Finite Group Databasebeta

← #18004130

Subgroups — #18004130

Order 4736.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 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#14558096C211yesmaximal, characteristic, complemented
4#14558012C211yesmaximal, characteristic, complemented
5#14557756C211yesmaximal, characteristic, complemented
6#14557754C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557746C211yesmaximal, characteristic, complemented
9#14557732C211yesmaximal, characteristic, complemented
10#14557730C211yesmaximal, characteristic, complemented
11#14557726C211yesmaximal, characteristic, complemented
12#14557558C211yesmaximal, characteristic, complemented
13#14557531C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic, complemented
15C37×#459C211yesmaximal, characteristic, complemented
16C2×#10596964C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19#11924560—24no—
20#11924555—24no—
21C2×Dic148C2211yescharacteristic, complemented
22C2×#10596930C2211yescharacteristic
23C2×#10596940C2211yescharacteristic
24C2×#10596940C2211yescharacteristic, complemented
25C2×#10596940C2211yescharacteristic, complemented
26C2×#10596939C2211yescharacteristic
27C2×#10596929C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic
29#11924532C2211yescharacteristic
30#11924524C2211yescharacteristic
31#11924523C2211yescharacteristic
32#11924508—21no—
33#11924508—21no—
34#11924504—21no—
35#11924504—21no—
36C4×Dic74C2211yescharacteristic, complemented
37#11924501C2211yescharacteristic, complemented
38D4×Dic37C2211yescharacteristic, complemented
39C4×C22⋊D37—21no—
40#11924496—21no—
41#11924493C2211yescharacteristic
42#11924492—21no—
43C2×#10596936—21no—
44C4⋊C4×D37C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic, complemented
46#11924465C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924459C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic
51#11924457C2211yescharacteristic
52#11924457C2211yescharacteristic, complemented
53#11924456C2211yescharacteristic
54C2×D8×C37C2211yescharacteristic
55C2×D8×C37C2211yescharacteristic, complemented
56#127×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic, complemented
58C4⋊C8×C37C2211yescharacteristic, complemented
59#102×C37C2211yescharacteristic
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—
73C22×Dic37—21no—
74C22×Dic37—21no—
75C22×Dic37—21no—
76#10596964—22no—
77#10596964—22no—
78#10596964—22no—
79#10596964D414yescomplemented
80D4×D37—22no—
81D4×D37—22no—
82C2×D148C2311yescharacteristic
83C2×C4×D37—21no—
84C2×C4×D37C2311yescharacteristic
85C2×Dic74C2311yescharacteristic
86C2×Dic74C2311yescharacteristic
87D8×C37—22no—
88D8×C37—22no—
89C2×C8×C37C2311yescharacteristic
90C2×C8×C37C2311yescharacteristic
91C4⋊C4×C37C2311yescharacteristic
92C22⋊C4×C37—21no—
93C42×C37C2311yescharacteristic
94C22⋊Dic37—21no—
95C22⋊Dic37—21no—
96C22⋊Dic37—21no—
97#10596940—22no—
98#10596940—22no—
99#10596940—22no—
100#10596939—22no—
101#10596938—21no—
102#10596938—21no—
103#10596938D411yescharacteristic
104#10596938D411yescharacteristic
105C4⋊Dic37C2311yescharacteristic
106#10596936—21no—
107#10596936—21no—
108#10596936—21no—
109#10596936D411yescharacteristic
110#10596936D411yescharacteristic
111C4×Dic37—21no—
112C4×Dic37—21no—
