Finite Group Databasebeta

← #18006143

Subgroups — #18006143

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×#11924564C211yesmaximal, characteristic, complemented
2C2×#11924557C211yesmaximal, characteristic, complemented
3#14558201C211yesmaximal, characteristic, complemented
4#14558174C211yesmaximal, characteristic, complemented
5#14557919C211yesmaximal, characteristic, complemented
6#14557770C211yesmaximal, characteristic, complemented
7#14557758C211yesmaximal, characteristic, complemented
8#14557727C211yesmaximal, characteristic, complemented
9#14557693C211yesmaximal, characteristic, complemented
10#14557681C211yesmaximal, characteristic, complemented
11#14557679C211yesmaximal, characteristic, complemented
12#14557666C211yesmaximal, characteristic, complemented
13#14557632C211yesmaximal, characteristic, complemented
14#14557602C211yesmaximal, characteristic, complemented
15C37×#468C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596964C2211yescharacteristic, complemented
19C22×D148C2211yescharacteristic
20#11924564—24no—
21#11924557—24no—
22C2×#10596942C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic
24C2×#10596930C2211yescharacteristic
25C2×#10596941C2211yescharacteristic, complemented
26C2×D296C2211yescharacteristic
27C2×D296C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596939C2211yescharacteristic
30C2×C8×D37C2211yescharacteristic, complemented
31#11924532—21no—
32#11924532C2211yescharacteristic, complemented
33#11924525C2211yescharacteristic
34#11924521—21no—
35#11924511—21no—
36#11924511C2211yescharacteristic
37#11924511C2211yescharacteristic, complemented
38#11924509—21no—
39#11924508—21no—
40#11924506—21no—
41#11924501C2211yescharacteristic, complemented
42#11924498C2211yescharacteristic
43C4×C22⋊D37C2211yescharacteristic
44#11924496—21no—
45C22⋊C4×D37—21no—
46#11924465C2211yescharacteristic, complemented
47#11924459C2211yescharacteristic, complemented
48#11924456C2211yescharacteristic
49#11924456C2211yescharacteristic
50#11924456C2211yescharacteristic, complemented
51C22⋊#64436C2211yescharacteristic
52#11924448C2211yescharacteristic, complemented
53#11924446C2211yescharacteristic, complemented
54C2×SD16×C37C2211yescharacteristic, complemented
55C2×M16×C37C2211yescharacteristic
56C22⋊Q8×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic
58#107×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—21no—
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37D411yescharacteristic
71C22×Dic37—21no—
72#10596966—22no—
73#10596966—41no—
74#10596964—22no—
75#10596964—41no—
76#10596962—22no—
77#10596962—41no—
78C2×D148—22no—
79C2×D148—21no—
80C2×D148—21no—
81C2×D148—21no—
82C2×D148—21no—
83C2×D148—41no—
84C2×D148C2311yescharacteristic
85C2×D148C2311yescharacteristic
86C2×D148C2311yescharacteristic
87C2×C4×D37—21no—
88C2×C4×D37—21no—
89C2×C4×D37—21no—
90C2×C4×D37C2311yescharacteristic
91C2×Dic74C2311yescharacteristic
92SD16×C37—22no—
93M16×C37—22no—
94C2×C8×C37C2311yescharacteristic
95C2×C8×C37C2311yescharacteristic
96C4⋊C4×C37—21no—
97C4⋊C4×C37C2311yescharacteristic
98C4⋊C4×C37C2311yescharacteristic
99C22⋊C4×C37—21no—
100C22⋊C4×C37—21no—
101C22⋊Dic37D411yescharacteristic
102#10596942—22no—
103#10596941—41no—
104#10596939—22no—
105#10596939—41no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109#10596938—21no—
110#10596938—21no—
111#10596938D411yescharacteristic
112#10596936—21no—
113#10596936D411yescharacteristic
114C4×Dic37—21no—
115C4×Dic37C2311yescharacteristic
116C2×#64436C2311yescharacteristic
117C2×#64436C2311yescharacteristic
118D296—22no—
119D296—22no—
120#10596930—22no—
121#10596930D414yescomplemented
122C8×D37—22no—
123C23×C37—21no—
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37—81no—
131C22×D37C2×D411yescharacteristic
132Q8×C37—21no—
133Q8×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—81no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37C2×D411yescharacteristic
143C2×C4×C37C2411yescharacteristic
144C22⋊D37—41no—
145C22⋊D37—42no—
146C22⋊D37—42no—
147C22⋊D37—42no—
148C22⋊D37—81no—
149C2×Dic37—21no—
150C2×Dic37—42no—
151C2×Dic37C2×D411yescharacteristic
152C2×Dic37C2×D411yescharacteristic
153C2×Dic37C2×D411yescharacteristic
154D148—21no—
155D148—21no—
156D148—21no—
157D148—21no—
158D148—21no—
159D148—42no—
160D148—42no—
161D148—81no—
162D148—81no—
163D148C2×D412yes—
164C4×D37—21no—
165C4×D37—21no—
166C4×D37—42no—
167C4×D37—42no—
168C4×D37—81no—
169Dic74—21no—
170Dic74C2×D412yes—
171C8×C37—21no—
172C8×C37C2×D412yes—
173#64436—21no—
174#64436—21no—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37C22×D411yescharacteristic
182C2×D37—21no—
183C2×D37—22no—
184C2×D37—21no—
185C2×D37—21no—
186C2×D37—41no—
187C2×D37—41no—
188C2×D37—41no—
189C2×D37—41no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—84no—
195C4×C37—21no—
196C4×C37—41no—
197C4×C37—41no—
198C4×C37—41no—
199C4×C37C22×D411yescharacteristic
