Finite Group Databasebeta

← #21451581

Subgroups — #21451581

Order 7808.

612 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519766C211yesmaximal, characteristic, complemented
2C2×#14519751C211yesmaximal, characteristic
3C2×#14519736C211yesmaximal, characteristic, complemented
4#16839684C214yesmaximal, complemented
5#16839677C214yesmaximal, complemented
6#16839669C211yesmaximal, characteristic, complemented
7#16839663C211yesmaximal, characteristic, complemented
8#16839631C211yesmaximal, characteristic, complemented
9C2×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12#14519766—24no—
13#14519751—24no—
14#14519736—24no—
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2214yes—
18C2×C22⋊Dic61C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2214yes—
21C2×#11758198C2214yes—
22C2×C4×Dic61C2211yescharacteristic
23C2×C4×Dic61C2211yescharacteristic
24#14519684C2214yes—
25C22×Q8×C61C2211yescharacteristic
26C23×C4×C61C2211yescharacteristic
27C22⋊Q8×C61—24no—
28C2×C4⋊C4×C61C2212yes—
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2212yes—
31C24×C61C2311yescharacteristic
32C23×D61C2312yes—
33C2×Q8×C61—22no—
34C2×Q8×C61—22no—
35C2×Q8×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61D414yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—24no—
44C2×C22⋊D61—44no—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C2×D244—22no—
49C2×D244—22no—
50C2×D244—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—24no—
53C22⋊C4×C61—24no—
54C22⋊Dic61—24no—
55#11758198—24no—
56#11758198—28no—
57#11758198—44no—
58C4⋊Dic61—22no—
59C4⋊Dic61—24no—
60#11758196—44no—
61C4×Dic61—22no—
62C4×Dic61D414yescomplemented
63C23×C61—21no—
64C23×C61—21no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61C2×D412yes—
68C23×C61C2411yescharacteristic
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—24no—
73C22×D61—24no—
74Q8×C61—44no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—28no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—24no—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D412yes—
86C2×C4×C61#4112yes—
87C22⋊D61—48no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—24no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61C2×D414yes—
96D244—44no—
97C22×C61—22no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61C22×D411yescharacteristic
103C22×C61C22×D411yescharacteristic
104C22×C61C2×#4111yescharacteristic
105C22×C61H(5,𝔽2)12yes—
106C22×C612−1+412yes—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—44no—
111C2×D61—44no—
112C4×C61—22no—
113C4×C61—42no—
114C4×C61—42no—
115C4×C61#12114yes—
116Dic61—24no—
117Dic61—42no—
118Dic61—42no—
119#2620—611nomaximal, Sylow
120C2×C61—42no—
121C2×C61C2×#12111yescharacteristic
122C2×C61#53511yescharacteristic
123C2×C61#53611yescharacteristic
124C2×C61#53712yes—
125C2×C61#54212yes—
126D61—82no—
127C2×#124—611no—
128C2×C22⋊Q8D6111yescharacteristic, complemented
129C2×#121—611no—
130C2×#117—611no—
131#396—614no—
132#394—614no—
133#391—611no—
134#390—611no—
135#384—611no—
136C61#262011yescharacteristic, complemented, Sylow
137C22×Q8C2×D6111yescharacteristic
138C22×D4—612no—
139C22×D4—611no—
140C23×C4C2×D6111yescharacteristic
141#124—1224no—
142C22⋊Q8—24no—
143#121—1224no—
144#117—1224no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—614no—
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C4⋊C4C2×D6112yes—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—614no—
153C2×C22⋊C4—614no—
154C2×C22⋊C4C2×D6112yes—
155C2×C42—611no—
156C2×C42—611no—
157#95—614no—
158C24—612no—
159C24C22×D6111yescharacteristic
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×D4—1224no—
164C2×D4—1222no—
165C2×D4—1222no—
166C2×D4—1222no—
167C2×D4—2444no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—612no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4C22⋊D6114yes—
174C22×C4C22×D6112yes—
175C22×C4C22×D6112yes—
176C22×C4C22×D6111yescharacteristic
177C22×C4C22×D6111yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—24no—
180C4⋊C4—1224no—
181C4⋊C4—1222no—
182C4⋊C4—2444no—
183C22⋊C4—24no—
184C22⋊C4—1228no—
185C22⋊C4—1224no—
186C22⋊C4—1224no—
187C22⋊C4—2444no—
188C42—614no—
189C42—1222no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23—22no—
194C23—1222no—
195C23—1222no—
196C23—1222no—
197C23—1224no—
198C23—1224no—
199C23C2×C22⋊D6112yes—
200C23C23×D6111yescharacteristic
201Q8—44no—
202D4—2448no—
203D4—2444no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—614no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1224no—
219C2×C4—1222no—
220C2×C4D4×D6112yes—
221C2×C4#1175822412yes—
222C2×C4C2×C22⋊D6112yes—
223C2×C4C2×C22⋊D6112yes—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—42no—
228C22—42no—
229C22—2442no—
230C22—2442no—
231C22—2442no—
232C22—2444no—
233C22—2444no—
234C22C2×D4×D6111yescharacteristic
235C22C22×C22⋊D6111yescharacteristic
236C22C2×#1175822411yescharacteristic
237C22#1451982312yes—
238C22#1451982512yes—
239C4—22no—
240C4—42no—
241C4—42no—
242C4—1224no—
243C4—2442no—
244C4—2442no—
245C4#1451974914yes—
246C2—42no—
247C2—4882no—
248C2C2×#1451974911yescharacteristic
249C2#1684032611yescharacteristic
250C2#1684033611yescharacteristic
251C2#1684034212yes—
252C2#1684038512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2620
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14519766C2semidirect
3. C2×#14519736C2semidirect
4. #16839684C2semidirect
5. #16839677C2semidirect
6. #16839669C2semidirect
7. #16839663C2semidirect
8. #16839631C2semidirect
9. C2×C22⋊Q8×C61C2semidirect
62. C4×Dic61D4semidirect
128. C2×C22⋊Q8D61semidirect
136. C61#2620semidirect