Finite Group Databasebeta

← #18006142

Subgroups — #18006142

Order 4736.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 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#14558203C211yesmaximal, characteristic, complemented
4#14558178C211yesmaximal, characteristic, complemented
5#14557920C211yesmaximal, characteristic, complemented
6#14557778C211yesmaximal, characteristic, complemented
7#14557768C211yesmaximal, characteristic, complemented
8#14557756C211yesmaximal, characteristic, complemented
9#14557696C211yesmaximal, characteristic, complemented
10#14557679C211yesmaximal, characteristic, complemented
11#14557675C211yesmaximal, characteristic, complemented
12#14557665C211yesmaximal, characteristic, complemented
13#14557633C211yesmaximal, characteristic, complemented
14#14557603C211yesmaximal, characteristic, complemented
15C37×#459C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×#10596964C2211yescharacteristic, complemented
19C2×D4×D37C2211yescharacteristic
20#11924560—24no—
21#11924555—24no—
22C2×Dic148C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596940C2211yescharacteristic, complemented
26C2×#10596940C2211yescharacteristic, complemented
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596929C2211yescharacteristic
30C2×C8×D37C2211yescharacteristic, complemented
31#11924532—21no—
32#11924524C2211yescharacteristic
33#11924520—21no—
34#11924516C2211yescharacteristic
35#11924511C2211yescharacteristic
36#11924510—21no—
37#11924508—21no—
38#11924508—21no—
39#11924507C2211yescharacteristic
40#11924507C2211yescharacteristic, complemented
41#11924506—21no—
42C4×Dic74C2211yescharacteristic, complemented
43C4×D148C2211yescharacteristic
44D4×Dic37—21no—
45C2×#10596938—21no—
46#11924469C2211yescharacteristic, complemented
47#11924461C2211yescharacteristic, complemented
48#11924459C2211yescharacteristic, complemented
49#11924458C2211yescharacteristic
50#11924457C2211yescharacteristic
51#11924448C2211yescharacteristic
52#11924448C2211yescharacteristic, complemented
53#11924447C2211yescharacteristic, complemented
54C2×D8×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic
56#127×C37C2211yescharacteristic, complemented
57C4×D4×C37C2211yescharacteristic
58C4⋊C8×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×D4×C37—21no—
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C2×D4×C37C2311yescharacteristic
66C2×D4×C37C2311yescharacteristic
67C22×C4×C37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C22×Dic37—21no—
75C22×Dic37—21no—
76C22×Dic37—21no—
77#10596964—22no—
78#10596964—22no—
79#10596964—22no—
80#10596964—41no—
81#10596964—41no—
82#10596964—41no—
83D4×D37—22no—
84D4×D37—41no—
85C2×D148—21no—
86C2×D148D411yescharacteristic
87C2×D148C2311yescharacteristic
88C2×C4×D37C2311yescharacteristic
89C2×C4×D37C2311yescharacteristic
90C2×Dic74C2311yescharacteristic
91C2×Dic74C2311yescharacteristic
92D8×C37—22no—
93D8×C37—22no—
94C2×C8×C37C2311yescharacteristic
95C2×C8×C37C2311yescharacteristic
96C4⋊C4×C37C2311yescharacteristic
97C22⋊C4×C37—21no—
98C42×C37C2311yescharacteristic
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101#10596940—22no—
102#10596940—41no—
103#10596940D414yescomplemented
104#10596939—22no—
105#10596939—41no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110#10596938D411yescharacteristic
111#10596938D411yescharacteristic
112C4⋊Dic37—21no—
113C4⋊Dic37D411yescharacteristic
