Finite Group Databasebeta

← #21457000

Subgroups — #21457000

Order 7808.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840164C212yesmaximal, complemented
4#16840117C212yesmaximal, complemented
5#16840104C212yesmaximal, complemented
6#16840087C212yesmaximal
7#16840058C211yesmaximal, characteristic, complemented
8#16840053C211yesmaximal, characteristic, complemented
9#16840048C211yesmaximal, characteristic, complemented
10#16840043C211yesmaximal, characteristic, complemented
11C61×#431C211yesmaximal, 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×C61C2211yescharacteristic
40C4⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2212yes—
42C4×C8×C61C2212yes—
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—21no—
82C2×C4×C61—21no—
83C2×C4×C61—41no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2411yescharacteristic
90C22⋊D61—42no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96D244—21no—
97D244—21no—
98C4×D61—42no—
99Dic122—21no—
100Dic122—21no—
101Dic122—42no—
102Dic122—42no—
103C8×C61—22no—
104C8×C61—22no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—21no—
108C22×C61C22×D411yescharacteristic
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61#13512yes—
117C4×C612−1+411yescharacteristic
118C4×C612−1+411yescharacteristic
119Dic61—41no—
120Dic61—42no—
121Dic61—41no—
122Dic61—42no—
123Dic61—41no—
124#3233—611nomaximal, Sylow
125C2×C61—41no—
126C2×C61#53611yescharacteristic
127C2×C61C2×#13511yescharacteristic
128C2×C61#57511yescharacteristic
129D61—81no—
130#533—611no—
131#529—611no—
132#499—612no—
133#488—612no—
134#485—612no—
135#482—612no—
136#477—611no—
137#476—611no—
138#475—611no—
139#474—611no—
140#431D6111yescharacteristic, complemented
141C61#323311yescharacteristic, complemented, Sylow
142C4⋊Q8—611no—
143C4⋊Q8—611no—
144#126—1221no—
145#125—611no—
146#125—612no—
147#124—611no—
148#123—1221no—
149C22⋊Q8—611no—
150C22⋊Q8—1221no—
151C22⋊Q8—1221no—
152#121—611no—
153C4×Q8—611no—
154C4×Q8—1221no—
155C4×Q8—1221no—
156C4×D4—611no—
157C4×D4—1221no—
158#117—612no—
159#117—1221no—
160C2×C42C2×D6111yescharacteristic
161#107—612no—
162#107—612no—
163#106—612no—
164#106—612no—
165C4⋊C8C2×D6111yescharacteristic
166C4⋊C8C2×D6111yescharacteristic
167#103—612no—
168#103—612no—
169#102—612no—
170#102—612no—
171C22⋊C8C2×D6112yes—
172C4×C8C2×D6112yes—
173C2×Q8—611no—
174C2×Q8—1221no—
175C2×Q8—1221no—
176C2×D4—611no—
177C2×D4—1221no—
178C22×C4—1221no—
179C22×C4D24411yescharacteristic
180C22×C4D24411yescharacteristic
181C22×C4C22×D6111yescharacteristic
182C2×C8C22×D6112yes—
183C2×C8C22×D6112yes—
184C4⋊C4—612no—
185C4⋊C4—612no—
186C4⋊C4—611no—
187C4⋊C4—611no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4—1222no—
193C4⋊C4—1222no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C22⋊C4—1222no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C22⋊C4—1221no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C42—1222no—
203C42—1221no—
204C42D24411yescharacteristic
205C42D24411yescharacteristic
206C42C22×D6111yescharacteristic
207C42C22×D6111yescharacteristic
208C23—1221no—
209C23C2×D24411yescharacteristic
210Q8—1221no—
211Q8—1221no—
212Q8—2442no—
213Q8—2442no—
214D4—1221no—
215D4—1221no—
216D4—2442no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—2442no—
227C2×C4C2×D24411yescharacteristic
228C2×C4C2×D24411yescharacteristic
229C2×C4C2×D24411yescharacteristic
230C2×C4C2×D24411yescharacteristic
231C2×C4C2×D24411yescharacteristic
232C2×C4C23×D6111yescharacteristic
233C8—22no—
234C8—22no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22C22×D24411yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—2441no—
247C4—2442no—
248C4—2441no—
249C4—2442no—
250C4—2441no—
251C4#1451979912yes—
252C4#1451982411yescharacteristic
253C4#1451982411yescharacteristic
254C2—41no—
255C2—4881no—
256C2#1684033811yescharacteristic
257C2C2×#1451979911yescharacteristic
258C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3233
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16840319C2semidirect
3. #16840164C2semidirect
4. #16840117C2semidirect
5. #16840104C2semidirect
7. #16840058C2semidirect
8. #16840053C2semidirect
9. #16840048C2semidirect
10. #16840043C2semidirect
11. C61×#431C2semidirect
140. #431D61semidirect
141. C61#3233semidirect