Finite Group Databasebeta

← #18003955

Subgroups — #18003955

Order 4736.

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

normal subgroups only

This group has 762 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×#11924582C211yesmaximal, characteristic, complemented
2#14558333C211yesmaximal, characteristic, complemented
3#14558331C211yesmaximal, characteristic, complemented
4#14558102C211yesmaximal, characteristic, complemented
5#14557712C214yesmaximal, complemented
6#14557702C214yesmaximal, complemented
7#14557551C211yesmaximal, characteristic, complemented
8C2×#11924452C211yesmaximal, characteristic, complemented
9C37×#421C211yesmaximal, characteristic, complemented
10#11924582—22no—
11#11924582—22no—
12#11924582—22no—
13#11924582C2214yes—
14C2×#10596966—21no—
15C2×#10596962—21no—
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic, complemented
18C22×D148—21no—
19C22×D148C2211yescharacteristic
20C2×D4×D37—22no—
21C2×D4×D37—21no—
22#11924569—21no—
23#11924569C2212yescomplemented
24#11924567—21no—
25#11924566C2212yescomplemented
26#11924564—21no—
27#11924564C2212yescomplemented
28#11924562—21no—
29#11924561C2212yescomplemented
30#11924558—22no—
31#11924556—22no—
32C2×#10596934C2211yescharacteristic, complemented
33#11924533C2212yescomplemented
34#11924524C2212yescomplemented
35#11924511—22no—
36#11924506—22no—
37#11924464C2214yescomplemented
38#11924452C2214yescomplemented
39C2×#41×C37C2211yescharacteristic
40C2×M16×C37C2211yescharacteristic, complemented
41#117×C37C2211yescharacteristic, complemented
42#104×C37C2214yescomplemented
43C23×D37—22no—
44C23×D37D412yes—
45#41×C37—21no—
46#41×C37—21no—
47#41×C37D412yescomplemented
48#41×C37C2312yes—
49C2×Q8×C37D411yescharacteristic, complemented
50C2×D4×C37—21no—
51C2×D4×C37D411yescharacteristic, complemented
52C22×C4×C37—21no—
53C22×C4×C37C2311yescharacteristic
54C2×C22⋊D37—22no—
55C2×C22⋊D37—21no—
56C2×C22⋊D37—21no—
57#10596966—24no—
58#10596966—24no—
59D4×D37—28no—
60D4×D37—24no—
61D4×D37—28no—
62D4×D37—24no—
63#10596962—24no—
64#10596962—21no—
65#10596962—21no—
66#10596962—21no—
67#10596962—21no—
68#10596962—21no—
69#10596962—21no—
70#10596962—24no—
71#10596962D412yescomplemented
72#10596962C2312yes—
73C2×D148—22no—
74C2×D148—24no—
75C2×D148—21no—
76C2×D148—21no—
77C2×D148—21no—
78C2×D148—21no—
79C2×D148—24no—
80C2×D148—24no—
81C2×D148D412yes—
82C2×D148D411yescharacteristic, complemented
83C2×D148C2312yes—
84C2×D148C2311yescharacteristic, complemented
85C2×C4×D37—22no—
86C2×C4×D37—21no—
87C2×C4×D37—21no—
88C2×Dic74D411yescharacteristic, complemented
89C2×Dic74C2311yescharacteristic, complemented
90M16×C37—21no—
91M16×C37C2312yescomplemented
92C2×C8×C37—21no—
93C4⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C42×C37C2312yescomplemented
96#10596942—22no—
97#10596941—22no—
98#10596940—22no—
99#10596939—22no—
100#10596938—24no—
101#10596934—21no—
102#10596934C2312yescomplemented
103C2×#64436—21no—
104Dic148—22no—
105D296—22no—
106#10596930—22no—
107#10596930—22no—
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—22no—
111C22×D37—21no—
112C22×D37—28no—
113C22×D37—22no—
114C22×D37—21no—
115C22×D37—82no—
116C22×D37—84no—
