Finite Group Databasebeta

← #16831321

Subgroups — #16831321

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#14271809C211yesmaximal, characteristic
2#14271520C211yesmaximal, characteristic, complemented
3#14271493C211yesmaximal, characteristic, complemented
4#14271487C211yesmaximal, characteristic, complemented
5#14271460C211yesmaximal, characteristic, complemented
6#14271402C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271385C211yesmaximal, characteristic, complemented
9#14271323C211yesmaximal, characteristic, complemented
10#14271313C211yesmaximal, characteristic, complemented
11C4×#90784C211yesmaximal, characteristic, complemented
12D4×#6597C211yesmaximal, characteristic, complemented
13#14271157C211yesmaximal, characteristic, complemented
14C2×#11745157C211yesmaximal, characteristic, complemented
15C29×#552C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C22×D116C2211yescharacteristic
18C29×#126—21no—
19C29×#125—21no—
20C29×#125C2211yescharacteristic, complemented
21C29×#123—21no—
22C29×C22⋊Q8C2211yescharacteristic
23C29×C22⋊Q8C2211yescharacteristic, complemented
24C4×Q8×C29C2211yescharacteristic, complemented
25C4×D4×C29C2211yescharacteristic
26C29×#117—21no—
27C29×#117C2211yescharacteristic, complemented
28C2×C4⋊C4×C29C2211yescharacteristic
29C2×#90785C2211yescharacteristic, complemented
30C2×#90784C2211yescharacteristic
31C2×#90784C2211yescharacteristic
32#11745299—21no—
33#11745292C2211yescharacteristic
34#11745286C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic, complemented
37#11745256—21no—
38#11745246—21no—
39C22⋊C4×D29—21no—
40#11745237C2211yescharacteristic
41C4×D116C2211yescharacteristic
42#11745183C2211yescharacteristic, complemented
43C22⋊#6597C2211yescharacteristic
44C22⋊#6597C2211yescharacteristic, complemented
45#11745158C2211yescharacteristic, complemented
46#11745158C2211yescharacteristic, complemented
47#11745158C2211yescharacteristic, complemented
48#11745157C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745157C2211yescharacteristic
52#11745157C2211yescharacteristic
53#11745157C2211yescharacteristic
54#11745156C2211yescharacteristic, complemented
55#11745156C2211yescharacteristic, complemented
56#11745155C2211yescharacteristic, complemented
57C4⋊#6597C2211yescharacteristic, complemented
58C4×#6597C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29D411yescharacteristic
62C22×C4×C29—21no—
63C22×C4×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67#90805—22no—
68#90805—41no—
69C2×D116—22no—
70C2×D116—21no—
71C2×D116—41no—
72C2×D116C2311yescharacteristic
73C2×D116C2311yescharacteristic
74C2×C4×D29—21no—
75C2×C4×D29—21no—
76C2×Dic58C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29—21no—
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29D411yescharacteristic
84C4⋊C4×C29C2311yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C4⋊C4×C29C2311yescharacteristic
87C22⋊C4×C29—21no—
88C22⋊C4×C29—21no—
89C22⋊C4×C29—21no—
90C22⋊C4×C29D411yescharacteristic
91C22⋊C4×C29D411yescharacteristic
92C42×C29—21no—
93C42×C29—21no—
94C42×C29C2311yescharacteristic
95C22⋊Dic29—21no—
96#90785—41no—
97#90784—22no—
98#90784—41no—
99#90781—21no—
100#90781—21no—
101#90781—21no—
102#90781—21no—
103C4⋊Dic29C2311yescharacteristic
104#90779—21no—
105C2×#6597—41no—
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29C2×D411yescharacteristic
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—42no—
116C22×D29—42no—
117C22×D29—81no—
118Q8×C29—21no—
119Q8×C29—21no—
120D4×C29—22no—
121C2×C4×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—21no—
129C2×C4×C29—42no—
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C22⋊D29—42no—
136C22⋊D29—81no—
137C2×Dic29—21no—
138C2×Dic29—21no—
139D116—21no—
140D116—21no—
141D116—21no—
142D116—42no—
143D116#4112yes—
144C4×D29—42no—
145C4×D29—81no—
146Dic58—21no—
147Dic58—21no—
148#6597—21no—
149#6597—21no—
150#6597—21no—
151#6597—21no—
152#3296—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—21no—
158C22×C29#13512yes—
159C22×C29C22×D411yescharacteristic
160C2×D29—22no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—84no—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—41no—
172C4×C29—41no—
173C4×C29—41no—
174C4×C29—41no—
175C4×C29C2×#4111yescharacteristic
176C4×C29H(5,𝔽2)11yescharacteristic
177Dic29—41no—
178Dic29—41no—
