Finite Group Databasebeta

← #16831344

Subgroups — #16831344

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#14271859C211yesmaximal, characteristic, complemented
2#14271809C211yesmaximal, characteristic, complemented
3#14271518C211yesmaximal, characteristic, complemented
4#14271499C211yesmaximal, characteristic, complemented
5#14271488C211yesmaximal, characteristic, complemented
6#14271464C211yesmaximal, characteristic, complemented
7#14271399C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271379C211yesmaximal, characteristic, complemented
10#14271310C211yesmaximal, characteristic, complemented
11#14271299C211yesmaximal, characteristic, complemented
12C4×D232C211yesmaximal, characteristic, complemented
13#14271160C211yesmaximal, characteristic, complemented
14C2×#11745169C211yesmaximal, characteristic, complemented
15C8×D4×C29C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C22×D116C2211yescharacteristic
18C22×C8×C29C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745301—21no—
22#11745299—21no—
23#11745292C2211yescharacteristic
24#11745292C2211yescharacteristic
25#11745292C2211yescharacteristic, complemented
26#11745288C2211yescharacteristic, complemented
27C2×C4⋊Dic29C2211yescharacteristic
28#11745286C2211yescharacteristic
29C2×D232C2211yescharacteristic
30C2×D232C2211yescharacteristic
31C2×#90773C2211yescharacteristic, complemented
32#11745260—21no—
33#11745256—21no—
34#11745246—21no—
35#11745245—21no—
36#11745243—21no—
37C22⋊C4×D29—21no—
38#11745237C2211yescharacteristic
39C4×D116C2211yescharacteristic
40C4×D116C2211yescharacteristic, complemented
41#11745232C2211yescharacteristic, complemented
42C29×C4⋊C8C2211yescharacteristic, complemented
43C29×C22⋊C8C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic, complemented
45C4×C8×C29C2211yescharacteristic, complemented
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745169C2211yescharacteristic, complemented
53#11745166C2211yescharacteristic, complemented
54#11745166C2211yescharacteristic, complemented
55#11745165C2211yescharacteristic, complemented
56#11745164C2211yescharacteristic, complemented
57#11745164C2211yescharacteristic, complemented
58#11745164C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29D411yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C22×Dic29—21no—
68#90805—22no—
69#90805—41no—
70C2×D116—22no—
71C2×D116—21no—
72C2×D116—41no—
73C2×D116C2311yescharacteristic
74C2×D116C2311yescharacteristic
75C2×D116C2311yescharacteristic
76C2×C4×D29—21no—
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×Dic58C2311yescharacteristic
80C2×C8×C29—41no—
81C2×C8×C29—41no—
82C2×C8×C29C2311yescharacteristic
83C2×C8×C29C2311yescharacteristic
84C2×C8×C29C2311yescharacteristic
85C2×C8×C29C2311yescharacteristic
86C4⋊C4×C29D411yescharacteristic
87C22⋊C4×C29D411yescharacteristic
88C22⋊C4×C29D411yescharacteristic
89C42×C29C2311yescharacteristic
90C22⋊Dic29—21no—
91C22⋊Dic29—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781—21no—
99C4⋊Dic29—21no—
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103C4⋊Dic29C2311yescharacteristic
104#90779—21no—
105#90779—21no—
106#90779—21no—
107C4×Dic29—21no—
108D232—22no—
109D232—41no—
110#90773—41no—
111C23×C29C2×D411yescharacteristic
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—42no—
117C22×D29—42no—
118C22×D29—81no—
119D4×C29—22no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2411yescharacteristic
129C22⋊D29—42no—
130C22⋊D29—42no—
131C22⋊D29—81no—
132C22⋊D29—81no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—81no—
139D116—21no—
140D116—21no—
141D116—21no—
142D116—21no—
143D116—21no—
144D116—42no—
145D116#4112yes—
146C4×D29—42no—
147C4×D29—81no—
148C4×D29—81no—
149Dic58—21no—
150Dic58—21no—
151C8×C29—21no—
152C8×C29—21no—
153C8×C29—21no—
154C8×C29—21no—
155#3297—291nomaximal, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29#13512yes—
162C22×C29C22×D411yescharacteristic
163C2×D29—22no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—41no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—84no—
173C4×C29—21no—
174C4×C29—21no—
175C4×C29—21no—
176C4×C29—21no—
177C4×C29C2×#4111yescharacteristic
178C4×C29H(5,𝔽2)11yescharacteristic
179Dic29—41no—
180Dic29—41no—
