Finite Group Databasebeta

← #16829843

Subgroups — #16829843

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#14271731C211yesmaximal, characteristic
3#14271528C211yesmaximal, characteristic, complemented
4#14271526C211yesmaximal, characteristic, complemented
5#14271524C211yesmaximal, characteristic, complemented
6#14271519C211yesmaximal, characteristic, complemented
7#14271517C211yesmaximal, characteristic, complemented
8#14271511C211yesmaximal, characteristic, complemented
9#14271508C211yesmaximal, characteristic, complemented
10#14271166C211yesmaximal, characteristic, complemented
11#14271163C211yesmaximal, characteristic, complemented
12#14271158C211yesmaximal, characteristic, complemented
13#102×D29C211yesmaximal, characteristic, complemented
14#14271120C211yesmaximal, characteristic, complemented
15C29×#489C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C29×C4⋊Q8C2211yescharacteristic, complemented
19C29×#124C2211yescharacteristic
20#11745309C2211yescharacteristic
21#11745308—21no—
22#11745306—21no—
23#11745302C2211yescharacteristic
24C2×#90772C2211yescharacteristic
25C2×C8×D29C2211yescharacteristic
26#11745258—21no—
27#11745254C2211yescharacteristic
28C4⋊C4×D29C2211yescharacteristic
29#11745252C2211yescharacteristic, complemented
30#11745251—21no—
31#11745250C2211yescharacteristic, complemented
32#11745246—21no—
33#11745246—21no—
34#11745244—21no—
35#11745244—21no—
36#11745236C2211yescharacteristic
37#11745234C2211yescharacteristic
38#11745232C2211yescharacteristic, complemented
39C29×#103C2211yescharacteristic, complemented
40C29×#103C2211yescharacteristic, complemented
41C29×#102C2211yescharacteristic
42C29×#102C2211yescharacteristic
43C29×#97C2211yescharacteristic, complemented
44#11745183C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic, complemented
51#11745169C2211yescharacteristic, complemented
52#11745163C2211yescharacteristic, complemented
53C8×Dic29C2211yescharacteristic, complemented
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic, complemented
57#11745157C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29—21no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66#90809—22no—
67#90809—22no—
68D4×D29—22no—
69D4×D29—22no—
70C2×D116—21no—
71C2×D116—21no—
72C2×D116—21no—
73C2×D116C2311yescharacteristic
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29C2311yescharacteristic
78C2×Dic58—21no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C42×C29C2311yescharacteristic
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—
109C22×D29—21no—
110C22×D29—21no—
111C22×D29—42no—
112C22×D29—81no—
113C22×D29—81no—
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—81no—
118D4×C29—21no—
119D4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2411yescharacteristic
126C22⋊D29—42no—
127C22⋊D29—81no—
128C22⋊D29—81no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29C2×D411yescharacteristic
132C2×Dic29C2×D411yescharacteristic
133C2×Dic29C2×D411yescharacteristic
134D116—21no—
135D116—21no—
136D116—21no—
137D116—21no—
138D116—42no—
139D116—81no—
140D116—81no—
141C4×D29—42no—
142C4×D29—81no—
143C4×D29#4112yes—
144C4×D29#4112yes—
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×C29C22×D411yescharacteristic
155C2×D29—21no—
156C2×D29—21no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
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×C29—41no—
170C4×C29C2×#4111yescharacteristic
171C4×C29C2×#4111yescharacteristic
172Dic29—21no—
173Dic29—21no—
174Dic29—41no—
175Dic29—41no—
176Dic29#12412yes—
177#544—291no—
178#535—291no—
179#490—291no—
180#490—291no—
181#489—291no—
182#489D2911yescharacteristic, complemented
