Finite Group Databasebeta

← #22620029

Subgroups — #22620029

Order 9344.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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#17989142C211yesmaximal, characteristic, complemented
2C4×D4×D73C211yesmaximal, characteristic
3#17988921C212yesmaximal, complemented
4#17988868C211yesmaximal, characteristic, complemented
5#17988867C211yesmaximal, characteristic, complemented
6#17988789C211yesmaximal, characteristic, complemented
7#17988736C212yesmaximal
8#17988690C212yesmaximal, complemented
9#17988688C212yesmaximal, complemented
10#17988643C211yesmaximal, characteristic, complemented
11#461×C73C211yesmaximal, characteristic, complemented
12C2×D4×D73C2211yescharacteristic
13C22×C4×D73—21no—
14C2×#11924015C2212yes—
15#14556591C2211yescharacteristic, complemented
16#14556582—21no—
17#14556571—21no—
18#14556567C2212yes—
19Q8×Dic73C2212yescomplemented
20#14556556—21no—
21C4×D292C2211yescharacteristic
22D4×Dic73C2211yescharacteristic
23#14556553C2211yescharacteristic
24C4×C22⋊D73—21no—
25#14556551—21no—
26#14556549—21no—
27C4⋊C4×D73C2211yescharacteristic
28C22⋊C4×D73—21no—
29C42×D73C2211yescharacteristic
30#14556525C2212yescomplemented
31#14556524C2212yescomplemented
32C4⋊#10596831C2211yescharacteristic, complemented
33#14556515C2212yescomplemented
34#14556513C2212yes—
35#14556512C2212yes—
36#14556503C2212yes—
37#14556501C2212yescomplemented
38C2×SD16×C73C2212yes—
39C4⋊Q8×C73C2211yescharacteristic, complemented
40C4×D4×C73C2211yescharacteristic
41C4⋊C8×C73C2211yescharacteristic, complemented
42#103×C73C2212yescomplemented
43C23×D73—21no—
44C2×Dic146—21no—
45C2×D292C2311yescharacteristic
46C2×C22⋊D73—21no—
47D4×D73—22no—
48D4×D73—22no—
49C22×Dic73—21no—
50C2×C4×D73—21no—
51C2×C4×D73—21no—
52C2×C4×D73—21no—
53C2×C4×D73—44no—
54C2×C4×D73D411yescharacteristic
55C2×C4×D73D411yescharacteristic
56C2×C4×D73C2311yescharacteristic
57#11924015—24no—
58C2×#10596831C2312yes—
59C4⋊Dic73—21no—
60C4⋊Dic73—22no—
61C4⋊Dic73C2312yes—
62C4⋊Dic73C2311yescharacteristic
63#11924007—21no—
64#11924007—22no—
65C22⋊Dic73—21no—
66#11924005—22no—
67#11924005—21no—
68#11924005—21no—
69C4×Dic73—22no—
70C4×Dic73D411yescharacteristic
71C4×Dic73D411yescharacteristic
72C4×Dic73C2311yescharacteristic
73C2×Q8×C73C2312yes—
74C2×D4×C73C2311yescharacteristic
75C22×C4×C73—21no—
76SD16×C73—24no—
77C2×C8×C73C2312yes—
78C4⋊C4×C73—21no—
79C4⋊C4×C73—21no—
80C4⋊C4×C73C2311yescharacteristic
81C22⋊C4×C73—21no—
82C42×C73C2311yescharacteristic
83C23×C73—21no—
84C22×D73—24no—
85C22×D73—21no—
86C22×D73—42no—
87C22×D73—42no—
88C22×D73C2×D411yescharacteristic
89Q8×C73—22no—
90Q8×C73—22no—
91D4×C73—21no—
92D4×C73#4112yes—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—42no—
96C2×C4×C73C2×D411yescharacteristic
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2411yescharacteristic
99C22⋊D73—24no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—42no—
103C2×Dic73C2×D411yescharacteristic
104C2×Dic73C2×D411yescharacteristic
105C2×Dic73C2×D411yescharacteristic
106D292—21no—
107D292#4112yes—
108C4×D73—22no—
109C4×D73—22no—
110C4×D73—21no—
111C4×D73—21no—
112C4×D73—42no—
113C4×D73—42no—
114C4×D73—42no—
115Dic146—42no—
116C8×C73—22no—
117#10596831—22no—
118C22×C73—22no—
119C22×C73—41no—
120C22×C73—41no—
121C22×C73C22×D411yescharacteristic
122C2×D73—21no—
123C2×D73—21no—
124C2×D73—22no—
125C2×D73—48no—
126C2×D73—41no—
127C2×D73—41no—
128C2×D73#13712yes—
129C4×C73—21no—
130C4×C73—42no—
131C4×C73—41no—
132C4×C73AGL(1,ℤ/8)12yes—
133C4×C73C2×#4111yescharacteristic
134C4×C73C2×#4111yescharacteristic
135Dic73—21no—
136Dic73—21no—
137Dic73—21no—
138Dic73—42no—
139Dic73—41no—
140C2×C73—42no—
