Finite Group Databasebeta

← #22619175

Subgroups — #22619175

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×#11924027C211yesmaximal, characteristic, complemented
2C2×#14556624C211yesmaximal, characteristic, complemented
3C2×#14556617C211yesmaximal, characteristic, complemented
4#17989099C211yesmaximal, characteristic, complemented
5#17988750C214yesmaximal, complemented
6#17988733C214yesmaximal, complemented
7#17988595C211yesmaximal, characteristic, complemented
8#17988550C211yesmaximal, characteristic, complemented
9#418×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C2×#11924027—24no—
12C2×#11924027—22no—
13C2×#11924027—24no—
14C2×#11924027C2214yes—
15C22×Dic146C2211yescharacteristic
16C22×C22⋊D73—21no—
17C23×Dic73—21no—
18C22×C4×D73C2211yescharacteristic
19#14556624—24no—
20#14556617—24no—
21C2×Dic292C2212yescomplemented
22C2×#11924017C2212yescomplemented
23C2×#11924016C2212yescomplemented
24C2×#11924013C2212yescomplemented
25C2×#11924012C2211yescharacteristic
26#14556575—21no—
27#14556571C2212yescomplemented
28#14556566C2212yescomplemented
29#14556561—21no—
30C4×D292—22no—
31#14556514C2214yescomplemented
32#14556503C2214yescomplemented
33C22×D4×C73C2211yescharacteristic
34C2×M16×C73C2211yescharacteristic
35#117×C73C2211yescharacteristic
36#102×C73C2214yescomplemented
37C23×D73D411yescharacteristic
38#11924028—22no—
39#11924028—22no—
40#11924027—216no—
41#11924027—28no—
42#11924027—28no—
43C2×Dic146—21no—
44C2×Dic146—22no—
45C2×Dic146D414yescomplemented
46C2×Dic146C2311yescharacteristic
47C2×Dic146C2312yes—
48C2×D292—22no—
49C2×D292C2311yescharacteristic
50C2×C22⋊D73—28no—
51C2×C22⋊D73—24no—
52C2×C22⋊D73—21no—
53C22×Dic73—28no—
54C22×Dic73—21no—
55C22×Dic73—24no—
56C22×Dic73D411yescharacteristic
57C2×C4×D73—22no—
58C2×C4×D73—22no—
59C2×C4×D73—21no—
60C2×C4×D73D412yes—
61C2×C4×D73C2312yes—
62Dic292—24no—
63#11924017—24no—
64#11924016—24no—
65#11924013—24no—
66#11924012—22no—
67C2×#10596831C2312yes—
68C4⋊Dic73—22no—
69#11924005—22no—
70#11924005—22no—
71C24×C73—21no—
72C2×D4×C73—21no—
73C2×D4×C73—22no—
74C2×D4×C73D414yescomplemented
75C2×D4×C73C2312yes—
76C22×C4×C73C2311yescharacteristic
77M16×C73—22no—
78C2×C8×C73C2312yes—
79C4⋊C4×C73C2312yes—
80C22⋊C4×C73—21no—
81C42×C73—21no—
82C23×C73—24no—
83C23×C73—22no—
84C23×C73—44no—
85C23×C73C2×D411yescharacteristic
86C22×D73—22no—
87C22×D73—21no—
88C22×D73—42no—
89C22×D73C2×D412yes—
90D4×C73—24no—
91D4×C73—22no—
92D4×C73C2×D414yes—
93C2×C4×C73—22no—
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2×D412yes—
96C2×C4×C73C2×D412yes—
97C2×C4×C73C2411yescharacteristic
98C22⋊D73—216no—
99C22⋊D73—42no—
100C2×Dic73—216no—
101C2×Dic73—22no—
102C2×Dic73—24no—
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73C2×D412yes—
106D292—21no—
107D292—21no—
108D292—44no—
109C4×D73—24no—
110C4×D73—22no—
111C4×D73—22no—
112C4×D73—42no—
113Dic146—24no—
114Dic146—22no—
115Dic146—21no—
116Dic146—21no—
117Dic146C2×D414yes—
118C8×C73—22no—
119#10596831—22no—
120C22×C73—22no—
121C22×C73—24no—
122C22×C73—48no—
123C22×C73—44no—
124C22×C73#12012yes—
125C22×C73C22×D411yescharacteristic
126C2×D73—22no—
127C2×D73—22no—
128C2×D73—22no—
129C2×D73—44no—
130C2×D73—41no—
131C2×D73—42no—
132C4×C73—42no—
133C4×C73#12012yes—
134C4×C73C22×D411yescharacteristic
135C4×C73C22×D411yescharacteristic
136Dic73—24no—
137Dic73—22no—
