Finite Group Databasebeta

← #22619172

Subgroups — #22619172

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×#11924029C211yesmaximal, characteristic, complemented
2C2×#14556616C211yesmaximal, characteristic, complemented
3#17989094C211yesmaximal, characteristic, complemented
4#17988748C214yesmaximal, complemented
5#17988731C214yesmaximal, complemented
6#17988596C211yesmaximal, characteristic, complemented
7#17988593C211yesmaximal, characteristic, complemented
8#17988550C211yesmaximal, characteristic, complemented
9C2×#137×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—24no—
11C2×#11924029—22no—
12C2×#11924029—24no—
13C2×#11924029C2214yes—
14C22×D292—21no—
15C22×D292C2211yescharacteristic
16C22×C4×D73—21no—
17C22×C4×D73C2211yescharacteristic
18#14556616—24no—
19C2×#11924015C2212yescomplemented
20C2×#11924013C2212yescomplemented
21C2×#11924012C2211yescharacteristic
22#14556572—21no—
23#14556567C2212yescomplemented
24#14556562C2212yescomplemented
25#14556559—21no—
26C4×C22⋊D73—22no—
27#14556550C2211yescharacteristic
28#14556515C2214yescomplemented
29#14556513C2214yescomplemented
30#14556503C2214yescomplemented
31C2×#41×C73C2211yescharacteristic
32C22×Q8×C73C2211yescharacteristic
33#137×C73—24no—
34C2×Q16×C73C2212yescomplemented
35C2×SD16×C73C2212yescomplemented
36C2×M16×C73C2211yescharacteristic
37C23×D73—21no—
38C23×D73D411yescharacteristic
39#11924029—216no—
40#11924029—28no—
41#11924029—28no—
42C2×D292—28no—
43C2×D292—24no—
44C2×D292—21no—
45C2×D292—22no—
46C2×D292D414yescomplemented
47C2×D292C2312yes—
48C2×C22⋊D73—22no—
49C22×Dic73D411yescharacteristic
50C2×C4×D73—28no—
51C2×C4×D73—22no—
52C2×C4×D73—22no—
53C2×C4×D73—24no—
54C2×C4×D73D412yes—
55C2×C4×D73C2312yes—
56#11924015—24no—
57#11924013—24no—
58#11924012—22no—
59C2×#10596831C2312yes—
60C4⋊Dic73C2312yes—
61#11924007—22no—
62C22⋊Dic73—21no—
63C22⋊Dic73—22no—
64#11924005—22no—
65C4×Dic73—21no—
66#41×C73—22no—
67#41×C73—22no—
68C2×Q8×C73—22no—
69C2×Q8×C73—21no—
70C2×Q8×C73D414yescomplemented
71C2×Q8×C73C2311yescharacteristic
72C2×Q8×C73C2312yes—
73C2×D4×C73—21no—
74C2×D4×C73C2311yescharacteristic
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73C2311yescharacteristic
78Q16×C73—24no—
79SD16×C73—24no—
80M16×C73—22no—
81C2×C8×C73C2312yes—
82C23×C73—21no—
83C23×C73C2×D411yescharacteristic
84C22×D73—22no—
85C22×D73—24no—
86C22×D73—22no—
87C22×D73—42no—
88C22×D73—44no—
89C22×D73C2×D412yes—
90Q8×C73—24no—
91Q8×C73—22no—
92Q8×C73—21no—
93Q8×C73—21no—
94Q8×C73C2×D414yes—
95D4×C73—21no—
96D4×C73—21no—
97D4×C73—42no—
98C2×C4×C73—24no—
99C2×C4×C73—22no—
100C2×C4×C73—21no—
101C2×C4×C73—42no—
102C2×C4×C73C2×D411yescharacteristic
103C2×C4×C73C2×D412yes—
104C2×C4×C73C2×D412yes—
105C2×C4×C73C2411yescharacteristic
106C22⋊D73—44no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73C2×D412yes—
110D292—216no—
111D292—24no—
112D292—22no—
113D292C2×D414yes—
114C4×D73—216no—
115C4×D73—24no—
116C4×D73—22no—
117C4×D73—22no—
118C8×C73—22no—
119#10596831—22no—
120C22×C73—22no—
121C22×C73—41no—
122C22×C73—42no—
123C22×C73#12012yes—
124C22×C73C22×D411yescharacteristic
125C2×D73—22no—
126C2×D73—24no—
127C2×D73—22no—
128C2×D73—22no—
129C2×D73—44no—
130C2×D73—48no—
131C2×D73—44no—
132C4×C73—24no—
133C4×C73—41no—
134C4×C73#12012yes—
135C4×C73C22×D411yescharacteristic
136C4×C73C22×D411yescharacteristic
137Dic73—22no—
138Dic73—42no—
139C2×C73—22no—
140C2×C73—81no—
141C2×C73C2×#12011yescharacteristic
142C2×C73#57512yes—
143D73—42no—
