Finite Group Databasebeta

← #22619176

Subgroups — #22619176

Order 9344.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924028C211yesmaximal, characteristic, complemented
2C2×#14556624C211yesmaximal, characteristic, complemented
3C2×#14556619C211yesmaximal, characteristic, complemented
4#17989098C211yesmaximal, characteristic, complemented
5#17988751C214yesmaximal, complemented
6#17988734C214yesmaximal, complemented
7#17988597C211yesmaximal, characteristic, complemented
8#17988593C211yesmaximal, characteristic, complemented
9#407×C73C211yesmaximal, characteristic, complemented
10C2×#11924028—24no—
11C2×#11924028—24no—
12C2×#11924028—22no—
13C2×#11924028C2211yescharacteristic
14C2×#11924028C2214yes—
15C22×Dic146C2211yescharacteristic
16C22×D292C2211yescharacteristic
17C22×C22⋊D73—21no—
18C22×C4×D73—21no—
19#14556624—24no—
20#14556619—24no—
21C2×Dic292C2212yescomplemented
22C2×#11924017C2212yescomplemented
23C2×#11924017C2212yescomplemented
24C2×D584C2212yescomplemented
25#14556574—21no—
26#14556570C2212yescomplemented
27#14556565C2212yescomplemented
28#14556560—21no—
29C4×C22⋊D73—22no—
30#14556550C2211yescharacteristic
31#14556516C2214yescomplemented
32#14556513C2214yescomplemented
33C23×C4×C73C2211yescharacteristic
34C2×M16×C73C2211yescharacteristic
35C2×M16×C73C2211yescharacteristic
36C22⋊C8×C73C2214yescomplemented
37C23×D73—21no—
38#11924028—216no—
39#11924028—28no—
40#11924028—22no—
41#11924028—22no—
42#11924028—28no—
43C2×Dic146—22no—
44C2×Dic146—21no—
45C2×Dic146D414yescomplemented
46C2×Dic146C2311yescharacteristic
47C2×Dic146C2312yes—
48C2×D292—22no—
49C2×D292—21no—
50C2×D292D414yescomplemented
51C2×D292C2311yescharacteristic
52C2×D292C2312yes—
53C2×C22⋊D73—28no—
54C2×C22⋊D73—24no—
55C2×C22⋊D73—22no—
56C2×C22⋊D73—21no—
57C22×Dic73—21no—
58C2×C4×D73—28no—
59C2×C4×D73—24no—
60C2×C4×D73—21no—
61Dic292—24no—
62#11924017—24no—
63#11924017—24no—
64D584—24no—
65C4⋊Dic73C2312yes—
66#11924007—22no—
67C22⋊Dic73—21no—
68C22⋊Dic73—22no—
69#11924005—22no—
70C4×Dic73—21no—
71C24×C73D411yescharacteristic
72C22×C4×C73—22no—
73C22×C4×C73—22no—
74C22×C4×C73D412yes—
75C22×C4×C73D411yescharacteristic
76C22×C4×C73C2312yes—
77C22×C4×C73C2311yescharacteristic
78M16×C73—22no—
79M16×C73—22no—
80C2×C8×C73C2312yes—
81C2×C8×C73C2312yes—
82C23×C73—22no—
83C23×C73—42no—
84C23×C73C2×D412yes—
85C23×C73C2×D411yescharacteristic
86C22×D73—24no—
87C22×D73—22no—
88C22×D73—21no—
89C22×D73—44no—
90C2×C4×C73—22no—
91C2×C4×C73—24no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73C2×D412yes—
95C2×C4×C73C2×D412yes—
96C2×C4×C73C2×D412yes—
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2411yescharacteristic
99C22⋊D73—216no—
100C22⋊D73—44no—
101C22⋊D73—42no—
102C2×Dic73—24no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—21no—
106D292—24no—
107D292—22no—
108D292—21no—
109D292—21no—
110D292C2×D414yes—
111C4×D73—216no—
112C4×D73—42no—
113Dic146—24no—
114Dic146—22no—
115Dic146—21no—
116Dic146—21no—
117Dic146C2×D414yes—
118C8×C73—22no—
119C8×C73—22no—
120C22×C73—22no—
121C22×C73—22no—
122C22×C73—22no—
123C22×C73—22no—
124C22×C73—44no—
125C22×C73#12012yes—
126C22×C73C22×D411yescharacteristic
127C2×D73—24no—
128C2×D73—48no—
129C2×D73—44no—
130C2×D73—41no—
131C2×D73—42no—
132C4×C73—22no—
133C4×C73#12012yes—
134C4×C73C22×D411yescharacteristic
135C4×C73C22×D411yescharacteristic
136Dic73—24no—
137Dic73—41no—
138Dic73—42no—
139C2×C73—22no—
140C2×C73—42no—
141C2×C73C2×#12011yescharacteristic
