Finite Group Databasebeta

← #17995662

Subgroups — #17995662

Order 4736.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558045C211yesmaximal, characteristic, complemented
3#14558040C211yesmaximal, characteristic, complemented
4#14557549C211yesmaximal, characteristic, complemented
5#14557496C211yesmaximal, characteristic, complemented
6#14557289C211yesmaximal, characteristic, complemented
7C37×#421C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×C4×D37C2211yescharacteristic
10#11924567—21no—
11#11924566—21no—
12#11924562—21no—
13#11924561—21no—
14#11924556—22no—
15C2×#10596934C2211yescharacteristic
16#11924520—21no—
17#11924517—21no—
18#11924516—21no—
19#11924512—21no—
20#11924511—21no—
21#11924507—21no—
22#11924506—21no—
23#11924504—21no—
24C4×D148—22no—
25C4×C22⋊D37—22no—
26#11924495C2211yescharacteristic
27#11924462—22no—
28#11924448—22no—
29C2×#41×C37C2211yescharacteristic
30C2×M16×C37C2211yescharacteristic
31#117×C37C2211yescharacteristic
32#104×C37—22no—
33C23×D37D411yescharacteristic
34#41×C37—21no—
35#41×C37—21no—
36#41×C37—21no—
37#41×C37—21no—
38C2×Q8×C37D411yescharacteristic, complemented
39C2×D4×C37—21no—
40C2×D4×C37D411yescharacteristic, complemented
41C22×C4×C37—21no—
42C22×C4×C37C2311yescharacteristic
43C2×C22⋊D37—22no—
44C2×C22⋊D37—21no—
45C22×Dic37D411yescharacteristic
46#10596962—21no—
47#10596962—21no—
48#10596962—21no—
49#10596962—21no—
50C2×D148—22no—
51C2×D148D411yescharacteristic, complemented
52C2×C4×D37—21no—
53C2×C4×D37—21no—
54C2×C4×D37—21no—
55C2×C4×D37—21no—
56C2×C4×D37—21no—
57C2×C4×D37—21no—
58C2×C4×D37—21no—
59C2×Dic74D411yescharacteristic, complemented
60M16×C37—21no—
61M16×C37—21no—
62C2×C8×C37—21no—
63C4⋊C4×C37—21no—
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—
73#10596938—22no—
74#10596938—22no—
75C4⋊Dic37—22no—
76C4⋊Dic37—21no—
77#10596936—22no—
78C4×Dic37D412yescomplemented
79#10596934—21no—
80#10596934—21no—
81C2×#64436D412yescomplemented
82C23×C37—21no—
83C23×C37C2×D411yescharacteristic
84C22×D37—21no—
85C22×D37—21no—
86C22×D37—21no—
87C22×D37—21no—
88C22×D37—42no—
89Q8×C37—21no—
90Q8×C37—21no—
91D4×C37—21no—
92D4×C37—21no—
93D4×C37—41no—
94D4×C37—41no—
95C2×C4×C37—21no—
96C2×C4×C37—22no—
97C2×C4×C37—41no—
98C2×C4×C37—41no—
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2×D411yescharacteristic
101C2×C4×C37C2×D411yescharacteristic
102C2×C4×C37C2×D411yescharacteristic
103C2×C4×C37C2×D411yescharacteristic
104C2×C4×C37#4111yescharacteristic
105C22⋊D37—44no—
106C22⋊D37—41no—
107C22⋊D37—41no—
108C2×Dic37—22no—
109C2×Dic37—21no—
110C2×Dic37—21no—
111C2×Dic37—21no—
112C2×Dic37—21no—
113D148—21no—
114D148—21no—
115D148—44no—
116C4×D37—41no—
117C4×D37—41no—
118C4×D37—41no—
119C4×D37—41no—
120C4×D37—41no—
121C4×D37—41no—
122Dic74—21no—
123Dic74—21no—
124C8×C37—41no—
125#64436—22no—
126C22×C37—41no—
127C22×C37—42no—
128C22×C37—41no—
129C22×C37#12011yescharacteristic
130C22×C37#12011yescharacteristic
131C22×C37#12111yescharacteristic
132C2×D37—22no—
133C2×D37—22no—
134C2×D37—22no—
135C2×D37—41no—
136C2×D37—41no—
137C2×D37—41no—
138C2×D37—41no—
139C2×D37—42no—
140C2×D37—41no—
141C4×C37—42no—
142C4×C37—41no—
143C4×C37#12011yescharacteristic
144C4×C37#12111yescharacteristic
145C4×C37#12111yescharacteristic
146C4×C37#12711yescharacteristic
147Dic37—42no—
148Dic37—41no—
149Dic37—41no—
150#2010—371nomaximal, Sylow
151C2×C37—21no—
152C2×C37—21no—
153C2×C37—21no—
154C2×C37—81no—
155C2×C37#39211yescharacteristic
156D37—42no—
157D37—81no—
158#575—371no—
159#525—371no—
160#525—371no—
