Finite Group Databasebeta

← #21456404

Subgroups — #21456404

Order 7808.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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#16840317C211yesmaximal, characteristic
2#16840317C211yesmaximal, characteristic
3#16840165C211yesmaximal, characteristic, complemented
4#16840141C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840002C214yesmaximal
7#16839854C214yesmaximal, complemented
8C4×C8×D61C211yesmaximal, characteristic
9C61×#487C211yesmaximal, characteristic, complemented
10C2×#11758202C2214yes—
11C2×C8×D61C2212yes—
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519768—21no—
15#14519768—21no—
16#14519757—21no—
17#14519757C2212yes—
18#14519753—21no—
19#14519753C2212yes—
20Q8×Dic61—21no—
21Q8×Dic61C2212yes—
22#14519742—21no—
23#14519742C2212yes—
24#14519735—21no—
25#14519735—21no—
26C42×D61C2211yescharacteristic
27#14519710C2214yes—
28#14519702C2214yes—
29C4×#92418C2211yescharacteristic
30C8×Dic61C2212yes—
31C4⋊Q8×C61C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33#103×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61C2312yes—
37C2×C4×D61D411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×C4×D61C2311yescharacteristic
40C2×Dic122—21no—
41C2×Dic122C2312yes—
42C2×C8×C61C2312yes—
43C4⋊C4×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2312yes—
47C42×C61C2311yescharacteristic
48#11758202—28no—
49#11758198—22no—
50#11758198—22no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58#11758196—22no—
59C4×Dic61—22no—
60C4×Dic61—22no—
61C4×Dic61D411yescharacteristic
62C4×Dic61D411yescharacteristic
63C4×Dic61C2311yescharacteristic
64C2×#92418C2312yes—
65C8×D61—24no—
66C22×D61C2×D411yescharacteristic
67Q8×C61—24no—
68Q8×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61C2×D411yescharacteristic
78C2×Dic61C2×D411yescharacteristic
79C4×D61—22no—
80C4×D61—22no—
81C4×D61Q1614yescomplemented
82Dic122—24no—
83Dic122—42no—
84C8×C61—22no—
85#92418#4114yes—
86C22×C61C22×D411yescharacteristic
87C2×D61—21no—
88C2×D61—21no—
89C2×D61C2×Q1612yes—
90C4×C61—42no—
91C4×C61—42no—
92C4×C61C2×Q1612yes—
93C4×C61#13512yes—
94C4×C61C2×#4112yes—
95Dic61—21no—
96Dic61—21no—
97Dic61—42no—
98Dic61—42no—
99Dic61C2×Q1612yes—
100#3170—611nomaximal, Sylow
101C2×C61#53211yescharacteristic
102C2×C61C22×Q1611yescharacteristic
103C2×C61C2×#13511yescharacteristic
104D61—22no—
105#533—611no—
106#533—611no—
107#500—611no—
108#494—611no—
109#487—611no—
110#487D6111yescharacteristic, complemented
111#467—614no—
112C4×Q16—614no—
113C2×C4×C8—611no—
114C61#317011yescharacteristic, complemented, Sylow
115C2×Q16—614no—
116C22×C8—612no—
117C4⋊Q8—611no—
118C4⋊Q8—611no—
119C4⋊Q8C2×D6111yescharacteristic
120C4⋊Q8C2×D6111yescharacteristic
121#125—1221no—
122#125—1221no—
123C22⋊Q8—612no—
124C22⋊Q8—612no—
125C22⋊Q8—1221no—
126C22⋊Q8—1221no—
127C4×Q8—612no—
128C4×Q8—612no—
129C4×Q8—1221no—
130C4×Q8—1221no—
131#117—1221no—
132#117—1221no—
133C2×C42—611no—
134#107—614no—
135#103—614no—
136#103C2×D6114yes—
137C4×C8—612no—
138C4×C8—611no—
139C4×C8C2×D6111yescharacteristic
140C2×Q8—21no—
141C2×Q8—612no—
142C2×Q8—1221no—
143C2×Q8C22×D6112yes—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147Q16—1228no—
148C2×C8—612no—
149C2×C8—1224no—
150C2×C8C22×D6112yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—612no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4C22×D6112yes—
163C22⋊C4—1222no—
164C22⋊C4—1222no—
165C42—611no—
166C42—611no—
167C42—611no—
168C42—1222no—
169C42—1222no—
170C42C22×D6111yescharacteristic
171C23—611no—
172Q8—24no—
173Q8—42no—
174Q8—1224no—
175Q8—2442no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—611no—
179C2×C4—614no—
180C2×C4—611no—
181C2×C4—611no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4D4×D6111yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4C23×D6111yescharacteristic
189C8—22no—
190C8—614no—
191C22—612no—
192C22—1221no—
193C22—1221no—
194C22C2×D4×D6111yescharacteristic
195C4—42no—
196C4—42no—
197C4—612no—
198C4—1221no—
199C4—1221no—
200C4—2442no—
201C4—2442no—
202C4Q16×D6112yes—
203C4#1451979812yes—
204C4#41×D6112yes—
205C2—1222no—
206C2#1684031111yescharacteristic
207C2C2×Q16×D6111yescharacteristic
208C2C2×#1451979811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3170
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16840165C2semidirect
4. #16840141C2semidirect
5. #16840113C2semidirect
7. #16839854C2semidirect
9. C61×#487C2semidirect
81. C4×D61Q16semidirect
110. #487D61semidirect
114. C61#3170semidirect