Finite Group Databasebeta

← #16831455

Subgroups — #16831455

Order 3712.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271817C211yesmaximal, characteristic, complemented
2#14271809C211yesmaximal, characteristic, complemented
3#14271523C211yesmaximal, characteristic, complemented
4#14271494C211yesmaximal, characteristic, complemented
5#14271482C211yesmaximal, characteristic, complemented
6#14271454C211yesmaximal, characteristic, complemented
7#14271416C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271379C211yesmaximal, characteristic, complemented
10#14271310C211yesmaximal, characteristic, complemented
11#14271299C211yesmaximal, characteristic, complemented
12#14271276C211yesmaximal, characteristic, complemented
13#14271165C211yesmaximal, characteristic, complemented
14C2×#11745169C211yesmaximal, characteristic, complemented
15C29×#435C211yesmaximal, characteristic, complemented
16C2×#90807—21no—
17C2×#90805C2211yescharacteristic
18C22×D116C2211yescharacteristic
19C2×M16×C29C2211yescharacteristic, complemented
20C22×C8×C29C2211yescharacteristic
21C4×D4×C29C2211yescharacteristic
22#11745299—21no—
23#11745292C2211yescharacteristic
24#11745292C2211yescharacteristic
25#11745292C2211yescharacteristic, complemented
26C2×C4⋊Dic29C2211yescharacteristic
27C2×C4⋊Dic29C2211yescharacteristic, complemented
28#11745286C2211yescharacteristic
29C2×D232C2211yescharacteristic
30C2×D232C2211yescharacteristic
31C2×#90773C2211yescharacteristic, complemented
32#11745259—21no—
33#11745256—21no—
34#11745248—21no—
35#11745248—21no—
36#11745246—21no—
37C22⋊C4×D29—21no—
38#11745237C2211yescharacteristic
39C4×D116C2211yescharacteristic
40C4×D116C2211yescharacteristic, complemented
41#11745231C2211yescharacteristic, complemented
42C29×C4⋊C8C2211yescharacteristic, complemented
43C29×C22⋊C8C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic, complemented
45C29×#97C2211yescharacteristic, complemented
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745169C2211yescharacteristic, complemented
53#11745165C2211yescharacteristic, complemented
54#11745165C2211yescharacteristic, 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—
68C22×Dic29—21no—
69#90807—44no—
70#90805—22no—
71#90805—41no—
72C2×D116—22no—
73C2×D116—21no—
74C2×D116—41no—
75C2×D116C2311yescharacteristic
76C2×D116C2311yescharacteristic
77C2×D116C2311yescharacteristic
78C2×C4×D29—21no—
79C2×C4×D29—21no—
80C2×C4×D29—21no—
81C2×Dic58—21no—
82C2×Dic58C2311yescharacteristic
83M16×C29—41no—
84C2×C8×C29—41no—
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C2×C8×C29C2311yescharacteristic
88C2×C8×C29C2311yescharacteristic
89C4⋊C4×C29D411yescharacteristic
90C22⋊C4×C29D411yescharacteristic
91C22⋊C4×C29D411yescharacteristic
92C42×C29C2311yescharacteristic
93C22⋊Dic29—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781—21no—
99#90781—21no—
100#90781—21no—
101C4⋊Dic29—21no—
102C4⋊Dic29—21no—
103C4⋊Dic29—21no—
104C4⋊Dic29C2311yescharacteristic
105C4⋊Dic29C2311yescharacteristic
106C4⋊Dic29C2311yescharacteristic
107C4⋊Dic29C2311yescharacteristic
108#90779—21no—
109D232—22no—
110D232—41no—
111#90773—41no—
112C23×C29C2×D411yescharacteristic
113C23×C29C2×D411yescharacteristic
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—21no—
117C22×D29—42no—
118C22×D29—42no—
119C22×D29—81no—
120D4×C29—22no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—42no—
131C22⋊D29—42no—
132C22⋊D29—42no—
133C22⋊D29—81no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—21no—
137C2×Dic29—21no—
138C2×Dic29—21no—
139C2×Dic29—42no—
140C2×Dic29—42no—
141D116—21no—
142D116—21no—
143D116—21no—
144D116—21no—
145D116—21no—
146D116—42no—
147D116#4112yescomplemented
148C4×D29—42no—
149C4×D29—42no—
150C4×D29—81no—
151Dic58—21no—
152Dic58—21no—
153Dic58—42no—
154C8×C29—21no—
155C8×C29—21no—
156C8×C29—21no—
157C8×C29—21no—
158#3306—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—21no—
164C22×C29AGL(1,ℤ/8)12yes—
165C22×C29C22×D411yescharacteristic
166C2×D29—22no—
167C2×D29—41no—
168C2×D29—41no—
169C2×D29—41no—
170C2×D29—41no—
171C2×D29—41no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—84no—
176C4×C29—21no—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29C2×#4111yescharacteristic
181C4×C29H(5,𝔽2)11yescharacteristic
182Dic29—41no—
183Dic29—41no—
184Dic29—41no—
185Dic29—41no—
186Dic29—41no—
187#547—291no—
188#546—291no—
189#489—291no—
190#483—291no—
191#481—291no—
192#476—291no—
193#469—291no—
194#465—291no—
195#463—291no—
196#449—291no—
197#447—291no—
198#442—291no—
199#435D2911yescharacteristic, complemented
200#417—291no—
201C2×#102—291no—
202C2×C29—22no—
203C2×C29—41no—
204C2×C29#54611yescharacteristic
