Finite Group Databasebeta

← #16831407

Subgroups — #16831407

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271881C211yesmaximal, characteristic, complemented
2#14271815C211yesmaximal, characteristic
3#14271512C211yesmaximal, characteristic, complemented
4#14271507C211yesmaximal, characteristic, complemented
5#14271442C211yesmaximal, characteristic, complemented
6#14271405C211yesmaximal, characteristic, complemented
7#14271402C211yesmaximal, characteristic, complemented
8#14271372C211yesmaximal, characteristic, complemented
9#14271328C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271250C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271158C211yesmaximal, characteristic, complemented
14#14271157C211yesmaximal, characteristic, complemented
15C29×#485C211yesmaximal, characteristic, complemented
16C2×#90809C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×C22⋊Q8C2211yescharacteristic
19C29×#117C2211yescharacteristic
20#11745306C2211yescharacteristic
21C2×#90785C2211yescharacteristic
22C4×C22⋊D29C2211yescharacteristic
23#11745286C2211yescharacteristic
24C22×#6597C2211yescharacteristic
25C2×Dic116C2211yescharacteristic
26C2×#90773C2211yescharacteristic
27C2×C8×D29C2211yescharacteristic
28#11745259C2211yescharacteristic
29#11745259C2211yescharacteristic
30#11745256—21no—
31#11745255C2211yescharacteristic
32#11745254C2211yescharacteristic
33C4⋊C4×D29—21no—
34#11745250C2211yescharacteristic
35#11745249C2211yescharacteristic
36#11745247—21no—
37#11745246—21no—
38#11745245—21no—
39#11745241—21no—
40#11745238—21no—
41C4×Dic58—21no—
42C29×#107C2211yescharacteristic
43C29×#106C2211yescharacteristic
44C29×#103C2211yescharacteristic
45C29×#103C2211yescharacteristic
46C29×C22⋊C8C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745164C2211yescharacteristic
51#11745162C2211yescharacteristic
52C8×Dic29C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745155C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C2×C22⋊D29—21no—
62C2×C22⋊D29D411yescharacteristic
63#90809—22no—
64#90809—41no—
65#90805—22no—
66#90805—41no—
67C2×D116—21no—
68C2×D116C2311yescharacteristic
69C2×C4×D29—21no—
70C2×C4×D29—21no—
71C2×C4×D29—21no—
72C2×C4×D29C2311yescharacteristic
73C2×Dic58—21no—
74C2×Dic58C2311yescharacteristic
75C2×Dic58C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C4⋊C4×C29—21no—
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C42×C29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29D411yescharacteristic
87#90785—41no—
88#90781—21no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781D411yescharacteristic
93C4⋊Dic29—21no—
94C4⋊Dic29—21no—
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779D411yescharacteristic
102C4×Dic29—21no—
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C2×#6597—41no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108Dic116—41no—
109#90773—22no—
110C8×D29—41no—
111C23×C29C2×D411yescharacteristic
112C22×D29—21no—
113C22×D29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C22⋊D29—22no—
125C22⋊D29—42no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29C2×D411yescharacteristic
130C2×Dic29C2×D411yescharacteristic
131C2×Dic29C2×D411yescharacteristic
132D116—21no—
133D116—42no—
134D116#4112yes—
135C4×D29—21no—
136C4×D29—21no—
137C4×D29—42no—
138C4×D29—42no—
139C4×D29—42no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
143Dic58—21no—
144Dic58—42no—
145C8×C29—21no—
146C8×C29—21no—
147#6597—21no—
148#6597—21no—
149#3302—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29C22×D411yescharacteristic
154C2×D29—21no—
155C2×D29—22no—
156C2×D29—21no—
157C2×D29—21no—
158C2×D29—41no—
159C2×D29—41no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29—41no—
165C4×C29C2×#4111yescharacteristic
166C4×C29H(5,𝔽2)11yescharacteristic
167Dic29—21no—