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116C4×Dic37—21no—
117C2×#64436C2311yescharacteristic
118C2×#64436C2311yescharacteristic
119Dic148—22no—
120#10596930—22no—
121#10596929—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—21no—
126C22×D37—21no—
127C22×D37—42no—
128C22×D37—42no—
129C22×D37—81no—
130C22×D37C2×D411yescharacteristic
131C22×D37C2×D411yescharacteristic
132D4×C37—21no—
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—42no—
138D4×C37—81no—
139D4×C37C2×D412yes—
140C2×C4×C37—21no—
141C2×C4×C37—81no—
142C2×C4×C37C2×D411yescharacteristic
143C2×C4×C37C2×D411yescharacteristic
144C2×C4×C37C2411yescharacteristic
145C22⋊D37—42no—
146C22⋊D37—42no—
147C22⋊D37—42no—
148C22⋊D37—42no—
149C22⋊D37—81no—
150C22⋊D37—81no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—42no—
155C2×Dic37—42no—
156C2×Dic37—42no—
157C2×Dic37C2×D411yescharacteristic
158C2×Dic37C2×D411yescharacteristic
159D148—21no—
160D148—21no—
161D148—41no—
162D148—81no—
163C4×D37—21no—
164C4×D37—21no—
165C4×D37—21no—
166C4×D37—21no—
167Dic74—21no—
168Dic74—21no—
169Dic74—21no—
170Dic74C2×D412yes—
171C8×C37—21no—
172C8×C37—21no—
173#64436—21no—
174#64436C2×D412yes—
175C22×C37—22no—
176C22×C37—41no—
177C22×C37—41no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37C22×D411yescharacteristic
185C2×D37—21no—
186C2×D37—21no—
187C2×D37—21no—
188C2×D37—21no—
189C2×D37—21no—
190C2×D37—21no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—84no—
195C4×C37—21no—
196C4×C37—21no—
197C4×C37—41no—
198C4×C37C22×D411yescharacteristic
199C4×C37H(5,𝔽2)11yescharacteristic
200Dic37—22no—
201Dic37—21no—
202Dic37—21no—
203Dic37—41no—
204Dic37—41no—
205#3268—371nomaximal, Sylow
206C2×C37—42no—
207C2×C37—81no—
208C2×C37—81no—
209C2×C37D4211yescharacteristic
210C2×C37#57511yescharacteristic
211C2×C37#57611yescharacteristic
212D37—41no—
213D37—41no—
214D37—81no—
215C2×AGL(1,ℤ/8)—371no—
216C2×#135—371no—
217#550—371no—
218#546—371no—
219#496—371no—
220#468—371no—
221#466—371no—
222#464—371no—
223#459D3711yescharacteristic, complemented
224#452—371no—
225#449—371no—
226#449—371no—
227#447—371no—
228#440—371no—
229#435—371no—
230C37#326811yescharacteristic, complemented, Sylow
231C2×#41—371no—
232C2×#41—371no—
233C2×#41—371no—
234C22×D4—371no—
235AGL(1,ℤ/8)—744no—
236#135—744no—
237C2×Q16—371no—
238C2×SD16—371no—
239C2×SD16—371no—
240C2×SD16—371no—
241C2×SD16—371no—
242C2×D8—371no—
243C2×D8—371no—
244C2×D8C2×D3711yescharacteristic
245C2×D8C2×D3711yescharacteristic
246C2×M16—371no—
247C22×C8—371no—
248#127—741no—
249#127C2×D3711yescharacteristic, complemented
250#124—371no—
251#123—741no—
252C22⋊Q8—371no—
253#121—371no—
254#121—371no—
255#121—371no—
256#121—741no—
257#121—741no—
258#121—741no—
259#120—741no—
260C4×Q8—371no—
261C4×D4—371no—
262C4×D4—741no—
263C4×D4C2×D3711yescharacteristic
264C2×C22⋊C4—741no—
265#107—371no—
266C4⋊C8C2×D3711yescharacteristic, complemented
267#103—371no—
268#103—371no—
269#102—371no—
270#102—371no—
271#102C2×D3711yescharacteristic, complemented
272#102C2×D3711yescharacteristic, complemented
273C22⋊C8—371no—
274C22⋊C8—371no—
275#97—371no—
276C24—741no—
277#41—742no—
278#41—742no—
279#41—742no—
280#41—1481no—
281#41—1481no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8—371no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—371no—
288C2×D4—371no—
289C2×D4—741no—
290C2×D4—741no—
291C2×D4—741no—
292C2×D4—741no—
293C2×D4—742no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—1481no—
