Finite Group Databasebeta

← #21450418

Subgroups — #21450418

Order 7808.

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

normal subgroups only

This group has 440 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
1#16839690C212yesmaximal, complemented
2#16839690C212yesmaximal, complemented
3#16839665C211yesmaximal, characteristic
4#16839665C211yesmaximal, characteristic
5#16839658C211yesmaximal, characteristic, complemented
6#16839656C212yesmaximal, complemented
7#16839650C212yesmaximal, complemented
8#16839628C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
10C4×#11758196C211yesmaximal, characteristic, complemented
11C61×#390C211yesmaximal, characteristic
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2211yescharacteristic
15C2×#11758196C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2211yescharacteristic
23C2×C4×Dic61C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2211yescharacteristic
30C22×D4×C61C2211yescharacteristic
31C2×C4⋊C4×C61C2211yescharacteristic
32C2×C22⋊C4×C61C2212yes—
33C2×C22⋊C4×C61C2212yes—
34C2×C42×C61C2211yescharacteristic
35C24×C61C2312yes—
36C2×D4×C61—22no—
37C2×D4×C61—22no—
38C2×D4×C61—22no—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C4⋊C4×C61—22no—
50C22⋊C4×C61—42no—
51C22⋊C4×C61—42no—
52C42×C61—22no—
53C22⋊Dic61—24no—
54C22⋊Dic61—24no—
55C22⋊Dic61—42no—
56C22⋊Dic61—42no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59#11758196—22no—
60#11758196—22no—
61#11758196—42no—
62C4×Dic61—22no—
63C4×Dic61—22no—
64C4×Dic61—42no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61C2411yescharacteristic
73D4×C61—44no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61#4112yes—
84C2×C4×C61#4112yes—
85C2×C4×C61#4112yes—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61#4112yes—
103C2×Dic61#4112yes—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61C2×#4111yescharacteristic
112C22×C61C2×#4111yescharacteristic
113C22×C61C2×#4111yescharacteristic
114C22×C61C2×#4111yescharacteristic
115C22×C61C2×#4111yescharacteristic
116C22×C61H(5,𝔽2)11yescharacteristic
117C22×C61H(5,𝔽2)11yescharacteristic
118C4×C61—42no—
119C4×C61—41no—
120C4×C61—41no—
121C4×C61#12614yes—
122Dic61—22no—
123Dic61—22no—
124Dic61—41no—
125Dic61—41no—
126Dic61—42no—
127Dic61—42no—
128#2513—611nomaximal, Sylow
129C2×C61—82no—
130C2×C61C2×#12611yescharacteristic
131C2×C61#52911yescharacteristic
132C2×C61#54011yescharacteristic
133C2×C61#55311yescharacteristic
134C2×C61#55511yescharacteristic
135C2×C61#55911yescharacteristic
136C2×C61#55911yescharacteristic
137#397—612no—
138#397—612no—
139#390—611no—
140#390—611no—
141#390D6111yescharacteristic
142#389—611no—
143#388—612no—
144#388—612no—
145#382—611no—
146C4×C4⋊C4—611no—
147C4×C4⋊C4—611no—
148C61#251311yescharacteristic, complemented, Sylow
149C22×D4C2×D6111yescharacteristic
150C2×C4⋊C4—611no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C22⋊C4—612no—
157C2×C22⋊C4—612no—
158C2×C22⋊C4—612no—
159C2×C22⋊C4—612no—
160C2×C22⋊C4C2×D6112yes—
161C2×C22⋊C4C2×D6112yes—
162C2×C42—611no—
163C2×C42—611no—
164C2×C42—612no—
165C2×C42C2×D6111yescharacteristic
166#95—611no—
167#95—612no—
168#95—611no—
169#95—612no—
170#95—612no—
171#95—612no—
172C24C22×D6112yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—22no—
176C22×C4—611no—
177C22×C4—611no—
178C22×C4—612no—
179C22×C4—611no—
180C22×C4—612no—
181C22×C4—611no—
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6112yes—
185C22×C4C22×D6111yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—2442no—
192C22⋊C4—42no—
193C22⋊C4—42no—
194C22⋊C4—1224no—
195C22⋊C4—1224no—
196C22⋊C4—2442no—
197C22⋊C4—2442no—
198C42—22no—
199C42—1222no—
200C42—1222no—
201C42—2442no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23C23×D6111yescharacteristic
210D4—44no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—612no—
221C2×C4—612no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1222no—
237C2×C4—1221no—
238C2×C4#1175822212yes—
239C2×C4#1175822412yes—
240C2×C4#1175822412yes—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22#41×D6111yescharacteristic
249C22#41×D6111yescharacteristic
250C22C2×#1175822411yescharacteristic
251C22C2×#1175822411yescharacteristic
252C22C2×#1175822211yescharacteristic
253C22#1451982211yescharacteristic
254C22#1451982211yescharacteristic
255C4—41no—
256C4—41no—
257C4—42no—
258C4—1222no—
259C4—1222no—
260C4—2441no—
261C4—2442no—
262C4—2442no—
263C4—2441no—
264C4#1451977014yes—
265C2—82no—
266C2C2×#1451977011yescharacteristic
267C2#1684029111yescharacteristic
268C2#1684036611yescharacteristic
269C2#1684045911yescharacteristic
270C2#1684047611yescharacteristic
271C2#1684049511yescharacteristic
272C2#1684049511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2513
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #16839690C2semidirect
2. #16839690C2semidirect
5. #16839658C2semidirect
6. #16839656C2semidirect
7. #16839650C2semidirect
8. #16839628C2semidirect
9. C4⋊C4×Dic61C2semidirect
10. C4×#11758196C2semidirect
148. C61#2513semidirect