Finite Group Databasebeta

← #16828323

Subgroups — #16828323

Order 3712.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745276C211yesmaximal, characteristic
2#14271645C211yesmaximal, characteristic, complemented
3#14271635C211yesmaximal, characteristic, complemented
4#14271276C211yesmaximal, characteristic, complemented
5#14271272C211yesmaximal, characteristic, complemented
6#14271266C211yesmaximal, characteristic, complemented
7SD16×Dic29C211yesmaximal, characteristic, complemented
8C4×#90784C211yesmaximal, characteristic, complemented
9#14271245C211yesmaximal, characteristic, complemented
10C4×#90782C211yesmaximal, characteristic, complemented
11#14271204C211yesmaximal, characteristic, complemented
12#14271158C211yesmaximal, characteristic, complemented
13#102×D29C211yesmaximal, characteristic, complemented
14#14271120C211yesmaximal, characteristic, complemented
15C29×#440C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C4×Q8×C29C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21Q8×Dic29C2211yescharacteristic, complemented
22C2×#90784C2211yescharacteristic
23D4×Dic29C2211yescharacteristic
24C2×#90782C2211yescharacteristic
25C4×C22⋊D29—21no—
26C2×#90781—21no—
27#11745276C418yescomplemented
28C2×D232C2211yescharacteristic
29C2×#90772C2211yescharacteristic
30C2×C8×D29C2211yescharacteristic
31#11745255—21no—
32#11745255C2211yescharacteristic
33#11745255C2211yescharacteristic, complemented
34#11745254C2211yescharacteristic
35C4⋊C4×D29—21no—
36C4⋊C4×D29C2211yescharacteristic
37#11745243—21no—
38C22⋊C4×D29—21no—
39C4×D116—21no—
40C4×D116C2211yescharacteristic
41C4×D116C2211yescharacteristic, complemented
42#11745234—21no—
43#11745234C2211yescharacteristic
44C29×#107C2211yescharacteristic, complemented
45C29×#103C2211yescharacteristic, complemented
46C29×#102C2211yescharacteristic
47C29×#97C2211yescharacteristic, complemented
48#11745183C2211yescharacteristic, complemented
49#11745180C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic, complemented
52#11745165C2211yescharacteristic, complemented
53#11745163C2211yescharacteristic, complemented
54C8×Dic29C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C4×#6597C2211yescharacteristic, complemented
60C23×D29—21no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29—21no—
64C2×C22⋊D29—21no—
65C22×Dic29—21no—
66#90809—22no—
67#90809C2×C414yescomplemented
68D4×D29—22no—
69D4×D29C2×C414yescomplemented
70C2×D116—21no—
71C2×D116C2311yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×C4×D29C2311yescharacteristic
80SD16×C29C2×C414yescomplemented
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊C4×C29—21no—
87C42×C29—21no—
88C42×C29C2311yescharacteristic
89C22⋊Dic29—21no—
90#90784C2×C414yescomplemented
91#90782C2×C414yescomplemented
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781D411yescharacteristic
98#90781D411yescharacteristic
99C4⋊Dic29—21no—
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779D411yescharacteristic
104#90779D411yescharacteristic
105C4×Dic29—21no—
106C4×Dic29—21no—
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110D232C2×C414yescomplemented
111#90772C2×C414yescomplemented
112C8×D29—22no—
113C23×C29—21no—
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—24no—
117C22×D29—81no—
118C22×D29—81no—
119C22×D29C2×D411yescharacteristic
120Q8×C29—21no—
121Q8×C29C22×C412yes—
122D4×C29—21no—
123D4×C29C22×C412yes—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—81no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—24no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—81no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—24no—
139D116—21no—
140D116—21no—
141D116C22×C412yes—
142D116C22×C412yes—
143C4×D29—24no—
144C4×D29—81no—
145C4×D29—81no—
146C4×D29—81no—
147C4×D29—81no—
148C4×D29—81no—
149C4×D29C22×C412yes—
150C4×D29#4112yes—
151C8×C29—21no—
152C8×C29C22×C412yes—
153#6597—21no—
154#6597C22×C412yes—
155#2946—291nomaximal, Sylow
156C22×C29—22no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—22no—
163C2×D29—22no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—84no—
169C2×D29C4×D412yes—
170C4×C29—22no—
171C4×C29—21no—
172C4×C29—21no—
173C4×C29—41no—
174C4×C29—41no—
175C4×C29C23×C411yescharacteristic
176C4×C29C2×#4111yescharacteristic
177Dic29—21no—
178Dic29—21no—
179Dic29—41no—
180Dic29—41no—
181Dic29C4×D412yes—
182C2×AGL(1,ℤ/8)—291no—
183#520—291no—
184#518—291no—
185#442—291no—
186#442—291no—
187#440—291no—
188#440D2911yescharacteristic, complemented
189C4×SD16—291no—
190C4×SD16—291no—
191C4×D8—291no—
192C4×D8—291no—
193#428—291no—
194#416—291no—
195C2×#102—291no—
196#405—291no—
197C2×C29—42no—
198C2×C29C2×C4×D411yescharacteristic
199C2×C29#57611yescharacteristic
200C2×C29#57711yescharacteristic
