Finite Group Databasebeta

← #21446278

Subgroups — #21446278

Order 7808.

378 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14519736C211yesmaximal, characteristic, complemented
2C2×#14519692C212yesmaximal
3#16839625C211yesmaximal, characteristic, complemented
4#16839529C212yesmaximal, complemented
5C2×#123×C61C211yesmaximal, characteristic
6#14519736—24no—
7C2×C4⋊Dic61—21no—
8C2×C22⋊Dic61C2212yes—
9C2×C22⋊Dic61C2212yes—
10C2×C4×Dic61—21no—
11#14519692—24no—
12#14519684—22no—
13C22×D4×C61C2211yescharacteristic
14C23×C4×C61C2211yescharacteristic
15#123×C61—22no—
16#123×C61—21no—
17#123×C61—21no—
18C2×C4⋊C4×C61C412yescomplemented
19C2×C22⋊C4×C61C412yescomplemented
20C2×C22⋊C4×C61C2211yescharacteristic
21C24×C61C2×C411yescharacteristic
22C24×C61C2311yescharacteristic
23C2×D4×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—22no—
26C2×D4×C61—22no—
27C22×C4×C61—22no—
28C22×C4×C61—22no—
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C412yes—
31C22×C4×C61C2×C412yes—
32C22×C4×C61D412yes—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×Dic61—22no—
36C22×Dic61—22no—
37C4⋊C4×C61—22no—
38C4⋊C4×C61—22no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—22no—
42C22⋊C4×C61—22no—
43C22⋊Dic61—22no—
44C22⋊Dic61—22no—
45C22⋊Dic61—22no—
46C22⋊Dic61D414yes—
47C4⋊Dic61—24no—
48C4×Dic61—24no—
49C23×C61—21no—
50C23×C61—22no—
51C23×C61—42no—
52C23×C61—42no—
53C23×C61C22×C411yescharacteristic
54C23×C61C2×D411yescharacteristic
55C23×C61C2×D411yescharacteristic
56C23×C61C2×D412yes—
57C23×C61#4112yes—
58D4×C61—41no—
59D4×C61—42no—
60D4×C61—41no—
61C2×C4×C61—24no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—24no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—42no—
71C2×C4×C61C22⋊C412yes—
72C2×C4×C61C22⋊C412yes—
73C2×Dic61—24no—
74C2×Dic61—44no—
75C2×Dic61—44no—
76C2×Dic61—42no—
77C22×C61—22no—
78C22×C61—22no—
79C22×C61—22no—
80C22×C61—42no—
81C22×C61—42no—
82C22×C61—41no—
83C22×C61—42no—
84C22×C61—82no—
85C22×C61C2×C22⋊C411yescharacteristic
86C22×C61C4×D412yes—
87C22×C61#12011yescharacteristic
88C22×C61#12112yes—
89C22×C61#12311yescharacteristic
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—41no—
93C4×C61—42no—
94Dic61—44no—
95Dic61—82no—
96#1899—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—22no—
99C2×C61—22no—
100C2×C61—21no—
101C2×C61—81no—
102C2×C61#38611yescharacteristic
103C2×C61#41012yes—
104C2×#123D6111yescharacteristic
105C2×#117—611no—
106C2×#99—612no—
107#381—611no—
108#342—612no—
109C61#189911yescharacteristic, complemented, Sylow
110C22×D4C2×D6111yescharacteristic
111C23×C4C2×D6111yescharacteristic
112#123—22no—
113#123—21no—
114#123—21no—
115#117—1224no—
116C2×C4⋊C4—1221no—
117C2×C4⋊C4Dic6112yescomplemented
118C2×C22⋊C4—612no—
119C2×C22⋊C4—612no—
120C2×C22⋊C4Dic6112yescomplemented
121C2×C22⋊C4C2×D6111yescharacteristic
122C2×C42—1221no—
123#99—1224no—
124#95—1222no—
125C24C2×Dic6111yescharacteristic
126C24C22×D6111yescharacteristic
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—21no—
130C2×D4—21no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—1222no—
134C22×C4—1222no—
135C22×C4C2×Dic6111yescharacteristic
136C22×C4C2×Dic6112yes—
137C22×C4C2×Dic6112yes—
138C22×C4C22⋊D6112yes—
139C22×C4C22⋊D6111yescharacteristic
140C22×C4C22⋊D6111yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—1224no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—614no—
149C22⋊C4—1222no—
150C22⋊C4—1222no—
151C22⋊C4—1222no—
152C42—1224no—
153C23—21no—
154C23—22no—
155C23—42no—
156C23—42no—
157C23D4×D6112yes—
158C23#1175822412yes—
159C23C22×Dic6111yescharacteristic
160C23C2×C22⋊D6111yescharacteristic
161C23C2×C22⋊D6111yescharacteristic
162D4—41no—
163D4—42no—
164D4—41no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—1224no—
176C2×C4—2444no—
177C2×C4—2442no—
178C2×C4—2444no—
179C2×C4C22⋊Dic6112yes—
180C2×C4C22⋊Dic6112yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—41no—
188C22—82no—
189C22C2×C22⋊Dic6111yescharacteristic
190C22D4×Dic6112yes—
191C22#1451974511yescharacteristic
192C22#1451974912yes—
193C22#1451975811yescharacteristic
194C4—22no—
195C4—22no—
196C4—42no—
197C4—41no—
198C4—4882no—
199C4—2444no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—81no—
205C2#1683964211yescharacteristic
206C2#1683973612yes—
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC2×#123×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#123D61
hypocenterC61#1899
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14519736C2semidirect
3. #16839625C2semidirect
4. #16839529C2semidirect
18. C2×C4⋊C4×C61C4semidirect
19. C2×C22⋊C4×C61C4semidirect
109. C61#1899semidirect
117. C2×C4⋊C4Dic61semidirect
120. C2×C22⋊C4Dic61semidirect