Finite Group Databasebeta

← #18006141

Subgroups — #18006141

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×#11924558C211yesmaximal, characteristic, complemented
3#14558204C211yesmaximal, characteristic, complemented
4#14558179C211yesmaximal, characteristic, complemented
5#14557922C211yesmaximal, characteristic, complemented
6#14557779C211yesmaximal, characteristic, complemented
7#14557769C211yesmaximal, characteristic, complemented
8#14557756C211yesmaximal, characteristic, complemented
9#14557729C211yesmaximal, characteristic, complemented
10#14557697C211yesmaximal, characteristic, complemented
11#14557680C211yesmaximal, characteristic, complemented
12#14557680C211yesmaximal, characteristic, complemented
13#14557669C211yesmaximal, characteristic, complemented
14#14557635C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596962C2211yescharacteristic, complemented
19C22×D148C2211yescharacteristic
20#11924564—24no—
21#11924558—24no—
22C2×Dic148C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic
24C2×#10596930C2211yescharacteristic
25C2×#10596930C2211yescharacteristic, complemented
26C2×#10596930C2211yescharacteristic, complemented
27C2×D296C2211yescharacteristic
28C2×D296C2211yescharacteristic
29C2×D296C2211yescharacteristic
30C2×D296C2211yescharacteristic
31#11924533C2211yescharacteristic, complemented
32#11924532—21no—
33#11924524C2211yescharacteristic
34#11924521—21no—
35#11924515C2211yescharacteristic
36#11924510C2211yescharacteristic
37#11924510C2211yescharacteristic
38#11924510C2211yescharacteristic, complemented
39#11924509—21no—
40#11924509—21no—
41#11924509—21no—
42#11924504—21no—
43C4×Dic74C2211yescharacteristic, complemented
44C4×D148C2211yescharacteristic
45#11924498—21no—
46C22⋊C4×D37—21no—
47#11924470C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924461C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic
52#11924458C2211yescharacteristic, complemented
53#11924458C2211yescharacteristic, complemented
54C2×M16×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic, complemented
56C4×D4×C37C2211yescharacteristic
57C4⋊C8×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic
59C22⋊C8×C37C2211yescharacteristic, complemented
60#97×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×D4×C37D411yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71#10596962—22no—
72#10596962—22no—
73#10596962—22no—
74#10596962—41no—
75#10596962—41no—
76#10596962—41no—
77C2×D148—22no—
78C2×D148—21no—
79C2×D148—21no—
80C2×D148—21no—
81C2×D148—41no—
82C2×D148C2311yescharacteristic
83C2×D148C2311yescharacteristic
84C2×D148C2311yescharacteristic
85C2×D148C2311yescharacteristic
86C2×C4×D37—21no—
87C2×C4×D37—21no—
88C2×C4×D37—21no—
89C2×C4×D37—21no—
90C2×Dic74C2311yescharacteristic
91C2×Dic74C2311yescharacteristic
92M16×C37—22no—
93C2×C8×C37—22no—
94C2×C8×C37C2311yescharacteristic
95C2×C8×C37C2311yescharacteristic
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C4⋊C4×C37D411yescharacteristic
99C22⋊C4×C37D411yescharacteristic
100C22⋊C4×C37D411yescharacteristic
101C42×C37C2311yescharacteristic
102C22⋊Dic37—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938—21no—
109C4⋊Dic37C2311yescharacteristic
110C4⋊Dic37C2311yescharacteristic
111#10596936—21no—
112#10596936—21no—
113C4×Dic37—21no—
114Dic148—22no—
115D296—22no—
116D296—22no—
117D296—22no—
118D296—41no—
119#10596930—22no—
120#10596930—22no—
121#10596930—41no—
122#10596930D414yescomplemented
123C23×C37C2×D411yescharacteristic
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—42no—
130C22×D37—42no—
131C22×D37—81no—
132D4×C37—41no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2×D411yescharacteristic
141C2×C4×C37C2411yescharacteristic
142C22⋊D37—42no—
143C22⋊D37—42no—
144C22⋊D37—42no—
145C22⋊D37—81no—
146C22⋊D37—81no—
147C22⋊D37—81no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37—21no—
151C2×Dic37—21no—
152D148—21no—
153D148—21no—
154D148—21no—
155D148—21no—
156D148—21no—
157D148—21no—
158D148—21no—
159D148—42no—
160D148—42no—
161D148—81no—
162D148C2×D412yes—
163C4×D37—42no—
164C4×D37—42no—
165C4×D37—42no—
166C4×D37—81no—
167Dic74—21no—
168Dic74—21no—
169Dic74—21no—
170Dic74C2×D412yes—
171C8×C37—21no—
172C8×C37—21no—
173C8×C37—21no—
174C8×C37C2×D412yes—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—21no—
179C22×C37—21no—
180C22×C37—21no—
181C22×C37C22×D411yescharacteristic
182C2×D37—22no—
183C2×D37—41no—
184C2×D37—41no—
185C2×D37—41no—
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—21no—
197C4×C37—21no—
198C4×C37—21no—
199C4×C37C22×D411yescharacteristic
200C4×C37H(5,𝔽2)11yescharacteristic
