Finite Group Databasebeta

← #18006115

Subgroups — #18006115

Order 4736.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924555C211yesmaximal, characteristic, complemented
2#14558182C211yesmaximal, characteristic, complemented
3#14558177C211yesmaximal, characteristic, complemented
4#14557924C211yesmaximal, characteristic, complemented
5#14557791C211yesmaximal, characteristic, complemented
6#14557759C211yesmaximal, characteristic, complemented
7#14557746C211yesmaximal, characteristic, complemented
8#14557736C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557692C211yesmaximal, characteristic, complemented
11#14557684C211yesmaximal, characteristic, complemented
12#14557675C211yesmaximal, characteristic, complemented
13#14557645C211yesmaximal, characteristic, complemented
14#14557602C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596964C2211yescharacteristic, complemented
18#11924555—24no—
19C2×Dic148C2211yescharacteristic, complemented
20C2×#10596942C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic
22C2×#10596940C2211yescharacteristic
23C2×#10596940C2211yescharacteristic, complemented
24C2×C8×D37C2211yescharacteristic, complemented
25#11924534C2211yescharacteristic, complemented
26#11924523C2211yescharacteristic
27#11924519—21no—
28#11924517—21no—
29#11924517—21no—
30#11924515C2211yescharacteristic
31#11924515C2211yescharacteristic
32#11924512C2211yescharacteristic, complemented
33#11924508—21no—
34#11924508—21no—
35#11924507C2211yescharacteristic
36#11924505—21no—
37D4×Dic37C2211yescharacteristic
38D4×Dic37C2211yescharacteristic, complemented
39C4×C22⋊D37C2211yescharacteristic
40C2×#10596936—21no—
41C2×C22⋊Dic37—21no—
42#11924468C2211yescharacteristic, complemented
43#11924465C2211yescharacteristic, complemented
44#11924461C2211yescharacteristic, complemented
45#11924461C2211yescharacteristic, complemented
46#11924460C2211yescharacteristic, complemented
47#11924457C2211yescharacteristic
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic, complemented
50C22⋊#64436C2211yescharacteristic
51#11924448C2211yescharacteristic, complemented
52#11924446C2211yescharacteristic, complemented
53C2×#41×C37C2211yescharacteristic
54C22×D4×C37C2211yescharacteristic
55AGL(1,ℤ/8)×C37—24no—
56C2×SD16×C37C2211yescharacteristic
57C2×SD16×C37C2211yescharacteristic
58C2×D8×C37C2211yescharacteristic
59C2×D8×C37C2211yescharacteristic
60C2×M16×C37C2211yescharacteristic
61C24×C37—21no—
62#41×C37—22no—
63#41×C37—41no—
64C2×Q8×C37C2311yescharacteristic
65C2×D4×C37—22no—
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37—41no—
69C2×D4×C37C2311yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C22×C4×C37—21no—
73C22×C4×C37C2311yescharacteristic
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C2×C22⋊D37D411yescharacteristic
78C22×Dic37—21no—
79C22×Dic37—21no—
80C22×Dic37—21no—
81C22×Dic37—21no—
82#10596964—22no—
83#10596964—22no—
84#10596964—41no—
85#10596964—41no—
86C2×C4×D37C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88C2×Dic74C2311yescharacteristic
89SD16×C37—22no—
90SD16×C37—22no—
91D8×C37—22no—
92D8×C37D414yescomplemented
93M16×C37—22no—
94C2×C8×C37C2311yescharacteristic
95C2×C8×C37C2311yescharacteristic
96C22⋊Dic37—21no—
97C22⋊Dic37—21no—
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37—21no—
102C22⋊Dic37—21no—
103C22⋊Dic37D411yescharacteristic
