Finite Group Databasebeta

← #21457056

Subgroups — #21457056

Order 7808.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840317C211yesmaximal, characteristic, complemented
2#16840291C211yesmaximal, characteristic
3#16840171C211yesmaximal, characteristic, complemented
4#16840168C211yesmaximal, characteristic, complemented
5#16840121C211yesmaximal, characteristic, complemented
6#16840102C212yesmaximal, complemented
7#16840085C212yesmaximal
8#16840067C212yesmaximal, complemented
9#16840060C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#489C211yesmaximal, characteristic, complemented
12#14519777C2211yescharacteristic
13#14519770—21no—
14#14519769C2211yescharacteristic
15#14519768C2212yes—
16#14519759—21no—
17#14519757—21no—
18#14519753—21no—
19#14519753C2211yescharacteristic
20#14519748C2211yescharacteristic
21Q8×Dic61—21no—
22Q8×Dic61C2211yescharacteristic
23#14519742—21no—
24D4×Dic61C2211yescharacteristic
25#14519737—21no—
26#14519735C2212yes—
27#14519733—21no—
28C42×D61C2211yescharacteristic
29#14519711C2212yes—
30#14519710C2212yes—
31#14519709C2212yes—
32#14519708C2212yes—
33#14519706C2212yes—
34#14519701C2212yes—
35#14519698C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic
38C4⋊Q8×C61C2211yescharacteristic
39#124×C61C2211yescharacteristic
40#103×C61C2212yes—
41#102×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48C2×C4×D61D411yescharacteristic
49C2×C4×D61D411yescharacteristic
50C2×C4×D61C2311yescharacteristic
51C2×Dic122—21no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—21no—
56C22⋊C4×C61—21no—
57C42×C61C2311yescharacteristic
58C22⋊Dic61—21no—
59C22⋊Dic61—21no—
60#11758198—22no—
61#11758198—21no—
62C4⋊Dic61—21no—
63C4⋊Dic61—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2312yes—
66C4⋊Dic61C2311yescharacteristic
67C4⋊Dic61C2311yescharacteristic
68#11758196—21no—
69#11758196—21no—
70#11758196—21no—
71#11758196—22no—
72C4×Dic61—21no—
73C4×Dic61—22no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C23×C61—21no—
79C22×D61C2×D411yescharacteristic
80Q8×C61—22no—
81Q8×C61—42no—
82D4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C22⋊D61—42no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—21no—
92C2×Dic61—42no—
93C2×Dic61C2×D411yescharacteristic
94C2×Dic61C2×D411yescharacteristic
95C2×Dic61C2×D411yescharacteristic
96C4×D61—22no—
97C4×D61—41no—
98C4×D61—41no—
99Dic122—42no—
100C8×C61—22no—
101#92418—22no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61C22×D411yescharacteristic
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—21no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—42no—
113C4×C612−1+412yes—
114Dic61—21no—
115Dic61—21no—
116Dic61—21no—
117Dic61—42no—
118Dic61—41no—
119Dic61—41no—
120#3240—611nomaximal, Sylow
121C2×C61—81no—
122C2×C61#53611yescharacteristic
123C2×C61#57511yescharacteristic
124C2×C61#57511yescharacteristic
125D61—41no—
126#533—611no—
127#529—611no—
128#501—611no—
129#501—611no—
130#489—611no—
131#489D6111yescharacteristic, complemented
132#485—612no—
133#482—612no—
134#479—612no—
135#478—612no—
136#432—611no—
137C61#324011yescharacteristic, complemented, Sylow
138C4⋊Q8—611no—
139C4⋊Q8C2×D6111yescharacteristic
140#126—1221no—
141#125—612no—
142#125—611no—
143#124C2×D6111yescharacteristic
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×C42—611no—
157#107—612no—
158#107—612no—
159#106—612no—
160#106—612no—
161C4⋊C8—612no—
162#103—612no—
163#103C2×D6112yes—
164#102—612no—
165#102C2×D6112yes—
166C22⋊C8—612no—
167#97—611no—
168#97C2×D6111yescharacteristic
169C2×Q8—21no—
170C2×Q8—1221no—
171C2×Q8C22×D6111yescharacteristic
172C2×D4—1221no—
173C2×D4C22×D6111yescharacteristic
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1221no—
178C2×C8—612no—
179C2×C8C22×D6112yes—
180C4⋊C4—21no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—1221no—
185C4⋊C4—1222no—
186C4⋊C4—1221no—
187C4⋊C4—1222no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4C22×D6112yes—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C42—611no—
199C42—611no—
200C42—611no—
201C42—1222no—
202C42—1221no—
203C42C22×D6111yescharacteristic
204C23—21no—
205C23—611no—
206Q8—22no—
207Q8—42no—
208Q8—2442no—
209D4—22no—
210D4—2442no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—611no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—1222no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2442no—
223C2×C4D4×D6111yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—22no—
227C8—1222no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—1221no—
232C22—1221no—
233C22—1221no—
234C22C2×D4×D6111yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—41no—
239C4—1221no—
240C4—1221no—
241C4—1221no—
242C4—2441no—
243C4—2441no—
244C4—2442no—
245C4#1451982412yes—
246C2—81no—
247C2—2441no—
248C2#1684033211yescharacteristic
249C2#1684055811yescharacteristic
250C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61#3240
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840171C2semidirect
4. #16840168C2semidirect
5. #16840121C2semidirect
6. #16840102C2semidirect
8. #16840067C2semidirect
9. #16840060C2semidirect
10. #16839817C2semidirect
11. C61×#489C2semidirect
131. #489D61semidirect
137. C61#3240semidirect