Finite Group Databasebeta

← #22616157

Subgroups — #22616157

Order 9344.

796 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 796 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556577C212yesmaximal, complemented
2C2×#14556560C212yesmaximal, complemented
3#17988502C212yesmaximal, complemented
4#17988499C211yesmaximal, characteristic, complemented
5#17988496C212yesmaximal, complemented
6#17988496C211yesmaximal, characteristic, complemented
7#17988487C212yesmaximal, complemented
8#17988481C212yesmaximal, complemented
9#379×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2211yescharacteristic, complemented
11C22×D292C2211yescharacteristic, complemented
12C22×C22⋊D73C2212yes—
13C22×C22⋊D73C2212yes—
14C22×C22⋊D73C2212yes—
15#14556577—28no—
16#14556560—28no—
17C2×#11924007C2212yescomplemented
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2212yes—
21C2×#11924005C2212yescomplemented
22C2×#11924005C2212yescomplemented
23C2×#11924005C2212yescomplemented
24C2×C4×Dic73C2212yescomplemented
25#14556498C2211yescharacteristic, complemented
26#14556498C2212yescomplemented
27#14556498C2211yescharacteristic, complemented
28C25×C73C2211yescharacteristic
29C2×C22⋊C4×C73C2212yes—
30C2×C22⋊C4×C73C2212yes—
31C2×C22⋊C4×C73C2211yescharacteristic
32C2×C22⋊C4×C73C2211yescharacteristic
33C23×D73C2312yes—
34C2×Dic146—24no—
35C2×Dic146—41no—
36C2×D292—42no—
37C2×D292—41no—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—24no—
40C2×C22⋊D73—24no—
41C2×C22⋊D73—24no—
42C2×C22⋊D73—24no—
43C2×C22⋊D73—42no—
44C2×C22⋊D73—42no—
45C2×C22⋊D73—42no—
46C2×C22⋊D73—42no—
47C22×Dic73C2312yes—
48C22×Dic73C2312yes—
49C22×Dic73C2312yes—
50#11924007—42no—
51C22⋊Dic73—24no—
52C22⋊Dic73—24no—
53C22⋊Dic73D418yescomplemented
54#11924005—24no—
55#11924005—24no—
56#11924005—42no—
57C4×Dic73—24no—
58C24×C73—24no—
59C24×C73—22no—
60C24×C73—41no—
61C24×C73—42no—
62C24×C73—41no—
63C24×C73C2312yes—
64C24×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2312yes—
68C22⋊C4×C73—24no—
69C22⋊C4×C73—41no—
70C22⋊C4×C73—42no—
71C22⋊C4×C73—41no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73—21no—
76C23×C73—21no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—44no—
83C23×C73—48no—
84C23×C73—48no—
85C23×C73—44no—
86C23×C73—44no—
87C23×C73C2×D414yes—
88C23×C73#4112yes—
89C23×C73C2411yescharacteristic
90C22×D73—22no—
91C22×D73—22no—
92C22×D73—22no—
93C22×D73—22no—
94C22×D73—22no—
95C22×D73—22no—
96C22×D73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C22⋊D73—48no—
105C22⋊D73—48no—
106C22⋊D73—48no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73C2×D414yes—
115C2×Dic73C2×D414yes—
116D292—44no—
117Dic146—44no—
118C22×C73—24no—
119C22×C73—22no—
120C22×C73—24no—
121C22×C73—24no—
122C22×C73—24no—
123C22×C73—416no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—41no—
128C22×C73—42no—
129C22×C73—42no—
130C22×C73—41no—
131C22×C73C22×D412yes—
132C22×C73C2×#4111yescharacteristic
133C22×C73H(5,𝔽2)11yescharacteristic
134C22×C73H(5,𝔽2)12yes—
135C22×C73H(5,𝔽2)11yescharacteristic
136C2×D73—42no—
137C2×D73—42no—
138C2×D73—42no—
139C2×D73—42no—
140C2×D73—42no—
141C2×D73—42no—
142C2×D73—42no—
143C4×C73—42no—
144C4×C73—41no—
145C4×C73—41no—
146Dic73—24no—
147Dic73—24no—
148Dic73—42no—
149C2×C73—44no—
150C2×C73—42no—
151C2×C73#53512yes—
152C2×C73#53811yescharacteristic
153C2×C73D4211yescharacteristic
