Finite Group Databasebeta

← #18004058

Subgroups — #18004058

Order 4736.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924563C211yesmaximal, characteristic, complemented
2C2×#11924560C211yesmaximal, characteristic, complemented
3#14558082C211yesmaximal, characteristic, complemented
4C4×D4×D37C211yesmaximal, characteristic, complemented
5#14557749C211yesmaximal, characteristic, complemented
6#14557748C211yesmaximal, characteristic, complemented
7#14557745C211yesmaximal, characteristic, complemented
8#14557737C211yesmaximal, characteristic, complemented
9#14557736C211yesmaximal, characteristic, complemented
10#14557727C211yesmaximal, characteristic, complemented
11#14557726C211yesmaximal, characteristic, complemented
12#14557555C211yesmaximal, characteristic, complemented
13#14557533C211yesmaximal, characteristic, complemented
14#14557531C211yesmaximal, characteristic, complemented
15C37×#463C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19C22×C4×D37—21no—
20#11924563—24no—
21#11924560—24no—
22C2×#10596930C2211yescharacteristic
23C2×#10596940C2211yescharacteristic
24C2×#10596941C2211yescharacteristic
25C2×D296C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C2×#10596929C2211yescharacteristic
29C2×#10596929C2211yescharacteristic
30#11924534C2211yescharacteristic, complemented
31#11924532C2211yescharacteristic, complemented
32#11924524C2211yescharacteristic, complemented
33#11924509—21no—
34#11924509—21no—
35C4×D148C2211yescharacteristic
36D4×Dic37C2211yescharacteristic
37#11924498C2211yescharacteristic
38C4×C22⋊D37—21no—
39#11924496—21no—
40#11924496—21no—
41#11924496—21no—
42C4⋊C4×D37C2211yescharacteristic
43C22⋊C4×D37—21no—
44C42×D37C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic, complemented
46#11924465C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924460C2211yescharacteristic, complemented
50#11924459C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic, complemented
52#11924457C2211yescharacteristic, complemented
53#11924456C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic, complemented
57C4×D4×C37C2211yescharacteristic
58C4⋊C8×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C22×Dic37—21no—
71C22×Dic37—21no—
72#10596966—22no—
73#10596966—22no—
74#10596964—22no—
75#10596964—22no—
76D4×D37—22no—
77D4×D37D414yescomplemented
78C2×D148—21no—
79C2×D148C2311yescharacteristic
80C2×D148C2311yescharacteristic
81C2×C4×D37—21no—
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×C4×D37—21no—
85C2×C4×D37—44no—
86C2×C4×D37D411yescharacteristic
87C2×C4×D37D411yescharacteristic
88C2×C4×D37C2311yescharacteristic
89C2×Dic74C2311yescharacteristic
90SD16×C37—22no—
91D8×C37—22no—
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C42×C37C2311yescharacteristic
99C22⋊Dic37—21no—
100#10596941—22no—
101#10596940—22no—
102#10596939—22no—
103#10596939—22no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108C4⋊Dic37C2311yescharacteristic
109#10596936—21no—
110#10596936—21no—
111#10596936—21no—
112C4×Dic37D411yescharacteristic
113C4×Dic37D411yescharacteristic
114C4×Dic37C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116C2×#64436C2311yescharacteristic
117D296—22no—
118#10596930—22no—
119#10596929—22no—
120#10596929—22no—
121C23×C37—21no—
122C23×C37—21no—
123C22×D37—21no—
124C22×D37—24no—