179#552D2911yescharacteristic, complemented
180#546—291no—
181#488—291no—
182#483—291no—
183#482—291no—
184#478—291no—
185#467—291no—
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—41no—
196C2×C29#54611yescharacteristic
197C2×C29C2×#13511yescharacteristic
198C2×C29#57711yescharacteristic
199D29—42no—
200D29—81no—
201C2×#41—291no—
202C22×D4—291no—
203C2×Q16—291no—
204C2×SD16—291no—
205C2×SD16—291no—
206C22×C8—291no—
207C22×C8—291no—
208#126—21no—
209#125—21no—
210#125C2×D2911yescharacteristic, complemented
211#124—291no—
212#123—21no—
213#123—581no—
214C22⋊Q8—291no—
215C22⋊Q8C2×D2911yescharacteristic
216C22⋊Q8C2×D2911yescharacteristic, complemented
217#121—291no—
218#121—581no—
219#120—581no—
220C4×Q8C2×D2911yescharacteristic, complemented
221C4×D4—291no—
222C4×D4C2×D2911yescharacteristic
223#117—21no—
224#117C2×D2911yescharacteristic, complemented
225C2×C4⋊C4C2×D2911yescharacteristic
226C2×C22⋊C4—581no—
227#107—291no—
228#106—291no—
229#106—291no—
230C4⋊C8—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103—291no—
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×Q8—291no—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—582no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—1161no—
257C2×D4C22⋊D2911yescharacteristic
258C22×C4—21no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4C22×D2911yescharacteristic
262C22×C4C22×D2911yescharacteristic
263Q16—1161no—
264SD16—582no—
265SD16—1161no—
266C2×C8—291no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—1161no—
271C2×C8—1161no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—291no—
279C4⋊C4—581no—
280C4⋊C4C22⋊D2911yescharacteristic
281C4⋊C4C22×D2911yescharacteristic
282C4⋊C4C22×D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4C22⋊D2911yescharacteristic
293C22⋊C4C22⋊D2911yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D2911yescharacteristic
297C23—581no—
298C23—581no—
299C23—1162no—
300C23—1162no—
301C23—2321no—
302C23C2×C22⋊D2911yescharacteristic
303C23C2×C22⋊D2911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—581no—
307Q8—581no—
308D4—22no—
309D4—292no—
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—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—1162no—
328C2×C4—2321no—
329C2×C4C2×C22⋊D2911yescharacteristic
330C2×C4C2×C22⋊D2911yescharacteristic
331C2×C4C2×C22⋊D2911yescharacteristic
332C2×C4C2×C22⋊D2911yescharacteristic
333C2×C4C23×D2911yescharacteristic
334C8—581no—
335C8—581no—
336C8—581no—
337C8—581no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—582no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22—2324no—
350C22#1174531212yes—
351C22C22×C22⋊D2911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1161no—
361C4—1161no—
362C4#41×D2911yescharacteristic
363C4#1174536411yescharacteristic
364C2—22no—
365C2—41no—
366C2—1162no—
367C2—2321no—
368C2#1427180111yescharacteristic
369C2C2×#1174531211yescharacteristic
370C2#1427197111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#552C2
socleC22×C29C22×D4
prime radical#14271809C2
hypercenter#552D29
hypocenterC29#3296
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14271520C2semidirect
3. #14271493C2semidirect
4. #14271487C2semidirect
5. #14271460C2semidirect
6. #14271402C2semidirect
7. #14271394C2semidirect
8. #14271385C2semidirect
9. #14271323C2semidirect
10. #14271313C2semidirect
11. C4×#90784C2semidirect
12. D4×#6597C2semidirect
13. #14271157C2semidirect
14. C2×#11745157C2semidirect
15. C29×#552C2semidirect
20. C29×#125C22semidirect
23. C29×C22⋊Q8C22semidirect
24. C4×Q8×C29C22semidirect
27. C29×#117C22semidirect
29. C2×#90785C22semidirect
36. C22×#6597C22semidirect
42. #11745183C22semidirect
44. C22⋊#6597C22semidirect
45. #11745158C22semidirect
46. #11745158C22semidirect
47. #11745158C22semidirect
54. #11745156C22semidirect
55. #11745156C22semidirect
56. #11745155C22semidirect
57. C4⋊#6597C22semidirect
58. C4×#6597C22semidirect
179. #552D29semidirect
210. #125C2×D29semidirect
216. C22⋊Q8C2×D29semidirect
220. C4×Q8C2×D29semidirect
224. #117C2×D29semidirect
244. C29#3296semidirect

Maximal subgroups

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

subgroupindex
#142718092
#142715202
#142714932
#142714872
#142714602
#142714022
#142713942
#142713852
#142713232
#142713132
C4×#907842
D4×#65972
#142711572
C2×#117451572
C29×#5522
#329629