Finite Group Databasebeta

← #22613291

Subgroups — #22613291

Order 9344.

840 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C22×Q8×D73C211yesmaximal, characteristic, complemented
2C2×#14556569C212yesmaximal, complemented
3C2×#14556553C211yesmaximal, characteristic
4#17988507C211yesmaximal, characteristic, complemented
5#17988500C211yesmaximal, characteristic, complemented
6#17988498C211yesmaximal, characteristic, complemented
7#17988491C212yesmaximal, complemented
8#17988465C212yesmaximal
9#17988458C212yesmaximal, complemented
10#17988446C211yesmaximal, characteristic, complemented
11#395×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×Dic146C2212yes—
14C2×Q8×D73—28no—
15C2×Q8×D73—24no—
16C22×D292C2211yescharacteristic
17C22×C4×D73C2212yes—
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556569—28no—
21#14556553—24no—
22C2×#11924007C2212yes—
23C2×#11924007C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×#11924005C2211yescharacteristic
29C2×C4×Dic73C2211yescharacteristic
30#14556498C2211yescharacteristic
31#14556498C2212yes—
32#14556498C2212yes—
33#14556498C2212yes—
34C22×Q8×C73C2211yescharacteristic
35C2×C4⋊C4×C73C2212yes—
36C2×C4⋊C4×C73C2211yescharacteristic
37#95×C73C2211yescharacteristic
38#95×C73C2212yes—
39C23×D73C2311yescharacteristic
40C23×D73C2311yescharacteristic
41C2×Dic146—22no—
42C2×Dic146—24no—
43C2×Dic146—24no—
44C2×Dic146—24no—
45C2×Dic146D418yescomplemented
46Q8×D73—232no—
47C2×D292—22no—
48C2×D292—22no—
49C2×D292Q814yescomplemented
50C22×Dic73C2311yescharacteristic
51C22×Dic73C2312yes—
52C22×Dic73C2312yes—
53C22×Dic73C2311yescharacteristic
54C2×C4×D73—24no—
55C2×C4×D73—24no—
56C2×C4×D73—24no—
57C2×C4×D73—24no—
58C2×C4×D73—22no—
59C2×C4×D73—24no—
60C2×C4×D73D414yes—
61#11924007—24no—
62#11924007—24no—
63#11924005—22no—
64#11924005—24no—
65#11924005—22no—
66#11924005—24no—
67#11924005—24no—
68C4×Dic73—22no—
69C2×Q8×C73—24no—
70C2×Q8×C73—22no—
71C22×C4×C73C2312yes—
72C22×C4×C73C2311yescharacteristic
73C22×C4×C73C2312yes—
74C22×C4×C73C2311yescharacteristic
75C22×C4×C73C2311yescharacteristic
76C4⋊C4×C73—22no—
77C4⋊C4×C73—24no—
78C23×C73C2411yescharacteristic
79C22×D73—22no—
80C22×D73—22no—
81C22×D73—22no—
82C22×D73—21no—
83C22×D73—21no—
84C22×D73—22no—
85C22×D73C2×D412yes—
86C22×D73C2×Q812yes—
87C22×D73C2×Q812yescomplemented
88C22×D73#4112yes—
89Q8×C73—28no—
90C2×C4×C73—21no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73C2×D414yes—
101C2×C4×C73C2×D412yes—
102C2×C4×C73C2×Q812yescomplemented
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73C2×D414yes—
111C2×Dic73C2×D412yes—
112C2×Dic73C2×D414yes—
113D292—28no—
114C4×D73—216no—
115C4×D73—28no—
116C4×D73—44no—
117Dic146—28no—
118Dic146—216no—
119C22×C73C22×D411yescharacteristic
120C22×C73C22×D412yes—
121C22×C73C22×Q811yescharacteristic
122C22×C73C2×#4111yescharacteristic
123C22×C732−1+412yes—
124C2×D73—22no—
125C2×D73—22no—
126C2×D73—24no—
127C2×D73—24no—
128C2×D73—22no—
129C2×D73—24no—
130C2×D73—41no—
131C2×D73—41no—
132C2×D73—42no—
133C2×D73C22⋊Q814yescomplemented
134C4×C73—22no—
135C4×C73—24no—
136C4×C73—22no—
137C4×C73—41no—
138C4×C73—42no—
139Dic73—24no—
140Dic73—41no—
141Dic73—42no—
142Dic73#12014yes—
143C2×C73C2×#12011yescharacteristic
144C2×C73C2×C22⋊Q811yescharacteristic
145C2×C73#53611yescharacteristic
146C2×C73#54812yes—
