Finite Group Databasebeta

← #21461700

Subgroups — #21461700

Order 7808.

272 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C2×#14519848C211yesmaximal, characteristic, complemented
2C2×#14519847C211yesmaximal, characteristic, complemented
3#16840733C212yesmaximal
4#16840638C212yesmaximal, complemented
5C2×M16×D61C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7C2×#11758213C2212yes—
8#14519848—22no—
9#14519847—22no—
10#14519834—22no—
11C22⋊#92420—22no—
12C22×C4×D61C2211yescharacteristic
13C2×#11758194C411yescharacteristic
14C2×#11758189C411yescharacteristic
15C2×#11758189C411yescharacteristic
16M16×D61—22no—
17M16×D61—22no—
18C2×C8×D61C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20C2×M16×C61C411yescharacteristic
21C23×D61Q811yescharacteristic
22C22×C4×C61C2×C411yescharacteristic
23C22×Dic61D411yescharacteristic
24C2×C4×D61—21no—
25C2×C4×D61—21no—
26C2×C4×D61—21no—
27C2×C4×D61—21no—
28C2×C4×D61C2×C411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61Q811yescharacteristic
31C2×C4×D61C2311yescharacteristic
32C2×#92420—22no—
33C2×#92420—22no—
34#11758213—22no—
35#11758213—22no—
36#11758213—22no—
37#11758213—22no—
38M16×C61—22no—
39C2×C8×C61C2×C411yescharacteristic
40C2×C8×C61C2×C411yescharacteristic
41#11758194—22no—
42C2×#92418C2×C411yescharacteristic
43C2×#92418C2×C411yescharacteristic
44#11758189—22no—
45#11758189—22no—
46C8×D61—21no—
47C8×D61—21no—
48C8×D61D412yes—
49C8×D61D412yes—
50C23×C61C4⋊C411yescharacteristic
51C22×D61—21no—
52C22×D61—21no—
53C22×D61—42no—
54C22×D61C4⋊C411yescharacteristic
55C22×D61C2×Q811yescharacteristic
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61C4⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61C4⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C4×D61—21no—
65C4×D61—21no—
66C4×D61—21no—
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—21no—
70C4×D61C2×D411yescharacteristic
71C4×D61C2×D411yescharacteristic
72C4×D61#4111yescharacteristic
73C4×D61#4111yescharacteristic
74#92420—42no—
75#92420—42no—
76C8×C61—21no—
77C8×C61C22⋊C412yes—
78#92418—21no—
79#92418C22⋊C412yes—
80C22×C61—21no—
81C22×C61—22no—
82C22×C61C2×C4⋊C411yescharacteristic
83C2×D61—22no—
84C2×D61—21no—
85C2×D61—22no—
86C2×D61—42no—
87C2×D61—42no—
88C2×D61C22⋊Q811yescharacteristic
89C2×D61C22⋊Q811yescharacteristic
90C4×C61—21no—
91C4×C61C2×C22⋊C411yescharacteristic
92C4×C61#11711yescharacteristic
93Dic61—21no—
94Dic61#12111yescharacteristic
95Dic61#12111yescharacteristic
96#1811—611nomaximal, Sylow
97C2×C61—41no—
98C2×C61#38011yescharacteristic
99C2×C61#43012yes—
100D61—21no—
101D61—21no—
102D61—41no—
103C22×M16—611no—
104C2×#108—611no—
105C2×#108—611no—
106#407—612no—
107#341—612no—
108C61#181111yescharacteristic, complemented, Sylow
109C23×C4—611no—
110C2×M16—611no—
111C2×M16—611no—
112C2×M16—611no—
113C2×M16—612no—
114C2×M16—612no—
115C2×M16—1222no—
116C2×M16—1222no—
117C2×M16#692311yescharacteristic
118C22×C8—611no—
119C22×C8—611no—
120#108—1222no—
121#108—1222no—
122C22⋊C8—1222no—
123C22⋊C8—1222no—
124C24—611no—
125C22×C4—611no—
126C22×C4—611no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4C2×#692311yescharacteristic
135M16—22no—
136M16—1222no—
137M16—1222no—
138M16—1222no—
139M16—1222no—
140M16—1222no—
141M16—1222no—
142M16—1222no—
143C2×C8—611no—
144C2×C8—612no—
145C2×C8—612no—
146C2×C8—611no—
147C2×C8—1221no—
148C2×C8—1221no—
149C2×C8—1222no—
150C2×C8—1222no—
151C2×C8C2×#692311yescharacteristic
152C2×C8C2×#692311yescharacteristic
153C23—611no—
154C23—611no—
155C23—1221no—
156C23—1221no—
157C23—2442no—
158C23C4⋊#692311yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—611no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4C4⋊#692311yescharacteristic
176C2×C4C22×#692311yescharacteristic
177C8—21no—
178C8—612no—
179C8—1221no—
180C8—2442no—
181C8—2442no—
182C8C22⋊#692312yes—
183C22—21no—
184C22—22no—
185C22—611no—
186C22—611no—
187C22—1222no—
188C22—1221no—
189C22—1222no—
190C22—2442no—
191C22—2442no—
192C22C2×C4⋊#692311yescharacteristic
193C4—21no—
194C4—611no—
195C4—611no—
196C4—1221no—
197C4C2×C22⋊#692311yescharacteristic
198C4#1451985611yescharacteristic
199C2—41no—
200C2—1221no—
201C2—1221no—
202C2—2441no—
203C2#1684070411yescharacteristic
204C2#1684077712yes—
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×M16×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC2×M16#6923
hypocenterC61#1811
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#14519848C2semidirect
2. C2×#14519847C2semidirect
4. #16840638C2semidirect
108. C61#1811semidirect