Finite Group Databasebeta

← #17994895

Subgroups — #17994895

Order 4736.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×M16×D37C211yesmaximal, characteristic, complemented
2#14558040C211yesmaximal, characteristic
3C2×#11924463C211yesmaximal, characteristic, complemented
4C4×#10596938C211yesmaximal, characteristic, complemented
5#14557294C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C22×C4×D37C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10C2×#10596929—21no—
11M16×D37—22no—
12M16×D37—22no—
13C2×C8×D37—21no—
14#11924517—21no—
15#11924512C411yescharacteristic, complemented
16#11924512C411yescharacteristic, complemented
17#11924507C411yescharacteristic, complemented
18#11924507C411yescharacteristic, complemented
19#11924504—21no—
20C4×C22⋊D37—21no—
21C4×C22⋊D37—21no—
22#11924495C2211yescharacteristic
23C2×#10596938—21no—
24C2×C4×Dic37C2211yescharacteristic
25#11924463—22no—
26#11924443—21no—
27C2×#41×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29C2×C42×C37C2211yescharacteristic
30#104×C37—22no—
31C23×D37D411yescharacteristic
32#41×C37—21no—
33#41×C37—21no—
34#41×C37—21no—
35#41×C37—21no—
36C2×Q8×C37C2×C411yescharacteristic
37C2×D4×C37—21no—
38C2×D4×C37C2×C411yescharacteristic
39C22×C4×C37—21no—
40C22×C4×C37—21no—
41C22×C4×C37C2311yescharacteristic
42C2×C22⋊D37—21no—
43C2×C22⋊D37—21no—
44C22×Dic37—21no—
45C22×Dic37D411yescharacteristic
46C2×C4×D37—21no—
47C2×C4×D37—21no—
48C2×C4×D37—21no—
49C2×C4×D37—21no—
50C2×C4×D37C2×C411yescharacteristic
51C2×C4×D37C2×C411yescharacteristic
52C2×C4×D37D411yescharacteristic
53C2×C4×D37D411yescharacteristic
54M16×C37—21no—
55M16×C37D412yescomplemented
56C2×C8×C37—21no—
57C42×C37—21no—
58C42×C37—21no—
59C22⋊Dic37—21no—
60C22⋊Dic37—21no—
61C22⋊Dic37—21no—
62#10596938—24no—
63#10596938—21no—
64#10596938—21no—
65C4⋊Dic37C2×C411yescharacteristic
66C4⋊Dic37C2×C411yescharacteristic
67#10596936—21no—
68#10596936—21no—
69C4×Dic37—21no—
70C4×Dic37—21no—
71C4×Dic37—21no—
72#10596934—21no—
73#10596934D412yescomplemented
74C2×#64436—21no—
75#10596929—24no—
76C8×D37—24no—
77C23×C37—21no—
78C23×C37C2×D411yescharacteristic
79C22×D37—21no—
80C22×D37—21no—
81C22×D37—22no—
82C22×D37—41no—
83C22×D37C22⋊C411yescharacteristic
84C22×D37C22⋊C411yescharacteristic
85Q8×C37—21no—
86Q8×C37—21no—
87D4×C37—21no—
88D4×C37—21no—
89D4×C37—41no—
90D4×C37—41no—
91C2×C4×C37—22no—
92C2×C4×C37—21no—
93C2×C4×C37—41no—
94C2×C4×C37—41no—
95C2×C4×C37—41no—
96C2×C4×C37—41no—
97C2×C4×C37C22×C411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2×D411yescharacteristic
101C2×C4×C37#4111yescharacteristic
102C2×C4×C37#4111yescharacteristic
103C22⋊D37—42no—
104C22⋊D37—42no—
105C2×Dic37—21no—
106C2×Dic37—21no—
107C2×Dic37—22no—
108C2×Dic37—21no—
109C2×Dic37—21no—
110C2×Dic37—41no—
111C2×Dic37—41no—
112C2×Dic37C22⋊C411yescharacteristic
113C2×Dic37C22⋊C411yescharacteristic
114C4×D37—21no—
115C4×D37—21no—
116C4×D37—21no—
117C4×D37—21no—
118C4×D37—21no—
119C4×D37—21no—
120C4×D37—21no—
121C4×D37—21no—
122C8×C37—22no—
123#64436—22no—
124C22×C37—21no—
125C22×C37—21no—
126C22×C37—41no—
127C22×C37—41no—
128C22×C37—41no—
129C22×C37C2×C22⋊C411yescharacteristic
130C22×C37#12111yescharacteristic
131C22×C37#12111yescharacteristic
132C2×D37—21no—
133C2×D37—21no—
134C2×D37—21no—
135C2×D37—21no—
136C2×D37—21no—
137C2×D37—42no—
138C2×D37—42no—
139C2×D37#10412yescomplemented
140C4×C37—42no—
141C4×C37—41no—
142C4×C37C4×D411yescharacteristic
143C4×C37C4×D411yescharacteristic
144C4×C37#12011yescharacteristic
145C4×C37#12311yescharacteristic
146Dic37—21no—
147Dic37—21no—
148Dic37—42no—
149Dic37—41no—
150Dic37—41no—
151#1871—371nomaximal, Sylow
152C2×C37—21no—
153C2×C37—21no—
154C2×C37—81no—
