Finite Group Databasebeta

← #18004774

Subgroups — #18004774

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#14558007C211yesmaximal, characteristic, complemented
2#14557871C211yesmaximal, characteristic, complemented
3#14557854C211yesmaximal, characteristic, complemented
4#14557820C211yesmaximal, characteristic, complemented
5#14557810C211yesmaximal, characteristic, complemented
6#14557745C211yesmaximal, characteristic, complemented
7#14557745C211yesmaximal, characteristic, complemented
8#14557683C211yesmaximal, characteristic, complemented
9#14557666C211yesmaximal, characteristic
10#14557643C211yesmaximal, characteristic, complemented
11#14557631C211yesmaximal, characteristic, complemented
12C4×#10596941C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557594C211yesmaximal, characteristic, complemented
15C37×#542C211yesmaximal, characteristic, complemented
16C22×D148C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C4×D148C2211yescharacteristic
22C4×D148C2211yescharacteristic
23C4×D148C2211yescharacteristic
24C4×D148C2211yescharacteristic
25#11924498—21no—
26#11924498—21no—
27#11924495C2211yescharacteristic
28C22⋊C4×D37—21no—
29C22⋊C4×D37—21no—
30#11924469C2211yescharacteristic, complemented
31#11924469C2211yescharacteristic, complemented
32#11924467C2211yescharacteristic, complemented
33#11924467C2211yescharacteristic, complemented
34C4⋊#64436C2211yescharacteristic, complemented
35C4⋊#64436C2211yescharacteristic, complemented
36#11924460C2211yescharacteristic, complemented
37#11924460C2211yescharacteristic, complemented
38#11924457C2211yescharacteristic, complemented
39#11924457C2211yescharacteristic, complemented
40#11924456C2211yescharacteristic
41#11924456C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44C22⋊#64436C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46#11924447C2211yescharacteristic, complemented
47C4×#64436C2211yescharacteristic, complemented
48C4⋊Q8×C37C2211yescharacteristic, complemented
49#126×C37—21no—
50#124×C37—21no—
51#124×C37C2211yescharacteristic, complemented
52#123×C37—21no—
53C22⋊Q8×C37—21no—
54C22⋊Q8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56C4×Q8×C37C2211yescharacteristic, complemented
57C4×D4×C37C2211yescharacteristic, complemented
58#117×C37C2211yescharacteristic
59C23×D37—21no—
60C2×Q8×C37—21no—
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37C2311yescharacteristic
66C2×D148—21no—
67C2×D148—22no—
68C2×D148—22no—
69C2×D148C2311yescharacteristic
70C2×D148C2311yescharacteristic
71C2×C4×D37—21no—
72C2×C4×D37—21no—
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C4⋊C4×C37—21no—
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37D411yescharacteristic
79C4⋊C4×C37D411yescharacteristic
80C4⋊C4×C37C2311yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C22⋊C4×C37—21no—
83C22⋊C4×C37—21no—
84C22⋊C4×C37—21no—
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C22⋊C4×C37D411yescharacteristic
88C22⋊C4×C37D411yescharacteristic
89C42×C37—21no—
90C42×C37C2311yescharacteristic
91C42×C37C2311yescharacteristic
92C22⋊Dic37—21no—
93#10596941—22no—
94#10596941—22no—
95#10596939—22no—
96#10596939—22no—
97#10596938—21no—
98#10596938—21no—
99#10596938—21no—
100#10596938—21no—
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—21no—
111C22×D37—21no—
112C22×D37—24no—
113C22×D37—81no—
114C22×D37—81no—
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—81no—
118D4×C37—21no—
119D4×C37—21no—
120D4×C37—81no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—81no—
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2×D411yescharacteristic
132C2×C4×C37C2411yescharacteristic
133C2×Dic37—21no—
134C2×Dic37—21no—
135D148—24no—
136D148—21no—
137D148—21no—
138D148#4112yes—
139D148#4112yes—
140C4×D37—81no—
141C4×D37—81no—
142C4×D37—81no—
143C4×D37—81no—
144#64436—21no—
145#64436—21no—
146#64436—21no—
147#64436—21no—
148C22×C37—21no—
149C22×C37—21no—
150C22×C37—21no—
