Finite Group Databasebeta

← #22620718

Subgroups — #22620718

Order 9344.

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

normal subgroups only

This group has 424 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#17989097C212yesmaximal, complemented
2#17988930C212yesmaximal, complemented
3#17988909C212yesmaximal, complemented
4#17988828C211yesmaximal, characteristic, complemented
5#17988814C212yesmaximal, complemented
6#17988750C212yesmaximal, complemented
7#17988729C212yesmaximal, complemented
8C2×#14556503C211yesmaximal, characteristic, complemented
9#466×C73C211yesmaximal, characteristic, complemented
10C2×#11924027C2212yes—
11C22×C4×D73C2211yescharacteristic
12C2×Dic292C2211yescharacteristic, complemented
13C2×#11924016C2212yescomplemented
14C22×#10596831C2211yescharacteristic
15#14556573—22no—
16#14556571C2212yes—
17#14556570C2212yes—
18#14556562C2212yes—
19#14556559—22no—
20D4×Dic73—22no—
21#14556551—22no—
22#14556549C2212yes—
23#14556525C2211yescharacteristic, complemented
24#14556522C2212yescomplemented
25#14556516C2212yescomplemented
26#14556514C2212yescomplemented
27#14556512C2212yescomplemented
28#14556503C2212yes—
29#14556503C2212yes—
30C2×D8×C73C2211yescharacteristic, complemented
31C22×C8×C73C2211yescharacteristic
32#121×C73C2212yes—
33#107×C73C2211yescharacteristic, complemented
34#102×C73C2212yescomplemented
35C23×D73D411yescharacteristic
36#11924027—42no—
37#11924027—42no—
38C2×Dic146C2312yes—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C22×Dic73—22no—
42C22×Dic73D411yescharacteristic
43C2×C4×D73—41no—
44C2×C4×D73—41no—
45C2×C4×D73D412yes—
46C2×C4×D73C2312yes—
47Dic292—41no—
48#11924016—42no—
49C2×#10596831—41no—
50C2×#10596831C2312yes—
51C4⋊Dic73—22no—
52C4⋊Dic73C2312yes—
53#11924007—22no—
54C22⋊Dic73—22no—
55C22⋊Dic73—22no—
56#11924005—22no—
57#11924005—22no—
58C4×Dic73—22no—
59C2×D4×C73—22no—
60C2×D4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62D8×C73—41no—
63C2×C8×C73—41no—
64C2×C8×C73C2311yescharacteristic
65C2×C8×C73C2311yescharacteristic
66C4⋊C4×C73C2312yes—
67C22⋊C4×C73—22no—
68C23×C73—22no—
69C23×C73C2×D411yescharacteristic
70C22×D73—22no—
71C22×D73—41no—
72C22×D73—41no—
73C22×D73C2×D412yes—
74D4×C73—22no—
75D4×C73—22no—
76D4×C73—44no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2411yescharacteristic
82C22⋊D73—44no—
83C22⋊D73—44no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—41no—
87C2×Dic73—44no—
88C2×Dic73C2×D412yes—
89C4×D73—22no—
90C4×D73—22no—
91C4×D73—42no—
92Dic146—22no—
93Dic146—22no—
94C8×C73—21no—
95C8×C73—21no—
96#10596831—22no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73—42no—
100C22×C73—42no—
101C22×C73—42no—
102C22×C73#13512yes—
103C22×C73C22×D411yescharacteristic
104C2×D73—22no—
105C2×D73—22no—
106C2×D73—22no—
107C2×D73—44no—
108C4×C73—21no—
109C4×C73—42no—
110C4×C73H(5,𝔽2)11yescharacteristic
111C4×C73H(5,𝔽2)11yescharacteristic
112Dic73—22no—
113Dic73—42no—
114Dic73—42no—
115C2×C73—22no—
116C2×C73—82no—
117C2×C73#53411yescharacteristic
118C2×C73C2×#13511yescharacteristic
119C2×C73#57511yescharacteristic
120D73—42no—