125C22×D37—21no—
126C22×D37—42no—
127C22×D37—42no—
128C22×D37C2×D411yescharacteristic
129Q8×C37—21no—
130Q8×C37—21no—
131D4×C37—21no—
132D4×C37—21no—
133D4×C37—21no—
134D4×C37C2×D412yes—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—42no—
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2411yescharacteristic
141C22⋊D37—24no—
142C22⋊D37—42no—
143C22⋊D37—42no—
144C22⋊D37—42no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—42no—
148C2×Dic37—42no—
149C2×Dic37C2×D411yescharacteristic
150C2×Dic37C2×D411yescharacteristic
151C2×Dic37C2×D411yescharacteristic
152D148—21no—
153D148—21no—
154D148—21no—
155D148—42no—
156D148C2×D412yes—
157C4×D37—22no—
158C4×D37—41no—
159C4×D37—42no—
160C4×D37—42no—
161C4×D37—42no—
162C4×D37—42no—
163C4×D37C2×D412yes—
164C4×D37#4112yes—
165Dic74—21no—
166Dic74—21no—
167C8×C37—21no—
168C8×C37—21no—
169#64436—21no—
170#64436—21no—
171C22×C37—22no—
172C22×C37—41no—
173C22×C37—41no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37C22×D411yescharacteristic
178C2×D37—21no—
179C2×D37—21no—
180C2×D37—22no—
181C2×D37—48no—
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37#12112yes—
188C4×C37—21no—
189C4×C37—21no—
190C4×C37—41no—
191C4×C37—41no—
192C4×C37C22×D411yescharacteristic
193C4×C37C2×#4111yescharacteristic
194Dic37—21no—
195Dic37—41no—
196Dic37—41no—
197Dic37#12112yes—
198Dic37AGL(1,ℤ/8)12yescomplemented
199#3036—371nomaximal, Sylow
200C2×C37—42no—
201C2×C37—81no—
202C2×C37C2×#12111yescharacteristic
203C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
204C2×C37#57511yescharacteristic
205D37—22no—
206D37—42no—
207D37—81no—
208C2×AGL(1,ℤ/8)—371no—
209C2×AGL(1,ℤ/8)—371no—
210#532—371no—
211C2×C4×D4—371no—
212#463—371no—
213#463—371no—
214#463—371no—
215#463D3711yescharacteristic, complemented
216#461—371no—
217#461—371no—
218#459—371no—
219#459—371no—
220#423—371no—
221#417—371no—
222#417—371no—
223C37#303611yescharacteristic, complemented, Sylow
224C2×#41—371no—
225C2×#41—371no—
226C22×D4—371no—
227C23×C4—741no—
228AGL(1,ℤ/8)—744no—
229AGL(1,ℤ/8)—744no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16—371no—
233C2×SD16C2×D3711yescharacteristic
234C2×D8—371no—
235C2×D8—371no—
236C2×D8—371no—
237C2×D8C2×D3711yescharacteristic
238C2×M16—371no—
239C2×M16—371no—
240C4⋊Q8—371no—
241#127—371no—
242#124—371no—
243#124C2×D3711yescharacteristic, complemented
244#121—741no—
245#121—741no—
246C4×D4—371no—
247C4×D4—371no—
248C4×D4—371no—
249C4×D4—741no—
250C4×D4—741no—
251C4×D4—741no—
252C4×D4—741no—
253C4×D4C2×D3711yescharacteristic
254C2×C4⋊C4—371no—
255C2×C22⋊C4—741no—
256C2×C42—371no—
257C4⋊C8—371no—
258C4⋊C8—371no—
259C4⋊C8—371no—
260C4⋊C8C2×D3711yescharacteristic, complemented
261#103—371no—
262#103—371no—
263#103—371no—
264#103C2×D3711yescharacteristic, complemented
265#102—371no—
266#102—371no—
267#102—371no—
268#102C2×D3711yescharacteristic, complemented
269C24—741no—
270#41—742no—
271#41—742no—
272#41—742no—
273#41—742no—
274C2×Q8—371no—
275C2×Q8C22×D3711yescharacteristic
276C2×D4—374no—
277C2×D4—371no—
278C2×D4—371no—
279C2×D4—741no—
280C2×D4—742no—
281C2×D4—741no—
282C2×D4—741no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4C22×D3711yescharacteristic
286C2×D4C22×D3711yescharacteristic
287C22×C4—21no—
288C22×C4—371no—
289C22×C4—371no—
290C22×C4—371no—
291C22×C4—741no—
