Finite Group Databasebeta

← #21454007

Subgroups — #21454007

Order 7808.

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

normal subgroups only

This group has 380 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#16839704C212yesmaximal, complemented
2#16839703C212yesmaximal, complemented
3#16839700C212yesmaximal, complemented
4#16839690C212yesmaximal
5#16839687C211yesmaximal, characteristic
6#16839682C212yesmaximal, complemented
7#16839674C211yesmaximal, characteristic
8#16839635C212yesmaximal
9C61×#385C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17#14519684C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C23×C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C22×C4×C61—41no—
33C22×C4×C61—42no—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×Dic122—41no—
43C2×Dic122—42no—
44C4⋊C4×C61—42no—
45C22⋊C4×C61—22no—
46C22⋊C4×C61—41no—
47C22⋊Dic61—24no—
48C22⋊Dic61—42no—
49C4⋊Dic61—41no—
50#11758196—42no—
51#11758196—42no—
52#11758196—42no—
53C23×C61—22no—
54C23×C61—21no—
55C23×C61—22no—
56C23×C61—21no—
57C23×C61#4112yes—
58C23×C61C2411yescharacteristic
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—44no—
70C2×Dic61—22no—
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—
82Dic122—44no—
83C22×C61—24no—
84C22×C61—22no—
85C22×C61—41no—
86C22×C61—42no—
87C22×C61—41no—
88C22×C61C2×#4111yescharacteristic
89C22×C61H(5,𝔽2)12yes—
90C22×C61H(5,𝔽2)11yescharacteristic
91C22×C612−1+412yes—
92C22×C612−1+411yescharacteristic
93C4×C61—42no—
94C4×C61—41no—
95C4×C61—42no—
96C4×C61—41no—
97Dic61—42no—
98Dic61—42no—
99Dic61—42no—
100Dic61—42no—
101#2835—611nomaximal, Sylow
102C2×C61—42no—
103C2×C61#53912yes—
104C2×C61#53911yescharacteristic
105C2×C61H(3,𝔽4)11yescharacteristic
106C2×C61#56312yes—
107C2×C61#56311yescharacteristic
108#400—612no—
109#400—612no—
110#400—612no—
111#397—611no—
112#397—612no—
113#395—612no—
114#393—611no—
115#385—612no—
116#385D6111yescharacteristic
117C61#283511yescharacteristic, complemented, Sylow
118C22×Q8—611no—
119C23×C4C2×D6111yescharacteristic
120C2×C4⋊C4—612no—
121C2×C4⋊C4—612no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4C2×D6112yes—
125C2×C22⋊C4—612no—
126C2×C22⋊C4—612no—
127C2×C22⋊C4C2×D6111yescharacteristic
128C2×C22⋊C4C2×D6111yescharacteristic
129#95—612no—
130#95—612no—
131#95—611no—
132#95—612no—
133#95—612no—
134#95—612no—
135#95—612no—
136#95—612no—
137#95—611no—
138#95C2×D6112yes—
139C24C22×D6111yescharacteristic
140C2×Q8—2441no—
141C2×Q8—2442no—
142C22×C4—42no—
143C22×C4—41no—
144C22×C4—612no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4C22×D6111yescharacteristic
149C22×C4C22×D6112yes—
150C22×C4C22×D6111yescharacteristic
151C22×C4C22×D6112yes—
152C4⋊C4—42no—
153C4⋊C4—2442no—
154C4⋊C4—2442no—
155C4⋊C4—2442no—
156C4⋊C4—2441no—
157C22⋊C4—22no—
158C22⋊C4—41no—
159C22⋊C4—1224no—
160C22⋊C4—2442no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23#1175822212yes—
166C23C23×D6111yescharacteristic
167Q8—2444no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
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—1222no—
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—
191C22—24no—
192C22—22no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22C2×#1175822211yescharacteristic
197C22#1451982212yes—
198C22#1451982211yescharacteristic
199C22#1451982412yes—
200C22#1451982511yescharacteristic
201C4—42no—
202C4—41no—
203C4—41no—
204C4—42no—
205C4—2442no—
206C4—2442no—
207C4—2442no—
208C4—2442no—
209C2—42no—
210C2#1684035412yes—
211C2#1684035911yescharacteristic
212C2#1684050511yescharacteristic
213C2#1684051312yes—
214C2#1684051511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2835
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839703C2semidirect
3. #16839700C2semidirect
6. #16839682C2semidirect
117. C61#2835semidirect