Finite Group Databasebeta

← #22621970

Subgroups — #22621970

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989305C211yesmaximal, characteristic, complemented
2#17989228C211yesmaximal, characteristic
3#17988948C211yesmaximal, characteristic, complemented
4#17988914C211yesmaximal, characteristic, complemented
5#17988876C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988817C211yesmaximal, characteristic, complemented
8#17988812C211yesmaximal, characteristic, complemented
9#17988752C211yesmaximal, characteristic, complemented
10#17988740C211yesmaximal, characteristic, complemented
11#17988686C211yesmaximal, characteristic, complemented
12#17988661C211yesmaximal, characteristic, complemented
13#17988591C211yesmaximal, characteristic, complemented
14#17988582C211yesmaximal, characteristic, complemented
15#485×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic, complemented
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21C2×#11924012C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic, complemented
23#14556590C2211yescharacteristic, complemented
24#14556585—21no—
25#14556584—21no—
26#14556580C2211yescharacteristic
27#14556577—21no—
28#14556576—21no—
29#14556571C2211yescharacteristic, complemented
30#14556570C2211yescharacteristic
31#14556566—21no—
32#14556566C2211yescharacteristic
33#14556561—21no—
34C4×Dic146—21no—
35#14556556C2211yescharacteristic, complemented
36#14556553C2211yescharacteristic
37C4×C22⋊D73C2211yescharacteristic
38#14556549C2211yescharacteristic, complemented
39C22⋊C4×D73—21no—
40#14556522C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556514C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C22⋊Q8×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#103×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic
59C23×D73—21no—
60#11924029—22no—
61#11924029—41no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×D292—22no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—41no—
69C2×D292C2311yescharacteristic
70C2×D292C2311yescharacteristic
71C2×C22⋊D73D411yescharacteristic
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73C2311yescharacteristic
75#11924018—41no—
76#11924017—22no—
77#11924017—41no—
78#11924012—41no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C8×D73—41no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007D411yescharacteristic
88C22⋊Dic73—21no—
89C22⋊Dic73D411yescharacteristic
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005D411yescharacteristic
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73C2311yescharacteristic
100C2×Q8×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C42×C73—21no—
111C23×C73C2×D411yescharacteristic
112C22×D73—21no—
113C22×D73—21no—
114C22×D73—42no—
115C22×D73—42no—
116C22×D73—81no—
117C22×D73C2×D411yescharacteristic
118Q8×C73—21no—
119Q8×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—41no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134D292—21no—
135D292—21no—
136D292—21no—
137D292—42no—
138D292—42no—
139D292—81no—
140D292#4112yes—
141C4×D73—21no—
142C4×D73—21no—
143C4×D73—42no—
144C4×D73—81no—
145Dic146—21no—
146Dic146—21no—
147Dic146—42no—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73C22×D411yescharacteristic
156C2×D73—21no—
157C2×D73—22no—
158C2×D73—21no—
159C2×D73—21no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—84no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73C2×#4111yescharacteristic
172C4×C73H(5,𝔽2)11yescharacteristic
173Dic73—21no—
174Dic73—21no—
175Dic73—21no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73#54611yescharacteristic
180C2×C73#57511yescharacteristic
181C2×C73#57711yescharacteristic
182D73—41no—
183D73—42no—
184D73—81no—
185#3311—731nomaximal, Sylow
186C73#331111yescharacteristic, complemented, Sylow
187#556—731no—
188#546—731no—
189#489—731no—
