Finite Group Databasebeta

← #18006136

Subgroups — #18006136

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×#11924563C211yesmaximal, characteristic, complemented
2#14558202C211yesmaximal, characteristic, complemented
3#14558171C211yesmaximal, characteristic, complemented
4#14557919C211yesmaximal, characteristic, complemented
5#14557776C211yesmaximal, characteristic, complemented
6#14557769C211yesmaximal, characteristic, complemented
7#14557757C211yesmaximal, characteristic, complemented
8#14557726C211yesmaximal, characteristic, complemented
9#14557694C211yesmaximal, characteristic, complemented
10#14557678C211yesmaximal, characteristic, complemented
11#14557678C211yesmaximal, characteristic, complemented
12#14557665C211yesmaximal, characteristic, complemented
13#14557634C211yesmaximal, characteristic, complemented
14#14557604C211yesmaximal, characteristic, complemented
15C2×#135×C37C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×D4×D37C2211yescharacteristic
18#11924563—24no—
19C2×#10596941C2211yescharacteristic
20C2×#10596941C2211yescharacteristic, complemented
21C2×D296C2211yescharacteristic
22C2×#10596939C2211yescharacteristic
23C2×#10596939C2211yescharacteristic
24C2×#10596929C2211yescharacteristic
25#11924532—21no—
26#11924532C2211yescharacteristic, complemented
27#11924525C2211yescharacteristic
28#11924519—21no—
29#11924512C2211yescharacteristic
30#11924510—21no—
31#11924510C2211yescharacteristic
32#11924510C2211yescharacteristic, complemented
33#11924508—21no—
34#11924507—21no—
35#11924507C2211yescharacteristic
36#11924504—21no—
37Q8×Dic37C2211yescharacteristic, complemented
38D4×Dic37C2211yescharacteristic
39C4×C22⋊D37—21no—
40C4×C22⋊D37C2211yescharacteristic
41C2×#10596938—21no—
42#11924470C2211yescharacteristic, complemented
43#11924465C2211yescharacteristic, complemented
44#11924460C2211yescharacteristic, complemented
45#11924460C2211yescharacteristic, complemented
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic, complemented
48#11924457C2211yescharacteristic
49#11924457C2211yescharacteristic, complemented
50C22⋊#64436C2211yescharacteristic, complemented
51#11924448C2211yescharacteristic
52#11924446C2211yescharacteristic, complemented
53C2×#41×C37C2211yescharacteristic
54C2×#41×C37C2211yescharacteristic, complemented
55#135×C37—24no—
56C2×Q16×C37C2211yescharacteristic, complemented
57C2×SD16×C37C2211yescharacteristic
58C2×SD16×C37C2211yescharacteristic, complemented
59C2×D8×C37C2211yescharacteristic
60C22×C8×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62#41×C37—22no—
63#41×C37—22no—
64#41×C37—41no—
65#41×C37—41no—
66C2×Q8×C37C2311yescharacteristic
67C2×Q8×C37C2311yescharacteristic
68C2×D4×C37—21no—
69C2×D4×C37—21no—
70C2×D4×C37C2311yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37C2311yescharacteristic
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C2×C22⋊D37—21no—
78C2×C22⋊D37—21no—
79C2×C22⋊D37—21no—
80C2×C22⋊D37—21no—
81C2×C22⋊D37D411yescharacteristic
82C22×Dic37—21no—
83#10596966—22no—
84#10596966—41no—
85D4×D37—22no—
86D4×D37—41no—
87C2×D148—21no—
88C2×D148C2311yescharacteristic
89C2×D148C2311yescharacteristic
90C2×C4×D37—21no—
91C2×C4×D37C2311yescharacteristic
92Q16×C37—22no—
93SD16×C37—22no—
94SD16×C37D414yescomplemented
95D8×C37—22no—
96C2×C8×C37—22no—
97C2×C8×C37C2311yescharacteristic
98C2×C8×C37C2311yescharacteristic
