Finite Group Databasebeta

← #21458855

Subgroups — #21458855

Order 7808.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840487C211yesmaximal, characteristic, complemented
2#16840486C211yesmaximal, characteristic
3#16840155C212yesmaximal
4#16839986C212yesmaximal
5#16839970C212yesmaximal, complemented
6#16839969C211yesmaximal, characteristic, complemented
7#16839964C211yesmaximal, characteristic
8#16839892C211yesmaximal, characteristic, complemented
9#16839869C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic
11C61×#494C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×#11758190C2211yescharacteristic
14C2×#11758201C2212yes—
15#14519775C2212yes—
16#14519772—22no—
17#14519768—21no—
18#14519767—22no—
19#14519766C2212yes—
20#14519757—21no—
21Q8×Dic61C2212yes—
22Q8×Dic61C2212yes—
23C4×Dic122C2211yescharacteristic
24C4×Dic122C2211yescharacteristic
25#14519742—21no—
26C4×D244C2211yescharacteristic
27#14519735—21no—
28#14519709C2211yescharacteristic
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519701C2212yes—
33#14519701C2212yes—
34#14519699C2211yescharacteristic
35#14519687C2212yes—
36C2×Q16×C61C2212yes—
37C2×Q16×C61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4⋊Q8×C61C2211yescharacteristic
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61C2312yes—
42C2×Q8×C61C2312yes—
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122D411yescharacteristic
46C2×Dic122C2311yescharacteristic
47Q16×C61—24no—
48Q16×C61—42no—
49C2×C8×C61C2311yescharacteristic
50C2×C8×C61C2311yescharacteristic
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C42×C61C2311yescharacteristic
56#11758202—42no—
57#11758201—42no—
58#11758198—21no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61D411yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66#11758196—21no—
67#11758196—22no—
68#11758196—22no—
69#11758196D412yes—
70C4×Dic61—21no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C4×Dic61C2312yes—
74C2×#92418C2312yes—
75#11758190—22no—
76C22×D61—21no—
77Q8×C61—22no—
78Q8×C61—22no—
79Q8×C61—22no—
80Q8×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61C2×D412yes—
90C2×Dic61C2×D412yes—
91D244—21no—
92D244—21no—
93C4×D61—42no—
94Dic122—22no—
95Dic122—21no—
96Dic122—21no—
97C8×C61—21no—
98C8×C61#4112yes—
99#92418—22no—
100C22×C61C22×D411yescharacteristic
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—41no—
104C4×C61—21no—
105C4×C61—42no—
106C4×C61—42no—
107C4×C61#13712yes—
108C4×C61C2×#4111yescharacteristic
109C4×C61H(5,𝔽2)11yescharacteristic
110Dic61—22no—
111Dic61—22no—
112Dic61—41no—
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#494D6111yescharacteristic, complemented
124#464—612no—
125#462—612no—
126#462—611no—
127#461—611no—
128#446—611no—
129#441—612no—
130C4×SD16—611no—
131C61#339811yescharacteristic, complemented, Sylow
132C2×Q16—612no—
133C2×Q16C2×D6112yes—
134C2×Q16C2×D6112yes—
135C2×SD16—612no—
136C2×SD16—611no—
137C4⋊Q8—612no—
138C4⋊Q8C2×D6111yescharacteristic
139C4⋊Q8C2×D6111yescharacteristic
140#126—1222no—
141#125—1222no—
142#125—1221no—
143#124—612no—
144C22⋊Q8—1221no—
145C4×Q8—611no—
146C4×Q8—612no—
147C4×Q8—612no—
148C4×Q8—611no—
149C4×Q8—1221no—
150C4×D4—611no—
151#117—1221no—
152#106—611no—
153C4⋊C8—612no—
154C4⋊C8—611no—
155#103—612no—
156#103—612no—
157#103—611no—
158#102—611no—
159#97—612no—
160C4×C8C2×D6111yescharacteristic
161C2×Q8—611no—
162C2×Q8—611no—
163C2×Q8C22×D6112yes—
164C2×Q8C22×D6112yes—
165C2×D4—611no—
166C22×C4—1221no—
167Q16—24no—
168Q16—42no—
169Q16—2442no—
170SD16—1222no—
171SD16—2442no—
172C2×C8—612no—
173C2×C8C22×D6111yescharacteristic
174C2×C8C22×D6111yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—612no—
180C4⋊C4—611no—
181C4⋊C4—611no—
182C4⋊C4—611no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1221no—
191C42—612no—
192C42—1222no—
193C42—1222no—
194C42—1221no—
195C42C22×D6111yescharacteristic
196C23—1221no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—22no—
201Q8—1222no—
202Q8—1221no—
203Q8—1221no—
204D4—1221no—
205D4—1221no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—612no—
209C2×C4—612no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—2442no—
214C2×C4D4×D6111yescharacteristic
215C2×C4D4×D6111yescharacteristic
216C2×C4C23×D6111yescharacteristic
217C8—21no—
218C8—1222no—
219C8#1175822412yes—
220C22—2441no—
221C22—2441no—
222C22—2441no—
223C22C2×D4×D6111yescharacteristic
224C4—21no—
225C4—42no—
226C4—42no—
227C4—1222no—
228C4—1222no—
229C4—2441no—
230C4—2441no—
231C4—2441no—
232C4#1451980912yes—
233C4C2×#1175822411yescharacteristic
234C4#1451982211yescharacteristic
235C2—4881no—
236C2#1684043211yescharacteristic
237C2C2×#1451980911yescharacteristic
238C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#494C2
socleC22×C61C22×D4
hypercenter#494D61
hypocenterC61#3398
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #16840487C2semidirect
5. #16839970C2semidirect
6. #16839969C2semidirect
8. #16839892C2semidirect
9. #16839869C2semidirect
11. C61×#494C2semidirect
123. #494D61semidirect
131. C61#3398semidirect