Finite Group Databasebeta

← #18004789

Subgroups — #18004789

Order 4736.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558013C211yesmaximal, characteristic, complemented
2#14557849C211yesmaximal, characteristic, complemented
3#14557844C211yesmaximal, characteristic, complemented
4#14557837C211yesmaximal, characteristic, complemented
5#14557830C211yesmaximal, characteristic, complemented
6#14557730C211yesmaximal, characteristic, complemented
7#14557725C211yesmaximal, characteristic, complemented
8#14557676C211yesmaximal, characteristic, complemented
9#14557676C211yesmaximal, characteristic, complemented
10#14557643C211yesmaximal, characteristic, complemented
11#14557633C211yesmaximal, characteristic, complemented
12C4×#10596940C211yesmaximal, characteristic, complemented
13C4×#10596939C211yesmaximal, characteristic, complemented
14#14557594C211yesmaximal, characteristic, complemented
15C37×#540C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596939C2211yescharacteristic
21C4×Dic74C2211yescharacteristic
22C4×Dic74C2211yescharacteristic
23C4×D148C2211yescharacteristic
24C4×D148C2211yescharacteristic
25#11924496—21no—
26#11924496—21no—
27#11924494—21no—
28C2×C4⋊Dic37C2211yescharacteristic
29C4⋊C4×D37—21no—
30#11924469C2211yescharacteristic
31#11924469C2211yescharacteristic
32#11924467C2211yescharacteristic
33#11924467C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35C4⋊#64436C2211yescharacteristic
36#11924459C2211yescharacteristic
37#11924459C2211yescharacteristic
38#11924457C2211yescharacteristic
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924456C2211yescharacteristic
43#11924456C2211yescharacteristic
44C22⋊#64436C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46#11924447C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48#127×C37C2211yescharacteristic
49#125×C37C2211yescharacteristic
50#123×C37—21no—
51#123×C37—21no—
52#121×C37—21no—
53#121×C37—21no—
54#121×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58#117×C37C2211yescharacteristic
59C2×D4×C37—21no—
60C2×D4×C37—21no—
61C2×D4×C37—21no—
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C22×C4×C37—21no—
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C22×Dic37—21no—
70#10596962—22no—
71#10596962—22no—
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×Dic74C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37—21no—
79C4⋊C4×C37D411yescharacteristic
80C4⋊C4×C37D411yescharacteristic
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C22⋊C4×C37—21no—
84C22⋊C4×C37—21no—
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C22⋊C4×C37D411yescharacteristic
88C22⋊C4×C37D411yescharacteristic
89C42×C37C2311yescharacteristic
90C42×C37C2311yescharacteristic
91#10596940—22no—
92#10596940—22no—
93#10596939—22no—
94#10596939—22no—
95#10596938—21no—
96#10596938—21no—
97C4⋊Dic37—21no—
98C4⋊Dic37C2311yescharacteristic
99C4⋊Dic37C2311yescharacteristic
100#10596936—21no—
101#10596936—21no—
102C4×Dic37—21no—
103C4×Dic37—21no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37—21no—
110C23×C37C2×D411yescharacteristic
111C22×D37—21no—
112D4×C37—21no—
113D4×C37—21no—
114D4×C37—21no—
115D4×C37—21no—
116D4×C37—81no—
117D4×C37—81no—
118D4×C37—81no—
119D4×C37—81no—
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×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2×D411yescharacteristic
130C2×C4×C37C2×D411yescharacteristic
131C2×C4×C37C2411yescharacteristic
132C22⋊D37—24no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—81no—
137D148—21no—
138D148#4112yes—
139C4×D37—24no—
140C4×D37—81no—
141C4×D37—81no—
142Dic74—21no—
143Dic74#4112yes—
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×C37—41no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37C22×D411yescharacteristic
158C2×D37—22no—
159C2×D37—41no—
160C2×D37—41no—
161C4×C37—21no—
162C4×C37—21no—
163C4×C37—21no—
164C4×C37—21no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37C2×#4111yescharacteristic
169C4×C37C2×#4111yescharacteristic
170Dic37—22no—
171Dic37—41no—
172Dic37—41no—
