Finite Group Databasebeta

← #22621954

Subgroups — #22621954

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#17989277C211yesmaximal, characteristic, complemented
2D4×D292C211yesmaximal, characteristic
3#17988952C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic, complemented
5#17988901C211yesmaximal, characteristic, complemented
6#17988888C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic, complemented
8#17988816C211yesmaximal, characteristic, complemented
9#17988788C211yesmaximal, characteristic, complemented
10#17988740C211yesmaximal, characteristic, complemented
11#17988740C211yesmaximal, characteristic, complemented
12#17988689C211yesmaximal, characteristic, complemented
13#17988593C211yesmaximal, characteristic, complemented
14C2×#14556513C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×D4×D73—21no—
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924017C2211yescharacteristic, complemented
22#14556588C2211yescharacteristic
23#14556584—21no—
24#14556583C2211yescharacteristic, complemented
25#14556581—21no—
26#14556572—21no—
27#14556570C2211yescharacteristic, complemented
28#14556570C2211yescharacteristic, complemented
29#14556566—21no—
30#14556565C2211yescharacteristic
31#14556565C2211yescharacteristic
32#14556561—21no—
33#14556561—21no—
34C4×Dic146C2211yescharacteristic, complemented
35C4×D292C2211yescharacteristic
36#14556550C2211yescharacteristic, complemented
37#14556547—21no—
38C2×C4⋊Dic73C2211yescharacteristic, complemented
39#14556525C2211yescharacteristic, complemented
40#14556525C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic, complemented
47#14556513C2211yescharacteristic, complemented
48#14556513C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic, complemented
50#14556513C2211yescharacteristic, complemented
51#14556513C2211yescharacteristic, complemented
52C2×M16×C73C2211yescharacteristic, complemented
53C22×C8×C73C2211yescharacteristic, complemented
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic, complemented
56C22⋊C8×C73C2211yescharacteristic, complemented
57C22⋊C8×C73C2211yescharacteristic, complemented
58#97×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73—21no—
61C2×Dic146C2311yescharacteristic
62C2×D292—22no—
63C2×D292—22no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—41no—
69C2×D292—41no—
70C2×D292C2311yescharacteristic
71C2×D292C2311yescharacteristic
72C2×D292C2311yescharacteristic
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75D4×D73—44no—
76C22×Dic73—21no—
77C2×C4×D73—21no—
78#11924017—22no—
79#11924017—41no—
80#11924017—41no—
81C4⋊Dic73—21no—
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90#11924007—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93C22⋊Dic73—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C2×D4×C73D411yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102M16×C73—41no—
103C2×C8×C73—41no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C22⋊C4×C73D411yescharacteristic
111C42×C73C2311yescharacteristic
112C23×C73C2×D411yescharacteristic
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—42no—
118C22×D73—42no—
119C22×D73—42no—
120C22×D73—42no—
121C22×D73—81no—
122C22×D73—81no—
123D4×C73—22no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—42no—
134C22⋊D73—42no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—42no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—21no—
145D292—21no—
146D292—42no—
147D292—42no—
148D292—42no—
149D292—81no—
150D292#4112yes—
151C4×D73—42no—
152Dic146—21no—
153Dic146—21no—
154C8×C73—21no—
155C8×C73—21no—
156C8×C73—21no—
157C8×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73AGL(1,ℤ/8)12yes—
164C22×C73C22×D411yescharacteristic
165C2×D73—22no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—84no—
175C2×D73—84no—
176C4×C73—21no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73C2×#4111yescharacteristic
181C4×C73H(5,𝔽2)11yescharacteristic
182Dic73—41no—
183Dic73—41no—
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187C2×C73—22no—
188C2×C73—41no—
189C2×C73#54611yescharacteristic
190C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C73#57711yescharacteristic
192D73—42no—
193D73—81no—
194D73—81no—
195#3310—731nomaximal, Sylow
196C73#331011yescharacteristic, complemented, Sylow
197#552—731no—
198D42—731no—
199#490—731no—
