Finite Group Databasebeta

← #21444381

Subgroups — #21444381

Order 7808.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840314C211yesmaximal, characteristic
2#16839812C211yesmaximal, characteristic
3#16839626C211yesmaximal, characteristic
4#16839500C211yesmaximal, characteristic
5#16839499C211yesmaximal, characteristic
6#16839498C211yesmaximal, characteristic
7C61×#328C211yesmaximal, characteristic
8#14519776C411yescharacteristic, complemented
9#14519775C411yescharacteristic, complemented
10#14519767—21no—
11#14519756C2211yescharacteristic
12#14519754—21no—
13Q8×Dic61C411yescharacteristic, complemented
14#14519742—21no—
15#14519742C411yescharacteristic, complemented
16#14519733—21no—
17C2×#11758196—21no—
18C2×C4×Dic61C2211yescharacteristic
19#14519706—21no—
20C22⋊#92418C2211yescharacteristic
21C8×Dic61—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
30C22×Dic61—21no—
31C22×Dic61D411yescharacteristic
32C22×Dic61D411yescharacteristic
33C2×Dic122—21no—
34C2×Dic122C2×C411yescharacteristic
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61C2×C411yescharacteristic
38C22⋊C4×C61—21no—
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—42no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50C4×Dic61C2×C411yescharacteristic
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C23×C61C2×D411yescharacteristic
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
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C22⋊C411yescharacteristic
75C2×Dic61SD1612yes—
76C2×Dic61Q1612yes—
77Dic122—42no—
78Dic122—41no—
79C8×C61—41no—
80#92418—41no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61C2×C22⋊C411yescharacteristic
84C22×C61C2×SD1611yescharacteristic
85C22×C61C2×Q1611yescharacteristic
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—41no—
89C4×C61—41no—
90C4×C61—81no—
91Dic61—21no—
92Dic61—21no—
93Dic61—41no—
94Dic61—41no—
95Dic61—81no—
96Dic61#10312yes—
97Dic61#10312yes—
98#1518—611nomaximal, Sylow
99C2×C61—21no—
100C2×C61—21no—
101C2×C61#41011yescharacteristic
102C2×C61C2×#10311yescharacteristic
103C2×C61#42111yescharacteristic
104#533—611no—
105#431—611no—
106#382—611no—
107#328—611no—
108#328—611no—
109#328—611no—
110#328D6111yescharacteristic
111C61#151811yescharacteristic, complemented, Sylow
112C4⋊Q8—611no—
113C4⋊Q8—611no—
114#125—1221no—
115C22⋊Q8—611no—
116C22⋊Q8—1221no—
117C22⋊Q8C2×D6111yescharacteristic
118C4×Q8—611no—
119C4×Q8—611no—
120C4×Q8—1221no—
121#117—1221no—
122C2×C4⋊C4—1221no—
123C2×C42—611no—
124C4⋊C8—1221no—
125C22⋊C8—611no—
126C22⋊C8C2×D6111yescharacteristic
127C4×C8—1221no—
128#95—611no—
129#95—1221no—
130#95C2×D6111yescharacteristic
131C2×Q8—611no—
132C2×Q8—1221no—
133C2×Q8C4×D6111yescharacteristic
134C22×C4—21no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—1221no—
138C22×C4C22×D6111yescharacteristic
139C2×C8—21no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—611no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—2442no—
150C4⋊C4C4×D6111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1221no—
153C42—611no—
154C42—611no—
155C42—611no—
156C42—611no—
157C42—1221no—
158C42—1221no—
159C23D4×D6111yescharacteristic
160Q8—41no—
161Q8—2441no—
162Q8—2442no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—611no—
170C2×C4—611no—
171C2×C4—612no—
172C2×C4—612no—
173C2×C4—611no—
174C2×C4—611no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4C2×C4×D6111yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C8—41no—
184C8—2441no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D6111yescharacteristic
188C22SD16×D6111yescharacteristic
189C22Q16×D6111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—612no—
196C4—612no—
197C4—1221no—
198C4—1221no—
199C4—4881no—
200C4—2441no—
201C4—2441no—
202C2—21no—
203C2—21no—
204C2#1683973411yescharacteristic
205C2#103×D6111yescharacteristic
206C2#1683977711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61C2×C22⋊C4
hypercenter#328D61
hypocenterC61#1518
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
8. #14519776C4semidirect
9. #14519775C4semidirect
13. Q8×Dic61C4semidirect
15. #14519742C4semidirect
111. C61#1518semidirect