Finite Group Databasebeta

← #21457061

Subgroups — #21457061

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#16840319C211yesmaximal, characteristic, complemented
2#16840296C211yesmaximal, characteristic
3#16840171C211yesmaximal, characteristic, complemented
4#16840171C211yesmaximal, characteristic, complemented
5#16840122C211yesmaximal, characteristic, complemented
6#16840122C211yesmaximal, characteristic, complemented
7#16840104C212yesmaximal, complemented
8#16840087C212yesmaximal
9#16840070C212yesmaximal, complemented
10#16840063C212yesmaximal, complemented
11C61×#432C211yesmaximal, characteristic, complemented
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519771—21no—
15#14519769C2211yescharacteristic
16#14519769C2212yes—
17#14519765C2211yescharacteristic
18#14519760—21no—
19#14519756—21no—
20#14519756—21no—
21#14519756C2211yescharacteristic
22#14519751C2211yescharacteristic
23C4×Dic122—21no—
24C4×Dic122—21no—
25C4×Dic122C2211yescharacteristic
26C4×D244C2211yescharacteristic
27C4×C22⋊D61—21no—
28#14519736C2212yes—
29#14519734—21no—
30#14519711C2212yes—
31#14519711C2212yes—
32#14519709C2212yes—
33#14519709C2212yes—
34#14519702C2212yes—
35#14519702C2212yes—
36#14519699C2212yes—
37#14519699C2212yes—
38C2×C42×C61C2211yescharacteristic
39C4⋊C8×C61C2212yes—
40C22⋊C8×C61C2212yes—
41#97×C61C2211yescharacteristic
42#97×C61C2211yescharacteristic
43C22×C4×C61D411yescharacteristic
44C22×C4×C61D411yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122C2311yescharacteristic
52C2×C8×C61C2312yes—
53C2×C8×C61C2312yes—
54C42×C61D411yescharacteristic
55C42×C61D411yescharacteristic
56C42×C61C2311yescharacteristic
57C42×C61C2311yescharacteristic
58C22⋊Dic61—22no—
59C22⋊Dic61—21no—
60#11758198—21no—
61#11758198—21no—
62#11758198—21no—
63#11758198—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61C2312yes—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73#11758196—22no—
74#11758196—22no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61—22no—
78C23×C61C2×D411yescharacteristic
79C22×D61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2411yescharacteristic
89C22⋊D61—42no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95D244—22no—
96C4×D61—42no—
97Dic122—22no—
98Dic122—42no—
99Dic122—42no—
100C8×C61—22no—
101C8×C61—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×C612−1+412yes—
115Dic61—41no—
116Dic61—42no—
117Dic61—42no—
118Dic61—41no—
119Dic61—41no—
120#3240—611nomaximal, Sylow
121C2×C61—41no—
122C2×C61#53611yescharacteristic
123C2×C61#57511yescharacteristic
124C2×C61#57511yescharacteristic
125D61—81no—
126#533—611no—
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#432D6111yescharacteristic, complemented
137C61#324011yescharacteristic, complemented, Sylow
138C4⋊Q8—611no—
139C4⋊Q8—611no—
140#126—1221no—
141#125—611no—
142#125—612no—
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×C42C2×D6111yescharacteristic
157#107—612no—
158#107—612no—
159#106—612no—
160#106—612no—
161C4⋊C8C2×D6112yes—
162#103—612no—
163#103—612no—
164#102—612no—
165#102—612no—
166C22⋊C8C2×D6112yes—
167#97C2×D6111yescharacteristic
168#97C2×D6111yescharacteristic
169C2×Q8—611no—
170C2×Q8—1221no—
171C2×Q8—1221no—
172C2×D4—611no—
173C2×D4—1221no—
174C22×C4—1221no—
175C22×C4D24411yescharacteristic
176C22×C4D24411yescharacteristic
177C22×C4C22×D6111yescharacteristic
178C2×C8C22×D6112yes—
179C2×C8C22×D6112yes—
180C4⋊C4—612no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C22⋊C4—1222no—
193C22⋊C4—1221no—
194C22⋊C4—1221no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C42—1222no—
199C42—1221no—
200C42D24411yescharacteristic
201C42D24411yescharacteristic
202C42C22×D6111yescharacteristic
203C42C22×D6111yescharacteristic
204C23—1221no—
205C23C2×D24411yescharacteristic
206Q8—1222no—
207Q8—2442no—
208Q8—2442no—
209D4—1222no—
210D4—2442no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—2442no—
220C2×C4C2×D24411yescharacteristic
221C2×C4C2×D24411yescharacteristic
222C2×C4C2×D24411yescharacteristic
223C2×C4C2×D24411yescharacteristic
224C2×C4C2×D24411yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—2441no—
232C22—2441no—
233C22—2441no—
234C22C22×D24411yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—2441no—
241C4—2441no—
242C4—2442no—
243C4—2442no—
244C4—2441no—
245C4#1451982412yes—
246C2—41no—
247C2—4881no—
248C2#1684033811yescharacteristic
249C2#1684056211yescharacteristic
250C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3240
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
3. #16840171C2semidirect
4. #16840171C2semidirect
5. #16840122C2semidirect
6. #16840122C2semidirect
7. #16840104C2semidirect
9. #16840070C2semidirect
10. #16840063C2semidirect
11. C61×#432C2semidirect
136. #432D61semidirect
137. C61#3240semidirect