Finite Group Databasebeta

← #16829634

Subgroups — #16829634

Order 3712.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271700C211yesmaximal, characteristic, complemented
2C4×D4×D29C211yesmaximal, characteristic, complemented
3#14271492C211yesmaximal, characteristic, complemented
4#14271478C211yesmaximal, characteristic, complemented
5#14271466C211yesmaximal, characteristic, complemented
6#14271465C211yesmaximal, characteristic, complemented
7#14271381C211yesmaximal, characteristic, complemented
8#14271380C211yesmaximal, characteristic, complemented
9#14271312C211yesmaximal, characteristic, complemented
10#14271298C211yesmaximal, characteristic
11#14271276C211yesmaximal, characteristic, complemented
12#14271273C211yesmaximal, characteristic, complemented
13#14271261C211yesmaximal, characteristic, complemented
14#14271218C211yesmaximal, characteristic, complemented
15C29×#440C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C22×C4×D29—21no—
18C2×SD16×C29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745309C2211yescharacteristic, complemented
22#11745308C2211yescharacteristic
23C2×#90784C2211yescharacteristic
24D4×Dic29C2211yescharacteristic
25C2×#90782C2211yescharacteristic
26C4×C22⋊D29—21no—
27C2×D232C2211yescharacteristic
28#11745260—21no—
29#11745257C2211yescharacteristic
30#11745256—21no—
31#11745255C2211yescharacteristic
32C4⋊C4×D29C2211yescharacteristic
33#11745252C2211yescharacteristic, complemented
34#11745243—21no—
35C22⋊C4×D29—21no—
36C4×D116—21no—
37C4×D116C2211yescharacteristic
38C4×D116C2211yescharacteristic, complemented
39#11745234—21no—
40C42×D29C2211yescharacteristic
41C29×#107C2211yescharacteristic, complemented
42C29×#103C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic
44C29×#97C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic, complemented
49#11745168C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745165C2211yescharacteristic, complemented
52#11745162C2211yescharacteristic, complemented
53#11745162C2211yescharacteristic, complemented
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58#11745151C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C2×C22⋊D29—21no—
64C22×Dic29—21no—
65D4×D29—22no—
66D4×D29—22no—
67C2×D116—21no—
68C2×D116C2311yescharacteristic
69C2×D116C2311yescharacteristic
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—44no—
75C2×C4×D29D411yescharacteristic
76C2×C4×D29D411yescharacteristic
77C2×C4×D29C2311yescharacteristic
78SD16×C29—22no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C42×C29—21no—
86C42×C29C2311yescharacteristic
87C22⋊Dic29—21no—
88#90784—22no—
89#90782—22no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101#90779—21no—
102#90779—21no—
103C4×Dic29D411yescharacteristic
104C4×Dic29D411yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108D232—22no—
109C23×C29—21no—
110C22×D29—24no—
111C22×D29—21no—
112C22×D29—21no—
113C22×D29—42no—
114C22×D29—42no—
115C22×D29C2×D411yescharacteristic
116Q8×C29—21no—
117Q8×C29—21no—
118D4×C29—21no—
119D4×C29#4112yes—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—42no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—24no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—42no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134D116—21no—
135D116—21no—
136D116—21no—
137D116—42no—
138D116#4112yes—
139C4×D29—22no—
140C4×D29—21no—
141C4×D29—21no—
142C4×D29—41no—
143C4×D29—42no—
144C4×D29—42no—
145C4×D29—42no—
146C4×D29—42no—
147C8×C29—21no—
148C8×C29—21no—
149#6597—21no—
150#6597—21no—
151#3114—291nomaximal, Sylow
152C22×C29—22no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29C22×D411yescharacteristic
156C2×D29—21no—
157C2×D29—21no—
158C2×D29—22no—
159C2×D29—48no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29AGL(1,ℤ/8)12yes—
166C4×C29—21no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29C2×#4111yescharacteristic
173Dic29—21no—
174Dic29—21no—
175Dic29—21no—
176Dic29—41no—
177Dic29—41no—
178#529—291no—
179C2×C4×D4—291no—
180#483—291no—
181#480—291no—
182#478—291no—
183#478—291no—
184#463—291no—
185#463—291no—
186#450—291no—
187#447—291no—
188#442—291no—
189#442—291no—
190#440—291no—
191#440D2911yescharacteristic, complemented
192#432—291no—
193C2×C29—42no—
194C2×C29#52511yescharacteristic
195C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C29#57511yescharacteristic