141C2×C73#52511yescharacteristic
142C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
143C2×C73C2×#13711yescharacteristic
144D73—22no—
145D73—42no—
146#3110—731nomaximal, Sylow
147C73#311011yescharacteristic, complemented, Sylow
148#533—731no—
149C2×C4×D4—731no—
150#484—732no—
151#474—731no—
152#474—731no—
153#461—731no—
154#461D7311yescharacteristic, complemented
155#450—732no—
156#440—732no—
157#440—732no—
158#432—731no—
159C22×D4—731no—
160C23×C4—1461no—
161C2×SD16—732no—
162C2×SD16C2×D7312yes—
163C4⋊Q8—731no—
164C4⋊Q8C2×D7311yescharacteristic, complemented
165#125—1461no—
166C22⋊Q8—732no—
167C22⋊Q8—1461no—
168C4×Q8—732no—
169C4×Q8—1461no—
170C4×D4—731no—
171C4×D4—731no—
172C4×D4—731no—
173C4×D4—1461no—
174C4×D4—1461no—
175C4×D4C2×D7311yescharacteristic
176#117—1461no—
177C2×C4⋊C4—731no—
178C2×C22⋊C4—1461no—
179C2×C42—731no—
180#107—732no—
181#107—732no—
182C4⋊C8—731no—
183C4⋊C8C2×D7311yescharacteristic, complemented
184#103—732no—
185#103C2×D7312yescomplemented
186#102—732no—
187#102—732no—
188C22⋊C8—732no—
189#97—732no—
190C24—1461no—
191C2×Q8—1461no—
192C2×Q8C22×D7312yes—
193C2×D4—731no—
194C2×D4—1461no—
195C2×D4—1462no—
196C2×D4—1462no—
197C2×D4C22×D7311yescharacteristic
198C22×C4—21no—
199C22×C4—2924no—
200C22×C4—731no—
201C22×C4—731no—
202C22×C4—731no—
203C22×C4—1461no—
204C22×C4—1461no—
205C22×C4—1461no—
206C22×C4—1461no—
207SD16—24no—
208SD16—1464no—
209C2×C8—732no—
210C2×C8C22×D7312yes—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—732no—
214C4⋊C4—731no—
215C4⋊C4—1461no—
216C4⋊C4—1462no—
217C4⋊C4—1462no—
218C4⋊C4—1461no—
219C4⋊C4C22×D7311yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—1461no—
222C22⋊C4—1462no—
223C22⋊C4—1461no—
224C22⋊C4—1461no—
225C42—731no—
226C42—731no—
227C42—731no—
228C42—1462no—
229C42C22×D7311yescharacteristic
230C23—21no—
231C23—2922no—
232C23—2922no—
233C23—731no—
234C23—1464no—
235C23—1461no—
236Q8—22no—
237Q8—22no—
238Q8—2922no—
239D4—21no—
240D4—732no—
241D4—1464no—
242D4—1461no—
243D4#1192402712yes—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—2922no—
248C2×C4—2922no—
249C2×C4—2922no—
250C2×C4—2922no—
251C2×C4—731no—
252C2×C4—731no—
253C2×C4—731no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1461no—
257C2×C4—1462no—
258C2×C4—1461no—
259C2×C4—1461no—
260C2×C4D4×D7311yescharacteristic
261C2×C4D4×D7311yescharacteristic
262C2×C4C23×D7311yescharacteristic
263C8—22no—
264C8—1462no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—2928no—
269C22—2921no—
270C22—2921no—
271C22—732no—
272C22—1462no—
273C22—1461no—
274C22—1461no—
275C22C2×D4×D7311yescharacteristic
276C4—21no—
277C4—42no—
278C4—41no—
279C4—2921no—
280C4—2922no—
281C4—1461no—
282C4—1461no—
283C4—1461no—
284C4#1455661812yes—
285C4#41×D7311yescharacteristic
286C4C2×#1192402711yescharacteristic
287C2—42no—
288C2—2922no—
289C2—1462no—
290C2#1798909711yescharacteristic
291C2C2×#1455661811yescharacteristic
292C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#461×C73C2
socleC22×C73C22×D4
hypercenter#461D73
hypocenterC73#3110
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988921C2semidirect
4. #17988868C2semidirect
5. #17988867C2semidirect
6. #17988789C2semidirect
8. #17988690C2semidirect
9. #17988688C2semidirect
10. #17988643C2semidirect
11. #461×C73C2semidirect
15. #14556591C22semidirect
19. Q8×Dic73C22semidirect
30. #14556525C22semidirect
31. #14556524C22semidirect
32. C4⋊#10596831C22semidirect
33. #14556515C22semidirect
37. #14556501C22semidirect
39. C4⋊Q8×C73C22semidirect
41. C4⋊C8×C73C22semidirect
42. #103×C73C22semidirect
147. C73#3110semidirect
154. #461D73semidirect
164. C4⋊Q8C2×D73semidirect
183. C4⋊C8C2×D73semidirect
185. #103C2×D73semidirect