Finite Group Databasebeta

← #22620728

Subgroups — #22620728

Order 9344.

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

normal subgroups only

This group has 514 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×#14556565C211yesmaximal, characteristic, complemented
2#17988905C212yesmaximal, complemented
3#17988903C212yesmaximal, complemented
4#17988838C214yesmaximal, complemented
5#17988721C212yesmaximal, complemented
6#17988720C212yesmaximal, complemented
7#17988551C211yesmaximal, characteristic, complemented
8C2×#121×C73C211yesmaximal, characteristic, complemented
9C22×D292C2211yescharacteristic, complemented
10C22×C22⋊D73—21no—
11C2×#11924013C2214yescomplemented
12C2×#11924012C2212yescomplemented
13#14556565—21no—
14#14556565—21no—
15#14556565C2212yes—
16#14556565C2212yescomplemented
17C2×C4⋊Dic73C2211yescharacteristic, complemented
18C2×#11924005—21no—
19#14556522C2214yescomplemented
20#14556512C2214yescomplemented
21#14556511C2214yescomplemented
22C22⋊#10596831C2212yescomplemented
23C22⋊#10596831C2212yescomplemented
24C22×D4×C73—21no—
25C22×D4×C73C2211yescharacteristic, complemented
26C23×C4×C73C2211yescharacteristic
27#121×C73—21no—
28#121×C73—21no—
29#121×C73C2212yes—
30#121×C73C2212yescomplemented
31C2×C4⋊C4×C73C2211yescharacteristic, complemented
32C2×C22⋊C4×C73—21no—
33C23×D73—21no—
34C2×D292—21no—
35C2×D292—42no—
36C2×D292C2312yes—
37C2×C22⋊D73—22no—
38C2×C22⋊D73—22no—
39C2×C22⋊D73—44no—
40C22×Dic73—21no—
41#11924013—44no—
42#11924012—42no—
43C2×#10596831C2314yes—
44C4⋊Dic73—21no—
45C4⋊Dic73C2312yes—
46#11924005—22no—
47#11924005—22no—
48C24×C73—21no—
49C24×C73D411yescharacteristic
50C2×D4×C73—22no—
51C2×D4×C73—22no—
52C2×D4×C73—21no—
53C2×D4×C73—42no—
54C2×D4×C73—44no—
55C2×D4×C73C2312yes—
56C22×C4×C73—21no—
57C22×C4×C73—42no—
58C22×C4×C73D411yescharacteristic
59C22×C4×C73D411yescharacteristic
60C22×C4×C73D411yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2311yescharacteristic
64C4⋊C4×C73—21no—
65C4⋊C4×C73C2312yes—
66C22⋊C4×C73—22no—
67C22⋊C4×C73—22no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73—22no—
71C23×C73—41no—
72C23×C73—42no—
73C23×C73—42no—
74C23×C73—42no—
75C23×C73C2×D411yescharacteristic
76C23×C73C2×D411yescharacteristic
77C23×C73C2×D411yescharacteristic
78C22×D73—22no—
79C22×D73—42no—
80C22×D73—42no—
81C22×D73—42no—
82D4×C73—24no—
83D4×C73—42no—
84D4×C73—44no—
85D4×C73—44no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—41no—
91C2×C4×C73—41no—
92C2×C4×C73—41no—
93C2×C4×C73—42no—
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2×D411yescharacteristic
97C2×C4×C73C2411yescharacteristic
98C22⋊D73—44no—
99C22⋊D73—44no—
100C2×Dic73—22no—
101C2×Dic73—42no—
102D292—24no—
103D292—42no—
104#10596831—24no—
105C22×C73—21no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73—21no—
111C22×C73—21no—
112C22×C73—44no—
113C22×C73—42no—
114C22×C73—42no—
115C22×C73—42no—
116C22×C73—84no—
117C22×C73AGL(1,ℤ/8)12yes—
118C22×C73AGL(1,ℤ/8)12yes—
119C22×C73C22×D411yescharacteristic
120C2×D73—42no—
121C2×D73—42no—
122C2×D73—42no—
123C2×D73—84no—
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—21no—
127C4×C73—42no—
128C4×C73H(5,𝔽2)12yes—
129Dic73—42no—
130C2×C73—22no—
131C2×C73—22no—
132C2×C73—41no—
133C2×C73—82no—
134C2×C73#53411yescharacteristic
135C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
137D73—82no—
138#3192—731nomaximal, Sylow
