Finite Group Databasebeta

← #21444199

Subgroups — #21444199

Order 7808.

276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C4×#11758222C211yesmaximal, characteristic
2C2×C4×#92418C211yesmaximal, characteristic, complemented
3#16839492C212yesmaximal, complemented
4#16839489C212yesmaximal, complemented
5C61×#431C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic
7C22×#92418—21no—
8C4×Dic122C411yescharacteristic
9C4×Dic122C2211yescharacteristic
10C4×D244C411yescharacteristic
11C4×D244C2211yescharacteristic
12C4×C22⋊D61—21no—
13C4×C22⋊D61—21no—
14#14519736C411yescharacteristic
15#14519734—21no—
16C42×D61—21no—
17C4×#92418—21no—
18C4×#92418C2212yes—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61C2212yes—
21C22⋊C8×C61—21no—
22C4×C8×C61—21no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—21no—
27#11758222—22no—
28#11758222C814yescomplemented
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122C2×C411yescharacteristic
34C2×C8×C61—22no—
35C42×C61C2×C411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61C2311yescharacteristic
39C22⋊Dic61—21no—
40#11758198—21no—
41#11758198—21no—
42C4⋊Dic61C2×C411yescharacteristic
43C4⋊Dic61C2×C411yescharacteristic
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—24no—
50C2×#92418—22no—
51C23×C61C22⋊C411yescharacteristic
52C22×D61—21no—
53C2×C4×C61—22no—
54C2×C4×C61—22no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C2×C812yes—
59C2×C4×C61M1612yes—
60C2×C4×C61C22×C411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C22⋊D61—24no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67D244—21no—
68D244C2×C812yescomplemented
69C4×D61—24no—
70C4×D61—42no—
71C4×D61—42no—
72Dic122—21no—
73Dic122C2×C812yescomplemented
74C8×C61—42no—
75#92418—24no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61C22⋊C812yes—
79C22×C61C2×C22⋊C411yescharacteristic
80C2×D61—22no—
81C2×D61—41no—
82C2×D61—41no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61C22⋊C812yes—
86C4×C61#10412yes—
87C4×C61C22×C811yescharacteristic
88C4×C61C2×M1611yescharacteristic
89C4×C61#13512yes—
90Dic61—22no—
91Dic61—41no—
92Dic61—41no—
93#1476—611nomaximal, Sylow
94C2×C61—22no—
95C2×C61C2×C22⋊C811yescharacteristic
96C2×C61#41611yescharacteristic
97C2×C61C2×#10411yescharacteristic
98D61—42no—
99C4×#41—611no—
100#431D6111yescharacteristic, complemented
101C2×C4×C8—611no—
102Q8⋊C8—612no—
103D4⋊C8—612no—
104C61#147611yescharacteristic, complemented, Sylow
105C2×#41—611no—
106C22×C8—1221no—
107C4×Q8—611no—
108C4×Q8—611no—
109C4×D4—611no—
110C4×D4—611no—
111C4×D4—1221no—
112C4×D4—1221no—
113#117—611no—
114#117—1221no—
115C2×C42—1221no—
116C2×C42C2×D6111yescharacteristic
117C4⋊C8C2×D6112yes—
118C22⋊C8—21no—
119C4×C8—21no—
120C4×C8—612no—
121C4×C8—1221no—
122#41—614no—
123#41—1222no—
124C2×Q8—611no—
125C2×D4—611no—
126C2×D4—1221no—
127C22×C4—1221no—
128C22×C4—1221no—
129C22×C4—1221no—
130C22×C4C4×D6111yescharacteristic
131C22×C4D24411yescharacteristic
132C22×C4C22⋊D6111yescharacteristic
133C2×C8—22no—
134C2×C8—1224no—
135C2×C8—1222no—
136C4⋊C4—611no—
137C4⋊C4—611no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C22⋊C4—1221no—
141C22⋊C4—1221no—
142C22⋊C4—1221no—
143C42—1221no—
144C42—1221no—
145C42—1221no—
146C42C4×D6111yescharacteristic
147C42D24411yescharacteristic
148C42C22⋊D6111yescharacteristic
149C42C22×D6111yescharacteristic
150C23—1221no—
151C23#1175819811yescharacteristic
152Q8—612no—
153Q8—1221no—
154D4—612no—
155D4—1224no—
156D4—1221no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—1221no—
160C2×C4—1224no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4C8×D6112yes—
166C2×C4#1175818912yes—
167C2×C4#1175819811yescharacteristic
168C2×C4#1175819811yescharacteristic
169C2×C4#1175819811yescharacteristic
170C2×C4C2×C4×D6111yescharacteristic
171C2×C4C2×D24411yescharacteristic
172C2×C4C2×C22⋊D6111yescharacteristic
173C8—42no—
174C8—1224no—
175C22—21no—
176C22—21no—
177C22—1222no—
178C22—2441no—
179C22—2441no—
180C22#1451968912yes—
181C22C2×#1175819811yescharacteristic
182C4—21no—
183C4—21no—
184C4—1222no—
185C4—2441no—
186C4—2441no—
187C4#1451968912yes—
188C4#1451970312yes—
189C4C2×C8×D6111yescharacteristic
190C4C2×#1175818911yescharacteristic
191C4#1451979712yes—
192C2—22no—
193C2—2442no—
194C2C2×#1451968911yescharacteristic
195C2#1683975611yescharacteristic
196C2C2×#1451970311yescharacteristic
subgroupG/H
centerC42C22⋊D61
commutatorC4×C61C22×C8
FrattiniC42C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1476
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×C4×#92418C2semidirect
3. #16839492C2semidirect
4. #16839489C2semidirect
5. C61×#431C2semidirect
28. #11758222C8semidirect
68. D244C2×C8semidirect
73. Dic122C2×C8semidirect
100. #431D61semidirect
104. C61#1476semidirect