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37D411yescharacteristic
102#10596941—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
112C4⋊Dic37—21no—
113C4⋊Dic37C2311yescharacteristic
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116#10596936D411yescharacteristic
117C4×Dic37—21no—
118C4×Dic37C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121D296—22no—
122#10596929—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37C2×D411yescharacteristic
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—42no—
129C22×D37—42no—
130C22×D37—81no—
131C22×D37C2×D411yescharacteristic
132Q8×C37—21no—
133Q8×C37—21no—
134Q8×C37—21no—
135Q8×C37C2×D412yes—
136D4×C37—21no—
137D4×C37—21no—
138D4×C37—21no—
139D4×C37—42no—
140D4×C37—42no—
141D4×C37C2×D412yes—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—42no—
147C2×C4×C37—42no—
148C2×C4×C37C2×D411yescharacteristic
149C2×C4×C37C2411yescharacteristic
150C22⋊D37—41no—
151C22⋊D37—42no—
152C22⋊D37—42no—
153C22⋊D37—81no—
154C22⋊D37—81no—
155C22⋊D37—81no—
156C22⋊D37—81no—
157C2×Dic37—21no—
158C2×Dic37—21no—
159C2×Dic37—81no—
160C2×Dic37C2×D411yescharacteristic
161C2×Dic37C2×D411yescharacteristic
162C2×Dic37C2×D411yescharacteristic
163D148—21no—
164D148—21no—
165D148—21no—
166D148—21no—
167D148—42no—
168C4×D37—21no—
169C4×D37—21no—
170C4×D37—42no—
171C8×C37—21no—
172C8×C37C2×D412yes—
173#64436—21no—
174#64436—21no—
175C22×C37—22no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—21no—
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—41no—
189C2×D37—41no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—84no—
195C4×C37—22no—
196C4×C37—21no—
197C4×C37—41no—
198C4×C37C22×D411yescharacteristic
199C4×C37H(5,𝔽2)11yescharacteristic
200Dic37—21no—
201Dic37—21no—
202Dic37—21no—
203Dic37—41no—
204Dic37—41no—
205#3268—371nomaximal, Sylow
206C2×C37—42no—
207C2×C37—41no—
208C2×C37—81no—
209C2×C37D4211yescharacteristic
210C2×C37#57511yescharacteristic
211C2×C37#57611yescharacteristic
212D37—41no—
213D37—81no—
214D37—81no—
215C2×AGL(1,ℤ/8)—371no—
216C2×#135D3711yescharacteristic, complemented
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#435—371no—
230C37#326811yescharacteristic, complemented, Sylow
231C2×#41—371no—
232C2×#41C2×D3711yescharacteristic
233C2×#41C2×D3711yescharacteristic, complemented
234C22×D4—371no—
235AGL(1,ℤ/8)—744no—
236#135—24no—
237C2×Q16C2×D3711yescharacteristic, complemented
238C2×SD16—371no—
239C2×SD16—371no—
240C2×SD16C2×D3711yescharacteristic
241C2×SD16C2×D3711yescharacteristic, complemented
242C2×D8—371no—
243C2×D8—371no—
244C2×D8—371no—
245C2×D8C2×D3711yescharacteristic
246C2×M16—371no—
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—371no—
263C4×D4—741no—
264C2×C22⋊C4—741no—
265#107—371no—
266C4⋊C8—371no—
267#103—371no—
268#103—371no—
269#102—371no—
270#102—371no—
271#102—371no—
272#102—371no—
273C22⋊C8—371no—
274C22⋊C8—371no—
275#97—371no—
276C24—741no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—742no—
282#41—1481no—
283C2×Q8C22×D3711yescharacteristic
284C2×Q8C22×D3711yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—371no—
288C2×D4—371no—
289C2×D4—371no—
290C2×D4—741no—
291C2×D4—741no—
292C2×D4—741no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—742no—
298C2×D4—1481no—
299C2×D4C22×D3711yescharacteristic
