Finite Group Databasebeta

← #18006123

Subgroups — #18006123

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×#11924560C211yesmaximal, characteristic, complemented
2C2×#11924555C211yesmaximal, characteristic, complemented
3#14558187C211yesmaximal, characteristic, complemented
4#14558178C211yesmaximal, characteristic, complemented
5#14557927C211yesmaximal, characteristic, complemented
6#14557792C211yesmaximal, characteristic, complemented
7#14557763C211yesmaximal, characteristic, complemented
8#14557748C211yesmaximal, characteristic, complemented
9#14557738C211yesmaximal, characteristic, complemented
10#14557696C211yesmaximal, characteristic, complemented
11#14557696C211yesmaximal, characteristic, complemented
12#14557685C211yesmaximal, characteristic, complemented
13#14557679C211yesmaximal, characteristic, complemented
14#14557606C211yesmaximal, characteristic, complemented
15C37×#442C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×#10596964C2211yescharacteristic, complemented
19C2×D4×D37C2211yescharacteristic
20#11924560—24no—
21#11924555—24no—
22C2×Dic148C2211yescharacteristic, complemented
23C2×Dic148C2211yescharacteristic, complemented
24C2×#10596930C2211yescharacteristic
25C2×#10596930C2211yescharacteristic
26C2×#10596940C2211yescharacteristic
27C2×#10596940C2211yescharacteristic
28C2×#10596940C2211yescharacteristic, complemented
29C2×#10596939C2211yescharacteristic
30C2×#10596929C2211yescharacteristic
31C2×C8×D37C2211yescharacteristic, complemented
32#11924536C2211yescharacteristic, complemented
33#11924524C2211yescharacteristic
34#11924520—21no—
35#11924520—21no—
36#11924520—21no—
37#11924516C2211yescharacteristic
38#11924516C2211yescharacteristic
39#11924516C2211yescharacteristic, complemented
40#11924511C2211yescharacteristic
41#11924510—21no—
42#11924510—21no—
43#11924506—21no—
44C4×D148C2211yescharacteristic
45C2×C4⋊Dic37—21no—
46C2×#10596938—21no—
47C4⋊#64436C2211yescharacteristic, complemented
48#11924459C2211yescharacteristic, complemented
49#11924459C2211yescharacteristic, complemented
50#11924459C2211yescharacteristic, complemented
51#11924456C2211yescharacteristic
52#11924448C2211yescharacteristic
53#11924448C2211yescharacteristic, complemented
54C2×D8×C37C2211yescharacteristic
55C4×D4×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic, complemented
57#106×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic
59#102×C37C2211yescharacteristic, complemented
60#97×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×D4×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
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—
72C22×Dic37—21no—
73#10596964—22no—
74#10596964—22no—
75#10596964—22no—
76#10596964—41no—
77#10596964—41no—
78#10596964—41no—
79D4×D37—22no—
80D4×D37—41no—
81C2×D148—21no—
82C2×D148D411yescharacteristic
83C2×D148C2311yescharacteristic
84C2×C4×D37C2311yescharacteristic
85C2×C4×D37C2311yescharacteristic
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88C2×Dic74C2311yescharacteristic
89D8×C37D414yescomplemented
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C42×C37C2311yescharacteristic
97#10596940—22no—
98#10596940—22no—
99#10596940—22no—
100#10596939—22no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938D411yescharacteristic
108#10596938D411yescharacteristic
