Finite Group Databasebeta

← #22619219

Subgroups — #22619219

Order 9344.

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

normal subgroups only

This group has 732 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
1C2×#14556638C211yesmaximal, characteristic, complemented
2C2×#14556619C211yesmaximal, characteristic, complemented
3C22×#11924017C211yesmaximal, characteristic, complemented
4#17989151C211yesmaximal, characteristic, complemented
5#17988734C214yesmaximal, complemented
6#17988728C214yesmaximal, complemented
7#17988597C211yesmaximal, characteristic, complemented
8#17988584C211yesmaximal, characteristic, complemented
9#408×C73C211yesmaximal, characteristic, complemented
10#14556638—24no—
11#14556638—24no—
12C2×#11924028C2211yescharacteristic
13C2×#11924028C2212yescomplemented
14C2×#11924027—22no—
15C2×#11924027—21no—
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2212yescomplemented
18C2×Q8×D73—21no—
19C22×D292C2211yescharacteristic
20#14556619—24no—
21C2×#11924017—24no—
22C2×#11924017C2212yes—
23C2×#11924017C2214yes—
24C2×D584C2212yes—
25#14556587—21no—
26#14556580—21no—
27#14556565C2214yes—
28#14556559—22no—
29#14556550C2211yescharacteristic
30#14556516C2212yescomplemented
31#14556516C2214yescomplemented
32#14556513C2212yescomplemented
33C2×#41×C73C2211yescharacteristic
34C2×M16×C73C2211yescharacteristic
35C22×C8×C73C2211yescharacteristic
36C22⋊C8×C73C2214yescomplemented
37C23×D73—21no—
38#11924028—22no—
39#11924028—24no—
40#11924028—24no—
41#11924028D414yescomplemented
42#11924027—216no—
43#11924027—28no—
44C2×Dic146—21no—
45C2×Dic146—22no—
46C2×Dic146—22no—
47C2×Dic146—24no—
48C2×Dic146—24no—
49C2×Dic146D414yescomplemented
50C2×Dic146C2312yes—
51C2×Dic146C2311yescharacteristic
52Q8×D73—28no—
53C2×D292—22no—
54C2×D292—22no—
55C2×D292—21no—
56C2×D292C2312yes—
57C2×D292C2311yescharacteristic
58C2×C22⋊D73—21no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—24no—
61C22×Dic73—21no—
62C22×Dic73—22no—
63C2×C4×D73—21no—
64C2×C4×D73—22no—
65#11924017—28no—
66#11924017—24no—
67D584—24no—
68C4⋊Dic73C2312yes—
69C22⋊Dic73—21no—
70#11924005—24no—
71C4×Dic73—21no—
72#41×C73—22no—
73#41×C73—22no—
74C2×Q8×C73D411yescharacteristic
75C2×D4×C73D412yes—
76C2×D4×C73D411yescharacteristic
77C22×C4×C73C2312yes—
78C22×C4×C73C2311yescharacteristic
79M16×C73—22no—
80C2×C8×C73—22no—
81C2×C8×C73C2312yes—
82C2×C8×C73C2312yes—
83C23×C73C2×D412yes—
84C23×C73C2×D411yescharacteristic
85C22×D73—21no—
86C22×D73—22no—
87C22×D73—42no—
88C22×D73—82no—
89Q8×C73—22no—
90D4×C73—24no—
91D4×C73—22no—
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—28no—
100C22⋊D73—24no—
101C22⋊D73—84no—
102C2×Dic73—28no—
103C2×Dic73—24no—
104C2×Dic73—21no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107D292—21no—
108D292—22no—
109D292—22no—
110D292—42no—
111D292C2×D412yes—
112C4×D73—28no—
113C4×D73—24no—
114Dic146—28no—
115Dic146—24no—
116Dic146—22no—
117Dic146—21no—
118Dic146C2×D412yes—
119Dic146C2×D414yes—
120C8×C73—22no—
121C8×C73—22no—
122C22×C73—22no—
123C22×C73—22no—
124C22×C73—24no—
125C22×C73#12012yes—
126C22×C73C22×D411yescharacteristic
127C2×D73—22no—
128C2×D73—42no—
129C2×D73—42no—
130C2×D73—44no—
131C2×D73—84no—
132C4×C73—22no—
133C4×C73#12012yes—
134C4×C73C22×D411yescharacteristic
135C4×C73C22×D411yescharacteristic
136Dic73—22no—
137Dic73—24no—
138Dic73—42no—
139C2×C73—22no—
140C2×C73—42no—
141C2×C73C2×#12011yescharacteristic
142C2×C73#57712yes—
