Finite Group Databasebeta

← #16820557

Subgroups — #16820557

Order 3712.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271961C211yesmaximal, characteristic, complemented
2#14271674C211yesmaximal, characteristic, complemented
3#14271181C211yesmaximal, characteristic, complemented
4#14271180C211yesmaximal, characteristic, complemented
5#14271127C211yesmaximal, characteristic, complemented
6#14270919C211yesmaximal, characteristic, complemented
7C29×#525C211yesmaximal, characteristic, complemented
8C2×#41×C29C2211yescharacteristic
9C23×C4×C29C2211yescharacteristic
10C2×#90805C2211yescharacteristic
11C29×#123—21no—
12C29×C22⋊Q8—21no—
13C29×#121—21no—
14C29×#120—21no—
15C4×D4×C29—22no—
16C29×#117C2211yescharacteristic
17#11745315—21no—
18#11745313—21no—
19#11745312—22no—
20#11745311—21no—
21#11745304—21no—
22#11745294—21no—
23#11745292—21no—
24#11745291—21no—
25C4×C22⋊D29—22no—
26#11745288C2211yescharacteristic
27#11745286—21no—
28C2×#90777C2211yescharacteristic
29C2×#90777C2211yescharacteristic
30#11745185—22no—
31C22⋊#6597—22no—
32#11745153—22no—
33C24×C29D411yescharacteristic
34#41×C29—21no—
35#41×C29—21no—
36#41×C29—21no—
37#41×C29—21no—
38C2×Q8×C29D411yescharacteristic, complemented
39C2×D4×C29—22no—
40C2×D4×C29—21no—
41C2×D4×C29D411yescharacteristic, complemented
42C22×C4×C29—21no—
43C22×C4×C29—21no—
44C22×C4×C29—21no—
45C22×C4×C29—21no—
46C22×C4×C29—21no—
47C22×C4×C29—21no—
48C22×C4×C29—21no—
49C22×C4×C29D411yescharacteristic
50C22×C4×C29C2311yescharacteristic
51C2×C22⋊D29—22no—
52C2×C22⋊D29—21no—
53#90805—21no—
54#90805—21no—
55#90805—21no—
56#90805—21no—
57C2×D116D411yescharacteristic, complemented
58C2×C4×D29—21no—
59C2×Dic58D411yescharacteristic, complemented
60C4⋊C4×C29—22no—
61C4⋊C4×C29—21no—
62C22⋊C4×C29—22no—
63C22⋊C4×C29—22no—
64C22⋊C4×C29—21no—
65C42×C29D412yescomplemented
66C22⋊Dic29—22no—
67C22⋊Dic29—21no—
68#90785—22no—
69#90784—22no—
70#90783—22no—
71#90782—22no—
72#90781—22no—
73C4⋊Dic29—21no—
74#90779—22no—
75C4×Dic29D412yescomplemented
76#90777—21no—
77#90777—21no—
78#90777—21no—
79#90777—21no—
80C2×#6597—21no—
81C2×#6597D412yescomplemented
82C23×C29—21no—
83C23×C29—21no—
84C23×C29—21no—
85C23×C29—21no—
86C23×C29—42no—
87C23×C29C2×D411yescharacteristic
88C22×D29—21no—
89Q8×C29—21no—
90Q8×C29—21no—
91D4×C29—21no—
92D4×C29—21no—
93D4×C29—44no—
94D4×C29—41no—
95D4×C29—41no—
96C2×C4×C29—21no—
97C2×C4×C29—22no—
98C2×C4×C29—21no—
99C2×C4×C29—21no—
100C2×C4×C29—21no—
101C2×C4×C29—41no—
102C2×C4×C29—41no—
103C2×C4×C29—41no—
104C2×C4×C29—41no—
105C2×C4×C29—41no—
106C2×C4×C29—41no—
107C2×C4×C29C2×D411yescharacteristic
108C2×C4×C29C2×D411yescharacteristic
109C2×C4×C29C2×D411yescharacteristic
110C2×C4×C29C2×D411yescharacteristic
111C2×C4×C29C2×D411yescharacteristic
112C2×C4×C29#4111yescharacteristic
113C22⋊D29—44no—
114C22⋊D29—41no—
115C22⋊D29—41no—
116C2×Dic29—22no—
117C2×Dic29—21no—
118D116—21no—
119D116—21no—
120C4×D29—41no—
121C4×D29—41no—
122Dic58—21no—
123Dic58—21no—
124#6597—22no—
125#6597—41no—
126#2010—291nomaximal, Sylow
127C22×C29—22no—
128C22×C29—22no—
129C22×C29—22no—
130C22×C29—41no—
131C22×C29—41no—
132C22×C29—41no—
133C22×C29—41no—
134C22×C29—42no—
135C22×C29—41no—
136C22×C29—41no—
137C22×C29#12011yescharacteristic
138C22×C29#12011yescharacteristic
139C22×C29#12111yescharacteristic
140C2×D29—42no—
141C2×D29—41no—
142C4×C29—42no—
143C4×C29—41no—
144C4×C29—41no—
145C4×C29#12011yescharacteristic
146C4×C29#12111yescharacteristic
147C4×C29#12111yescharacteristic
