Finite Group Databasebeta

← #16831515

Subgroups — #16831515

Order 3712.

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#14271853C211yesmaximal, characteristic, complemented
2D4×D116C211yesmaximal, characteristic
3#14271528C211yesmaximal, characteristic, complemented
4#14271488C211yesmaximal, characteristic, complemented
5#14271477C211yesmaximal, characteristic, complemented
6#14271464C211yesmaximal, characteristic, complemented
7#14271409C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271364C211yesmaximal, characteristic, complemented
10#14271316C211yesmaximal, characteristic, complemented
11#14271316C211yesmaximal, characteristic, complemented
12#14271265C211yesmaximal, characteristic, complemented
13#14271169C211yesmaximal, characteristic, complemented
14C2×#11745169C211yesmaximal, characteristic, complemented
15C29×#435C211yesmaximal, characteristic, complemented
16C2×D4×D29—21no—
17C22×D116C2211yescharacteristic
18C22×D116C2211yescharacteristic
19C2×M16×C29C2211yescharacteristic, complemented
20C22×C8×C29C2211yescharacteristic, complemented
21C4×D4×C29C2211yescharacteristic
22#11745297—21no—
23#11745292C2211yescharacteristic
24#11745292C2211yescharacteristic
25#11745288C2211yescharacteristic, complemented
26C2×C4⋊Dic29C2211yescharacteristic, complemented
27#11745286C2211yescharacteristic, complemented
28#11745286C2211yescharacteristic, complemented
29C2×#90773C2211yescharacteristic
30C2×#90773C2211yescharacteristic, complemented
31C2×#90773C2211yescharacteristic, complemented
32#11745257—21no—
33#11745251—21no—
34#11745244—21no—
35#11745244—21no—
36#11745241—21no—
37#11745239—21no—
38#11745236C2211yescharacteristic
39C4×D116C2211yescharacteristic
40#11745232C2211yescharacteristic, complemented
41C4×Dic58C2211yescharacteristic, complemented
42C29×C4⋊C8C2211yescharacteristic, complemented
43C29×C22⋊C8C2211yescharacteristic, complemented
44C29×C22⋊C8C2211yescharacteristic, complemented
45C29×#97C2211yescharacteristic, complemented
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic, complemented
50#11745169C2211yescharacteristic, complemented
51#11745169C2211yescharacteristic, complemented
52#11745169C2211yescharacteristic, complemented
53#11745169C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic, complemented
55#11745166C2211yescharacteristic, complemented
56#11745166C2211yescharacteristic, complemented
57#11745165C2211yescharacteristic, complemented
58#11745164C2211yescharacteristic, complemented
59C23×D29—21no—
60C23×D29—21no—
61C2×D4×C29D411yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C22×Dic29—21no—
67D4×D29—44no—
68C2×D116—22no—
69C2×D116—22no—
70C2×D116—21no—
71C2×D116—21no—
72C2×D116—21no—
73C2×D116—21no—
74C2×D116—41no—
75C2×D116—41no—
76C2×D116C2311yescharacteristic
77C2×D116C2311yescharacteristic
78C2×D116C2311yescharacteristic
79C2×C4×D29—21no—
80C2×Dic58C2311yescharacteristic
81M16×C29—41no—
82C2×C8×C29—41no—
83C2×C8×C29C2311yescharacteristic
84C2×C8×C29C2311yescharacteristic
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C4⋊C4×C29D411yescharacteristic
88C22⋊C4×C29D411yescharacteristic
89C22⋊C4×C29D411yescharacteristic
90C42×C29C2311yescharacteristic
91C22⋊Dic29—21no—
92C22⋊Dic29—21no—