300C2×D4C22×D3711yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—371no—
304C22×C4—741no—
305C22×C4—741no—
306C22×C4C22×D3711yescharacteristic
307Q16—22no—
308SD16—22no—
309SD16—742no—
310SD16—1481no—
311SD16C22⋊D3714yescomplemented
312D8—22no—
313D8—742no—
314D8—742no—
315D8—1481no—
316M16—742no—
317C2×C8—22no—
318C2×C8—371no—
319C2×C8—371no—
320C2×C8C22×D3711yescharacteristic
321C2×C8C22×D3711yescharacteristic
322C4⋊C4—371no—
323C4⋊C4—371no—
324C4⋊C4—371no—
325C4⋊C4—741no—
326C4⋊C4—741no—
327C22⋊C4—371no—
328C22⋊C4—371no—
329C22⋊C4—741no—
330C22⋊C4—741no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4—741no—
335C22⋊C4—741no—
336C42—371no—
337C42—741no—
338C23—21no—
339C23—21no—
340C23—371no—
341C23—2961no—
342C23—741no—
343C23—741no—
344C23—1482no—
345C23—1482no—
346C23D4×D3711yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8C2×C22⋊D3712yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—42no—
356D4—2961no—
357D4—2961no—
358D4—2961no—
359D4—2961no—
360D4—741no—
361D4—741no—
362D4—741no—
363D4—741no—
364D4—1482no—
365D4—1481no—
366D4—1482no—
367D4—1482no—
368D4C2×C22⋊D3712yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—371no—
376C2×C4—371no—
377C2×C4—371no—
378C2×C4—2961no—
379C2×C4—741no—
380C2×C4—741no—
381C2×C4—741no—
382C2×C4—741no—
383C2×C4—1482no—
384C2×C4D4×D3711yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—21no—
387C8—741no—
388C8—741no—
389C8C2×C22⋊D3712yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—2964no—
400C22—741no—
401C22—741no—
402C22—741no—
403C22—1481no—
404C22—1481no—
405C22—1481no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22C2×D4×D3711yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—741no—
414C4—741no—
415C4—741no—
416C4—1481no—
417C4—1481no—
418C4C22×C22⋊D3711yescharacteristic
419C4#1192458111yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—2961no—
424C2—2961no—
425C2—1481no—
426C2D4×C22⋊D3711yescharacteristic
427C2#1455833011yescharacteristic
428C2#1455833511yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#135×C37C2
socleC22×C37C22×D4
hypercenterC2×#135D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11924563C2semidirect
2. #14558202C2semidirect
3. #14558171C2semidirect
4. #14557919C2semidirect
5. #14557776C2semidirect
6. #14557769C2semidirect
7. #14557757C2semidirect
8. #14557726C2semidirect
9. #14557694C2semidirect
10. #14557678C2semidirect
11. #14557678C2semidirect
12. #14557665C2semidirect
13. #14557634C2semidirect
14. #14557604C2semidirect
15. C2×#135×C37C2semidirect
20. C2×#10596941C22semidirect
26. #11924532C22semidirect
32. #11924510C22semidirect
37. Q8×Dic37C22semidirect
42. #11924470C22semidirect
43. #11924465C22semidirect
44. #11924460C22semidirect
45. #11924460C22semidirect
47. #11924458C22semidirect
49. #11924457C22semidirect
50. C22⋊#64436C22semidirect
52. #11924446C22semidirect
54. C2×#41×C37C22semidirect
56. C2×Q16×C37C22semidirect
58. C2×SD16×C37C22semidirect
60. C22×C8×C37C22semidirect
94. SD16×C37D4semidirect
216. C2×#135D37semidirect
230. C37#3268semidirect
233. C2×#41C2×D37semidirect
237. C2×Q16C2×D37semidirect
241. C2×SD16C2×D37semidirect
247. C22×C8C2×D37semidirect
311. SD16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245632
#145582022
#145581712
#145579192
#145577762
#145577692
#145577572
#145577262
#145576942
#145576782
#145576652
#145576342
#145576042
C2×#135×C372
#326837