Finite Group Databasebeta

← #21461085

Subgroups — #21461085

Order 7808.

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

normal subgroups only

This group has 280 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#16840733C211yesmaximal, characteristic, complemented
2D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#16840607C212yesmaximal, complemented
4#16840605C212yesmaximal, complemented
5C2×#14519759C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×D61⋊C8—21no—
8#14519834—21no—
9#14519834—21no—
10C22⋊#92420C2212yes—
11C22⋊#92420C2212yes—
12C22×C22⋊D61C411yescharacteristic
13C22×C4×D61C2211yescharacteristic
14#14519759—21no—
15#14519759—21no—
16#14519759—21no—
17#14519759—21no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C411yescharacteristic
20C2×C22⋊Dic61C2211yescharacteristic
21C2×#11758198C411yescharacteristic
22C2×C22⋊C4×C61C411yescharacteristic
23C24×C61C2×C411yescharacteristic
24C23×D61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×C4×C61C2×C411yescharacteristic
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29C2×C22⋊D61—42no—
30C22×Dic61C2×C411yescharacteristic
31C22×Dic61C2×C411yescharacteristic
32C22×Dic61C2311yescharacteristic
33C2×C4×D61—42no—
34C2×C4×D61D411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×#92420—22no—
39C2×#92420—22no—
40#11758213—42no—
41D61⋊C8—42no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50#11758196—21no—
51#11758196—21no—
52C23×C61—21no—
53C23×C61—22no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61C22×C411yescharacteristic
57C22×D61—22no—
58C22×D61—22no—
59C22×D61—41no—
60C22×D61C22⋊C411yescharacteristic
61C22×D61C22⋊C411yescharacteristic
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—41no—
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22⋊C411yescharacteristic
67C22⋊D61—42no—
68C22⋊D61—42no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61C2×D411yescharacteristic
75C2×Dic61C2×D411yescharacteristic
76C4×D61—22no—
77C4×D61—22no—
78C4×D61—41no—
79C4×D61—41no—
80#92420—42no—
81#92420—42no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61—82no—
88C22×C61C2×C22⋊C411yescharacteristic
89C22×C61#13112yes—
90C2×D61—21no—
91C2×D61—21no—
92C2×D61—21no—
93C2×D61—21no—
94C2×D61—21no—
95C2×D61—44no—
96C2×D61#9912yes—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—41no—
100Dic61—21no—
101Dic61—21no—
102Dic61—41no—
103Dic61—41no—
104#1468—611nomaximal, Sylow
105C2×C61—22no—
106C2×C61—81no—
107C2×C61#40811yescharacteristic
108C2×C61C2×#9911yescharacteristic
109C2×C61#41311yescharacteristic
110D61—22no—
111D61—41no—
112C2×#123—611no—
113#407—611no—
114C2×C22⋊C8—611no—
115#324—612no—
116#323—612no—
117C61#146811yescharacteristic, complemented, Sylow
118C22×D4—611no—
119C23×C4—611no—
120C2×M16—1221no—
121C22×C8—1221no—
122#123—1221no—
123#123—1221no—
124#123—1221no—
125#123—1221no—
126C2×C4⋊C4—611no—
127C2×C4⋊C4—611no—
128C2×C22⋊C4—611no—
129C2×C22⋊C4—611no—
130C2×C22⋊C4#692311yescharacteristic
131C22⋊C8—612no—
132C22⋊C8—612no—
133C22⋊C8—1221no—
134C22⋊C8—1221no—
135C24—611no—
136C24C2×#692311yescharacteristic
137C2×D4—1221no—
138C2×D4—1221no—
139C2×D4—2442no—
140C22×C4—611no—
141C22×C4—611no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—2442no—
148C22×C4C2×#692311yescharacteristic
149C22×C4C2×#692311yescharacteristic
150M16—2442no—
151C2×C8—1222no—
152C2×C8—1222no—
153C2×C8—2442no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C23—21no—
165C23—22no—
166C23—41no—
167C23—41no—
168C23—611no—
169C23—611no—
170C23—1222no—
171C23—1222no—
172C23—2441no—
173C23C22×#692311yescharacteristic
174D4—2442no—
175D4—2442no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4C22⋊#692311yescharacteristic
191C2×C4C22⋊#692311yescharacteristic
192C8—2442no—
193C8—2442no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—82no—
200C22—612no—
201C22—1221no—
202C22—1221no—
203C22—1221no—
204C22—1221no—
205C22—1221no—
206C22—2444no—
207C22C2×C22⋊#692311yescharacteristic
208C22#1451986412yes—
209C4—21no—
210C4—21no—
211C4—41no—
212C4—1221no—
213C4—1221no—
214C4—2441no—
215C4—2441no—
216C2—22no—
217C2—81no—
218C2—1222no—
219C2—2441no—
220C2#1684073611yescharacteristic
221C2D61⋊#9911yescharacteristic
222C2#1684074811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #16840733C2semidirect
2. D61⋊(C22⋊C8)C2semidirect
3. #16840607C2semidirect
4. #16840605C2semidirect
117. C61#1468semidirect