93C22⋊Dic29—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779—21no—
105#90779—21no—
106#90779—21no—
107C4×Dic29—21no—
108C4×Dic29—21no—
109#90773—22no—
110#90773—41no—
111#90773—41no—
112C23×C29C2×D411yescharacteristic
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—21no—
117C22×D29—42no—
118C22×D29—42no—
119C22×D29—42no—
120C22×D29—42no—
121C22×D29—81no—
122C22×D29—81no—
123D4×C29—22no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2411yescharacteristic
133C22⋊D29—42no—
134C22⋊D29—42no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—21no—
139C2×Dic29—21no—
140C2×Dic29—42no—
141D116—21no—
142D116—21no—
143D116—21no—
144D116—21no—
145D116—21no—
146D116—42no—
147D116—42no—
148D116—42no—
149D116—81no—
150D116#4112yes—
151C4×D29—42no—
152Dic58—21no—
153Dic58—21no—
154C8×C29—21no—
155C8×C29—21no—
156C8×C29—21no—
157C8×C29—21no—
158#3310—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—21no—
164C22×C29AGL(1,ℤ/8)12yes—
165C22×C29C22×D411yescharacteristic
166C2×D29—22no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—84no—
176C2×D29—84no—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—21no—
181C4×C29C2×#4111yescharacteristic
182C4×C29H(5,𝔽2)11yescharacteristic
183Dic29—41no—
184Dic29—41no—
185Dic29—41no—
186Dic29—41no—
187Dic29—41no—
188#552—291no—
189D42—291no—
190#490—291no—
191#482—291no—
192#480—291no—
193#478—291no—
194#468—291no—
195#465—291no—
196#460—291no—
197#450—291no—
198#450—291no—
199#440—291no—
200#435D2911yescharacteristic, complemented
201#418—291no—
202C2×#102—291no—
203C2×C29—22no—
204C2×C29—41no—
205C2×C29#54611yescharacteristic
206C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C29#57711yescharacteristic
208D29—42no—
209D29—81no—
210D29—81no—
211C22×D4—291no—
212C22×D4—291no—
213C22×D4—581no—
214C2×SD16—291no—
215C2×SD16—291no—
216C2×SD16—291no—
217C2×M16C2×D2911yescharacteristic, complemented
218C22×C8C2×D2911yescharacteristic, complemented
219#127—291no—
220#126—581no—
221#125—291no—
222#125—581no—
223#123—581no—
224C22⋊Q8—291no—
225C22⋊Q8—291no—
226#121—291no—
227#121—291no—
228#121—581no—
229#120—581no—
230#120—581no—
231C4×Q8—291no—
232C4×D4—291no—
233C4×D4C2×D2911yescharacteristic
234#117—291no—
235#117—581no—
236C2×C4⋊C4—291no—
237#107—291no—
238#107—291no—
239#106—291no—
240C4⋊C8C2×D2911yescharacteristic, complemented
241#103—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250#102—291no—
251C22⋊C8C2×D2911yescharacteristic, complemented
252C22⋊C8C2×D2911yescharacteristic, complemented
253#97C2×D2911yescharacteristic, complemented
254C29#331011yescharacteristic, complemented, Sylow
255C24—581no—
256C24—581no—
257C2×Q8—291no—
258C2×D4—291no—
259C2×D4—291no—
260C2×D4—291no—
261C2×D4—582no—
262C2×D4—582no—
263C2×D4—581no—
264C2×D4—581no—
265C2×D4—581no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4—1161no—
270C2×D4—1161no—
271C2×D4—1164no—
272C2×D4D11611yescharacteristic
273C22×C4—581no—
274C22×C4—581no—
275C22×C4C22×D2911yescharacteristic
276C22×C4C22×D2911yescharacteristic
277SD16—582no—
278SD16—1161no—
279SD16—1161no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D2911yescharacteristic
283C2×C8C22×D2911yescharacteristic
284C2×C8C22×D2911yescharacteristic
285C2×C8C22×D2911yescharacteristic
286C4⋊C4—291no—
287C4⋊C4—291no—
