Finite Group Databasebeta

← #21444419

Subgroups — #21444419

Order 7808.

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

normal subgroups only

This group has 212 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#125×D61C211yesmaximal, characteristic
2#16839817C211yesmaximal, characteristic
3#16839714C211yesmaximal, characteristic
4#16839504C211yesmaximal, characteristic, complemented
5#16839503C211yesmaximal, characteristic, complemented
6#16839503C211yesmaximal, characteristic, complemented
7C61×#330C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9#14519769C2211yescharacteristic
10#14519768C411yescharacteristic
11#14519768C411yescharacteristic
12#14519767—21no—
13#14519767—21no—
14C4⋊C4×D61—21no—
15C4⋊C4×D61—21no—
16C4⋊C4×D61C411yescharacteristic
17C4⋊C4×D61C411yescharacteristic
18C42×D61C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519688C2211yescharacteristic
22#14519688C2211yescharacteristic
23C8×Dic61—21no—
24#125×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×C4×D61—21no—
28C2×C4×D61—21no—
29C2×C4×D61C2×C411yescharacteristic
30C2×C4×D61D411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C4⋊C4×C61C2×C411yescharacteristic
38C42×C61C2311yescharacteristic
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48#11758196—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54#11758189—24no—
55C22×D61C22⋊C411yescharacteristic
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61C22×C411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66C4×D61—22no—
67C4×D61—22no—
68C4×D61—41no—
69C4×D61—42no—
70C4×D61—42no—
71C8×C61—22no—
72C8×C61—41no—
73#92418—22no—
74#92418—41no—
75C22×C61C2×C22⋊C411yescharacteristic
76C2×D61—21no—
77C2×D61—21no—
78C2×D61#10412yes—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—41no—
83C4×C61—41no—
84Dic61—21no—
85Dic61—21no—
86Dic61—41no—
87Dic61—41no—
88Dic61#10112yes—
89#1528—611nomaximal, Sylow
90C2×C61C2×#10111yescharacteristic
91C2×C61C2×#10411yescharacteristic
92C2×C61#42111yescharacteristic
93D61—22no—
94C2×#125—611no—
95#432—611no—
96C4×M16—611no—
97#330—611no—
98#330—611no—
99#330—611no—
100#330D6111yescharacteristic, complemented
101C61#152811yescharacteristic, complemented, Sylow
102C2×M16—1221no—
103#125—611no—
104#125—611no—
105#125—611no—
106#125—1221no—
107#125—1221no—
108#125C2×D6111yescharacteristic
109C2×C4⋊C4—611no—
110C2×C4⋊C4—611no—
111C2×C4⋊C4—1221no—
112C2×C4⋊C4—1221no—
113C2×C42—611no—
114C4⋊C8—1221no—
115C22⋊C8—1221no—
116#97—611no—
117#97—611no—
118#97C2×D6111yescharacteristic
119#97C2×D6111yescharacteristic
120C4×C8—1221no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—611no—
124C22×C4—1221no—
125C22×C4—1221no—
126M16—1224no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1221no—
130C2×C8—1221no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—611no—
134C4⋊C4—611no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4C4×D6111yescharacteristic
144C4⋊C4C4×D6111yescharacteristic
145C42—611no—
146C42—611no—
147C42—611no—
148C42C22×D6111yescharacteristic
149C23—611no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—611no—
153C2×C4—611no—
154C2×C4—611no—
155C2×C4—1222no—
156C2×C4—1222no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—2441no—
160C2×C4—2442no—
161C2×C4—2442no—
162C2×C4C2×C4×D6111yescharacteristic
163C2×C4D4×D6111yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C8—22no—
166C8—41no—
167C8—1222no—
168C8—2441no—
169C22—612no—
170C22—1221no—
171C22—1221no—
172C22C22⋊C4×D6111yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—612no—
179C4—1221no—
180C4—1221no—
181C4—2441no—
182C4—2441no—
183C2—1222no—
184C2#101×D6111yescharacteristic
185C2#104×D6111yescharacteristic
186C2#1683977711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#330C2
socleC22×C61C2×C22⋊C4
hypercenter#330D61
hypocenterC61#1528
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #16839504C2semidirect
5. #16839503C2semidirect
6. #16839503C2semidirect
7. C61×#330C2semidirect
100. #330D61semidirect
101. C61#1528semidirect