Finite Group Databasebeta

← #16829740

Subgroups — #16829740

Order 3712.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271773C211yesmaximal, characteristic, complemented
2#14271637C211yesmaximal, characteristic
3#14271504C211yesmaximal, characteristic, complemented
4#14271466C211yesmaximal, characteristic, complemented
5#14271462C211yesmaximal, characteristic, complemented
6#14271367C211yesmaximal, characteristic, complemented
7#14271367C211yesmaximal, characteristic, complemented
8#14271316C211yesmaximal, characteristic
9#14271313C211yesmaximal, characteristic
10#14271266C211yesmaximal, characteristic, complemented
11#14271262C211yesmaximal, characteristic, complemented
12#14271250C211yesmaximal, characteristic, complemented
13#14271248C211yesmaximal, characteristic, complemented
14#14271221C211yesmaximal, characteristic, complemented
15C29×#485C211yesmaximal, characteristic, complemented
16C22×D116C2211yescharacteristic
17C29×C22⋊Q8C2211yescharacteristic
18C29×#117C2211yescharacteristic
19Q8×Dic29C2211yescharacteristic, complemented
20#11745306C2211yescharacteristic, complemented
21C2×#90784C2211yescharacteristic
22C2×#90784C2211yescharacteristic
23#11745288C2211yescharacteristic
24#11745286C2211yescharacteristic
25C2×#90773C2211yescharacteristic
26C2×#90773C2211yescharacteristic
27#11745255C2211yescharacteristic
28#11745255C2211yescharacteristic
29#11745255C2211yescharacteristic
30#11745255C2211yescharacteristic
31#11745252—21no—
32#11745252C2211yescharacteristic, complemented
33#11745251—21no—
34#11745249C2211yescharacteristic, complemented
35C22⋊C4×D29—21no—
36C22⋊C4×D29—21no—
37#11745241—21no—
38#11745241—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#11745158C2211yescharacteristic, complemented
54#11745158C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C2×D116—21no—
63C2×D116—22no—
64C2×D116—22no—
65C2×D116C2311yescharacteristic
66C2×D116C2311yescharacteristic
67C2×C4×D29—21no—
68C2×C4×D29—21no—
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×Dic58C2311yescharacteristic
72C2×C8×C29C2311yescharacteristic
73C2×C8×C29C2311yescharacteristic
74C4⋊C4×C29—21no—
75C4⋊C4×C29C2311yescharacteristic
76C4⋊C4×C29C2311yescharacteristic
77C4⋊C4×C29C2311yescharacteristic
78C22⋊C4×C29—21no—
79C22⋊C4×C29—21no—
80C42×C29—21no—
81C22⋊Dic29—21no—
82C22⋊Dic29D411yescharacteristic
83C22⋊Dic29D411yescharacteristic
84#90784—22no—
85#90784—22no—
86#90781—21no—
87#90781—21no—
88#90781—21no—
89#90781—21no—
90C4⋊Dic29—21no—
91C4⋊Dic29—21no—
92C4⋊Dic29D411yescharacteristic
93C4⋊Dic29D411yescharacteristic
94C4⋊Dic29C2311yescharacteristic
95#90779—21no—
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100C4×Dic29—21no—
101C4×Dic29—21no—
102C4×Dic29C2311yescharacteristic
103C4×Dic29C2311yescharacteristic
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106#90773—22no—
107#90773—22no—
108C23×C29C2×D411yescharacteristic
109C22×D29—21no—
110C22×D29—21no—
111C22×D29—24no—
112C22×D29—81no—
113C22×D29—81no—
114Q8×C29—21no—
115Q8×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C2×Dic29—21no—
125C2×Dic29—21no—
126C2×Dic29C2×D411yescharacteristic
127C2×Dic29C2×D411yescharacteristic
128C2×Dic29C2×D411yescharacteristic
129C2×Dic29C2×D411yescharacteristic
130D116—24no—
131D116—21no—
132D116—21no—
133D116#4112yes—
134D116#4112yes—
135C4×D29—81no—
136C4×D29—81no—
137C4×D29—81no—
138C4×D29—81no—
139Dic58—21no—
140Dic58—21no—
141C8×C29—21no—
142C8×C29—21no—
143#6597—21no—
144#6597—21no—
145#3123—291nomaximal, Sylow
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—21no—
149C22×C29C22×D411yescharacteristic
150C2×D29—22no—
151C2×D29—22no—
152C2×D29—41no—
153C2×D29—41no—
154C2×D29—41no—
155C2×D29—41no—
156C2×D29—84no—
157C4×C29—21no—
158C4×C29—41no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29—41no—
162C4×C29C2×#4111yescharacteristic
163C4×C29C2×#4111yescharacteristic
164Dic29—21no—
165Dic29—21no—
166Dic29—21no—
167Dic29—21no—
168Dic29—41no—
169Dic29—41no—
170#541—291no—
171#518—291no—
172#485—291no—
173#485D2911yescharacteristic, complemented
174#478—291no—
175#478—291no—
176#461—291no—
177#461—291no—
178#450—291no—
179#450—291no—
180#440—291no—
181#440—291no—
182C4×SD16—291no—
183C4×SD16—291no—
184#433—291no—
