Finite Group Databasebeta

← #16831451

Subgroups — #16831451

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#14271814C211yesmaximal, characteristic, complemented
2#14271804C211yesmaximal, characteristic, complemented
3#14271524C211yesmaximal, characteristic, complemented
4#14271483C211yesmaximal, characteristic, complemented
5#14271452C211yesmaximal, characteristic, complemented
6#14271417C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271381C211yesmaximal, characteristic, complemented
9#14271311C211yesmaximal, characteristic, complemented
10#14271299C211yesmaximal, characteristic, complemented
11#14271274C211yesmaximal, characteristic, complemented
12#14271231C211yesmaximal, characteristic, complemented
13#14271163C211yesmaximal, characteristic, complemented
14C2×#11745157C211yesmaximal, characteristic, complemented
15C29×#483C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90805—21no—
18C22×D116C2211yescharacteristic
19C29×C22⋊Q8C2211yescharacteristic
20C2×C4⋊C4×C29C2211yescharacteristic
21#11745309C2211yescharacteristic
22C2×#90784C2211yescharacteristic, complemented
23#11745292C2211yescharacteristic
24#11745291—21no—
25C4×C22⋊D29C2211yescharacteristic
26C22×#6597C2211yescharacteristic
27C2×D232C2211yescharacteristic
28C2×D232C2211yescharacteristic
29C2×#90772C2211yescharacteristic, complemented
30#11745258—21no—
31#11745257—21no—
32#11745257C2211yescharacteristic
33#11745257C2211yescharacteristic, complemented
34#11745256—21no—
35#11745256—21no—
36#11745255C2211yescharacteristic
37#11745255C2211yescharacteristic, complemented
38C4⋊C4×D29C2211yescharacteristic, complemented
39#11745250C2211yescharacteristic, complemented
40#11745244—21no—
41C22⋊C4×D29—21no—
42C29×#106C2211yescharacteristic, complemented
43C29×#106C2211yescharacteristic, complemented
44C29×#103C2211yescharacteristic, complemented
45C29×#103C2211yescharacteristic, complemented
46C29×C22⋊C8C2211yescharacteristic
47#11745183C2211yescharacteristic, complemented
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic, complemented
51#11745163C2211yescharacteristic, complemented
52#11745162C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic
54#11745157C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic, complemented
58#11745156C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C22×C4×C29—21no—
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29D411yescharacteristic
65#90809—22no—
66#90809—41no—
67#90805—44no—
68C2×D116—22no—
69C2×D116—21no—
70C2×D116—21no—
71C2×D116—21no—
72C2×D116—21no—
73C2×D116—41no—
74C2×D116C2311yescharacteristic
75C2×D116C2311yescharacteristic
76C2×D116C2311yescharacteristic
77C2×C4×D29—21no—
78C2×C4×D29—21no—
79C2×C4×D29—21no—
80C2×C4×D29—21no—
81C2×C4×D29C2311yescharacteristic
82C2×Dic58—21no—
83C2×C8×C29C2311yescharacteristic
84C2×C8×C29C2311yescharacteristic
85C4⋊C4×C29—21no—
86C4⋊C4×C29—21no—
87C4⋊C4×C29C2311yescharacteristic
88C4⋊C4×C29C2311yescharacteristic
89C4⋊C4×C29C2311yescharacteristic
90C22⋊C4×C29—21no—
91C22⋊Dic29D411yescharacteristic
92#90784—41no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781—21no—
99#90781—21no—
100#90781D411yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779D411yescharacteristic
105C4×Dic29C2311yescharacteristic
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109D232—22no—
110D232—41no—
111#90772—41no—
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—42no—
117C22×D29—42no—
118C22×D29—81no—
119C22×D29C2×D411yescharacteristic
120Q8×C29—21no—
121Q8×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—42no—
129C2×C4×C29C2×D411yescharacteristic
130C2×C4×C29C2411yescharacteristic
131C22⋊D29—22no—
132C22⋊D29—42no—
133C2×Dic29—21no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137D116—21no—
138D116—21no—
139D116—21no—
140D116—21no—
141D116—21no—
142D116—42no—
143D116—42no—
144D116—42no—
145D116—81no—
146D116#4112yescomplemented
147C4×D29—21no—
148C4×D29—21no—
149C4×D29—42no—
150C4×D29—42no—
151C4×D29—42no—
152C4×D29—81no—
153Dic58—42no—
154C8×C29—21no—
155C8×C29—21no—
156#6597—21no—
157#6597—21no—
158#3306—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29AGL(1,ℤ/8)12yes—
162C22×C29C22×D411yescharacteristic
163C2×D29—21no—
164C2×D29—22no—
165C2×D29—21no—
166C2×D29—21no—
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—41no—
178C4×C29—41no—
179C4×C29—41no—
180C4×C29—41no—
181C4×C29C2×#4111yescharacteristic
182C4×C29H(5,𝔽2)11yescharacteristic
183Dic29—21no—
184Dic29—21no—
185Dic29—21no—
186Dic29—41no—
187#547—291no—
188#546—291no—
189#489—291no—
190#483D2911yescharacteristic, complemented
