Finite Group Databasebeta

← #21458852

Subgroups — #21458852

Order 7808.

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

normal subgroups only

This group has 350 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
1#16840491C211yesmaximal, characteristic, complemented
2#16840485C211yesmaximal, characteristic
3#16840156C212yesmaximal
4#16840142C211yesmaximal, characteristic, complemented
5#16839985C212yesmaximal
6#16839973C211yesmaximal, characteristic, complemented
7#16839973C212yesmaximal, complemented
8#16839968C211yesmaximal, characteristic
9#16839870C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic
11C61×#446C211yesmaximal, characteristic, complemented
12C2×Dic244C2212yes—
13C2×Dic244C2212yes—
14C2×Dic244C2212yes—
15C2×#11758190C2211yescharacteristic
16C2×#11758190C2212yes—
17#14519777C2211yescharacteristic
18#14519777C2211yescharacteristic
19#14519777C2212yes—
20#14519772—22no—
21#14519768—21no—
22#14519768—22no—
23#14519765C2212yes—
24#14519753—21no—
25Q8×Dic61—21no—
26C4×Dic122C2212yes—
27C4×Dic122C2211yescharacteristic
28C4×Dic122C2212yes—
29C4×D244C2211yescharacteristic
30#14519735—21no—
31#14519709C2211yescharacteristic
32#14519702C2212yes—
33#14519702C2211yescharacteristic
34#14519702C2212yes—
35#14519699C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2211yescharacteristic
38C4⋊C8×C61C2212yes—
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42C2×D244C2311yescharacteristic
43C2×C4×D61—21no—
44C2×Dic122C2312yes—
45C2×Dic122C2311yescharacteristic
46C2×Dic122C2312yes—
47C2×C8×C61C2311yescharacteristic
48C2×C8×C61C2312yes—
49C2×C8×C61C2311yescharacteristic
50C4⋊C4×C61D411yescharacteristic
51C4⋊C4×C61D412yes—
52C42×C61C2311yescharacteristic
53C42×C61C2312yes—
54#11758198—22no—
55#11758198—21no—
56#11758198—22no—
57C4⋊Dic61—21no—
58C4⋊Dic61—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65#11758196—22no—
66#11758196—22no—
67#11758196—21no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61—21no—
71Dic244—24no—
72Dic244—42no—
73Dic244—42no—
74#11758190—22no—
75#11758190—42no—
76C22×D61—21no—
77Q8×C61—22no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88D244—21no—
89D244—21no—
90C4×D61—42no—
91Dic122—21no—
92Dic122—22no—
93Dic122—22no—
94Dic122—22no—
95Dic122—22no—
96Dic122—21no—
97C8×C61—22no—
98C8×C61—21no—
99C8×C61#4112yes—
100C22×C61C22×D411yescharacteristic
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—41no—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—21no—
107C4×C61#13712yes—
108C4×C61C2×#4111yescharacteristic
109C4×C61H(5,𝔽2)11yescharacteristic
110Dic61—41no—
111Dic61—42no—
112Dic61—42no—
113Dic61—41no—
114Dic61—41no—
115#3398—611nomaximal, Sylow
116C2×C61#55011yescharacteristic
117C2×C61C2×#13711yescharacteristic
118C2×C61#57811yescharacteristic
119D61—81no—
120#557—611no—
121#556—611no—
122#497—612no—
123#494—611no—
124#464—612no—
125#462—612no—
126#462—611no—
127#461—611no—
128#446D6111yescharacteristic, complemented
129#441—612no—
130C4×SD16—611no—
131C61#339811yescharacteristic, complemented, Sylow
132C2×Q16—612no—
133C2×Q16—612no—
134C2×Q16—612no—
135C2×SD16—611no—
136C2×SD16—612no—
137C4⋊Q8—611no—
138C4⋊Q8—611no—
139C4⋊Q8—612no—
140#126—1222no—
141#125—1221no—
142#125—1222no—
143#124—612no—
144C22⋊Q8—1221no—
145C4×Q8—612no—
146C4×Q8—611no—
147C4×Q8—612no—
148C4×Q8—1221no—
149C4×Q8C2×D6111yescharacteristic
150C4×D4—611no—
151#117—1221no—
152#106—611no—
153C4⋊C8C2×D6111yescharacteristic
154C4⋊C8C2×D6112yes—
155#103—611no—
156#103—612no—
157#103—612no—
158#102—611no—
159#97C2×D6112yes—
160C4×C8C2×D6111yescharacteristic
161C2×Q8—612no—
162C2×Q8—611no—
163C2×Q8—612no—
164C2×Q8D24411yescharacteristic
165C2×D4—611no—
166C22×C4—1221no—
167Q16—1224no—
168Q16—2442no—
169Q16—2442no—
170SD16—1222no—
171SD16—2442no—
172C2×C8C22×D6111yescharacteristic
173C2×C8C22×D6112yes—
174C2×C8C22×D6111yescharacteristic
175C4⋊C4—611no—
176C4⋊C4—611no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1221no—
180C4⋊C4—1221no—
181C4⋊C4—1222no—
182C4⋊C4—1221no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4D24411yescharacteristic
187C4⋊C4D24412yes—
188C22⋊C4—1222no—
189C22⋊C4—1221no—
190C22⋊C4—1222no—
191C42—1222no—
192C42—1222no—
193C42—1221no—
194C42C22×D6111yescharacteristic
195C42C22×D6112yes—
196C23—1221no—
197Q8—22no—
198Q8—1221no—
199Q8—1222no—
200Q8—1222no—
201Q8—1222no—
202Q8—1222no—
203Q8—1221no—
204D4—1221no—
205D4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—1221no—
210C2×C4—1222no—
211C2×C4—2442no—
212C2×C4C2×D24412yes—
213C2×C4C2×D24412yes—
214C2×C4C2×D24411yescharacteristic
215C2×C4C2×D24411yescharacteristic
216C2×C4C23×D6111yescharacteristic
217C8—22no—
218C8—21no—
219C8#1175822612yes—
220C22—2441no—
221C22—2441no—
222C22—2441no—
223C22C22×D24411yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—2441no—
228C4—2441no—
229C4—2442no—
230C4—2441no—
231C4—2442no—
232C4#1451981012yes—
233C4C2×#1175822611yescharacteristic
234C4#1451982311yescharacteristic
235C2—4881no—
236C2#1684043411yescharacteristic
237C2C2×#1451981011yescharacteristic
238C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3398
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #16840491C2semidirect
4. #16840142C2semidirect
6. #16839973C2semidirect
7. #16839973C2semidirect
9. #16839870C2semidirect
11. C61×#446C2semidirect
128. #446D61semidirect
131. C61#3398semidirect