200C4×C37H(5,𝔽2)11yescharacteristic
201Dic37—22no—
202Dic37—21no—
203Dic37—21no—
204Dic37—21no—
205#3268—371nomaximal, Sylow
206C2×C37—41no—
207C2×C37—81no—
208C2×C37D4211yescharacteristic
209C2×C37#57511yescharacteristic
210C2×C37#57611yescharacteristic
211D37—41no—
212D37—42no—
213D37—81no—
214D37—81no—
215C2×AGL(1,ℤ/8)—371no—
216C2×#135—371no—
217#550—371no—
218#546—371no—
219#496—371no—
220#468D3711yescharacteristic, complemented
221#466—371no—
222#464—371no—
223#459—371no—
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×SD16C2×D3711yescharacteristic, complemented
242C2×D8—371no—
243C2×D8—371no—
244C2×D8—371no—
245C2×D8—371no—
246C2×M16C2×D3711yescharacteristic
247C22×C8—371no—
248#127—371no—
249#127—741no—
250#124—371no—
251#123—741no—
252C22⋊Q8C2×D3711yescharacteristic
253#121—371no—
254#121—371no—
255#121—741no—
256#121—741no—
257#121—741no—
258#121C2×D3711yescharacteristic
259#120—741no—
260C4×Q8—371no—
261C4×D4—371no—
262C4×D4—371no—
263C4×D4—741no—
264C2×C22⋊C4—741no—
265#107C2×D3711yescharacteristic, complemented
266C4⋊C8—371no—
267#103—371no—
268#103C2×D3711yescharacteristic, complemented
269#102—371no—
270#102—371no—
271#102—371no—
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×Q8C22×D3711yescharacteristic
285C2×D4—21no—
286C2×D4—371no—
287C2×D4—371no—
288C2×D4—371no—
289C2×D4—371no—
290C2×D4—742no—
291C2×D4—741no—
292C2×D4—741no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—741no—
298C2×D4—741no—
299C2×D4—1481no—
300C2×D4C22×D3711yescharacteristic
301C22×C4—371no—
302C22×C4—741no—
303C22×C4—741no—
304C22×C4—741no—
305C22×C4—741no—
306C22×C4C22×D3711yescharacteristic
307Q16—742no—
308SD16—22no—
309SD16—374no—
310SD16—742no—
311SD16—1481no—
312D8—742no—
313D8—742no—
314D8—742no—
315D8—1481no—
316M16—22no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8—742no—
320C2×C8C22×D3711yescharacteristic
321C2×C8C22×D3711yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—371no—
324C4⋊C4—741no—
325C4⋊C4C22×D3711yescharacteristic
326C4⋊C4C22×D3711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—371no—
330C22⋊C4—371no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4—741no—
335C22⋊C4—741no—
336C42—371no—
337C42—741no—
338C23—21no—
339C23—371no—
340C23—2961no—
341C23—741no—
342C23—741no—
343C23—741no—
344C23—1482no—
345C23—1482no—
346C23D4×D3711yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—372no—
350Q8—741no—
351D4—21no—
352D4—21no—
353D4—81no—
354D4—372no—
355D4—2961no—
356D4—2961no—
357D4—2961no—
358D4—741no—
359D4—741no—
360D4—741no—
361D4—741no—
362D4—741no—
363D4—1482no—
364D4—1482no—
365D4—1481no—
366D4—1482no—
367D4—1482no—
368D4—1482no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—371no—
375C2×C4—371no—
376C2×C4—371no—
377C2×C4—2961no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—741no—
381C2×C4—1482no—
382C2×C4—1482no—
383C2×C4—1482no—
384C2×C4D4×D3711yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—21no—
387C8—741no—
388C8—741no—
389C8D4×D3712yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—2964no—
397C22—741no—
398C22—741no—
399C22—741no—
400C22—742no—
401C22—1481no—
402C22—1481no—
403C22—1481no—
404C22—1481no—
405C22—1481no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22C2×D4×D3711yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—741no—
415C4—741no—
416C4—741no—
417C4—742no—
418C4C2×D4×D3711yescharacteristic
419C4#1192458211yescharacteristic
420C2—41no—
421C2—81no—
422C2—2961no—
423C2—2961no—
424C2—1482no—
425C2—1481no—
426C2#1455816711yescharacteristic
427C2#1455833211yescharacteristic
428C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#468C2
socleC22×C37C22×D4
hypercenter#468D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. C2×#11924557C2semidirect
3. #14558201C2semidirect
4. #14558174C2semidirect
5. #14557919C2semidirect
6. #14557770C2semidirect
7. #14557758C2semidirect
8. #14557727C2semidirect
9. #14557693C2semidirect
10. #14557681C2semidirect
11. #14557679C2semidirect
12. #14557666C2semidirect
13. #14557632C2semidirect
14. #14557602C2semidirect
15. C37×#468C2semidirect
18. C2×#10596964C22semidirect
22. C2×#10596942C22semidirect
25. C2×#10596941C22semidirect
30. C2×C8×D37C22semidirect
32. #11924532C22semidirect
37. #11924511C22semidirect
41. #11924501C22semidirect
46. #11924465C22semidirect
47. #11924459C22semidirect
50. #11924456C22semidirect
52. #11924448C22semidirect
53. #11924446C22semidirect
54. C2×SD16×C37C22semidirect
58. #107×C37C22semidirect
59. #103×C37C22semidirect
60. #102×C37C22semidirect
121. #10596930D4semidirect
220. #468D37semidirect
230. C37#3268semidirect
241. C2×SD16C2×D37semidirect
265. #107C2×D37semidirect
268. #103C2×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×#119245642
C2×#119245572
#145582012
#145581742
#145579192
#145577702
#145577582
#145577272
#145576932
#145576812
#145576792
#145576662
#145576322
#145576022
C37×#4682
#326837