142C2×C73#57512yes—
143D73—44no—
144D73—81no—
145#3005—731nomaximal, Sylow
146C73#300511yescharacteristic, complemented, Sylow
147C22×#41—731no—
148C2×#137—731no—
149C2×AGL(1,ℤ/8)—731no—
150#525—731no—
151#452—734no—
152#449—734no—
153#419—731no—
154#418—731no—
155#407D7311yescharacteristic, complemented
156C2×#41—731no—
157C2×#41—734no—
158C2×#41—1464no—
159C2×#41—1464no—
160C2×#41—1462no—
161C22×Q8—731no—
162C22×D4—731no—
163C22×D4—1461no—
164C23×C4—1461no—
165C23×C4C2×D7311yescharacteristic
166#137—1464no—
167AGL(1,ℤ/8)—1464no—
168C2×Q16—732no—
169C2×SD16—732no—
170C2×SD16—732no—
171C2×D8—732no—
172C2×M16C2×D7311yescharacteristic
173C2×M16C2×D7311yescharacteristic
174#123—1461no—
175C22⋊Q8—732no—
176#121—732no—
177#120—1461no—
178C4×D4—1462no—
179#117—731no—
180#103—734no—
181#102—734no—
182C22⋊C8C2×D7314yescomplemented
183C24—1461no—
184C24D29211yescharacteristic
185#41—1468no—
186#41—1468no—
187#41—14616no—
188#41—1462no—
189#41—1462no—
190C2×Q8—734no—
191C2×Q8—732no—
192C2×Q8—731no—
193C2×Q8—1462no—
194C2×Q8—1461no—
195C2×D4—734no—
196C2×D4—732no—
197C2×D4—731no—
198C2×D4—1462no—
199C2×D4—1461no—
200C2×D4—1468no—
201C2×D4—1464no—
202C2×D4—1462no—
203C2×D4—1461no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—1468no—
207C22×C4—1461no—
208C22×C4—1461no—
209C22×C4—1464no—
210C22×C4D29212yes—
211C22×C4D29211yescharacteristic
212C22×C4C22×D7312yes—
213C22×C4C22×D7311yescharacteristic
214Q16—1464no—
215SD16—1464no—
216SD16—1464no—
217D8—1464no—
218M16—22no—
219M16—22no—
220C2×C8C22×D7312yes—
221C2×C8C22×D7312yes—
222C4⋊C4—732no—
223C4⋊C4—1462no—
224C22⋊C4—1461no—
225C22⋊C4—1462no—
226C22⋊C4—1462no—
227C42—1461no—
228C23—22no—
229C23—42no—
230C23—2924no—
231C23—1461no—
232C23—1464no—
233C23—1462no—
234C23C2×D29212yes—
235C23C2×D29211yescharacteristic
236Q8—734no—
237Q8—1461no—
238Q8—1461no—
239Q8—1464no—
240Q8—1462no—
241D4—2924no—
242D4—2922no—
243D4—734no—
244D4—14616no—
245D4—1464no—
246D4—1461no—
247D4—1461no—
248D4—1462no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—2922no—
254C2×C4—14616no—
255C2×C4—1462no—
256C2×C4—1461no—
257C2×C4—1464no—
258C2×C4—1462no—
259C2×C4D4×D7312yes—
260C2×C4D4×D7312yes—
261C2×C4C2×D29212yes—
262C2×C4C2×D29211yescharacteristic
263C2×C4C23×D7311yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—2928no—
272C22—2924no—
273C22—2922no—
274C22—2921no—
275C22—1464no—
276C22#1455656112yes—
277C22C22×D29211yescharacteristic
278C4—22no—
279C4—2922no—
280C4—2921no—
281C4—1464no—
282C4#1455656112yes—
283C4C2×D4×D7311yescharacteristic
284C4C2×D4×D7311yescharacteristic
285C2—22no—
286C2—42no—
287C2—2924no—
288C2—5841no—
289C2C2×#1455656111yescharacteristic
290C2#1798938712yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#407×C73C2
socleC22×C73C22×D4
hypercenter#407D73
hypocenterC73#3005
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#11924028C2semidirect
2. C2×#14556624C2semidirect
3. C2×#14556619C2semidirect
4. #17989098C2semidirect
5. #17988751C2semidirect
6. #17988734C2semidirect
7. #17988597C2semidirect
8. #17988593C2semidirect
9. #407×C73C2semidirect
21. C2×Dic292C22semidirect
22. C2×#11924017C22semidirect
23. C2×#11924017C22semidirect
24. C2×D584C22semidirect
26. #14556570C22semidirect
27. #14556565C22semidirect
31. #14556516C22semidirect
32. #14556513C22semidirect
36. C22⋊C8×C73C22semidirect
45. C2×Dic146D4semidirect
50. C2×D292D4semidirect
146. C73#3005semidirect
155. #407D73semidirect
182. C22⋊C8C2×D73semidirect