138Dic73—41no—
139C2×C73—22no—
140C2×C73—44no—
141C2×C73C2×#12011yescharacteristic
142C2×C73#57512yes—
143D73—42no—
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#418D7311yescharacteristic, complemented
155#407—731no—
156C2×#41—734no—
157C2×#41—731no—
158C2×#41—1462no—
159C2×#41—1464no—
160C2×#41—1464no—
161C22×Q8—731no—
162C22×D4—1461no—
163C22×D4C2×D7311yescharacteristic
164C23×C4—731no—
165C23×C4—1461no—
166#137—1464no—
167AGL(1,ℤ/8)—1464no—
168C2×Q16—732no—
169C2×SD16—732no—
170C2×SD16—732no—
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#117C2×D7311yescharacteristic
180#103—734no—
181#102C2×D7314yescomplemented
182C22⋊C8—734no—
183C24—21no—
184C24—731no—
185#41—1462no—
186#41—1462no—
187#41—1468no—
188#41—14616no—
189#41—1468no—
190C2×Q8—734no—
191C2×Q8—732no—
192C2×Q8—731no—
193C2×Q8—1461no—
194C2×Q8—1462no—
195C2×D4—21no—
196C2×D4—22no—
197C2×D4—731no—
198C2×D4—1462no—
199C2×D4—1461no—
200C2×D4—1464no—
201C2×D4—1468no—
202C2×D4D29214yescomplemented
203C2×D4C22×D7312yes—
204C22×C4—731no—
205C22×C4—732no—
206C22×C4—732no—
207C22×C4—1461no—
208C22×C4—1464no—
209C22×C4—1468no—
210C22×C4—1461no—
211C22×C4—1462no—
212C22×C4—1462no—
213C22×C4C22×D7311yescharacteristic
214Q16—1464no—
215SD16—1464no—
216SD16—1464no—
217D8—1464no—
218M16—22no—
219M16—1462no—
220C2×C8—732no—
221C2×C8C22×D7312yes—
222C4⋊C4—1462no—
223C4⋊C4C22×D7312yes—
224C22⋊C4—21no—
225C22⋊C4—1462no—
226C22⋊C4—1462no—
227C42—21no—
228C23—24no—
229C23—22no—
230C23—44no—
231C23—2922no—
232C23—732no—
233C23—1461no—
234C23—1462no—
235C23D4×D7311yescharacteristic
236Q8—734no—
237Q8—1461no—
238Q8—1461no—
239Q8—1464no—
240Q8—1462no—
241D4—24no—
242D4—22no—
243D4—2924no—
244D4—2922no—
245D4—14616no—
246D4—1461no—
247D4—1461no—
248D4C2×D29214yes—
249C2×C4—22no—
250C2×C4—2922no—
251C2×C4—732no—
252C2×C4—1461no—
253C2×C4—14616no—
254C2×C4—1462no—
255C2×C4—1464no—
256C2×C4—1462no—
257C2×C4—1464no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4D4×D7311yescharacteristic
261C2×C4D4×D7312yes—
262C2×C4C2×D29212yes—
263C2×C4C23×D7311yescharacteristic
264C8—22no—
265C8—1462no—
266C22—22no—
267C22—24no—
268C22—48no—
269C22—44no—
270C22—2924no—
271C22—2922no—
272C22—2921no—
273C22—1462no—
274C22—1462no—
275C22—1462no—
276C22#1455656112yes—
277C22C2×D4×D7311yescharacteristic
278C4—42no—
279C4—2921no—
280C4—1462no—
281C4—1464no—
282C4#1455656112yes—
283C4C2×D4×D7311yescharacteristic
284C4C22×D29211yescharacteristic
285C2—22no—
286C2—44no—
287C2—2922no—
288C2—5841no—
289C2C2×#1455656111yescharacteristic
290C2#1798938312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#418×C73C2
socleC22×C73C22×D4
hypercenter#418D73
hypocenterC73#3005
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×#11924027C2semidirect
2. C2×#14556624C2semidirect
3. C2×#14556617C2semidirect
4. #17989099C2semidirect
5. #17988750C2semidirect
6. #17988733C2semidirect
7. #17988595C2semidirect
8. #17988550C2semidirect
9. #418×C73C2semidirect
21. C2×Dic292C22semidirect
22. C2×#11924017C22semidirect
23. C2×#11924016C22semidirect
24. C2×#11924013C22semidirect
27. #14556571C22semidirect
28. #14556566C22semidirect
31. #14556514C22semidirect
32. #14556503C22semidirect
36. #102×C73C22semidirect
45. C2×Dic146D4semidirect
74. C2×D4×C73D4semidirect
146. C73#3005semidirect
154. #418D73semidirect
181. #102C2×D73semidirect
202. C2×D4D292semidirect