Finite Group Databasebeta

← #18003995

Subgroups — #18003995

Order 4736.

800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11924581C211yesmaximal, characteristic, complemented
2#14558095C212yesmaximal, complemented
3#14558092C211yesmaximal, characteristic, complemented
4#14557724C214yesmaximal, complemented
5#14557721C214yesmaximal, complemented
6C2×#11924450C212yesmaximal, complemented
7C2×#99×C37C211yesmaximal, characteristic, complemented
8#11924581—22no—
9#11924581—24no—
10#11924581C2214yes—
11C2×#10596962—21no—
12C2×#10596964—22no—
13C22×C22⋊D37—21no—
14C22×C22⋊D37C2212yes—
15C22×C22⋊D37C2211yescharacteristic, complemented
16C2×D4×D37—22no—
17#11924520—22no—
18#11924520C2214yescomplemented
19#11924519—21no—
20#11924517C2212yescomplemented
21#11924510—24no—
22#11924508—22no—
23#11924506—22no—
24#11924506C2214yescomplemented
25#11924505—21no—
26#11924504C2212yescomplemented
27C2×C22⋊Dic37C2211yescharacteristic, complemented
28#11924450C2218yescomplemented
29C22×D4×C37C2211yescharacteristic
30C2×C22⋊C4×C37C2212yescomplemented
31#99×C37C2214yescomplemented
32C24×C37D411yescharacteristic, complemented
33C24×C37C2311yescharacteristic
34C23×D37—21no—
35C23×D37D412yescomplemented
36C23×D37C2311yescharacteristic, complemented
37C2×D4×C37—22no—
38C2×D4×C37—22no—
39C2×D4×C37D412yescomplemented
40C2×D4×C37C2312yes—
41C22×C4×C37—22no—
42C22×C4×C37D411yescharacteristic, complemented
43C2×C22⋊D37—22no—
44C2×C22⋊D37—24no—
45C2×C22⋊D37—22no—
46C2×C22⋊D37—22no—
47C2×C22⋊D37—24no—
48C2×C22⋊D37—22no—
49C2×C22⋊D37—22no—
50C2×C22⋊D37—21no—
51C2×C22⋊D37—22no—
52C2×C22⋊D37—21no—
53C2×C22⋊D37—22no—
54C2×C22⋊D37—22no—
55C2×C22⋊D37D414yescomplemented
56C2×C22⋊D37C2314yes—
57C22×Dic37—21no—
58C22×Dic37—21no—
59C22×Dic37D412yescomplemented
60C22×Dic37C2311yescharacteristic, complemented
61#10596964—28no—
62#10596964—28no—
63D4×D37—28no—
64D4×D37—28no—
65#10596962—24no—
66#10596962—24no—
67C2×D148—21no—
68C2×D148—24no—
69C2×C4×D37—22no—
70C2×Dic74—21no—
71C22⋊C4×C37—22no—
72C22⋊C4×C37C2314yescomplemented
73C22⋊Dic37—21no—
74C22⋊Dic37—22no—
75C22⋊Dic37C2312yescomplemented
76#10596938—24no—
77#10596938—22no—
78#10596938—24no—
79C4⋊Dic37—24no—
80#10596936—22no—
81C23×C37—21no—
82C23×C37—21no—
83C23×C37—81no—
84C23×C37—81no—
85C23×C37C2×D412yes—
86C23×C37C2×D411yescharacteristic
87C23×C37C2×D411yescharacteristic
88C23×C37C2×D412yes—
89C23×C37C2×D412yes—
90C23×C37C2411yescharacteristic
91C22×D37—22no—
92C22×D37—24no—
93C22×D37—22no—
94C22×D37—22no—
95C22×D37—21no—
96C22×D37—81no—
97C22×D37—82no—
98C22×D37—82no—
99C22×D37C2×D414yes—
100D4×C37—24no—
101D4×C37—24no—
102C2×C4×C37—21no—
103C2×C4×C37—21no—
104C2×C4×C37—24no—
105C2×C4×C37—82no—
106C2×C4×C37C2×D412yes—
107C22⋊D37—28no—
108C22⋊D37—24no—
109C22⋊D37—24no—
110C22⋊D37—24no—
111C22⋊D37—24no—
112C22⋊D37—41no—
113C22⋊D37—42no—
114C22⋊D37—41no—
115C22⋊D37—82no—
116C2×Dic37—24no—
117C2×Dic37—22no—
118C2×Dic37—22no—
119C2×Dic37—21no—
120C2×Dic37—22no—
121C2×Dic37—22no—
122C2×Dic37—81no—
123C2×Dic37C2×D414yes—
124D148—24no—
125D148—84no—
126C4×D37—28no—
127Dic74—24no—
128C22×C37—22no—
129C22×C37—41no—
130C22×C37—42no—
131C22×C37—42no—
132C22×C37—41no—
133C22×C37—41no—
134C22×C37—42no—
135C22×C37—42no—
136C22×C37—81no—
137C22×C37#12011yescharacteristic
138C22×C37#12012yes—
139C22×C37#12011yescharacteristic
140C22×C37C22×D412yes—
141C22×C37C22×D411yescharacteristic
142C2×D37—24no—
143C2×D37—44no—
144C2×D37—44no—
145C2×D37—44no—
146C2×D37—42no—
147C2×D37—41no—
148C2×D37—82no—
149C2×D37—84no—
150C4×C37—22no—
151C4×C37—44no—
152Dic37—24no—
153Dic37—42no—
154Dic37—41no—
155#3026—371nomaximal, Sylow
156C2×C37—21no—
157C2×C37—22no—
158C2×C37—21no—
159C2×C37—22no—
160C2×C37—21no—
161C2×C37—42no—
162C2×C37C2×#12011yescharacteristic
163D37—44no—
164D37—81no—
165C2×H(5,𝔽2)—371no—
166#534—371no—
167#534—372no—
168#458—374no—
169B(4,𝔽2)—374no—
170C2×#99—372no—
171C2×#99D3711yescharacteristic, complemented
