Finite Group Databasebeta

← #21453990

Subgroups — #21453990

Order 7808.

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

normal subgroups only

This group has 416 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#16839687C212yesmaximal, complemented
3#16839682C211yesmaximal, characteristic, complemented
4#16839676C212yesmaximal
5#16839674C212yesmaximal, complemented
6#16839674C212yesmaximal, complemented
7#16839667C211yesmaximal, characteristic, complemented
8#16839655C212yesmaximal, complemented
9C61×#394C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C4×Dic61C2211yescharacteristic
19#14519684C2211yescharacteristic
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26C22×D4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2212yes—
30#95×C61C2211yescharacteristic
31C24×C61C2312yes—
32C2×D4×C61—42no—
33C2×D4×C61—41no—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×Dic122—22no—
43C2×Dic122—41no—
44C2×Dic122—41no—
45C2×Dic122—42no—
46C2×Dic122—41no—
47C4⋊C4×C61—41no—
48C22⋊C4×C61—24no—
49C22⋊C4×C61—42no—
50C22⋊Dic61—42no—
51C22⋊Dic61—42no—
52C22⋊Dic61—42no—
53C22⋊Dic61—42no—
54C4⋊Dic61—42no—
55#11758196—42no—
56C4×Dic61—41no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61C2411yescharacteristic
65D4×C61—44no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61#4112yes—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88Dic122—44no—
89Dic122—44no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61C2×#4111yescharacteristic
98C22×C61H(5,𝔽2)11yescharacteristic
99C22×C61H(5,𝔽2)12yes—
100C22×C61H(5,𝔽2)11yescharacteristic
101C22×C612−1+412yes—
102C4×C61—22no—
103C4×C61—42no—
104C4×C61—41no—
105C4×C61—41no—
106Dic61—42no—
107Dic61—42no—
108Dic61—42no—
109Dic61—42no—
110#2832—611nomaximal, Sylow
111C2×C61—82no—
112C2×C61#53811yescharacteristic
113C2×C61#54212yes—
114C2×C61H(3,𝔽4)11yescharacteristic
115C2×C61#56212yes—
116C2×C61#56311yescharacteristic
117#400—612no—
118#397—612no—
119#395—611no—
120#394—612no—
121#394D6111yescharacteristic
122#393—612no—
123#393—612no—
124#391—611no—
125#388—612no—
126C61#283211yescharacteristic, complemented, Sylow
127C22×Q8—611no—
128C22×Q8—611no—
129C22×D4C2×D6111yescharacteristic
130C2×C4⋊C4—612no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C22⋊C4—612no—
134C2×C22⋊C4—612no—
135C2×C22⋊C4—612no—
136C2×C22⋊C4—612no—
137C2×C22⋊C4C2×D6112yes—
138C2×C22⋊C4C2×D6112yes—
139C2×C42—611no—
140#95—612no—
141#95—612no—
142#95—612no—
143#95—612no—
144#95—612no—
145#95—612no—
146#95—611no—
147#95C2×D6111yescharacteristic
148C24C22×D6112yes—
149C2×Q8—1222no—
150C2×Q8—2441no—
151C2×Q8—2441no—
152C2×Q8—2442no—
153C2×Q8—2441no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—612no—
159C22×C4—612no—
160C22×C4C22×D6112yes—
161C22×C4C22×D6111yescharacteristic
162C22×C4C22×D6111yescharacteristic
163C22×C4C22×D6111yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—2442no—
166C4⋊C4—2442no—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C22⋊C4—2442no—
170C22⋊C4—2442no—
171C22⋊C4—2442no—
172C22⋊C4—2442no—
173C42—2441no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23C23×D6111yescharacteristic
182Q8—2444no—
183Q8—2444no—
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4#1175822412yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×#1175822411yescharacteristic
215C22#1451982212yes—
216C22#1451982211yescharacteristic
217C22#1451982311yescharacteristic
218C22#1451982412yes—
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—2442no—
224C4—2442no—
225C4—2442no—
226C4—2442no—
227C2—82no—
228C2#1684034911yescharacteristic
229C2#1684037912yes—
230C2#1684050511yescharacteristic
231C2#1684050912yes—
232C2#1684051211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2832
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839687C2semidirect
3. #16839682C2semidirect
5. #16839674C2semidirect
6. #16839674C2semidirect
7. #16839667C2semidirect
8. #16839655C2semidirect
126. C61#2832semidirect