298C2×D4C22×D3711yescharacteristic
299C2×D4C22×D3711yescharacteristic
300C2×D4C22×D3711yescharacteristic
301C22×C4—21no—
302C22×C4—371no—
303C22×C4—371no—
304C22×C4—741no—
305C22×C4—741no—
306C22×C4—741no—
307Q16—742no—
308SD16—374no—
309SD16—742no—
310SD16—742no—
311SD16—1481no—
312D8—22no—
313D8—22no—
314D8—742no—
315D8—1481no—
316M16—742no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8—742no—
320C2×C8C22×D3711yescharacteristic
321C2×C8C22×D3711yescharacteristic
322C4⋊C4—371no—
323C4⋊C4—371no—
324C4⋊C4—741no—
325C4⋊C4—741no—
326C4⋊C4C22×D3711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—371no—
329C22⋊C4—371no—
330C22⋊C4—741no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4—741no—
335C22⋊C4—741no—
336C42—741no—
337C42C22×D3711yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—371no—
342C23—371no—
343C23—2961no—
344C23—741no—
345C23—1482no—
346C23—1482no—
347Q8—372no—
348Q8—741no—
349Q8—741no—
350Q8—741no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—2961no—
359D4—2961no—
360D4—2961no—
361D4—741no—
362D4—741no—
363D4—1481no—
364D4—1482no—
365D4—1482no—
366D4—1482no—
367D4—1482no—
368D4D4×D3712yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—371no—
372C2×C4—371no—
373C2×C4—741no—
374C2×C4—741no—
375C2×C4—741no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—1482no—
381C2×C4—1482no—
382C2×C4—1482no—
383C2×C4D4×D3711yescharacteristic
384C2×C4D4×D3711yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—21no—
387C8—21no—
388C8—372no—
389C8—741no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—2964no—
400C22—741no—
401C22—741no—
402C22—741no—
403C22—741no—
404C22—741no—
405C22—741no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22C2×D4×D3711yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—741no—
414C4—741no—
415C4—742no—
416C4—1481no—
417C4—1481no—
418C4C2×D4×D3711yescharacteristic
419C4#1192458211yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—2961no—
424C2—1481no—
425C2—1481no—
426C2#1455816711yescharacteristic
427C2#1455832911yescharacteristic
428C2#1455833411yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#459C2
socleC22×C37C22×D4
hypercenter#459D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#11924560C2semidirect
2. C2×#11924555C2semidirect
3. #14558203C2semidirect
4. #14558178C2semidirect
5. #14557920C2semidirect
6. #14557778C2semidirect
7. #14557768C2semidirect
8. #14557756C2semidirect
9. #14557696C2semidirect
10. #14557679C2semidirect
11. #14557675C2semidirect
12. #14557665C2semidirect
13. #14557633C2semidirect
14. #14557603C2semidirect
15. C37×#459C2semidirect
18. C2×#10596964C22semidirect
22. C2×Dic148C22semidirect
25. C2×#10596940C22semidirect
26. C2×#10596940C22semidirect
30. C2×C8×D37C22semidirect
40. #11924507C22semidirect
42. C4×Dic74C22semidirect
46. #11924469C22semidirect
47. #11924461C22semidirect
48. #11924459C22semidirect
52. #11924448C22semidirect
53. #11924447C22semidirect
56. #127×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #102×C37C22semidirect
60. #102×C37C22semidirect
103. #10596940D4semidirect
223. #459D37semidirect
230. C37#3268semidirect
249. #127C2×D37semidirect
266. C4⋊C8C2×D37semidirect
271. #102C2×D37semidirect
272. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245602
C2×#119245552
#145582032
#145581782
#145579202
#145577782
#145577682
#145577562
#145576962
#145576792
#145576752
#145576652
#145576332
#145576032
C37×#4592
#326837