Finite Group Databasebeta

← #21461982

Subgroups — #21461982

Order 7808.

336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#14519842C214yesmaximal, complemented
2C4×#11758213C211yesmaximal, characteristic, complemented
3C4×C4⋊#6923C211yesmaximal, characteristic, complemented
4#16840313C211yesmaximal, characteristic
5C2×#11758213C2212yes—
6C2×C4⋊#6923—21no—
7C2×C4×#6923C2212yes—
8#14519842—28no—
9#14519832—21no—
10C4×#92420—21no—
11(C2×#6923)⋊C4—21no—
12C2×#11758226C2212yes—
13#14519774C411yescharacteristic, complemented
14#14519766C412yescomplemented
15#14519752—21no—
16#14519752—21no—
17#14519739—21no—
18#14519739—21no—
19C42×D61C2211yescharacteristic
20C4⋊Q8×C61C411yescharacteristic, complemented
21C22×#6923—22no—
22C2×Q8×C61C2×C412yes—
23#11758226—24no—
24#11758226—24no—
25C2×D244—22no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244C2×C412yes—
29C2×C4×D61—22no—
30C2×C4×D61D411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61C2311yescharacteristic
33C2×#92420—22no—
34C4⋊#6923—24no—
35C4×#6923—24no—
36#11758213—22no—
37#11758213D414yescomplemented
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C42×C61C2×C411yescharacteristic
41#11758198—22no—
42#11758198—22no—
43C4×Dic61C2×C411yescharacteristic
44C4×Dic61D411yescharacteristic
45C4×Dic61D411yescharacteristic
46C22×D61—22no—
47C22×D61C2×D411yescharacteristic
48C2×#6923—24no—
49C2×#6923—42no—
50C2×#6923—42no—
51Q8×C61—24no—
52C2×C4×C61—22no—
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22×C411yescharacteristic
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59D244—24no—
60D244—42no—
61D244—42no—
62D244—42no—
63D244—42no—
64C4×D61—22no—
65C4×D61—41no—
66C4×D61—44no—
67C4×D61C2×D412yes—
68C4×D61#4112yes—
69#92420—24no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—42no—
74C2×D61—42no—
75C2×D61—42no—
76C2×D61#12411yescharacteristic
77C2×D61#12711yescharacteristic
78#6923—44no—
79C4×C61—21no—
80C4×C61—42no—
81C4×C61#10412yescomplemented
82C4×C61C4×D412yes—
83Dic61—21no—
84Dic61—21no—
85Dic61#12112yes—
86#1980—611nomaximal, Sylow
87C2×C61#39011yescharacteristic
88C2×C61C2×#10411yescharacteristic
89C2×C61#42111yescharacteristic
90D61—21no—
91D61—21no—
92D61—82no—
93#532—611no—
94C2×#104—614no—
95C4×M16—611no—
96C4×C4⋊C4—611no—
97C61#198011yescharacteristic, complemented, Sylow
98C2×#41—612no—
99C2×M16—612no—
100C4⋊Q8#692311yescharacteristic, complemented
101#127—611no—
102#124—612no—
103#121—1221no—
104#121—1221no—
105C4×D4—1221no—
106C4×D4—1221no—
107C2×C4⋊C4—1221no—
108C2×C42—611no—
109C2×C42—612no—
110#104—1228no—
111#97—1221no—
112C4×C8—1221no—
113#95—1221no—
114#41—1224no—
115#41—1224no—
116C2×Q8C2×#692312yes—
117C2×D4—612no—
118C2×D4—1222no—
119C2×D4—1221no—
120C2×D4—1221no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—611no—
124C22×C4—1222no—
125C22×C4—1222no—
126M16—614no—
127M16—1222no—
128C2×C8—1222no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1224no—
132C22⋊C4—1222no—
133C22⋊C4—1222no—
134C42—611no—
135C42—611no—
136C42—611no—
137C42—1224no—
138C42C2×#692311yescharacteristic
139C23—611no—
140C23—1222no—
141Q8—24no—
142D4—1224no—
143D4—2442no—
144D4—2442no—
145D4—2442no—
146D4—2442no—
147C2×C4—22no—
148C2×C4—611no—
149C2×C4—612no—
150C2×C4—612no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—1222no—
154C2×C4—1224no—
155C2×C4—2441no—
156C2×C4—2444no—
157C2×C4—2442no—
158C2×C4—2442no—
159C2×C4C22⋊#692311yescharacteristic
160C2×C4C22⋊#692311yescharacteristic
161C2×C4C22×#692311yescharacteristic
162C8—1224no—
163C22—611no—
164C22—611no—
165C22—1221no—
166C22—1221no—
167C22—2442no—
168C22—2442no—
169C22—2442no—
170C22C2×C22⋊#692311yescharacteristic
171C4—21no—
172C4—42no—
173C4—612no—
174C4—1221no—
175C4—1221no—
176C4—2444no—
177C4#1451984212yescomplemented
178C4D4×#692312yes—
179C2—1221no—
180C2—1221no—
181C2—4882no—
182C2#1684071411yescharacteristic
183C2C2×#1451984211yescharacteristic
184C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1980
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14519842C2semidirect
2. C4×#11758213C2semidirect
3. C4×C4⋊#6923C2semidirect
13. #14519774C4semidirect
14. #14519766C4semidirect
20. C4⋊Q8×C61C4semidirect
37. #11758213D4semidirect
81. C4×C61#104semidirect
97. C61#1980semidirect
100. C4⋊Q8#6923semidirect
177. C4#14519842semidirect