288C4⋊C4—291no—
289C4⋊C4—291no—
290C4⋊C4—581no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4—581no—
295C4⋊C4—581no—
296C4⋊C4D11611yescharacteristic
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4D11611yescharacteristic
304C22⋊C4D11611yescharacteristic
305C42—581no—
306C42—581no—
307C42C22×D2911yescharacteristic
308C23—581no—
309C23—581no—
310C23—581no—
311C23—1162no—
312C23—1162no—
313C23—1162no—
314C23—1162no—
315C23—2321no—
316C23—2321no—
317C23C2×D11611yescharacteristic
318C23C2×D11611yescharacteristic
319Q8—581no—
320Q8—581no—
321D4—22no—
322D4—292no—
323D4—581no—
324D4—581no—
325D4—581no—
326D4—581no—
327D4—581no—
328D4—1162no—
329D4—1162no—
330D4—1162no—
331D4—1162no—
332D4—1162no—
333D4—2321no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—581no—
339C2×C4—581no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—1162no—
344C2×C4—1162no—
345C2×C4C2×D11611yescharacteristic
346C2×C4C2×D11611yescharacteristic
347C2×C4C2×D11611yescharacteristic
348C2×C4C2×D11611yescharacteristic
349C2×C4C23×D2911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—582no—
360C22—1161no—
361C22—1161no—
362C22—1161no—
363C22—1161no—
364C22—1161no—
365C22—1161no—
366C22—1161no—
367C22—1161no—
368C22—2324no—
369C22—2324no—
370C22#1174527012yes—
371C22C22×D11611yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—1161no—
377C4—1161no—
378C4—1161no—
379C4—1161no—
380C4—1161no—
381C4#1174535911yescharacteristic
382C4#41×D2911yescharacteristic
383C2—22no—
384C2—41no—
385C2—1162no—
386C2—2321no—
387C2—2321no—
388C2#1427180811yescharacteristic
389C2C2×#1174527011yescharacteristic
390C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#435C2
socleC22×C29C22×D4
prime radicalD4×D116C2
hypercenter#435D29
hypocenterC29#3310
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14271853C2semidirect
3. #14271528C2semidirect
4. #14271488C2semidirect
5. #14271477C2semidirect
6. #14271464C2semidirect
7. #14271409C2semidirect
8. #14271392C2semidirect
9. #14271364C2semidirect
10. #14271316C2semidirect
11. #14271316C2semidirect
12. #14271265C2semidirect
13. #14271169C2semidirect
14. C2×#11745169C2semidirect
15. C29×#435C2semidirect
19. C2×M16×C29C22semidirect
20. C22×C8×C29C22semidirect
25. #11745288C22semidirect
26. C2×C4⋊Dic29C22semidirect
27. #11745286C22semidirect
28. #11745286C22semidirect
30. C2×#90773C22semidirect
31. C2×#90773C22semidirect
40. #11745232C22semidirect
41. C4×Dic58C22semidirect
42. C29×C4⋊C8C22semidirect
43. C29×C22⋊C8C22semidirect
44. C29×C22⋊C8C22semidirect
45. C29×#97C22semidirect
49. #11745169C22semidirect
50. #11745169C22semidirect
51. #11745169C22semidirect
52. #11745169C22semidirect
53. #11745169C22semidirect
54. #11745169C22semidirect
55. #11745166C22semidirect
56. #11745166C22semidirect
57. #11745165C22semidirect
58. #11745164C22semidirect
200. #435D29semidirect
217. C2×M16C2×D29semidirect
218. C22×C8C2×D29semidirect
240. C4⋊C8C2×D29semidirect
251. C22⋊C8C2×D29semidirect
252. C22⋊C8C2×D29semidirect
253. #97C2×D29semidirect
254. C29#3310semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#142718532
D4×D1162
#142715282
#142714882
#142714772
#142714642
#142714092
#142713922
#142713642
#142713162
#142712652
#142711692
C2×#117451692
C29×#4352
#331029