Finite Group Databasebeta

← #21457034

Subgroups — #21457034

Order 7808.

322 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 111 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#16840318C211yesmaximal, characteristic
2#16840317C211yesmaximal, characteristic
3#16840168C211yesmaximal, characteristic, complemented
4#16840132C211yesmaximal, characteristic, complemented
5#16840131C211yesmaximal, characteristic, complemented
6#16840106C212yesmaximal
7#16840105C212yesmaximal
8#16840056C212yesmaximal, complemented
9#16840046C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic
11C61×#501C211yesmaximal, characteristic, complemented
12#14519777C2211yescharacteristic
13#14519776C2211yescharacteristic
14#14519776C2211yescharacteristic
15#14519769C2211yescharacteristic
16#14519768—21no—
17#14519757C2212yes—
18#14519755—21no—
19#14519755—21no—
20#14519753—21no—
21Q8×Dic61—21no—
22#14519742—21no—
23#14519742—21no—
24#14519742C2212yes—
25#14519735—21no—
26#14519735C2211yescharacteristic
27#14519735C2211yescharacteristic
28C42×D61C2211yescharacteristic
29#14519710C2212yes—
30#14519708C2212yes—
31#14519706C2212yes—
32#14519702C2212yes—
33#14519702C2212yes—
34#14519700C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic
38C4⋊Q8×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#107×C61C2212yes—
41#106×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×C4×D61D411yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61C2311yescharacteristic
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122C2312yes—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2311yescharacteristic
55C4⋊C4×C61C2312yes—
56C4⋊C4×C61C2311yescharacteristic
57C42×C61C2311yescharacteristic
58#11758198—22no—
59#11758198—21no—
60#11758198—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C4⋊Dic61—22no—
64C4⋊Dic61C2311yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66#11758196—21no—
67#11758196—21no—
68#11758196—21no—
69#11758196—21no—
70#11758196—22no—
71C4×Dic61—22no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C22×D61C2×D411yescharacteristic
79Q8×C61—42no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61C2×D411yescharacteristic
90C2×Dic61C2×D411yescharacteristic
91C2×Dic61C2×D411yescharacteristic
92C4×D61—22no—
93C4×D61—22no—
94C4×D61—41no—
95Dic122—24no—
96Dic122—42no—
97Dic122—42no—
98C8×C61—22no—
99#92418—22no—
100C22×C61C22×D411yescharacteristic
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—21no—
104C4×C61—21no—
105C4×C61—21no—
106C4×C61—41no—
107C4×C61—41no—
108C4×C61—42no—
109C4×C612−1+412yes—
110Dic61—21no—
111Dic61—21no—
112Dic61—42no—
113Dic61—41no—
114Dic61—41no—
115Dic61#13712yes—
116#3237—611nomaximal, Sylow
117C2×C61#53611yescharacteristic
118C2×C61C2×#13711yescharacteristic
119C2×C61#57511yescharacteristic
120D61—41no—
121#533—611no—
122#533—611no—
123#501—611no—
124#501D6111yescharacteristic, complemented
125#491—611no—
126#491—611no—
127#485—612no—
128#485—612no—
129#477—612no—
130#475—612no—
131#432—611no—
132C61#323711yescharacteristic, complemented, Sylow
133C4⋊Q8—611no—
134C4⋊Q8—611no—
135C4⋊Q8—611no—
136C4⋊Q8C2×D6111yescharacteristic
137#125—611no—
138#125—1221no—
139#125C2×D6111yescharacteristic
140C22⋊Q8—612no—
141C22⋊Q8—1221no—
142C22⋊Q8—1221no—
143C22⋊Q8—1221no—
144C4×Q8—612no—
145C4×Q8—1221no—
146C4×Q8—1221no—
147C4×Q8—1221no—
148#117—611no—
149#117—611no—
150#117—1221no—
151C2×C42—611no—
152#107—612no—
153#107C2×D6112yes—
154#106—612no—
155#106C2×D6112yes—
156C4⋊C8—612no—
157#103—612no—
158#103—612no—
159#103—612no—
160#103—612no—
161C22⋊C8—612no—
162#97—611no—
163#97C2×D6111yescharacteristic
164C2×Q8—21no—
165C2×Q8—612no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C2×C8—612no—
172C2×C8C22×D6112yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—611no—
177C4⋊C4—611no—
178C4⋊C4—1222no—
179C4⋊C4—1221no—
180C4⋊C4—1221no—
181C4⋊C4—1222no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4C22×D6111yescharacteristic
187C4⋊C4C22×D6111yescharacteristic
188C4⋊C4C22×D6112yes—
189C22⋊C4—1221no—
190C22⋊C4—1221no—
191C22⋊C4—1222no—
192C42—611no—
193C42—611no—
194C42—611no—
195C42—1221no—
196C42—1221no—
197C42—1222no—
198C42C22×D6111yescharacteristic
199C23—611no—
200Q8—42no—
201Q8—1224no—
202Q8—2442no—
203Q8—2442no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—611no—
208C2×C4—611no—
209C2×C4—611no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—2441no—
216C2×C4D4×D6111yescharacteristic
217C2×C4D4×D6111yescharacteristic
218C2×C4C23×D6111yescharacteristic
219C8—22no—
220C8—1222no—
221C22—1221no—
222C22—1221no—
223C22—1221no—
224C22C2×D4×D6111yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—42no—
229C4—41no—
230C4—612no—
231C4—1221no—
232C4—1221no—
233C4—2441no—
234C4—2441no—
235C4—2442no—
236C4#1451982512yes—
237C2—2441no—
238C2#1684033711yescharacteristic
239C2#137×D6111yescharacteristic
240C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3237
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
3. #16840168C2semidirect
4. #16840132C2semidirect
5. #16840131C2semidirect
8. #16840056C2semidirect
9. #16840046C2semidirect
11. C61×#501C2semidirect
124. #501D61semidirect
132. C61#3237semidirect