Finite Group Databasebeta

← #22613549

Subgroups — #22613549

Order 9344.

952 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 169 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×#11924027C211yesmaximal, characteristic, complemented
2C2×#14556587C211yesmaximal, characteristic, complemented
3C2×#14556579C211yesmaximal, characteristic, complemented
4C2×#14556566C211yesmaximal, characteristic, complemented
5#17988496C214yesmaximal, complemented
6#17988492C211yesmaximal, characteristic, complemented
7#17988464C214yesmaximal, complemented
8C4×#11924005C211yesmaximal, characteristic, complemented
9#390×C73C211yesmaximal, characteristic, complemented
10C2×#11924027—24no—
11C2×#11924027—24no—
12C2×#11924027—24no—
13C22×Dic146C2211yescharacteristic
14C22×D292C2211yescharacteristic
15C22×D292C2212yes—
16C22×C22⋊D73C2212yes—
17C22×C22⋊D73C2214yes—
18C23×Dic73C2212yes—
19C22×C4×D73C2211yescharacteristic
20#14556587—24no—
21#14556579—24no—
22#14556566—24no—
23C2×#11924005C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2214yes—
26C2×C4×Dic73C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2214yes—
29C22×D4×C73C2211yescharacteristic
30C2×C4⋊C4×C73C2211yescharacteristic
31C2×C22⋊C4×C73C2214yes—
32C2×C42×C73C2211yescharacteristic
33C23×D73C2312yes—
34C23×D73C2311yescharacteristic
35#11924027—232no—
36C2×Dic146—22no—
37C2×Dic146—22no—
38C2×Dic146D414yescomplemented
39C2×D292—24no—
40C2×D292—22no—
41C2×D292—22no—
42C2×D292—22no—
43C2×D292—44no—
44C2×C22⋊D73—24no—
45C2×C22⋊D73—24no—
46C2×C22⋊D73—28no—
47C2×C22⋊D73—24no—
48C2×C22⋊D73—28no—
49C2×C22⋊D73—44no—
50C22×Dic73—24no—
51C22×Dic73—24no—
52C22×Dic73—24no—
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2312yes—
55C22×Dic73C2312yes—
56C2×C4×D73—22no—
57C2×C4×D73—22no—
58C2×C4×D73D414yescomplemented
59#11924005—24no—
60#11924005—28no—
61#11924005—24no—
62C4×Dic73—22no—
63C24×C73C2312yes—
64C2×D4×C73—22no—
65C2×D4×C73—22no—
66C2×D4×C73D414yescomplemented
67C22×C4×C73C2312yes—
68C22×C4×C73C2312yes—
69C22×C4×C73C2311yescharacteristic
70C4⋊C4×C73—22no—
71C22⋊C4×C73—44no—
72C42×C73—22no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73—24no—
76C23×C73—24no—
77C23×C73C2×D414yes—
78C23×C73C2411yescharacteristic
79C22×D73—21no—
80C22×D73—21no—
81C22×D73—22no—
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—22no—
85C22×D73—22no—
86C22×D73—24no—
87C22×D73—24no—
88C22×D73C2×D412yes—
89D4×C73—28no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—24no—
95C2×C4×C73C2×D412yes—
96C2×C4×C73C2×D412yes—
97C2×C4×C73C2×D412yes—
98C22⋊D73—216no—
99C22⋊D73—416no—
100C2×Dic73—216no—
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73C2×D412yes—
108C2×Dic73C2×D414yes—
109C2×Dic73#4114yescomplemented
110D292—48no—
111D292—44no—
112C4×D73—28no—
113Dic146—28no—
114C22×C73—24no—
115C22×C73—28no—
116C22×C73—42no—
117C22×C73—42no—
118C22×C73—44no—
119C22×C73C22×D411yescharacteristic
120C22×C73C22×D411yescharacteristic
121C22×C73C22×D411yescharacteristic
122C22×C73C2×#4112yes—
123C22×C73H(5,𝔽2)12yes—
124C2×D73—22no—
125C2×D73—22no—
126C2×D73—22no—
127C2×D73—42no—
128C2×D73—42no—
129C2×D73—42no—
130C2×D73—42no—
131C2×D73—42no—
132C2×D73—44no—
133C2×D73—44no—
134C4×C73—42no—
135C4×C73—42no—
136C4×C73#12014yes—
137Dic73—24no—
138Dic73—22no—
139Dic73—24no—
140C2×C73—44no—
141C2×C73C2×#12011yescharacteristic
142C2×C73#53211yescharacteristic
143C2×C73#53511yescharacteristic
