Finite Group Databasebeta

← #22620701

Subgroups — #22620701

Order 9344.

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

normal subgroups only

This group has 472 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
1#17989100C211yesmaximal, characteristic, complemented
2C2×#14556566C211yesmaximal, characteristic, complemented
3#17988914C212yesmaximal, complemented
4#17988905C211yesmaximal, characteristic, complemented
5#17988824C212yesmaximal, complemented
6#17988819C212yesmaximal, complemented
7#17988737C211yesmaximal, characteristic, complemented
8#17988735C212yesmaximal, complemented
9#17988723C211yesmaximal, characteristic, complemented
10C22⋊C8×D73C211yesmaximal, characteristic, complemented
11#484×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2211yescharacteristic, complemented
13C22×D292—21no—
14C22×D292C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16C2×#11924015C2212yescomplemented
17C2×D584C2212yescomplemented
18C2×C8×D73C2212yescomplemented
19#14556576—21no—
20#14556567C2211yescharacteristic, complemented
21#14556566—21no—
22#14556566—21no—
23#14556566C2212yes—
24#14556566C2212yes—
25#14556566C2211yescharacteristic, complemented
26#14556565C2211yescharacteristic
27#14556561—21no—
28#14556553—21no—
29#14556551—21no—
30#14556549C2211yescharacteristic, complemented
31C2×#11924005—21no—
32#14556522C2212yescomplemented
33#14556513C2212yescomplemented
34#14556511C2212yescomplemented
35#14556511C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic
37#14556503C2212yescomplemented
38C22⋊Q8×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#107×C73C2212yescomplemented
41#103×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic
43C23×D73—21no—
44C23×D73D411yescharacteristic
45#11924029—42no—
46C2×D292—21no—
47C2×D292—21no—
48C2×D292—22no—
49C2×D292—22no—
50C2×D292—21no—
51C2×D292—42no—
52C2×D292—44no—
53C2×D292C2311yescharacteristic
54C2×D292C2312yes—
55C2×C22⋊D73—21no—
56C22×Dic73D411yescharacteristic
57C2×C4×D73—21no—
58C2×C4×D73—42no—
59C2×C4×D73D411yescharacteristic
60C2×C4×D73D411yescharacteristic
61C2×C4×D73C2311yescharacteristic
62C2×C4×D73C2311yescharacteristic
63#11924015—42no—
64D584—42no—
65C2×#10596831C2312yes—
66C8×D73—42no—
67C4⋊Dic73C2311yescharacteristic
68#11924007—21no—
69#11924005—21no—
70#11924005—21no—
71#11924005—21no—
72#11924005—22no—
73#11924005—22no—
74#11924005—21no—
75C4×Dic73—21no—
76C2×Q8×C73C2311yescharacteristic
77C22×C4×C73—21no—
78C22×C4×C73C2311yescharacteristic
79C2×C8×C73C2312yes—
80C4⋊C4×C73—21no—
81C4⋊C4×C73—21no—
82C4⋊C4×C73C2312yes—
83C4⋊C4×C73C2311yescharacteristic
84C22⋊C4×C73—21no—
85C23×C73C2×D411yescharacteristic
86C22×D73—22no—
87C22×D73—22no—
88C22×D73—21no—
89C22×D73—22no—
90C22×D73—41no—
91C22×D73—42no—
92C22×D73—42no—
93C22×D73—42no—
94C22×D73C2×D411yescharacteristic
95C22×D73C2×D411yescharacteristic
96Q8×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—22no—
101C2×C4×C73—42no—
102C2×C4×C73C2×D411yescharacteristic
103C2×C4×C73C2411yescharacteristic
104C22⋊D73—42no—
105C2×Dic73—21no—
106C2×Dic73—41no—
107C2×Dic73C2×D411yescharacteristic
108C2×Dic73C2×D411yescharacteristic
109D292—22no—
110D292—22no—
111D292—22no—
112D292—42no—
113D292—44no—
114D292—42no—
115D292—42no—
116D292—44no—
117C4×D73—22no—
118C4×D73—22no—
119C4×D73—41no—
120C4×D73—41no—
121C4×D73—42no—
122C8×C73—22no—
123#10596831—22no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73#13512yes—
127C22×C73C22×D411yescharacteristic
128C2×D73—21no—
129C2×D73—21no—
130C2×D73—21no—
131C2×D73—21no—
132C2×D73—21no—
133C2×D73—44no—
134C2×D73—41no—
135C2×D73—42no—
136C2×D73—41no—
137C2×D73—42no—
138C2×D73—42no—
139C2×D73—41no—
140C2×D73—84no—
141C2×D73AGL(1,ℤ/8)12yes—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73—42no—
145C4×C73—41no—
146C4×C73H(5,𝔽2)12yes—
147Dic73—21no—
148Dic73—21no—
149Dic73—41no—
150C2×C73—22no—
