Finite Group Databasebeta

← #18006132

Subgroups — #18006132

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×#11924562C211yesmaximal, characteristic, complemented
2C2×#11924556C211yesmaximal, characteristic, complemented
3#14558204C211yesmaximal, characteristic, complemented
4#14557923C211yesmaximal, characteristic, complemented
5#14557781C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557752C211yesmaximal, characteristic, complemented
8#14557728C211yesmaximal, characteristic, complemented
9#14557693C211yesmaximal, characteristic, complemented
10#14557678C211yesmaximal, characteristic, complemented
11#14557676C211yesmaximal, characteristic, complemented
12#14557667C211yesmaximal, characteristic, complemented
13#14557633C211yesmaximal, characteristic, complemented
14#14557605C211yesmaximal, characteristic, complemented
15C37×#546C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic, complemented
18#11924562—24no—
19#11924556—24no—
20C2×#10596942C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic
22C2×#10596940C2211yescharacteristic
23C2×#10596941C2211yescharacteristic, complemented
24C2×#10596941C2211yescharacteristic, complemented
25C2×#10596939C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596934C2211yescharacteristic
30C22×#64436C2211yescharacteristic, complemented
31#11924533C2211yescharacteristic, complemented
32#11924532—21no—
33#11924510C2211yescharacteristic
34#11924510C2211yescharacteristic, complemented
35#11924509—21no—
36#11924509—21no—
37C4×Dic74C2211yescharacteristic, complemented
38#11924498—21no—
39#11924469C2211yescharacteristic, complemented
40C4⋊#64436C2211yescharacteristic, complemented
41#11924460C2211yescharacteristic, complemented
42#11924459C2211yescharacteristic, complemented
43#11924457C2211yescharacteristic
44#11924457C2211yescharacteristic
45#11924456C2211yescharacteristic, complemented
46#11924456C2211yescharacteristic, complemented
47C22⋊#64436C2211yescharacteristic
48C22⋊#64436C2211yescharacteristic, complemented
49#11924447C2211yescharacteristic, complemented
50C2×#41×C37C2211yescharacteristic
51C22×D4×C37C2211yescharacteristic
52#124×C37C2211yescharacteristic
53#123×C37—21no—
54C22⋊Q8×C37C2211yescharacteristic
55#121×C37—21no—
56#121×C37C2211yescharacteristic
57#120×C37—21no—
58C4×D4×C37C2211yescharacteristic
59C4×D4×C37C2211yescharacteristic
60C2×C22⋊C4×C37—21no—
61C24×C37—21no—
62#41×C37—22no—
63#41×C37—41no—
64C2×Q8×C37C2311yescharacteristic
65C2×D4×C37—22no—
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37—41no—
70C2×D4×C37D411yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C2×D4×C37C2311yescharacteristic
73C22×C4×C37—21no—
74C22×C4×C37—21no—
75C22×C4×C37C2311yescharacteristic
76C22×C4×C37C2311yescharacteristic
77C2×C22⋊D37—21no—
78C2×C22⋊D37—21no—
79C2×C22⋊D37—21no—
80C2×C22⋊D37—21no—
81#10596962—22no—
82#10596962—22no—
83#10596962—41no—
84#10596962—41no—
85C2×D148—21no—
86C2×D148—21no—
87C2×D148C2311yescharacteristic
88C2×D148C2311yescharacteristic
89C2×C4×D37—21no—
90C2×C4×D37—21no—
91C2×Dic74C2311yescharacteristic
92C4⋊C4×C37—21no—
93C4⋊C4×C37D411yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37—21no—
99C22⋊C4×C37—21no—
100C22⋊C4×C37D411yescharacteristic
101C22⋊C4×C37D411yescharacteristic
102C42×C37C2311yescharacteristic
103#10596942—22no—
104#10596941—22no—
105#10596941—41no—
106#10596940—22no—
107#10596940D414yescomplemented
108#10596939—22no—
109#10596939—22no—
110#10596939—22no—
111#10596939—41no—
112#10596938—21no—
113#10596938—21no—
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116C4×Dic37—21no—
117#10596934—22no—
118C2×#64436—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—42no—
126C23×C37—42no—
127C23×C37—81no—
128C23×C37C2×D411yescharacteristic
129C23×C37C2×D411yescharacteristic
130C22×D37—21no—
131C22×D37—21no—
132Q8×C37—21no—
133Q8×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—41no—
138D4×C37—42no—
139D4×C37—42no—
140D4×C37—81no—
141D4×C37C2×D412yes—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—42no—
149C2×C4×C37—81no—
150C2×C4×C37C2×D411yescharacteristic
151C2×C4×C37C2×D411yescharacteristic
152C2×C4×C37C2×D411yescharacteristic
153C2×C4×C37C2×D411yescharacteristic
154C2×C4×C37C2411yescharacteristic
155C22⋊D37—42no—
156C22⋊D37—42no—
157C22⋊D37—81no—
158C22⋊D37—81no—
159C2×Dic37—21no—
160C2×Dic37—21no—
161D148—21no—
162D148—21no—
163D148—21no—
164D148—21no—
165D148—42no—
166D148—81no—
167C4×D37—42no—
168C4×D37—42no—
169Dic74—21no—
170Dic74C2×D412yes—
171#64436—21no—
172#64436—21no—
173#64436—21no—
174#64436C2×D412yes—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—22no—
178C22×C37—21no—
179C22×C37—21no—
