Finite Group Databasebeta

← #21457027

Subgroups — #21457027

Order 7808.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840319C211yesmaximal, characteristic
2C2×#14519769C211yesmaximal, characteristic
3#16840171C212yesmaximal, complemented
4#16840131C212yesmaximal, complemented
5#16840098C212yesmaximal
6#16840093C212yesmaximal
7#16840070C214yesmaximal, complemented
8C61×#432C211yesmaximal, characteristic
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519769—21no—
12#14519769—21no—
13#14519769—21no—
14#14519769C2212yes—
15#14519769C2212yes—
16#14519756—21no—
17#14519756C2212yes—
18C4×Dic122—21no—
19C4×Dic122C2212yes—
20#14519736—21no—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196—21no—
24C2×#11758196—21no—
25#14519711C2214yes—
26#14519709C2214yes—
27#14519702C2214yes—
28#14519702C2214yes—
29C2×C42×C61C2211yescharacteristic
30C4⋊C8×C61C2212yes—
31C22⋊C8×C61C2212yes—
32#97×C61C2212yes—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61—21no—
38C2×Dic122—21no—
39C2×Dic122C2312yes—
40C2×C8×C61C2314yes—
41C42×C61D411yescharacteristic
42C42×C61D411yescharacteristic
43C42×C61C2311yescharacteristic
44C42×C61C2311yescharacteristic
45C22⋊Dic61—22no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61C2312yes—
52C4⋊Dic61C2312yes—
53C4⋊Dic61C2312yes—
54#11758196—22no—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C23×C61C2×D411yescharacteristic
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—41no—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2411yescharacteristic
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77Dic122—24no—
78Dic122—42no—
79C8×C61—24no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61#13712yes—
83C22×C61C22×D411yescharacteristic
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C612−1+412yes—
90Dic61—42no—
91Dic61—42no—
92Dic61—42no—
93Dic61—42no—
94#3236—611nomaximal, Sylow
95C2×C61—22no—
96C2×C61#53611yescharacteristic
97C2×C61C2×#13711yescharacteristic
98C2×C61#57511yescharacteristic
99#533—611no—
100C2×#125—611no—
101#501—612no—
102#491—612no—
103#484—612no—
104#483—612no—
105#479—614no—
106#432D6111yescharacteristic
107C61#323611yescharacteristic, complemented, Sylow
108C4⋊Q8—611no—
109C4⋊Q8—611no—
110#125—612no—
111#125—612no—
112#125—1221no—
113#125—1221no—
114#125—1221no—
115C22⋊Q8—612no—
116C22⋊Q8—1221no—
117C4×Q8—612no—
118C4×Q8—1221no—
119#117—1221no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—1221no—
123C2×C4⋊C4—1221no—
124C2×C42C2×D6111yescharacteristic
125#107—614no—
126#106—614no—
127C4⋊C8C2×D6112yes—
128#103—614no—
129#103—614no—
130C22⋊C8C2×D6112yes—
131#97C2×D6112yes—
132C2×Q8—612no—
133C2×Q8—1221no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4D24411yescharacteristic
137C22×C4D24411yescharacteristic
138C22×C4C22×D6111yescharacteristic
139C2×C8C22×D6114yes—
140C4⋊C4—612no—
141C4⋊C4—612no—
142C4⋊C4—612no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1222no—
146C4⋊C4—1222no—
147C4⋊C4—1222no—
148C4⋊C4—1222no—
149C4⋊C4—1222no—
150C4⋊C4—1222no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C22⋊C4—1222no—
155C42—1222no—
156C42D24411yescharacteristic
157C42D24411yescharacteristic
158C42C22×D6111yescharacteristic
159C42C22×D6111yescharacteristic
160C23C2×D24411yescharacteristic
161Q8—1224no—
162Q8—2442no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4C2×D24411yescharacteristic
173C2×C4C2×D24411yescharacteristic
174C2×C4C2×D24411yescharacteristic
175C2×C4C2×D24411yescharacteristic
176C2×C4C2×D24411yescharacteristic
177C2×C4C23×D6111yescharacteristic
178C8—24no—
179C22—21no—
180C22—21no—
181C22#1451981012yes—
182C22C22×D24411yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—2442no—
189C4—2442no—
190C4—2442no—
191C4—2442no—
192C4#1451982412yes—
193C2—22no—
194C2#1684033811yescharacteristic
195C2C2×#1451981011yescharacteristic
196C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3236
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #16840171C2semidirect
4. #16840131C2semidirect
7. #16840070C2semidirect
107. C61#3236semidirect