Finite Group Databasebeta

← #21453881

Subgroups — #21453881

Order 7808.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#14519775C211yesmaximal, characteristic, complemented
2C2×#14519770C211yesmaximal, characteristic
3#16839704C212yesmaximal, complemented
4#16839698C212yesmaximal
5#16839696C212yesmaximal, complemented
6#16839690C212yesmaximal
7#16839683C211yesmaximal, characteristic, complemented
8#16839681C211yesmaximal, characteristic, complemented
9#16839674C211yesmaximal, characteristic
10#16839629C211yesmaximal, characteristic, complemented
11C61×#393C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13#14519775—24no—
14#14519770—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C2×Q8×C61—22no—
39C2×Q8×C61—42no—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C2×Dic122—22no—
51C2×Dic122—42no—
52C22⋊C4×C61—22no—
53C22⋊C4×C61—42no—
54C22⋊Dic61—22no—
55C22⋊Dic61—22no—
56C22⋊Dic61—42no—
57C4⋊Dic61—22no—
58C4⋊Dic61—42no—
59#11758196—22no—
60#11758196—22no—
61#11758196—24no—
62#11758196—24no—
63#11758196—42no—
64C4×Dic61D414yes—
65C23×C61—21no—
66C23×C61—22no—
67C23×C61—22no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61C2411yescharacteristic
71Q8×C61—44no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61C2×D412yes—
97C2×Dic61C2×D412yes—
98Dic122—44no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61C22×D411yescharacteristic
105C22×C61H(5,𝔽2)12yes—
106C22×C612−1+411yescharacteristic
107C22×C612−1+412yes—
108C22×C612−1+411yescharacteristic
109C4×C61—22no—
110C4×C61—42no—
111C4×C61—41no—
112C4×C61—42no—
113Dic61—22no—
114Dic61—22no—
115Dic61—42no—
116Dic61—41no—
117Dic61—41no—
118Dic61—42no—
119#2821—611nomaximal, Sylow
120C2×C61—81no—
121C2×C61#53511yescharacteristic
122C2×C61#53611yescharacteristic
123C2×C61#53611yescharacteristic
124C2×C61#56312yes—
125C2×C61#56312yes—
126C2×C4⋊Q8—611no—
127C2×#126—611no—
128#400—612no—
129#399—612no—
130#398—612no—
131#397—612no—
132#395—611no—
133#395—611no—
134#393—611no—
135#393D6111yescharacteristic
136#383—611no—
137C61#282111yescharacteristic, complemented, Sylow
138C22×Q8—611no—
139C22×Q8C2×D6111yescharacteristic
140C4⋊Q8—1224no—
141#126—1224no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—611no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—612no—
149C2×C22⋊C4—611no—
150C2×C22⋊C4—611no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4C2×D6111yescharacteristic
153C2×C22⋊C4C2×D6112yes—
154C2×C42—611no—
155#95—611no—
156#95—612no—
157#95—612no—
158#95—612no—
159#95—612no—
160#95—612no—
161#95C2×D6111yescharacteristic
162#95C2×D6112yes—
163C24C22×D6111yescharacteristic
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—1222no—
167C2×Q8—2442no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—612no—
171C22×C4—611no—
172C22×C4—612no—
173C22×C4—611no—
174C22×C4C22×D6112yes—
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6112yes—
177C22×C4C22×D6111yescharacteristic
178C4⋊C4—1222no—
179C4⋊C4—1224no—
180C4⋊C4—1224no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—2442no—
184C4⋊C4—2442no—
185C22⋊C4—22no—
186C22⋊C4—42no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C22⋊C4—2442no—
190C42—614no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23C23×D6111yescharacteristic
197Q8—44no—
198Q8—2444no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—612no—
209C2×C4—612no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—1221no—
224C2×C4D4×D6112yes—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22C2×D4×D6111yescharacteristic
231C22#1451982212yes—
232C22#1451982411yescharacteristic
233C22#1451982412yes—
234C22#1451982511yescharacteristic
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—1222no—
240C4—1222no—
241C4—2442no—
242C4—2441no—
243C4—2442no—
244C4—2441no—
245C2—81no—
246C2#1684032711yescharacteristic
247C2#1684033211yescharacteristic
248C2#1684033511yescharacteristic
249C2#1684051212yes—
250C2#1684051312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2821
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
3. #16839704C2semidirect
5. #16839696C2semidirect
7. #16839683C2semidirect
8. #16839681C2semidirect
10. #16839629C2semidirect
137. C61#2821semidirect