205C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C29#57711yescharacteristic
207D29—42no—
208D29—81no—
209D29—81no—
210C2×#41—291no—
211C2×#41—581no—
212C22×D4—291no—
213C2×SD16—291no—
214C2×D8—291no—
215C2×D8—291no—
216C2×M16C2×D2911yescharacteristic, complemented
217C22×C8C2×D2911yescharacteristic
218C4⋊Q8—291no—
219#124—291no—
220#123—581no—
221#123—581no—
222#123—581no—
223C22⋊Q8—291no—
224C22⋊Q8—581no—
225#121—291no—
226#121—291no—
227#121—291no—
228#121—581no—
229#120—581no—
230C4×D4—291no—
231C4×D4—291no—
232C4×D4C2×D2911yescharacteristic
233C2×C4⋊C4—291no—
234C2×C4⋊C4—291no—
235C2×C22⋊C4—581no—
236#106—291no—
237#106—291no—
238#106—291no—
239C4⋊C8C2×D2911yescharacteristic, complemented
240#103—291no—
241#103—291no—
242#103—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250C22⋊C8C2×D2911yescharacteristic
251C22⋊C8C2×D2911yescharacteristic, complemented
252#97C2×D2911yescharacteristic, complemented
253C29#330611yescharacteristic, complemented, Sylow
254C24—581no—
255#41—582no—
256#41—1161no—
257#41—1164no—
258C2×Q8—291no—
259C2×Q8—581no—
260C2×D4—291no—
261C2×D4—291no—
262C2×D4—291no—
263C2×D4—582no—
264C2×D4—581no—
265C2×D4—581no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4—1161no—
270C2×D4D11611yescharacteristic
271C22×C4—581no—
272C22×C4—581no—
273C22×C4—581no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4C22×D2911yescharacteristic
277C22×C4C22×D2911yescharacteristic
278SD16—1161no—
279D8—582no—
280D8—1161no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D2911yescharacteristic
284C2×C8C22×D2911yescharacteristic
285C2×C8C22×D2911yescharacteristic
286C2×C8C22×D2911yescharacteristic
287C4⋊C4—291no—
288C4⋊C4—291no—
289C4⋊C4—291no—
290C4⋊C4—291no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4—581no—
295C4⋊C4D11611yescharacteristic
296C22⋊C4—581no—
297C22⋊C4—581no—
298C22⋊C4—581no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4D11611yescharacteristic
305C22⋊C4D11611yescharacteristic
306C42C22×D2911yescharacteristic
307C23—581no—
308C23—581no—
309C23—581no—
310C23—1162no—
311C23—1162no—
312C23—2321no—
313C23C2×D11611yescharacteristic
314C23C2×D11611yescharacteristic
315Q8—581no—
316Q8—581no—
317Q8—1162no—
318D4—22no—
319D4—292no—
320D4—581no—
321D4—581no—
322D4—581no—
323D4—581no—
324D4—581no—
325D4—1162no—
326D4—1162no—
327D4—1162no—
328D4—1162no—
329D4—2321no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—581no—
335C2×C4—581no—
336C2×C4—581no—
337C2×C4—581no—
338C2×C4—581no—
339C2×C4—1162no—
340C2×C4—1162no—
341C2×C4—1162no—
342C2×C4—1162no—
343C2×C4—2321no—
344C2×C4C2×D11611yescharacteristic
345C2×C4C2×D11611yescharacteristic
346C2×C4C2×D11611yescharacteristic
347C2×C4C2×D11611yescharacteristic
348C2×C4C23×D2911yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—582no—
359C22—1161no—
360C22—1161no—
361C22—1161no—
362C22—1161no—
363C22—1161no—
364C22—1161no—
365C22—1161no—
366C22—1161no—
367C22—2324no—
368C22#1174527012yes—
369C22C22×D11611yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—1161no—
375C4—1161no—
376C4—1161no—
377C4—1161no—
378C4—1161no—
379C4#1174535911yescharacteristic
380C4#41×D2911yescharacteristic
381C2—22no—
382C2—41no—
383C2—1162no—
384C2—2321no—
385C2—2321no—
386C2#1427180811yescharacteristic
387C2C2×#1174527011yescharacteristic
388C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#435C2
socleC22×C29C22×D4
hypercenter#435D29
hypocenterC29#3306
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14271817C2semidirect
2. #14271809C2semidirect
3. #14271523C2semidirect
4. #14271494C2semidirect
5. #14271482C2semidirect
6. #14271454C2semidirect
7. #14271416C2semidirect
8. #14271392C2semidirect
9. #14271379C2semidirect
10. #14271310C2semidirect
11. #14271299C2semidirect
12. #14271276C2semidirect
13. #14271165C2semidirect
14. C2×#11745169C2semidirect
15. C29×#435C2semidirect
19. C2×M16×C29C22semidirect
25. #11745292C22semidirect
27. C2×C4⋊Dic29C22semidirect
31. C2×#90773C22semidirect
40. C4×D116C22semidirect
41. #11745231C22semidirect
42. C29×C4⋊C8C22semidirect
44. C29×C22⋊C8C22semidirect
45. C29×#97C22semidirect
52. #11745169C22semidirect
53. #11745165C22semidirect
54. #11745165C22semidirect
55. #11745165C22semidirect
56. #11745164C22semidirect
57. #11745164C22semidirect
58. #11745164C22semidirect
147. D116#41semidirect
199. #435D29semidirect
216. C2×M16C2×D29semidirect
239. C4⋊C8C2×D29semidirect
251. C22⋊C8C2×D29semidirect
252. #97C2×D29semidirect
253. C29#3306semidirect

Maximal subgroups

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

subgroupindex
#142718172
#142718092
#142715232
#142714942
#142714822
#142714542
#142714162
#142713922
#142713792
#142713102
#142712992
#142712762
#142711652
C2×#117451692
C29×#4352
#330629