Finite Group Databasebeta

← #18006574

Subgroups — #18006574

Order 4736.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558229C211yesmaximal, characteristic, complemented
2#14558188C211yesmaximal, characteristic, complemented
3#14557902C211yesmaximal, characteristic, complemented
4#14557875C211yesmaximal, characteristic, complemented
5#14557864C211yesmaximal, characteristic, complemented
6#14557834C211yesmaximal, characteristic, complemented
7#14557779C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557739C211yesmaximal, characteristic, complemented
10#14557680C211yesmaximal, characteristic, complemented
11#14557680C211yesmaximal, characteristic, complemented
12#14557646C211yesmaximal, characteristic, complemented
13#14557535C211yesmaximal, characteristic, complemented
14#14557530C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×D296C2211yescharacteristic
21#11924536C2211yescharacteristic
22#11924531—21no—
23#11924528C2211yescharacteristic
24#11924518—21no—
25#11924518—21no—
26#11924518—21no—
27#11924515C2211yescharacteristic
28#11924515C2211yescharacteristic
29#11924510C2211yescharacteristic
30#11924510C2211yescharacteristic
31#11924508—21no—
32#11924507—21no—
33C4×D148C2211yescharacteristic
34C4×D148C2211yescharacteristic
35#11924496—21no—
36#11924495C2211yescharacteristic
37C2×C4⋊Dic37C2211yescharacteristic
38C4⋊C4×D37—21no—
39#11924470C2211yescharacteristic
40#11924468C2211yescharacteristic
41#11924468C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924461C2211yescharacteristic
46#11924461C2211yescharacteristic
47#11924461C2211yescharacteristic
48#11924458C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924458C2211yescharacteristic
52C2×M16×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54C4×D4×C37C2211yescharacteristic
55C4⋊C8×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57C22⋊C8×C37C2211yescharacteristic
58#97×C37C2211yescharacteristic
59C2×D4×C37D411yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C2×C22⋊D37—21no—
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C22×Dic37—21no—
67#10596962—22no—
68#10596962—22no—
69#10596962—41no—
70#10596962—41no—
71C2×D148C2311yescharacteristic
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×Dic74C2311yescharacteristic
78C2×Dic74C2311yescharacteristic
79M16×C37—41no—
80C2×C8×C37—41no—
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C2×C8×C37C2311yescharacteristic
85C4⋊C4×C37D411yescharacteristic
86C22⋊C4×C37D411yescharacteristic
87C22⋊C4×C37D411yescharacteristic
88C42×C37C2311yescharacteristic
89C22⋊Dic37—21no—
90C22⋊Dic37—21no—
91C22⋊Dic37—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106#10596936—21no—
107C4×Dic37—21no—
108D296—22no—
109#10596930—41no—
110#10596930—41no—
111C23×C37C2×D411yescharacteristic
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37—21no—
115D4×C37—41no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37—42no—
126C22⋊D37—42no—
127C22⋊D37—42no—
128C22⋊D37—81no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—81no—
136D148—21no—
137D148—21no—
138D148—21no—
139D148#4112yes—
140C4×D37—42no—
141C4×D37—42no—
142C4×D37—42no—
143C4×D37—81no—
144Dic74—21no—
145Dic74—21no—
146Dic74—21no—
147Dic74—21no—
148C8×C37—21no—
149C8×C37—21no—
150C8×C37—21no—
151C8×C37—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37C22×D411yescharacteristic
159C2×D37—22no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37C2×#4111yescharacteristic
170C4×C37H(5,𝔽2)11yescharacteristic
171Dic37—41no—
172Dic37—41no—
173Dic37—41no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3307—371nomaximal, Sylow
178C2×C37—41no—
179C2×C37—41no—
180C2×C37#54611yescharacteristic
181C2×C37#57511yescharacteristic
182C2×C37#57711yescharacteristic
183D37—42no—
