Finite Group Databasebeta

← #18004272

Subgroups — #18004272

Order 4736.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11924562C211yesmaximal, characteristic, complemented
2C2×#11924543C211yesmaximal, characteristic, complemented
3#14558111C211yesmaximal, characteristic, complemented
4#14557784C212yesmaximal, complemented
5#14557777C212yesmaximal, complemented
6#14557767C212yesmaximal, complemented
7#14557760C212yesmaximal, complemented
8#14557576C211yesmaximal, characteristic, complemented
9#14557527C211yesmaximal, characteristic, complemented
10C2×#11924457C211yesmaximal, characteristic, complemented
11C37×#535C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13#11924562—24no—
14C2×#10596940C2212yes—
15C2×#10596939C2212yes—
16#11924543—24no—
17C2×#10596934C2211yescharacteristic
18C2×#10596934C2212yescomplemented
19C22×#64436C2211yescharacteristic
20C22×#64436C2212yescomplemented
21#11924515C2212yescomplemented
22#11924512—21no—
23#11924510C2212yescomplemented
24#11924508—22no—
25#11924507—21no—
26C2×C4⋊Dic37C2211yescharacteristic
27#11924469C2212yescomplemented
28#11924467C2212yescomplemented
29#11924459C2211yescharacteristic, complemented
30#11924459C2211yescharacteristic, complemented
31#11924457C2212yes—
32#11924457C2212yes—
33#11924456C2211yescharacteristic, complemented
34#11924456C2211yescharacteristic, complemented
35C2×#41×C37C2211yescharacteristic
36C22×D4×C37C2211yescharacteristic
37#127×C37—21no—
38#124×C37—21no—
39#121×C37C2212yes—
40#121×C37C2212yes—
41#120×C37—22no—
42#117×C37C2211yescharacteristic
43C24×C37—21no—
44#41×C37—22no—
45#41×C37—22no—
46C2×Q8×C37D411yescharacteristic
47C2×D4×C37—22no—
48C2×D4×C37—22no—
49C2×D4×C37—22no—
50C2×D4×C37—21no—
51C2×D4×C37—22no—
52C2×D4×C37D411yescharacteristic
53C2×D4×C37D412yes—
54C2×D4×C37C2312yes—
55C22×C4×C37C2312yes—
56C22×C4×C37C2311yescharacteristic
57C2×C22⋊D37—21no—
58C2×C22⋊D37—22no—
59C22×Dic37—21no—
60#10596962—22no—
61#10596962—22no—
62C2×D148C2311yescharacteristic
63C2×C4×D37—21no—
64C2×Dic74C2311yescharacteristic
65C4⋊C4×C37C2311yescharacteristic
66C4⋊C4×C37C2311yescharacteristic
67C22⋊C4×C37—21no—
68C22⋊C4×C37—22no—
69C22⋊C4×C37—22no—
70C42×C37—21no—
71C22⋊Dic37—22no—
72#10596940—24no—
73#10596939—24no—
74#10596938—22no—
75C4⋊Dic37—21no—
76C4⋊Dic37C2312yes—
77#10596936—22no—
78#10596934—24no—
79#10596934D414yescomplemented
80C2×#64436—22no—
81C2×#64436—24no—
82C2×#64436C2311yescharacteristic
83C2×#64436C2311yescharacteristic
84C2×#64436C2312yes—
85C23×C37—22no—
86C23×C37—42no—
87C23×C37—81no—
88C23×C37—81no—
89C23×C37C2×D412yes—
90C23×C37C2×D411yescharacteristic
91C22×D37—21no—
92Q8×C37—22no—
93D4×C37—24no—
94D4×C37—22no—
95D4×C37—22no—
96D4×C37—22no—
97D4×C37—42no—
98D4×C37—82no—
99D4×C37—82no—
100C2×C4×C37—22no—
101C2×C4×C37—22no—
102C2×C4×C37—21no—
103C2×C4×C37—21no—
104C2×C4×C37C2×D412yes—
105C2×C4×C37C2×D412yes—
106C2×C4×C37C2×D411yescharacteristic
107C2×C4×C37#4112yes—
108C2×C4×C37C2411yescharacteristic
109C22⋊D37—42no—
110C22⋊D37—82no—
111C2×Dic37—21no—
112C2×Dic37—22no—
113C2×Dic37—81no—
114D148—21no—
115D148—21no—
116C4×D37—42no—
117Dic74—21no—
118Dic74—21no—
119#64436—21no—
120#64436—21no—
121#64436C2×D414yes—
122C22×C37—21no—
123C22×C37—21no—
124C22×C37—22no—
125C22×C37—22no—
126C22×C37—22no—
127C22×C37—42no—
128C22×C37—42no—
129C22×C37—42no—
130C22×C37—84no—
131C22×C37#12112yes—
132C22×C37C22×D411yescharacteristic
133C2×D37—41no—
134C2×D37—41no—
135C2×D37—41no—
136C4×C37—22no—
137C4×C37—41no—
138C4×C37—41no—
139C4×C37#12112yes—
140C4×C37C22×D411yescharacteristic
141C4×C37C2×#4111yescharacteristic
142Dic37—41no—
143Dic37—42no—
144#3062—371nomaximal, Sylow
145C2×C37—22no—
146C2×C37—42no—
