Finite Group Databasebeta

← #18003948

Subgroups — #18003948

Order 4736.

724 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 133 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#14558370C211yesmaximal, characteristic, complemented
2#14558332C212yesmaximal, complemented
3#14558084C211yesmaximal, characteristic, complemented
4#14557715C211yesmaximal, characteristic, complemented
5#14557709C212yesmaximal, complemented
6#14557708C211yesmaximal, characteristic, complemented
7#14557706C211yesmaximal, characteristic, complemented
8#14557702C212yesmaximal, complemented
9#104×D37C212yesmaximal, complemented
10#14557516C211yesmaximal, characteristic, complemented
11C37×#456C211yesmaximal, characteristic, complemented
12#11924584—22no—
13#11924584C2211yescharacteristic
14#11924582—22no—
15#11924582—22no—
16#11924582C2212yes—
17C2×#10596966—22no—
18C2×#10596966C2211yescharacteristic
19C2×#10596966C2211yescharacteristic, complemented
20#41×D37—22no—
21#41×D37—22no—
22#41×D37C2212yes—
23#11924568—22no—
24#11924567C2212yescomplemented
25#11924564C2212yescomplemented
26#11924563—22no—
27#11924561C2212yescomplemented
28#11924559—22no—
29#11924557—22no—
30M16×D37C2212yescomplemented
31#11924533C2211yescharacteristic, complemented
32#11924525C2211yescharacteristic, complemented
33#11924525C2211yescharacteristic, complemented
34#11924511—22no—
35#11924498—22no—
36C42×D37C2211yescharacteristic, complemented
37#11924464C2212yescomplemented
38#11924463C2212yescomplemented
39#11924462C2212yescomplemented
40#11924455C2211yescharacteristic, complemented
41#11924452C2212yescomplemented
422−1+4×C37C2211yescharacteristic
43#137×C37C2212yescomplemented
44C4⋊Q8×C37C2211yescharacteristic, complemented
45#104×C37C2212yescomplemented
46#101×C37C2211yescharacteristic, complemented
47#41×C37—22no—
48#41×C37—22no—
49#41×C37C2312yes—
50C2×Q8×C37—22no—
51C2×Q8×C37C2311yescharacteristic
52C2×Q8×C37C2311yescharacteristic
53#10596966—22no—
54#10596966—24no—
55#10596966—22no—
56#10596966—22no—
57#10596966—22no—
58#10596966—22no—
59#10596966—22no—
60#10596966—22no—
61#10596966D412yescomplemented
62Q8×D37—22no—
63Q8×D37—22no—
64Q8×D37D412yescomplemented
65#10596964—22no—
66#10596964—22no—
67#10596964D412yescomplemented
68D4×D37—24no—
69D4×D37—22no—
70D4×D37—24no—
71D4×D37—22no—
72D4×D37—22no—
73D4×D37D412yescomplemented
74#10596962—24no—
75#10596962—24no—
76#10596962—22no—
77#10596962—22no—
78#10596962—22no—
79#10596962C2312yes—
80C2×D148—24no—
81C2×D148—22no—
82C2×D148—22no—
83C2×D148—21no—
84C2×D148D412yes—
85C2×D148C2311yescharacteristic
86C2×D148C2311yescharacteristic
87C2×C4×D37—24no—
88C2×C4×D37—22no—
89C2×C4×D37—21no—
90C2×C4×D37—21no—
91C2×C4×D37D412yes—
92C2×C4×D37C2311yescharacteristic
93Q16×C37—22no—
94SD16×C37—22no—
95M16×C37C2312yes—
96C4⋊C4×C37—22no—
97C42×C37C2311yescharacteristic
98#10596942—22no—
99#10596941—22no—
100#10596941—22no—
101#10596939—22no—
102#10596938—22no—
103#10596938—22no—
104C4×Dic37—21no—
105C4×Dic37C2311yescharacteristic
106#10596934C2312yes—
