Finite Group Databasebeta

← #22620735

Subgroups — #22620735

Order 9344.

462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14556567C211yesmaximal, characteristic, complemented
2#121×D73C211yesmaximal, characteristic
3#17988921C212yesmaximal, complemented
4#17988901C211yesmaximal, characteristic, complemented
5#17988898C211yesmaximal, characteristic, complemented
6#17988836C212yesmaximal, complemented
7#17988830C212yesmaximal, complemented
8#17988736C212yesmaximal, complemented
9#17988726C211yesmaximal, characteristic, complemented
10#17988549C211yesmaximal, characteristic, complemented
11#448×C73C211yesmaximal, characteristic, complemented
12C2×D4×D73—21no—
13C2×D4×D73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C2×#11924015C2212yescomplemented
16C2×#11924011C2212yescomplemented
17#14556567—21no—
18#14556567—21no—
19#14556567C2212yes—
20#14556567C2212yescomplemented
21#14556566C2211yescharacteristic
22#14556565C2211yescharacteristic
23#14556564—21no—
24#14556563—21no—
25#14556562C2211yescharacteristic
26C2×C4⋊Dic73C2211yescharacteristic, complemented
27C2×#11924007—21no—
28C4⋊C4×D73C2211yescharacteristic
29C2×#11924005—21no—
30C22⋊C4×D73—21no—
31#14556525C2212yescomplemented
32#14556524C2212yescomplemented
33#14556515C2212yescomplemented
34#14556513C2212yescomplemented
35#14556512C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic, complemented
37#14556503C2212yes—
38C22×Q8×C73C2211yescharacteristic, complemented
39C2×SD16×C73C2212yescomplemented
40#121×C73C2211yescharacteristic
41#103×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic, complemented
43C23×D73—21no—
44C23×D73D411yescharacteristic
45C2×D292—21no—
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C22⋊D73—21no—
49C2×C22⋊D73—21no—
50D4×D73—42no—
51D4×D73—44no—
52C22×Dic73—21no—
53C22×Dic73D411yescharacteristic
54C2×C4×D73—21no—
55C2×C4×D73—42no—
56C2×C4×D73D411yescharacteristic
57C2×C4×D73D411yescharacteristic
58C2×C4×D73C2311yescharacteristic
59C2×C4×D73C2311yescharacteristic
60#11924015—42no—
61#11924011—42no—
62C2×#10596831C2312yes—
63C4⋊Dic73—21no—
64C4⋊Dic73C2312yes—
65C4⋊Dic73C2311yescharacteristic
66#11924007—21no—
67#11924007—22no—
68#11924007—22no—
69C22⋊Dic73—21no—
70#11924005—22no—
71#11924005—22no—
72#11924005—21no—
73#11924005—21no—
74C2×Q8×C73—21no—
75C2×Q8×C73—42no—
76C2×Q8×C73C2312yes—
77C2×D4×C73—21no—
78C2×D4×C73C2311yescharacteristic
79C22×C4×C73—21no—
80C22×C4×C73C2311yescharacteristic
81SD16×C73—42no—
82C2×C8×C73C2312yes—
83C4⋊C4×C73C2311yescharacteristic
84C22⋊C4×C73—21no—
85C23×C73—21no—
86C23×C73C2×D411yescharacteristic
87C22×D73—22no—
88C22×D73—22no—
89C22×D73—21no—
90C22×D73—41no—
91C22×D73—42no—
92C22×D73—42no—
93C22×D73—42no—
94C22×D73C2×D411yescharacteristic
95C22×D73C2×D411yescharacteristic
96Q8×C73—22no—
97Q8×C73—22no—
98Q8×C73—42no—
99D4×C73—22no—
100D4×C73—42no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—22no—
104C2×C4×C73—42no—
105C2×C4×C73C2×D411yescharacteristic
106C2×C4×C73C2411yescharacteristic
107C22⋊D73—42no—
108C22⋊D73—42no—
109C22⋊D73—42no—
110C2×Dic73—22no—
111C2×Dic73—21no—
112C2×Dic73—41no—
113C2×Dic73—42no—
114C2×Dic73C2×D411yescharacteristic
115C2×Dic73C2×D411yescharacteristic
116D292—22no—
117D292—42no—
118C4×D73—22no—
119C4×D73—22no—
120C4×D73—41no—
121C4×D73—41no—
122C4×D73—42no—
123C8×C73—22no—
124#10596831—22no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—41no—
128C22×C73—41no—
129C22×C73—41no—
130C22×C73AGL(1,ℤ/8)12yes—
131C22×C73C22×D411yescharacteristic
132C2×D73—21no—
133C2×D73—21no—
134C2×D73—21no—
135C2×D73—21no—
136C2×D73—21no—
137C2×D73—44no—
138C2×D73—41no—
139C2×D73—41no—
140C2×D73—41no—
141C2×D73—84no—
142C2×D73#13712yes—
143C4×C73—21no—
144C4×C73—42no—
145C4×C73—41no—
146C4×C73H(5,𝔽2)12yes—
147Dic73—21no—
148Dic73—21no—
149Dic73—41no—
150Dic73—42no—
151C2×C73—22no—
152C2×C73—81no—
153C2×C73#53411yescharacteristic
154C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