201D29—22no—
202D29—42no—
203D29—42no—
204C2×#41—291no—
205C22×D4—291no—
206AGL(1,ℤ/8)—298no—
207C2×SD16—291no—
208C2×SD16C2×D2911yescharacteristic
209C2×D8—291no—
210C2×D8—291no—
211C2×M16—291no—
212C22×C8—291no—
213C4×Q8—291no—
214C4×Q8C2×D2911yescharacteristic, complemented
215C4×D4—291no—
216C4×D4—291no—
217C4×D4—291no—
218C4×D4—291no—
219C4×D4—291no—
220C4×D4—581no—
221C4×D4—581no—
222C4×D4—581no—
223C4×D4—581no—
224C4×D4C2×D2911yescharacteristic
225#117—291no—
226#117—291no—
227#117—581no—
228C2×C4⋊C4—291no—
229C2×C4⋊C4—581no—
230C2×C22⋊C4—581no—
231C2×C22⋊C4—581no—
232#107—291no—
233#107C2×D2911yescharacteristic, complemented
234#106—291no—
235#106—291no—
236#103—291no—
237#103C2×D2911yescharacteristic, complemented
238#102—291no—
239#102—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102C2×D2911yescharacteristic
244#97—291no—
245#97C2×D2911yescharacteristic, complemented
246C4×C8—291no—
247C4×C8—291no—
248C29#294611yescharacteristic, complemented, Sylow
249C24—581no—
250#41—294no—
251#41—582no—
252C2×Q8C22×D2911yescharacteristic
253C2×D4—294no—
254C2×D4—291no—
255C2×D4—291no—
256C2×D4—581no—
257C2×D4—582no—
258C2×D4—581no—
259C2×D4C22×D2911yescharacteristic
260C22×C4—21no—
261C22×C4—291no—
262C22×C4—581no—
263C22×C4—581no—
264C22×C4—581no—
265C22×C4—581no—
266C22×C4—581no—
267C22×C4—581no—
268C22×C4—581no—
269SD16—294no—
270SD16C4×D2914yescomplemented
271D8—294no—
272D8—294no—
273M16—294no—
274C2×C8—291no—
275C2×C8—291no—
276C2×C8—582no—
277C2×C8C22×D2911yescharacteristic
278C2×C8C22×D2911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—291no—
281C4⋊C4—291no—
282C4⋊C4—291no—
283C4⋊C4—291no—
284C4⋊C4—581no—
285C4⋊C4—581no—
286C4⋊C4C22×D2911yescharacteristic
287C4⋊C4C22×D2911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—291no—
290C22⋊C4—291no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C42—21no—
298C42—291no—
299C42—581no—
300C42—581no—
301C42C22×D2911yescharacteristic
302C23—21no—
303C23—291no—
304C23—584no—
305C23—581no—
306C23—581no—
307C23—2321no—
308C23—2321no—
309Q8—21no—
310Q8C2×C4×D2912yes—
311D4—21no—
312D4—292no—
313D4—292no—
314D4—584no—
315D4—584no—
316D4—581no—
317D4—581no—
318D4C2×C4×D2912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—291no—
324C2×C4—292no—
325C2×C4—292no—
326C2×C4—291no—
327C2×C4—291no—
328C2×C4—584no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—2321no—
332C2×C4—2321no—
333C2×C4—2321no—
334C2×C4—2321no—
335C2×C4—2321no—
336C2×C4—2321no—
337C2×C4D4×D2911yescharacteristic
338C2×C4D4×D2911yescharacteristic
339C2×C4C23×D2911yescharacteristic
340C8—21no—
341C8—292no—
342C8—581no—
343C8C2×C4×D2912yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—292no—
348C22—581no—
349C22—581no—
350C22—582no—
351C22—582no—
352C22—1161no—
353C22—1161no—
354C22—1161no—
355C22—1161no—
356C22—2324no—
357C22C2×D4×D2911yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—292no—
364C4—581no—
365C4—581no—
366C4—1161no—
367C4—1161no—
368C4C22×C4×D2911yescharacteristic
369C4#41×D2911yescharacteristic
370C2—42no—
371C2—582no—
372C2—1162no—
373C2—1162no—
374C2C4×D4×D2911yescharacteristic
375C2#1427196711yescharacteristic
376C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC29×#440C2
socleC22×C29C22×D4
prime radicalC2×#11745276C2
cosocleC2×C4×C29C24
hypercenter#440D29
hypocenterC29#2946
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #14271645C2semidirect
3. #14271635C2semidirect
4. #14271276C2semidirect
5. #14271272C2semidirect
6. #14271266C2semidirect
7. SD16×Dic29C2semidirect
8. C4×#90784C2semidirect
9. #14271245C2semidirect
10. C4×#90782C2semidirect
11. #14271204C2semidirect
12. #14271158C2semidirect
13. #102×D29C2semidirect
14. #14271120C2semidirect
15. C29×#440C2semidirect
19. C4×Q8×C29C22semidirect
21. Q8×Dic29C22semidirect
27. #11745276C4semidirect
33. #11745255C22semidirect
41. C4×D116C22semidirect
44. C29×#107C22semidirect
45. C29×#103C22semidirect
47. C29×#97C22semidirect
48. #11745183C22semidirect
51. #11745169C22semidirect
52. #11745165C22semidirect
53. #11745163C22semidirect
54. C8×Dic29C22semidirect
56. #11745157C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
59. C4×#6597C22semidirect
67. #90809C2×C4semidirect
69. D4×D29C2×C4semidirect
80. SD16×C29C2×C4semidirect
90. #90784C2×C4semidirect
91. #90782C2×C4semidirect
110. D232C2×C4semidirect
111. #90772C2×C4semidirect
188. #440D29semidirect
214. C4×Q8C2×D29semidirect
233. #107C2×D29semidirect
237. #103C2×D29semidirect
245. #97C2×D29semidirect
248. C29#2946semidirect
270. SD16C4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452762
#142716452
#142716352
#142712762
#142712722
#142712662
SD16×Dic292
C4×#907842
#142712452
C4×#907822
#142712042
#142711582
#102×D292
#142711202
C29×#4402
#294629