147C2×C73D4×Q812yes—
148D73—24no—
149D73—42no—
150#2409—731nomaximal, Sylow
151C73#240911yescharacteristic, complemented, Sylow
152C23×Q8—731no—
153C2×C22⋊Q8—732no—
154C2×C4×D4—731no—
155#395—731no—
156#395D7311yescharacteristic, complemented
157#393—731no—
158#393—731no—
159#391—732no—
160#386—732no—
161#385—732no—
162#380—731no—
163C22×Q8—732no—
164C22×Q8—731no—
165C22×Q8—1464no—
166C22×Q8—1468no—
167C22×Q8C2×D7311yescharacteristic
168C22×D4—731no—
169C23×C4—731no—
170C23×C4—731no—
171C23×C4—732no—
172C22⋊Q8—1468no—
173C4×D4—1464no—
174C2×C4⋊C4—732no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4C2×D7311yescharacteristic
177C2×C4⋊C4C2×D7312yes—
178C2×C22⋊C4—731no—
179C2×C22⋊C4—731no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C42—731no—
184#95—731no—
185#95—732no—
186#95—732no—
187#95—732no—
188#95C2×D7311yescharacteristic
189#95C2×D7312yes—
190C24—731no—
191C24—731no—
192C2×Q8—22no—
193C2×Q8—24no—
194C2×Q8—738no—
195C2×Q8—1464no—
196C2×Q8—1464no—
197C2×Q8—1464no—
198C2×Q8—14632no—
199C2×Q8—1462no—
200C2×D4—734no—
201C2×D4—1462no—
202C2×D4—1462no—
203C22×C4—731no—
204C22×C4—732no—
205C22×C4—734no—
206C22×C4—731no—
207C22×C4—732no—
208C22×C4—1462no—
209C22×C4—1464no—
210C22×C4—1464no—
211C22×C4—1464no—
212C22×C4—1464no—
213C22×C4—1464no—
214C22×C4C22×D7312yes—
215C22×C4C22×D7311yescharacteristic
216C22×C4C22×D7311yescharacteristic
217C22×C4C22×D7312yes—
218C22×C4C22×D7311yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—24no—
221C4⋊C4—1464no—
222C4⋊C4—1464no—
223C22⋊C4—1464no—
224C22⋊C4—1464no—
225C22⋊C4—1462no—
226C22⋊C4—1462no—
227C22⋊C4—1464no—
228C42—1462no—
229C23—732no—
230C23—732no—
231C23—732no—
232C23—732no—
233C23—1462no—
234C23—1461no—
235C23—1461no—
236C23—1462no—
237C23—1462no—
238C23—1462no—
239C23C23×D7311yescharacteristic
240Q8—28no—
241Q8—14616no—
242Q8—1468no—
243D4—1468no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—2924no—
255C2×C4—732no—
256C2×C4—734no—
257C2×C4—734no—
258C2×C4—1468no—
259C2×C4—14616no—
260C2×C4—1461no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1462no—
265C2×C4—1462no—
266C2×C4—1462no—
267C2×C4D4×D7312yes—
268C2×C4D4×D7314yes—
269C2×C4Q8×D7312yescomplemented
270C22—2921no—
271C22—2922no—
272C22—2921no—
273C22—734no—
274C22—1464no—
275C22—1462no—
276C22—1462no—
277C22—1464no—
278C22—1464no—
279C22—1462no—
280C22C2×D4×D7311yescharacteristic
281C22C2×D4×D7312yes—
282C22C2×Q8×D7311yescharacteristic
283C22#41×D7311yescharacteristic
284C22#1455663912yes—
285C4—22no—
286C4—24no—
287C4—22no—
288C4—42no—
289C4—41no—
290C4—2921no—
291C4—2922no—
292C4—734no—
293C4—1464no—
294C2—2922no—
295C2—1464no—
296C2#120×D7311yescharacteristic
297C2C22⋊Q8×D7311yescharacteristic
298C2#1798916211yescharacteristic
299C2#1798924712yes—
300C2#1798925212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2409
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D73C2semidirect
2. C2×#14556569C2semidirect
4. #17988507C2semidirect
5. #17988500C2semidirect
6. #17988498C2semidirect
7. #17988491C2semidirect
9. #17988458C2semidirect
10. #17988446C2semidirect
11. #395×C73C2semidirect
45. C2×Dic146D4semidirect
49. C2×D292Q8semidirect
87. C22×D73C2×Q8semidirect
102. C2×C4×C73C2×Q8semidirect
133. C2×D73C22⋊Q8semidirect
151. C73#2409semidirect
156. #395D73semidirect
269. C2×C4Q8×D73semidirect