Finite Group Databasebeta

← #21457019

Subgroups — #21457019

Order 7808.

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

normal subgroups only

This group has 366 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, complemented
2#16840312C211yesmaximal, characteristic
3#16840171C212yesmaximal, complemented
4#16840127C212yesmaximal, complemented
5#16840087C214yesmaximal, complemented
6#16840053C212yesmaximal, complemented
7#16840043C212yesmaximal, complemented
8C61×#432C211yesmaximal, characteristic, complemented
9C2×#11758222—21no—
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519774C2211yescharacteristic
14#14519769C2212yes—
15#14519765—21no—
16#14519756—21no—
17#14519756—21no—
18#14519751—21no—
19#14519751C2212yes—
20C4×Dic122—21no—
21C4×Dic122—21no—
22C4×D244—21no—
23C4×D244C2212yes—
24#14519736C2212yes—
25#14519711C2214yes—
26#14519709C2214yes—
27#14519699C2214yes—
28#14519699C2214yes—
29C2×C42×C61C2211yescharacteristic
30C4⋊C8×C61C2212yes—
31C22⋊C8×C61C2212yes—
32#97×C61C2212yes—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37#11758222—44no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244C2312yes—
41C2×C4×D61—22no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×C8×C61C2314yes—
46C42×C61D411yescharacteristic
47C42×C61D411yescharacteristic
48C42×C61C2311yescharacteristic
49C42×C61C2311yescharacteristic
50C22⋊Dic61—22no—
51#11758198—22no—
52#11758198—22no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56C4⋊Dic61C2312yes—
57C4⋊Dic61C2312yes—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60#11758196—22no—
61C4×Dic61—22no—
62C23×C61C2×D411yescharacteristic
63C22×D61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—41no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2411yescharacteristic
73C22⋊D61—44no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77D244—24no—
78D244—42no—
79D244—42no—
80C4×D61—44no—
81Dic122—42no—
82Dic122—42no—
83Dic122—42no—
84C8×C61—24no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61C22×D411yescharacteristic
89C2×D61—42no—
90C2×D61—42no—
91C2×D61—42no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61AGL(1,ℤ/8)12yes—
97C4×C612−1+412yes—
98Dic61—42no—
99Dic61—42no—
100Dic61—42no—
101#3235—611nomaximal, Sylow
102C2×C61—41no—
103C2×C61#53611yescharacteristic
104C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C61#57511yescharacteristic
106D61—82no—
107#533—611no—
108#532—611no—
109#501—612no—
110#490—612no—
111#482—614no—
112#476—612no—
113#474—612no—
114#432D6111yescharacteristic, complemented
115C61#323511yescharacteristic, complemented, Sylow
116C2×#41—1221no—
117C4⋊Q8—611no—
118C4⋊Q8—611no—
119C4⋊Q8—611no—
120#127—611no—
121#125—612no—
122#124—1221no—
123C22⋊Q8—1221no—
124C22⋊Q8—1221no—
125#121—612no—
126#121—1221no—
127C4×Q8—1221no—
128C4×Q8—1221no—
129C4×D4—612no—
130C4×D4—1221no—
131#117—612no—
132C2×C42C2×D6111yescharacteristic
133#107—614no—
134#106—614no—
135C4⋊C8C2×D6112yes—
136#102—614no—
137#102—614no—
138C22⋊C8C2×D6112yes—
139#97C2×D6112yes—
140#41—2444no—
141C2×Q8—1221no—
142C2×Q8—1221no—
143C2×Q8—1221no—
144C2×D4—612no—
145C2×D4—1222no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—1222no—
149C22×C4D24411yescharacteristic
150C22×C4D24411yescharacteristic
151C22×C4C22×D6111yescharacteristic
152C2×C8C22×D6114yes—
153C4⋊C4—612no—
154C4⋊C4—612no—
155C4⋊C4—612no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C22⋊C4—1222no—
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C42—1222no—
165C42D24411yescharacteristic
166C42D24411yescharacteristic
167C42C22×D6111yescharacteristic
168C42C22×D6111yescharacteristic
169C23—1222no—
170C23C2×D24411yescharacteristic
171Q8—2442no—
172Q8—2442no—
173Q8—2442no—
174D4—1224no—
175D4—2442no—
176D4—2442no—
177D4—2444no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—2444no—
185C2×C4C2×D24411yescharacteristic
186C2×C4C2×D24411yescharacteristic
187C2×C4C2×D24411yescharacteristic
188C2×C4C2×D24411yescharacteristic
189C2×C4C2×D24411yescharacteristic
190C2×C4C23×D6111yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—2442no—
196C22—2442no—
197C22—2442no—
198C22C22×D24411yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—2442no—
204C4—2442no—
205C4—2442no—
206C4#1451980512yes—
207C4#1451982412yes—
208C2—41no—
209C2—4882no—
210C2#1684033811yescharacteristic
211C2C2×#1451980511yescharacteristic
212C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3235
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
1. #16840319C2semidirect
3. #16840171C2semidirect
4. #16840127C2semidirect
5. #16840087C2semidirect
6. #16840053C2semidirect
7. #16840043C2semidirect
8. C61×#432C2semidirect
114. #432D61semidirect
115. C61#3235semidirect