168Dic29—21no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172Dic29#13512yes—
173#556—291no—
174#547—291no—
175#487—291no—
176#485—291no—
177#485D2911yescharacteristic, complemented
178#474—291no—
179#467—291no—
180#467—291no—
181#462—291no—
182#452—291no—
183#452—291no—
184C4×SD16—291no—
185C8×D4—291no—
186#416—291no—
187#416—291no—
188C2×C29—41no—
189C2×C29#54611yescharacteristic
190C2×C29C2×#13511yescharacteristic
191C2×C29#57811yescharacteristic
192D29—41no—
193D29—42no—
194C2×#41—291no—
195C2×#41—291no—
196C2×Q16—291no—
197C2×Q16—291no—
198C2×SD16—291no—
199C22×C8—291no—
200C22×C8—291no—
201C4⋊Q8—291no—
202C4⋊Q8—291no—
203#126—581no—
204#126—581no—
205#124—581no—
206#123—581no—
207#123—581no—
208C22⋊Q8—291no—
209C22⋊Q8—291no—
210C22⋊Q8—291no—
211C22⋊Q8C2×D2911yescharacteristic
212#121—581no—
213C4×Q8—291no—
214C4×Q8—581no—
215C4×D4—291no—
216C4×D4—291no—
217#117—291no—
218#117C2×D2911yescharacteristic
219C2×C4⋊C4—581no—
220#107—291no—
221#107C2×D2911yescharacteristic
222#106C2×D2911yescharacteristic
223C4⋊C8—291no—
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103C2×D2911yescharacteristic
230#103C2×D2911yescharacteristic
231#102—291no—
232#102—291no—
233#102—291no—
234C22⋊C8—291no—
235C22⋊C8C2×D2911yescharacteristic
236C4×C8—291no—
237C29#330211yescharacteristic, complemented, Sylow
238#41—582no—
239#41—582no—
240#41—1161no—
241#41—1161no—
242C2×Q8—291no—
243C2×Q8—291no—
244C2×Q8—581no—
245C2×Q8C22×D2911yescharacteristic
246C2×D4—291no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4—581no—
250C22×C4—291no—
251C22×C4—581no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4C22×D2911yescharacteristic
255Q16—1161no—
256Q16—1161no—
257SD16—582no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8—1161no—
261C2×C8—1161no—
262C2×C8C22×D2911yescharacteristic
263C2×C8C22×D2911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4C22×D2911yescharacteristic
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—291no—
280C22⋊C4—291no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—21no—
287C42—291no—
288C42—581no—
289C42—581no—
290C23—291no—
291C23—581no—
292C23D4×D2911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—581no—
299Q8—1162no—
300D4—292no—
301D4—582no—
302D4—581no—
303D4—1162no—
304D4—1162no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—1162no—
320C2×C4—1162no—
321C2×C4—1162no—
322C2×C4D4×D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—21no—
325C8—21no—
326C8—581no—
327C8—581no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—581no—
332C22—582no—
333C22—581no—
334C22—581no—
335C22—1161no—
336C22—1161no—
337C22C2×D4×D2911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—292no—
344C4—581no—
345C4—581no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4#41×D2911yescharacteristic
350C4#1174536411yescharacteristic
351C2—41no—
352C2—1161no—
353C2—1162no—
354C2#1427180511yescharacteristic
355C2#135×D2911yescharacteristic
356C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#485C2
socleC22×C29C22×D4
prime radical#14271815C2
hypercenter#485D29
hypocenterC29#3302
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14271881C2semidirect
3. #14271512C2semidirect
4. #14271507C2semidirect
5. #14271442C2semidirect
6. #14271405C2semidirect
7. #14271402C2semidirect
8. #14271372C2semidirect
9. #14271328C2semidirect
10. #14271327C2semidirect
11. #14271250C2semidirect
12. #14271226C2semidirect
13. #14271158C2semidirect
14. #14271157C2semidirect
15. C29×#485C2semidirect
177. #485D29semidirect
237. C29#3302semidirect

Maximal subgroups

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

subgroupindex
#142718812
#142718152
#142715122
#142715072
#142714422
#142714052
#142714022
#142713722
#142713282
#142713272
#142712502
#142712262
#142711582
#142711572
C29×#4852
#330229