Finite Group Databasebeta

← #21461217

Subgroups — #21461217

Order 7808.

294 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 60 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#16840734C211yesmaximal, characteristic
2C4×C22⋊#6923C211yesmaximal, characteristic
3#16840616C212yesmaximal, complemented
4#16840615C212yesmaximal, complemented
5C22⋊Q8×D61C211yesmaximal, characteristic
6C2×#11758217—21no—
7C2×C22⋊#6923—21no—
8C2×C4×#6923—21no—
9#14519834—21no—
10#14519834C2212yes—
11(C2×#6923)⋊C4C2212yes—
12C2×Q8×D61C411yescharacteristic, complemented
13C22×C4×D61C2211yescharacteristic
14#14519757C2211yescharacteristic
15#14519756C411yescharacteristic, complemented
16#14519755—21no—
17#14519754—21no—
18#14519753C2211yescharacteristic
19C4⋊C4×D61—21no—
20C4⋊C4×D61C411yescharacteristic, complemented
21C22⋊C4×D61—21no—
22C22⋊Q8×C61C411yescharacteristic, complemented
23C23×D61D411yescharacteristic
24C22×#6923—22no—
25C2×Q8×C61C2×C411yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C22×Dic61D411yescharacteristic
28Q8×D61—42no—
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×C4×D61—42no—
32C2×C4×D61C2×C411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×C4×D61C2311yescharacteristic
36C2×Dic122—21no—
37C2×Dic122C2×C411yescharacteristic
38C22⋊#6923—24no—
39#11758217—42no—
40C2×#92420—22no—
41C4×#6923—42no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61C2×C411yescharacteristic
44C22⋊C4×C61—21no—
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51#11758196—21no—
52#11758196—21no—
53C23×C61C22⋊C411yescharacteristic
54C22×D61—22no—
55C22×D61—22no—
56C22×D61—41no—
57C22×D61C22⋊C411yescharacteristic
58C22×D61C2×D411yescharacteristic
59C2×#6923—24no—
60C2×#6923—42no—
61C2×#6923—42no—
62Q8×C61—41no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—41no—
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C22×C411yescharacteristic
68C2×Dic61—22no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C2×D411yescharacteristic
73C4×D61—22no—
74C4×D61—22no—
75C4×D61—41no—
76C4×D61—41no—
77C4×D61—42no—
78C4×D61—42no—
79Dic122—42no—
80Dic122—41no—
81#92420—42no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61C2×C22⋊C411yescharacteristic
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—21no—
89C2×D61—21no—
90C2×D61—44no—
91C2×D61#10412yes—
92C2×D61#13712yes—
93#6923—44no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—41no—
97C4×C61—41no—
98Dic61—21no—
99Dic61—41no—
100Dic61—41no—
101Dic61#9912yes—
102#1508—611nomaximal, Sylow
103C2×C61—41no—
104C2×C61C2×#9911yescharacteristic
105C2×C61#41911yescharacteristic
106C2×C61C2×#10411yescharacteristic
107D61—22no—
108D61—22no—
109C2×C22⋊Q8—611no—
110#407—611no—
111C4×C22⋊C4—611no—
112#328—612no—
113#328—612no—
114C61#150811yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C23×C4—611no—
117C2×M16—1221no—
118C22⋊Q8—611no—
119C22⋊Q8—611no—
120C22⋊Q8—611no—
121C22⋊Q8—1221no—
122C22⋊Q8—1221no—
123C22⋊Q8#692311yescharacteristic, complemented
124C2×C4⋊C4—611no—
125C2×C4⋊C4—1221no—
126C2×C22⋊C4—1221no—
127C2×C22⋊C4—1221no—
128C2×C42—1221no—
129C22⋊C8—612no—
130C22⋊C8—1221no—
131#95—612no—
132C24—611no—
133C2×Q8—611no—
134C2×Q8—1221no—
135C2×Q8—2442no—
136C2×Q8C2×#692311yescharacteristic
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—611no—
140C22×C4—611no—
141C22×C4—611no—
142C22×C4—1221no—
143C22×C4—1221no—
144C22×C4—1222no—
145C22×C4—2442no—
146C22×C4C2×#692311yescharacteristic
147M16—2442no—
148C2×C8—1222no—
149C4⋊C4—21no—
150C4⋊C4—611no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C4⋊C4C2×#692311yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—1221no—
158C22⋊C4—1221no—
159C22⋊C4—1224no—
160C22⋊C4—1221no—
161C42—2442no—
162C23—611no—
163C23—611no—
164C23—1222no—
165C23—1222no—
166C23—2441no—
167C23C22⋊#692311yescharacteristic
168Q8—41no—
169Q8—2441no—
170Q8—2442no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1224no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4C22⋊#692311yescharacteristic
189C2×C4C22×#692311yescharacteristic
190C8—2442no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—612no—
195C22—612no—
196C22—1221no—
197C22—1221no—
198C22—1221no—
199C22—1221no—
200C22—2444no—
201C22C2×C22⋊#692311yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—612no—
207C4—1221no—
208C4—2444no—
209C4—2441no—
210C4—2441no—
211C2—41no—
212C2—1222no—
213C2—1222no—
214C2D61⋊#9911yescharacteristic
215C2#1684075511yescharacteristic
216C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1508
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #16840616C2semidirect
4. #16840615C2semidirect
12. C2×Q8×D61C4semidirect
15. #14519756C4semidirect
20. C4⋊C4×D61C4semidirect
22. C22⋊Q8×C61C4semidirect
114. C61#1508semidirect
123. C22⋊Q8#6923semidirect