147C2×C37—82no—
148C2×C37C2×#12111yescharacteristic
149C2×C37#57611yescharacteristic
150C2×C37#57711yescharacteristic
151D37—81no—
152C2×AGL(1,ℤ/8)—371no—
153C2×#131—371no—
154#537—371no—
155#535D3711yescharacteristic, complemented
156#469—372no—
157#468—372no—
158#466—372no—
159#465—372no—
160#428—371no—
161#416—371no—
162C2×#102—371no—
163C37#306211yescharacteristic, complemented, Sylow
164C2×#41—371no—
165C2×#41C2×D3711yescharacteristic
166C22×D4C2×D3711yescharacteristic
167AGL(1,ℤ/8)—744no—
168C2×SD16—372no—
169C2×D8—372no—
170#131—744no—
171C2×M16—371no—
172C2×M16—372no—
173C22×C8—371no—
174C22×C8—372no—
175#127—21no—
176#124—21no—
177C22⋊Q8—372no—
178C22⋊Q8—741no—
179#121—372no—
180#121—741no—
181#121—742no—
182#121C2×D3712yes—
183#121C2×D3712yes—
184#120—22no—
185#117C2×D3711yescharacteristic
186C2×C4⋊C4—371no—
187#107—372no—
188#106—372no—
189#103—371no—
190#103—371no—
191#102—372no—
192#102—372no—
193#102—371no—
194#102—371no—
195C24—21no—
196#41—22no—
197#41—22no—
198#41—742no—
199#41—742no—
200C2×Q8—371no—
201C2×Q8C22⋊D3711yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—371no—
208C2×D4—742no—
209C2×D4—741no—
210C2×D4C22⋊D3712yes—
211C2×D4C22⋊D3711yescharacteristic
212C2×D4C22×D3712yes—
213C22×C4—741no—
214C22×C4—741no—
215C22×C4C22×D3712yes—
216C22×C4C22×D3711yescharacteristic
217SD16—744no—
218D8—744no—
219M16—374no—
220M16—744no—
221C2×C8—372no—
222C2×C8—371no—
223C2×C8—371no—
224C2×C8—744no—
225C2×C8—742no—
226C4⋊C4—372no—
227C4⋊C4—742no—
228C4⋊C4—741no—
229C4⋊C4C22×D3711yescharacteristic
230C4⋊C4C22×D3711yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—742no—
235C22⋊C4—742no—
236C42—21no—
237C23—22no—
238C23—42no—
239C23—81no—
240C23—81no—
241C23—741no—
242C23C2×C22⋊D3712yes—
243C23C2×C22⋊D3711yescharacteristic
244Q8—22no—
245Q8—741no—
246Q8—741no—
247D4—24no—
248D4—22no—
249D4—22no—
250D4—22no—
251D4—42no—
252D4—82no—
253D4—82no—
254D4—2962no—
255D4—741no—
256D4—741no—
257D4—1482no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—2961no—
263C2×C4—742no—
264C2×C4—741no—
265C2×C4—1482no—
266C2×C4D4×D3712yes—
267C2×C4#1059696412yes—
268C2×C4C2×C22⋊D3712yes—
269C2×C4C2×C22⋊D3711yescharacteristic
270C2×C4C23×D3711yescharacteristic
271C8—374no—
272C8—741no—
273C8—741no—
274C22—21no—
275C22—21no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—84no—
283C22—1481no—
284C22—1481no—
285C22—1481no—
286C22#1192450812yes—
287C22C22×C22⋊D3711yescharacteristic
288C4—22no—
289C4—41no—
290C4—41no—
291C4—1481no—
292C4—1482no—
293C4#1192450812yes—
294C4C2×D4×D3711yescharacteristic
295C4C2×#1059696411yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—2961no—
300C2C2×#1192450811yescharacteristic
301C2#1455833611yescharacteristic
302C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#535C2
socleC22×C37C22×D4
hypercenter#535D37
hypocenterC37#3062
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C2×#11924543C2semidirect
3. #14558111C2semidirect
4. #14557784C2semidirect
5. #14557777C2semidirect
6. #14557767C2semidirect
7. #14557760C2semidirect
8. #14557576C2semidirect
9. #14557527C2semidirect
10. C2×#11924457C2semidirect
11. C37×#535C2semidirect
18. C2×#10596934C22semidirect
20. C22×#64436C22semidirect
21. #11924515C22semidirect
23. #11924510C22semidirect
27. #11924469C22semidirect
28. #11924467C22semidirect
29. #11924459C22semidirect
30. #11924459C22semidirect
33. #11924456C22semidirect
34. #11924456C22semidirect
79. #10596934D4semidirect
155. #535D37semidirect
163. C37#3062semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245432
#145581112
#145577842
#145577772
#145577672
#145577602
#145575762
#145575272
C2×#119244572
C37×#5352
#306237