Finite Group Databasebeta

← #22615646

Subgroups — #22615646

Order 9344.

1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C23×C22⋊D73C211yesmaximal, characteristic, complemented
2C2×#14556575C211yesmaximal, characteristic, complemented
3C2×#14556561C211yesmaximal, characteristic, complemented
4C2×#14556560C211yesmaximal, characteristic, complemented
5#17988503C214yesmaximal, complemented
6#17988496C214yesmaximal, complemented
7#17988448C211yesmaximal, characteristic, complemented
8#17988442C211yesmaximal, characteristic, complemented
9#379×C73C211yesmaximal, characteristic, complemented
10C24×D73C2211yescharacteristic
11C22×D292C2212yescomplemented
12C22×C22⋊D73—24no—
13C22×C22⋊D73—24no—
14C22×C22⋊D73—24no—
15C22×C22⋊D73C2214yes—
16C22×C22⋊D73C2211yescharacteristic
17C22×C22⋊D73C2212yescomplemented
18C23×Dic73C2211yescharacteristic
19#14556575—24no—
20#14556561—24no—
21#14556560—24no—
22C2×C4⋊Dic73C2212yescomplemented
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2212yescomplemented
25C2×#11924005C2212yescomplemented
26C2×#11924005C2212yescomplemented
27C2×#11924005C2214yescomplemented
28#14556498C2214yescomplemented
29C25×C73C2211yescharacteristic
30C2×C22⋊C4×C73C2211yescharacteristic
31C2×C22⋊C4×C73C2211yescharacteristic
32C2×C22⋊C4×C73C2214yescomplemented
33C23×D73—22no—
34C23×D73—22no—
35C23×D73—44no—
36C23×D73D414yescomplemented
37C23×D73C2311yescharacteristic
38C23×D73C2312yes—
39C2×D292—24no—
40C2×D292—44no—
41C2×C22⋊D73—232no—
42C2×C22⋊D73—28no—
43C2×C22⋊D73—28no—
44C2×C22⋊D73—22no—
45C2×C22⋊D73—24no—
46C2×C22⋊D73—22no—
47C2×C22⋊D73—22no—
48C2×C22⋊D73—28no—
49C2×C22⋊D73—44no—
50C22×Dic73—22no—
51C22×Dic73—22no—
52C22×Dic73D414yescomplemented
53C22×Dic73C2312yes—
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2312yes—
56C4⋊Dic73—24no—
57C22⋊Dic73—22no—
58C22⋊Dic73—24no—
59#11924005—24no—
60#11924005—24no—
61#11924005—44no—
62C24×C73—22no—
63C24×C73—22no—
64C24×C73—44no—
65C24×C73D414yescomplemented
66C24×C73C2312yes—
67C24×C73C2311yescharacteristic
68C22×C4×C73C2312yes—
69C22×C4×C73C2312yes—
70C22⋊C4×C73—22no—
71C22⋊C4×C73—22no—
72C22⋊C4×C73—44no—
73C23×C73—24no—
74C23×C73—28no—
75C23×C73—22no—
76C23×C73—22no—
77C23×C73—24no—
78C23×C73—24no—
79C23×C73—48no—
80C23×C73—48no—
81C23×C73—48no—
82C23×C73C2×D412yes—
83C23×C73C2×D412yes—
84C23×C73C2×D414yes—
85C23×C73C2×D412yes—
86C23×C73C2411yescharacteristic
87C22×D73—28no—
88C22×D73—22no—
89C22×D73—22no—
90C22×D73—24no—
91C22×D73—24no—
92C22×D73—21no—
93C22×D73—21no—
94C22×D73—21no—
95C22×D73—24no—
96C22×D73—48no—
97C22×D73—48no—
98C22×D73—48no—
99C22×D73C2×D414yes—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—24no—
103C2×C4×C73—24no—
104C22⋊D73—232no—
105C22⋊D73—48no—
106C22⋊D73—44no—
107C2×Dic73—28no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—21no—
111C2×Dic73—21no—
112C2×Dic73—22no—
113C2×Dic73—21no—
114C2×Dic73—24no—
115C2×Dic73C2×D414yes—
116D292—48no—
117C22×C73—24no—
118C22×C73—24no—
119C22×C73—24no—
120C22×C73—24no—
121C22×C73—24no—
122C22×C73—24no—
123C22×C73—416no—
124C22×C73—44no—
125C22×C73—44no—
126C22×C73#12014yes—
127C22×C73C22×D411yescharacteristic
128C22×C73C22×D411yescharacteristic
129C22×C73C22×D411yescharacteristic
130C22×C73H(5,𝔽2)14yes—
131C2×D73—24no—
132C2×D73—24no—
133C2×D73—24no—
134C2×D73—416no—
135C2×D73—44no—
136C2×D73—44no—
137C2×D73—41no—
138C2×D73—42no—
139C2×D73—42no—
140C2×D73—42no—
141C4×C73—42no—
142C4×C73—42no—
143Dic73—24no—
144Dic73—41no—
145Dic73—42no—
146C2×C73—24no—
147C2×C73—44no—
148C2×C73C2×#12011yescharacteristic
149C2×C73#53412yes—
150C2×C73#53412yes—
151C2×C73#53512yes—