172C37#302611yescharacteristic, complemented, Sylow
173H(5,𝔽2)—374no—
174H(5,𝔽2)—744no—
175H(5,𝔽2)—742no—
176C2×#41—742no—
177C2×#41—741no—
178C22×D4—372no—
179C22×D4—371no—
180C22×D4—742no—
181C22×D4—741no—
182C22×D4C2×D3711yescharacteristic
183#123—372no—
184#123—374no—
185#123—742no—
186#123—741no—
187#121—744no—
188#121—742no—
189#120—372no—
190#120—374no—
191#120—742no—
192#120—741no—
193C2×C22⋊C4—371no—
194C2×C22⋊C4C2×D3712yescomplemented
195#99—378no—
196#99C2×D3714yescomplemented
197C24—372no—
198C24—371no—
199C24—741no—
200C24D14811yescharacteristic, complemented
201C24C22×D3711yescharacteristic
202#41—744no—
203#41—748no—
204#41—748no—
205#41—744no—
206C2×Q8—741no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—374no—
210C2×D4—374no—
211C2×D4—744no—
212C2×D4—741no—
213C2×D4—748no—
214C2×D4—748no—
215C2×D4—742no—
216C2×D4—742no—
217C2×D4—744no—
218C2×D4—742no—
219C2×D4—742no—
220C2×D4—744no—
221C2×D4—742no—
222C2×D4—742no—
223C2×D4—741no—
224C2×D4—741no—
225C2×D4—742no—
226C2×D4—742no—
227C2×D4D14812yescomplemented
228C2×D4C22×D3712yes—
229C22×C4—22no—
230C22×C4—372no—
231C22×C4—371no—
232C22×C4—742no—
233C22×C4—741no—
234C22×C4—741no—
235C22×C4D14811yescharacteristic, complemented
236C4⋊C4—744no—
237C4⋊C4—742no—
238C22⋊C4—22no—
239C22⋊C4—372no—
240C22⋊C4—744no—
241C22⋊C4—744no—
242C22⋊C4—741no—
243C22⋊C4—742no—
244C22⋊C4—742no—
245C22⋊C4C22×D3714yescomplemented
246C23—21no—
247C23—21no—
248C23—81no—
249C23—81no—
250C23—374no—
251C23—2962no—
252C23—2962no—
253C23—2961no—
254C23—744no—
255C23—742no—
256C23—742no—
257C23—742no—
258C23—741no—
259C23C2×D14812yes—
260C23C2×D14811yescharacteristic
261C23C2×D14811yescharacteristic
262C23D4×D3712yes—
263C23D4×D3712yes—
264C23C23×D3711yescharacteristic
265Q8—744no—
266D4—24no—
267D4—24no—
268D4—2964no—
269D4—2962no—
270D4—744no—
271D4—748no—
272D4—744no—
273D4—744no—
274D4—744no—
275D4—744no—
276D4—1481no—
277D4—1481no—
278D4—1482no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—82no—
283C2×C4—374no—
284C2×C4—2961no—
285C2×C4—748no—
286C2×C4—744no—
287C2×C4—742no—
288C2×C4—742no—
289C2×C4—742no—
290C2×C4—742no—
291C2×C4—741no—
292C2×C4C2×D14812yes—
293C22—22no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—81no—
302C22—2962no—
303C22—2964no—
304C22—744no—
305C22—1484no—
306C22—1482no—
307C22—1484no—
308C22—1484no—
309C22—1481no—
310C22#1192450611yescharacteristic
311C22#1192450611yescharacteristic
312C22#1192450612yes—
313C22C2×D4×D3712yes—
314C22C22×D14811yescharacteristic
315C4—22no—
316C4—44no—
317C4—744no—
318C4—1482no—
319C4—1481no—
320C2—22no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—42no—
326C2—2961no—
327C2—1484no—
328C2C2×#1192450611yescharacteristic
subgroupG/H
centerC2C2×#11924506
commutator, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC2×#99×C37C2
socleC2×C37C2×#120
hypercenterC2×#99D37
hypocenterC37#3026
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#11924581C2semidirect
2. #14558095C2semidirect
3. #14558092C2semidirect
4. #14557724C2semidirect
5. #14557721C2semidirect
6. C2×#11924450C2semidirect
7. C2×#99×C37C2semidirect
15. C22×C22⋊D37C22semidirect
18. #11924520C22semidirect
20. #11924517C22semidirect
24. #11924506C22semidirect
26. #11924504C22semidirect
27. C2×C22⋊Dic37C22semidirect
28. #11924450C22semidirect
30. C2×C22⋊C4×C37C22semidirect
31. #99×C37C22semidirect
32. C24×C37D4semidirect
35. C23×D37D4semidirect
36. C23×D37C23semidirect
39. C2×D4×C37D4semidirect
42. C22×C4×C37D4semidirect
55. C2×C22⋊D37D4semidirect
59. C22×Dic37D4semidirect
60. C22×Dic37C23semidirect
72. C22⋊C4×C37C23semidirect
75. C22⋊Dic37C23semidirect
171. C2×#99D37semidirect
172. C37#3026semidirect
194. C2×C22⋊C4C2×D37semidirect
196. #99C2×D37semidirect
200. C24D148semidirect
227. C2×D4D148semidirect
235. C22×C4D148semidirect
245. C22⋊C4C22×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245812
#145580952
#145580922
#145577242
#145577212
C2×#119244502
C2×#99×C372
#302637