197D29—22no—
198D29—42no—
199D29—81no—
200C22×D4—291no—
201C23×C4—581no—
202C2×SD16—291no—
203C2×SD16C2×D2911yescharacteristic
204C2×D8—291no—
205C2×D8—291no—
206#126—581no—
207#125—291no—
208#124—291no—
209#123—581no—
210C22⋊Q8—291no—
211#121—291no—
212C4×Q8C2×D2911yescharacteristic, complemented
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—291no—
216C4×D4—291no—
217C4×D4—581no—
218C4×D4—581no—
219C4×D4—581no—
220C4×D4C2×D2911yescharacteristic
221#117—581no—
222C2×C4⋊C4—291no—
223C2×C22⋊C4—581no—
224C2×C42—291no—
225#107—291no—
226#107C2×D2911yescharacteristic, complemented
227#106—291no—
228#106—291no—
229C4⋊C8—291no—
230C4⋊C8—291no—
231#103—291no—
232#103C2×D2911yescharacteristic, complemented
233#102—291no—
234#102—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102C2×D2911yescharacteristic
239C22⋊C8—291no—
240C22⋊C8—291no—
241#97—291no—
242#97C2×D2911yescharacteristic, complemented
243C29#311411yescharacteristic, complemented, Sylow
244C24—581no—
245C2×Q8C22×D2911yescharacteristic
246C2×D4—291no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4—581no—
250C2×D4—582no—
251C2×D4—582no—
252C2×D4C22×D2911yescharacteristic
253C22×C4—21no—
254C22×C4—291no—
255C22×C4—291no—
256C22×C4—291no—
257C22×C4—581no—
258C22×C4—581no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4—1164no—
263SD16—22no—
264SD16—582no—
265D8—582no—
266D8—582no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8C22×D2911yescharacteristic
270C2×C8C22×D2911yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—291no—
273C4⋊C4—291no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4C22×D2911yescharacteristic
279C4⋊C4C22×D2911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C42—21no—
290C42—291no—
291C42—291no—
292C42—291no—
293C42C22×D2911yescharacteristic
294C23—21no—
295C23—291no—
296C23—584no—
297C23—581no—
298C23—581no—
299C23—1162no—
300C23—1162no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—292no—
305D4—584no—
306D4—581no—
307D4—581no—
308D4—581no—
309D4—1162no—
310D4#9080512yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—291no—
316C2×C4—291no—
317C2×C4—291no—
318C2×C4—582no—
319C2×C4—581no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—581no—
323C2×C4—1161no—
324C2×C4—1162no—
325C2×C4—1162no—
326C2×C4—1162no—
327C2×C4—1162no—
328C2×C4—1162no—
329C2×C4D4×D2911yescharacteristic
330C2×C4D4×D2911yescharacteristic
331C2×C4C23×D2911yescharacteristic
332C8—21no—
333C8—21no—
334C8—581no—
335C8—581no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—292no—
340C22—581no—
341C22—581no—
342C22—582no—
343C22—1168no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—581no—
356C4—581no—
357C4—581no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080511yescharacteristic
361C4#41×D2911yescharacteristic
362C2—42no—
363C2—582no—
364C2—1162no—
365C2—2321no—
366C2#1427167211yescharacteristic
367C2AGL(1,ℤ/8)×D2911yescharacteristic
368C2#1427196211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#440C2
socleC22×C29C22×D4
prime radical#14271298C2
hypercenter#440D29
hypocenterC29#3114
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14271700C2semidirect
2. C4×D4×D29C2semidirect
3. #14271492C2semidirect
4. #14271478C2semidirect
5. #14271466C2semidirect
6. #14271465C2semidirect
7. #14271381C2semidirect
8. #14271380C2semidirect
9. #14271312C2semidirect
11. #14271276C2semidirect
12. #14271273C2semidirect
13. #14271261C2semidirect
14. #14271218C2semidirect
15. C29×#440C2semidirect
19. C4×Q8×C29C22semidirect
21. #11745309C22semidirect
33. #11745252C22semidirect
38. C4×D116C22semidirect
41. C29×#107C22semidirect
42. C29×#103C22semidirect
44. C29×#97C22semidirect
45. #11745183C22semidirect
48. #11745169C22semidirect
51. #11745165C22semidirect
52. #11745162C22semidirect
53. #11745162C22semidirect
55. #11745157C22semidirect
56. #11745156C22semidirect
57. #11745155C22semidirect
58. #11745151C22semidirect
191. #440D29semidirect
212. C4×Q8C2×D29semidirect
226. #107C2×D29semidirect
232. #103C2×D29semidirect
242. #97C2×D29semidirect
243. C29#3114semidirect

Maximal subgroups

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

subgroupindex
#142717002
C4×D4×D292
#142714922
#142714782
#142714662
#142714652
#142713812
#142713802
#142713122
#142712982
#142712762
#142712732
#142712612
#142712182
C29×#4402
#311429