292C22×C4—741no—
293C22×C4—741no—
294C22×C4—741no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4—1484no—
298SD16—22no—
299SD16—742no—
300SD16—742no—
301SD16—742no—
302D8—22no—
303D8—742no—
304D8—742no—
305D8—742no—
306M16—742no—
307M16—742no—
308C2×C8—371no—
309C2×C8—371no—
310C2×C8C22×D3711yescharacteristic
311C2×C8C22×D3711yescharacteristic
312C4⋊C4—371no—
313C4⋊C4—741no—
314C4⋊C4—741no—
315C4⋊C4—741no—
316C4⋊C4C22×D3711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C42—371no—
326C42—371no—
327C42—371no—
328C42C22×D3711yescharacteristic
329C23—21no—
330C23—21no—
331C23—371no—
332C23—744no—
333C23—741no—
334C23—741no—
335C23—1482no—
336C23—1482no—
337Q8—21no—
338Q8—21no—
339Q8—741no—
340Q8—741no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—372no—
345D4—744no—
346D4—741no—
347D4—741no—
348D4—741no—
349D4—1482no—
350D4—1482no—
351D4—1482no—
352D4—1482no—
353D4D4×D3712yes—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—371no—
358C2×C4—371no—
359C2×C4—372no—
360C2×C4—372no—
361C2×C4—371no—
362C2×C4—742no—
363C2×C4—741no—
364C2×C4—741no—
365C2×C4—1481no—
366C2×C4—1482no—
367C2×C4—1482no—
368C2×C4—1482no—
369C2×C4—1482no—
370C2×C4—1482no—
371C2×C4—1482no—
372C2×C4D4×D3711yescharacteristic
373C2×C4D4×D3711yescharacteristic
374C2×C4C23×D3711yescharacteristic
375C8—21no—
376C8—21no—
377C8—741no—
378C8—741no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—372no—
386C22—741no—
387C22—741no—
388C22—742no—
389C22—1488no—
390C22—1481no—
391C22—1481no—
392C22—1481no—
393C22—1481no—
394C22—1481no—
395C22C2×D4×D3711yescharacteristic
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—372no—
401C4—372no—
402C4—741no—
403C4—1481no—
404C4—1481no—
405C4C2×D4×D3711yescharacteristic
406C4#41×D3711yescharacteristic
407C2—42no—
408C2—81no—
409C2—2961no—
410C2—742no—
411C2—1482no—
412C2#121×D3711yescharacteristic
413C2AGL(1,ℤ/8)×D3711yescharacteristic
414C2#1455833011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#463C2
socleC22×C37C22×D4
hypercenter#463D37
hypocenterC37#3036
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#11924563C2semidirect
2. C2×#11924560C2semidirect
3. #14558082C2semidirect
4. C4×D4×D37C2semidirect
5. #14557749C2semidirect
6. #14557748C2semidirect
7. #14557745C2semidirect
8. #14557737C2semidirect
9. #14557736C2semidirect
10. #14557727C2semidirect
11. #14557726C2semidirect
12. #14557555C2semidirect
13. #14557533C2semidirect
14. #14557531C2semidirect
15. C37×#463C2semidirect
30. #11924534C22semidirect
31. #11924532C22semidirect
32. #11924524C22semidirect
45. C4⋊#64436C22semidirect
46. #11924465C22semidirect
47. #11924465C22semidirect
48. #11924461C22semidirect
49. #11924460C22semidirect
50. #11924459C22semidirect
51. #11924458C22semidirect
52. #11924457C22semidirect
53. #11924456C22semidirect
56. #124×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #103×C37C22semidirect
60. #102×C37C22semidirect
77. D4×D37D4semidirect
198. Dic37AGL(1,ℤ/8)semidirect
215. #463D37semidirect
223. C37#3036semidirect
243. #124C2×D37semidirect
260. C4⋊C8C2×D37semidirect
264. #103C2×D37semidirect
268. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
C2×#119245602
#145580822
C4×D4×D372
#145577492
#145577482
#145577452
#145577372
#145577362
#145577272
#145577262
#145575552
#145575332
#145575312
C37×#4632
#303637