107D296—22no—
108#10596930—22no—
109#10596929—22no—
110C8×D37—22no—
111C22×D37—24no—
112C22×D37—22no—
113C22×D37—21no—
114C22×D37C2×D412yes—
115C22×D37C2×D411yescharacteristic
116Q8×C37—22no—
117Q8×C37—22no—
118Q8×C37—22no—
119Q8×C37C2×D412yes—
120D4×C37—22no—
121D4×C37—22no—
122D4×C37C2×D412yes—
123C2×C4×C37—24no—
124C2×C4×C37—21no—
125C2×C4×C37—22no—
126C2×C4×C37—21no—
127C2×C4×C37C2×D412yes—
128C2×C4×C37C2411yescharacteristic
129C22⋊D37—24no—
130C22⋊D37—22no—
131C22⋊D37—22no—
132C22⋊D37—22no—
133C2×Dic37—22no—
134C2×Dic37—21no—
135C2×Dic37C2×D411yescharacteristic
136D148—24no—
137D148—22no—
138D148—22no—
139D148—24no—
140D148—22no—
141D148—22no—
142D148—44no—
143D148—42no—
144D148C2×D412yes—
145C4×D37—24no—
146C4×D37—24no—
147C4×D37—22no—
148C4×D37—22no—
149C4×D37—22no—
150C4×D37—22no—
151C4×D37—22no—
152C4×D37—42no—
153C4×D37—41no—
154C4×D37—41no—
155C4×D37C2×D412yes—
156C4×D37C2×D412yes—
157Dic74—22no—
158Dic74—22no—
159Dic74C2×D412yes—
160C8×C37—22no—
161#64436—22no—
162C22×C37—22no—
163C22×C37C22×D411yescharacteristic
164C2×D37—22no—
165C2×D37—22no—
166C2×D37—41no—
167C2×D37—42no—
168C2×D37—42no—
169C2×D37—41no—
170C2×D37—82no—
171C2×D37—84no—
172C2×D37#12012yes—
173C4×C37—22no—
174C4×C37—22no—
175C4×C37—22no—
176C4×C37—41no—
177C4×C37C22×D412yes—
178Dic37—22no—
179Dic37—41no—
180Dic37#12011yescharacteristic
181Dic37#12011yescharacteristic
182#3018—371nomaximal, Sylow
183C2×C37—21no—
184C2×C37—42no—
185C2×C37C2×#12011yescharacteristic
186D37—22no—
187D37—42no—
188D37—42no—
189D37—81no—
190#585—371no—
191#575—372no—
192#532—371no—
193#456—371no—
194#456D3711yescharacteristic, complemented
195#455—372no—
196#454—371no—
197#454—371no—
198#453—372no—
199C2×#104—372no—
200#413—371no—
201C37#301811yescharacteristic, complemented, Sylow
2022−1+4—371no—
2032−1+4—742no—
2042−1+4C2×D3711yescharacteristic
205H(5,𝔽2)—372no—
206H(5,𝔽2)—742no—
207H(5,𝔽2)—742no—
208C2×#41—371no—
209C2×#41—372no—
210C2×#41—371no—
211C2×#41—742no—
212C2×#41—742no—
213C2×#41—742no—
214#137—372no—
215#137—742no—
216#137C2×D3712yescomplemented
217AGL(1,ℤ/8)—372no—
218AGL(1,ℤ/8)—372no—
219AGL(1,ℤ/8)—742no—
220#135—742no—
221#135—742no—
222C2×M16—372no—
223C4⋊Q8C2×D3711yescharacteristic, complemented
224#127—371no—
225#124—371no—
226#124—371no—
227#121—742no—
228C4×D4—742no—
229C2×C42—371no—
230#104—372no—
231#104—372no—
232#104—372no—
233#104C2×D3712yescomplemented
234#101—371no—
235#101C2×D3711yescharacteristic, complemented
236#100—372no—
237#41—22no—
238#41—22no—
239#41—372no—
240#41—372no—
241#41—372no—
242#41—742no—
243#41—742no—
244#41—744no—
245#41—744no—
246#41—742no—
247#41—742no—
248#41—742no—
249#41—742no—
250#41—742no—
251#41—742no—
252#41—742no—
253#41—742no—
254#41—744no—
255#41—742no—
256#41—742no—
257#41C22×D3712yes—
258C2×Q8—22no—
259C2×Q8—372no—
260C2×Q8—742no—
261C2×Q8—742no—
262C2×Q8C22×D3711yescharacteristic
263C2×Q8C22×D3711yescharacteristic
264C2×D4—372no—
265C2×D4—372no—
266C2×D4—371no—
267C2×D4—371no—
268C2×D4—742no—
269C2×D4—744no—
270C2×D4—742no—
