Finite Group Databasebeta

← #17994553

Subgroups — #17994553

Order 4736.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11924583C211yesmaximal, characteristic
2C2×#11924463C211yesmaximal, characteristic, complemented
3C2×#11924462C211yesmaximal, characteristic, complemented
4#14557532C211yesmaximal, characteristic, complemented
5C2×#11924454C211yesmaximal, characteristic, complemented
6#14557438C211yesmaximal, characteristic, complemented
7C37×#417C211yesmaximal, characteristic, complemented
8#11924583—22no—
9#11924583—22no—
10#11924583—22no—
11#11924583C414yescomplemented
12C2×#10596962—21no—
13C2×#10596962C2211yescharacteristic
14C2×#10596964—21no—
15C2×#10596964—22no—
16C22×Dic74—21no—
17C22×Dic74C2211yescharacteristic
18C2×Q8×D37—21no—
19C2×#10596934C2211yescharacteristic
20C2×C4×Dic37C2211yescharacteristic
21#11924463—22no—
22#11924462—22no—
23#11924459—21no—
24#11924456—21no—
25#11924454—22no—
26#11924443—22no—
27C2×#41×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29C2×C4⋊C4×C37C2211yescharacteristic
30#103×C37—21no—
31#102×C37—21no—
32#41×C37—21no—
33#41×C37—21no—
34#41×C37C2×C412yes—
35#41×C37D412yes—
36C2×Q8×C37D411yescharacteristic
37C2×D4×C37—21no—
38C2×D4×C37D411yescharacteristic
39C22×C4×C37—21no—
40C22×C4×C37—21no—
41C22×C4×C37C2311yescharacteristic
42C2×C22⋊D37—22no—
43C2×C22⋊D37—21no—
44C22×Dic37—22no—
45C22×Dic37—21no—
46C22×Dic37D412yes—
47Q8×D37—24no—
48Q8×D37—24no—
49#10596964—28no—
50#10596964—24no—
51#10596964—24no—
52#10596964—28no—
53#10596962—24no—
54#10596962—21no—
55#10596962—21no—
56#10596962—24no—
57#10596962C2×C412yes—
58#10596962D412yes—
59C2×D148D411yescharacteristic
60C2×C4×D37—22no—
61C2×C4×D37—21no—
62C2×Dic74—22no—
63C2×Dic74—24no—
64C2×Dic74—21no—
65C2×Dic74—21no—
66C2×Dic74—21no—
67C2×Dic74—21no—
68C2×Dic74—24no—
69C2×Dic74C2×C412yes—
70C2×Dic74D412yes—
71C2×Dic74D411yescharacteristic
72M16×C37—21no—
73M16×C37—21no—
74C2×C8×C37—21no—
75C4⋊C4×C37—21no—
76C4⋊C4×C37—21no—
77C4×Dic37—21no—
78C4×Dic37—21no—
79#10596934—21no—
80#10596934—21no—
81C2×#64436—21no—
82C23×C37—21no—
83C23×C37C2×D411yescharacteristic
84C22×D37—21no—
85Q8×C37—21no—
86Q8×C37C22⋊C412yes—
87D4×C37—22no—
88D4×C37—22no—
89D4×C37—21no—
90D4×C37C22⋊C412yes—
91C2×C4×C37—21no—
92C2×C4×C37—22no—
93C2×C4×C37—22no—
94C2×C4×C37—42no—
95C2×C4×C37—41no—
96C2×C4×C37C22×C411yescharacteristic
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2×D411yescharacteristic
101C2×C4×C37C2×D411yescharacteristic
102C22⋊D37—28no—
103C22⋊D37—22no—
104C22⋊D37—22no—
105C2×Dic37—28no—
106C2×Dic37—22no—
107C2×Dic37—21no—
108C2×Dic37—22no—
109C2×Dic37—22no—
110C2×Dic37—41no—
111C2×Dic37—41no—
112C2×Dic37C22⋊C414yes—
113D148—21no—
114D148C22⋊C412yes—
115C4×D37—28no—
116C4×D37—22no—
117C4×D37—22no—
118Dic74—28no—
119Dic74—22no—
120Dic74—22no—
121Dic74—22no—
122Dic74—21no—
123Dic74—22no—
124Dic74C22⋊C412yes—
125C8×C37—41no—
126#64436—41no—
127C22×C37—21no—
128C22×C37—21no—
129C22×C37—22no—
130C22×C37—41no—
131C22×C37—41no—
132C22×C37C2×C22⋊C411yescharacteristic
133C22×C37#12011yescharacteristic
134C22×C37#12011yescharacteristic
135C2×D37—22no—
136C2×D37—41no—
137C2×D37—41no—
138C4×C37—22no—
139C4×C37—81no—
140C4×C37C2×C22⋊C411yescharacteristic
141C4×C37C2×C22⋊C411yescharacteristic
142C4×C37#12011yescharacteristic
143C4×C37#12011yescharacteristic
144Dic37—24no—
145Dic37—22no—
146Dic37—42no—
147#1793—371nomaximal, Sylow
148C2×C37—21no—
149C2×C37—21no—
150C2×C37—42no—
151C2×C37#37911yescharacteristic
