Finite Group Databasebeta

← #16831333

Subgroups — #16831333

Order 3712.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271855C211yesmaximal, characteristic, complemented
2#14271804C211yesmaximal, characteristic
3#14271519C211yesmaximal, characteristic, complemented
4#14271491C211yesmaximal, characteristic, complemented
5#14271490C211yesmaximal, characteristic, complemented
6#14271466C211yesmaximal, characteristic, complemented
7#14271395C211yesmaximal, characteristic, complemented
8#14271387C211yesmaximal, characteristic, complemented
9#14271324C211yesmaximal, characteristic, complemented
10#14271313C211yesmaximal, characteristic, complemented
11#14271248C211yesmaximal, characteristic, complemented
12C8×C22⋊D29C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14C2×#11745169C211yesmaximal, characteristic, complemented
15C29×#467C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C22×D116C2211yescharacteristic
18C2×Q16×C29C2211yescharacteristic, complemented
19C22×C8×C29C2211yescharacteristic
20C29×C22⋊Q8C2211yescharacteristic
21C29×C22⋊Q8C2211yescharacteristic
22#11745309C2211yescharacteristic
23#11745308C2211yescharacteristic, complemented
24Q8×Dic29C2211yescharacteristic, complemented
25C2×#90784C2211yescharacteristic
26C2×#90784C2211yescharacteristic
27C4×C22⋊D29C2211yescharacteristic
28C2×C4⋊Dic29C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic, complemented
30#11745260—21no—
31#11745257—21no—
32#11745257C2211yescharacteristic
33#11745256—21no—
34#11745255C2211yescharacteristic
35#11745254C2211yescharacteristic, complemented
36#11745252—21no—
37#11745252C2211yescharacteristic, complemented
38#11745248—21no—
39#11745244—21no—
40C22⋊C4×D29—21no—
41#11745239—21no—
42C29×#107C2211yescharacteristic, complemented
43C29×#103C2211yescharacteristic, complemented
44C29×#103C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745183C2211yescharacteristic, complemented
47C22⋊#6597C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745168C2211yescharacteristic, complemented
53#11745162C2211yescharacteristic, complemented
54C8×Dic29C2211yescharacteristic, complemented
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic, complemented
58#11745156C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29D411yescharacteristic
64C22×Dic29—21no—
65#90809—22no—
66#90809—41no—
67C2×D116—22no—
68C2×D116—21no—
69C2×D116—21no—
70C2×D116—21no—
71C2×D116—41no—
72C2×D116C2311yescharacteristic
73C2×D116C2311yescharacteristic
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×C4×D29C2311yescharacteristic
77Q16×C29—41no—
78C2×C8×C29—41no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29C2311yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C22⋊C4×C29—21no—
86C22⋊C4×C29—21no—
87C22⋊Dic29D411yescharacteristic
88#90784—22no—
89#90784—41no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781—21no—
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29—21no—
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779D411yescharacteristic
105C4×Dic29—21no—
106C4×Dic29—21no—
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C8×D29—41no—
111C23×C29C2×D411yescharacteristic
112C22×D29—21no—
113C22×D29—21no—
114C22×D29—42no—
115C22×D29—42no—
116C22×D29—81no—
117C22×D29C2×D411yescharacteristic
118Q8×C29—21no—
119Q8×C29—21no—
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×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—22no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—42no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137D116—21no—
138D116—21no—
139D116—21no—
140D116—42no—
141D116—42no—
142D116—81no—
143D116#4112yes—
144C4×D29—21no—
145C4×D29—21no—
146C4×D29—42no—
147C4×D29—81no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3296—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29#13512yes—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—22no—
159C2×D29—21no—
160C2×D29—21no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—84no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29—41no—
172C4×C29C2×#4111yescharacteristic
173C4×C29H(5,𝔽2)11yescharacteristic
174Dic29—21no—
175Dic29—21no—
176Dic29—21no—
177Dic29—41no—
178Dic29—41no—
179#552—291no—
180#546—291no—
181#488—291no—
182#483—291no—
183#482—291no—
184#478—291no—
185#467D2911yescharacteristic, complemented
186#465—291no—
187#464—291no—
188#452—291no—
