Finite Group Databasebeta

← #18004780

Subgroups — #18004780

Order 4736.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558154C211yesmaximal, characteristic, complemented
2#14557874C211yesmaximal, characteristic, complemented
3#14557857C211yesmaximal, characteristic, complemented
4#14557823C211yesmaximal, characteristic, complemented
5#14557813C211yesmaximal, characteristic, complemented
6#14557748C211yesmaximal, characteristic, complemented
7#14557748C211yesmaximal, characteristic, complemented
8#14557684C211yesmaximal, characteristic, complemented
9#14557667C211yesmaximal, characteristic
10#14557643C211yesmaximal, characteristic, complemented
11#14557633C211yesmaximal, characteristic, complemented
12C4×#10596940C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557594C211yesmaximal, characteristic, complemented
15C37×#518C211yesmaximal, characteristic, complemented
16C2×#10596940C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20#11924536C2211yescharacteristic, complemented
21#11924531—21no—
22#11924524C2211yescharacteristic, complemented
23#11924522—21no—
24#11924518—21no—
25#11924515C2211yescharacteristic
26#11924514—21no—
27#11924510C2211yescharacteristic
28C4×Dic74C2211yescharacteristic, complemented
29C4×D148C2211yescharacteristic, complemented
30#11924469C2211yescharacteristic, complemented
31#11924469C2211yescharacteristic, complemented
32#11924467C2211yescharacteristic, complemented
33#11924467C2211yescharacteristic, complemented
34C4⋊#64436C2211yescharacteristic, complemented
35C4⋊#64436C2211yescharacteristic, complemented
36#11924459C2211yescharacteristic, complemented
37#11924459C2211yescharacteristic, complemented
38#11924457C2211yescharacteristic
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924456C2211yescharacteristic, complemented
43#11924456C2211yescharacteristic, complemented
44C22⋊#64436C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46#11924447C2211yescharacteristic, complemented
47C4×#64436C2211yescharacteristic, complemented
48C22×D4×C37C2211yescharacteristic
49C4×D4×C37—21no—
50C4×D4×C37—21no—
51C4×D4×C37C2211yescharacteristic
52C4×D4×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55#117×C37C2211yescharacteristic
56#117×C37C2211yescharacteristic
57C2×C22⋊C4×C37—21no—
58C2×C22⋊C4×C37—21no—
59C24×C37—21no—
60C2×D4×C37—22no—
61C2×D4×C37—22no—
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C22×C4×C37—21no—
68C22×C4×C37—21no—
69C22×C4×C37C2311yescharacteristic
70C2×C22⋊D37—21no—
71C2×D148C2311yescharacteristic
72C2×C4×D37—21no—
73C2×Dic74—21no—
74C2×Dic74C2311yescharacteristic
75C4⋊C4×C37D411yescharacteristic
76C4⋊C4×C37D411yescharacteristic
77C4⋊C4×C37C2311yescharacteristic
78C4⋊C4×C37C2311yescharacteristic
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37—21no—
83C22⋊C4×C37—21no—
84C22⋊C4×C37D411yescharacteristic
85C22⋊C4×C37D411yescharacteristic
86C42×C37—21no—
87C42×C37C2311yescharacteristic
88C42×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90#10596940—22no—
91#10596940—22no—
92#10596939—22no—
93#10596939—22no—
94#10596938—21no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936—21no—
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—24no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37—81no—
112C23×C37—81no—
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115D4×C37—24no—
116D4×C37—21no—
117D4×C37—21no—
118D4×C37#4112yes—
119D4×C37#4112yes—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—81no—
125C2×C4×C37—81no—
126C2×C4×C37—81no—
127C2×C4×C37—81no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2411yescharacteristic
134C22⋊D37—81no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138D148—21no—
139D148—21no—
140C4×D37—81no—
141Dic74—21no—
142Dic74—21no—
143Dic74—81no—
144#64436—21no—
145#64436—21no—
146#64436—21no—
147#64436—21no—
148C22×C37—21no—
149C22×C37—22no—
150C22×C37—22no—
151C22×C37—21no—
152C22×C37—21no—
153C22×C37—41no—
154C22×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—84no—
158C22×C37C22×D411yescharacteristic
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37C2×#4111yescharacteristic
170C4×C37C2×#4111yescharacteristic
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174#3118—371nomaximal, Sylow