155C2×C37#38611yescharacteristic
156C2×C37C2×#10411yescharacteristic
157C2×C37#42111yescharacteristic
158D37—22no—
159D37—41no—
160C22×M16—371no—
161#525—371no—
162C2×#104—371no—
163C2×#104D3711yescharacteristic, complemented
164C4×C22⋊C4—371no—
165#339—371no—
166#339—371no—
167C37#187111yescharacteristic, complemented, Sylow
168C2×#41C2×D3711yescharacteristic
169C23×C4—371no—
170C2×M16—371no—
171C2×M16—741no—
172C2×M16—742no—
173C2×M16—742no—
174C2×M16C2×D3711yescharacteristic
175C22×C8—741no—
176#123—741no—
177C22⋊Q8—371no—
178C22⋊Q8—371no—
179#121—371no—
180#121—371no—
181#120—741no—
182C4×D4—741no—
183C4×D4—741no—
184#117—371no—
185C2×C22⋊C4—741no—
186C2×C42—371no—
187C2×C42C2×D3711yescharacteristic
188#104—22no—
189#104—742no—
190#95—741no—
191C24—371no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196C2×Q8C4×D3711yescharacteristic
197C2×D4—21no—
198C2×D4—741no—
199C2×D4—741no—
200C2×D4C4×D3711yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—371no—
204C22×C4—371no—
205C22×C4—371no—
206C22×C4—371no—
207C22×C4—371no—
208C22×C4—741no—
209C22×C4—741no—
210C22×C4—741no—
211C22×C4—741no—
212C22×C4—741no—
213C22×C4C22×D3711yescharacteristic
214M16—21no—
215M16—372no—
216M16—744no—
217M16—741no—
218M16C22⋊D3712yescomplemented
219C2×C8—21no—
220C2×C8—744no—
221C2×C8—741no—
222C4⋊C4—371no—
223C4⋊C4—371no—
224C4⋊C4—741no—
225C4⋊C4—741no—
226C22⋊C4—741no—
227C22⋊C4—741no—
228C22⋊C4—744no—
229C22⋊C4—741no—
230C22⋊C4—741no—
231C22⋊C4—741no—
232C42—21no—
233C42—21no—
234C42—741no—
235C42—741no—
236C42—741no—
237C23—21no—
238C23—371no—
239C23—371no—
240C23—742no—
241C23—741no—
242C23—741no—
243C23—1481no—
244C23D4×D3711yescharacteristic
245Q8—21no—
246Q8—21no—
247D4—21no—
248D4—21no—
249D4—41no—
250D4—41no—
251D4—1482no—
252D4—1482no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—371no—
260C2×C4—371no—
261C2×C4—741no—
262C2×C4—741no—
263C2×C4—741no—
264C2×C4—741no—
265C2×C4—741no—
266C2×C4—741no—
267C2×C4—741no—
268C2×C4—741no—
269C2×C4—741no—
270C2×C4—741no—
271C2×C4—742no—
272C2×C4—741no—
273C2×C4—741no—
274C2×C4—1481no—
275C2×C4—1481no—
276C2×C4C2×C4×D3711yescharacteristic
277C2×C4#1059696211yescharacteristic
278C2×C4D4×D3711yescharacteristic
279C2×C4D4×D3711yescharacteristic
280C2×C4#1059696411yescharacteristic
281C2×C4C2×C22⋊D3711yescharacteristic
282C8—22no—
283C8—742no—
284C22—21no—
285C22—21no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—372no—
290C22—741no—
291C22—741no—
292C22—741no—
293C22—741no—
294C22—741no—
295C22—1482no—
296C22—1482no—
297C22C22⋊C4×D3711yescharacteristic
298C22#1192450711yescharacteristic
299C22#1192450911yescharacteristic
300C4—42no—
301C4—41no—
302C4—741no—
303C4—741no—
304C4—1482no—
305C4—1481no—
306C4—1481no—
307C4#1192449611yescharacteristic
308C4C4×C22⋊D3711yescharacteristic
309C4#1192450411yescharacteristic
310C4#1192451811yescharacteristic
311C2—21no—
312C2—21no—
313C2—81no—
314C2—742no—
315C2—1481no—
316C2#1455740911yescharacteristic
317C2#104×D3711yescharacteristic
318C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558040C2
cosocleC22×C4×C37C23
hypercenterC2×#104D37
hypocenterC37#1871
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×M16×D37C2semidirect
3. C2×#11924463C2semidirect
4. C4×#10596938C2semidirect
5. #14557294C2semidirect
6. #14557293C2semidirect
7. C2×#104×C37C2semidirect
15. #11924512C4semidirect
16. #11924512C4semidirect
17. #11924507C4semidirect
18. #11924507C4semidirect
55. M16×C37D4semidirect
73. #10596934D4semidirect
139. C2×D37#104semidirect
163. C2×#104D37semidirect
167. C37#1871semidirect
218. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D372
#145580402
C2×#119244632
C4×#105969382
#145572942
#145572932
C2×#104×C372
#187137