Finite Group Databasebeta

← #16829679

Subgroups — #16829679

Order 3712.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271786C211yesmaximal, characteristic, complemented
2#14271637C211yesmaximal, characteristic, complemented
3#14271487C211yesmaximal, characteristic, complemented
4#14271452C211yesmaximal, characteristic, complemented
5#14271442C211yesmaximal, characteristic, complemented
6#14271381C211yesmaximal, characteristic, complemented
7#14271381C211yesmaximal, characteristic, complemented
8#14271313C211yesmaximal, characteristic, complemented
9#14271299C211yesmaximal, characteristic
10#14271274C211yesmaximal, characteristic, complemented
11#14271266C211yesmaximal, characteristic, complemented
12#14271248C211yesmaximal, characteristic, complemented
13#14271245C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#485C211yesmaximal, characteristic, complemented
16C22×D116C2211yescharacteristic
17C29×C22⋊Q8C2211yescharacteristic
18C29×#117C2211yescharacteristic
19#11745309C2211yescharacteristic, complemented
20Q8×Dic29C2211yescharacteristic, complemented
21C2×#90784C2211yescharacteristic
22C2×#90784C2211yescharacteristic
23#11745292C2211yescharacteristic
24#11745288C2211yescharacteristic
25C2×D232C2211yescharacteristic
26C2×D232C2211yescharacteristic
27#11745260—21no—
28#11745259—21no—
29#11745255C2211yescharacteristic
30#11745255C2211yescharacteristic
31#11745255C2211yescharacteristic
32#11745255C2211yescharacteristic
33#11745255C2211yescharacteristic, complemented
34#11745250C2211yescharacteristic, complemented
35#11745247—21no—
36#11745245—21no—
37C22⋊C4×D29—21no—
38C22⋊C4×D29—21no—
39C4×D116—21no—
40C4×D116—21no—
41C29×#107C2211yescharacteristic, complemented
42C29×#106C2211yescharacteristic, complemented
43C29×#103C2211yescharacteristic, complemented
44C29×#103C2211yescharacteristic, complemented
45C29×C22⋊C8C2211yescharacteristic
46C22⋊#6597C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745163C2211yescharacteristic, complemented
50#11745162C2211yescharacteristic, complemented
51#11745162C2211yescharacteristic, complemented
52C8×Dic29C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic, complemented
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29—21no—
63C2×D116—21no—
64C2×D116—22no—
65C2×D116—22no—
66C2×D116C2311yescharacteristic
67C2×D116C2311yescharacteristic
68C2×D116C2311yescharacteristic
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×Dic58—21no—
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C42×C29—21no—
84C22⋊Dic29D411yescharacteristic
85C22⋊Dic29D411yescharacteristic
86#90784—22no—
87#90784—22no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96C4⋊Dic29—21no—
97C4⋊Dic29D411yescharacteristic
98C4⋊Dic29D411yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101C4×Dic29—21no—
102C4×Dic29C2311yescharacteristic
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106D232—22no—
107D232—22no—
108C23×C29C2×D411yescharacteristic
109C22×D29—21no—
110C22×D29—21no—
111C22×D29—24no—
112C22×D29—21no—
113C22×D29—81no—
114C22×D29—81no—
115Q8×C29—21no—
116Q8×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2411yescharacteristic
125C22⋊D29—81no—
126C2×Dic29—21no—
127C2×Dic29C2×D411yescharacteristic
128C2×Dic29C2×D411yescharacteristic
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131D116—24no—
132D116—21no—
133D116—21no—
134D116—21no—
135D116—21no—
136D116#4112yes—
137D116#4112yes—
138C4×D29—81no—
139C4×D29—81no—
140C4×D29—81no—
141C4×D29—81no—
142C4×D29—81no—
143Dic58—81no—
144C8×C29—21no—
145C8×C29—21no—
146#6597—21no—
147#6597—21no—
148#3118—291nomaximal, Sylow
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29C22×D411yescharacteristic
153C2×D29—22no—
154C2×D29—22no—
155C2×D29—41no—
156C2×D29—41no—
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C2×D29—41no—
161C2×D29—41no—
162C2×D29—84no—
163C4×C29—21no—
164C4×C29—41no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29—41no—
168C4×C29C2×#4111yescharacteristic
169C4×C29C2×#4111yescharacteristic
170Dic29—21no—
171Dic29—21no—
172Dic29—21no—
173Dic29—21no—
174Dic29—41no—
175#542—291no—
176#518—291no—
177#485D2911yescharacteristic, complemented
178#482—291no—
179#476—291no—
180#474—291no—
181#463—291no—
182#463—291no—
183#450—291no—
184#447—291no—
185#442—291no—
186#440—291no—
187C4×SD16—291no—
188C4×D8—291no—