109C4⋊Dic37—21no—
110C4⋊Dic37—21no—
111C4⋊Dic37—21no—
112C4⋊Dic37—21no—
113C4⋊Dic37—21no—
114C4⋊Dic37D411yescharacteristic
115C2×#64436C2311yescharacteristic
116C2×#64436C2311yescharacteristic
117Dic148—22no—
118Dic148—41no—
119#10596930—22no—
120#10596930—41no—
121#10596929—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C22×D37—21no—
126C22×D37—42no—
127C22×D37—42no—
128C22×D37—81no—
129C22×D37C2×D411yescharacteristic
130C22×D37C2×D411yescharacteristic
131D4×C37—21no—
132D4×C37—21no—
133D4×C37C2×D412yes—
134D4×C37C2×D412yes—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—42no—
138C2×C4×C37—81no—
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2×D411yescharacteristic
141C2×C4×C37C2411yescharacteristic
142C22⋊D37—42no—
143C22⋊D37—42no—
144C22⋊D37—42no—
145C22⋊D37—42no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—21no—
149C2×Dic37—42no—
150C2×Dic37—42no—
151C2×Dic37—42no—
152C2×Dic37C2×D411yescharacteristic
153C2×Dic37C2×D411yescharacteristic
154D148—21no—
155D148—21no—
156D148—41no—
157D148—81no—
158C4×D37—21no—
159C4×D37—21no—
160C4×D37—21no—
161C4×D37—21no—
162Dic74—21no—
163Dic74—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—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37C22×D411yescharacteristic
179C2×D37—21no—
180C2×D37—21no—
181C2×D37—21no—
182C2×D37—21no—
183C2×D37—21no—
184C2×D37—21no—
185C2×D37—41no—
186C2×D37—41no—
187C2×D37—41no—
188C2×D37—84no—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—41no—
192C4×C37—41no—
193C4×C37C22×D411yescharacteristic
194C4×C37H(5,𝔽2)11yescharacteristic
195Dic37—21no—
196Dic37—21no—
197Dic37—41no—
198Dic37—41no—
199Dic37—41no—
200#3267—371nomaximal, Sylow
201C2×C37—42no—
202C2×C37—42no—
203C2×C37D4211yescharacteristic
204C2×C37#57511yescharacteristic
205C2×C37#57711yescharacteristic
206D37—41no—
207D37—41no—
208D37—81no—
209C2×AGL(1,ℤ/8)—371no—
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#442D3711yescharacteristic, complemented
223#435—371no—
224C37#326711yescharacteristic, complemented, Sylow
225C2×#41—371no—
226C2×#41—371no—
227C2×#41—371no—
228C22×D4—371no—
229AGL(1,ℤ/8)—744no—
230#135—744no—
231C2×Q16—371no—
232C2×Q16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16—371no—
237C2×SD16—371no—
238C2×D8—371no—
239C2×D8C2×D3711yescharacteristic
240C2×M16—371no—
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×D4C2×D3711yescharacteristic
256C4×D4C2×D3711yescharacteristic, complemented
257C2×C4⋊C4—741no—
258C2×C22⋊C4—741no—
259#106C2×D3711yescharacteristic, complemented
260C4⋊C8—371no—
261#103—371no—
262#103—371no—
263#103—371no—
264#102—371no—
265#102C2×D3711yescharacteristic
266#102C2×D3711yescharacteristic, complemented
267C22⋊C8—371no—
268C22⋊C8—371no—
269#97C2×D3711yescharacteristic, complemented
270C24—741no—
271#41—742no—
272#41—742no—
273#41—742no—
274#41—1481no—
275#41—1481no—
276#41—1481no—
277C2×Q8—371no—
278C2×Q8—371no—
279C2×Q8—371no—
280C2×D4—371no—
281C2×D4—371no—
282C2×D4—741no—
283C2×D4—741no—
284C2×D4—742no—
285C2×D4—741no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4—1481no—
289C2×D4C22×D3711yescharacteristic
290C2×D4C22×D3711yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—371no—
294C22×C4—371no—
295C22×C4—741no—
296C22×C4—741no—
297C22×C4—741no—
298Q16—742no—
299Q16—1481no—
300SD16—742no—
301SD16—742no—