271C2×D4—741no—
272C2×D4—742no—
273C2×D4—744no—
274C2×D4—742no—
275C2×D4—744no—
276C2×D4—742no—
277C22×C4—371no—
278C22×C4—372no—
279C22×C4—742no—
280C22×C4—741no—
281C22×C4—744no—
282C22×C4—741no—
283Q16—22no—
284Q16—742no—
285SD16—22no—
286SD16—742no—
287SD16—742no—
288SD16—742no—
289D8—742no—
290D8—742no—
291M16—372no—
292M16—742no—
293M16C22×D3712yes—
294C2×C8—742no—
295C4⋊C4—22no—
296C22⋊C4—742no—
297C22⋊C4—742no—
298C42—371no—
299C42—741no—
300C42C22×D3711yescharacteristic
301C23—371no—
302C23—372no—
303C23—742no—
304C23—744no—
305C23—741no—
306Q8—22no—
307Q8—22no—
308Q8—22no—
309Q8—372no—
310Q8—742no—
311Q8—742no—
312Q8D4×D3712yes—
313D4—22no—
314D4—22no—
315D4—372no—
316D4—744no—
317D4—742no—
318D4—744no—
319D4—742no—
320D4—742no—
321D4—742no—
322D4—744no—
323D4—742no—
324D4—742no—
325D4—742no—
326D4—1484no—
327D4—1482no—
328D4D4×D3712yes—
329C2×C4—24no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—371no—
334C2×C4—372no—
335C2×C4—372no—
336C2×C4—742no—
337C2×C4—742no—
338C2×C4—742no—
339C2×C4—742no—
340C2×C4—744no—
341C2×C4—744no—
342C2×C4—742no—
343C2×C4—742no—
344C2×C4—741no—
345C2×C4—1482no—
346C2×C4—1481no—
347C2×C4—1481no—
348C2×C4D4×D3712yes—
349C2×C4C23×D3711yescharacteristic
350C8—22no—
351C8—742no—
352C22—22no—
353C22—372no—
354C22—2962no—
355C22—2964no—
356C22—742no—
357C22—742no—
358C22—1482no—
359C22—1481no—
360C22—1482no—
361C22—1481no—
362C22C2×D4×D3711yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—371no—
368C4—371no—
369C4—742no—
370C4—1481no—
371C4C2×D4×D3712yes—
372C2—21no—
373C2—42no—
374C2—2961no—
375C2—742no—
376C2—1482no—
377C2—1482no—
378C2#120×D3711yescharacteristic
subgroupG/H
centerC2#120×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#456C2
socleC2×C37C2×#120
hypercenter#456D37
hypocenterC37#3018
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14558370C2semidirect
2. #14558332C2semidirect
3. #14558084C2semidirect
4. #14557715C2semidirect
5. #14557709C2semidirect
6. #14557708C2semidirect
7. #14557706C2semidirect
8. #14557702C2semidirect
9. #104×D37C2semidirect
10. #14557516C2semidirect
11. C37×#456C2semidirect
19. C2×#10596966C22semidirect
24. #11924567C22semidirect
25. #11924564C22semidirect
27. #11924561C22semidirect
30. M16×D37C22semidirect
31. #11924533C22semidirect
32. #11924525C22semidirect
33. #11924525C22semidirect
36. C42×D37C22semidirect
37. #11924464C22semidirect
38. #11924463C22semidirect
39. #11924462C22semidirect
40. #11924455C22semidirect
41. #11924452C22semidirect
43. #137×C37C22semidirect
44. C4⋊Q8×C37C22semidirect
45. #104×C37C22semidirect
46. #101×C37C22semidirect
61. #10596966D4semidirect
64. Q8×D37D4semidirect
67. #10596964D4semidirect
73. D4×D37D4semidirect
194. #456D37semidirect
201. C37#3018semidirect
216. #137C2×D37semidirect
223. C4⋊Q8C2×D37semidirect
233. #104C2×D37semidirect
235. #101C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583702
#145583322
#145580842
#145577152
#145577092
#145577082
#145577062
#145577022
#104×D372
#145575162
C37×#4562
#301837