143D73—42no—
144D73—82no—
145#3010—731nomaximal, Sylow
146C73#301011yescharacteristic, complemented, Sylow
147C2×2−1+4—731no—
148C2×AGL(1,ℤ/8)—731no—
149C22×SD16—731no—
150#535—731no—
151#449—734no—
152#448—734no—
153#419—731no—
154#416—731no—
155#408D7311yescharacteristic, complemented
1562−1+4—1464no—
1572−1+4—1464no—
158C2×#41—731no—
159C2×#41—732no—
160C2×#41—1462no—
161C2×#41—1461no—
162C2×#41C2×D7311yescharacteristic
163C22×Q8—731no—
164C22×Q8—732no—
165C22×Q8—1461no—
166C22×D4—731no—
167AGL(1,ℤ/8)—1464no—
168C2×SD16—734no—
169C2×SD16—732no—
170C2×SD16—1464no—
171C2×D8—732no—
172C2×M16C2×D7311yescharacteristic
173C22×C8C2×D7311yescharacteristic
174#127—1461no—
175#124—1461no—
176#121—734no—
177#120—1462no—
178#117—731no—
179#103—732no—
180#103—734no—
181#102—732no—
182C22⋊C8C2×D7314yescomplemented
183C24—1461no—
184#41—22no—
185#41—22no—
186#41—734no—
187#41—1464no—
188#41—1464no—
189#41—14616no—
190#41—1468no—
191#41—1462no—
192C2×Q8—734no—
193C2×Q8—732no—
194C2×Q8—731no—
195C2×Q8—1464no—
196C2×Q8—1464no—
197C2×Q8—1468no—
198C2×Q8—1462no—
199C2×Q8—1462no—
200C2×Q8—1461no—
201C2×Q8D29211yescharacteristic
202C2×D4—731no—
203C2×D4—732no—
204C2×D4—1464no—
205C2×D4—1462no—
206C2×D4—1461no—
207C2×D4—1462no—
208C2×D4—1462no—
209C2×D4—1461no—
210C2×D4D29212yes—
211C2×D4D29211yescharacteristic
212C22×C4—1462no—
213C22×C4—1461no—
214C22×C4—1462no—
215C22×C4—1461no—
216C22×C4C22×D7312yes—
217C22×C4C22×D7311yescharacteristic
218SD16—1468no—
219SD16—1464no—
220D8—1464no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D7312yes—
224C2×C8C22×D7312yes—
225C4⋊C4—732no—
226C22⋊C4—1461no—
227C22⋊C4—1464no—
228C42—1461no—
229C23—2922no—
230C23—5842no—
231C23—1462no—
232C23—1461no—
233C23C2×D29212yes—
234C23C2×D29211yescharacteristic
235Q8—22no—
236Q8—734no—
237Q8—732no—
238Q8—1468no—
239Q8—1464no—
240Q8—1462no—
241Q8—1461no—
242D4—24no—
243D4—22no—
244D4—2922no—
245D4—5844no—
246D4—732no—
247D4—1468no—
248D4—1464no—
249D4—1462no—
250D4—1462no—
251D4—1461no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—1468no—
255C2×C4—1462no—
256C2×C4—1468no—
257C2×C4—1464no—
258C2×C4—1462no—
259C2×C4—1461no—
260C2×C4—1464no—
261C2×C4D4×D7312yes—
262C2×C4D4×D7312yes—
263C2×C4C2×D29212yes—
264C2×C4C2×D29211yescharacteristic
265C2×C4C23×D7311yescharacteristic
266C8—22no—
267C8—22no—
268C22—22no—
269C22—24no—
270C22—22no—
271C22—2922no—
272C22—2924no—
273C22—2922no—
274C22—5844no—
275C22—1462no—
276C22#1455656112yes—
277C22C22×D29211yescharacteristic
278C4—22no—
279C4—2922no—
280C4—1464no—
281C4—1462no—
282C4#1455656112yes—
283C4C2×D4×D7311yescharacteristic
284C4C2×D4×D7311yescharacteristic
285C2—22no—
286C2—42no—
287C2—2922no—
288C2—5842no—
289C2C2×#1455656111yescharacteristic
290C2#1798939912yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#408×C73C2
socleC22×C73C22×D4
hypercenter#408D73
hypocenterC73#3010
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#14556638C2semidirect
2. C2×#14556619C2semidirect
3. C22×#11924017C2semidirect
4. #17989151C2semidirect
5. #17988734C2semidirect
6. #17988728C2semidirect
7. #17988597C2semidirect
8. #17988584C2semidirect
9. #408×C73C2semidirect
13. C2×#11924028C22semidirect
17. C22×Dic146C22semidirect
30. #14556516C22semidirect
31. #14556516C22semidirect
32. #14556513C22semidirect
36. C22⋊C8×C73C22semidirect
41. #11924028D4semidirect
49. C2×Dic146D4semidirect
146. C73#3010semidirect
155. #408D73semidirect
182. C22⋊C8C2×D73semidirect