Finite Group Databasebeta

← #21456992

Subgroups — #21456992

Order 7808.

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

normal subgroups only

This group has 334 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
1#16840298C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic, complemented
3#16840163C212yesmaximal, complemented
4#16840118C212yesmaximal, complemented
5#16840090C211yesmaximal, characteristic, complemented
6#16840080C211yesmaximal, characteristic
7#16840076C211yesmaximal, characteristic
8#16840071C212yesmaximal, complemented
9#16840065C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#484C211yesmaximal, characteristic, complemented
12#14519772—21no—
13#14519768—21no—
14#14519768—21no—
15#14519768C2212yes—
16#14519768C2212yes—
17#14519768C2211yescharacteristic
18#14519766C2211yescharacteristic
19#14519761—21no—
20#14519751C2211yescharacteristic
21Q8×Dic61C2211yescharacteristic
22#14519739C2211yescharacteristic
23#14519737—21no—
24#14519735—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—21no—
28C2×C4×Dic61C2211yescharacteristic
29#14519711C2212yes—
30#14519708C2212yes—
31#14519708C2212yes—
32#14519706C2212yes—
33#14519701C2212yes—
34#14519699C2212yes—
35#14519697C2212yes—
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yes—
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yes—
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48C22×Dic61D411yescharacteristic
49C22×Dic61D411yescharacteristic
50C2×D244C2311yescharacteristic
51C2×C4×D61—21no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61C2312yes—
56C4⋊C4×C61C2311yescharacteristic
57C22⋊C4×C61—21no—
58#11758198—21no—
59#11758198—21no—
60#11758198—21no—
61#11758198—21no—
62C4⋊Dic61—21no—
63C4⋊Dic61—22no—
64C4⋊Dic61—22no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69#11758196—22no—
70#11758196—22no—
71#11758196—21no—
72C4×Dic61—21no—
73C4×Dic61D411yescharacteristic
74C4×Dic61D411yescharacteristic
75C4×Dic61C2311yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C23×C61C2×D411yescharacteristic
79C22×D61—21no—
80Q8×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—42no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C22⋊D61—42no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—41no—
93C2×Dic61—42no—
94C2×Dic61C2×D411yescharacteristic
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98D244—22no—
99C4×D61—42no—
100C8×C61—22no—
101#92418—22no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61#13512yes—
105C22×C61C22×D411yescharacteristic
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61—41no—
112C4×C61—42no—
113C4×C612−1+412yes—
114Dic61—21no—
115Dic61—21no—
116Dic61—21no—
117Dic61—21no—
118Dic61—42no—
119Dic61—41no—
120#3232—611nomaximal, Sylow
121C2×C61—22no—
122C2×C61#53611yescharacteristic
123C2×C61C2×#13511yescharacteristic
124C2×C61#57511yescharacteristic
125D61—81no—
126#529—611no—
127C2×#125—611no—
128#499—612no—
129#488—612no—
130#484D6111yescharacteristic, complemented
131#483—611no—
132#481—611no—
133#480—611no—
134#479—612no—
135#478—612no—
136#431—611no—
137C61#323211yescharacteristic, complemented, Sylow
138#126—1221no—
139#125—612no—
140#125—612no—
141#125—611no—
142#125—1221no—
143#125—1221no—
144#124—611no—
145#123—1221no—
146C22⋊Q8C2×D6111yescharacteristic
147#121—611no—
148C4×Q8—611no—
149C4×D4—611no—
150C4×D4—1221no—
151#117—1221no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C42—611no—
157#107—612no—
158#107C2×D6112yes—
159#106—612no—
160#106—612no—
161C4⋊C8—612no—
162#103—612no—
163#103C2×D6112yes—
164#102—612no—
165#102—612no—
166C22⋊C8—611no—
167C22⋊C8C2×D6111yescharacteristic
168C4×C8—612no—
169C2×Q8C22×D6111yescharacteristic
170C2×D4—611no—
171C2×D4—1221no—
172C22×C4—21no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178C2×C8—612no—
179C2×C8C22×D6112yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—612no—
183C4⋊C4—611no—
184C4⋊C4—1222no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4C22×D6112yes—
193C4⋊C4C22×D6111yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C42—611no—
200C42—611no—
201C42—611no—
202C42—611no—
203C42—1221no—
204C23—1221no—
205C23D4×D6111yescharacteristic
206Q8—22no—
207D4—1222no—
208D4—2442no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—2442no—
222C2×C4—2441no—
223C2×C4—2442no—
224C2×C4D4×D6111yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—22no—
227C8—1222no—
228C22—21no—
229C22—21no—
230C22—2441no—
231C22—2441no—
232C22—2441no—
233C22#1451980012yes—
234C22C2×D4×D6111yescharacteristic
235C4—21no—
236C4—42no—
237C4—41no—
238C4—41no—
239C4—1221no—
240C4—1221no—
241C4—1221no—
242C4—1221no—
243C4—2442no—
244C4—2441no—
245C4#1451982412yes—
246C2—22no—
247C2—4881no—
248C2#1684033411yescharacteristic
249C2C2×#1451980011yescharacteristic
250C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#484C2
socleC22×C61C22×D4
hypercenter#484D61
hypocenterC61#3232
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#14519768C2semidirect
3. #16840163C2semidirect
4. #16840118C2semidirect
5. #16840090C2semidirect
8. #16840071C2semidirect
9. #16840065C2semidirect
10. #16839812C2semidirect
11. C61×#484C2semidirect
130. #484D61semidirect
137. C61#3232semidirect