183#488—291no—
184#488—291no—
185#486—291no—
186#486—291no—
187#418—291no—
188#417—291no—
189#416—291no—
190C2×#102—291no—
191#405—291no—
192C2×C29—81no—
193C2×C29C2×#12411yescharacteristic
194C2×C29#57611yescharacteristic
195C2×C29#57711yescharacteristic
196D29—22no—
197D29—81no—
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#127—291no—
208#125—291no—
209#125—291no—
210#125—581no—
211#124—291no—
212#124C2×D2911yescharacteristic
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#103C2×D2911yescharacteristic, complemented
225#103C2×D2911yescharacteristic, complemented
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#102—291no—
235#102—291no—
236#102C2×D2911yescharacteristic
237#102C2×D2911yescharacteristic
238#97—291no—
239#97C2×D2911yescharacteristic, complemented
240C4×C8—291no—
241C4×C8—291no—
242C29#313611yescharacteristic, complemented, Sylow
243C24—581no—
244#41—582no—
245#41—582no—
246C2×Q8—21no—
247C2×Q8—581no—
248C2×Q8C22×D2911yescharacteristic
249C2×D4—291no—
250C2×D4—291no—
251C2×D4—581no—
252C2×D4—582no—
253C2×D4—582no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4—581no—
258C2×D4—581no—
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—21no—
283C22⋊C4—21no—
284C22⋊C4—291no—
285C22⋊C4—291no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C42—291no—
290C42—581no—
291C42C22×D2911yescharacteristic
292C23—21no—
293C23—291no—
294C23—581no—
295C23—581no—
296C23—1162no—
297C23—2321no—
298C23—2321no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—2321no—
303D4—21no—
304D4—21no—
305D4—581no—
306D4—581no—
307D4—581no—
308D4—581no—
309D4—1162no—
310D4—1162no—
311D4—2321no—
312D4—2321no—
313D4—2321no—
314D4—2321no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—291no—
319C2×C4—292no—
320C2×C4—292no—
321C2×C4—291no—
322C2×C4—291no—
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—292no—
338C22—581no—
339C22—581no—
340C22—1161no—
341C22—1161no—
342C22—1161no—
343C22—1161no—
344C22—1161no—
345C22—1161no—
346C22—2324no—
347C22C2×D4×D2911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—292no—
354C4—581no—
355C4—581no—
356C4—1161no—
357C4—1161no—
358C4#41×D2911yescharacteristic
359C4#41×D2911yescharacteristic
360C2—81no—
361C2—582no—
362C2—2321no—
363C2—2321no—
364C2#124×D2911yescharacteristic
365C2#1427196711yescharacteristic
366C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#489C2
socleC22×C29C22×D4
prime radical#14271731C2
hypercenter#489D29
hypocenterC29#3136
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #14271790C2semidirect
3. #14271528C2semidirect
4. #14271526C2semidirect
5. #14271524C2semidirect
6. #14271519C2semidirect
7. #14271517C2semidirect
8. #14271511C2semidirect
9. #14271508C2semidirect
10. #14271166C2semidirect
11. #14271163C2semidirect
12. #14271158C2semidirect
13. #102×D29C2semidirect
14. #14271120C2semidirect
15. C29×#489C2semidirect
18. C29×C4⋊Q8C22semidirect
29. #11745252C22semidirect
31. #11745250C22semidirect
38. #11745232C22semidirect
39. C29×#103C22semidirect
40. C29×#103C22semidirect
43. C29×#97C22semidirect
44. #11745183C22semidirect
45. #11745183C22semidirect
50. #11745169C22semidirect
51. #11745169C22semidirect
52. #11745163C22semidirect
53. C8×Dic29C22semidirect
56. #11745157C22semidirect
57. #11745157C22semidirect
58. C4×#6597C22semidirect
182. #489D29semidirect
205. C4⋊Q8C2×D29semidirect
224. #103C2×D29semidirect
225. #103C2×D29semidirect
239. #97C2×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
#142717312
#142715282
#142715262
#142715242
#142715192
#142715172
#142715112
#142715082
#142711662
#142711632
#142711582
#102×D292
#142711202
C29×#4892
#313629