154C2×C73#54612yes—
155C2×C73H(3,𝔽4)11yescharacteristic
156D73—82no—
157#2670—731nomaximal, Sylow
158C73#267011yescharacteristic, complemented, Sylow
159C2×#124—732no—
160C2×#120—732no—
161#394—732no—
162#393—731no—
163#392—731no—
164#392—732no—
165#390—732no—
166#388—732no—
167#379D7311yescharacteristic, complemented
168C25C2×D7311yescharacteristic
169C22×Q8—731no—
170C22×D4—732no—
171C22×D4—732no—
172C22×D4—732no—
173C22×D4—731no—
174#124—1468no—
175#120—1468no—
176C2×C4⋊C4—732no—
177C2×C22⋊C4—732no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C22⋊C4C2×D7312yes—
184C2×C22⋊C4C2×D7312yes—
185C2×C22⋊C4C2×D7311yescharacteristic
186C2×C22⋊C4C2×D7311yescharacteristic
187C2×C42—732no—
188#95—731no—
189#95—732no—
190#95—731no—
191C24—24no—
192C24—22no—
193C24—41no—
194C24—42no—
195C24—41no—
196C24—732no—
197C24C22×D7312yes—
198C24C22×D7311yescharacteristic
199C2×Q8—2921no—
200C2×Q8—1464no—
201C2×D4—2922no—
202C2×D4—2921no—
203C2×D4—2922no—
204C2×D4—2922no—
205C2×D4—2922no—
206C2×D4—2922no—
207C2×D4—1464no—
208C2×D4—1464no—
209C2×D4—1464no—
210C2×D4—1464no—
211C2×D4—1464no—
212C22×C4—732no—
213C22×C4—732no—
214C22×C4—732no—
215C22×C4C22×D7311yescharacteristic
216C22×C4C22×D7311yescharacteristic
217C22×C4C22×D7312yes—
218C4⋊C4—2922no—
219C22⋊C4—24no—
220C22⋊C4—41no—
221C22⋊C4—42no—
222C22⋊C4—41no—
223C22⋊C4—2922no—
224C22⋊C4—738no—
225C22⋊C4—1464no—
226C22⋊C4—1464no—
227C22⋊C4—1464no—
228C22⋊C4—1464no—
229C42—1464no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—44no—
241C23—48no—
242C23—48no—
243C23—44no—
244C23—44no—
245C23—1462no—
246C23—1462no—
247C23—1462no—
248C23—1462no—
249C23—1462no—
250C23—1462no—
251C23—1462no—
252C23D4×D7314yes—
253C23#1192402812yes—
254C23C23×D7311yescharacteristic
255Q8—2924no—
256D4—2924no—
257D4—2928no—
258D4—2928no—
259D4—2928no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—734no—
268C2×C4—734no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1462no—
273C2×C4—1462no—
274C2×C4—1462no—
275C2×C4—1462no—
276C22—24no—
277C22—22no—
278C22—24no—
279C22—24no—
280C22—24no—
281C22—416no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—2922no—
290C22—2922no—
291C22—2922no—
292C22—2922no—
293C22—2922no—
294C22—2922no—
295C22—2922no—
296C22C2×D4×D7312yes—
297C22C2×#1192402811yescharacteristic
298C22#1455663611yescharacteristic
299C22#1455663612yes—
300C22#1455663611yescharacteristic
301C4—42no—
302C4—41no—
303C4—41no—
304C4—2922no—
305C4—1464no—
306C4—1464no—
307C2—44no—
308C2—42no—
309C2—5842no—
310C2#1798915212yes—
311C2#1798917511yescharacteristic
312C2#1798921911yescharacteristic
313C2#1798922712yes—
314C2#1798933011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#379×C73C2
hypercenter#379D73
hypocenterC73#2670
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14556577C2semidirect
2. C2×#14556560C2semidirect
3. #17988502C2semidirect
4. #17988499C2semidirect
5. #17988496C2semidirect
6. #17988496C2semidirect
7. #17988487C2semidirect
8. #17988481C2semidirect
9. #379×C73C2semidirect
10. C22×Dic146C22semidirect
11. C22×D292C22semidirect
17. C2×#11924007C22semidirect
21. C2×#11924005C22semidirect
22. C2×#11924005C22semidirect
23. C2×#11924005C22semidirect
24. C2×C4×Dic73C22semidirect
25. #14556498C22semidirect
26. #14556498C22semidirect
27. #14556498C22semidirect
53. C22⋊Dic73D4semidirect
158. C73#2670semidirect
167. #379D73semidirect