Finite Group Databasebeta

← #21444395

Subgroups — #21444395

Order 7808.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#16840298C211yesmaximal, characteristic
2#16839812C211yesmaximal, characteristic, complemented
3#16839629C211yesmaximal, characteristic, complemented
4#16839499C211yesmaximal, characteristic, complemented
5#16839497C211yesmaximal, characteristic
6#16839495C211yesmaximal, characteristic
7C61×#328C211yesmaximal, characteristic, complemented
8#14519772—21no—
9#14519768C411yescharacteristic, complemented
10#14519766C411yescharacteristic, complemented
11#14519761—21no—
12#14519751C2211yescharacteristic
13Q8×Dic61C411yescharacteristic, complemented
14#14519739C411yescharacteristic, complemented
15#14519737—21no—
16#14519735—21no—
17C2×C4×Dic61C2211yescharacteristic
18#14519706—21no—
19C22⋊#92418C2211yescharacteristic
20C8×Dic61—21no—
21#14519684—21no—
22#14519684—21no—
23#14519684C2211yescharacteristic
24C22⋊Q8×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C2×Q8×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32C22×Dic61D411yescharacteristic
33C22×Dic61D411yescharacteristic
34C2×D244C2×C411yescharacteristic
35C2×C4×D61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61C2×C411yescharacteristic
39C22⋊C4×C61—21no—
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61C2×C411yescharacteristic
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61C2×C411yescharacteristic
51C4×Dic61D411yescharacteristic
52C4×Dic61D411yescharacteristic
53C2×#92418—21no—
54C23×C61C2×D411yescharacteristic
55C22×D61—21no—
56Q8×C61—41no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61C22×C411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C22⋊D61—41no—
66C22⋊D61—41no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74C2×Dic61C22⋊C411yescharacteristic
75C2×Dic61C22⋊C411yescharacteristic
76C2×Dic61C22⋊C411yescharacteristic
77C2×Dic61C22⋊C411yescharacteristic
78D244—41no—
79C4×D61—42no—
80C8×C61—41no—
81#92418—41no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61C2×C22⋊C411yescharacteristic
85C22×C61#13511yescharacteristic
86C22×C61#13511yescharacteristic
87C2×D61—41no—
88C2×D61—41no—
89C2×D61—41no—
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—41no—
93C4×C61—41no—
94C4×C61—81no—
95Dic61—21no—
96Dic61—21no—
97Dic61—21no—
98Dic61—21no—
99Dic61—41no—
100Dic61—81no—
101#1521—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—21no—
104C2×C61#41011yescharacteristic
105C2×C61#41611yescharacteristic
106C2×C61#42111yescharacteristic
107D61—81no—
108#529—611no—
109#431—611no—
110#383—611no—
111#328—611no—
112#328D6111yescharacteristic, complemented
113#327—611no—
114#327—611no—
115C61#152111yescharacteristic, complemented, Sylow
116#126—1221no—
117#125—611no—
118#124—611no—
119#123—1221no—
120C22⋊Q8C2×D6111yescharacteristic
121#121—611no—
122C4×Q8—611no—
123C4×D4—611no—
124C4×D4—1221no—
125#117—1221no—
126C2×C42—611no—
127C4⋊C8—1221no—
128C22⋊C8—611no—
129C22⋊C8C2×D6111yescharacteristic
130C4×C8—1221no—
131#95—611no—
132#95—1221no—
133#95—1221no—
134#95C2×D6111yescharacteristic
135C2×Q8C4×D6111yescharacteristic
136C2×D4—611no—
137C2×D4—1221no—
138C22×C4—21no—
139C22×C4—611no—
140C22×C4—611no—
141C22×C4—1221no—
142C22×C4—1221no—
143C22×C4C22×D6111yescharacteristic
144C2×C8—21no—
145C2×C8—1221no—
146C4⋊C4—21no—
147C4⋊C4—611no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4C4×D6111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C42—611no—
158C42—611no—
159C42—611no—
160C42—611no—
161C42—1221no—
162C23—1221no—
163C23D4×D6111yescharacteristic
164Q8—41no—
165D4—2441no—
166D4—2441no—
167D4—2441no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—2442no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4C2×C4×D6111yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C8—41no—
189C8—2441no—
190C22—21no—
191C22—21no—
192C22—2441no—
193C22—2441no—
194C22—2441no—
195C22C22⋊C4×D6111yescharacteristic
196C22#1451979811yescharacteristic
197C22#1451980011yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—1221no—
204C4—1221no—
205C4—1221no—
206C4—1221no—
207C4—4881no—
208C4—2441no—
209C2—21no—
210C2—21no—
211C2—4881no—
212C2#1683973411yescharacteristic
213C2#1683975711yescharacteristic
214C2#1683977711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61C2×C22⋊C4
hypercenter#328D61
hypocenterC61#1521
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #16839812C2semidirect
3. #16839629C2semidirect
4. #16839499C2semidirect
7. C61×#328C2semidirect
9. #14519768C4semidirect
10. #14519766C4semidirect
13. Q8×Dic61C4semidirect
14. #14519739C4semidirect
112. #328D61semidirect
115. C61#1521semidirect