Finite Group Databasebeta

← #21457062

Subgroups — #21457062

Order 7808.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840317C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840124C211yesmaximal, characteristic, complemented
5#16840122C211yesmaximal, characteristic, complemented
6#16840106C212yesmaximal, complemented
7#16840089C212yesmaximal
8#16840068C212yesmaximal, complemented
9#16840061C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#501C211yesmaximal, characteristic, complemented
12#14519777C2211yescharacteristic
13#14519772—21no—
14#14519768C2212yes—
15#14519765C2211yescharacteristic
16#14519762—21no—
17#14519757—21no—
18#14519757C2211yescharacteristic
19#14519753—21no—
20#14519752C2211yescharacteristic
21Q8×Dic61—21no—
22#14519742—21no—
23#14519742C2211yescharacteristic
24#14519739—21no—
25#14519739C2211yescharacteristic
26#14519735—21no—
27#14519735C2212yes—
28C42×D61C2211yescharacteristic
29#14519710C2212yes—
30#14519708C2212yes—
31#14519706C2212yes—
32#14519702C2212yes—
33#14519700C2212yes—
34#14519699C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic
38C4⋊Q8×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#107×C61C2212yes—
41#106×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×D244—21no—
45C2×D244C2311yescharacteristic
46C2×C4×D61—21no—
47C2×C4×D61D411yescharacteristic
48C2×C4×D61D411yescharacteristic
49C2×C4×D61C2311yescharacteristic
50C2×Dic122—21no—
51C2×Dic122C2311yescharacteristic
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2311yescharacteristic
57C4⋊C4×C61C2312yes—
58C4⋊C4×C61C2311yescharacteristic
59C42×C61C2311yescharacteristic
60#11758198—22no—
61#11758198—21no—
62#11758198—21no—
63#11758198—21no—
64#11758198—21no—
65#11758198—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—22no—
69C4⋊Dic61C2312yes—
70#11758196—22no—
71#11758196—21no—
72C4×Dic61—21no—
73C4×Dic61—22no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C22×D61—21no—
79C22×D61C2×D411yescharacteristic
80Q8×C61—42no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—22no—
88C2×Dic61—21no—
89C2×Dic61C2×D411yescharacteristic
90C2×Dic61C2×D411yescharacteristic
91C2×Dic61C2×D411yescharacteristic
92D244—22no—
93D244—42no—
94C4×D61—22no—
95C4×D61—41no—
96C4×D61—41no—
97C4×D61—42no—
98Dic122—22no—
99Dic122—42no—
100C8×C61—22no—
101#92418—22no—
102C22×C61C22×D411yescharacteristic
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—41no—
113C4×C61—42no—
114C4×C612−1+412yes—
115Dic61—21no—
116Dic61—21no—
117Dic61—21no—
118Dic61—41no—
119Dic61—42no—
120#3240—611nomaximal, Sylow
121C2×C61#53611yescharacteristic
122C2×C61#57511yescharacteristic
123C2×C61#57511yescharacteristic
124D61—41no—
125D61—81no—
126#533—611no—
127#529—611no—
128#501—611no—
129#501D6111yescharacteristic, complemented
130#489—611no—
131#489—611no—
132#485—612no—
133#482—612no—
134#479—612no—
135#478—612no—
136#432—611no—
137C61#324011yescharacteristic, complemented, Sylow
138C4⋊Q8—611no—
139C4⋊Q8C2×D6111yescharacteristic
140#126—1221no—
141#125—612no—
142#125C2×D6111yescharacteristic
143#124—611no—
144#123—1221no—
145C22⋊Q8—611no—
146C22⋊Q8—1221no—
147C22⋊Q8—1221no—
148#121—611no—
149C4×Q8—611no—
150C4×Q8—1221no—
151C4×Q8—1221no—
152C4×D4—611no—
153C4×D4—1221no—
154#117—612no—
155#117—1221no—
156C2×C42—611no—
157#107—612no—
158#107C2×D6112yes—
159#106—612no—
160#106C2×D6112yes—
161C4⋊C8—612no—
162#103—612no—
163#103—612no—
164#102—612no—
165#102—612no—
166C22⋊C8—612no—
167#97—611no—
168#97C2×D6111yescharacteristic
169C2×Q8—21no—
170C2×Q8—611no—
171C2×Q8—1221no—
172C2×D4—611no—
173C2×D4—1221no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1221no—
178C2×C8—612no—
179C2×C8C22×D6112yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—612no—
184C4⋊C4—1221no—
185C4⋊C4—1222no—
186C4⋊C4—1221no—
187C4⋊C4—1222no—
188C4⋊C4—1221no—
189C4⋊C4C22×D6112yes—
190C4⋊C4C22×D6111yescharacteristic
191C4⋊C4C22×D6111yescharacteristic
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C42—611no—
199C42—611no—
200C42—611no—
201C42—1222no—
202C42—1221no—
203C42C22×D6111yescharacteristic
204C23—611no—
205C23—1221no—
206Q8—42no—
207Q8—1222no—
208Q8—2442no—
209D4—1222no—
210D4—2442no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2442no—
223C2×C4D4×D6111yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—22no—
227C8—1222no—
228C22—1221no—
229C22—1221no—
230C22—1221no—
231C22—2441no—
232C22—2441no—
233C22—2441no—
234C22C2×D4×D6111yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—1221no—
241C4—1221no—
242C4—1221no—
243C4—2442no—
244C4—2441no—
245C4#1451982512yes—
246C2—4881no—
247C2—2441no—
248C2#1684033711yescharacteristic
249C2#1684055811yescharacteristic
250C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3240
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840172C2semidirect
4. #16840124C2semidirect
5. #16840122C2semidirect
6. #16840106C2semidirect
8. #16840068C2semidirect
9. #16840061C2semidirect
10. #16839817C2semidirect
11. C61×#501C2semidirect
129. #501D61semidirect
137. C61#3240semidirect