Finite Group Databasebeta

← #21458874

Subgroups — #21458874

Order 7808.

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

normal subgroups only

This group has 362 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#16840497C211yesmaximal, characteristic
2#16840491C211yesmaximal, characteristic, complemented
3#16840156C212yesmaximal, complemented
4#16840135C211yesmaximal, characteristic
5#16839985C212yesmaximal, complemented
6#16839973C211yesmaximal, characteristic, complemented
7#16839968C212yesmaximal, complemented
8#16839963C211yesmaximal, characteristic
9#16839864C212yesmaximal, complemented
10C4×Dic244C211yesmaximal, characteristic, complemented
11C61×#446C211yesmaximal, characteristic, complemented
12C2×Dic244C2211yescharacteristic
13C2×Dic244C2212yes—
14C2×#11758190C2212yes—
15C2×#11758190C2212yes—
16C2×#11758190C2212yes—
17#14519777C2212yes—
18#14519777C2211yescharacteristic
19#14519774C2211yescharacteristic
20#14519768—21no—
21#14519768—22no—
22#14519766—21no—
23#14519765C2212yes—
24#14519762—22no—
25Q8×Dic61—21no—
26C4×Dic122C2211yescharacteristic
27C4×Dic122C2211yescharacteristic
28C4×Dic122C2212yes—
29C4×D244C2212yes—
30#14519739—21no—
31#14519711C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519702C2212yes—
34#14519702C2211yescharacteristic
35#14519699C2212yes—
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2211yescharacteristic
38C4⋊C8×C61C2212yes—
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42C2×D244—21no—
43C2×D244—21no—
44C2×D244C2312yes—
45C2×C4×D61—22no—
46C2×Dic122C2311yescharacteristic
47C2×Dic122C2312yes—
48C2×Dic122C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C2×C8×C61C2312yes—
51C2×C8×C61C2311yescharacteristic
52C4⋊C4×C61D411yescharacteristic
53C4⋊C4×C61D412yes—
54C42×C61C2311yescharacteristic
55C42×C61C2312yes—
56#11758198—22no—
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61—22no—
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65#11758196—21no—
66#11758196—21no—
67#11758196—22no—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61—21no—
71Dic244—22no—
72Dic244—42no—
73#11758190—24no—
74#11758190—42no—
75#11758190—42no—
76C22×D61—22no—
77Q8×C61—22no—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88D244—22no—
89D244—22no—
90D244—42no—
91D244—81no—
92C4×D61—82no—
93Dic122—22no—
94Dic122—21no—
95Dic122—21no—
96Dic122—21no—
97Dic122—22no—
98Dic122—21no—
99C8×C61—21no—
100C8×C61—22no—
101C8×C61#4112yes—
102C22×C61C22×D411yescharacteristic
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—22no—
107C4×C61—22no—
108C4×C61—21no—
109C4×C61#13712yes—
110C4×C61C2×#4111yescharacteristic
111C4×C61H(5,𝔽2)11yescharacteristic
112Dic61—42no—
113Dic61—41no—
114Dic61—41no—
115Dic61—41no—
116Dic61—41no—
117#3400—611nomaximal, Sylow
118C2×C61#55011yescharacteristic
119C2×C61C2×#13711yescharacteristic
120C2×C61#57711yescharacteristic
121D61—82no—
122#559—611no—
123#557—611no—
124#497—612no—
125#492—611no—
126#464—612no—
127#462—611no—
128#461—612no—
129#460—611no—
130#446D6111yescharacteristic, complemented
131#440—612no—
132C4×Q16—611no—
133C61#340011yescharacteristic, complemented, Sylow
134C2×Q16—611no—
135C2×Q16—612no—
136C2×SD16—612no—
137C2×SD16—612no—
138C2×SD16—612no—
139C4⋊Q8—612no—
140C4⋊Q8—611no—
141#127—611no—
142#125—1221no—
143#125—1222no—
144#124—612no—
145#124—1221no—
146#123—1222no—
147C4×Q8—611no—
148C4×Q8—612no—
149C4×Q8—611no—
150C4×Q8—1221no—
151C4×Q8C2×D6111yescharacteristic
152C4×D4—612no—
153C4×D4—1221no—
154#107—611no—
155C4⋊C8C2×D6111yescharacteristic
156C4⋊C8C2×D6112yes—
157#103—611no—
158#103—611no—
159#103—612no—
160#102—612no—
161#97C2×D6112yes—
162C4×C8C2×D6111yescharacteristic
163C2×Q8—611no—
164C2×Q8—612no—
165C2×Q8—611no—
166C2×Q8D24411yescharacteristic
167C2×D4—612no—
168C2×D4—1221no—
169C2×D4—1221no—
170C22×C4—1222no—
171Q16—1222no—
172Q16—2442no—
173SD16—1224no—
174SD16—2442no—
175SD16—2442no—
176C2×C8C22×D6111yescharacteristic
177C2×C8C22×D6112yes—
178C2×C8C22×D6111yescharacteristic
179C4⋊C4—611no—
180C4⋊C4—611no—
181C4⋊C4—1221no—
182C4⋊C4—1222no—
183C4⋊C4—1221no—
184C4⋊C4—1222no—
185C4⋊C4—1221no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C4⋊C4D24411yescharacteristic
189C4⋊C4D24412yes—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C42—1221no—
194C42—1222no—
195C42—1221no—
196C42C22×D6111yescharacteristic
197C42C22×D6112yes—
198C23—1222no—
199Q8—22no—
200Q8—1222no—
201Q8—1221no—
202Q8—1221no—
203Q8—1221no—
204Q8—1222no—
205Q8—1221no—
206D4—1222no—
207D4—1222no—
208D4—4881no—
209D4—2442no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—4882no—
216C2×C4C2×D24412yes—
217C2×C4C2×D24412yes—
218C2×C4C2×D24411yescharacteristic
219C2×C4C2×D24411yescharacteristic
220C2×C4C23×D6111yescharacteristic
221C8—21no—
222C8—22no—
223C8#1175822612yes—
224C22—2442no—
225C22—2442no—
226C22—2442no—
227C22C22×D24411yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—2441no—
232C4—2441no—
233C4—2441no—
234C4—2442no—
235C4—2441no—
236C4#1451981012yes—
237C4C2×#1175822611yescharacteristic
238C4#1451982311yescharacteristic
239C2—4882no—
240C2#1684043411yescharacteristic
241C2C2×#1451981011yescharacteristic
242C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3400
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
2. #16840491C2semidirect
3. #16840156C2semidirect
5. #16839985C2semidirect
6. #16839973C2semidirect
7. #16839968C2semidirect
9. #16839864C2semidirect
10. C4×Dic244C2semidirect
11. C61×#446C2semidirect
130. #446D61semidirect
133. C61#3400semidirect