113C4×Dic37C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116Dic148—22no—
117#10596930—22no—
118#10596929—22no—
119C8×D37—22no—
120C23×C37—21no—
121C23×C37—21no—
122C23×C37—21no—
123C22×D37—21no—
124C22×D37—42no—
125C22×D37—81no—
126C22×D37—81no—
127C22×D37C2×D411yescharacteristic
128D4×C37—21no—
129D4×C37—21no—
130D4×C37—21no—
131D4×C37—21no—
132D4×C37—21no—
133D4×C37—81no—
134D4×C37—81no—
135D4×C37C2×D412yes—
136C2×C4×C37—21no—
137C2×C4×C37—81no—
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2411yescharacteristic
141C22⋊D37—24no—
142C22⋊D37—42no—
143C22⋊D37—42no—
144C22⋊D37—81no—
145C22⋊D37—81no—
146C2×Dic37—21no—
147C2×Dic37—24no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37—42no—
151C2×Dic37—81no—
152C2×Dic37C2×D411yescharacteristic
153C2×Dic37C2×D411yescharacteristic
154C2×Dic37C2×D411yescharacteristic
155D148—21no—
156D148—21no—
157C4×D37—81no—
158C4×D37C2×D412yes—
159C4×D37#4112yes—
160Dic74—21no—
161Dic74—21no—
162Dic74—21no—
163Dic74C2×D412yes—
164C8×C37—21no—
165C8×C37—21no—
166#64436—21no—
167#64436—21no—
168C22×C37—22no—
169C22×C37—41no—
170C22×C37—41no—
171C22×C37—41no—
172C22×C37—41no—
173C22×C37—41no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37C22×D411yescharacteristic
178C2×D37—21no—
179C2×D37—21no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—84no—
184C2×D37#12112yes—
185C4×C37—21no—
186C4×C37—21no—
187C4×C37—41no—
188C4×C37C22×D411yescharacteristic
189C4×C37C2×#4111yescharacteristic
190Dic37—22no—
191Dic37—21no—
192Dic37—21no—
193Dic37—41no—
194Dic37—41no—
195Dic37#12112yes—
196#3045—371nomaximal, Sylow
197C2×C37—42no—
198C2×C37—81no—
199C2×C37—81no—
200C2×C37C2×#12111yescharacteristic
201C2×C37#57611yescharacteristic
202C2×C37#57711yescharacteristic
203D37—22no—
204D37—81no—
205C2×AGL(1,ℤ/8)—371no—
206C2×#135—371no—
207#535—371no—
208#520—371no—
209#464—371no—
210#464—371no—
211#463—371no—
212#463—371no—
213#460—371no—
214#460—371no—
215#459—371no—
216#459D3711yescharacteristic, complemented
217#424—371no—
218#417—371no—
219C2×#102—371no—
220C37#304511yescharacteristic, complemented, Sylow
221C2×#41—371no—
222C2×#41—371no—
223C22×D4—371no—
224AGL(1,ℤ/8)—744no—
225#135—744no—
226C2×Q16—371no—
227C2×SD16—371no—
228C2×SD16—371no—
229C2×SD16—371no—
230C2×SD16—371no—
231C2×D8—371no—
232C2×D8C2×D3711yescharacteristic
233C2×D8C2×D3711yescharacteristic, complemented
234C2×M16—371no—
235C22×C8—371no—
236#127—371no—
237#127C2×D3711yescharacteristic
238#124—371no—
239#124—371no—
240#121—741no—
241#121—741no—
242#120—741no—
243#120—741no—
244C4×Q8—371no—
245C4×Q8—371no—
246C4×D4—371no—
247C4×D4—741no—
248C4×D4—741no—
249C4×D4C2×D3711yescharacteristic, complemented
250#117—371no—
251#117—741no—
252C2×C4⋊C4—371no—
253C2×C4⋊C4—741no—
254C4⋊C8—371no—
255C4⋊C8—371no—
256C4⋊C8—371no—
257C4⋊C8C2×D3711yescharacteristic, complemented
258#103—371no—
259#103—371no—
260#102—371no—
261#102—371no—
262#102—371no—
263#102—371no—
264#102C2×D3711yescharacteristic
265#102C2×D3711yescharacteristic, complemented
266C24—741no—
267#41—374no—
268#41—742no—
269#41—742no—
270#41—742no—
271C2×Q8—371no—
272C2×Q8—371no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—371no—
276C2×D4—742no—
277C2×D4—742no—
278C2×D4—741no—
279C2×D4—741no—
280C2×D4—741no—
281C2×D4—741no—
282C2×D4—741no—
283C2×D4C22×D3711yescharacteristic