189#433—291no—
190C2×C29—41no—
191C2×C29#52511yescharacteristic
192C2×C29#57611yescharacteristic
193C2×C29#57711yescharacteristic
194D29—42no—
195D29—42no—
196D29—81no—
197C22×D4—291no—
198C2×SD16—291no—
199C2×SD16—291no—
200C2×D8—291no—
201C2×D8—291no—
202C4⋊Q8—291no—
203#126—581no—
204#124—291no—
205#124—581no—
206#123—581no—
207C22⋊Q8—581no—
208C22⋊Q8C2×D2911yescharacteristic
209#121—291no—
210C4×Q8—291no—
211C4×D4—291no—
212C4×D4—291no—
213C4×D4—291no—
214C4×D4—291no—
215C4×D4—291no—
216C4×D4—581no—
217C4×D4—581no—
218#117—291no—
219#117C2×D2911yescharacteristic
220C2×C22⋊C4—581no—
221C2×C22⋊C4—581no—
222#107—291no—
223#107C2×D2911yescharacteristic, complemented
224#106—291no—
225#106C2×D2911yescharacteristic, complemented
226C4⋊C8—291no—
227C4⋊C8—291no—
228#103C2×D2911yescharacteristic, complemented
229#103C2×D2911yescharacteristic, complemented
230#102—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234#102—291no—
235#102—291no—
236C22⋊C8—291no—
237C22⋊C8C2×D2911yescharacteristic
238#97—291no—
239C4×C8—291no—
240C29#311811yescharacteristic, complemented, Sylow
241C24—581no—
242C2×Q8—581no—
243C2×Q8C22×D2911yescharacteristic
244C2×D4—291no—
245C2×D4—291no—
246C2×D4—291no—
247C2×D4—582no—
248C2×D4—582no—
249C2×D4—581no—
250C2×D4—581no—
251C22×C4—581no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4—581no—
255C22×C4—581no—
256C22×C4C22×D2911yescharacteristic
257SD16—582no—
258SD16—582no—
259D8—582no—
260D8—582no—
261C2×C8—291no—
262C2×C8—291no—
263C2×C8C22×D2911yescharacteristic
264C2×C8C22×D2911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4C22×D2911yescharacteristic
272C4⋊C4C22×D2911yescharacteristic
273C4⋊C4C22×D2911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—291no—
277C22⋊C4—291no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—21no—
287C42—291no—
288C42—291no—
289C42—581no—
290C23—584no—
291C23—581no—
292C23—581no—
293C23—581no—
294C23—2321no—
295C23—2321no—
296C23D4×D2911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—2321no—
300D4—292no—
301D4—292no—
302D4—584no—
303D4—581no—
304D4—581no—
305D4—581no—
306D4—581no—
307D4—2321no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—291no—
315C2×C4—291no—
316C2×C4—291no—
317C2×C4—291no—
318C2×C4—581no—
319C2×C4—2321no—
320C2×C4—2321no—
321C2×C4—2321no—
322C2×C4—2321no—
323C2×C4—2321no—
324C2×C4D4×D2911yescharacteristic
325C2×C4C23×D2911yescharacteristic
326C8—21no—
327C8—21no—
328C8—581no—
329C8—581no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—582no—
334C22—582no—
335C22—1161no—
336C22—1161no—
337C22—1161no—
338C22—1161no—
339C22—1161no—
340C22—1161no—
341C22—1161no—
342C22—2324no—
343C22C2×D4×D2911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—581no—
350C4—581no—
351C4—581no—
352C4—581no—
353C4—1161no—
354C4#41×D2911yescharacteristic
355C4#41×D2911yescharacteristic
356C2—41no—
357C2—1162no—
358C2—1162no—
359C2—2321no—
360C2#1427167111yescharacteristic
361C2#1427196511yescharacteristic
362C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#485C2
socleC22×C29C22×D4
prime radical#14271299C2
hypercenter#485D29
hypocenterC29#3118
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14271786C2semidirect
2. #14271637C2semidirect
3. #14271487C2semidirect
4. #14271452C2semidirect
5. #14271442C2semidirect
6. #14271381C2semidirect
7. #14271381C2semidirect
8. #14271313C2semidirect
10. #14271274C2semidirect
11. #14271266C2semidirect
12. #14271248C2semidirect
13. #14271245C2semidirect
14. #14271221C2semidirect
15. C29×#485C2semidirect
19. #11745309C22semidirect
20. Q8×Dic29C22semidirect
33. #11745255C22semidirect
34. #11745250C22semidirect
41. C29×#107C22semidirect
42. C29×#106C22semidirect
43. C29×#103C22semidirect
44. C29×#103C22semidirect
49. #11745163C22semidirect
50. #11745162C22semidirect
51. #11745162C22semidirect
52. C8×Dic29C22semidirect
55. #11745157C22semidirect
56. #11745157C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
177. #485D29semidirect
223. #107C2×D29semidirect
225. #106C2×D29semidirect
228. #103C2×D29semidirect
229. #103C2×D29semidirect
240. C29#3118semidirect

Maximal subgroups

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

subgroupindex
#142717862
#142716372
#142714872
#142714522
#142714422
#142713812
#142713132
#142712992
#142712742
#142712662
#142712482
#142712452
#142712212
C29×#4852
#311829