173#3119—371nomaximal, Sylow
174C2×C37—41no—
175C2×C37—81no—
176C2×C37—81no—
177C2×C37#52511yescharacteristic
178C2×C37#57611yescharacteristic
179C2×C37#57711yescharacteristic
180D37—42no—
181#540D3711yescharacteristic, complemented
182#520—371no—
183#481—371no—
184#480—371no—
185#479—371no—
186#478—371no—
187#460—371no—
188#459—371no—
189#449—371no—
190#449—371no—
191#442—371no—
192#440—371no—
193C4×SD16—371no—
194C4×D8—371no—
195#433—371no—
196C37#311911yescharacteristic, complemented, Sylow
197C2×#41—371no—
198C2×SD16—371no—
199C2×SD16—371no—
200C2×D8—371no—
201C2×D8—371no—
202#127C2×D3711yescharacteristic
203#125C2×D3711yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D3711yescharacteristic
209#121C2×D3711yescharacteristic
210C4×Q8—371no—
211C4×Q8—371no—
212C4×D4—371no—
213C4×D4—371no—
214C4×D4—741no—
215C4×D4—741no—
216C4×D4C2×D3711yescharacteristic
217C4×D4C2×D3711yescharacteristic
218#117—741no—
219#117C2×D3711yescharacteristic
220C2×C4⋊C4—371no—
221C2×C4⋊C4—741no—
222#107—371no—
223#107—371no—
224#106—371no—
225#106—371no—
226C4⋊C8—371no—
227C4⋊C8—371no—
228#103—371no—
229#103—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102—371no—
234#102—371no—
235#102—371no—
236C22⋊C8—371no—
237C22⋊C8—371no—
238#97—371no—
239C4×C8—371no—
240#41—742no—
241#41—742no—
242C2×Q8—371no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—371no—
248C2×D4—741no—
249C2×D4C22×D3711yescharacteristic
250C2×D4C22×D3711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—741no—
254C22×C4—741no—
255C22×C4—741no—
256C22×C4—741no—
257C22×C4C22×D3711yescharacteristic
258SD16—742no—
259SD16—742no—
260D8—742no—
261D8—742no—
262C2×C8—371no—
263C2×C8—371no—
264C2×C8—371no—
265C2×C8—371no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—371no—
269C4⋊C4—371no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4C22⋊D3711yescharacteristic
274C4⋊C4C22⋊D3711yescharacteristic
275C4⋊C4C22×D3711yescharacteristic
276C4⋊C4C22×D3711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4C22⋊D3711yescharacteristic
284C22⋊C4C22⋊D3711yescharacteristic
285C42—741no—
286C42—741no—
287C42C22×D3711yescharacteristic
288C42C22×D3711yescharacteristic
289C23—21no—
290C23—21no—
291C23—741no—
292C23C2×C22⋊D3711yescharacteristic
293Q8—372no—
294Q8—741no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—372no—
304D4—744no—
305D4—741no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—2961no—
313C2×C4—2961no—
314C2×C4—2961no—
315C2×C4—744no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4C2×C22⋊D3711yescharacteristic
320C2×C4C2×C22⋊D3711yescharacteristic
321C2×C4C2×C22⋊D3711yescharacteristic
322C2×C4C2×C22⋊D3711yescharacteristic
323C2×C4C2×C22⋊D3711yescharacteristic
324C2×C4C23×D3711yescharacteristic
325C8—741no—
326C8—741no—
327C8—741no—
328C8—741no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—742no—
339C22—1481no—
340C22—1481no—
341C22C22×C22⋊D3711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—742no—
350C4—1481no—
351C4—1481no—
352C4#41×D3711yescharacteristic
353C4#41×D3711yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—1482no—
358C2#1455804011yescharacteristic
359C2#1455833611yescharacteristic
360C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#540C2
socleC22×C37C22×D4
hypercenter#540D37
hypocenterC37#3119
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14558013C2semidirect
2. #14557849C2semidirect
3. #14557844C2semidirect
4. #14557837C2semidirect
5. #14557830C2semidirect
6. #14557730C2semidirect
7. #14557725C2semidirect
8. #14557676C2semidirect
9. #14557676C2semidirect
10. #14557643C2semidirect
11. #14557633C2semidirect
12. C4×#10596940C2semidirect
13. C4×#10596939C2semidirect
14. #14557594C2semidirect
15. C37×#540C2semidirect
181. #540D37semidirect
196. C37#3119semidirect

Maximal subgroups

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

subgroupindex
#145580132
#145578492
#145578442
#145578372
#145578302
#145577302
#145577252
#145576762
#145576432
#145576332
C4×#105969402
C4×#105969392
#145575942
C37×#5402
#311937