117C22×D37C2×D414yes—
118Q8×C37—21no—
119Q8×C37C2×D412yes—
120D4×C37—22no—
121D4×C37—22no—
122D4×C37—21no—
123D4×C37C2×D412yes—
124C2×C4×C37—21no—
125C2×C4×C37—22no—
126C2×C4×C37—22no—
127C2×C4×C37—22no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2411yescharacteristic
134C22⋊D37—28no—
135C22⋊D37—22no—
136C22⋊D37—22no—
137C22⋊D37—41no—
138C22⋊D37—41no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141D148—28no—
142D148—22no—
143D148—21no—
144D148—22no—
145D148—22no—
146D148—22no—
147D148—21no—
148D148—21no—
149D148—84no—
150D148C2×D412yes—
151C4×D37—28no—
152C4×D37—22no—
153C4×D37—22no—
154C4×D37—41no—
155C4×D37—41no—
156Dic74—21no—
157Dic74—21no—
158Dic74—21no—
159Dic74C2×D412yes—
160C8×C37—22no—
161#64436—22no—
162C22×C37—22no—
163C22×C37—41no—
164C22×C37—42no—
165C22×C37#12011yescharacteristic
166C22×C37#12011yescharacteristic
167C22×C37C22×D411yescharacteristic
168C2×D37—24no—
169C2×D37—22no—
170C2×D37—44no—
171C2×D37—42no—
172C2×D37—44no—
173C2×D37—42no—
174C2×D37—41no—
175C2×D37—82no—
176C2×D37—88no—
177C4×C37—22no—
178C4×C37—42no—
179C4×C37#12011yescharacteristic
180C4×C37#12011yescharacteristic
181C4×C37C22×D411yescharacteristic
182C4×C37C22×D411yescharacteristic
183Dic37—22no—
184Dic37—41no—
185#3019—371nomaximal, Sylow
186C2×C37—21no—
187C2×C37—21no—
188C2×C37—21no—
189C2×C37—42no—
190C2×C37C2×#12011yescharacteristic
191D37—44no—
192D37—42no—
193D37—81no—
194C2×H(5,𝔽2)—371no—
195#575—371no—
196#575—371no—
197#535—371no—
198#455—374no—
199#453—374no—
200#421—371no—
201#421D3711yescharacteristic, complemented
202C2×#100—371no—
203C37#301911yescharacteristic, complemented, Sylow
204H(5,𝔽2)—374no—
205H(5,𝔽2)—742no—
206H(5,𝔽2)—742no—
207H(5,𝔽2)—742no—
208C2×#41—371no—
209C2×#41—371no—
210C2×#41—741no—
211C2×#41—741no—
212C2×#41C2×D3711yescharacteristic
213C22×D4—371no—
214C22×D4—741no—
215C22×D4—742no—
216C22×D4—741no—
217#137—372no—
218#137—372no—
219#137—741no—
220#137—741no—
221AGL(1,ℤ/8)—372no—
222AGL(1,ℤ/8)—372no—
223AGL(1,ℤ/8)—741no—
224AGL(1,ℤ/8)—741no—
225#135—742no—
226#135—742no—
227C2×M16—371no—
228C2×M16C2×D3711yescharacteristic, complemented
229#127—372no—
230#124—372no—
231#121—742no—
232#120—742no—
233#117C2×D3711yescharacteristic, complemented
234#104—374no—
235#104C2×D3714yescomplemented
236#100—374no—
237C24—372no—
238C24—742no—
239#41—21no—
240#41—21no—
241#41—372no—
242#41—372no—
243#41—744no—
244#41—744no—
245#41—744no—
246#41—744no—
247#41—741no—
248#41—741no—
249#41—741no—
250#41—741no—
251#41—741no—
252#41—741no—
253#41D14812yescomplemented
254#41C22×D3712yes—
255C2×Q8—371no—
256C2×Q8—371no—
257C2×Q8D14811yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—371no—
260C2×D4—372no—
261C2×D4—372no—
262C2×D4—371no—
263C2×D4—744no—
264C2×D4—744no—
265C2×D4—742no—
266C2×D4—744no—
267C2×D4—748no—
268C2×D4—748no—
269C2×D4—744no—
270C2×D4—742no—
271C2×D4—741no—
272C2×D4—744no—
273C2×D4—741no—
274C2×D4—741no—
275C2×D4—741no—
276C2×D4—741no—
277C2×D4—741no—
278C2×D4D14811yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—742no—
281C22×C4—741no—
282C22×C4—741no—
283C22×C4C22×D3711yescharacteristic
284Q16—742no—
285Q16—742no—
286SD16—742no—
287SD16—742no—
288SD16—742no—
289SD16—742no—
