Finite Group Databasebeta

← #17995661

Subgroups — #17995661

Order 4736.

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#14558331C211yesmaximal, characteristic, complemented
2#14558044C211yesmaximal, characteristic, complemented
3#14557551C211yesmaximal, characteristic, complemented
4#14557550C211yesmaximal, characteristic, complemented
5#14557497C211yesmaximal, characteristic, complemented
6#14557289C211yesmaximal, characteristic, complemented
7C37×#525C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—21no—
10#11924566—21no—
11#11924562—21no—
12#11924561—21no—
13#11924556—22no—
14C2×#10596934C2211yescharacteristic
15C2×#10596934C2211yescharacteristic
16#11924519—21no—
17#11924515—21no—
18#11924510—21no—
19#11924505—21no—
20C4×C22⋊D37—22no—
21#11924495C2211yescharacteristic
22#11924464—22no—
23#11924463—22no—
24C22⋊#64436—22no—
25C2×#41×C37C2211yescharacteristic
26C23×C4×C37C2211yescharacteristic
27#123×C37—21no—
28C22⋊Q8×C37—21no—
29#121×C37—21no—
30#120×C37—21no—
31C4×D4×C37—22no—
32#117×C37C2211yescharacteristic
33C24×C37D411yescharacteristic
34#41×C37—21no—
35#41×C37—21no—
36#41×C37—21no—
37#41×C37—21no—
38C2×Q8×C37D411yescharacteristic, complemented
39C2×D4×C37—22no—
40C2×D4×C37—21no—
41C2×D4×C37D411yescharacteristic, complemented
42C22×C4×C37—21no—
43C22×C4×C37—21no—
44C22×C4×C37—21no—
45C22×C4×C37—21no—
46C22×C4×C37—21no—
47C22×C4×C37—21no—
48C22×C4×C37—21no—
49C22×C4×C37D411yescharacteristic
50C22×C4×C37C2311yescharacteristic
51C2×C22⋊D37—22no—
52C2×C22⋊D37—21no—
53#10596962—21no—
54#10596962—21no—
55#10596962—21no—
56#10596962—21no—
57C2×D148D411yescharacteristic, complemented
58C2×C4×D37—21no—
59C2×Dic74D411yescharacteristic, complemented
60C4⋊C4×C37—22no—
61C4⋊C4×C37—21no—
62C22⋊C4×C37—22no—
63C22⋊C4×C37—22no—
64C22⋊C4×C37—21no—
65C42×C37D412yescomplemented
66C22⋊Dic37—22no—
67C22⋊Dic37—21no—
68#10596942—22no—
69#10596941—22no—
70#10596940—22no—
71#10596939—22no—
72#10596938—22no—
73C4⋊Dic37—21no—
74#10596936—22no—
75C4×Dic37D412yescomplemented
76#10596934—21no—
77#10596934—21no—
78#10596934—21no—
79#10596934—21no—
80C2×#64436—21no—
81C2×#64436D412yescomplemented
82C23×C37—21no—
83C23×C37—21no—
84C23×C37—21no—
85C23×C37—21no—
86C23×C37—42no—
87C23×C37C2×D411yescharacteristic
88C22×D37—21no—
89Q8×C37—21no—
90Q8×C37—21no—
91D4×C37—21no—
92D4×C37—21no—
93D4×C37—44no—
94D4×C37—41no—
95D4×C37—41no—
96C2×C4×C37—21no—
97C2×C4×C37—22no—
98C2×C4×C37—21no—
99C2×C4×C37—21no—
100C2×C4×C37—21no—
101C2×C4×C37—41no—
102C2×C4×C37—41no—
103C2×C4×C37—41no—
104C2×C4×C37—41no—
105C2×C4×C37—41no—
106C2×C4×C37—41no—
107C2×C4×C37C2×D411yescharacteristic
108C2×C4×C37C2×D411yescharacteristic
109C2×C4×C37C2×D411yescharacteristic
110C2×C4×C37C2×D411yescharacteristic
111C2×C4×C37C2×D411yescharacteristic
112C2×C4×C37#4111yescharacteristic
113C22⋊D37—44no—
114C22⋊D37—41no—
115C22⋊D37—41no—
116C2×Dic37—22no—
117C2×Dic37—21no—
118D148—21no—
119D148—21no—
120C4×D37—41no—
121C4×D37—41no—
122Dic74—21no—
123Dic74—21no—
124#64436—22no—
125#64436—41no—
126C22×C37—22no—
127C22×C37—22no—
128C22×C37—22no—
129C22×C37—41no—
130C22×C37—41no—
131C22×C37—41no—
132C22×C37—41no—
133C22×C37—42no—
134C22×C37—41no—
135C22×C37—41no—
136C22×C37#12011yescharacteristic
137C22×C37#12011yescharacteristic
138C22×C37#12111yescharacteristic
139C2×D37—42no—
140C2×D37—41no—
141C4×C37—42no—
142C4×C37—41no—
143C4×C37—41no—
144C4×C37#12011yescharacteristic
145C4×C37#12111yescharacteristic
146C4×C37#12111yescharacteristic
147C4×C37#12711yescharacteristic