185C2×C29—41no—
186C2×C29#52511yescharacteristic
187C2×C29#57711yescharacteristic
188C2×C29#57711yescharacteristic
189D29—42no—
190D29—42no—
191C22×D4—291no—
192C2×SD16—291no—
193C2×SD16—291no—
194C2×SD16—291no—
195C2×SD16—291no—
196C4⋊Q8—291no—
197#126—581no—
198#126—581no—
199#125—291no—
200#125—581no—
201#125—581no—
202C22⋊Q8—291no—
203C22⋊Q8C2×D2911yescharacteristic
204C4×Q8—291no—
205C4×Q8—291no—
206C4×D4—291no—
207C4×D4—291no—
208C4×D4—291no—
209C4×D4—291no—
210C4×D4—581no—
211C4×D4—581no—
212#117—291no—
213#117C2×D2911yescharacteristic
214C2×C22⋊C4—581no—
215C2×C22⋊C4—581no—
216#107—291no—
217#107C2×D2911yescharacteristic, complemented
218#106—291no—
219#106C2×D2911yescharacteristic, complemented
220C4⋊C8—291no—
221C4⋊C8—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—
230C22⋊C8—291no—
231C22⋊C8C2×D2911yescharacteristic
232#97—291no—
233C4×C8—291no—
234C29#312311yescharacteristic, complemented, Sylow
235C24—581no—
236C2×Q8—291no—
237C2×Q8C22×D2911yescharacteristic
238C2×D4—291no—
239C2×D4—291no—
240C2×D4—582no—
241C2×D4—582no—
242C2×D4—581no—
243C22×C4—581no—
244C22×C4—581no—
245C22×C4—581no—
246C22×C4—581no—
247C22×C4C22×D2911yescharacteristic
248SD16—582no—
249SD16—582no—
250SD16—582no—
251SD16—582no—
252C2×C8—291no—
253C2×C8—291no—
254C2×C8C22×D2911yescharacteristic
255C2×C8C22×D2911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—291no—
258C4⋊C4—291no—
259C4⋊C4—291no—
260C4⋊C4—581no—
261C4⋊C4—581no—
262C4⋊C4—581no—
263C4⋊C4—581no—
264C4⋊C4—581no—
265C4⋊C4—581no—
266C4⋊C4—581no—
267C4⋊C4C22×D2911yescharacteristic
268C4⋊C4C22×D2911yescharacteristic
269C4⋊C4C22×D2911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—291no—
273C22⋊C4—291no—
274C22⋊C4—581no—
275C22⋊C4—581no—
276C22⋊C4—581no—
277C22⋊C4—581no—
278C22⋊C4—581no—
279C42—21no—
280C42—291no—
281C42—291no—
282C42—581no—
283C42—581no—
284C23—584no—
285C23—581no—
286C23—581no—
287C23—2321no—
288C23—2321no—
289C23D4×D2911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—581no—
293Q8—581no—
294D4—292no—
295D4—292no—
296D4—584no—
297D4—581no—
298D4—581no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—291no—
306C2×C4—291no—
307C2×C4—291no—
308C2×C4—291no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—2321no—
312C2×C4—2321no—
313C2×C4—2321no—
314C2×C4—2321no—
315C2×C4D4×D2911yescharacteristic
316C2×C4C23×D2911yescharacteristic
317C8—21no—
318C8—21no—
319C8—581no—
320C8—581no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—582no—
325C22—582no—
326C22—1161no—
327C22—1161no—
328C22—1161no—
329C22—1161no—
330C22—2324no—
331C22C2×D4×D2911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—581no—
338C4—581no—
339C4—581no—
340C4—581no—
341C4—1161no—
342C4—1161no—
343C4#41×D2911yescharacteristic
344C4#41×D2911yescharacteristic
345C2—41no—
346C2—1162no—
347C2—1162no—
348C2#1427167111yescharacteristic
349C2#1427197011yescharacteristic
350C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#485C2
socleC22×C29C22×D4
prime radicalC22×D116C22
hypercenter#485D29
hypocenterC29#3123
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. #14271773C2semidirect
3. #14271504C2semidirect
4. #14271466C2semidirect
5. #14271462C2semidirect
6. #14271367C2semidirect
7. #14271367C2semidirect
10. #14271266C2semidirect
11. #14271262C2semidirect
12. #14271250C2semidirect
13. #14271248C2semidirect
14. #14271221C2semidirect
15. C29×#485C2semidirect
19. Q8×Dic29C22semidirect
20. #11745306C22semidirect
32. #11745252C22semidirect
34. #11745249C22semidirect
41. C29×#107C22semidirect
42. C29×#106C22semidirect
43. C29×#103C22semidirect
44. C29×#103C22semidirect
49. #11745163C22semidirect
50. #11745162C22semidirect
51. #11745162C22semidirect
52. C8×Dic29C22semidirect
53. #11745158C22semidirect
54. #11745158C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
173. #485D29semidirect
217. #107C2×D29semidirect
219. #106C2×D29semidirect
224. #103C2×D29semidirect
225. #103C2×D29semidirect
234. C29#3123semidirect

Maximal subgroups

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

subgroupindex
#142717732
#142716372
#142715042
#142714662
#142714622
#142713672
#142713162
#142713132
#142712662
#142712622
#142712502
#142712482
#142712212
C29×#4852
#312329