290D8—742no—
291D8—742no—
292M16—21no—
293M16—372no—
294M16—741no—
295M16C22×D3712yescomplemented
296C2×C8—21no—
297C2×C8—741no—
298C4⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—744no—
301C42C22×D3712yescomplemented
302C23—21no—
303C23—374no—
304C23—2964no—
305C23—2962no—
306C23—748no—
307C23—742no—
308C23—741no—
309C23—742no—
310C23—741no—
311C23D4×D3711yescharacteristic
312Q8—21no—
313Q8—372no—
314Q8—741no—
315Q8—741no—
316Q8—741no—
317Q8C2×D14812yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—372no—
322D4—2964no—
323D4—748no—
324D4—748no—
325D4—742no—
326D4—742no—
327D4—741no—
328D4—742no—
329D4—742no—
330D4—742no—
331D4—741no—
332D4—742no—
333D4—741no—
334D4—1481no—
335D4—1481no—
336D4C2×D14812yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—748no—
342C2×C4—741no—
343C2×C4—742no—
344C2×C4—742no—
345C2×C4—741no—
346C2×C4—1481no—
347C2×C4—1481no—
348C2×C4C2×D14811yescharacteristic
349C2×C4C2×D14811yescharacteristic
350C2×C4D4×D3711yescharacteristic
351C2×C4D4×D3711yescharacteristic
352C2×C4D4×D3711yescharacteristic
353C2×C4C23×D3711yescharacteristic
354C8—22no—
355C8—742no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—2962no—
360C22—2968no—
361C22—742no—
362C22—744no—
363C22—1482no—
364C22—1484no—
365C22—1482no—
366C22—1484no—
367C22—1481no—
368C22#1192450611yescharacteristic
369C22#1192450611yescharacteristic
370C22C2×D4×D3711yescharacteristic
371C4—22no—
372C4—42no—
373C4—742no—
374C4—1481no—
375C4#1192450611yescharacteristic
376C4#1192450611yescharacteristic
377C4C2×D4×D3711yescharacteristic
378C4C22×D14811yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—2961no—
384C2—1482no—
385C2—1484no—
386C2C2×#1192450611yescharacteristic
subgroupG/H
centerC2C2×#11924506
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#421C2
socleC2×C37C2×#120
hypercenter#421D37
hypocenterC37#3019
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. C2×#11924582C2semidirect
2. #14558333C2semidirect
3. #14558331C2semidirect
4. #14558102C2semidirect
5. #14557712C2semidirect
6. #14557702C2semidirect
7. #14557551C2semidirect
8. C2×#11924452C2semidirect
9. C37×#421C2semidirect
17. C2×#10596962C22semidirect
23. #11924569C22semidirect
25. #11924566C22semidirect
27. #11924564C22semidirect
29. #11924561C22semidirect
32. C2×#10596934C22semidirect
33. #11924533C22semidirect
34. #11924524C22semidirect
37. #11924464C22semidirect
38. #11924452C22semidirect
40. C2×M16×C37C22semidirect
41. #117×C37C22semidirect
42. #104×C37C22semidirect
47. #41×C37D4semidirect
49. C2×Q8×C37D4semidirect
51. C2×D4×C37D4semidirect
71. #10596962D4semidirect
82. C2×D148D4semidirect
84. C2×D148C23semidirect
88. C2×Dic74D4semidirect
89. C2×Dic74C23semidirect
91. M16×C37C23semidirect
95. C42×C37C23semidirect
102. #10596934C23semidirect
201. #421D37semidirect
203. C37#3019semidirect
228. C2×M16C2×D37semidirect
233. #117C2×D37semidirect
235. #104C2×D37semidirect
253. #41D148semidirect
257. C2×Q8D148semidirect
278. C2×D4D148semidirect
295. M16C22×D37semidirect
301. C42C22×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245822
#145583332
#145583312
#145581022
#145577122
#145577022
#145575512
C2×#119244522
C37×#4212
#301937