Finite Group Databasebeta

← #22619873

Subgroups — #22619873

Order 9344.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14556566C211yesmaximal, characteristic
2#117×D73C211yesmaximal, characteristic, complemented
3#17988914C212yesmaximal, complemented
4#17988913C212yesmaximal, complemented
5#17988907C212yesmaximal, complemented
6#17988902C212yesmaximal, complemented
7#17988627C211yesmaximal, characteristic, complemented
8#17988593C211yesmaximal, characteristic, complemented
9#17988591C211yesmaximal, characteristic, complemented
10#17988550C211yesmaximal, characteristic, complemented
11#428×C73C211yesmaximal, characteristic, complemented
12C22×D292—21no—
13C22×D292C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C2×#11924012C2211yescharacteristic
16#14556566—21no—
17#14556566—21no—
18#14556566C2212yes—
19#14556566C2212yes—
20#14556550C2211yescharacteristic
21#14556549C2211yescharacteristic, complemented
22#14556549C2211yescharacteristic, complemented
23#14556548—21no—
24#14556547—21no—
25C4⋊C4×D73C2211yescharacteristic, complemented
26C4⋊C4×D73C2211yescharacteristic, complemented
27C2×#11924005—21no—
28C22⋊C4×D73—21no—
29C42×D73—21no—
30#14556524C2212yescomplemented
31#14556522C2212yescomplemented
32#14556513C2212yescomplemented
33#14556513C2212yescomplemented
34#14556511C2212yescomplemented
35#14556511C2212yescomplemented
36#14556503C2212yescomplemented
37#14556503C2212yescomplemented
38C2×M16×C73C2211yescharacteristic
39#117×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#107×C73C2212yescomplemented
42#106×C73C2212yescomplemented
43C23×D73—21no—
44C23×D73D411yescharacteristic
45C2×D292—22no—
46C2×D292—22no—
47C2×D292—22no—
48C2×D292—22no—
49C2×D292—21no—
50C2×D292—44no—
51C2×D292C2312yes—
52C22×Dic73D411yescharacteristic
53C2×C4×D73—22no—
54C2×C4×D73—22no—
55C2×C4×D73—21no—
56C2×C4×D73—21no—
57C2×C4×D73D411yescharacteristic
58C2×C4×D73D411yescharacteristic
59C2×C4×D73C2311yescharacteristic
60C2×C4×D73C2311yescharacteristic
61#11924012—22no—
62C2×#10596831C2312yes—
63C4⋊Dic73C2311yescharacteristic
64C4⋊Dic73C2311yescharacteristic
65#11924007—21no—
66#11924007—21no—
67C22⋊Dic73—21no—
68#11924005—21no—
69#11924005—21no—
70#11924005—22no—
71#11924005—22no—
72C4×Dic73—21no—
73C4×Dic73—21no—
74C4×Dic73—21no—
75C22×C4×C73—21no—
76C22×C4×C73C2311yescharacteristic
77M16×C73—22no—
78C2×C8×C73C2312yes—
79C4⋊C4×C73—21no—
80C4⋊C4×C73C2311yescharacteristic
81C4⋊C4×C73C2312yes—
82C4⋊C4×C73C2311yescharacteristic
83C22⋊C4×C73—21no—
84C42×C73—21no—
85C23×C73C2×D411yescharacteristic
86C22×D73—22no—
87C22×D73—22no—
88C22×D73—22no—
89C22×D73—41no—
90C22×D73—42no—
91C22×D73—42no—
92C22×D73—42no—
93C22×D73C2×D411yescharacteristic
94C22×D73C2×D411yescharacteristic
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—42no—
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73#4112yes—
101C2×C4×C73#4112yes—
102C2×C4×C73C2411yescharacteristic
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73C2×D411yescharacteristic
107C2×Dic73C2×D411yescharacteristic
108D292—22no—
109D292—22no—
110D292—44no—
111D292—44no—
112D292—42no—
113C4×D73—22no—
114C4×D73—22no—
115C4×D73—21no—
116C4×D73—21no—
117C4×D73—21no—
118C4×D73—21no—
119C4×D73—42no—
120C4×D73—42no—
121C8×C73—22no—
122#10596831—22no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73#12312yes—
126C22×C73C22×D411yescharacteristic
127C2×D73—21no—
128C2×D73—21no—
129C2×D73—21no—
130C2×D73—21no—
131C2×D73—21no—
132C2×D73—44no—
133C2×D73—42no—
134C2×D73—42no—
135C2×D73—42no—
136C2×D73—84no—
137C2×D73AGL(1,ℤ/8)12yes—
138C4×C73—41no—
139C4×C73—42no—
140C4×C73—41no—
141C4×C73#12312yes—
142C4×C73C2×#4111yescharacteristic
143C4×C73C2×#4111yescharacteristic
144Dic73—21no—
145Dic73—21no—
146Dic73—41no—
147Dic73—41no—
148C2×C73—22no—
149C2×C73C2×#12311yescharacteristic
