Finite Group Databasebeta

← #21457059

Subgroups — #21457059

Order 7808.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 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#16840296C211yesmaximal, characteristic
2#16840168C211yesmaximal, characteristic, complemented
3#16840168C211yesmaximal, characteristic, complemented
4#16840124C211yesmaximal, characteristic, complemented
5#16840124C211yesmaximal, characteristic, complemented
6#16840103C212yesmaximal, complemented
7#16840086C212yesmaximal
8#16840066C212yesmaximal, complemented
9#16840059C212yesmaximal, complemented
10#16839819C211yesmaximal, characteristic, complemented
11C61×#533C211yesmaximal, characteristic, complemented
12#14519771—21no—
13#14519769C2211yescharacteristic
14#14519765C2211yescharacteristic
15#14519760—21no—
16#14519756C2211yescharacteristic
17#14519751C2211yescharacteristic
18C4×Dic122C2211yescharacteristic
19C4×D244C2211yescharacteristic
20C4×C22⋊D61—21no—
21#14519734—21no—
22#14519710C2212yes—
23#14519710C2212yes—
24#14519708C2212yes—
25#14519708C2212yes—
26C4⋊#92418C2212yes—
27#14519700C2212yes—
28#14519700C2212yes—
29#14519697C2212yes—
30#14519697C2212yes—
31C22⋊#92418C2212yes—
32#14519688C2211yescharacteristic
33#14519688C2211yescharacteristic
34C4⋊Q8×C61C2211yescharacteristic
35C4⋊Q8×C61C2211yescharacteristic
36#125×C61C2212yes—
37C22⋊Q8×C61—21no—
38C22⋊Q8×C61—21no—
39C4×Q8×C61—21no—
40C4×Q8×C61—21no—
41#117×C61C2212yes—
42C2×C42×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61—21no—
45C22×C4×C61D411yescharacteristic
46C22×C4×C61D411yescharacteristic
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122C2311yescharacteristic
52C4⋊C4×C61—22no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2312yes—
57C4⋊C4×C61C2312yes—
58C22⋊C4×C61—22no—
59C42×C61—22no—
60C42×C61D411yescharacteristic
61C42×C61D411yescharacteristic
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758198—21no—
66#11758198—21no—
67#11758198—21no—
68#11758198—21no—
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75C4×Dic61—21no—
76C2×#92418C2312yes—
77C2×#92418C2312yes—
78C23×C61C2×D411yescharacteristic
79C22×D61—21no—
80Q8×C61—42no—
81Q8×C61—42no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—42no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97D244—22no—
98C4×D61—42no—
99Dic122—22no—
100#92418—22no—
101#92418—22no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61C22×D411yescharacteristic
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61—42no—
116C4×C612−1+412yes—
117Dic61—41no—
118Dic61—41no—
119Dic61—41no—
120#3240—611nomaximal, Sylow
121C2×C61—41no—
122C2×C61#53611yescharacteristic
123C2×C61#57511yescharacteristic
124C2×C61#57511yescharacteristic
125D61—81no—
126#533D6111yescharacteristic, complemented
127#529—611no—
128#501—611no—
129#501—611no—
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⋊Q8C2×D6111yescharacteristic
139C4⋊Q8C2×D6111yescharacteristic
140#126—1221no—
141#125—611no—
142#125C2×D6112yes—
143#124—611no—
144#123—1221no—
145C22⋊Q8—21no—
146C22⋊Q8—21no—
147C22⋊Q8—611no—
148#121—611no—
149C4×Q8—21no—
150C4×Q8—21no—
151C4×Q8—611no—
152C4×D4—611no—
153C4×D4—1221no—
154#117—1221no—
155#117C2×D6112yes—
156C2×C42C2×D6111yescharacteristic
157#107—612no—
158#107—612no—
159#106—612no—
160#106—612no—
161C4⋊C8—612no—
162#103—612no—
163#103—612no—
164#102—612no—
165#102—612no—
166C22⋊C8—612no—
167#97—611no—
168#97—611no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—611no—
172C2×D4—611no—
173C2×D4—1221no—
174C22×C4—1221no—
175C22×C4C22⋊D6111yescharacteristic
176C22×C4C22⋊D6111yescharacteristic
177C22×C4C22×D6111yescharacteristic
178C2×C8—612no—
179C2×C8—612no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—611no—
185C4⋊C4—611no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4C22×D6112yes—
191C4⋊C4C22×D6112yes—
192C22⋊C4—22no—
193C22⋊C4—1221no—
194C22⋊C4—1221no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C42—22no—
199C42—1221no—
200C42C22⋊D6111yescharacteristic
201C42C22⋊D6111yescharacteristic
202C42C22×D6111yescharacteristic
203C42C22×D6111yescharacteristic
204C23—1221no—
205C23C2×C22⋊D6111yescharacteristic
206Q8—42no—
207Q8—42no—
208Q8—1222no—
209D4—1222no—
210D4—2442no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—2442no—
220C2×C4C2×C22⋊D6111yescharacteristic
221C2×C4C2×C22⋊D6111yescharacteristic
222C2×C4C2×C22⋊D6111yescharacteristic
223C2×C4C2×C22⋊D6111yescharacteristic
224C2×C4C2×C22⋊D6111yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—1222no—
227C8—1222no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—2441no—
232C22—2441no—
233C22—2441no—
234C22C22×C22⋊D6111yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—2441no—
243C4—2441no—
244C4—2441no—
245C4#1451982512yes—
246C2—41no—
247C2—4881no—
248C2#1684033611yescharacteristic
249C2#1684056011yescharacteristic
250C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3240
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840168C2semidirect
3. #16840168C2semidirect
4. #16840124C2semidirect
5. #16840124C2semidirect
6. #16840103C2semidirect
8. #16840066C2semidirect
9. #16840059C2semidirect
10. #16839819C2semidirect
11. C61×#533C2semidirect
126. #533D61semidirect
137. C61#3240semidirect