Finite Group Databasebeta

← #21453986

Subgroups — #21453986

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#16839703C212yesmaximal, complemented
2#16839691C212yesmaximal, complemented
3#16839682C211yesmaximal, characteristic, complemented
4#16839680C212yesmaximal
5#16839679C211yesmaximal, characteristic
6#16839675C212yesmaximal, complemented
7#16839673C212yesmaximal, complemented
8#16839653C212yesmaximal, complemented
9C61×#391C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×#11758198C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20#14519684C2211yescharacteristic
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29#95×C61C2212yes—
30#95×C61C2212yes—
31C23×D61C2312yes—
32C2×Q8×C61—22no—
33C2×Q8×C61—41no—
34C2×Q8×C61—41no—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C2×D244—42no—
44C2×D244—41no—
45C2×Dic122—42no—
46C2×Dic122—41no—
47C4⋊C4×C61—41no—
48C42×C61—41no—
49#11758198—24no—
50#11758198—42no—
51#11758198—42no—
52#11758198—42no—
53#11758198—42no—
54#11758198—42no—
55#11758196—42no—
56#11758196—42no—
57C23×C61C2411yescharacteristic
58C22×D61—22no—
59C22×D61—22no—
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65Q8×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—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61#4112yes—
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—
88D244—44no—
89Dic122—44no—
90C22×C61C2×#4111yescharacteristic
91C22×C61H(5,𝔽2)11yescharacteristic
92C22×C61H(5,𝔽2)11yescharacteristic
93C22×C61H(5,𝔽2)12yes—
94C22×C612−1+412yes—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C4×C61—22no—
103C4×C61—42no—
104C4×C61—41no—
105C4×C61—41no—
106C4×C61—42no—
107Dic61—42no—
108Dic61—42no—
109Dic61—42no—
110#2832—611nomaximal, Sylow
111C2×C61#53811yescharacteristic
112C2×C61#54212yes—
113C2×C61H(3,𝔽4)11yescharacteristic
114C2×C61#56212yes—
115C2×C61#56311yescharacteristic
116D61—82no—
117#400—612no—
118#397—612no—
119#395—611no—
120#394—611no—
121#394—612no—
122#393—612no—
123#393—612no—
124#391D6111yescharacteristic, complemented
125#388—612no—
126C61#283211yescharacteristic, complemented, Sylow
127C22×Q8—611no—
128C22×Q8C2×D6111yescharacteristic
129C22×D4—611no—
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⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C42C2×D6111yescharacteristic
140#95—612no—
141#95—612no—
142#95—612no—
143#95—612no—
144#95—611no—
145#95—611no—
146#95C2×D6112yes—
147#95C2×D6112yes—
148C24—612no—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—2441no—
153C2×Q8—2442no—
154C2×D4—2441no—
155C2×D4—2442no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—612no—
159C22×C4C22×D6112yes—
160C22×C4C22×D6112yes—
161C22×C4C22×D6111yescharacteristic
162C22×C4C22×D6111yescharacteristic
163C22×C4C22×D6111yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—2442no—
166C4⋊C4—2442no—
167C22⋊C4—1224no—
168C22⋊C4—2442no—
169C22⋊C4—2442no—
170C22⋊C4—2442no—
171C22⋊C4—2442no—
172C22⋊C4—2442no—
173C42—41no—
174C23—1222no—
175C23—1222no—
176C23—1222no—
177C23—1222no—
178C23—1222no—
179C23—1222no—
180C23—1222no—
181C23C23×D6111yescharacteristic
182Q8—44no—
183Q8—2444no—
184D4—2444no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
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#1175822212yes—
207C22—2442no—
208C22—2442no—
209C22—2442no—
210C22—2442no—
211C22—2442no—
212C22—2442no—
213C22—2442no—
214C22C2×#1175822211yescharacteristic
215C22#1451982211yescharacteristic
216C22#1451982211yescharacteristic
217C22#1451982312yes—
218C22#1451982512yes—
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—42no—
224C4—2442no—
225C4—2442no—
226C4—2442no—
227C2—4882no—
228C2#1684035011yescharacteristic
229C2#1684038412yes—
230C2#1684050411yescharacteristic
231C2#1684050812yes—
232C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2832
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #16839703C2semidirect
2. #16839691C2semidirect
3. #16839682C2semidirect
6. #16839675C2semidirect
7. #16839673C2semidirect
8. #16839653C2semidirect
9. C61×#391C2semidirect
124. #391D61semidirect
126. C61#2832semidirect