Finite Group Databasebeta

← #21456973

Subgroups — #21456973

Order 7808.

326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840160C211yesmaximal, characteristic, complemented
5#16840112C211yesmaximal, characteristic, complemented
6#16840101C214yesmaximal
7#16840067C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic
9C61×#487C211yesmaximal, characteristic, complemented
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519768—21no—
13#14519768C2212yes—
14#14519757—21no—
15#14519757—21no—
16#14519753—21no—
17#14519753C2212yes—
18Q8×Dic61—21no—
19Q8×Dic61C2212yes—
20#14519742—21no—
21#14519742—21no—
22#14519735—21no—
23#14519735C2212yes—
24C42×D61C2211yescharacteristic
25#14519710C2214yes—
26#14519709C2214yes—
27#14519706C2212yes—
28#14519701C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
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×Dic122—21no—
42C2×C8×C61C2312yes—
43C4⋊C4×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2312yes—
47C42×C61C2311yescharacteristic
48#11758198—22no—
49#11758198—22no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61C2312yes—
55C4⋊Dic61C2312yes—
56#11758196—22no—
57#11758196—22no—
58C4×Dic61—22no—
59C4×Dic61—22no—
60C4×Dic61D411yescharacteristic
61C4×Dic61D411yescharacteristic
62C4×Dic61C2311yescharacteristic
63C2×#92418C2312yes—
64C22×D61C2×D411yescharacteristic
65Q8×C61—24no—
66Q8×C61—42no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2411yescharacteristic
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61C2×D411yescharacteristic
75C2×Dic61C2×D411yescharacteristic
76C2×Dic61C2×D411yescharacteristic
77C4×D61—22no—
78C4×D61—22no—
79C4×D61—22no—
80Dic122—42no—
81Dic122—42no—
82C8×C61—22no—
83#92418—22no—
84C22×C61C22×D411yescharacteristic
85C2×D61—21no—
86C2×D61—21no—
87C2×D61—21no—
88C4×C61—42no—
89C4×C61—42no—
90C4×C61#13512yes—
91C4×C61#13712yes—
92C4×C612−1+412yes—
93Dic61—21no—
94Dic61—21no—
95Dic61—21no—
96Dic61—42no—
97Dic61—42no—
98#3231—611nomaximal, Sylow
99C2×C61#53611yescharacteristic
100C2×C61C2×#13511yescharacteristic
101C2×C61C2×#13711yescharacteristic
102D61—41no—
103#533—611no—
104#533—611no—
105#500—611no—
106#498—611no—
107#487—611no—
108#487D6111yescharacteristic, complemented
109#485—614no—
110#479—614no—
111#431—611no—
112C61#323111yescharacteristic, complemented, Sylow
113C4⋊Q8—611no—
114C4⋊Q8—611no—
115C4⋊Q8C2×D6111yescharacteristic
116C4⋊Q8C2×D6111yescharacteristic
117#125—612no—
118#125—1221no—
119C22⋊Q8—612no—
120C22⋊Q8—1221no—
121C22⋊Q8—1221no—
122C22⋊Q8—1221no—
123C4×Q8—612no—
124C4×Q8—1221no—
125C4×Q8—1221no—
126C4×Q8—1221no—
127#117—612no—
128#117—1221no—
129C2×C42—611no—
130#107—614no—
131#106—614no—
132C4⋊C8—612no—
133#103—614no—
134#103C2×D6114yes—
135C22⋊C8—612no—
136C4×C8—611no—
137C4×C8C2×D6111yescharacteristic
138C2×Q8—21no—
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8C22×D6112yes—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C2×C8—612no—
146C2×C8C22×D6112yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—612no—
151C4⋊C4—612no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4C22×D6112yes—
159C22⋊C4—1222no—
160C22⋊C4—1222no—
161C42—611no—
162C42—611no—
163C42—611no—
164C42—1222no—
165C42—1222no—
166C42C22×D6111yescharacteristic
167C23—611no—
168Q8—24no—
169Q8—42no—
170Q8—2442no—
171Q8—2442no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4D4×D6111yescharacteristic
183C2×C4D4×D6111yescharacteristic
184C2×C4C23×D6111yescharacteristic
185C8—22no—
186C8—1222no—
187C22—1221no—
188C22—1221no—
189C22—1221no—
190C22C2×D4×D6111yescharacteristic
191C4—42no—
192C4—42no—
193C4—1221no—
194C4—1221no—
195C4—1221no—
196C4—2442no—
197C4—2442no—
198C4#1451979812yes—
199C4#1451980912yes—
200C4#1451982412yes—
201C2—2441no—
202C2#1684033211yescharacteristic
203C2C2×#1451979811yescharacteristic
204C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3231
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. #16840160C2semidirect
5. #16840112C2semidirect
7. #16840067C2semidirect
9. C61×#487C2semidirect
108. #487D61semidirect
112. C61#3231semidirect