Finite Group Databasebeta

← #16829841

Subgroups — #16829841

Order 3712.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271790C211yesmaximal, characteristic, complemented
2#14271726C211yesmaximal, characteristic
3#14271527C211yesmaximal, characteristic, complemented
4#14271526C211yesmaximal, characteristic, complemented
5#14271525C211yesmaximal, characteristic, complemented
6#14271521C211yesmaximal, characteristic, complemented
7#14271518C211yesmaximal, characteristic, complemented
8#14271516C211yesmaximal, characteristic, complemented
9#14271508C211yesmaximal, characteristic, complemented
10#14271166C211yesmaximal, characteristic, complemented
11#14271161C211yesmaximal, characteristic, complemented
12#14271156C211yesmaximal, characteristic, complemented
13#102×D29C211yesmaximal, characteristic, complemented
14#14271117C211yesmaximal, characteristic, complemented
15C29×#486C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C29×C4⋊Q8C2211yescharacteristic, complemented
19C29×#127C2211yescharacteristic
20#11745308—21no—
21#11745306—21no—
22#11745302C2211yescharacteristic
23#11745301—21no—
24#11745301—21no—
25#11745299—21no—
26#11745299—21no—
27#11745298C2211yescharacteristic
28C2×#90772C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic
30#11745258—21no—
31#11745254C2211yescharacteristic
32C4⋊C4×D29C2211yescharacteristic
33#11745252C2211yescharacteristic, complemented
34#11745251—21no—
35#11745250C2211yescharacteristic, complemented
36#11745237C2211yescharacteristic
37#11745234C2211yescharacteristic
38#11745232C2211yescharacteristic, complemented
39C29×#102C2211yescharacteristic
40C29×#102C2211yescharacteristic
41C29×#102C2211yescharacteristic, complemented
42C29×#102C2211yescharacteristic, complemented
43C4×C8×C29C2211yescharacteristic, complemented
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic, complemented
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745164C2211yescharacteristic, complemented
51#11745164C2211yescharacteristic, complemented
52#11745163C2211yescharacteristic, complemented
53C8×Dic29C2211yescharacteristic, complemented
54#11745158C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745151C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29—21no—
61C2×D4×C29—21no—
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C2×D4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C22×Dic29—21no—
70#90807—22no—
71#90807—22no—
72D4×D29—22no—
73D4×D29—22no—
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29C2311yescharacteristic
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C42×C29C2311yescharacteristic
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90#90781D411yescharacteristic
91#90781D411yescharacteristic
92C4⋊Dic29—21no—
93C4⋊Dic29C2311yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95#90779—21no—
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779D411yescharacteristic
101#90779D411yescharacteristic
102C4×Dic29—21no—
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106#90772—22no—
107C8×D29—22no—
108C23×C29—21no—
109C23×C29—21no—
110C22×D29—21no—
111C22×D29—42no—
112C22×D29—81no—
113C22×D29—81no—
114C22×D29C2×D411yescharacteristic
115Q8×C29—81no—
116D4×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—81no—
121D4×C29—81no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—42no—
128C22⋊D29—42no—
129C22⋊D29—81no—
130C22⋊D29—81no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—42no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138D116—21no—
139D116—21no—
140C4×D29—81no—
141C4×D29#4112yes—
142C4×D29#4112yes—
143Dic58—21no—
144Dic58—21no—
145Dic58—81no—
146C8×C29—21no—
147C8×C29—21no—
148#6597—21no—
149#6597—21no—
150#3136—291nomaximal, Sylow
151C22×C29—41no—
152C22×C29—41no—
153C22×C29—41no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29C22×D411yescharacteristic
158C2×D29—21no—
159C2×D29—21no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—84no—
164C2×D29#12412yes—
165C4×C29—21no—
166C4×C29—21no—
167C4×C29—41no—
168C4×C29—41no—
169C4×C29C2×#4111yescharacteristic
170C4×C29C2×#4111yescharacteristic
171Dic29—21no—
172Dic29—21no—
173Dic29—41no—
174Dic29—41no—
175Dic29—41no—
176Dic29#12412yes—
177#544—291no—
178#535—291no—
179#490—291no—
180#490—291no—
181#489—291no—
182#489—291no—
183#488—291no—
184#488—291no—
185#486—291no—
186#486D2911yescharacteristic, complemented
187#418—291no—
188#417—291no—
189#416—291no—
190C2×#102—291no—