175C2×C37—41no—
176C2×C37—42no—
177C2×C37—42no—
178C2×C37#52511yescharacteristic
179C2×C37#57611yescharacteristic
180C2×C37#57711yescharacteristic
181D37—81no—
182#542—371no—
183#518D3711yescharacteristic, complemented
184#485—371no—
185#482—371no—
186#476—371no—
187#474—371no—
188#463—371no—
189#463—371no—
190#450—371no—
191#447—371no—
192#442—371no—
193#440—371no—
194C4×SD16—371no—
195C4×D8—371no—
196#433—371no—
197C37#311811yescharacteristic, complemented, Sylow
198C22×D4C2×D3711yescharacteristic
199C2×SD16—371no—
200C2×SD16—371no—
201C2×D8—371no—
202C2×D8—371no—
203C4⋊Q8—371no—
204#126—741no—
205#124—371no—
206#124—741no—
207#123—741no—
208C22⋊Q8—371no—
209C22⋊Q8—741no—
210#121—371no—
211C4×Q8—371no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—371no—
215C4×D4C2×D3711yescharacteristic
216C4×D4C2×D3711yescharacteristic
217C4×D4C2×D3711yescharacteristic
218C4×D4C2×D3711yescharacteristic
219#117C2×D3711yescharacteristic
220#117C2×D3711yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—371no—
224#107—371no—
225#106—371no—
226#106—371no—
227C4⋊C8—371no—
228C4⋊C8—371no—
229#103—371no—
230#103—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102—371no—
236#102—371no—
237C22⋊C8—371no—
238C22⋊C8—371no—
239#97—371no—
240C4×C8—371no—
241C24—21no—
242C2×Q8—371no—
243C2×Q8—741no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—371no—
248C2×D4—741no—
249C2×D4C22×D3711yescharacteristic
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—741no—
256C22×C4C22×D3711yescharacteristic
257SD16—742no—
258SD16—742no—
259D8—742no—
260D8—742no—
261C2×C8—371no—
262C2×C8—371no—
263C2×C8—371no—
264C2×C8—371no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4—741no—
270C4⋊C4C22⋊D3711yescharacteristic
271C4⋊C4C22⋊D3711yescharacteristic
272C4⋊C4C22×D3711yescharacteristic
273C4⋊C4C22×D3711yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4C22⋊D3711yescharacteristic
285C22⋊C4C22⋊D3711yescharacteristic
286C42—21no—
287C42—741no—
288C42C22×D3711yescharacteristic
289C42C22×D3711yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—741no—
296C23C2×C22⋊D3711yescharacteristic
297Q8—2961no—
298Q8—741no—
299Q8—741no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—2961no—
304D4—741no—
305D4—741no—
306D4#1059696212yes—
307D4#1059696212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—2961no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4C2×C22⋊D3711yescharacteristic
321C2×C4C2×C22⋊D3711yescharacteristic
322C2×C4C2×C22⋊D3711yescharacteristic
323C2×C4C2×C22⋊D3711yescharacteristic
324C2×C4C2×C22⋊D3711yescharacteristic
325C2×C4C23×D3711yescharacteristic
326C8—741no—
327C8—741no—
328C8—741no—
329C8—741no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22C22×C22⋊D3711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—1481no—
352C4—1481no—
353C4—1481no—
354C4C2×#1059696211yescharacteristic
355C4C2×#1059696211yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—2961no—
360C2#1455804411yescharacteristic
361C2#1455833611yescharacteristic
362C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#518C2
socleC22×C37C22×D4
prime radical#14557667C2
hypercenter#518D37
hypocenterC37#3118
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14557874C2semidirect
3. #14557857C2semidirect
4. #14557823C2semidirect
5. #14557813C2semidirect
6. #14557748C2semidirect
7. #14557748C2semidirect
8. #14557684C2semidirect
10. #14557643C2semidirect
11. #14557633C2semidirect
12. C4×#10596940C2semidirect
13. C4×#10596939C2semidirect
14. #14557594C2semidirect
15. C37×#518C2semidirect
20. #11924536C22semidirect
22. #11924524C22semidirect
28. C4×Dic74C22semidirect
29. C4×D148C22semidirect
30. #11924469C22semidirect
31. #11924469C22semidirect
32. #11924467C22semidirect
33. #11924467C22semidirect
34. C4⋊#64436C22semidirect
35. C4⋊#64436C22semidirect
36. #11924459C22semidirect
37. #11924459C22semidirect
42. #11924456C22semidirect
43. #11924456C22semidirect
46. #11924447C22semidirect
47. C4×#64436C22semidirect
183. #518D37semidirect
197. C37#3118semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145578742
#145578572
#145578232
#145578132
#145577482
#145576842
#145576672
#145576432
#145576332
C4×#105969402
C4×#105969392
#145575942
C37×#5182
#311837