152D73—44no—
153D73—81no—
154#2613—731nomaximal, Sylow
155C73#261311yescharacteristic, complemented, Sylow
156C23×D4—731no—
157C2×#123—731no—
158C2×#120—731no—
159C2×#120—731no—
160#394—734no—
161#392—734no—
162#381—731no—
163#379—731no—
164#379D7311yescharacteristic, complemented
165C25—731no—
166C25C2×D7311yescharacteristic
167C22×D4—732no—
168C22×D4—731no—
169C22×D4—734no—
170C22×D4—732no—
171C22×D4—1464no—
172C22×D4—1464no—
173C22×D4—1464no—
174C23×C4—731no—
175#123—1464no—
176#120—1464no—
177#120—1464no—
178C2×C4⋊C4—732no—
179C2×C22⋊C4—734no—
180C2×C22⋊C4—731no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4C2×D7311yescharacteristic
185C2×C22⋊C4C2×D7311yescharacteristic
186C2×C22⋊C4C2×D7314yescomplemented
187#95—734no—
188C24—22no—
189C24—22no—
190C24—44no—
191C24—2924no—
192C24—734no—
193C24—732no—
194C24—731no—
195C24—1462no—
196C24—1462no—
197C24D29214yescomplemented
198C24C22×D7312yes—
199C24C22×D7311yescharacteristic
200C2×D4—2924no—
201C2×D4—2924no—
202C2×D4—1464no—
203C2×D4—1468no—
204C2×D4—1462no—
205C2×D4—1462no—
206C2×D4—1464no—
207C2×D4—1462no—
208C2×D4—1468no—
209C2×D4—14632no—
210C2×D4—1468no—
211C22×C4—734no—
212C22×C4—732no—
213C22×C4—732no—
214C22×C4—731no—
215C22×C4—1462no—
216C22×C4—1462no—
217C22×C4C22×D7312yes—
218C22×C4C22×D7312yes—
219C4⋊C4—1464no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—44no—
223C22⋊C4—2924no—
224C22⋊C4—1464no—
225C22⋊C4—1464no—
226C22⋊C4—1464no—
227C22⋊C4—1462no—
228C23—24no—
229C23—28no—
230C23—22no—
231C23—22no—
232C23—24no—
233C23—24no—
234C23—48no—
235C23—48no—
236C23—48no—
237C23—2928no—
238C23—2928no—
239C23—2928no—
240C23—734no—
241C23—1461no—
242C23—1461no—
243C23—1461no—
244C23—1464no—
245C23—1468no—
246C23—1462no—
247C23—1462no—
248C23—1464no—
249C23—1464no—
250C23D4×D7312yes—
251C23D4×D7312yes—
252C23C2×D29214yes—
253C23C2×D29212yes—
254C23C23×D7311yescharacteristic
255D4—2928no—
256D4—2928no—
257D4—2924no—
258D4—14632no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—734no—
264C2×C4—1461no—
265C2×C4—1461no—
266C2×C4—1462no—
267C2×C4—1461no—
268C2×C4—1464no—
269C2×C4—1468no—
270C2×C4—1462no—
271C2×C4—1462no—
272C22—24no—
273C22—24no—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—24no—
278C22—416no—
279C22—44no—
280C22—44no—
281C22—29216no—
282C22—2924no—
283C22—2924no—
284C22—2922no—
285C22—2922no—
286C22—2922no—
287C22—2921no—
288C22—1464no—
289C22—1464no—
290C22—1464no—
291C22#1455656114yes—
292C22C2×D4×D7311yescharacteristic
293C22C2×D4×D7311yescharacteristic
294C22C22×D29211yescharacteristic
295C22#1455663614yes—
296C4—42no—
297C4—42no—
298C4—2922no—
299C4—2921no—
300C4—1464no—
301C2—24no—
302C2—44no—
303C2—2924no—
304C2—5841no—
305C2C2×#1455656111yescharacteristic
306C2#1798914712yes—
307C2#1798914912yes—
308C2#1798915212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#379×C73C2
hypercenter#379D73
hypocenterC73#2613
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D73C2semidirect
2. C2×#14556575C2semidirect
3. C2×#14556561C2semidirect
4. C2×#14556560C2semidirect
5. #17988503C2semidirect
6. #17988496C2semidirect
7. #17988448C2semidirect
8. #17988442C2semidirect
9. #379×C73C2semidirect
11. C22×D292C22semidirect
17. C22×C22⋊D73C22semidirect
22. C2×C4⋊Dic73C22semidirect
24. C2×C22⋊Dic73C22semidirect
25. C2×#11924005C22semidirect
26. C2×#11924005C22semidirect
27. C2×#11924005C22semidirect
28. #14556498C22semidirect
32. C2×C22⋊C4×C73C22semidirect
36. C23×D73D4semidirect
52. C22×Dic73D4semidirect
65. C24×C73D4semidirect
155. C73#2613semidirect
164. #379D73semidirect
186. C2×C22⋊C4C2×D73semidirect
197. C24D292semidirect