Finite Group Databasebeta

← #21457041

Subgroups — #21457041

Order 7808.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2#16840297C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840124C211yesmaximal, characteristic, complemented
5#16840122C211yesmaximal, characteristic, complemented
6#16840094C212yesmaximal, complemented
7#16840077C212yesmaximal
8#16840056C212yesmaximal, complemented
9#16840051C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#501C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13#14519777C2211yescharacteristic
14#14519776—21no—
15#14519776C2212yes—
16#14519775—21no—
17#14519772—21no—
18#14519765C2211yescharacteristic
19#14519762—21no—
20#14519757C2211yescharacteristic
21#14519752C2211yescharacteristic
22#14519742C2211yescharacteristic
23#14519739—21no—
24#14519739C2211yescharacteristic
25#14519735—21no—
26C4⋊C4×D61—21no—
27C4⋊C4×D61C2212yes—
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—
44Q8×D61—44no—
45C2×D244—21no—
46C2×D244C2311yescharacteristic
47C2×C4×D61—22no—
48C2×C4×D61—21no—
49C2×C4×D61D411yescharacteristic
50C2×C4×D61D411yescharacteristic
51C2×C4×D61C2311yescharacteristic
52C2×Dic122—21no—
53C2×Dic122—22no—
54C2×Dic122C2311yescharacteristic
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2311yescharacteristic
60C4⋊C4×C61C2312yes—
61C4⋊C4×C61C2311yescharacteristic
62C42×C61C2311yescharacteristic
63#11758198—21no—
64#11758198—21no—
65#11758198—21no—
66#11758198—21no—
67#11758198—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61C2312yes—
71#11758196—22no—
72#11758196—22no—
73#11758196—21no—
74C4×Dic61—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C22×D61—21no—
80C22×D61C2×D411yescharacteristic
81Q8×C61—42no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61C2×D411yescharacteristic
91C2×Dic61C2×D411yescharacteristic
92C2×Dic61C2×D411yescharacteristic
93D244—22no—
94D244—42no—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—44no—
99C4×D61—42no—
100Dic122—22no—
101Dic122—44no—
102Dic122—42no—
103C8×C61—22no—
104#92418—22no—
105C22×C61C22×D411yescharacteristic
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61AGL(1,ℤ/8)12yes—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C612−1+412yes—
118Dic61—21no—
119Dic61—21no—
120Dic61—41no—
121Dic61—42no—
122Dic61#13712yes—
123#3238—611nomaximal, Sylow
124C2×C61#53611yescharacteristic
125C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C61C2×#13711yescharacteristic
127D61—22no—
128D61—81no—
129C2×C4⋊Q8—611no—
130#529—611no—
131#501—611no—
132#501D6111yescharacteristic, complemented
133#489—611no—
134#489—611no—
135#483—612no—
136#480—612no—
137#477—612no—
138#476—612no—
139#432—611no—
140C61#323811yescharacteristic, complemented, Sylow
141C22×Q8—1221no—
142C4⋊Q8—612no—
143C4⋊Q8—611no—
144C4⋊Q8—1221no—
145C4⋊Q8—1221no—
146C4⋊Q8C2×D6111yescharacteristic
147#126—1221no—
148#125C2×D6111yescharacteristic
149#124—611no—
150#123—1221no—
151C22⋊Q8—611no—
152#121—611no—
153C4×Q8—611no—
154C4×D4—611no—
155C4×D4—1221no—
156#117—1221no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4—1221no—
159C2×C42—611no—
160#107—612no—
161#107C2×D6112yes—
162#106—612no—
163#106C2×D6112yes—
164C4⋊C8—612no—
165#103—612no—
166#103—612no—
167#102—612no—
168#102—612no—
169C22⋊C8—612no—
170#97—611no—
171#97C2×D6111yescharacteristic
172C2×Q8—21no—
173C2×Q8—611no—
174C2×Q8—1222no—
175C2×Q8—1221no—
176C2×Q8—2444no—
177C2×D4—611no—
178C2×D4—1221no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—1221no—
183C22×C4—1222no—
184C2×C8—612no—
185C2×C8C22×D6112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—612no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4C22×D6112yes—
196C4⋊C4C22×D6111yescharacteristic
197C4⋊C4C22×D6111yescharacteristic
198C22⋊C4—1221no—
199C22⋊C4—1221no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C22⋊C4—1221no—
203C42—611no—
204C42—611no—
205C42—611no—
206C42—1221no—
207C42C22×D6111yescharacteristic
208C23—611no—
209C23—1221no—
210Q8—42no—
211Q8—1222no—
212Q8—2442no—
213Q8—2444no—
214D4—1222no—
215D4—2442no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—1222no—
227C2×C4—2442no—
228C2×C4—2444no—
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4C23×D6111yescharacteristic
232C8—22no—
233C8—1222no—
234C22—612no—
235C22—1221no—
236C22—1221no—
237C22—2441no—
238C22—2441no—
239C22—2441no—
240C22C2×D4×D6111yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—612no—
247C4—1221no—
248C4—1221no—
249C4—2442no—
250C4—2441no—
251C4#1451982512yes—
252C2—1222no—
253C2—4881no—
254C2#1684033711yescharacteristic
255C2AGL(1,ℤ/8)×D6111yescharacteristic
256C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3238
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. C4⋊Q8×D61C2semidirect
3. #16840172C2semidirect
4. #16840124C2semidirect
5. #16840122C2semidirect
6. #16840094C2semidirect
8. #16840056C2semidirect
9. #16840051C2semidirect
10. #16839817C2semidirect
11. C61×#501C2semidirect
132. #501D61semidirect
140. C61#3238semidirect