144D73—44no—
145#3005—731nomaximal, Sylow
146C73#300511yescharacteristic, complemented, Sylow
147C22×#41—731no—
148C2×#137D7311yescharacteristic, complemented
149C2×AGL(1,ℤ/8)—731no—
150#525—731no—
151#452—734no—
152#449—734no—
153#419—731no—
154#418—731no—
155#407—731no—
156C2×#41—734no—
157C2×#41—1462no—
158C2×#41—1464no—
159C2×#41—1464no—
160C2×#41C2×D7311yescharacteristic
161C22×Q8C2×D7311yescharacteristic
162C22×D4—731no—
163C22×D4—1461no—
164C23×C4—731no—
165C23×C4—1461no—
166#137—24no—
167AGL(1,ℤ/8)—1464no—
168C2×Q16C2×D7312yescomplemented
169C2×SD16—732no—
170C2×SD16C2×D7312yescomplemented
171C2×D8—732no—
172C2×M16—731no—
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⋊C8—734no—
183C24—731no—
184C24—1461no—
185#41—22no—
186#41—22no—
187#41—1468no—
188#41—14616no—
189#41—1468no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8C22⋊D7314yescomplemented
193C2×Q8C22×D7311yescharacteristic
194C2×Q8C22×D7312yes—
195C2×D4—21no—
196C2×D4—734no—
197C2×D4—732no—
198C2×D4—1464no—
199C2×D4—1468no—
200C2×D4—1462no—
201C2×D4—1461no—
202C2×D4—1462no—
203C2×D4C22×D7311yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—731no—
207C22×C4—732no—
208C22×C4—732no—
209C22×C4—1464no—
210C22×C4—1468no—
211C22×C4—1462no—
212C22×C4—1462no—
213C22×C4C22×D7311yescharacteristic
214Q16—24no—
215SD16—24no—
216SD16—1464no—
217D8—1464no—
218M16—22no—
219M16—1462no—
220C2×C8—732no—
221C2×C8C22×D7312yes—
222C4⋊C4—732no—
223C4⋊C4—1462no—
224C22⋊C4—1462no—
225C22⋊C4—1462no—
226C22⋊C4—1461no—
227C42—1461no—
228C23—21no—
229C23—2924no—
230C23—2922no—
231C23—732no—
232C23—1464no—
233C23—1462no—
234C23—1462no—
235C23D4×D7311yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—21no—
239Q8—21no—
240Q8C2×C22⋊D7314yes—
241D4—21no—
242D4—21no—
243D4—42no—
244D4—2924no—
245D4—734no—
246D4—14616no—
247D4—1464no—
248D4—1462no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—732no—
254C2×C4—14616no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4—1464no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4D4×D7311yescharacteristic
261C2×C4D4×D7312yes—
262C2×C4C2×C22⋊D7312yes—
263C2×C4C23×D7311yescharacteristic
264C8—22no—
265C8—1462no—
266C22—22no—
267C22—42no—
268C22—41no—
269C22—2928no—
270C22—2924no—
271C22—2924no—
272C22—1462no—
273C22—1462no—
274C22—1464no—
275C22—1462no—
276C22#1455655912yes—
277C22C2×D4×D7311yescharacteristic
278C4—24no—
279C4—41no—
280C4—2922no—
281C4—1462no—
282C4#1455655912yes—
283C4C2×D4×D7311yescharacteristic
284C4C22×C22⋊D7311yescharacteristic
285C2—22no—
286C2—81no—
287C2—2924no—
288C2—2922no—
289C2C2×#1455655911yescharacteristic
290C2#1798938612yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#137×C73C2
socleC22×C73C22×D4
hypercenterC2×#137D73
hypocenterC73#3005
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#11924029C2semidirect
2. C2×#14556616C2semidirect
3. #17989094C2semidirect
4. #17988748C2semidirect
5. #17988731C2semidirect
6. #17988596C2semidirect
7. #17988593C2semidirect
8. #17988550C2semidirect
9. C2×#137×C73C2semidirect
19. C2×#11924015C22semidirect
20. C2×#11924013C22semidirect
23. #14556567C22semidirect
24. #14556562C22semidirect
28. #14556515C22semidirect
29. #14556513C22semidirect
30. #14556503C22semidirect
34. C2×Q16×C73C22semidirect
35. C2×SD16×C73C22semidirect
46. C2×D292D4semidirect
70. C2×Q8×C73D4semidirect
146. C73#3005semidirect
148. C2×#137D73semidirect
168. C2×Q16C2×D73semidirect
170. C2×SD16C2×D73semidirect
192. C2×Q8C22⋊D73semidirect