Finite Group Databasebeta

← #21451992

Subgroups — #21451992

Order 7808.

424 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 137 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#16839701C212yesmaximal, complemented
2#16839685C212yesmaximal
3#16839682C212yesmaximal, complemented
4#16839674C212yesmaximal
5#16839666C212yesmaximal, complemented
6#16839649C212yesmaximal, complemented
7#16839625C211yesmaximal, characteristic
8C4×C22⋊Dic61C211yesmaximal, characteristic
9C61×#380C211yesmaximal, characteristic
10C22×Dic122C2212yes—
11C2×C4⋊Dic61C2212yes—
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C4×Dic61C2212yes—
17#14519684C2211yescharacteristic
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2211yescharacteristic
26C23×C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C22×C4×C61—42no—
33C22×C4×C61Q814yescomplemented
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×Dic122—24no—
43C2×Dic122—42no—
44C2×Dic122—42no—
45C4⋊C4×C61—42no—
46C22⋊C4×C61—41no—
47C22⋊C4×C61—41no—
48C22⋊Dic61—24no—
49C22⋊Dic61—42no—
50C4⋊Dic61—42no—
51#11758196—24no—
52#11758196—42no—
53C4×Dic61—42no—
54C23×C61—22no—
55C23×C61—22no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61C2×Q812yes—
59C23×C61C2411yescharacteristic
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—44no—
69C2×C4×C61C2×Q812yes—
70C2×C4×C61C2×Q812yes—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61#4114yes—
83Dic122—48no—
84C22×C61—22no—
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61C22×Q811yescharacteristic
90C22×C61C2×#4112yes—
91C22×C61H(5,𝔽2)11yescharacteristic
92C22×C61H(5,𝔽2)12yes—
93C22×C612−1+411yescharacteristic
94C4×C61—22no—
95C4×C61—22no—
96C4×C61—42no—
97C4×C61—42no—
98Dic61—24no—
99Dic61—42no—
100Dic61—42no—
101Dic61—42no—
102#2665—611nomaximal, Sylow
103C2×C61—42no—
104C2×C61#53311yescharacteristic
105C2×C61#53812yes—
106C2×C61#54212yes—
107C2×C61#54311yescharacteristic
108C2×C61#54411yescharacteristic
109#400—612no—
110#396—612no—
111#395—612no—
112#393—612no—
113#391—612no—
114#387—612no—
115#381—611no—
116#380D6111yescharacteristic
117C4×C22⋊C4—611no—
118C61#266511yescharacteristic, complemented, Sylow
119C22×Q8—612no—
120C23×C4C2×D6111yescharacteristic
121C2×C4⋊C4—612no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4C2×D6112yes—
125C2×C22⋊C4—612no—
126C2×C22⋊C4—612no—
127C2×C22⋊C4C2×D6111yescharacteristic
128C2×C22⋊C4C2×D6111yescharacteristic
129C2×C42—612no—
130#95—611no—
131#95—611no—
132#95—611no—
133#95—611no—
134#95—612no—
135#95—612no—
136#95—612no—
137#95—612no—
138#95—612no—
139#95C2×D6112yes—
140C24C22×D6111yescharacteristic
141C2×Q8—1224no—
142C2×Q8—2442no—
143C2×Q8—2442no—
144C22×C4—42no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4—612no—
149C22×C4Dic12214yescomplemented
150C22×C4C22×D6112yes—
151C22×C4C22×D6112yes—
152C22×C4C22×D6111yescharacteristic
153C22×C4C22×D6111yescharacteristic
154C4⋊C4—42no—
155C4⋊C4—1224no—
156C4⋊C4—2442no—
157C4⋊C4—2442no—
158C22⋊C4—41no—
159C22⋊C4—41no—
160C22⋊C4—1224no—
161C22⋊C4—2442no—
162C42—2442no—
163C23—22no—
164C23—21no—
165C23—22no—
166C23—21no—
167C23C2×Dic12212yes—
168C23C23×D6111yescharacteristic
169Q8—2448no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—614no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4C2×Dic12212yes—
192C2×C4C2×Dic12212yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C22×Dic12211yescharacteristic
199C22#41×D6112yes—
200C22#1451982211yescharacteristic
201C22#1451982212yes—
202C22#1451982511yescharacteristic
203C4—22no—
204C4—22no—
205C4—42no—
206C4—42no—
207C4—1224no—
208C4—2442no—
209C4—2442no—
210C4—2442no—
211C2—42no—
212C2#1684031511yescharacteristic
213C2#1684034412yes—
214C2#1684038212yes—
215C2#1684038811yescharacteristic
216C2#1684039311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2665
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #16839701C2semidirect
3. #16839682C2semidirect
5. #16839666C2semidirect
6. #16839649C2semidirect
33. C22×C4×C61Q8semidirect
118. C61#2665semidirect
149. C22×C4Dic122semidirect