Finite Group Databasebeta

← #21446805

Subgroups — #21446805

Order 7808.

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

normal subgroups only

This group has 324 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
1#16839622C211yesmaximal, characteristic
2C4×C22⋊Dic61C211yesmaximal, characteristic
3#16839529C214yesmaximal
4C2×C22⋊Q8×C61C211yesmaximal, characteristic
5C2×C4⋊Dic61—21no—
6C2×C22⋊Dic61C2212yes—
7C2×C22⋊Dic61C2212yes—
8C2×C4×Dic61—21no—
9#14519684—21no—
10#14519684—21no—
11C22×Q8×C61C411yescharacteristic, complemented
12C23×C4×C61C2211yescharacteristic
13C22⋊Q8×C61—21no—
14C22⋊Q8×C61—21no—
15C22⋊Q8×C61—21no—
16C22⋊Q8×C61—21no—
17C2×C4⋊C4×C61C411yescharacteristic, complemented
18C2×C4⋊C4×C61C412yescomplemented
19C2×C22⋊C4×C61C2212yes—
20C24×C61C2311yescharacteristic
21C2×Q8×C61—21no—
22C2×Q8×C61—21no—
23C2×Q8×C61—42no—
24C22×C4×C61—42no—
25C22×C4×C61C2×C411yescharacteristic
26C22×C4×C61C2×C412yes—
27C22×C4×C61C2×C412yes—
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×Dic61—22no—
34C22×Dic61—22no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—22no—
38C4⋊C4×C61—22no—
39C22⋊C4×C61—22no—
40C22⋊C4×C61—22no—
41C22⋊Dic61—22no—
42C22⋊Dic61—24no—
43C22⋊Dic61Q814yescomplemented
44C4⋊Dic61—42no—
45C4×Dic61—42no—
46C23×C61—41no—
47C23×C61—41no—
48C23×C61C22×C411yescharacteristic
49C23×C61C2×D411yescharacteristic
50C23×C61C2×D411yescharacteristic
51C23×C61C2×Q812yes—
52C23×C61#4112yes—
53Q8×C61—42no—
54Q8×C61—42no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—42no—
64C2×C4×C61—42no—
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C22⋊C411yescharacteristic
68C2×C4×C61C22⋊C411yescharacteristic
69C2×Dic61—24no—
70C2×Dic61—42no—
71C2×Dic61—42no—
72C2×Dic61—42no—
73C2×Dic61—42no—
74C2×Dic61—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61—42no—
82C22×C61—42no—
83C22×C61C2×C22⋊C411yescharacteristic
84C22×C61C4×Q812yes—
85C22×C61C22⋊Q812yes—
86C22×C61#12411yescharacteristic
87C22×C61C4⋊Q811yescharacteristic
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—42no—
92C4×C61—42no—
93C4×C61#9912yes—
94Dic61—44no—
95Dic61—82no—
96#1996—611nomaximal, Sylow
97C2×C61—22no—
98C2×C61—21no—
99C2×C61—22no—
100C2×C61—21no—
101C2×C61#39111yescharacteristic
102C2×C61C2×#9911yescharacteristic
103C2×C61#41011yescharacteristic
104C2×C22⋊Q8D6111yescharacteristic
105#380—611no—
106C4×C22⋊C4—611no—
107#342—614no—
108C61#199611yescharacteristic, complemented, Sylow
109C22×Q8Dic6111yescharacteristic, complemented
110C23×C4C2×D6111yescharacteristic
111C22⋊Q8—21no—
112C22⋊Q8—21no—
113C22⋊Q8—21no—
114C22⋊Q8—21no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4Dic6111yescharacteristic, complemented
117C2×C4⋊C4Dic6112yescomplemented
118C2×C22⋊C4—612no—
119C2×C22⋊C4—612no—
120C2×C22⋊C4C2×D6112yes—
121C2×C42—1221no—
122#95—1221no—
123#95—1221no—
124C24C22×D6111yescharacteristic
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—42no—
129C22×C4—1222no—
130C22×C4—1222no—
131C22×C4C2×Dic6111yescharacteristic
132C22×C4C2×Dic6112yes—
133C22×C4C2×Dic6112yes—
134C22×C4C2×Dic6111yescharacteristic
135C22×C4C22⋊D6111yescharacteristic
136C22×C4C22⋊D6111yescharacteristic
137C22×C4C22⋊D6111yescharacteristic
138C22×C4C22⋊D6111yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—2442no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—614no—
147C22⋊C4—1222no—
148C22⋊C4—1224no—
149C42—2442no—
150C23—41no—
151C23—41no—
152C23Q8×D6112yes—
153C23#1175822612yes—
154C23C22×Dic6111yescharacteristic
155C23C2×C22⋊D6111yescharacteristic
156C23C2×C22⋊D6111yescharacteristic
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—1224no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4—2442no—
174C2×C4—2442no—
175C2×C4C22⋊Dic6111yescharacteristic
176C2×C4C22⋊Dic6111yescharacteristic
177C2×C4C22⋊Dic6111yescharacteristic
178C2×C4C22⋊Dic6111yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×C22⋊Dic6111yescharacteristic
188C22Q8×Dic6112yes—
189C22#1451975312yes—
190C22#1451976611yescharacteristic
191C22#1451977511yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—42no—
196C4—42no—
197C4—4882no—
198C4—2444no—
199C4#1451969212yes—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2#1683966911yescharacteristic
205C2C2×#1451969211yescharacteristic
206C2#1683973611yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC2×C22⋊Q8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊Q8D61
hypocenterC61#1996
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
11. C22×Q8×C61C4semidirect
17. C2×C4⋊C4×C61C4semidirect
18. C2×C4⋊C4×C61C4semidirect
43. C22⋊Dic61Q8semidirect
108. C61#1996semidirect
109. C22×Q8Dic61semidirect
116. C2×C4⋊C4Dic61semidirect
117. C2×C4⋊C4Dic61semidirect