151C2×C73#53411yescharacteristic
152C2×C73C2×#13511yescharacteristic
153C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
154D73—22no—
155D73—41no—
156D73—81no—
157D73—82no—
158#3188—731nomaximal, Sylow
159C73#318811yescharacteristic, complemented, Sylow
160#525—731no—
161C2×#121—731no—
162#484D7311yescharacteristic, complemented
163#482—732no—
164#481—731no—
165#466—732no—
166#465—732no—
167#450—731no—
168#449—732no—
169#447—731no—
170C2×C22⋊C8—731no—
171C2×#41—731no—
172C22×D4—731no—
173C22×D4—1461no—
174C23×C4—731no—
175C2×SD16—732no—
176C2×D8—732no—
177C22×C8—732no—
178#123—1461no—
179C22⋊Q8—731no—
180C22⋊Q8C2×D7311yescharacteristic
181#121—731no—
182#121—732no—
183#121—732no—
184#121—731no—
185#121—1461no—
186#121—1461no—
187#120—1461no—
188C4×D4—1461no—
189C4×D4—1461no—
190#117—731no—
191C2×C4⋊C4C2×D7311yescharacteristic
192C2×C22⋊C4—1461no—
193#107C2×D7312yescomplemented
194#106—732no—
195#103C2×D7312yescomplemented
196#102—732no—
197#102—732no—
198#102—732no—
199C22⋊C8—731no—
200C22⋊C8—732no—
201C22⋊C8C2×D7311yescharacteristic
202C24—731no—
203C24—1461no—
204#41—2922no—
205C2×Q8C22×D7311yescharacteristic
206C2×D4—2922no—
207C2×D4—2924no—
208C2×D4—731no—
209C2×D4—732no—
210C2×D4—1461no—
211C2×D4—1461no—
212C2×D4—1462no—
213C2×D4—1462no—
214C2×D4—1461no—
215C2×D4—1461no—
216C22×C4—21no—
217C22×C4—2922no—
218C22×C4—731no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—731no—
223C22×C4—1461no—
224C22×C4C22×D7311yescharacteristic
225SD16—2922no—
226D8—2922no—
227C2×C8—2922no—
228C2×C8—732no—
229C2×C8C22×D7312yes—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—731no—
233C4⋊C4—1461no—
234C4⋊C4C22×D7311yescharacteristic
235C4⋊C4C22×D7312yes—
236C22⋊C4—21no—
237C22⋊C4—1462no—
238C22⋊C4—1462no—
239C22⋊C4—1461no—
240C22⋊C4—1461no—
241C22⋊C4—1461no—
242C22⋊C4—1461no—
243C42—1461no—
244C23—2921no—
245C23—2922no—
246C23—2922no—
247C23—2922no—
248C23—731no—
249C23—731no—
250C23—1462no—
251C23—1461no—
252C23—1462no—
253C23—1462no—
254C23D4×D7311yescharacteristic
255Q8—22no—
256D4—2922no—
257D4—2924no—
258D4—2922no—
259D4—2924no—
260D4—2922no—
261D4—2922no—
262D4—1462no—
263D4—1462no—
264D4—1462no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—2921no—
271C2×C4—2921no—
272C2×C4—2922no—
273C2×C4—2921no—
274C2×C4—731no—
275C2×C4—731no—
276C2×C4—1461no—
277C2×C4—1462no—
278C2×C4—1462no—
279C2×C4D4×D7311yescharacteristic
280C2×C4C23×D7311yescharacteristic
281C8—22no—
282C8—1462no—
283C22—21no—
284C22—21no—
285C22—2924no—
286C22—2921no—
287C22—2922no—
288C22—2921no—
289C22—2922no—
290C22—2922no—
291C22—2921no—
292C22—5844no—
293C22—732no—
294C22—1461no—
295C22—1461no—
296C22—1461no—
297C22—1461no—
298C22—1461no—
299C22#1455661412yes—
300C22C2×D4×D7311yescharacteristic
301C4—21no—
302C4—41no—
303C4—42no—
304C4—41no—
305C4—2921no—
306C4—1461no—
307C4—1461no—
308C4#1455663712yes—
309C2—22no—
310C2—2921no—
311C2—5842no—
312C2—5841no—
313C2—1462no—
314C2#1798914811yescharacteristic
315C2C2×#1455661411yescharacteristic
316C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3188
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #17989100C2semidirect
2. C2×#14556566C2semidirect
3. #17988914C2semidirect
4. #17988905C2semidirect
5. #17988824C2semidirect
6. #17988819C2semidirect
7. #17988737C2semidirect
8. #17988735C2semidirect
9. #17988723C2semidirect
10. C22⋊C8×D73C2semidirect
11. #484×C73C2semidirect
12. C2×#11924029C22semidirect
16. C2×#11924015C22semidirect
17. C2×D584C22semidirect
18. C2×C8×D73C22semidirect
20. #14556567C22semidirect
25. #14556566C22semidirect
30. #14556549C22semidirect
32. #14556522C22semidirect
33. #14556513C22semidirect
34. #14556511C22semidirect
35. #14556511C22semidirect
37. #14556503C22semidirect
40. #107×C73C22semidirect
41. #103×C73C22semidirect
159. C73#3188semidirect
162. #484D73semidirect
193. #107C2×D73semidirect
195. #103C2×D73semidirect