190#485D7311yescharacteristic, complemented
191#482—731no—
192#476—731no—
193#470—731no—
194#465—731no—
195#464—731no—
196#452—731no—
197#450—731no—
198#440—731no—
199#435—731no—
200#418—731no—
201#416—731no—
202C2×#41—731no—
203C22×D4—731no—
204C2×Q16—731no—
205C2×SD16—731no—
206C2×SD16—731no—
207C2×M16—731no—
208C22×C8—731no—
209C4⋊Q8—731no—
210#126—1461no—
211#126—1461no—
212#124—731no—
213#124—1461no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8C2×D7311yescharacteristic
218#121—731no—
219#121—1461no—
220#120—1461no—
221C4×Q8—731no—
222C4×Q8—1461no—
223C4×D4—731no—
224C4×D4—731no—
225#117—731no—
226#117C2×D7311yescharacteristic
227C2×C22⋊C4—1461no—
228#107C2×D7311yescharacteristic, complemented
229#106—731no—
230#106C2×D7311yescharacteristic, complemented
231C4⋊C8—731no—
232#103—731no—
233#103—731no—
234#103C2×D7311yescharacteristic, complemented
235#103C2×D7311yescharacteristic, complemented
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242C22⋊C8—731no—
243C22⋊C8C2×D7311yescharacteristic
244#97—731no—
245C24—1461no—
246#41—2921no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8—1461no—
250C2×Q8C22×D7311yescharacteristic
251C2×D4—2921no—
252C2×D4—731no—
253C2×D4—731no—
254C2×D4—731no—
255C2×D4—1461no—
256C2×D4—1462no—
257C2×D4—1461no—
258C2×D4—1461no—
259C22×C4—731no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4C22×D7311yescharacteristic
263Q16—2921no—
264SD16—2921no—
265SD16—1462no—
266M16—2921no—
267C2×C8—2921no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4C22×D7311yescharacteristic
280C4⋊C4C22×D7311yescharacteristic
281C4⋊C4C22×D7311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—731no—
285C22⋊C4—731no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C42—21no—
294C42—731no—
295C42—1461no—
296C42—1461no—
297C23—2922no—
298C23—2922no—
299C23—5841no—
300C23—731no—
301C23—1461no—
302C23—1461no—
303C23D4×D7311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2922no—
307Q8—1461no—
308Q8—1461no—
309D4—2922no—
310D4—2922no—
311D4—2921no—
312D4—5841no—
313D4—732no—
314D4—1461no—
315D4—1461no—
316D4—1461no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—2922no—
324C2×C4—5841no—
325C2×C4—731no—
326C2×C4—731no—
327C2×C4—731no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—2921no—
342C22—2921no—
343C22—2921no—
344C22—2921no—
345C22—2921no—
346C22—5844no—
347C22—1461no—
348C22—1461no—
349C22—1462no—
350C22—1461no—
351C22C2×D4×D7311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—2921no—
358C4—2921no—
359C4—1461no—
360C4—1461no—
361C4—1461no—
362C4#41×D7311yescharacteristic
363C4#1455663711yescharacteristic
364C2—41no—
365C2—2922no—
366C2—2921no—
367C2—5841no—
368C2#1798922911yescharacteristic
369C2#1798938611yescharacteristic
370C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#485×C73C2
socleC22×C73C22×D4
hypercenter#485D73
hypocenterC73#3311
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #17989305C2semidirect
3. #17988948C2semidirect
4. #17988914C2semidirect
5. #17988876C2semidirect
6. #17988843C2semidirect
7. #17988817C2semidirect
8. #17988812C2semidirect
9. #17988752C2semidirect
10. #17988740C2semidirect
11. #17988686C2semidirect
12. #17988661C2semidirect
13. #17988591C2semidirect
14. #17988582C2semidirect
15. #485×C73C2semidirect
18. C2×#11924018C22semidirect
22. C2×C8×D73C22semidirect
23. #14556590C22semidirect
29. #14556571C22semidirect
35. #14556556C22semidirect
38. #14556549C22semidirect
40. #14556522C22semidirect
41. #14556520C22semidirect
42. #14556515C22semidirect
43. #14556514C22semidirect
50. #14556503C22semidirect
51. #14556501C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. #103×C73C22semidirect
57. #103×C73C22semidirect
186. C73#3311semidirect
190. #485D73semidirect
228. #107C2×D73semidirect
230. #106C2×D73semidirect
234. #103C2×D73semidirect
235. #103C2×D73semidirect