201Dic37—22no—
202Dic37—41no—
203Dic37—41no—
204Dic37—41no—
205#3268—371nomaximal, Sylow
206C2×C37—41no—
207C2×C37—41no—
208C2×C37D4211yescharacteristic
209C2×C37#57511yescharacteristic
210C2×C37#57611yescharacteristic
211D37—42no—
212D37—81no—
213D37—81no—
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#459—371no—
224#452—371no—
225#449—371no—
226#449—371no—
227#447—371no—
228#440—371no—
229#435D3711yescharacteristic, complemented
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×D8—371no—
245C2×D8—371no—
246C2×M16C2×D3711yescharacteristic
247C22×C8C2×D3711yescharacteristic, complemented
248#127—371no—
249#127—741no—
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#102—371no—
272#102—371no—
273C22⋊C8C2×D3711yescharacteristic
274C22⋊C8C2×D3711yescharacteristic, complemented
275#97C2×D3711yescharacteristic, complemented
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—371no—
286C2×D4—371no—
287C2×D4—371no—
288C2×D4—371no—
289C2×D4—742no—
290C2×D4—741no—
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×D4D14811yescharacteristic
301C22×C4—741no—
302C22×C4—741no—
303C22×C4—741no—
304C22×C4—741no—
305C22×C4C22×D3711yescharacteristic
306C22×C4C22×D3711yescharacteristic
307Q16—742no—
308SD16—374no—
309SD16—742no—
310SD16—742no—
311SD16—1481no—
312D8—742no—
313D8—742no—
314D8—742no—
315D8—1481no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D3711yescharacteristic
319C2×C8C22×D3711yescharacteristic
320C2×C8C22×D3711yescharacteristic
321C2×C8C22×D3711yescharacteristic
322C4⋊C4—371no—
323C4⋊C4—371no—
324C4⋊C4—741no—
325C4⋊C4—741no—
326C4⋊C4D14811yescharacteristic
327C22⋊C4—741no—
328C22⋊C4—741no—
329C22⋊C4—741no—
330C22⋊C4—741no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4D14811yescharacteristic
335C22⋊C4D14811yescharacteristic
336C42—741no—
337C42C22×D3711yescharacteristic
338C23—2961no—
339C23—741no—
340C23—741no—
341C23—741no—
342C23—741no—
343C23—1482no—
344C23—1482no—
345C23C2×D14811yescharacteristic
346C23C2×D14811yescharacteristic
347Q8—372no—
348Q8—741no—
349Q8—741no—
350Q8—741no—
351D4—41no—
352D4—372no—
353D4—2961no—
354D4—2961no—
355D4—2961no—
356D4—2961no—
357D4—741no—
358D4—741no—
359D4—741no—
360D4—741no—
361D4—741no—
362D4—741no—
363D4—741no—
364D4—1482no—
365D4—1482no—
366D4—1482no—
367D4—1482no—
368D4—1482no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—2961no—
374C2×C4—741no—
375C2×C4—741no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—1482no—
379C2×C4—1482no—
380C2×C4—1482no—
381C2×C4C2×D14811yescharacteristic
382C2×C4C2×D14811yescharacteristic
383C2×C4C2×D14811yescharacteristic
384C2×C4C2×D14811yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D3712yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—2964no—
397C22—742no—
398C22—1481no—
399C22—1481no—
400C22—1481no—
401C22—1481no—
402C22—1481no—
403C22—1481no—
404C22—1481no—
405C22—1481no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22C22×D14811yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—742no—
415C4—1481no—
416C4—1481no—
417C4—1481no—
418C4C2×D4×D3711yescharacteristic
419C4#1192458211yescharacteristic
420C2—41no—
421C2—41no—
422C2—2961no—
423C2—2961no—
424C2—2961no—
425C2—1482no—
426C2D4×D14811yescharacteristic
427C2#1455833311yescharacteristic
428C2#1455833811yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
hypercenter#435D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11924564C2semidirect
2. C2×#11924558C2semidirect
3. #14558204C2semidirect
4. #14558179C2semidirect
5. #14557922C2semidirect
6. #14557779C2semidirect
7. #14557769C2semidirect
8. #14557756C2semidirect
9. #14557729C2semidirect
10. #14557697C2semidirect
11. #14557680C2semidirect
12. #14557680C2semidirect
13. #14557669C2semidirect
14. #14557635C2semidirect
15. C37×#435C2semidirect
18. C2×#10596962C22semidirect
22. C2×Dic148C22semidirect
25. C2×#10596930C22semidirect
26. C2×#10596930C22semidirect
31. #11924533C22semidirect
38. #11924510C22semidirect
43. C4×Dic74C22semidirect
47. #11924470C22semidirect
48. #11924461C22semidirect
49. #11924461C22semidirect
52. #11924458C22semidirect
53. #11924458C22semidirect
55. C22×C8×C37C22semidirect
57. C4⋊C8×C37C22semidirect
59. C22⋊C8×C37C22semidirect
60. #97×C37C22semidirect
122. #10596930D4semidirect
229. #435D37semidirect
230. C37#3268semidirect
247. C22×C8C2×D37semidirect
266. C4⋊C8C2×D37semidirect
274. C22⋊C8C2×D37semidirect
275. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C2×#119245582
#145582042
#145581792
#145579222
#145577792
#145577692
#145577562
#145577292
#145576972
#145576802
#145576692
#145576352
C37×#4352
#326837