Finite Group Databasebeta

← #16831339

Subgroups — #16831339

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#14271866C211yesmaximal, characteristic, complemented
2#14271808C211yesmaximal, characteristic, complemented
3#14271520C211yesmaximal, characteristic, complemented
4#14271500C211yesmaximal, characteristic, complemented
5#14271489C211yesmaximal, characteristic, complemented
6#14271400C211yesmaximal, characteristic, complemented
7#14271393C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271309C211yesmaximal, characteristic, complemented
10#14271298C211yesmaximal, characteristic, complemented
11C4×#90782C211yesmaximal, characteristic, complemented
12#14271228C211yesmaximal, characteristic, complemented
13#14271156C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#478C211yesmaximal, characteristic, complemented
16C2×#90807C2211yescharacteristic
17C2×D4×D29C2211yescharacteristic
18C29×#125C2211yescharacteristic, complemented
19C4×D4×C29C2211yescharacteristic
20C2×#90782C2211yescharacteristic
21#11745292—21no—
22C2×#90781—21no—
23C2×D232C2211yescharacteristic
24C2×#90773C2211yescharacteristic, complemented
25C2×C8×D29C2211yescharacteristic
26C2×C8×D29C2211yescharacteristic, complemented
27#11745260—21no—
28#11745259C2211yescharacteristic
29#11745257—21no—
30#11745257C2211yescharacteristic
31#11745257C2211yescharacteristic
32#11745257C2211yescharacteristic, complemented
33#11745256—21no—
34#11745255—21no—
35#11745254C2211yescharacteristic, complemented
36C4⋊C4×D29C2211yescharacteristic
37#11745248—21no—
38#11745244—21no—
39#11745237C2211yescharacteristic
40C4×D116C2211yescharacteristic
41C4×D116C2211yescharacteristic, complemented
42C29×#107C2211yescharacteristic, complemented
43C29×#106C2211yescharacteristic, complemented
44C29×C4⋊C8C2211yescharacteristic, complemented
45C29×#102C2211yescharacteristic
46C29×#102C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745168C2211yescharacteristic, complemented
51#11745164C2211yescharacteristic, complemented
52#11745158C2211yescharacteristic, complemented
53#11745158C2211yescharacteristic, complemented
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic, complemented
57#11745155C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C22×Dic29—21no—
65#90807—22no—
66#90807—41no—
67D4×D29—22no—
68D4×D29—41no—
69C2×D116—21no—
70C2×D116—21no—
71C2×D116—21no—
72C2×D116D411yescharacteristic
73C2×D116C2311yescharacteristic
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29—21no—
77C2×C4×D29C2311yescharacteristic
78C2×C4×D29C2311yescharacteristic
79C2×Dic58C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C42×C29C2311yescharacteristic
89#90782—22no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781D411yescharacteristic
99#90781D411yescharacteristic
100C4⋊Dic29—21no—
101C4⋊Dic29D411yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104C4×Dic29—21no—
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107D232—41no—
108#90773—41no—
109C8×D29—41no—
110C8×D29—41no—
111C23×C29—21no—
112C22×D29—21no—
113C22×D29—21no—
114C22×D29—42no—
115C22×D29—42no—
116C22×D29—81no—
117C22×D29C2×D411yescharacteristic
118C22×D29C2×D411yescharacteristic
119D4×C29—21no—
120D4×C29#4112yes—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—81no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—42no—
129C22⋊D29—42no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—42no—
133C2×Dic29C2×D411yescharacteristic
134C2×Dic29C2×D411yescharacteristic
135D116—22no—
136D116—21no—
137D116—21no—
138D116—21no—
139D116—21no—
140D116—42no—
141D116—81no—
142D116—81no—
143C4×D29—21no—
144C4×D29—21no—
145C4×D29—21no—
146C4×D29—21no—
147C4×D29—81no—
148C4×D29—81no—
149Dic58—21no—
150Dic58—21no—
151C8×C29—21no—
152C8×C29—21no—
153#6597—21no—
154#6597—21no—
155#3297—291nomaximal, Sylow
156C22×C29—22no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—21no—
163C2×D29—21no—
164C2×D29—21no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—84no—
172C2×D29#13512yes—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—41no—
176C4×C29—41no—
177C4×C29—41no—
178C4×C29C2×#4111yescharacteristic
179C4×C29H(5,𝔽2)11yescharacteristic
180Dic29—21no—
181Dic29—21no—
182Dic29—41no—
183Dic29—41no—
184#553—291no—
185#546—291no—
186#488—291no—
187#484—291no—
188#482—291no—
189#478D2911yescharacteristic, complemented
190#466—291no—
191#465—291no—
192#463—291no—
193#449—291no—
194#447—291no—
195C4×D8—291no—
196C8×D4—291no—
