Finite Group Databasebeta

← #21461678

Subgroups — #21461678

Order 7808.

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

normal subgroups only

This group has 312 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×#14519844C211yesmaximal, characteristic, complemented
2C2×C4⋊#92420C211yesmaximal, characteristic, complemented
3C2×#14519834C212yesmaximal
4#16840628C212yesmaximal, complemented
5C2×#14519735C211yesmaximal, characteristic
6C22×#92420C2212yes—
7C22×#92420C2212yes—
8#14519844—22no—
9C4⋊#92420—22no—
10#14519834—24no—
11C22×C4×D61C2211yescharacteristic
12#14519735—22no—
13#14519735—22no—
14C2×C4⋊Dic61C411yescharacteristic
15C2×#11758198C411yescharacteristic
16C2×#11758198C411yescharacteristic
17C2×C4×Dic61C2211yescharacteristic
18C2×C4×Dic61C2211yescharacteristic
19C2×C4⋊C4×C61C411yescharacteristic
20C23×D61C2×C411yescharacteristic
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61C2×C411yescharacteristic
25C22×Dic61C2×C411yescharacteristic
26C22×Dic61C2311yescharacteristic
27C2×C4×D61—21no—
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×C4×D61D412yes—
32C2×C4×D61Q812yes—
33C2×#92420—22no—
34C2×#92420—22no—
35C2×#92420—22no—
36C2×#92420—22no—
37C2×#92420—22no—
38C2×#92420—22no—
39C4⋊C4×C61—22no—
40#11758198—22no—
41#11758198—22no—
42C4⋊Dic61—22no—
43C4×Dic61—21no—
44C4×Dic61—21no—
45C4×Dic61D412yes—
46C4×Dic61D412yes—
47C23×C61C22×C411yescharacteristic
48C22×D61—21no—
49C22×D61—21no—
50C22×D61—22no—
51C22×D61—22no—
52C22×D61C4⋊C412yes—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—22no—
56C2×C4×C61—21no—
57C2×C4×C61—22no—
58C2×C4×C61C22⋊C412yes—
59C2×C4×C61C4⋊C412yes—
60C2×Dic61—22no—
61C2×Dic61—21no—
62C2×Dic61—22no—
63C2×Dic61C22⋊C412yes—
64C2×Dic61C2×D411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67C2×Dic61C2×Q811yescharacteristic
68C2×Dic61#4111yescharacteristic
69C2×Dic61#4111yescharacteristic
70C4×D61—22no—
71C4×D61—22no—
72C4×D61—22no—
73C4×D61—22no—
74#92420—42no—
75#92420—42no—
76C22×C61C2×C22⋊C411yescharacteristic
77C22×C61C2×C4⋊C411yescharacteristic
78C22×C61#11711yescharacteristic
79C22×C61#13112yes—
80C22×C61#13112yes—
81C2×D61—22no—
82C2×D61—24no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—42no—
86C4×C61—22no—
87C4×C61—22no—
88C4×C61—41no—
89Dic61—22no—
90Dic61—41no—
91Dic61#12111yescharacteristic
92Dic61#12111yescharacteristic
93Dic61C22⋊Q811yescharacteristic
94Dic61C22⋊Q811yescharacteristic
95#1798—611nomaximal, Sylow
96C2×C61#38011yescharacteristic
97C2×C61#40811yescharacteristic
98C2×C61#40811yescharacteristic
99C2×C61#42412yes—
100C2×C61#43312yes—
101D61—42no—
102C2×#117—611no—
103C2×C4⋊C8—611no—
104C2×C4⋊C8—611no—
105C2×C22⋊C8—612no—
106#336—612no—
107C61#179811yescharacteristic, complemented, Sylow
108C23×C4—611no—
109C22×C8—612no—
110C22×C8—612no—
111#117—1222no—
112#117—1222no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4#692311yescharacteristic
115C2×C22⋊C4—611no—
116C2×C22⋊C4—611no—
117C2×C42—611no—
118C2×C42—611no—
119C4⋊C8—1222no—
120C4⋊C8—1222no—
121C22⋊C8—1224no—
122C24—611no—
123C22×C4—611no—
124C22×C4—611no—
125C22×C4—612no—
126C22×C4—612no—
127C22×C4—611no—
128C22×C4—1221no—
129C22×C4—1221no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4C2×#692311yescharacteristic
133C22×C4C2×#692311yescharacteristic
134C22×C4C2×#692311yescharacteristic
135C2×C8—1222no—
136C2×C8—1222no—
137C2×C8—1222no—
138C2×C8—1222no—
139C2×C8—1222no—
140C2×C8—1222no—
141C4⋊C4—22no—
142C4⋊C4—1222no—
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C42—612no—
146C42—612no—
147C42—1221no—
148C42—1221no—
149C23—612no—
150C23—1221no—
151C23—1221no—
152C23—1222no—
153C23—1222no—
154C23C22×#692311yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—612no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—1222no—
174C2×C4C4⋊#692312yes—
175C2×C4C22⋊#692312yes—
176C8—2442no—
177C8—2442no—
178C22—1222no—
179C22—1224no—
180C22—2441no—
181C22—2441no—
182C22—2442no—
183C22C2×C22⋊#692311yescharacteristic
184C22C2×C4⋊#692311yescharacteristic
185C22#1451985611yescharacteristic
186C22#1451986412yes—
187C22#1451986512yes—
188C4—22no—
189C4—22no—
190C4—41no—
191C4—611no—
192C4—611no—
193C4—611no—
194C4—611no—
195C4—1222no—
196C4—2441no—
197C2—2442no—
198C2#1684070411yescharacteristic
199C2#1684073511yescharacteristic
200C2#1684073711yescharacteristic
201C2#1684076912yes—
202C2#1684078712yes—
subgroupG/H
center, FrattiniC23C22×#6923
commutator, socleC23×C61C22×C4
FittingC2×C4⋊C4×C61C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1798
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519844C2semidirect
2. C2×C4⋊#92420C2semidirect
4. #16840628C2semidirect
107. C61#1798semidirect