Finite Group Databasebeta

← #21452827

Subgroups — #21452827

Order 7808.

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

normal subgroups only

This group has 492 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
1C2×#14519775C211yesmaximal, characteristic, complemented
2#16839685C212yesmaximal, complemented
3#16839676C212yesmaximal
4#16839674C212yesmaximal, complemented
5#16839669C211yesmaximal, characteristic, complemented
6#16839656C212yesmaximal, complemented
7#16839650C212yesmaximal, complemented
8#16839646C212yesmaximal, complemented
9C2×#124×C61C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11#14519775—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C4×Dic61C2211yescharacteristic
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×Q8×C61C2211yescharacteristic
28C22×D4×C61C2211yescharacteristic
29#124×C61—24no—
30C2×C22⋊C4×C61C2212yes—
31C2×C22⋊C4×C61C2212yes—
32C2×C42×C61C2211yescharacteristic
33C24×C61C2312yes—
34C2×Q8×C61—41no—
35C2×Q8×C61—41no—
36C2×Q8×C61D414yes—
37C2×D4×C61—22no—
38C2×D4×C61—41no—
39C2×D4×C61—41no—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C2×Dic122—22no—
49C2×Dic122—41no—
50C2×Dic122—41no—
51C22⋊C4×C61—24no—
52C22⋊C4×C61—24no—
53C42×C61—22no—
54C22⋊Dic61—24no—
55C22⋊Dic61—24no—
56C22⋊Dic61—42no—
57C22⋊Dic61—42no—
58C4⋊Dic61—41no—
59#11758196—24no—
60#11758196—24no—
61#11758196—24no—
62C4×Dic61—22no—
63C4×Dic61—41no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61C2411yescharacteristic
72Q8×C61—44no—
73D4×C61—44no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D412yes—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61#4114yes—
98Dic122—44no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61C22×D411yescharacteristic
107C22×C61C2×#4112yes—
108C22×C61H(5,𝔽2)11yescharacteristic
109C22×C61H(5,𝔽2)11yescharacteristic
110C22×C612−1+412yes—
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—42no—
115Dic61—24no—
116Dic61—42no—
117Dic61—42no—
118Dic61—42no—
119#2731—611nomaximal, Sylow
120C2×C61—82no—
121C2×C61#53411yescharacteristic
122C2×C61#54212yes—
123C2×C61#54812yes—
124C2×C61#55511yescharacteristic
125C2×C61#56311yescharacteristic
126C2×C4⋊Q8—611no—
127C2×#124D6111yescharacteristic
128#396—612no—
129#394—612no—
130#393—612no—
131#391—611no—
132#388—612no—
133#388—612no—
134#387—612no—
135C61#273111yescharacteristic, complemented, Sylow
136C22×Q8—611no—
137C22×Q8C2×D6111yescharacteristic
138C22×D4C2×D6111yescharacteristic
139C4⋊Q8—1224no—
140#124—24no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—611no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4C2×D6112yes—
150C2×C22⋊C4C2×D6112yes—
151C2×C42—611no—
152C2×C42—611no—
153C2×C42C2×D6111yescharacteristic
154#95—612no—
155#95—612no—
156#95—612no—
157#95—612no—
158#95—612no—
159C24C22×D6112yes—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—1222no—
163C2×Q8—2441no—
164C2×Q8—2441no—
165C2×Q8C22⋊D6114yes—
166C2×D4—22no—
167C2×D4—41no—
168C2×D4—41no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4C22×D6112yes—
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C4⋊C4—1224no—
178C4⋊C4—1224no—
179C4⋊C4—1224no—
180C4⋊C4—2441no—
181C22⋊C4—24no—
182C22⋊C4—24no—
183C22⋊C4—1224no—
184C22⋊C4—1224no—
185C22⋊C4—2442no—
186C22⋊C4—2442no—
187C42—22no—
188C42—1222no—
189C42—2441no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—22no—
197C23C23×D6111yescharacteristic
198Q8—44no—
199Q8—2444no—
200D4—44no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—614no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4C2×C22⋊D6112yes—
223C2×C4C2×C22⋊D6112yes—
224C2×C4C2×C22⋊D6112yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22C22×C22⋊D6111yescharacteristic
233C22#41×D6112yes—
234C22#1451982211yescharacteristic
235C22#1451982211yescharacteristic
236C22#1451982412yes—
237C4—22no—
238C4—22no—
239C4—22no—
240C4—42no—
241C4—1224no—
242C4—2442no—
243C4—2442no—
244C4—2442no—
245C2—82no—
246C2#1684032111yescharacteristic
247C2#1684037612yes—
248C2#1684041912yes—
249C2#1684047411yescharacteristic
250C2#1684051211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2731
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
2. #16839685C2semidirect
4. #16839674C2semidirect
5. #16839669C2semidirect
6. #16839656C2semidirect
7. #16839650C2semidirect
8. #16839646C2semidirect
135. C61#2731semidirect