121#3191—731nomaximal, Sylow
122C73#319111yescharacteristic, complemented, Sylow
123#525—732no—
124#485—732no—
125#482—732no—
126#467—731no—
127#466D7311yescharacteristic, complemented
128#465—732no—
129#452—732no—
130#449—732no—
131C2×C22⋊C8—731no—
132C2×#41—732no—
133C23×C4—731no—
134C2×Q16—731no—
135C2×SD16—732no—
136C2×D8C2×D7311yescharacteristic, complemented
137C22×C8—731no—
138C22×C8C2×D7311yescharacteristic
139#123—1462no—
140C22⋊Q8—732no—
141C22⋊Q8—732no—
142#121—732no—
143#121C2×D7312yes—
144#120—1462no—
145C4×D4—1462no—
146C4×D4—1462no—
147#117—732no—
148#107—731no—
149#107C2×D7311yescharacteristic, complemented
150#106—732no—
151#103—732no—
152#103—732no—
153#102—732no—
154#102C2×D7312yescomplemented
155C22⋊C8—732no—
156C22⋊C8—732no—
157C24—731no—
158#41—2922no—
159#41—2922no—
160C2×Q8—732no—
161C2×D4—22no—
162C2×D4—1462no—
163C2×D4—1462no—
164C2×D4C22×D7312yes—
165C22×C4—2921no—
166C22×C4—2921no—
167C22×C4—731no—
168C22×C4—732no—
169C22×C4—732no—
170C22×C4—1462no—
171C22×C4C22×D7311yescharacteristic
172Q16—2921no—
173SD16—2922no—
174D8—41no—
175C2×C8—41no—
176C2×C8—2921no—
177C2×C8—732no—
178C2×C8C22×D7311yescharacteristic
179C2×C8C22×D7311yescharacteristic
180C4⋊C4—732no—
181C4⋊C4—1462no—
182C4⋊C4—1462no—
183C4⋊C4C22×D7312yes—
184C22⋊C4—22no—
185C22⋊C4—1462no—
186C22⋊C4—1462no—
187C22⋊C4—1462no—
188C22⋊C4—1462no—
189C42—1462no—
190C23—22no—
191C23—2921no—
192C23—2921no—
193C23—732no—
194C23—1462no—
195C23D4×D7311yescharacteristic
196Q8—1462no—
197Q8—1462no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—2924no—
202D4—2924no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—2922no—
207C2×C4—2924no—
208C2×C4—2921no—
209C2×C4—732no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4—1462no—
213C2×C4—1462no—
214C2×C4D4×D7311yescharacteristic
215C2×C4C23×D7311yescharacteristic
216C8—21no—
217C8—21no—
218C8—1462no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—2924no—
225C22—1462no—
226C22—1462no—
227C22—1462no—
228C22#1455661012yes—
229C22C2×D4×D7311yescharacteristic
230C4—21no—
231C4—42no—
232C4—2922no—
233C4—2922no—
234C4—1462no—
235C4#1455663611yescharacteristic
236C4#1455663711yescharacteristic
237C2—22no—
238C2—82no—
239C2—2922no—
240C2#1798914511yescharacteristic
241C2C2×#1455661011yescharacteristic
242C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#466×C73C2
socleC22×C73C22×D4
hypercenter#466D73
hypocenterC73#3191
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #17989097C2semidirect
2. #17988930C2semidirect
3. #17988909C2semidirect
4. #17988828C2semidirect
5. #17988814C2semidirect
6. #17988750C2semidirect
7. #17988729C2semidirect
8. C2×#14556503C2semidirect
9. #466×C73C2semidirect
12. C2×Dic292C22semidirect
13. C2×#11924016C22semidirect
23. #14556525C22semidirect
24. #14556522C22semidirect
25. #14556516C22semidirect
26. #14556514C22semidirect
27. #14556512C22semidirect
30. C2×D8×C73C22semidirect
33. #107×C73C22semidirect
34. #102×C73C22semidirect
122. C73#3191semidirect
127. #466D73semidirect
136. C2×D8C2×D73semidirect
149. #107C2×D73semidirect
154. #102C2×D73semidirect