Finite Group Databasebeta

← #21461944

Subgroups — #21461944

Order 7808.

384 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 92 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×C4⋊#92420C211yesmaximal, characteristic, complemented
2C2×#14519834C212yesmaximal, complemented
3C2×C22⋊#92420C212yesmaximal, complemented
4C2×#14519832C211yesmaximal, characteristic, complemented
5C2×#14519737C211yesmaximal, characteristic
6C22×#92420C2212yes—
7C22×#92420C2212yes—
8C4⋊#92420—22no—
9#14519834—24no—
10C22⋊#92420—24no—
11#14519832—22no—
12C22×C22⋊D61C411yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519737—22no—
16#14519737—22no—
17C2×#11758196C411yescharacteristic
18C2×#11758198C411yescharacteristic
19C2×C4×Dic61C2211yescharacteristic
20C2×C22⋊C4×C61C411yescharacteristic
21C24×C61C2×C411yescharacteristic
22C23×D61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C2×C22⋊D61—22no—
26C2×C22⋊D61—22no—
27C2×C22⋊D61—22no—
28C22×Dic61—22no—
29C22×Dic61—21no—
30C22×Dic61—21no—
31C22×Dic61—22no—
32C22×Dic61C2×C411yescharacteristic
33C22×Dic61C2×C411yescharacteristic
34C22×Dic61C2311yescharacteristic
35C2×C4×D61—22no—
36C2×C4×D61—21no—
37C2×C4×D61—21no—
38C2×C4×D61—22no—
39C2×#92420—22no—
40C2×#92420—22no—
41C2×#92420—22no—
42C2×#92420—22no—
43C2×#92420—22no—
44C2×#92420D414yescomplemented
45C22⋊C4×C61—22no—
46#11758198—22no—
47#11758196—22no—
48C4×Dic61D412yes—
49C4×Dic61D412yes—
50C23×C61—21no—
51C23×C61—22no—
52C23×C61—21no—
53C23×C61—22no—
54C23×C61M1612yes—
55C23×C61C22×C411yescharacteristic
56C22×D61—21no—
57C22×D61—22no—
58C22×D61—21no—
59C22×D61—22no—
60C22×D61M1612yes—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61C22⋊C412yes—
65C22⋊D61—28no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—22no—
70C2×Dic61—42no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61C22⋊C412yes—
74C2×Dic61C2×D411yescharacteristic
75C2×Dic61C2×D412yes—
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61#4112yes—
78C4×D61—42no—
79C4×D61—41no—
80C4×D61—41no—
81#92420—24no—
82#92420—42no—
83C22×C61—22no—
84C22×C61—24no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61—42no—
88C22×C61C2×C22⋊C411yescharacteristic
89C22×C61C4×D412yes—
90C22×C61C2×M1611yescharacteristic
91C22×C61C2×M1611yescharacteristic
92C22×C61#13112yes—
93C2×D61—22no—
94C2×D61—24no—
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—42no—
98C4×C61—22no—
99C4×C61—41no—
100Dic61—22no—
101Dic61—41no—
102Dic61#12112yes—
103Dic61#12411yescharacteristic
104Dic61#12711yescharacteristic
105#1955—611nomaximal, Sylow
106C2×C61—42no—
107C2×C61#39011yescharacteristic
108C2×C61#40711yescharacteristic
109C2×C61#40811yescharacteristic
110C2×C61#43512yes—
111C2×C61#43512yes—
112D61—42no—
113C2×C4×D4—611no—
114C2×C4⋊C8—611no—
115C2×C22⋊C8—612no—
116C2×C22⋊C8—612no—
117C2×#97—611no—
118C61#195511yescharacteristic, complemented, Sylow
119C22×D4—611no—
120C23×C4—611no—
121C23×C4—611no—
122C22×C8—612no—
123C22×C8—612no—
124C4×D4—1222no—
125C4×D4—1222no—
126C2×C4⋊C4—611no—
127C2×C22⋊C4—611no—
128C2×C22⋊C4#692311yescharacteristic
129C2×C42—611no—
130C4⋊C8—1222no—
131C22⋊C8—1224no—
132C22⋊C8—1224no—
133#97—1222no—
134C24—611no—
135C24C2×#692311yescharacteristic
136C2×D4—1222no—
137C2×D4—1222no—
138C2×D4—1222no—
139C22×C4—611no—
140C22×C4—611no—
141C22×C4—611no—
142C22×C4—1222no—
143C22×C4—1221no—
144C22×C4—1221no—
145C22×C4—1222no—
146C22×C4—1222no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—1222no—
150C22×C4C2×#692311yescharacteristic
151C22×C4C2×#692311yescharacteristic
152C2×C8—614no—
153C2×C8—1222no—
154C2×C8—1222no—
155C2×C8—1222no—
156C2×C8—1222no—
157C2×C8—1222no—
158C4⋊C4—1222no—
159C22⋊C4—22no—
160C22⋊C4—1222no—
161C42—612no—
162C42—612no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23—612no—
168C23—1221no—
169C23—1222no—
170C23—1221no—
171C23—1222no—
172C23#1175821312yes—
173C23C22×#692311yescharacteristic
174D4—1228no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—611no—
179C2×C4—611no—
180C2×C4—612no—
181C2×C4—612no—
182C2×C4—612no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—1222no—
187C2×C4—2442no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2442no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4C22⋊#692312yes—
194C8—1224no—
195C8—2442no—
196C22—22no—
197C22—24no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—1222no—
202C22—1224no—
203C22—2441no—
204C22—2441no—
205C22—2442no—
206C22C2×C22⋊#692311yescharacteristic
207C22D4×#692312yes—
208C22D61⋊M1611yescharacteristic
209C22C2×#1175821311yescharacteristic
210C22#1451986412yes—
211C4—22no—
212C4—41no—
213C4—612no—
214C4—611no—
215C4—611no—
216C4—1222no—
217C4—2441no—
218C2—42no—
219C2—2442no—
220C2#1684071411yescharacteristic
221C2#1684073311yescharacteristic
222C2#1684073511yescharacteristic
223C2#1684079112yes—
224C2#1684079412yes—
subgroupG/H
center, FrattiniC23C22×#6923
commutator, socleC23×C61C22×C4
FittingC2×C22⋊C4×C61C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1955
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#92420C2semidirect
2. C2×#14519834C2semidirect
3. C2×C22⋊#92420C2semidirect
4. C2×#14519832C2semidirect
44. C2×#92420D4semidirect
118. C61#1955semidirect