148C4×C29#12711yescharacteristic
149Dic29—42no—
150Dic29—41no—
151#575—291no—
152#525—291no—
153#525D2911yescharacteristic, complemented
154#421—291no—
155#421—291no—
156#407—291no—
157H(3,ℤ/4)—291no—
158C2×C29—21no—
159C2×C29—21no—
160C2×C29—21no—
161C2×C29—42no—
162C2×C29—81no—
163C2×C29#39211yescharacteristic
164D29—81no—
165C2×#41—291no—
166C2×#41C2×D2911yescharacteristic
167C23×C4C2×D2911yescharacteristic
168#137—581no—
169#137—581no—
170AGL(1,ℤ/8)—581no—
171AGL(1,ℤ/8)—581no—
172#135—582no—
173C2×M16—291no—
174C2×M16—291no—
175#123—21no—
176#123—581no—
177C22⋊Q8—21no—
178C22⋊Q8—581no—
179#121—21no—
180#121—581no—
181#120—21no—
182#120—581no—
183C4×D4—22no—
184C4×D4—582no—
185#117—291no—
186#117C2×D2911yescharacteristic
187#104—582no—
188#104—582no—
189C22⋊C8—582no—
190C29#201011yescharacteristic, complemented, Sylow
191C24C22⋊D2911yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—581no—
197#41—581no—
198#41—581no—
199#41—581no—
200C2×Q8—291no—
201C2×Q8C22⋊D2911yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—291no—
205C2×D4—582no—
206C2×D4—581no—
207C2×D4C22⋊D2911yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—581no—
216C22×C4C22⋊D2911yescharacteristic
217C22×C4C22×D2911yescharacteristic
218Q16—582no—
219SD16—582no—
220SD16—582no—
221D8—582no—
222M16—581no—
223M16—581no—
224M16—581no—
225M16—581no—
226C2×C8—292no—
227C2×C8—581no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—582no—
231C4⋊C4—581no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—582no—
236C22⋊C4—582no—
237C22⋊C4—581no—
238C42—292no—
239C42C22⋊D2912yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—581no—
246C23C2×C22⋊D2911yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—581no—
250Q8—581no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—581no—
257D4—581no—
258D4—1164no—
259D4—1161no—
260D4—1161no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—582no—
273C2×C4—581no—
274C2×C4—1161no—
275C2×C4—1161no—
276C2×C4D4×D2911yescharacteristic
277C2×C4D4×D2911yescharacteristic
278C2×C4D4×D2911yescharacteristic
279C2×C4#9080711yescharacteristic
280C2×C4C2×C22⋊D2911yescharacteristic
281C2×C4C2×C22⋊D2911yescharacteristic
282C8—582no—
283C8—1161no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—1162no—
295C22—1161no—
296C22#1174529911yescharacteristic
297C22#1174530111yescharacteristic
298C22#1174531511yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—1162no—
303C4—1161no—
304C4#1174529911yescharacteristic
305C4#1174530011yescharacteristic
306C4#1174530111yescharacteristic
307C4#1174530211yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—2321no—
314C2#1427107111yescharacteristic
subgroupG/H
centerC4#11745302
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#525C2
socleC2×C29#392
hypercenter#525D29
hypocenterC29#2010
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14271961C2semidirect
2. #14271674C2semidirect
3. #14271181C2semidirect
4. #14271180C2semidirect
5. #14271127C2semidirect
6. #14270919C2semidirect
7. C29×#525C2semidirect
38. C2×Q8×C29D4semidirect
41. C2×D4×C29D4semidirect
57. C2×D116D4semidirect
59. C2×Dic58D4semidirect
65. C42×C29D4semidirect
75. C4×Dic29D4semidirect
81. C2×#6597D4semidirect
153. #525D29semidirect
190. C29#2010semidirect
201. C2×Q8C22⋊D29semidirect
207. C2×D4C22⋊D29semidirect
239. C42C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142719612
#142716742
#142711812
#142711802
#142711272
#142709192
C29×#5252
#201029