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#435D7311yescharacteristic, complemented
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×M16C2×D7311yescharacteristic, complemented
219C22×C8C2×D7311yescharacteristic, complemented
220#127—731no—
221#126—1461no—
222#125—731no—
223#125—1461no—
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×D4C2×D7311yescharacteristic
235#117—731no—
236#117—1461no—
237C2×C4⋊C4—731no—
238#107—731no—
239#107—731no—
240#106—731no—
241C4⋊C8C2×D7311yescharacteristic, complemented
242#103—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102—731no—
249#102—731no—
250#102—731no—
251#102—731no—
252C22⋊C8C2×D7311yescharacteristic, complemented
253C22⋊C8C2×D7311yescharacteristic, complemented
254#97C2×D7311yescharacteristic, complemented
255C24—1461no—
256C24—1461no—
257C2×Q8—731no—
258C2×D4—2921no—
259C2×D4—2921no—
260C2×D4—2924no—
261C2×D4—731no—
262C2×D4—731no—
263C2×D4—731no—
264C2×D4—1462no—
265C2×D4—1462no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4—1461no—
272C2×D4D29211yescharacteristic
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4C22×D7311yescharacteristic
276C22×C4C22×D7311yescharacteristic
277SD16—2921no—
278SD16—2921no—
279SD16—1462no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D7311yescharacteristic
283C2×C8C22×D7311yescharacteristic
284C2×C8C22×D7311yescharacteristic
285C2×C8C22×D7311yescharacteristic
286C4⋊C4—731no—
287C4⋊C4—731no—
288C4⋊C4—731no—
289C4⋊C4—731no—
290C4⋊C4—1461no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4—1461no—
296C4⋊C4D29211yescharacteristic
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4D29211yescharacteristic
304C22⋊C4D29211yescharacteristic
305C42—1461no—
306C42—1461no—
307C42C22×D7311yescharacteristic
308C23—2922no—
309C23—2922no—
310C23—2922no—
311C23—2922no—
312C23—5841no—
313C23—5841no—
314C23—1461no—
315C23—1461no—
316C23—1461no—
317C23C2×D29211yescharacteristic
318C23C2×D29211yescharacteristic
319Q8—1461no—
320Q8—1461no—
321D4—22no—
322D4—2922no—
323D4—2922no—
324D4—2922no—
325D4—2922no—
326D4—2922no—
327D4—5841no—
328D4—732no—
329D4—1461no—
330D4—1461no—
331D4—1461no—
332D4—1461no—
333D4—1461no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—2922no—
339C2×C4—2922no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4C2×D29211yescharacteristic
346C2×C4C2×D29211yescharacteristic
347C2×C4C2×D29211yescharacteristic
348C2×C4C2×D29211yescharacteristic
349C2×C4C23×D7311yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—2921no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—2921no—
365C22—2921no—
366C22—2921no—
367C22—5844no—
368C22—5844no—
369C22—1462no—
370C22#1455661912yes—
371C22C22×D29211yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—2921no—
377C4—2921no—
378C4—2921no—
379C4—2921no—
380C4—2921no—
381C4#41×D7311yescharacteristic
382C4#1455663611yescharacteristic
383C2—22no—
384C2—41no—
385C2—2922no—
386C2—5841no—
387C2—5841no—
388C2#1798923211yescharacteristic
389C2C2×#1455661911yescharacteristic
390C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3310
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17989277C2semidirect
3. #17988952C2semidirect
4. #17988912C2semidirect
5. #17988901C2semidirect
6. #17988888C2semidirect
7. #17988833C2semidirect
8. #17988816C2semidirect
9. #17988788C2semidirect
10. #17988740C2semidirect
11. #17988740C2semidirect
12. #17988689C2semidirect
13. #17988593C2semidirect
14. C2×#14556513C2semidirect
15. #435×C73C2semidirect
20. C2×#11924017C22semidirect
21. C2×#11924017C22semidirect
24. #14556583C22semidirect
27. #14556570C22semidirect
28. #14556570C22semidirect
34. C4×Dic146C22semidirect
36. #14556550C22semidirect
38. C2×C4⋊Dic73C22semidirect
39. #14556525C22semidirect
40. #14556525C22semidirect
41. #14556523C22semidirect
42. #14556516C22semidirect
46. #14556513C22semidirect
47. #14556513C22semidirect
48. #14556513C22semidirect
49. #14556513C22semidirect
50. #14556513C22semidirect
51. #14556513C22semidirect
52. C2×M16×C73C22semidirect
53. C22×C8×C73C22semidirect
55. C4⋊C8×C73C22semidirect
56. C22⋊C8×C73C22semidirect
57. C22⋊C8×C73C22semidirect
58. #97×C73C22semidirect
196. C73#3310semidirect
209. #435D73semidirect
218. C2×M16C2×D73semidirect
219. C22×C8C2×D73semidirect
241. C4⋊C8C2×D73semidirect
252. C22⋊C8C2×D73semidirect
253. C22⋊C8C2×D73semidirect
254. #97C2×D73semidirect