61—42no—
96C2×C61#38611yescharacteristic
97D61—21no—
98D61—42no—
99D61#45512yes—
100C2×#124—611no—
101#518—611no—
102#419—612no—
103C2×#100—611no—
104#339—612no—
105C61#188511yescharacteristic, complemented, Sylow
106C22×Q8—611no—
107C22×D4—611no—
108C2×M16—612no—
109#124—611no—
110#124—611no—
111#124—611no—
112#124—1222no—
113#124#692311yescharacteristic, complemented
114C4×D4—1224no—
115#117—612no—
116C2×C22⋊C4—1222no—
117C2×C22⋊C4—1222no—
118C2×C42—611no—
119#103—1224no—
120#100—1222no—
121C24—612no—
122C2×Q8—611no—
123C2×Q8—1221no—
124C2×Q8—1222no—
125C2×Q8—1222no—
126C2×Q8C2×#692311yescharacteristic, complemented
127C2×D4—612no—
128C2×D4—611no—
129C2×D4—1222no—
130C2×D4—1222no—
131C2×D4C2×#692311yescharacteristic
132C22×C4—611no—
133C22×C4—1221no—
134C22×C4—1221no—
135C22×C4—1224no—
136M16—1222no—
137M16—1222no—
138C2×C8—1222no—
139C4⋊C4—614no—
140C22⋊C4—22no—
141C22⋊C4—1222no—
142C22⋊C4—1222no—
143C22⋊C4—1222no—
144C22⋊C4—1224no—
145C22⋊C4—1222no—
146C42—611no—
147C42—1221no—
148C42—1222no—
149C42C2×#692311yescharacteristic, complemented
150C23—611no—
151C23—612no—
152C23—1222no—
153C23—1222no—
154C23—2444no—
155C23C22⋊#692312yes—
156Q8—22no—
157Q8—1222no—
158Q8—2442no—
159D4—22no—
160D4—1224no—
161D4—1222no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—611no—
165C2×C4—612no—
166C2×C4—612no—
167C2×C4—1224no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—4884no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2442no—
174C2×C4C22×#692311yescharacteristic
175C8—2442no—
176C22—22no—
177C22—42no—
178C22—611no—
179C22—611no—
180C22—1222no—
181C22—1222no—
182C22—4882no—
183C22—2442no—
184C22—2444no—
185C22C2×C22⋊#692311yescharacteristic
186C4—41no—
187C4—41no—
188C4—612no—
189C4—2441no—
190C4—2444no—
191C4—2441no—
192C4D4×#692312yes—
193C2—21no—
194C2—42no—
195C2—612no—
196C2—1221no—
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#1885
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
2. #16840755C2semidirect
4. #16840633C2semidirect
14. #14519766C4semidirect
15. #14519765C4semidirect
16. #14519764C4semidirect
20. #124×C61C4semidirect
23. C2×Q8×C61C2×C4semidirect
35. C2×Dic122C2×C4semidirect
44. C42×C61C2×C4semidirect
49. C4×Dic61C2×C4semidirect
105. C61#1885semidirect
113. #124#6923semidirect
126. C2×Q8C2×#6923semidirect
149. C42C2×#6923semidirect