151C22×C37—41no—
152C22×C37—41no—
153C22×C37—41no—
154C22×C37C22×D411yescharacteristic
155C2×D37—22no—
156C2×D37—22no—
157C2×D37—41no—
158C2×D37—41no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—84no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37C2×#4111yescharacteristic
171C4×C37C2×#4111yescharacteristic
172Dic37—41no—
173Dic37—41no—
174#3118—371nomaximal, Sylow
175C2×C37—41no—
176C2×C37—81no—
177C2×C37#52511yescharacteristic
178C2×C37#57611yescharacteristic
179C2×C37#57711yescharacteristic
180D37—42no—
181D37—42no—
182#542D3711yescharacteristic, complemented
183#518—371no—
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×D4—371no—
199C2×SD16—371no—
200C2×SD16—371no—
201C2×D8—371no—
202C2×D8—371no—
203C4⋊Q8C2×D3711yescharacteristic, complemented
204#126—21no—
205#124—21no—
206#124C2×D3711yescharacteristic, complemented
207#123—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×D3711yescharacteristic
210#121C2×D3711yescharacteristic
211C4×Q8C2×D3711yescharacteristic, complemented
212C4×D4—371no—
213C4×D4—371no—
214C4×D4—371no—
215C4×D4—371no—
216C4×D4—741no—
217C4×D4—741no—
218C4×D4C2×D3711yescharacteristic, complemented
219#117—371no—
220#117C2×D3711yescharacteristic
221C2×C22⋊C4—741no—
222C2×C22⋊C4—741no—
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—741no—
242C2×Q8—21no—
243C2×Q8C22×D3711yescharacteristic
244C2×D4—21no—
245C2×D4—371no—
246C2×D4—371no—
247C2×D4—742no—
248C2×D4—742no—
249C2×D4—741no—
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—741no—
253C22×C4—741no—
254C22×C4—741no—
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—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—371no—
269C4⋊C4—371no—
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—21no—
291C23—2961no—
292C23—2961no—
293C23—744no—
294C23—741no—
295C23—741no—
296C23C2×C22⋊D3711yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—372no—
304D4—372no—
305D4—744no—
306D4—741no—
307D4—741no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—2961no—
315C2×C4—2961no—
316C2×C4—2961no—
317C2×C4—2961no—
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—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—2964no—
337C22—742no—
338C22—742no—
339C22—1481no—
340C22—1481no—
341C22—1481no—
342C22—1481no—
343C22C22×C22⋊D3711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—1481no—
353C4—1481no—
354C4#41×D3711yescharacteristic
355C4#41×D3711yescharacteristic
356C2—41no—
357C2—81no—
358C2—1482no—
359C2—1482no—
360C2#1455804011yescharacteristic
361C2#1455833611yescharacteristic
362C2#1455834111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#542C2
socleC22×C37C22×D4
prime radical#14557666C2
hypercenter#542D37
hypocenterC37#3118
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #14558007C2semidirect
2. #14557871C2semidirect
3. #14557854C2semidirect
4. #14557820C2semidirect
5. #14557810C2semidirect
6. #14557745C2semidirect
7. #14557745C2semidirect
8. #14557683C2semidirect
10. #14557643C2semidirect
11. #14557631C2semidirect
12. C4×#10596941C2semidirect
13. C4×#10596939C2semidirect
14. #14557594C2semidirect
15. C37×#542C2semidirect
30. #11924469C22semidirect
31. #11924469C22semidirect
32. #11924467C22semidirect
33. #11924467C22semidirect
34. C4⋊#64436C22semidirect
35. C4⋊#64436C22semidirect
36. #11924460C22semidirect
37. #11924460C22semidirect
38. #11924457C22semidirect
39. #11924457C22semidirect
46. #11924447C22semidirect
47. C4×#64436C22semidirect
48. C4⋊Q8×C37C22semidirect
51. #124×C37C22semidirect
56. C4×Q8×C37C22semidirect
57. C4×D4×C37C22semidirect
182. #542D37semidirect
197. C37#3118semidirect
203. C4⋊Q8C2×D37semidirect
206. #124C2×D37semidirect
211. C4×Q8C2×D37semidirect
218. C4×D4C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580072
#145578712
#145578542
#145578202
#145578102
#145577452
#145576832
#145576662
#145576432
#145576312
C4×#105969412
C4×#105969392
#145575942
C37×#5422
#311837