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#449—291no—
194#447—291no—
195C4×D8—291no—
196C8×D4D2911yescharacteristic, complemented
197#416—291no—
198C2×#102—291no—
199C2×C29—22no—
200C2×C29—41no—
201C2×C29#54611yescharacteristic
202C2×C29C2×#13511yescharacteristic
203C2×C29#57611yescharacteristic
204D29—42no—
205D29—81no—
206D29—81no—
207C2×#41—291no—
208C22×D4—291no—
209C2×SD16—291no—
210C2×D8—291no—
211C2×D8—291no—
212C22×C8C2×D2911yescharacteristic
213C22×C8C2×D2911yescharacteristic, complemented
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—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#107—291no—
235#106—291no—
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#102—291no—
246#102—291no—
247C22⋊C8C2×D2911yescharacteristic
248C22⋊C8C2×D2911yescharacteristic, complemented
249C4×C8C2×D2911yescharacteristic, complemented
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—582no—
259C2×D4—581no—
260C2×D4—581no—
261C2×D4—581no—
262C2×D4—581no—
263C2×D4—581no—
264C2×D4—1161no—
265C2×D4D11611yescharacteristic
266C22×C4—581no—
267C22×C4—581no—
268C22×C4—581no—
269C22×C4—581no—
270C22×C4C22×D2911yescharacteristic
271C22×C4C22×D2911yescharacteristic
272SD16—1161no—
273D8—582no—
274D8—1161no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D2911yescharacteristic
278C2×C8C22×D2911yescharacteristic
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⋊C4D11611yescharacteristic
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C22⋊C4—581no—
295C22⋊C4—581no—
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4D11611yescharacteristic
300C22⋊C4D11611yescharacteristic
301C42—581no—
302C42C22×D2911yescharacteristic
303C23—581no—
304C23—581no—
305C23—581no—
306C23—1162no—
307C23—1162no—
308C23—2321no—
309C23C2×D11611yescharacteristic
310C23C2×D11611yescharacteristic
311Q8—581no—
312Q8—581no—
313D4—22no—
314D4—292no—
315D4—581no—
316D4—581no—
317D4—581no—
318D4—581no—
319D4—581no—
320D4—1162no—
321D4—1162no—
322D4—1162no—
323D4—2321no—
324D4—2321no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—581no—
330C2×C4—581no—
331C2×C4—581no—
332C2×C4—581no—
333C2×C4—581no—
334C2×C4—1162no—
335C2×C4—2321no—
336C2×C4—2321no—
337C2×C4—2321no—
338C2×C4C2×D11611yescharacteristic
339C2×C4C2×D11611yescharacteristic
340C2×C4C2×D11611yescharacteristic
341C2×C4C2×D11611yescharacteristic
342C2×C4C23×D2911yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—582no—
353C22—1161no—
354C22—1161no—
355C22—1161no—
356C22—1161no—
357C22—1161no—
358C22—1161no—
359C22—1161no—
360C22—1161no—
361C22—2324no—
362C22#1174526612yes—
363C22C22×D11611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—1161no—
369C4—1161no—
370C4—1161no—
371C4—1161no—
372C4—1161no—
373C4#1174535911yescharacteristic
374C4#41×D2911yescharacteristic
375C2—22no—
376C2—41no—
377C2—1162no—
378C2—2321no—
379C2—2321no—
380C2#1427180811yescharacteristic
381C2C2×#1174526611yescharacteristic
382C2#1427196811yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC8×D4×C29C2
socleC22×C29C22×D4
hypercenterC8×D4D29
hypocenterC29#3297
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14271859C2semidirect
2. #14271809C2semidirect
3. #14271518C2semidirect
4. #14271499C2semidirect
5. #14271488C2semidirect
6. #14271464C2semidirect
7. #14271399C2semidirect
8. #14271392C2semidirect
9. #14271379C2semidirect
10. #14271310C2semidirect
11. #14271299C2semidirect
12. C4×D232C2semidirect
13. #14271160C2semidirect
14. C2×#11745169C2semidirect
15. C8×D4×C29C2semidirect
19. C22×C8×C29C22semidirect
25. #11745292C22semidirect
26. #11745288C22semidirect
31. C2×#90773C22semidirect
40. C4×D116C22semidirect
41. #11745232C22semidirect
42. C29×C4⋊C8C22semidirect
44. C29×C22⋊C8C22semidirect
45. C4×C8×C29C22semidirect
52. #11745169C22semidirect
53. #11745166C22semidirect
54. #11745166C22semidirect
55. #11745165C22semidirect
56. #11745164C22semidirect
57. #11745164C22semidirect
58. #11745164C22semidirect
196. C8×D4D29semidirect
213. C22×C8C2×D29semidirect
236. C4⋊C8C2×D29semidirect
248. C22⋊C8C2×D29semidirect
249. 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
#142718592
#142718092
#142715182
#142714992
#142714882
#142714642
#142713992
#142713922
#142713792
#142713102
#142712992
C4×D2322
#142711602
C2×#117451692
C8×D4×C292
#329729