Finite Group Databasebeta

← #21456980

Subgroups — #21456980

Order 7808.

326 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#16840319C211yesmaximal, characteristic
3#16840167C211yesmaximal, characteristic, complemented
4#16840160C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840113C211yesmaximal, characteristic, complemented
7#16840104C214yesmaximal
8#16840070C214yesmaximal, complemented
9C61×#431C211yesmaximal, characteristic
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519769—21no—
15#14519769C2212yes—
16#14519756—21no—
17#14519756—21no—
18#14519756—21no—
19#14519756C2212yes—
20C4×Dic122—21no—
21C4×Dic122—21no—
22C4×Dic122—21no—
23C4×Dic122C2212yes—
24#14519736—21no—
25#14519736C2212yes—
26#14519711C2214yes—
27#14519709C2214yes—
28#14519702C2214yes—
29#14519702C2214yes—
30C2×C42×C61C2211yescharacteristic
31C4⋊C8×C61C2212yes—
32C22⋊C8×C61C2212yes—
33C4×C8×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122C2312yes—
42C2×C8×C61C2312yes—
43C2×C8×C61C2312yes—
44C42×C61D411yescharacteristic
45C42×C61D411yescharacteristic
46C42×C61C2311yescharacteristic
47C42×C61C2311yescharacteristic
48C22⋊Dic61—22no—
49C22⋊Dic61—22no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61C2312yes—
56C4⋊Dic61C2312yes—
57C4⋊Dic61C2312yes—
58#11758196—22no—
59#11758196—22no—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61—22no—
63C4×Dic61—22no—
64C23×C61C2×D411yescharacteristic
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78Dic122—24no—
79Dic122—42no—
80Dic122—42no—
81Dic122—42no—
82C8×C61—22no—
83C8×C61—22no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61C22×D411yescharacteristic
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61#13512yes—
92C4×C61#13712yes—
93C4×C612−1+412yes—
94Dic61—42no—
95Dic61—42no—
96Dic61—42no—
97Dic61—42no—
98#3231—611nomaximal, Sylow
99C2×C61—41no—
100C2×C61#53611yescharacteristic
101C2×C61C2×#13511yescharacteristic
102C2×C61C2×#13711yescharacteristic
103#533—611no—
104#533—611no—
105#500—611no—
106#498—611no—
107#487—611no—
108#487—611no—
109#485—614no—
110#479—614no—
111#431D6111yescharacteristic
112C61#323111yescharacteristic, complemented, Sylow
113C4⋊Q8—611no—
114C4⋊Q8—611no—
115C4⋊Q8—611no—
116C4⋊Q8—611no—
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×C42C2×D6111yescharacteristic
130#107—614no—
131#106—614no—
132C4⋊C8C2×D6112yes—
133#103—614no—
134#103—614no—
135C22⋊C8C2×D6112yes—
136C4×C8C2×D6111yescharacteristic
137C4×C8C2×D6111yescharacteristic
138C2×Q8—612no—
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8—1221no—
142C22×C4D24411yescharacteristic
143C22×C4D24411yescharacteristic
144C22×C4C22×D6111yescharacteristic
145C2×C8C22×D6112yes—
146C2×C8C22×D6112yes—
147C4⋊C4—612no—
148C4⋊C4—612no—
149C4⋊C4—612no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C22⋊C4—1222no—
160C22⋊C4—1222no—
161C42—1222no—
162C42—1222no—
163C42D24411yescharacteristic
164C42D24411yescharacteristic
165C42C22×D6111yescharacteristic
166C42C22×D6111yescharacteristic
167C23C2×D24411yescharacteristic
168Q8—1224no—
169Q8—2442no—
170Q8—2442no—
171Q8—2442no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4C2×D24411yescharacteristic
180C2×C4C2×D24411yescharacteristic
181C2×C4C2×D24411yescharacteristic
182C2×C4C2×D24411yescharacteristic
183C2×C4C2×D24411yescharacteristic
184C2×C4C23×D6111yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22C22×D24411yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—2442no—
195C4—2442no—
196C4—2442no—
197C4—2442no—
198C4#1451979912yes—
199C4#1451981012yes—
200C4#1451982412yes—
201C2—41no—
202C2#1684033811yescharacteristic
203C2C2×#1451979911yescharacteristic
204C2C2×#1451981011yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3231
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
3. #16840167C2semidirect
4. #16840160C2semidirect
5. #16840113C2semidirect
6. #16840113C2semidirect
8. #16840070C2semidirect
112. C61#3231semidirect