Finite Group Databasebeta

← #22620071

Subgroups — #22620071

Order 9344.

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

normal subgroups only

This group has 450 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
1#17989121C211yesmaximal, characteristic, complemented
2C2×C4×D292C211yesmaximal, characteristic, complemented
3#17988918C211yesmaximal, characteristic, complemented
4#17988901C211yesmaximal, characteristic, complemented
5#17988888C212yesmaximal, complemented
6#17988803C212yesmaximal, complemented
7#17988740C211yesmaximal, characteristic, complemented
8#17988723C211yesmaximal, characteristic
9#17988700C212yesmaximal, complemented
10#17988689C212yesmaximal, complemented
11#432×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C4×D73—21no—
14C2×#11924017C2212yes—
15C2×D584C2212yes—
16#14556585—21no—
17#14556583C2211yescharacteristic, complemented
18#14556579C2211yescharacteristic, complemented
19#14556574—21no—
20#14556570C2211yescharacteristic
21#14556565C2211yescharacteristic
22C4×Dic146C2211yescharacteristic, complemented
23C4×D292—21no—
24C4×D292—21no—
25C4×D292C2212yes—
26C4×D292C2212yes—
27C4×D292C2211yescharacteristic, complemented
28C4×C22⋊D73—21no—
29#14556548—21no—
30C2×C4⋊Dic73C2211yescharacteristic
31C2×#11924005—21no—
32#14556525C2212yescomplemented
33#14556523C2212yescomplemented
34#14556516C2212yescomplemented
35#14556513C2212yes—
36#14556513C2212yes—
37#14556513C2212yescomplemented
38C2×C42×C73C2211yescharacteristic
39C4⋊C8×C73C2212yescomplemented
40C22⋊C8×C73C2211yescharacteristic
41C22⋊C8×C73C2211yescharacteristic
42#97×C73C2212yescomplemented
43C23×D73—21no—
44C2×Dic146C2311yescharacteristic
45C2×D292—21no—
46C2×D292—24no—
47C2×D292C2311yescharacteristic
48C2×D292C2312yes—
49C2×C22⋊D73—21no—
50C22×Dic73—21no—
51C2×C4×D73—21no—
52C2×C4×D73—22no—
53C2×C4×D73—22no—
54C2×C4×D73—44no—
55#11924017—24no—
56D584—24no—
57C4⋊Dic73—21no—
58C4⋊Dic73C2311yescharacteristic
59C4⋊Dic73C2311yescharacteristic
60C4⋊Dic73C2312yes—
61#11924007—21no—
62#11924007—21no—
63#11924007—21no—
64#11924007—21no—
65C22⋊Dic73—21no—
66#11924005—22no—
67#11924005—22no—
68#11924005—21no—
69#11924005—21no—
70#11924005—21no—
71#11924005—21no—
72C4×Dic73—21no—
73C22×C4×C73D411yescharacteristic
74C22×C4×C73D411yescharacteristic
75C22×C4×C73C2311yescharacteristic
76C2×C8×C73C2312yes—
77C2×C8×C73C2312yes—
78C42×C73D411yescharacteristic
79C42×C73D411yescharacteristic
80C42×C73C2311yescharacteristic
81C42×C73C2311yescharacteristic
82C23×C73C2×D411yescharacteristic
83C22×D73—24no—
84C22×D73—22no—
85C22×D73—21no—
86C22×D73—42no—
87C22×D73—42no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—41no—
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73C2×D411yescharacteristic
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2411yescharacteristic
97C22⋊D73—42no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—42no—
103D292—24no—
104D292—22no—
105D292—22no—
106D292#4114yes—
107C4×D73—42no—
108C4×D73—44no—
109C4×D73—44no—
110Dic146—22no—
111C8×C73—22no—
112C8×C73—22no—
113C22×C73—21no—
114C22×C73—21no—
115C22×C73AGL(1,ℤ/8)12yes—
116C22×C73C22×D411yescharacteristic
117C2×D73—24no—
118C2×D73—48no—
119C2×D73—42no—
120C2×D73—42no—
121C2×D73—41no—
122C2×D73—41no—
123C2×D73—41no—
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—21no—
127C4×C73—21no—
128C4×C73—21no—
129C4×C73C2×#4112yes—
130Dic73—41no—
131Dic73—42no—
132Dic73—41no—
133Dic73—41no—
134C2×C73—22no—
135C2×C73#52511yescharacteristic