191#405—291no—
192C2×C29—81no—
193C2×C29—81no—
194C2×C29C2×#12411yescharacteristic
195C2×C29#57611yescharacteristic
196C2×C29#57711yescharacteristic
197D29—22no—
198D29—81no—
199C2×#41—291no—
200C22×D4—291no—
201C2×M16—291no—
202C22×C8—291no—
203C4⋊Q8—291no—
204C4⋊Q8—581no—
205C4⋊Q8C2×D2911yescharacteristic, complemented
206#127—291no—
207#127C2×D2911yescharacteristic
208#125—291no—
209#125—291no—
210#125—581no—
211#124—291no—
212#124—291no—
213C22⋊Q8—581no—
214C22⋊Q8—581no—
215#121—581no—
216#121—581no—
217#120—581no—
218#120—581no—
219#117—291no—
220#117—291no—
221C2×C4⋊C4—291no—
222#103—291no—
223#103—291no—
224#103—291no—
225#103—291no—
226#102—291no—
227#102—291no—
228#102—291no—
229#102—291no—
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102C2×D2911yescharacteristic
235#102C2×D2911yescharacteristic
236#102C2×D2911yescharacteristic, complemented
237#102C2×D2911yescharacteristic, complemented
238#97—291no—
239#97—291no—
240C4×C8—291no—
241C4×C8C2×D2911yescharacteristic, complemented
242C29#313611yescharacteristic, complemented, Sylow
243C24—581no—
244#41—582no—
245#41—582no—
246C2×Q8—21no—
247C2×Q8—291no—
248C2×Q8—581no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—291no—
252C2×D4—582no—
253C2×D4—582no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4—581no—
258C2×D4C22×D2911yescharacteristic
259C2×D4C22×D2911yescharacteristic
260C22×C4—291no—
261C22×C4—581no—
262C22×C4—581no—
263M16—582no—
264C2×C8—291no—
265C2×C8—291no—
266C2×C8—582no—
267C2×C8C22×D2911yescharacteristic
268C2×C8C22×D2911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—291no—
271C4⋊C4—291no—
272C4⋊C4—291no—
273C4⋊C4—291no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4C22×D2911yescharacteristic
281C4⋊C4C22×D2911yescharacteristic
282C22⋊C4—291no—
283C22⋊C4—291no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C42—291no—
290C42—581no—
291C42C22×D2911yescharacteristic
292C23—21no—
293C23—21no—
294C23—291no—
295C23—581no—
296C23—1162no—
297C23—2321no—
298C23—2321no—
299Q8—81no—
300Q8—581no—
301Q8—581no—
302Q8—2321no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—581no—
310D4—581no—
311D4—1162no—
312D4—1162no—
313D4—2321no—
314D4—2321no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—291no—
318C2×C4—292no—
319C2×C4—292no—
320C2×C4—291no—
321C2×C4—291no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—1162no—
326C2×C4—2321no—
327C2×C4D4×D2911yescharacteristic
328C2×C4D4×D2911yescharacteristic
329C2×C4C23×D2911yescharacteristic
330C8—21no—
331C8—21no—
332C8—581no—
333C8—581no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—292no—
341C22—581no—
342C22—581no—
343C22—1161no—
344C22—1161no—
345C22—1161no—
346C22—2324no—
347C22C2×D4×D2911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—292no—
353C4—581no—
354C4—581no—
355C4—1161no—
356C4—1161no—
357C4—1161no—
358C4#41×D2911yescharacteristic
359C4#41×D2911yescharacteristic
360C2—81no—
361C2—81no—
362C2—582no—
363C2—2321no—
364C2#124×D2911yescharacteristic
365C2#1427196411yescharacteristic
366C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#486C2
socleC22×C29C22×D4
prime radical#14271726C2
hypercenter#486D29
hypocenterC29#3136
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14271790C2semidirect
3. #14271527C2semidirect
4. #14271526C2semidirect
5. #14271525C2semidirect
6. #14271521C2semidirect
7. #14271518C2semidirect
8. #14271516C2semidirect
9. #14271508C2semidirect
10. #14271166C2semidirect
11. #14271161C2semidirect
12. #14271156C2semidirect
13. #102×D29C2semidirect
14. #14271117C2semidirect
15. C29×#486C2semidirect
18. C29×C4⋊Q8C22semidirect
33. #11745252C22semidirect
35. #11745250C22semidirect
38. #11745232C22semidirect
41. C29×#102C22semidirect
42. C29×#102C22semidirect
43. C4×C8×C29C22semidirect
46. #11745180C22semidirect
47. #11745180C22semidirect
50. #11745164C22semidirect
51. #11745164C22semidirect
52. #11745163C22semidirect
53. C8×Dic29C22semidirect
54. #11745158C22semidirect
55. #11745158C22semidirect
58. #11745151C22semidirect
186. #486D29semidirect
205. C4⋊Q8C2×D29semidirect
236. #102C2×D29semidirect
237. #102C2×D29semidirect
241. C4×C8C2×D29semidirect
242. C29#3136semidirect

Maximal subgroups

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

subgroupindex
#142717902
#142717262
#142715272
#142715262
#142715252
#142715212
#142715182
#142715162
#142715082
#142711662
#142711612
#142711562
#102×D292
#142711172
C29×#4862
#313629