Finite Group Databasebeta

← #22620747

Subgroups — #22620747

Order 9344.

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

normal subgroups only

This group has 466 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#17989098C211yesmaximal, characteristic, complemented
2C2×#14556565C211yesmaximal, characteristic, complemented
3#17988918C211yesmaximal, characteristic, complemented
4#17988912C212yesmaximal, complemented
5#17988901C211yesmaximal, characteristic, complemented
6#17988840C212yesmaximal, complemented
7#17988833C212yesmaximal, complemented
8#17988740C211yesmaximal, characteristic, complemented
9#17988734C212yesmaximal, complemented
10#17988723C211yesmaximal, characteristic, complemented
11#407×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic, complemented
13C22×D292C2211yescharacteristic
14C22×C22⋊D73—21no—
15C2×#11924017C2212yescomplemented
16C2×D584C2212yescomplemented
17#14556574—21no—
18#14556570C2211yescharacteristic
19#14556570C2211yescharacteristic, complemented
20#14556565—21no—
21#14556565—21no—
22#14556565C2211yescharacteristic
23#14556565C2212yes—
24#14556565C2212yes—
25#14556565C2211yescharacteristic, complemented
26#14556560—21no—
27C4×C22⋊D73—21no—
28C4×C22⋊D73—21no—
29#14556550C2211yescharacteristic, complemented
30C2×C4⋊Dic73C2211yescharacteristic
31C2×#11924005—21no—
32#14556525C2212yescomplemented
33#14556523C2212yescomplemented
34#14556516C2212yescomplemented
35#14556513C2212yescomplemented
36#14556513C2212yescomplemented
37#14556513C2212yescomplemented
38C23×C4×C73C2211yescharacteristic
39C2×M16×C73C2212yescomplemented
40C22⋊C8×C73C2211yescharacteristic
41C22⋊C8×C73C2211yescharacteristic
42C22⋊C8×C73C2212yescomplemented
43C23×D73—21no—
44#11924028—42no—
45C2×Dic146C2311yescharacteristic
46C2×D292—21no—
47C2×D292—42no—
48C2×D292C2312yes—
49C2×D292C2311yescharacteristic
50C2×C22⋊D73—21no—
51C2×C22⋊D73—21no—
52C2×C22⋊D73—21no—
53C2×C22⋊D73—22no—
54C2×C22⋊D73—22no—
55C2×C22⋊D73—44no—
56C22×Dic73—21no—
57C2×C4×D73—21no—
58#11924017—42no—
59D584—42no—
60C4⋊Dic73—21no—
61C4⋊Dic73C2311yescharacteristic
62C4⋊Dic73C2311yescharacteristic
63C4⋊Dic73C2312yes—
64#11924007—21no—
65#11924007—21no—
66C22⋊Dic73—21no—
67C22⋊Dic73—21no—
68C22⋊Dic73—21no—
69#11924005—22no—
70#11924005—22no—
71#11924005—21no—
72#11924005—21no—
73C4×Dic73—21no—
74C24×C73D411yescharacteristic
75C22×C4×C73—42no—
76C22×C4×C73D411yescharacteristic
77C22×C4×C73D411yescharacteristic
78C22×C4×C73D411yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C22×C4×C73C2311yescharacteristic
82M16×C73—42no—
83C2×C8×C73C2312yes—
84C2×C8×C73C2312yes—
85C23×C73—22no—
86C23×C73—41no—
87C23×C73—41no—
88C23×C73C2×D411yescharacteristic
89C23×C73C2×D411yescharacteristic
90C23×C73C2×D411yescharacteristic
91C22×D73—21no—
92C22×D73—22no—
93C22×D73—42no—
94C22×D73—42no—
95C22×D73—42no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73—41no—
102C2×C4×C73C2×D411yescharacteristic
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2×D411yescharacteristic
105C2×C4×C73C2411yescharacteristic
106C22⋊D73—42no—
107C22⋊D73—44no—
108C22⋊D73—44no—
109C22⋊D73—42no—
110C22⋊D73—42no—
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—22no—
114C2×Dic73—21no—
115C2×Dic73—42no—
116D292—22no—
117D292—22no—
118D292—22no—
119D292—42no—
120C4×D73—42no—
121Dic146—22no—
122C8×C73—22no—
123C8×C73—22no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73—21no—
131C22×C73—21no—
132C22×C73—44no—
133C22×C73AGL(1,ℤ/8)12yes—
134C22×C73C22×D411yescharacteristic
135C2×D73—41no—
136C2×D73—42no—
137C2×D73—42no—
138C2×D73—41no—
139C2×D73—41no—
140C2×D73—42no—
141C2×D73—84no—
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73H(5,𝔽2)12yes—
146Dic73—41no—
147Dic73—42no—
148Dic73—41no—
149Dic73—41no—
150C2×C73—22no—
151C2×C73—41no—
152C2×C73—41no—
153C2×C73#53411yescharacteristic