136C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C73#57511yescharacteristic
138D73—44no—
139D73—81no—
140#3114—731nomaximal, Sylow
141C73#311411yescharacteristic, complemented, Sylow
142#529—731no—
143C2×C4×D4—731no—
144#483—731no—
145#480—731no—
146#478—732no—
147#463—732no—
148#450—731no—
149#447—731no—
150#442—732no—
151#440—732no—
152#432D7311yescharacteristic, complemented
153C22×D4—731no—
154C23×C4—1461no—
155C2×SD16—732no—
156C2×D8—732no—
157#126—1461no—
158#125—731no—
159#124—731no—
160#123—1461no—
161C22⋊Q8—731no—
162#121—731no—
163C4×Q8—731no—
164C4×D4—732no—
165C4×D4—732no—
166C4×D4—731no—
167C4×D4—1461no—
168C4×D4—1461no—
169C4×D4—1461no—
170#117—1461no—
171C2×C4⋊C4—731no—
172C2×C22⋊C4—1461no—
173C2×C42C2×D7311yescharacteristic
174#107—732no—
175#106—732no—
176C4⋊C8C2×D7312yescomplemented
177#103—732no—
178#102—732no—
179#102—732no—
180#102—732no—
181C22⋊C8C2×D7311yescharacteristic
182C22⋊C8C2×D7311yescharacteristic
183#97C2×D7312yescomplemented
184C24—1461no—
185C2×Q8—731no—
186C2×D4—732no—
187C2×D4—731no—
188C2×D4—1464no—
189C2×D4—1461no—
190C2×D4—1461no—
191C22×C4—2924no—
192C22×C4—1461no—
193C22×C4—1461no—
194C22×C4—1462no—
195C22×C4—1462no—
196C22×C4D29211yescharacteristic
197C22×C4D29211yescharacteristic
198C22×C4C22×D7311yescharacteristic
199SD16—1464no—
200D8—1464no—
201C2×C8C22×D7312yes—
202C2×C8C22×D7312yes—
203C4⋊C4—731no—
204C4⋊C4—731no—
205C4⋊C4—732no—
206C4⋊C4—1461no—
207C4⋊C4—1461no—
208C4⋊C4—1461no—
209C4⋊C4—1461no—
210C4⋊C4—1461no—
211C22⋊C4—1461no—
212C22⋊C4—1462no—
213C22⋊C4—1462no—
214C22⋊C4—1461no—
215C22⋊C4—1461no—
216C22⋊C4—1461no—
217C22⋊C4—1461no—
218C42—1461no—
219C42D29211yescharacteristic
220C42D29211yescharacteristic
221C42C22×D7311yescharacteristic
222C42C22×D7311yescharacteristic
223C23—2922no—
224C23—2922no—
225C23—1464no—
226C23—1461no—
227C23—1462no—
228C23C2×D29211yescharacteristic
229Q8—1462no—
230D4—2922no—
231D4—734no—
232D4—1464no—
233D4—1462no—
234D4—1462no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—2924no—
239C2×C4—2924no—
240C2×C4—2922no—
241C2×C4—2922no—
242C2×C4—1461no—
243C2×C4—1461no—
244C2×C4—1461no—
245C2×C4—1462no—
246C2×C4C2×D29211yescharacteristic
247C2×C4C2×D29211yescharacteristic
248C2×C4C2×D29211yescharacteristic
249C2×C4C2×D29211yescharacteristic
250C2×C4C2×D29211yescharacteristic
251C2×C4C23×D7311yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—2928no—
257C22—2922no—
258C22—2922no—
259C22—2921no—
260C22—2921no—
261C22—2921no—
262C22—1464no—
263C22#1455661912yes—
264C22C22×D29211yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—2922no—
271C4—2921no—
272C4—2921no—
273C4—2921no—
274C4#41×D7312yes—
275C2—22no—
276C2—2924no—
277C2—5841no—
278C2#1798909911yescharacteristic
279C2C2×#1455661911yescharacteristic
280C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#432×C73C2
socleC22×C73C22×D4
hypercenter#432D73
hypocenterC73#3114
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #17989121C2semidirect
2. C2×C4×D292C2semidirect
3. #17988918C2semidirect
4. #17988901C2semidirect
5. #17988888C2semidirect
6. #17988803C2semidirect
7. #17988740C2semidirect
9. #17988700C2semidirect
10. #17988689C2semidirect
11. #432×C73C2semidirect
17. #14556583C22semidirect
18. #14556579C22semidirect
22. C4×Dic146C22semidirect
27. C4×D292C22semidirect
32. #14556525C22semidirect
33. #14556523C22semidirect
34. #14556516C22semidirect
37. #14556513C22semidirect
39. C4⋊C8×C73C22semidirect
42. #97×C73C22semidirect
141. C73#3114semidirect
152. #432D73semidirect
176. C4⋊C8C2×D73semidirect
183. #97C2×D73semidirect