152C2×C37#45411yescharacteristic
153C2×C37#45611yescharacteristic
154D37—42no—
155C2×2−1+4—371no—
156C2×#104—371no—
157C2×#104—371no—
158#417—371no—
159#417D3711yescharacteristic, complemented
160C2×#101—371no—
161#391—371no—
162C37#179311yescharacteristic, complemented, Sylow
1632−1+4—374no—
1642−1+4—742no—
1652−1+4—742no—
1662−1+4—742no—
167C2×#41—371no—
168C2×#41—741no—
169C2×#41—742no—
170C2×#41—741no—
171C2×#41C2×D3711yescharacteristic
172C22×Q8—371no—
173C22×Q8—741no—
174C22×Q8—741no—
175C2×M16—371no—
176C2×M16C2×D3711yescharacteristic
177C2×C4⋊C4C2×D3711yescharacteristic
178C2×C42—371no—
179#104—742no—
180#104—742no—
181#103—21no—
182#103—741no—
183#102—21no—
184#102—741no—
185#101—742no—
186#95—742no—
187#41—21no—
188#41—21no—
189#41—372no—
190#41—372no—
191#41—744no—
192#41—744no—
193#41—748no—
194#41—748no—
195#41—744no—
196#41—744no—
197#41—741no—
198#41—741no—
199#41C4×D3712yes—
200#41D14812yes—
201C2×Q8—372no—
202C2×Q8—372no—
203C2×Q8—371no—
204C2×Q8—744no—
205C2×Q8—742no—
206C2×Q8—744no—
207C2×Q8—744no—
208C2×Q8—744no—
209C2×Q8—741no—
210C2×Q8—741no—
211C2×Q8—741no—
212C2×Q8—741no—
213C2×Q8C22⋊D3711yescharacteristic
214C2×D4—21no—
215C2×D4—371no—
216C2×D4—742no—
217C2×D4—741no—
218C2×D4C22⋊D3711yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—372no—
222C22×C4—742no—
223C22×C4—742no—
224C22×C4—741no—
225C22×C4—741no—
226C22×C4C22×D3711yescharacteristic
227M16—21no—
228M16—21no—
229M16—741no—
230M16—741no—
231C2×C8—21no—
232C2×C8—741no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C42—741no—
236C42—741no—
237C23—21no—
238C23—741no—
239C23D4×D3711yescharacteristic
240Q8—21no—
241Q8—372no—
242Q8—748no—
243Q8—742no—
244Q8—742no—
245Q8—742no—
246Q8—742no—
247Q8—741no—
248Q8#1059693812yes—
249D4—22no—
250D4—22no—
251D4—21no—
252D4—372no—
253D4—748no—
254D4—742no—
255D4—742no—
256D4—741no—
257D4#1059693812yes—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—374no—
264C2×C4—748no—
265C2×C4—748no—
266C2×C4—742no—
267C2×C4—741no—
268C2×C4—742no—
269C2×C4—742no—
270C2×C4—742no—
271C2×C4—742no—
272C2×C4—1481no—
273C2×C4—1481no—
274C2×C4C2×C4×D3711yescharacteristic
275C2×C4C2×D14811yescharacteristic
276C2×C4D4×D3711yescharacteristic
277C2×C4D4×D3711yescharacteristic
278C2×C4D4×D3711yescharacteristic
279C2×C4C2×C22⋊D3711yescharacteristic
280C8—41no—
281C8—1481no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—742no—
288C22—1481no—
289C22—1481no—
290C22C22⋊C4×D3711yescharacteristic
291C22#1192450411yescharacteristic
292C22#1192450611yescharacteristic
293C4—22no—
294C4—81no—
295C4—744no—
296C4—742no—
297C4—1482no—
298C4C22⋊C4×D3711yescharacteristic
299C4C2×#1059693811yescharacteristic
300C4#1192450411yescharacteristic
301C4#1192450611yescharacteristic
302C2—21no—
303C2—21no—
304C2—42no—
305C2—1482no—
306C2#1455738811yescharacteristic
307C2#1455770411yescharacteristic
308C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#417C2
socleC22×C37#120
prime radicalC2×#11924583C2
cosocleC22×C4×C37C23
hypercenter#417D37
hypocenterC37#1793
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#11924463C2semidirect
3. C2×#11924462C2semidirect
4. #14557532C2semidirect
5. C2×#11924454C2semidirect
6. #14557438C2semidirect
7. C37×#417C2semidirect
11. #11924583C4semidirect
159. #417D37semidirect
162. C37#1793semidirect

Maximal subgroups

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

subgroupindex
C2×#119245832
C2×#119244632
C2×#119244622
#145575322
C2×#119244542
#145574382
C37×#4172
#179337