Finite Group Databasebeta

← #16831335

Subgroups — #16831335

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271860C211yesmaximal, characteristic, complemented
2#14271801C211yesmaximal, characteristic, complemented
3#14271519C211yesmaximal, characteristic, complemented
4#14271497C211yesmaximal, characteristic, complemented
5#14271488C211yesmaximal, characteristic, complemented
6#14271465C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic, complemented
8#14271389C211yesmaximal, characteristic, complemented
9#14271380C211yesmaximal, characteristic, complemented
10#14271295C211yesmaximal, characteristic, complemented
11D8×Dic29C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271159C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic, complemented
19C2×D8×C29C2211yescharacteristic
20C29×#121C2211yescharacteristic, complemented
21#11745309C2211yescharacteristic
22#11745308C2211yescharacteristic
23#11745301—21no—
24#11745300—21no—
25#11745300C2211yescharacteristic
26#11745299—21no—
27#11745297—21no—
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic, complemented
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745291—21no—
33C4×C22⋊D29C2211yescharacteristic
34C2×#90781—21no—
35#11745288C2211yescharacteristic, complemented
36C22×#6597C2211yescharacteristic, complemented
37C2×C8×D29C2211yescharacteristic
38C4⋊C4×D29C2211yescharacteristic
39#11745252C2211yescharacteristic, complemented
40#11745243—21no—
41#11745241—21no—
42C29×#103C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745183C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic, complemented
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745168C2211yescharacteristic
53#11745166C2211yescharacteristic, complemented
54#11745165C2211yescharacteristic, complemented
55#11745162C2211yescharacteristic, complemented
56C8×Dic29C2211yescharacteristic, complemented
57#11745157C2211yescharacteristic
58#11745155C2211yescharacteristic, complemented
59C23×D29—21no—
60#41×C29—22no—
61#41×C29—41no—
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—21no—
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29—21no—
68C22×C4×C29C2311yescharacteristic
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29D411yescharacteristic
73C22×Dic29—21no—
74C22×Dic29—21no—
75D4×D29—22no—
76D4×D29—41no—
77C2×D116C2311yescharacteristic
78C2×C4×D29—21no—
79C2×C4×D29C2311yescharacteristic
80SD16×C29—41no—
81D8×C29—22no—
82C2×C8×C29C2311yescharacteristic
83C2×C8×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29D411yescharacteristic
91#90782—41no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779D411yescharacteristic
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C8×D29—41no—
111C23×C29—21no—
112C23×C29—21no—
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29—42no—
116C22×D29—42no—
117C22×D29—81no—
118C22×D29C2×D411yescharacteristic
119Q8×C29—21no—
120Q8×C29—21no—
121D4×C29—21no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—42no—
125D4×C29—81no—
126D4×C29#4112yes—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—42no—
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2411yescharacteristic
134C22⋊D29—22no—
135C22⋊D29—42no—
136C22⋊D29—42no—
137C22⋊D29—81no—
138C2×Dic29—21no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29—81no—
142C2×Dic29—81no—
143C2×Dic29C2×D411yescharacteristic
144C2×Dic29C2×D411yescharacteristic
145C2×Dic29C2×D411yescharacteristic
146D116—21no—
147D116—21no—
148C4×D29—21no—
149C4×D29—21no—
150C4×D29—81no—
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3297—291nomaximal, Sylow
156C22×C29—22no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—41no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29C22×D411yescharacteristic
166C2×D29—21no—
167C2×D29—21no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—84no—
172C2×D29#13512yes—
173C4×C29—21no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29C2×#4111yescharacteristic
177C4×C29H(5,𝔽2)11yescharacteristic
178Dic29—21no—
179Dic29—21no—
180Dic29—21no—
181Dic29—41no—
182Dic29—41no—
183Dic29—41no—
184#553—291no—
185#546—291no—
186#488—291no—
187#484—291no—
188#482—291no—
189#478—291no—
190#466—291no—
191#465—291no—
192#463—291no—
193#449D2911yescharacteristic, complemented
194#447—291no—
195C4×D8—291no—
196C8×D4—291no—
197#416—291no—
198C2×#102—291no—
199C2×C29—42no—
200C2×C29—41no—