104#10596942—41no—
105#10596940—22no—
106#10596940—22no—
107#10596940—41no—
108#10596938—21no—
109#10596938D411yescharacteristic
110C4⋊Dic37C2311yescharacteristic
111C4⋊Dic37C2311yescharacteristic
112#10596936—21no—
113#10596936—21no—
114#10596936—21no—
115#10596936—21no—
116#10596936—21no—
117#10596936D411yescharacteristic
118C4×Dic37C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121Dic148—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—21no—
126C23×C37—42no—
127C23×C37—42no—
128C23×C37—81no—
129C23×C37C2×D411yescharacteristic
130C22×D37C2×D411yescharacteristic
131Q8×C37—21no—
132Q8×C37—21no—
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—42no—
138D4×C37—42no—
139D4×C37C2×D412yes—
140D4×C37C2×D412yes—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—42no—
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2411yescharacteristic
147C22⋊D37—41no—
148C22⋊D37—42no—
149C22⋊D37—42no—
150C22⋊D37—81no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—42no—
156C2×Dic37—42no—
157C2×Dic37—42no—
158C2×Dic37—81no—
159C2×Dic37C2×D411yescharacteristic
160C2×Dic37C2×D411yescharacteristic
161C2×Dic37C2×D411yescharacteristic
162C4×D37—21no—
163C4×D37—21no—
164Dic74—21no—
165Dic74—21no—
166Dic74—21no—
167Dic74—21no—
168C8×C37—21no—
169C8×C37C2×D412yes—
170#64436—21no—
171#64436—21no—
172C22×C37—22no—
173C22×C37—22no—
174C22×C37—21no—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—84no—
185C22×C37C22×D411yescharacteristic
186C2×D37—21no—
187C2×D37—21no—
188C2×D37—21no—
189C4×C37—21no—
190C4×C37—41no—
191C4×C37C22×D411yescharacteristic
192C4×C37H(5,𝔽2)11yescharacteristic
193Dic37—21no—
194Dic37—21no—
195Dic37—21no—
196Dic37—41no—
197Dic37—41no—
198Dic37—41no—
199Dic37—41no—
200#3267—371nomaximal, Sylow
201C2×C37—41no—
202C2×C37—42no—
203C2×C37—42no—
204C2×C37—81no—
205C2×C37D4211yescharacteristic
206C2×C37#57511yescharacteristic
207C2×C37#57711yescharacteristic
208D37—41no—
209C2×AGL(1,ℤ/8)D3711yescharacteristic, complemented
210C2×#135—371no—
211#547—371no—
212#546—371no—
213#497—371no—
214#470—371no—
215#465—371no—
216#463—371no—
217#461—371no—
218#452—371no—
219#452—371no—
220#450—371no—
221#449—371no—
222#442—371no—
223#435—371no—
224C37#326711yescharacteristic, complemented, Sylow
225C2×#41—371no—
226C2×#41—371no—
227C2×#41C2×D3711yescharacteristic
228C22×D4C2×D3711yescharacteristic
229AGL(1,ℤ/8)—24no—
230#135—744no—
231C2×Q16—371no—
232C2×Q16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16C2×D3711yescharacteristic
237C2×SD16C2×D3711yescharacteristic
238C2×D8C2×D3711yescharacteristic
239C2×D8C2×D3711yescharacteristic
240C2×M16C2×D3711yescharacteristic
241C22×C8—371no—
242C4⋊Q8—371no—
243#124—371no—
244#123—741no—
245#123—741no—
246#123—741no—
247C22⋊Q8—371no—
248C22⋊Q8—371no—
249C22⋊Q8—371no—
250#121—371no—
251#121—741no—
252#121—741no—
253#120—741no—
254C4×D4—371no—
255C4×D4—371no—
256C4×D4—371no—
257C2×C4⋊C4—741no—
258C2×C22⋊C4—741no—
259#106—371no—
260C4⋊C8—371no—
261#103—371no—
262#103—371no—
263#103—371no—
264#102—371no—
265#102—371no—
266#102—371no—
267C22⋊C8—371no—
268C22⋊C8—371no—
269#97—371no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—742no—
274#41—742no—
275#41—1481no—
276#41—1481no—
277C2×Q8—371no—
278C2×Q8—371no—
279C2×Q8C22×D3711yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—371no—
