Finite Group Databasebeta

← #22621951

Subgroups — #22621951

Order 9344.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989275C211yesmaximal, characteristic, complemented
2#17989222C211yesmaximal, characteristic
3#17988909C211yesmaximal, characteristic, complemented
4#17988899C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988832C211yesmaximal, characteristic, complemented
7#17988815C211yesmaximal, characteristic, complemented
8#17988784C211yesmaximal, characteristic, complemented
9#17988739C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988689C211yesmaximal, characteristic, complemented
12#17988660C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#102×D73C211yesmaximal, characteristic, complemented
15#490×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73—21no—
17C2×D4×D73C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924016C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×#11924011C2211yescharacteristic, complemented
23C2×C8×D73C2211yescharacteristic, complemented
24#14556586—21no—
25#14556582—21no—
26#14556576—21no—
27#14556571C2211yescharacteristic, complemented
28#14556571C2211yescharacteristic, complemented
29#14556562—21no—
30#14556562C2211yescharacteristic
31#14556562C2211yescharacteristic
32#14556559—21no—
33#14556559—21no—
34C4×Dic146C2211yescharacteristic, complemented
35C4×D292C2211yescharacteristic
36C4×D292C2211yescharacteristic
37#14556549—21no—
38#14556549C2211yescharacteristic, complemented
39C4⋊C4×D73C2211yescharacteristic, complemented
40#14556525C2211yescharacteristic, complemented
41#14556524C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43C4⋊#10596831C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52#127×C73C2211yescharacteristic
53#125×C73C2211yescharacteristic, complemented
54#102×C73C2211yescharacteristic, complemented
55#102×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58#97×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73—21no—
61C2×Dic146C2311yescharacteristic
62C2×D292D411yescharacteristic
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68D4×D73—22no—
69D4×D73—22no—
70D4×D73—41no—
71D4×D73—41no—
72D4×D73—44no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76C2×C4×D73C2311yescharacteristic
77#11924017—22no—
78#11924016—41no—
79#11924016—41no—
80#11924011—41no—
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C8×D73—41no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73D411yescharacteristic
87C4⋊Dic73C2311yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89#11924007—21no—
90#11924007—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005D411yescharacteristic
98#11924005D411yescharacteristic
99C4×Dic73—21no—
100C4×Dic73—21no—
101C2×D4×C73—21no—
102C2×D4×C73—21no—
103C2×D4×C73C2311yescharacteristic
104C2×D4×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C42×C73C2311yescharacteristic
112C23×C73—21no—
113C23×C73—21no—
114C22×D73—21no—
115C22×D73—42no—
116C22×D73—42no—
117C22×D73—42no—
118C22×D73—42no—
119C22×D73—81no—
120C22×D73—81no—
121C22×D73C2×D411yescharacteristic
122C22×D73C2×D411yescharacteristic
123D4×C73—21no—
124D4×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—42no—
128D4×C73—81no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2411yescharacteristic
134C22⋊D73—42no—
135C22⋊D73—42no—
136C22⋊D73—42no—
137C22⋊D73—42no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143D292—22no—
144D292—21no—
145D292#4112yes—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—42no—
151C4×D73—42no—
152Dic146—21no—
153Dic146—21no—
154C8×C73—21no—
155C8×C73—21no—
156#10596831—21no—
157#10596831—21no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73C22×D411yescharacteristic
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—21no—
168C2×D73—22no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—84no—
174C2×D73—84no—
175C2×D73AGL(1,ℤ/8)12yes—
176C4×C73—21no—
177C4×C73—21no—
178C4×C73—41no—
179C4×C73—41no—
180C4×C73C2×#4111yescharacteristic
181C4×C73H(5,𝔽2)11yescharacteristic
182Dic73—21no—
183Dic73—21no—
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187C2×C73—81no—
188C2×C73—81no—
189C2×C73#54611yescharacteristic
190C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C73#57711yescharacteristic
192D73—22no—
193D73—41no—
194D73—42no—
195#3310—731nomaximal, Sylow
196C73#331011yescharacteristic, complemented, Sylow
197#552—731no—
198D42—731no—
199#490D7311yescharacteristic, complemented
200#482—731no—
201#480—731no—
202#478—731no—
203#468—731no—
204#465—731no—
