Finite Group Databasebeta

← #21461256

Subgroups — #21461256

Order 7808.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#16840704C211yesmaximal, characteristic, complemented
3#16840614C214yesmaximal, complemented
4C2×#14519752C211yesmaximal, characteristic
5C2×D61⋊C8—21no—
6C2×C4⋊#6923—21no—
7C2×C22⋊#6923—21no—
8#14519834C2212yescomplemented
9C22⋊#92420—21no—
10(C2×#6923)⋊C4C2212yescomplemented
11C22×D244—21no—
12C22×D244C411yescharacteristic, complemented
13C22×C4×D61C2211yescharacteristic
14#14519752—21no—
15#14519752—21no—
16#14519752C412yescomplemented
17#14519752C2212yes—
18C2×#11758198—21no—
19C2×C4⋊C4×C61C411yescharacteristic, complemented
20C23×D61—21no—
21C23×D61D411yescharacteristic
22C22×#6923—22no—
23C22×C4×C61—21no—
24C22×C4×C61C2×C411yescharacteristic
25C22×Dic61D411yescharacteristic
26C2×D244—22no—
27C2×D244—22no—
28C2×D244—21no—
29C2×D244—42no—
30C2×D244—42no—
31C2×D244—42no—
32C2×D244C2×C412yes—
33C2×C4×D61—42no—
34C2×C4×D61C2×C411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61C2311yescharacteristic
38C22⋊#6923—42no—
39C2×#92420—22no—
40C4⋊#6923—42no—
41D61⋊C8—42no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61C2×C412yes—
44#11758198—22no—
45#11758198—22no—
46C23×C61C22⋊C411yescharacteristic
47C22×D61—22no—
48C22×D61—41no—
49C22×D61—41no—
50C22×D61—42no—
51C22×D61—42no—
52C22×D61—42no—
53C22×D61C22⋊C411yescharacteristic
54C22×D61D812yes—
55C22×D61SD1612yes—
56C22×D61C2×D411yescharacteristic
57C2×#6923—42no—
58C2×#6923—42no—
59C2×#6923—42no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—42no—
63C2×C4×C61C22⋊C411yescharacteristic
64C2×C4×C61C22×C411yescharacteristic
65C2×Dic61—41no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68D244—42no—
69D244—44no—
70D244—42no—
71D244—42no—
72D244—42no—
73C4×D61—22no—
74C4×D61—22no—
75C4×D61—41no—
76C4×D61—41no—
77#92420—42no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61#10212yes—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—42no—
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—42no—
90C2×D61—42no—
91C2×D61—84no—
92C2×D61#10212yes—
93C2×D61C2×D811yescharacteristic
94C2×D61C2×SD1611yescharacteristic
95#6923—82no—
96C4×C61—21no—
97C4×C61—42no—
98C4×C61#9912yes—
99Dic61—21no—
100Dic61—21no—
101#1519—611nomaximal, Sylow
102C2×C61—22no—
103C2×C61C2×#9911yescharacteristic
104C2×C61C2×#10211yescharacteristic
105C2×C61#42111yescharacteristic
106D61—21no—
107D61—22no—
108D61—21no—
109D61—82no—
110C2×#121—611no—
111C2×C22⋊C8—611no—
112#380—611no—
113#327—614no—
114C61#151911yescharacteristic, complemented, Sylow
115C22×D4—611no—
116C22×D4—1221no—
117C23×C4—611no—
118C22×C8—1221no—
119#121—612no—
120#121—612no—
121#121—1221no—
122#121—1221no—
123C2×C4⋊C4—1221no—
124C2×C4⋊C4#692311yescharacteristic, complemented
125C2×C22⋊C4—1221no—
126C2×C22⋊C4—1221no—
127C22⋊C8—612no—
128C22⋊C8—1221no—
129#95—612no—
130C24—611no—
131C24—1221no—
132C2×D4—612no—
133C2×D4—1222no—
134C2×D4—1222no—
135C2×D4—1221no—
136C2×D4—2442no—
137C2×D4—2442no—
138C2×D4—2442no—
139C22×C4—21no—
140C22×C4—611no—
141C22×C4—611no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—1222no—
146C22×C4—2442no—
147C22×C4C2×#692311yescharacteristic
148C2×C8—1222no—
149C2×C8—2442no—
150C4⋊C4—21no—
151C4⋊C4—2442no—
152C4⋊C4C2×#692312yes—
153C22⋊C4—1222no—
154C22⋊C4—1222no—
155C22⋊C4—2442no—
156C23—611no—
157C23—611no—
158C23—612no—
159C23—612no—
160C23—1222no—
161C23—2441no—
162C23—2441no—
163C23—2442no—
164C23—2442no—
165C23—2442no—
166C23C22⋊#692311yescharacteristic
167D4—2442no—
168D4—2442no—
169D4—2444no—
170D4—2442no—
171D4—2442no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4—2442no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4C22⋊#692311yescharacteristic
186C2×C4C22×#692311yescharacteristic
187C8—2442no—
188C22—21no—
189C22—21no—
190C22—611no—
191C22—612no—
192C22—611no—
193C22—1221no—
194C22—1221no—
195C22—1221no—
196C22—1221no—
197C22—4884no—
198C22—2442no—
199C22—2442no—
200C22—2442no—
201C22—2442no—
202C22—2442no—
203C22#1451983912yes—
204C22C2×C22⋊#692311yescharacteristic
205C4—21no—
206C4—42no—
207C4—1221no—
208C4—1221no—
209C4—4882no—
210C4#1451983612yes—
211C2—22no—
212C2—1221no—
213C2—1222no—
214C2—1221no—
215C2—4882no—
216C2C2×#1451983611yescharacteristic
217C2C2×#1451983911yescharacteristic
218C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1519
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. D61⋊(C22⋊C8)C2semidirect
2. #16840704C2semidirect
3. #16840614C2semidirect
8. #14519834C22semidirect
10. (C2×#6923)⋊C4C22semidirect
12. C22×D244C4semidirect
16. #14519752C4semidirect
19. C2×C4⋊C4×C61C4semidirect
114. C61#1519semidirect
124. C2×C4⋊C4#6923semidirect