154C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
155C2×C73#57511yescharacteristic
156D73—81no—
157D73—82no—
158#3194—731nomaximal, Sylow
159C73#319411yescharacteristic, complemented, Sylow
160#525—731no—
161C2×#121—731no—
162#483—731no—
163#482—732no—
164#480—731no—
165#469—732no—
166#468—732no—
167#450—731no—
168#449—732no—
169#447—731no—
170#407D7311yescharacteristic, complemented
171C2×#41—731no—
172C22×D4—731no—
173C22×D4—1461no—
174C23×C4C2×D7311yescharacteristic
175C2×SD16—732no—
176C2×D8—732no—
177C2×M16C2×D7312yescomplemented
178#123—1461no—
179C22⋊Q8—731no—
180C22⋊Q8—731no—
181#121—732no—
182#121—732no—
183#121—731no—
184#121—731no—
185#121—1461no—
186#121—1461no—
187#120—1461no—
188C4×D4—1461no—
189C4×D4—1461no—
190#117—731no—
191C2×C4⋊C4—731no—
192C2×C22⋊C4—1461no—
193#107—732no—
194#106—732no—
195#103—732no—
196#102—732no—
197#102—732no—
198#102—732no—
199C22⋊C8C2×D7311yescharacteristic
200C22⋊C8C2×D7311yescharacteristic
201C22⋊C8C2×D7312yescomplemented
202C24—1461no—
203C24D29211yescharacteristic
204#41—2922no—
205C2×Q8—731no—
206C2×D4—2922no—
207C2×D4—2924no—
208C2×D4—731no—
209C2×D4—732no—
210C2×D4—1461no—
211C2×D4—1461no—
212C2×D4—1461no—
213C2×D4—1462no—
214C2×D4—1462no—
215C2×D4—1461no—
216C22×C4—42no—
217C22×C4—1461no—
218C22×C4—1461no—
219C22×C4D29211yescharacteristic
220C22×C4D29211yescharacteristic
221C22×C4D29211yescharacteristic
222C22×C4C22×D7311yescharacteristic
223C22×C4C22×D7311yescharacteristic
224C22×C4C22×D7311yescharacteristic
225SD16—2922no—
226D8—2922no—
227M16—42no—
228C2×C8C22×D7312yes—
229C2×C8C22×D7312yes—
230C4⋊C4—731no—
231C4⋊C4—731no—
232C4⋊C4—732no—
233C4⋊C4—1461no—
234C4⋊C4—1461no—
235C4⋊C4—1461no—
236C22⋊C4—1461no—
237C22⋊C4—1461no—
238C22⋊C4—1461no—
239C22⋊C4—1462no—
240C22⋊C4—1462no—
241C22⋊C4—1461no—
242C22⋊C4—1461no—
243C42—1461no—
244C23—22no—
245C23—41no—
246C23—41no—
247C23—2922no—
248C23—2922no—
249C23—2922no—
250C23—1461no—
251C23—1462no—
252C23C2×D29211yescharacteristic
253C23C2×D29211yescharacteristic
254C23C2×D29211yescharacteristic
255Q8—1462no—
256D4—2922no—
257D4—2924no—
258D4—2924no—
259D4—2922no—
260D4—2922no—
261D4—2922no—
262D4—1462no—
263D4—1462no—
264D4—1462no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—2922no—
272C2×C4—2922no—
273C2×C4—1461no—
274C2×C4—1461no—
275C2×C4—1462no—
276C2×C4—1461no—
277C2×C4C2×D29211yescharacteristic
278C2×C4C2×D29211yescharacteristic
279C2×C4C2×D29211yescharacteristic
280C2×C4C23×D7311yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—2922no—
293C22—2921no—
294C22—2921no—
295C22—2922no—
296C22—2921no—
297C22—2922no—
298C22—5844no—
299C22#1455661912yes—
300C22C22×D29211yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—2922no—
305C4—2921no—
306C4—2921no—
307C4—2921no—
308C4#1455663612yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—5842no—
313C2—5841no—
314C2#1798914911yescharacteristic
315C2C2×#1455661911yescharacteristic
316C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#407×C73C2
socleC22×C73C22×D4
hypercenter#407D73
hypocenterC73#3194
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #17989098C2semidirect
2. C2×#14556565C2semidirect
3. #17988918C2semidirect
4. #17988912C2semidirect
5. #17988901C2semidirect
6. #17988840C2semidirect
7. #17988833C2semidirect
8. #17988740C2semidirect
9. #17988734C2semidirect
10. #17988723C2semidirect
11. #407×C73C2semidirect
12. C2×#11924028C22semidirect
15. C2×#11924017C22semidirect
16. C2×D584C22semidirect
19. #14556570C22semidirect
25. #14556565C22semidirect
29. #14556550C22semidirect
32. #14556525C22semidirect
33. #14556523C22semidirect
34. #14556516C22semidirect
35. #14556513C22semidirect
36. #14556513C22semidirect
37. #14556513C22semidirect
39. C2×M16×C73C22semidirect
42. C22⋊C8×C73C22semidirect
159. C73#3194semidirect
170. #407D73semidirect
177. C2×M16C2×D73semidirect
201. C22⋊C8C2×D73semidirect