184D37—81no—
185#553—371no—
186#547—371no—
187#491—371no—
188#485—371no—
189#483—371no—
190#478—371no—
191#468—371no—
192#465—371no—
193#461—371no—
194#449—371no—
195#449—371no—
196#442—371no—
197#435D3711yescharacteristic, complemented
198#417—371no—
199#416—371no—
200C37#330711yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C2×#41—371no—
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C2×M16C2×D3711yescharacteristic
207C22×C8C2×D3711yescharacteristic
208C4⋊Q8—371no—
209#126—741no—
210#125—371no—
211#123—741no—
212#123—741no—
213#123—741no—
214C22⋊Q8—371no—
215C22⋊Q8—371no—
216#121—371no—
217#121—371no—
218#121—741no—
219#121—741no—
220C4×D4—371no—
221C4×D4—371no—
222C4×D4—741no—
223C4×D4C2×D3711yescharacteristic
224#117—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—741no—
227#107—371no—
228#106—371no—
229#106—371no—
230C4⋊C8C2×D3711yescharacteristic
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#103—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241C22⋊C8C2×D3711yescharacteristic
242C22⋊C8C2×D3711yescharacteristic
243#97C2×D3711yescharacteristic
244#41—742no—
245#41—742no—
246#41—1481no—
247#41—1481no—
248C2×Q8—371no—
249C2×Q8—371no—
250C2×D4—371no—
251C2×D4—371no—
252C2×D4—741no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4D14811yescharacteristic
257C22×C4—741no—
258C22×C4—741no—
259C22×C4—741no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263C22×C4C22×D3711yescharacteristic
264SD16—1481no—
265SD16—1481no—
266D8—742no—
267M16—41no—
268C2×C8—41no—
269C2×C8C22×D3711yescharacteristic
270C2×C8C22×D3711yescharacteristic
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
273C4⋊C4—371no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4—741no—
283C4⋊C4—741no—
284C4⋊C4D14811yescharacteristic
285C22⋊C4—741no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4D14811yescharacteristic
293C22⋊C4D14811yescharacteristic
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—741no—
297C23—741no—
298C23C2×D14811yescharacteristic
299C23C2×D14811yescharacteristic
300Q8—741no—
301Q8—741no—
302Q8—741no—
303Q8—741no—
304D4—41no—
305D4—372no—
306D4—2961no—
307D4—741no—
308D4—741no—
309D4—741no—
310D4—1482no—
311D4—1482no—
312D4—1482no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—2961no—
318C2×C4—2961no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—1482no—
326C2×C4—1482no—
327C2×C4—1482no—
328C2×C4C2×D14811yescharacteristic
329C2×C4C2×D14811yescharacteristic
330C2×C4C2×D14811yescharacteristic
331C2×C4C2×D14811yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—742no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22—1481no—
348C22—1481no—
349C22C22×D14811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—1481no—
355C4—1481no—
356C4—1481no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4#41×D3711yescharacteristic
361C4#1192458111yescharacteristic
362C2—41no—
363C2—41no—
364C2—2961no—
365C2—1482no—
366C2#1455817811yescharacteristic
367C2#1455833311yescharacteristic
368C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
hypercenter#435D37
hypocenterC37#3307
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14558229C2semidirect
2. #14558188C2semidirect
3. #14557902C2semidirect
4. #14557875C2semidirect
5. #14557864C2semidirect
6. #14557834C2semidirect
7. #14557779C2semidirect
8. #14557762C2semidirect
9. #14557739C2semidirect
10. #14557680C2semidirect
11. #14557680C2semidirect
12. #14557646C2semidirect
13. #14557535C2semidirect
14. #14557530C2semidirect
15. C37×#435C2semidirect
197. #435D37semidirect
200. C37#3307semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145581882
#145579022
#145578752
#145578642
#145578342
#145577792
#145577622
#145577392
#145576802
#145576462
#145575352
#145575302
C37×#4352
#330737