197#416—291no—
198C2×#102—291no—
199C2×C29—42no—
200C2×C29#54611yescharacteristic
201C2×C29C2×#13511yescharacteristic
202C2×C29#57611yescharacteristic
203D29—22no—
204D29—41no—
205D29—81no—
206D29—81no—
207C2×#41—291no—
208C22×D4—291no—
209C2×SD16—291no—
210C2×D8—291no—
211C2×D8—291no—
212C22×C8—291no—
213C22×C8—291no—
214#126—581no—
215#125C2×D2911yescharacteristic, complemented
216#124—291no—
217#123—581no—
218#123—581no—
219C22⋊Q8—291no—
220#121—291no—
221#121—291no—
222#121—291no—
223#121—581no—
224#121—581no—
225#120—581no—
226C4×D4—291no—
227C4×D4—291no—
228C4×D4—581no—
229C4×D4C2×D2911yescharacteristic
230#117—291no—
231C2×C4⋊C4—291no—
232C2×C22⋊C4—581no—
233#107—291no—
234#107C2×D2911yescharacteristic, complemented
235#106C2×D2911yescharacteristic, complemented
236C4⋊C8C2×D2911yescharacteristic, complemented
237#103—291no—
238#103—291no—
239#103—291no—
240#102—291no—
241#102—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102C2×D2911yescharacteristic
246#102C2×D2911yescharacteristic
247C22⋊C8—291no—
248C22⋊C8—291no—
249C4×C8—291no—
250C29#329711yescharacteristic, complemented, Sylow
251C24—581no—
252#41—582no—
253#41—1161no—
254C2×Q8—291no—
255C2×D4—291no—
256C2×D4—291no—
257C2×D4—291no—
258C2×D4—581no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—582no—
263C2×D4—581no—
264C2×D4—1161no—
265C2×D4C22×D2911yescharacteristic
266C22×C4—21no—
267C22×C4—291no—
268C22×C4—291no—
269C22×C4—581no—
270C22×C4—581no—
271C22×C4—581no—
272SD16—1161no—
273D8—582no—
274D8—1161no—
275C2×C8—291no—
276C2×C8—291no—
277C2×C8—1161no—
278C2×C8—1161no—
279C2×C8C22×D2911yescharacteristic
280C2×C8C22×D2911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—291no—
284C4⋊C4—291no—
285C4⋊C4—581no—
286C4⋊C4—581no—
287C4⋊C4C22×D2911yescharacteristic
288C4⋊C4C22×D2911yescharacteristic
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—581no—
302C42C22×D2911yescharacteristic
303C23—21no—
304C23—291no—
305C23—291no—
306C23—581no—
307C23—581no—
308C23—1162no—
309C23—1162no—
310C23—2321no—
311Q8—581no—
312Q8—581no—
313D4—21no—
314D4—582no—
315D4—581no—
316D4—581no—
317D4—581no—
318D4—581no—
319D4—1162no—
320D4—1162no—
321D4—1162no—
322D4—2321no—
323D4—2321no—
324D4#9080912yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—291no—
330C2×C4—291no—
331C2×C4—581no—
332C2×C4—581no—
333C2×C4—581no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—1162no—
338C2×C4—2321no—
339C2×C4—2321no—
340C2×C4D4×D2911yescharacteristic
341C2×C4D4×D2911yescharacteristic
342C2×C4C23×D2911yescharacteristic
343C8—21no—
344C8—21no—
345C8—581no—
346C8—581no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—292no—
351C22—581no—
352C22—581no—
353C22—581no—
354C22—581no—
355C22—581no—
356C22—1161no—
357C22—1161no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22—1161no—
362C22—2324no—
363C22C2×D4×D2911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—581no—
370C4—581no—
371C4—1161no—
372C4—1161no—
373C4C2×#9080911yescharacteristic
374C4#1174536411yescharacteristic
375C2—42no—
376C2—582no—
377C2—1161no—
378C2—2321no—
379C2—2321no—
380C2#1427180411yescharacteristic
381C2#135×D2911yescharacteristic
382C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#478C2
socleC22×C29C22×D4
hypercenter#478D29
hypocenterC29#3297
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14271866C2semidirect
2. #14271808C2semidirect
3. #14271520C2semidirect
4. #14271500C2semidirect
5. #14271489C2semidirect
6. #14271400C2semidirect
7. #14271393C2semidirect
8. #14271379C2semidirect
9. #14271309C2semidirect
10. #14271298C2semidirect
11. C4×#90782C2semidirect
12. #14271228C2semidirect
13. #14271156C2semidirect
14. #102×D29C2semidirect
15. C29×#478C2semidirect
18. C29×#125C22semidirect
24. C2×#90773C22semidirect
26. C2×C8×D29C22semidirect
32. #11745257C22semidirect
35. #11745254C22semidirect
41. C4×D116C22semidirect
42. C29×#107C22semidirect
43. C29×#106C22semidirect
44. C29×C4⋊C8C22semidirect
50. #11745168C22semidirect
51. #11745164C22semidirect
52. #11745158C22semidirect
53. #11745158C22semidirect
56. #11745157C22semidirect
57. #11745155C22semidirect
58. C4×#6597C22semidirect
189. #478D29semidirect
215. #125C2×D29semidirect
234. #107C2×D29semidirect
235. #106C2×D29semidirect
236. C4⋊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
#142718662
#142718082
#142715202
#142715002
#142714892
#142714002
#142713932
#142713792
#142713092
#142712982
C4×#907822
#142712282
#142711562
#102×D292
C29×#4782
#329729