155C2×C73C2×#13711yescharacteristic
156D73—22no—
157D73—41no—
158D73—81no—
159#3193—731nomaximal, Sylow
160C73#319311yescharacteristic, complemented, Sylow
161C2×C22⋊Q8—731no—
162C2×#121—731no—
163#484—732no—
164#480—731no—
165#480—731no—
166#468—732no—
167#468—732no—
168#450—732no—
169#448—731no—
170#448D7311yescharacteristic, complemented
171#407—731no—
172C22×Q8C2×D7311yescharacteristic, complemented
173C22×D4—731no—
174C22×D4—1461no—
175C23×C4—731no—
176C2×SD16—732no—
177C2×SD16C2×D7312yescomplemented
178C2×M16—732no—
179C22⋊Q8—732no—
180C22⋊Q8—732no—
181C22⋊Q8—1461no—
182C22⋊Q8—1461no—
183#121—731no—
184#121—731no—
185#121—731no—
186#121—1461no—
187#121—1461no—
188#121C2×D7311yescharacteristic
189C2×C4⋊C4—731no—
190C2×C4⋊C4—731no—
191C2×C4⋊C4—1461no—
192C2×C22⋊C4—1461no—
193C2×C22⋊C4—1461no—
194#107—732no—
195#107—732no—
196#103—732no—
197#103C2×D7312yescomplemented
198#102—732no—
199#102—732no—
200C22⋊C8—731no—
201C22⋊C8—732no—
202C22⋊C8C2×D7311yescharacteristic, complemented
203C24—731no—
204C24—1461no—
205C2×Q8—21no—
206C2×Q8—42no—
207C2×Q8C22×D7312yes—
208C2×D4—21no—
209C2×D4—2924no—
210C2×D4—2922no—
211C2×D4—731no—
212C2×D4—1461no—
213C2×D4—1461no—
214C2×D4—1461no—
215C2×D4—1461no—
216C2×D4C22×D7311yescharacteristic
217C22×C4—21no—
218C22×C4—2922no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—731no—
223C22×C4—731no—
224C22×C4—1461no—
225C22×C4—1461no—
226C22×C4C22×D7311yescharacteristic
227SD16—42no—
228SD16—2922no—
229M16—2922no—
230C2×C8—732no—
231C2×C8C22×D7312yes—
232C4⋊C4—732no—
233C4⋊C4—731no—
234C4⋊C4—1461no—
235C4⋊C4—1462no—
236C4⋊C4—1462no—
237C4⋊C4—1461no—
238C4⋊C4C22×D7311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—1461no—
241C22⋊C4—1462no—
242C22⋊C4—1462no—
243C22⋊C4—1461no—
244C22⋊C4—1461no—
245C23—21no—
246C23—2921no—
247C23—2922no—
248C23—2922no—
249C23—2922no—
250C23—731no—
251C23—731no—
252C23—1462no—
253C23—1461no—
254C23—1462no—
255C23D4×D7311yescharacteristic
256Q8—22no—
257Q8—22no—
258Q8—42no—
259D4—22no—
260D4—42no—
261D4—2922no—
262D4—2922no—
263D4—2922no—
264D4—2922no—
265D4—1462no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—2921no—
271C2×C4—2921no—
272C2×C4—2922no—
273C2×C4—2922no—
274C2×C4—2921no—
275C2×C4—731no—
276C2×C4—731no—
277C2×C4—1462no—
278C2×C4—1461no—
279C2×C4—1462no—
280C2×C4—1462no—
281C2×C4D4×D7311yescharacteristic
282C2×C4C23×D7311yescharacteristic
283C8—22no—
284C8—1462no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—2924no—
291C22—2921no—
292C22—2921no—
293C22—2921no—
294C22—5844no—
295C22—732no—
296C22—1461no—
297C22—1461no—
298C22—1461no—
299C22—1461no—
300C22—1461no—
301C22#1455661812yes—
302C22C2×D4×D7311yescharacteristic
303C4—21no—
304C4—42no—
305C4—41no—
306C4—2921no—
307C4—2922no—
308C4—1461no—
309C4—1461no—
310C4#1455663612yes—
311C2—22no—
312C2—81no—
313C2—2921no—
314C2—5841no—
315C2—1462no—
316C2#1798914711yescharacteristic
317C2C2×#1455661811yescharacteristic
318C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#448×C73C2
socleC22×C73C22×D4
hypercenter#448D73
hypocenterC73#3193
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#14556567C2semidirect
3. #17988921C2semidirect
4. #17988901C2semidirect
5. #17988898C2semidirect
6. #17988836C2semidirect
7. #17988830C2semidirect
8. #17988736C2semidirect
9. #17988726C2semidirect
10. #17988549C2semidirect
11. #448×C73C2semidirect
15. C2×#11924015C22semidirect
16. C2×#11924011C22semidirect
20. #14556567C22semidirect
26. C2×C4⋊Dic73C22semidirect
31. #14556525C22semidirect
32. #14556524C22semidirect
33. #14556515C22semidirect
34. #14556513C22semidirect
35. #14556512C22semidirect
36. C22⋊#10596831C22semidirect
38. C22×Q8×C73C22semidirect
39. C2×SD16×C73C22semidirect
41. #103×C73C22semidirect
42. C22⋊C8×C73C22semidirect
160. C73#3193semidirect
170. #448D73semidirect
172. C22×Q8C2×D73semidirect
177. C2×SD16C2×D73semidirect
197. #103C2×D73semidirect
202. C22⋊C8C2×D73semidirect