144C2×C73#54612yes—
145C2×C73#55012yes—
146D73—42no—
147D73—82no—
148#2431—731nomaximal, Sylow
149C73#243111yescharacteristic, complemented, Sylow
150C22×#41—731no—
151C2×#127—731no—
152C2×#124—731no—
153C2×#121—731no—
154#392—734no—
155#391—731no—
156#390D7311yescharacteristic, complemented
157#386—734no—
158C4×C22⋊C4—731no—
159C2×#41—1464no—
160C2×#41—1464no—
161C2×#41—1464no—
162C22×Q8—731no—
163C22×D4—734no—
164C22×D4—732no—
165C22×D4—732no—
166C22×D4—731no—
167C22×D4C2×D7311yescharacteristic
168C23×C4—731no—
169C23×C4—732no—
170#127—1464no—
171#124—1464no—
172#121—1464no—
173C2×C4⋊C4C2×D7311yescharacteristic
174C2×C22⋊C4—732no—
175C2×C22⋊C4—734no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4C2×D7314yes—
178C2×C42—731no—
179C2×C42C2×D7311yescharacteristic
180#95—732no—
181#95—734no—
182C24—731no—
183C24—732no—
184C24C22×D7312yes—
185#41—14632no—
186C2×Q8—734no—
187C2×Q8—1462no—
188C2×Q8—1462no—
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—2924no—
192C2×D4—2924no—
193C2×D4—1464no—
194C2×D4—1468no—
195C2×D4—1464no—
196C2×D4—1468no—
197C2×D4—1464no—
198C2×D4—1464no—
199C2×D4—1462no—
200C2×D4—1462no—
201C2×D4—1462no—
202C2×D4D29214yescomplemented
203C22×C4—732no—
204C22×C4—731no—
205C22×C4—732no—
206C22×C4—734no—
207C22×C4—1464no—
208C22×C4—1464no—
209C22×C4—1464no—
210C22×C4—1462no—
211C22×C4—1462no—
212C22×C4C22×D7312yes—
213C22×C4C22×D7312yes—
214C22×C4C22×D7311yescharacteristic
215C4⋊C4—22no—
216C22⋊C4—44no—
217C22⋊C4—1464no—
218C22⋊C4—1464no—
219C22⋊C4—1468no—
220C42—22no—
221C42—1462no—
222C23—22no—
223C23—22no—
224C23—24no—
225C23—24no—
226C23—732no—
227C23—1462no—
228C23—1462no—
229C23—1462no—
230C23—1464no—
231C23—1464no—
232C23—1461no—
233C23—1461no—
234C23—1462no—
235C23—1462no—
236C23C2×D29214yes—
237C23C23×D7311yescharacteristic
238Q8—1468no—
239D4—28no—
240D4—2928no—
241D4—29216no—
242D4—2924no—
243D4—14616no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—732no—
250C2×C4—734no—
251C2×C4—734no—
252C2×C4—14616no—
253C2×C4—1461no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1461no—
257C2×C4—1462no—
258C2×C4—1462no—
259C2×C4—1468no—
260C2×C4D4×D7312yes—
261C2×C4D4×D7312yes—
262C2×C4C2×D29212yes—
263C22—28no—
264C22—24no—
265C22—42no—
266C22—42no—
267C22—44no—
268C22—2922no—
269C22—2922no—
270C22—2922no—
271C22—2922no—
272C22—2924no—
273C22—2924no—
274C22—2922no—
275C22—1462no—
276C22—1462no—
277C22—1462no—
278C22C2×D4×D7311yescharacteristic
279C22C2×D4×D7311yescharacteristic
280C22C22×D29211yescharacteristic
281C22#41×D7312yes—
282C22#1455663612yes—
283C4—42no—
284C4—42no—
285C4—1464no—
286C4—1462no—
287C4—1464no—
288C4#1455656114yes—
289C2—44no—
290C2—2922no—
291C2—5842no—
292C2C2×#1455656111yescharacteristic
293C2#1798913611yescharacteristic
294C2#1798915011yescharacteristic
295C2#1798923212yes—
296C2#1798925512yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#390×C73C2
hypercenter#390D73
hypocenterC73#2431
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C22×#11924027C2semidirect
2. C2×#14556587C2semidirect
3. C2×#14556579C2semidirect
4. C2×#14556566C2semidirect
5. #17988496C2semidirect
6. #17988492C2semidirect
7. #17988464C2semidirect
8. C4×#11924005C2semidirect
9. #390×C73C2semidirect
38. C2×Dic146D4semidirect
58. C2×C4×D73D4semidirect
66. C2×D4×C73D4semidirect
109. C2×Dic73#41semidirect
149. C73#2431semidirect
156. #390D73semidirect
202. C2×D4D292semidirect