201C2×C29—81no—
202C2×C29#54611yescharacteristic
203C2×C29C2×#13511yescharacteristic
204C2×C29#57611yescharacteristic
205D29—22no—
206D29—81no—
207C2×#41C2×D2911yescharacteristic
208C22×D4—291no—
209C2×SD16C2×D2911yescharacteristic, complemented
210C2×D8—291no—
211C2×D8C2×D2911yescharacteristic
212C22×C8—291no—
213C22×C8—291no—
214#126—581no—
215#125—291no—
216#124—291no—
217#123—581no—
218#123—581no—
219C22⋊Q8—291no—
220#121—291no—
221#121—291no—
222#121—581no—
223#121—581no—
224#121C2×D2911yescharacteristic, complemented
225#120—581no—
226C4×D4—291no—
227C4×D4—291no—
228C4×D4—291no—
229C4×D4—581no—
230#117—291no—
231C2×C4⋊C4—291no—
232C2×C22⋊C4—581no—
233#107—291no—
234#107—291no—
235#106—291no—
236C4⋊C8—291no—
237#103—291no—
238#103—291no—
239#103C2×D2911yescharacteristic, complemented
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102C2×D2911yescharacteristic
247C22⋊C8—291no—
248C22⋊C8C2×D2911yescharacteristic, complemented
249C4×C8—291no—
250C29#329711yescharacteristic, complemented, Sylow
251C24—581no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D2911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—291no—
258C2×D4—291no—
259C2×D4—581no—
260C2×D4—582no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—1161no—
264C2×D4C22×D2911yescharacteristic
265C2×D4C22×D2911yescharacteristic
266C22×C4—21no—
267C22×C4—291no—
268C22×C4—581no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4C22×D2911yescharacteristic
272SD16—41no—
273D8—22no—
274D8—1161no—
275C2×C8—291no—
276C2×C8—291no—
277C2×C8—1161no—
278C2×C8—1161no—
279C2×C8C22×D2911yescharacteristic
280C2×C8C22×D2911yescharacteristic
281C4⋊C4—291no—
282C4⋊C4—291no—
283C4⋊C4—291no—
284C4⋊C4—291no—
285C4⋊C4—581no—
286C4⋊C4—581no—
287C4⋊C4—581no—
288C4⋊C4—581no—
289C4⋊C4C22×D2911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—291no—
292C22⋊C4—291no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C42—291no—
302C42—581no—
303C23—21no—
304C23—21no—
305C23—291no—
306C23—581no—
307C23—1162no—
308C23—1162no—
309C23—2321no—
310C23D4×D2911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—582no—
319D4—581no—
320D4—581no—
321D4—1162no—
322D4—1162no—
323D4—2321no—
324D4#9080712yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—291no—
331C2×C4—291no—
332C2×C4—291no—
333C2×C4—581no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—581no—
338C2×C4—2321no—
339C2×C4—2321no—
340C2×C4—2321no—
341C2×C4D4×D2911yescharacteristic
342C2×C4C23×D2911yescharacteristic
343C8—21no—
344C8—21no—
345C8—581no—
346C8—581no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—292no—
357C22—581no—
358C22—581no—
359C22—1161no—
360C22—1161no—
361C22—1161no—
362C22—2324no—
363C22C2×D4×D2911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—581no—
368C4—581no—
369C4—581no—
370C4—1161no—
371C4—1161no—
372C4—1161no—
373C4C2×#9080711yescharacteristic
374C4#1174535911yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—582no—
379C2—2321no—
380C2#1427180011yescharacteristic
381C2#135×D2911yescharacteristic
382C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3297
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14271860C2semidirect
2. #14271801C2semidirect
3. #14271519C2semidirect
4. #14271497C2semidirect
5. #14271488C2semidirect
6. #14271465C2semidirect
7. #14271397C2semidirect
8. #14271389C2semidirect
9. #14271380C2semidirect
10. #14271295C2semidirect
11. D8×Dic29C2semidirect
12. #14271226C2semidirect
13. #14271159C2semidirect
14. #102×D29C2semidirect
15. C29×#449C2semidirect
18. C2×SD16×C29C22semidirect
20. C29×#121C22semidirect
29. D4×Dic29C22semidirect
35. #11745288C22semidirect
36. C22×#6597C22semidirect
39. #11745252C22semidirect
42. C29×#103C22semidirect
44. C29×C22⋊C8C22semidirect
45. #11745183C22semidirect
46. #11745183C22semidirect
49. #11745180C22semidirect
53. #11745166C22semidirect
54. #11745165C22semidirect
55. #11745162C22semidirect
56. C8×Dic29C22semidirect
58. #11745155C22semidirect
193. #449D29semidirect
209. C2×SD16C2×D29semidirect
224. #121C2×D29semidirect
239. #103C2×D29semidirect
248. C22⋊C8C2×D29semidirect
250. C29#3297semidirect

Maximal subgroups

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

subgroupindex
#142718602
#142718012
#142715192
#142714972
#142714882
#142714652
#142713972
#142713892
#142713802
#142712952
D8×Dic292
#142712262
#142711592
#102×D292
C29×#4492
#329729