189#450—291no—
190C4×SD16—291no—
191C8×D4—291no—
192#416—291no—
193C2×#102—291no—
194C2×C29—22no—
195C2×C29#54611yescharacteristic
196C2×C29C2×#13511yescharacteristic
197C2×C29#57711yescharacteristic
198D29—41no—
199D29—42no—
200D29—81no—
201C2×#41—291no—
202C22×D4—291no—
203C2×Q16C2×D2911yescharacteristic, complemented
204C2×SD16—291no—
205C2×SD16—291no—
206C22×C8—291no—
207C22×C8C2×D2911yescharacteristic
208#126—581no—
209#125—291no—
210#125—581no—
211#124—291no—
212#123—581no—
213#123—581no—
214C22⋊Q8—291no—
215C22⋊Q8C2×D2911yescharacteristic
216C22⋊Q8C2×D2911yescharacteristic
217#121—291no—
218#121—581no—
219#120—581no—
220C4×Q8—291no—
221C4×D4—291no—
222C4×D4—291no—
223#117—291no—
224#117—581no—
225C2×C4⋊C4—291no—
226C2×C22⋊C4—581no—
227#107C2×D2911yescharacteristic, complemented
228#106—291no—
229#106—291no—
230C4⋊C8—291no—
231#103—291no—
232#103—291no—
233#103C2×D2911yescharacteristic, complemented
234#103C2×D2911yescharacteristic, complemented
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102—291no—
241C22⋊C8—291no—
242C22⋊C8—291no—
243C4×C8—291no—
244C29#329611yescharacteristic, complemented, Sylow
245C24—581no—
246#41—582no—
247#41—1161no—
248C2×Q8C22×D2911yescharacteristic
249C2×Q8C22×D2911yescharacteristic
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—291no—
253C2×D4—582no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4—1161no—
258C22×C4—291no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4C22×D2911yescharacteristic
263Q16—41no—
264SD16—582no—
265SD16—1161no—
266C2×C8—41no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—1161no—
270C2×C8C22×D2911yescharacteristic
271C2×C8C22×D2911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—291no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—291no—
287C22⋊C4—291no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C42—291no—
295C42—581no—
296C42—581no—
297C23—291no—
298C23—581no—
299C23—581no—
300C23—1162no—
301C23—1162no—
302C23—2321no—
303C23D4×D2911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—292no—
309D4—582no—
310D4—581no—
311D4—581no—
312D4—581no—
313D4—1162no—
314D4—1162no—
315D4—2321no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—291no—
323C2×C4—291no—
324C2×C4—291no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—581no—
329C2×C4—1162no—
330C2×C4—1162no—
331C2×C4—2321no—
332C2×C4D4×D2911yescharacteristic
333C2×C4C23×D2911yescharacteristic
334C8—21no—
335C8—21no—
336C8—581no—
337C8—581no—
338C22—21no—
339C22—21no—
340C22—581no—
341C22—582no—
342C22—581no—
343C22—581no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22—2324no—
350C22#1174528112yes—
351C22C2×D4×D2911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—581no—
358C4—581no—
359C4—581no—
360C4—1161no—
361C4—1161no—
362C4#1174535911yescharacteristic
363C4#41×D2911yescharacteristic
364C2—22no—
365C2—1161no—
366C2—1162no—
367C2—2321no—
368C2#1427180211yescharacteristic
369C2C2×#1174528111yescharacteristic
370C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#467C2
socleC22×C29C22×D4
prime radical#14271804C2
hypercenter#467D29
hypocenterC29#3296
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #14271855C2semidirect
3. #14271519C2semidirect
4. #14271491C2semidirect
5. #14271490C2semidirect
6. #14271466C2semidirect
7. #14271395C2semidirect
8. #14271387C2semidirect
9. #14271324C2semidirect
10. #14271313C2semidirect
11. #14271248C2semidirect
12. C8×C22⋊D29C2semidirect
13. #14271158C2semidirect
14. C2×#11745169C2semidirect
15. C29×#467C2semidirect
18. C2×Q16×C29C22semidirect
23. #11745308C22semidirect
24. Q8×Dic29C22semidirect
29. C2×C8×D29C22semidirect
35. #11745254C22semidirect
37. #11745252C22semidirect
42. C29×#107C22semidirect
43. C29×#103C22semidirect
44. C29×#103C22semidirect
45. #11745183C22semidirect
46. #11745183C22semidirect
52. #11745168C22semidirect
53. #11745162C22semidirect
54. C8×Dic29C22semidirect
57. #11745156C22semidirect
58. #11745156C22semidirect
185. #467D29semidirect
203. C2×Q16C2×D29semidirect
227. #107C2×D29semidirect
233. #103C2×D29semidirect
234. #103C2×D29semidirect
244. C29#3296semidirect

Maximal subgroups

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

subgroupindex
#142718552
#142718042
#142715192
#142714912
#142714902
#142714662
#142713952
#142713872
#142713242
#142713132
#142712482
C8×C22⋊D292
#142711582
C2×#117451692
C29×#4672
#329629