161#421—371no—
162#421D3711yescharacteristic, complemented
163#407—371no—
164H(3,ℤ/4)—371no—
165C37#201011yescharacteristic, complemented, Sylow
166C2×#41—371no—
167C2×#41C2×D3711yescharacteristic
168C23×C4—371no—
169#137—741no—
170#137—741no—
171AGL(1,ℤ/8)—741no—
172AGL(1,ℤ/8)—741no—
173#135—742no—
174C2×M16—371no—
175C2×M16C2×D3711yescharacteristic
176#123—741no—
177#123—741no—
178C22⋊Q8—741no—
179C22⋊Q8—741no—
180#121—741no—
181#121—741no—
182#120—741no—
183#120—741no—
184C4×D4—742no—
185C4×D4—742no—
186#117—371no—
187#117C2×D3711yescharacteristic
188#104—22no—
189#104—742no—
190C22⋊C8—742no—
191C24—371no—
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×Q8D14811yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—371no—
204C2×D4—742no—
205C2×D4—742no—
206C2×D4—741no—
207C2×D4D14811yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—371no—
210C22×C4—741no—
211C22×C4—741no—
212C22×C4—741no—
213C22×C4—741no—
214C22×C4—741no—
215C22×C4—741no—
216C22×C4—741no—
217C22×C4C22×D3711yescharacteristic
218Q16—742no—
219SD16—742no—
220SD16—742no—
221D8—742no—
222M16—21no—
223M16—21no—
224M16—741no—
225M16—741no—
226C2×C8—21no—
227C2×C8—372no—
228C4⋊C4—21no—
229C4⋊C4—742no—
230C4⋊C4—742no—
231C4⋊C4—741no—
232C22⋊C4—21no—
233C22⋊C4—742no—
234C22⋊C4—742no—
235C22⋊C4—742no—
236C22⋊C4—742no—
237C22⋊C4—741no—
238C42—372no—
239C42C22⋊D3712yescomplemented
240C23—21no—
241C23—741no—
242C23—741no—
243C23—741no—
244C23—741no—
245C23—1482no—
246C23D4×D3711yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—741no—
250Q8—741no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—741no—
256D4—741no—
257D4—1484no—
258D4—1484no—
259D4—1481no—
260D4—1481no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—741no—
266C2×C4—741no—
267C2×C4—742no—
268C2×C4—741no—
269C2×C4—741no—
270C2×C4—1481no—
271C2×C4—1481no—
272C2×C4—1481no—
273C2×C4—1481no—
274C2×C4—1481no—
275C2×C4—1481no—
276C2×C4C2×D14811yescharacteristic
277C2×C4#1059696211yescharacteristic
278C2×C4D4×D3711yescharacteristic
279C2×C4D4×D3711yescharacteristic
280C2×C4D4×D3711yescharacteristic
281C2×C4C2×C22⋊D3711yescharacteristic
282C8—41no—
283C8—742no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—742no—
288C22—742no—
289C22—742no—
290C22—1482no—
291C22—1481no—
292C22—1481no—
293C22—1481no—
294C22—1481no—
295C22—1481no—
296C22#1192450411yescharacteristic
297C22#1192450611yescharacteristic
298C22#1192450911yescharacteristic
299C4—42no—
300C4—41no—
301C4—1482no—
302C4—1481no—
303C4—1481no—
304C4#1192450611yescharacteristic
305C4#1192450911yescharacteristic
306C4#1192451011yescharacteristic
307C4#1192453211yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—2961no—
313C2—1482no—
314C2#1455744211yescharacteristic
subgroupG/H
centerC4#11924532
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#421C2
socleC2×C37#392
hypercenter#421D37
hypocenterC37#2010
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #14558331C2semidirect
2. #14558045C2semidirect
3. #14558040C2semidirect
4. #14557549C2semidirect
5. #14557496C2semidirect
6. #14557289C2semidirect
7. C37×#421C2semidirect
38. C2×Q8×C37D4semidirect
40. C2×D4×C37D4semidirect
51. C2×D148D4semidirect
59. C2×Dic74D4semidirect
65. C42×C37D4semidirect
78. C4×Dic37D4semidirect
81. C2×#64436D4semidirect
162. #421D37semidirect
165. C37#2010semidirect
201. C2×Q8D148semidirect
207. C2×D4D148semidirect
239. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145580452
#145580402
#145575492
#145574962
#145572892
C37×#4212
#201037