284C2×D4C22×D3711yescharacteristic
285C2×D4C22×D3711yescharacteristic
286C22×C4—21no—
287C22×C4—371no—
288C22×C4—741no—
289C22×C4—741no—
290C22×C4—741no—
291C22×C4—741no—
292Q16—742no—
293SD16—742no—
294SD16—742no—
295SD16—742no—
296SD16—742no—
297D8—22no—
298D8—22no—
299D8—742no—
300M16—742no—
301C2×C8—371no—
302C2×C8—371no—
303C2×C8—742no—
304C2×C8C22×D3711yescharacteristic
305C2×C8C22×D3711yescharacteristic
306C4⋊C4—371no—
307C4⋊C4—371no—
308C4⋊C4—371no—
309C4⋊C4—741no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4C22×D3711yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—371no—
315C22⋊C4—371no—
316C22⋊C4—741no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C42—371no—
322C42—741no—
323C42—741no—
324C42C22×D3711yescharacteristic
325C23—21no—
326C23—21no—
327C23—21no—
328C23—371no—
329C23—2961no—
330C23—2961no—
331C23—741no—
332C23—1482no—
333Q8—372no—
334Q8—741no—
335Q8—741no—
336Q8—741no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—81no—
343D4—81no—
344D4—2961no—
345D4—2961no—
346D4—744no—
347D4—741no—
348D4—741no—
349D4—1482no—
350D4—1482no—
351D4D4×D3712yes—
352C2×C4—21no—
353C2×C4—81no—
354C2×C4—371no—
355C2×C4—372no—
356C2×C4—372no—
357C2×C4—371no—
358C2×C4—371no—
359C2×C4—2961no—
360C2×C4—2961no—
361C2×C4—744no—
362C2×C4—741no—
363C2×C4—741no—
364C2×C4—741no—
365C2×C4—1482no—
366C2×C4D4×D3711yescharacteristic
367C2×C4D4×D3711yescharacteristic
368C2×C4C23×D3711yescharacteristic
369C8—21no—
370C8—21no—
371C8—741no—
372C8—741no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—372no—
383C22—2964no—
384C22—741no—
385C22—741no—
386C22—1481no—
387C22—1481no—
388C22—1481no—
389C22C2×D4×D3711yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—372no—
394C4—742no—
395C4—741no—
396C4—741no—
397C4—1481no—
398C4—1481no—
399C4C2×D4×D3711yescharacteristic
400C4#41×D3711yescharacteristic
401C2—42no—
402C2—81no—
403C2—81no—
404C2—2961no—
405C2—742no—
406C2#121×D3711yescharacteristic
407C2#1455833411yescharacteristic
408C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#459C2
socleC22×C37C22×D4
hypercenter#459D37
hypocenterC37#3045
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. #14558096C2semidirect
4. #14558012C2semidirect
5. #14557756C2semidirect
6. #14557754C2semidirect
7. #14557748C2semidirect
8. #14557746C2semidirect
9. #14557732C2semidirect
10. #14557730C2semidirect
11. #14557726C2semidirect
12. #14557558C2semidirect
13. #14557531C2semidirect
14. #102×D37C2semidirect
15. C37×#459C2semidirect
21. C2×Dic148C22semidirect
24. C2×#10596940C22semidirect
25. C2×#10596940C22semidirect
36. C4×Dic74C22semidirect
37. #11924501C22semidirect
38. D4×Dic37C22semidirect
45. C4⋊#64436C22semidirect
46. #11924465C22semidirect
47. #11924465C22semidirect
48. #11924461C22semidirect
49. #11924459C22semidirect
52. #11924457C22semidirect
55. C2×D8×C37C22semidirect
57. C4×D4×C37C22semidirect
58. C4⋊C8×C37C22semidirect
60. #102×C37C22semidirect
79. #10596964D4semidirect
216. #459D37semidirect
220. C37#3045semidirect
233. C2×D8C2×D37semidirect
249. C4×D4C2×D37semidirect
257. C4⋊C8C2×D37semidirect
265. #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
#145580962
#145580122
#145577562
#145577542
#145577482
#145577462
#145577322
#145577302
#145577262
#145575582
#145575312
#102×D372
C37×#4592
#304537