180C22×C37—21no—
181C22×C37—21no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—84no—
188C22×C37C22×D411yescharacteristic
189C2×D37—41no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C2×D37—41no—
195C4×C37—21no—
196C4×C37—21no—
197C4×C37—21no—
198C4×C37—21no—
199C4×C37—41no—
200C4×C37—41no—
201C4×C37C22×D411yescharacteristic
202C4×C37H(5,𝔽2)11yescharacteristic
203Dic37—22no—
204Dic37—41no—
205#3268—371nomaximal, Sylow
206C2×C37—41no—
207C2×C37—41no—
208C2×C37—42no—
209C2×C37—81no—
210C2×C37D4211yescharacteristic
211C2×C37#57511yescharacteristic
212C2×C37#57611yescharacteristic
213D37—81no—
214D37—81no—
215C2×AGL(1,ℤ/8)—371no—
216C2×#135—371no—
217#550—371no—
218#546D3711yescharacteristic, complemented
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×#41—371no—
233C2×#41C2×D3711yescharacteristic
234C22×D4C2×D3711yescharacteristic
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×M16—371no—
247C22×C8—371no—
248#127—371no—
249#127—741no—
250#124C2×D3711yescharacteristic
251#123—21no—
252C22⋊Q8C2×D3711yescharacteristic
253#121—21no—
254#121—371no—
255#121—371no—
256#121—741no—
257#121—741no—
258#121C2×D3711yescharacteristic
259#120—21no—
260C4×Q8—371no—
261C4×D4—741no—
262C4×D4C2×D3711yescharacteristic
263C4×D4C2×D3711yescharacteristic
264C2×C22⋊C4—21no—
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—21no—
277#41—22no—
278#41—41no—
279#41—742no—
280#41—742no—
281#41—1481no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8C22×D3711yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—371no—
291C2×D4—371no—
292C2×D4—741no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—741no—
298C2×D4C22⋊D3711yescharacteristic
299C2×D4C22×D3711yescharacteristic
300C2×D4C22×D3711yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
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—742no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8—371no—
320C2×C8—371no—
321C2×C8—742no—
322C4⋊C4—21no—
323C4⋊C4—371no—
324C4⋊C4—741no—
325C4⋊C4C22⋊D3711yescharacteristic
326C4⋊C4C22×D3711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C22⋊C4C22⋊D3711yescharacteristic
335C22⋊C4C22⋊D3711yescharacteristic
336C42—741no—
337C42C22×D3711yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—42no—
342C23—81no—
343C23—741no—
344C23—741no—
345C23C2×C22⋊D3711yescharacteristic
346C23C2×C22⋊D3711yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—372no—
350Q8—741no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4—2961no—
359D4—2961no—
360D4—2961no—
361D4—741no—
362D4—741no—
363D4—741no—
364D4—741no—
365D4—1482no—
366D4—1482no—
367D4—1482no—
368D4D4×D3712yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—1482no—
380C2×C4—1482no—
381C2×C4C2×C22⋊D3711yescharacteristic
382C2×C4C2×C22⋊D3711yescharacteristic
383C2×C4C2×C22⋊D3711yescharacteristic
384C2×C4C2×C22⋊D3711yescharacteristic
385C2×C4C23×D3711yescharacteristic
386C8—372no—
387C8—741no—
388C8—741no—
389C8—741no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—1481no—
404C22—1481no—
405C22—1481no—
406C22—1481no—
407C22—1481no—
408C22—1481no—
409C22C22×C22⋊D3711yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—742no—
417C4—1481no—
418C4C2×D4×D3711yescharacteristic
419C4#1192458111yescharacteristic
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—2961no—
425C2—2961no—
426C2D4×C22⋊D3711yescharacteristic
427C2#1455833111yescharacteristic
428C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#546C2
socleC22×C37C22×D4
hypercenter#546D37
hypocenterC37#3268
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C2×#11924556C2semidirect
3. #14558204C2semidirect
4. #14557923C2semidirect
5. #14557781C2semidirect
6. #14557767C2semidirect
7. #14557752C2semidirect
8. #14557728C2semidirect
9. #14557693C2semidirect
10. #14557678C2semidirect
11. #14557676C2semidirect
12. #14557667C2semidirect
13. #14557633C2semidirect
14. #14557605C2semidirect
15. C37×#546C2semidirect
17. C2×#10596962C22semidirect
20. C2×#10596942C22semidirect
23. C2×#10596941C22semidirect
24. C2×#10596941C22semidirect
30. C22×#64436C22semidirect
31. #11924533C22semidirect
34. #11924510C22semidirect
37. C4×Dic74C22semidirect
39. #11924469C22semidirect
40. C4⋊#64436C22semidirect
41. #11924460C22semidirect
42. #11924459C22semidirect
45. #11924456C22semidirect
46. #11924456C22semidirect
48. C22⋊#64436C22semidirect
49. #11924447C22semidirect
107. #10596940D4semidirect
218. #546D37semidirect
230. C37#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245562
#145582042
#145579232
#145577812
#145577672
#145577522
#145577282
#145576932
#145576782
#145576762
#145576672
#145576332
#145576052
C37×#5462
#326837