302SD16—742no—
303SD16—742no—
304SD16—1481no—
305D8—742no—
306D8D14814yescomplemented
307M16—742no—
308C2×C8—371no—
309C2×C8—371no—
310C2×C8—742no—
311C2×C8C22×D3711yescharacteristic
312C2×C8C22×D3711yescharacteristic
313C4⋊C4—371no—
314C4⋊C4—741no—
315C4⋊C4—741no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4C22×D3711yescharacteristic
320C4⋊C4C22×D3711yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—371no—
324C22⋊C4—371no—
325C22⋊C4—741no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C22⋊C4—741no—
330C22⋊C4—741no—
331C42C22×D3711yescharacteristic
332C23—21no—
333C23—21no—
334C23—371no—
335C23—371no—
336C23—2961no—
337C23—741no—
338C23—1482no—
339C23—1482no—
340Q8—741no—
341Q8—741no—
342Q8—741no—
343Q8—741no—
344Q8—741no—
345Q8—741no—
346D4—21no—
347D4—21no—
348D4—2961no—
349D4—741no—
350D4—741no—
351D4—1481no—
352D4—1482no—
353D4—1482no—
354D4—1482no—
355D4—1482no—
356D4C2×D14812yes—
357D4C2×D14812yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—371no—
363C2×C4—371no—
364C2×C4—741no—
365C2×C4—741no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—741no—
369C2×C4—741no—
370C2×C4—741no—
371C2×C4—1482no—
372C2×C4—1482no—
373C2×C4—1482no—
374C2×C4D4×D3711yescharacteristic
375C2×C4D4×D3711yescharacteristic
376C2×C4C23×D3711yescharacteristic
377C8—21no—
378C8—741no—
379C8—741no—
380C8C2×D14812yes—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—2964no—
388C22—741no—
389C22—741no—
390C22—741no—
391C22—741no—
392C22—741no—
393C22—741no—
394C22—1481no—
395C22—1481no—
396C22—1481no—
397C22C2×D4×D3711yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—741no—
403C4—741no—
404C4—1481no—
405C4—1481no—
406C4—1481no—
407C4C22×D14811yescharacteristic
408C4#1192458211yescharacteristic
409C2—42no—
410C2—42no—
411C2—2961no—
412C2—1481no—
413C2—1481no—
414C2D4×D14811yescharacteristic
415C2#1455832911yescharacteristic
416C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#442C2
socleC22×C37C22×D4
hypercenter#442D37
hypocenterC37#3267
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#11924560C2semidirect
2. C2×#11924555C2semidirect
3. #14558187C2semidirect
4. #14558178C2semidirect
5. #14557927C2semidirect
6. #14557792C2semidirect
7. #14557763C2semidirect
8. #14557748C2semidirect
9. #14557738C2semidirect
10. #14557696C2semidirect
11. #14557696C2semidirect
12. #14557685C2semidirect
13. #14557679C2semidirect
14. #14557606C2semidirect
15. C37×#442C2semidirect
18. C2×#10596964C22semidirect
22. C2×Dic148C22semidirect
23. C2×Dic148C22semidirect
28. C2×#10596940C22semidirect
31. C2×C8×D37C22semidirect
32. #11924536C22semidirect
39. #11924516C22semidirect
47. C4⋊#64436C22semidirect
48. #11924459C22semidirect
49. #11924459C22semidirect
50. #11924459C22semidirect
53. #11924448C22semidirect
56. C4×D4×C37C22semidirect
57. #106×C37C22semidirect
59. #102×C37C22semidirect
60. #97×C37C22semidirect
89. D8×C37D4semidirect
222. #442D37semidirect
224. C37#3267semidirect
256. C4×D4C2×D37semidirect
259. #106C2×D37semidirect
266. #102C2×D37semidirect
269. #97C2×D37semidirect
306. D8D148semidirect

Maximal subgroups

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

subgroupindex
C2×#119245602
C2×#119245552
#145581872
#145581782
#145579272
#145577922
#145577632
#145577482
#145577382
#145576962
#145576852
#145576792
#145576062
C37×#4422
#326737