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#435—291no—
200#417—291no—
201C2×#102—291no—
202C2×C29—22no—
203C2×C29#54611yescharacteristic
204C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
205C2×C29#57711yescharacteristic
206D29—41no—
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×M16—291no—
217C22×C8—291no—
218C4⋊Q8—291no—
219#124—291no—
220#123—581no—
221#123—581no—
222#123—581no—
223C22⋊Q8—581no—
224C22⋊Q8C2×D2911yescharacteristic
225#121—291no—
226#121—291no—
227#121—291no—
228#121—581no—
229#120—581no—
230C4×D4—291no—
231C4×D4—291no—
232C4×D4—291no—
233C2×C4⋊C4—291no—
234C2×C4⋊C4C2×D2911yescharacteristic
235C2×C22⋊C4—581no—
236#106—291no—
237#106C2×D2911yescharacteristic, complemented
238#106C2×D2911yescharacteristic, complemented
239C4⋊C8—291no—
240#103—291no—
241#103C2×D2911yescharacteristic, complemented
242#103C2×D2911yescharacteristic, complemented
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250C22⋊C8—291no—
251C22⋊C8C2×D2911yescharacteristic
252#97—291no—
253C29#330611yescharacteristic, complemented, Sylow
254C24—581no—
255#41—582no—
256#41—1164no—
257#41—1161no—
258C2×Q8—581no—
259C2×Q8C22×D2911yescharacteristic
260C2×D4—291no—
261C2×D4—291no—
262C2×D4—291no—
263C2×D4—291no—
264C2×D4—582no—
265C2×D4—581no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4—581no—
270C2×D4—1161no—
271C22×C4—21no—
272C22×C4—291no—
273C22×C4—581no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4—581no—
277C22×C4C22×D2911yescharacteristic
278SD16—1161no—
279D8—582no—
280D8—1161no—
281M16—1161no—
282C2×C8—291no—
283C2×C8—291no—
284C2×C8—1161no—
285C2×C8C22×D2911yescharacteristic
286C2×C8C22×D2911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—291no—
290C4⋊C4—291no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4C22×D2911yescharacteristic
294C4⋊C4C22×D2911yescharacteristic
295C4⋊C4C22×D2911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—291no—
298C22⋊C4—291no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4—581no—
305C22⋊C4—581no—
306C42—291no—
307C23—291no—
308C23—581no—
309C23—581no—
310C23—581no—
311C23—1162no—
312C23—1162no—
313C23—2321no—
314C23D4×D2911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1162no—
318D4—292no—
319D4—582no—
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—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—291no—
338C2×C4—291no—
339C2×C4—291no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—1162no—
344C2×C4—1162no—
345C2×C4—1162no—
346C2×C4—2321no—
347C2×C4D4×D2911yescharacteristic
348C2×C4C23×D2911yescharacteristic
349C8—21no—
350C8—21no—
351C8—581no—
352C8—581no—
353C22—21no—
354C22—21no—
355C22—581no—
356C22—582no—
357C22—581no—
358C22—581no—
359C22—1161no—
360C22—1161no—
361C22—1161no—
362C22—1161no—
363C22—1161no—
364C22—1161no—
365C22—1161no—
366C22—1161no—
367C22—2324no—
368C22#1174527612yes—
369C22C2×D4×D2911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—581no—
376C4—581no—
377C4—581no—
378C4—1161no—
379C4#41×D2911yescharacteristic
380C4#1174536411yescharacteristic
381C2—22no—
382C2—1161no—
383C2—1162no—
384C2—2321no—
385C2—2321no—
386C2#1427180511yescharacteristic
387C2C2×#1174527611yescharacteristic
388C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#483C2
socleC22×C29C22×D4
hypercenter#483D29
hypocenterC29#3306
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #14271814C2semidirect
2. #14271804C2semidirect
3. #14271524C2semidirect
4. #14271483C2semidirect
5. #14271452C2semidirect
6. #14271417C2semidirect
7. #14271394C2semidirect
8. #14271381C2semidirect
9. #14271311C2semidirect
10. #14271299C2semidirect
11. #14271274C2semidirect
12. #14271231C2semidirect
13. #14271163C2semidirect
14. C2×#11745157C2semidirect
15. C29×#483C2semidirect
22. C2×#90784C22semidirect
29. C2×#90772C22semidirect
33. #11745257C22semidirect
37. #11745255C22semidirect
38. C4⋊C4×D29C22semidirect
39. #11745250C22semidirect
42. C29×#106C22semidirect
43. C29×#106C22semidirect
44. C29×#103C22semidirect
45. C29×#103C22semidirect
47. #11745183C22semidirect
50. #11745168C22semidirect
51. #11745163C22semidirect
52. #11745162C22semidirect
57. #11745157C22semidirect
58. #11745156C22semidirect
146. D116#41semidirect
190. #483D29semidirect
237. #106C2×D29semidirect
238. #106C2×D29semidirect
241. #103C2×D29semidirect
242. #103C2×D29semidirect
253. C29#3306semidirect

Maximal subgroups

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

subgroupindex
#142718142
#142718042
#142715242
#142714832
#142714522
#142714172
#142713942
#142713812
#142713112
#142712992
#142712742
#142712312
#142711632
C2×#117451572
C29×#4832
#330629