139C73#319211yescharacteristic, complemented, Sylow
140C2×#121—731no—
141C2×#121D7311yescharacteristic, complemented
142#481—732no—
143#481—732no—
144#469—734no—
145#447—732no—
146#447—732no—
147#407—731no—
148C22×D4—21no—
149C22×D4—731no—
150C22×D4—1461no—
151C22×D4C2×D7311yescharacteristic, complemented
152C23×C4C2×D7311yescharacteristic
153C2×D8—734no—
154C2×M16—732no—
155#121—21no—
156#121—21no—
157#121—732no—
158#121—732no—
159#121—1461no—
160#121—1461no—
161#121C2×D7312yes—
162#121C2×D7312yescomplemented
163C2×C4⋊C4—731no—
164C2×C4⋊C4C2×D7311yescharacteristic, complemented
165C2×C22⋊C4—21no—
166C2×C22⋊C4—1461no—
167#106—734no—
168#102—734no—
169#102—734no—
170C22⋊C8—732no—
171C22⋊C8—732no—
172C24—21no—
173C24—1461no—
174C24C22⋊D7311yescharacteristic
175C2×D4—22no—
176C2×D4—22no—
177C2×D4—21no—
178C2×D4—42no—
179C2×D4—44no—
180C2×D4—2922no—
181C2×D4—2924no—
182C2×D4—732no—
183C2×D4—1462no—
184C2×D4—1462no—
185C2×D4—1461no—
186C2×D4C22×D7312yes—
187C22×C4—21no—
188C22×C4—42no—
189C22×C4—1461no—
190C22×C4C22⋊D7311yescharacteristic
191C22×C4C22⋊D7311yescharacteristic
192C22×C4C22⋊D7311yescharacteristic
193C22×C4C22×D7311yescharacteristic
194C22×C4C22×D7311yescharacteristic
195C22×C4C22×D7311yescharacteristic
196D8—2924no—
197M16—2922no—
198C2×C8—734no—
199C4⋊C4—21no—
200C4⋊C4—732no—
201C4⋊C4—1461no—
202C4⋊C4C22×D7312yes—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—1462no—
206C22⋊C4—1462no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—41no—
211C23—42no—
212C23—42no—
213C23—42no—
214C23—2922no—
215C23—2922no—
216C23—2922no—
217C23—1462no—
218C23C2×C22⋊D7311yescharacteristic
219C23C2×C22⋊D7311yescharacteristic
220C23C2×C22⋊D7311yescharacteristic
221D4—24no—
222D4—42no—
223D4—44no—
224D4—44no—
225D4—2922no—
226D4—2924no—
227D4—2924no—
228D4—1464no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—2922no—
238C2×C4—1462no—
239C2×C4C2×C22⋊D7311yescharacteristic
240C2×C4C2×C22⋊D7311yescharacteristic
241C2×C4C2×C22⋊D7311yescharacteristic
242C2×C4C23×D7311yescharacteristic
243C8—1464no—
244C22—21no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—84no—
256C22—2922no—
257C22—2922no—
258C22—2922no—
259C22—5844no—
260C22#1455661612yes—
261C22#1455661712yes—
262C22C22×C22⋊D7311yescharacteristic
263C4—21no—
264C4—21no—
265C4—21no—
266C4—42no—
267C4—2922no—
268C4#1455663612yes—
269C2—22no—
270C2—22no—
271C2—41no—
272C2—82no—
273C2—5842no—
274C2#1798914611yescharacteristic
275C2C2×#1455661611yescharacteristic
276C2C2×#1455661711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#121×C73C2
socleC22×C73C22×D4
hypercenterC2×#121D73
hypocenterC73#3192
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14556565C2semidirect
2. #17988905C2semidirect
3. #17988903C2semidirect
4. #17988838C2semidirect
5. #17988721C2semidirect
6. #17988720C2semidirect
7. #17988551C2semidirect
8. C2×#121×C73C2semidirect
9. C22×D292C22semidirect
11. C2×#11924013C22semidirect
12. C2×#11924012C22semidirect
16. #14556565C22semidirect
17. C2×C4⋊Dic73C22semidirect
19. #14556522C22semidirect
20. #14556512C22semidirect
21. #14556511C22semidirect
22. C22⋊#10596831C22semidirect
23. C22⋊#10596831C22semidirect
25. C22×D4×C73C22semidirect
30. #121×C73C22semidirect
31. C2×C4⋊C4×C73C22semidirect
139. C73#3192semidirect
141. C2×#121D73semidirect
151. C22×D4C2×D73semidirect
162. #121C2×D73semidirect
164. C2×C4⋊C4C2×D73semidirect