148Dic37—42no—
149Dic37—41no—
150#2010—371nomaximal, Sylow
151C2×C37—21no—
152C2×C37—21no—
153C2×C37—21no—
154C2×C37—42no—
155C2×C37—81no—
156C2×C37#39211yescharacteristic
157D37—81no—
158#575—371no—
159#525—371no—
160#525D3711yescharacteristic, complemented
161#421—371no—
162#421—371no—
163#407—371no—
164H(3,ℤ/4)—371no—
165C37#201011yescharacteristic, complemented, Sylow
166C2×#41—371no—
167C2×#41C2×D3711yescharacteristic
168C23×C4C2×D3711yescharacteristic
169#137—741no—
170#137—741no—
171AGL(1,ℤ/8)—741no—
172AGL(1,ℤ/8)—741no—
173#135—742no—
174C2×M16—371no—
175C2×M16—371no—
176#123—21no—
177#123—741no—
178C22⋊Q8—21no—
179C22⋊Q8—741no—
180#121—21no—
181#121—741no—
182#120—21no—
183#120—741no—
184C4×D4—22no—
185C4×D4—742no—
186#117—371no—
187#117C2×D3711yescharacteristic
188#104—742no—
189#104—742no—
190C22⋊C8—742no—
191C24C22⋊D3711yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—741no—
197#41—741no—
198#41—741no—
199#41—741no—
200C2×Q8—371no—
201C2×Q8C22⋊D3711yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—371no—
205C2×D4—742no—
206C2×D4—741no—
207C2×D4C22⋊D3711yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—741no—
216C22×C4C22⋊D3711yescharacteristic
217C22×C4C22×D3711yescharacteristic
218Q16—742no—
219SD16—742no—
220SD16—742no—
221D8—742no—
222M16—741no—
223M16—741no—
224M16—741no—
225M16—741no—
226C2×C8—372no—
227C2×C8—741no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—742no—
231C4⋊C4—741no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—742no—
236C22⋊C4—742no—
237C22⋊C4—741no—
238C42—372no—
239C42C22⋊D3712yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—741no—
246C23C2×C22⋊D3711yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—741no—
250Q8—741no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—741no—
257D4—741no—
258D4—1484no—
259D4—1481no—
260D4—1481no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
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—742no—
273C2×C4—741no—
274C2×C4—1481no—
275C2×C4—1481no—
276C2×C4D4×D3711yescharacteristic
277C2×C4D4×D3711yescharacteristic
278C2×C4D4×D3711yescharacteristic
279C2×C4#1059696411yescharacteristic
280C2×C4C2×C22⋊D3711yescharacteristic
281C2×C4C2×C22⋊D3711yescharacteristic
282C8—742no—
283C8—1481no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—1482no—
295C22—1481no—
296C22#1192450411yescharacteristic
297C22#1192450511yescharacteristic
298C22#1192450811yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—1482no—
303C4—1481no—
304C4#1192450411yescharacteristic
305C4#1192450711yescharacteristic
306C4#1192450811yescharacteristic
307C4#1192453211yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—2961no—
314C2#1455744111yescharacteristic
subgroupG/H
centerC4#11924532
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#525C2
socleC2×C37#392
hypercenter#525D37
hypocenterC37#2010
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14558331C2semidirect
2. #14558044C2semidirect
3. #14557551C2semidirect
4. #14557550C2semidirect
5. #14557497C2semidirect
6. #14557289C2semidirect
7. C37×#525C2semidirect
38. C2×Q8×C37D4semidirect
41. C2×D4×C37D4semidirect
57. C2×D148D4semidirect
59. C2×Dic74D4semidirect
65. C42×C37D4semidirect
75. C4×Dic37D4semidirect
81. C2×#64436D4semidirect
160. #525D37semidirect
165. C37#2010semidirect
201. C2×Q8C22⋊D37semidirect
207. C2×D4C22⋊D37semidirect
239. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145580442
#145575512
#145575502
#145574972
#145572892
C37×#5252
#201037