205#460—731no—
206#450—731no—
207#450—731no—
208#440—731no—
209#435—731no—
210#418—731no—
211C2×#102—731no—
212C22×D4—731no—
213C22×D4—731no—
214C22×D4—1461no—
215C2×SD16—731no—
216C2×SD16—731no—
217C2×SD16—731no—
218C2×M16—731no—
219C22×C8—731no—
220#127C2×D7311yescharacteristic
221#126—1461no—
222#125—1461no—
223#125C2×D7311yescharacteristic, complemented
224#123—1461no—
225C22⋊Q8—731no—
226C22⋊Q8—731no—
227#121—731no—
228#121—731no—
229#121—1461no—
230#120—1461no—
231#120—1461no—
232C4×Q8—731no—
233C4×D4—731no—
234C4×D4—731no—
235#117—731no—
236#117—1461no—
237C2×C4⋊C4—731no—
238#107—731no—
239#107—731no—
240#106—731no—
241C4⋊C8—731no—
242#103—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102C2×D7311yescharacteristic, complemented
249#102C2×D7311yescharacteristic, complemented
250#102C2×D7311yescharacteristic, complemented
251#102C2×D7311yescharacteristic, complemented
252C22⋊C8—731no—
253C22⋊C8—731no—
254#97C2×D7311yescharacteristic, complemented
255C24—1461no—
256C24—1461no—
257C2×Q8—731no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—2924no—
261C2×D4—2921no—
262C2×D4—2921no—
263C2×D4—731no—
264C2×D4—731no—
265C2×D4—1461no—
266C2×D4—1461no—
267C2×D4—1462no—
268C2×D4—1462no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4C22×D7311yescharacteristic
272C2×D4C22×D7311yescharacteristic
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—1461no—
276C22×C4—1461no—
277SD16—2921no—
278SD16—2921no—
279SD16—1462no—
280M16—2921no—
281C2×C8—2921no—
282C2×C8—731no—
283C2×C8—731no—
284C2×C8C22×D7311yescharacteristic
285C2×C8C22×D7311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—731no—
289C4⋊C4—731no—
290C4⋊C4—731no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4C22×D7311yescharacteristic
296C4⋊C4C22×D7311yescharacteristic
297C22⋊C4—731no—
298C22⋊C4—731no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4—1461no—
305C42—1461no—
306C42—1461no—
307C42C22×D7311yescharacteristic
308C23—21no—
309C23—21no—
310C23—2922no—
311C23—2922no—
312C23—2922no—
313C23—2922no—
314C23—5841no—
315C23—5841no—
316C23—731no—
317C23—731no—
318C23—1461no—
319Q8—1461no—
320Q8—1461no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—2922no—
328D4—2922no—
329D4—2922no—
330D4—2922no—
331D4—732no—
332D4—1462no—
333D4—1461no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—731no—
339C2×C4—731no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4D4×D7311yescharacteristic
348C2×C4D4×D7311yescharacteristic
349C2×C4C23×D7311yescharacteristic
350C8—21no—
351C8—21no—
352C8—1461no—
353C8—1461no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—2921no—
361C22—2921no—
362C22—5844no—
363C22—5844no—
364C22—732no—
365C22—1461no—
366C22—1461no—
367C22—1462no—
368C22—1461no—
369C22—1461no—
370C22—1461no—
371C22C2×D4×D7311yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—2921no—
377C4—2921no—
378C4—2921no—
379C4—1461no—
380C4—1461no—
381C4#41×D7311yescharacteristic
382C4#1455663711yescharacteristic
383C2—81no—
384C2—81no—
385C2—2922no—
386C2—2921no—
387C2—1462no—
388C2#1798923011yescharacteristic
389C2AGL(1,ℤ/8)×D7311yescharacteristic
390C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#490×C73C2
socleC22×C73C22×D4
hypercenter#490D73
hypocenterC73#3310
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #17989275C2semidirect
3. #17988909C2semidirect
4. #17988899C2semidirect
5. #17988884C2semidirect
6. #17988832C2semidirect
7. #17988815C2semidirect
8. #17988784C2semidirect
9. #17988739C2semidirect
10. #17988739C2semidirect
11. #17988689C2semidirect
12. #17988660C2semidirect
13. #17988590C2semidirect
14. #102×D73C2semidirect
15. #490×C73C2semidirect
20. C2×#11924016C22semidirect
21. C2×#11924016C22semidirect
22. C2×#11924011C22semidirect
23. C2×C8×D73C22semidirect
27. #14556571C22semidirect
28. #14556571C22semidirect
34. C4×Dic146C22semidirect
38. #14556549C22semidirect
39. C4⋊C4×D73C22semidirect
40. #14556525C22semidirect
41. #14556524C22semidirect
42. #14556522C22semidirect
43. C4⋊#10596831C22semidirect
44. #14556516C22semidirect
46. #14556512C22semidirect
47. #14556512C22semidirect
50. #14556503C22semidirect
51. #14556503C22semidirect
53. #125×C73C22semidirect
54. #102×C73C22semidirect
55. #102×C73C22semidirect
56. #102×C73C22semidirect
57. #102×C73C22semidirect
58. #97×C73C22semidirect
196. C73#3310semidirect
199. #490D73semidirect
223. #125C2×D73semidirect
248. #102C2×D73semidirect
249. #102C2×D73semidirect
250. #102C2×D73semidirect
251. #102C2×D73semidirect
254. #97C2×D73semidirect