150C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
151C2×C73#57511yescharacteristic
152D73—22no—
153D73—41no—
154D73—82no—
155#3094—731nomaximal, Sylow
156C73#309411yescharacteristic, complemented, Sylow
157C2×#121—731no—
158C2×#117—731no—
159#482—732no—
160#482—732no—
161#481—732no—
162#480—732no—
163#428—731no—
164#428D7311yescharacteristic, complemented
165#418—731no—
166#418—731no—
167#407—731no—
168C22×D4—731no—
169C22×D4—1461no—
170C23×C4—731no—
171C2×M16—731no—
172C2×M16C2×D7311yescharacteristic
173#121—732no—
174#121—732no—
175#121—1461no—
176#121—1461no—
177#117—731no—
178#117—731no—
179#117—731no—
180#117—1461no—
181#117—1461no—
182#117C2×D7311yescharacteristic
183C2×C4⋊C4—731no—
184C2×C4⋊C4—731no—
185C2×C4⋊C4C2×D7311yescharacteristic
186C2×C22⋊C4—1461no—
187C2×C22⋊C4—1461no—
188C2×C42—1461no—
189#107—732no—
190#107C2×D7312yescomplemented
191#106—732no—
192#106C2×D7312yescomplemented
193#102—732no—
194#102—732no—
195#102—732no—
196#102—732no—
197C22⋊C8—732no—
198C22⋊C8—732no—
199C24—731no—
200C24—1461no—
201C2×D4—2924no—
202C2×D4—732no—
203C2×D4—1462no—
204C2×D4—1462no—
205C2×D4—1461no—
206C2×D4—1462no—
207C2×D4—1462no—
208C22×C4—21no—
209C22×C4—731no—
210C22×C4—731no—
211C22×C4—731no—
212C22×C4—731no—
213C22×C4—731no—
214C22×C4—1461no—
215C22×C4—1461no—
216C22×C4—1462no—
217C22×C4—1462no—
218C22×C4C22×D7311yescharacteristic
219M16—22no—
220M16—1462no—
221C2×C8—732no—
222C2×C8C22×D7312yes—
223C4⋊C4—21no—
224C4⋊C4—731no—
225C4⋊C4—731no—
226C4⋊C4—1461no—
227C4⋊C4—1461no—
228C4⋊C4C22×D7311yescharacteristic
229C4⋊C4C22×D7311yescharacteristic
230C4⋊C4C22×D7312yes—
231C22⋊C4—21no—
232C22⋊C4—1462no—
233C22⋊C4—1462no—
234C22⋊C4—1461no—
235C22⋊C4—1461no—
236C22⋊C4—1461no—
237C42—21no—
238C42—1461no—
239C42—1461no—
240C42—1461no—
241C23—2921no—
242C23—2922no—
243C23—2922no—
244C23—2922no—
245C23—731no—
246C23—731no—
247C23—1462no—
248C23—1462no—
249C23—1462no—
250C23D4×D7311yescharacteristic
251D4—2924no—
252D4—2924no—
253D4—2922no—
254D4—1462no—
255D4—1462no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—2922no—
261C2×C4—2922no—
262C2×C4—731no—
263C2×C4—731no—
264C2×C4—1461no—
265C2×C4—1461no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4—1461no—
270C2×C4—1461no—
271C2×C4—1461no—
272C2×C4—1461no—
273C2×C4D4×D7311yescharacteristic
274C2×C4#1192402812yes—
275C2×C4#1192402912yes—
276C2×C4C23×D7311yescharacteristic
277C8—22no—
278C8—1462no—
279C22—21no—
280C22—21no—
281C22—2924no—
282C22—2922no—
283C22—2922no—
284C22—2922no—
285C22—5844no—
286C22—732no—
287C22—1461no—
288C22—1461no—
289C22—1461no—
290C22—1461no—
291C22—1461no—
292C22#1455657612yes—
293C22C2×D4×D7311yescharacteristic
294C4—41no—
295C4—42no—
296C4—41no—
297C4—2921no—
298C4—2921no—
299C4—1461no—
300C4—1461no—
301C4#1455657612yes—
302C4C2×#1192402811yescharacteristic
303C4C2×#1192402911yescharacteristic
304C2—22no—
305C2—2921no—
306C2—5842no—
307C2—1462no—
308C2C2×#1455657611yescharacteristic
309C2AGL(1,ℤ/8)×D7311yescharacteristic
310C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3094
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #117×D73C2semidirect
3. #17988914C2semidirect
4. #17988913C2semidirect
5. #17988907C2semidirect
6. #17988902C2semidirect
7. #17988627C2semidirect
8. #17988593C2semidirect
9. #17988591C2semidirect
10. #17988550C2semidirect
11. #428×C73C2semidirect
21. #14556549C22semidirect
22. #14556549C22semidirect
25. C4⋊C4×D73C22semidirect
26. C4⋊C4×D73C22semidirect
30. #14556524C22semidirect
31. #14556522C22semidirect
32. #14556513C22semidirect
33. #14556513C22semidirect
34. #14556511C22semidirect
35. #14556511C22semidirect
36. #14556503C22semidirect
37. #14556503C22semidirect
41. #107×C73C22semidirect
42. #106×C73C22semidirect
156. C73#3094semidirect
164. #428D73semidirect
190. #107C2×D73semidirect
192. #106C2×D73semidirect