285C2×D4—741no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4C22×D3711yescharacteristic
289C2×D4C22×D3711yescharacteristic
290C2×D4C22×D3711yescharacteristic
291C22×C4—21no—
292C22×C4—371no—
293C22×C4—741no—
294C22×C4—741no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4C22×D3711yescharacteristic
298Q16—742no—
299Q16—1481no—
300SD16—22no—
301SD16—22no—
302SD16—742no—
303SD16—742no—
304SD16—1481no—
305D8—22no—
306D8C22⋊D3714yescomplemented
307M16—22no—
308C2×C8—371no—
309C2×C8—371no—
310C2×C8—742no—
311C2×C8C22×D3711yescharacteristic
312C2×C8C22×D3711yescharacteristic
313C4⋊C4—371no—
314C4⋊C4—371no—
315C4⋊C4—371no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4—741no—
320C4⋊C4—741no—
321C22⋊C4—371no—
322C22⋊C4—371no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C22⋊C4—741no—
330C22⋊C4—741no—
331C42—371no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—371no—
339C23D4×D3711yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—741no—
343Q8—741no—
344Q8—741no—
345Q8—741no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—42no—
352D4—2961no—
353D4—1481no—
354D4—1482no—
355D4—1482no—
356D4C2×C22⋊D3712yes—
357D4C2×C22⋊D3712yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—371no—
363C2×C4—371no—
364C2×C4—371no—
365C2×C4—2961no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—741no—
369C2×C4—741no—
370C2×C4—741no—
371C2×C4—741no—
372C2×C4—1482no—
373C2×C4—1482no—
374C2×C4—1482no—
375C2×C4D4×D3711yescharacteristic
376C2×C4C23×D3711yescharacteristic
377C8—21no—
378C8—741no—
379C8—741no—
380C8C2×C22⋊D3712yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—741no—
395C22—741no—
396C22—741no—
397C22C2×D4×D3711yescharacteristic
398C4—21no—
399C4—41no—
400C4—741no—
401C4—741no—
402C4—741no—
403C4—1481no—
404C4—1481no—
405C4—1481no—
406C4—1481no—
407C4C22×C22⋊D3711yescharacteristic
408C4#1192458111yescharacteristic
409C2—41no—
410C2—42no—
411C2—42no—
412C2—81no—
413C2—1481no—
414C2D4×C22⋊D3711yescharacteristic
415C2#1455832911yescharacteristic
416C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×AGL(1,ℤ/8)×C37C2
socleC22×C37C22×D4
hypercenterC2×AGL(1,ℤ/8)D37
hypocenterC37#3267
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#11924555C2semidirect
2. #14558182C2semidirect
3. #14558177C2semidirect
4. #14557924C2semidirect
5. #14557791C2semidirect
6. #14557759C2semidirect
7. #14557746C2semidirect
8. #14557736C2semidirect
9. #14557695C2semidirect
10. #14557692C2semidirect
11. #14557684C2semidirect
12. #14557675C2semidirect
13. #14557645C2semidirect
14. #14557602C2semidirect
15. C2×AGL(1,ℤ/8)×C37C2semidirect
17. C2×#10596964C22semidirect
19. C2×Dic148C22semidirect
20. C2×#10596942C22semidirect
23. C2×#10596940C22semidirect
24. C2×C8×D37C22semidirect
25. #11924534C22semidirect
32. #11924512C22semidirect
38. D4×Dic37C22semidirect
42. #11924468C22semidirect
43. #11924465C22semidirect
44. #11924461C22semidirect
45. #11924461C22semidirect
46. #11924460C22semidirect
49. #11924457C22semidirect
51. #11924448C22semidirect
52. #11924446C22semidirect
92. D8×C37D4semidirect
209. C2×AGL(1,ℤ/8)D37semidirect
224. C37#3267semidirect
306. D8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245552
#145581822
#145581772
#145579242
#145577912
#145577592
#145577462
#145577362
#145576952
#145576922
#145576842
#145576752
#145576452
#145576022
C2×AGL(1,ℤ/8)×C372
#326737