Finite Group Databasebeta

← #18006494

Subgroups — #18006494

Order 4736.

398 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#14558231C211yesmaximal, characteristic, complemented
2#14558194C211yesmaximal, characteristic, complemented
3#14557889C211yesmaximal, characteristic, complemented
4#14557873C211yesmaximal, characteristic, complemented
5#14557851C211yesmaximal, characteristic, complemented
6#14557842C211yesmaximal, characteristic, complemented
7#14557769C211yesmaximal, characteristic, complemented
8#14557765C211yesmaximal, characteristic, complemented
9#14557751C211yesmaximal, characteristic, complemented
10#14557681C211yesmaximal, characteristic, complemented
11#14557672C211yesmaximal, characteristic, complemented
12#14557618C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#14557528C211yesmaximal, characteristic, complemented
15C2×#103×C37C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×D296C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924531—21no—
22#11924527C2211yescharacteristic
23#11924525—21no—
24#11924525C2211yescharacteristic
25#11924521—21no—
26#11924512—21no—
27#11924512C2211yescharacteristic
28#11924511C2211yescharacteristic
29#11924510—21no—
30#11924510—21no—
31#11924510C2211yescharacteristic
32#11924510C2211yescharacteristic
33Q8×Dic37C2211yescharacteristic
34#11924498C2211yescharacteristic
35C4×C22⋊D37—21no—
36C4×C22⋊D37—21no—
37C4×C22⋊D37C2211yescharacteristic
38#11924494C2211yescharacteristic
39#11924470C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924458C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C22×Q8×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54C2×C4⋊C4×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×Q8×C37—22no—
61C2×Q8×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37—21no—
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37—21no—
69C2×C22⋊D37D411yescharacteristic
70#10596966—22no—
71#10596966—41no—
72C2×D148—21no—
73C2×D148—21no—
74C2×D148C2311yescharacteristic
75C2×D148C2311yescharacteristic
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37C2311yescharacteristic
79C2×C8×C37—41no—
80C2×C8×C37C2311yescharacteristic
81C2×C8×C37C2311yescharacteristic
82C4⋊C4×C37—21no—
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊Dic37D411yescharacteristic
86#10596941—22no—
87#10596941—41no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938D411yescharacteristic
97C4⋊Dic37—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101#10596936—21no—
102#10596936—21no—
103#10596936D411yescharacteristic
104C4×Dic37—21no—
105C4×Dic37—21no—
106C4×Dic37C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109D296—41no—
110C8×D37—41no—
111C23×C37C2×D411yescharacteristic
112C22×D37—21no—
113C22×D37—21no—
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—21no—
118Q8×C37—42no—
119Q8×C37#4112yes—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—42no—
127C2×C4×C37—81no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—22no—
131C22⋊D37—42no—
132C22⋊D37—42no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138D148—21no—
139D148—21no—
140D148—21no—
141D148—21no—
142D148—42no—
143D148—81no—
144C4×D37—21no—
145C4×D37—21no—
146C4×D37—42no—
147C4×D37—81no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37#13512yes—
155C22×C37C22×D411yescharacteristic
156C2×D37—21no—
157C2×D37—21no—
158C2×D37—21no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—22no—
166C4×C37—21no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170C4×C37C2×#4111yescharacteristic
171C4×C37H(5,𝔽2)11yescharacteristic
172Dic37—21no—
173Dic37—21no—
174Dic37—21no—
175Dic37—41no—
176Dic37—41no—
177#3301—371nomaximal, Sylow
178C2×C37—22no—
179C2×C37#54611yescharacteristic
180C2×C37C2×#13511yescharacteristic
181C2×C37#57711yescharacteristic
182D37—41no—
183D37—81no—
184D37—81no—
185#553—371no—
186#548—371no—
187#488—371no—
188#485—371no—
189#481—371no—
190#479—371no—
191#466—371no—
192#465—371no—
193#463—371no—
194#449—371no—
195#448—371no—
196C4×SD16—371no—
197C8×D4—371no—
198#416—371no—
199C2×#103D3711yescharacteristic, complemented
200C37#330111yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C22×Q8C2×D3711yescharacteristic
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C22×C8—371no—
207C22×C8C2×D3711yescharacteristic
208#126—741no—
209#125—371no—
210#124—371no—
211#124—741no—
212#123—741no—
213C22⋊Q8—371no—
214C22⋊Q8—741no—
215#121—371no—
216#121—371no—
217#121—371no—
218#121—741no—
219#121—741no—
220C4×Q8—371no—
221C4×D4—371no—
222C4×D4—371no—
223C4×D4—741no—
224C4×D4—741no—
225#117—371no—
226C2×C4⋊C4C2×D3711yescharacteristic
227#107—371no—
228#106—371no—
229#106—371no—
230C4⋊C8—371no—
231#103—371no—
232#103—371no—
233#103C2×D3711yescharacteristic
234#103C2×D3711yescharacteristic
235#103C2×D3711yescharacteristic
236#103C2×D3711yescharacteristic
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241C22⋊C8—371no—
242C22⋊C8—371no—
243C4×C8—371no—
244#41—742no—
245#41—1481no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D3711yescharacteristic
250C2×Q8C22×D3711yescharacteristic
251C2×D4—371no—
252C2×D4—371no—
253C2×D4—371no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4—741no—
257C2×D4—741no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—371no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4C22×D3711yescharacteristic
264SD16—742no—
265SD16—1481no—
266D8—1481no—
267C2×C8—41no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—1481no—
271C2×C8C22×D3711yescharacteristic
272C2×C8C22×D3711yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—371no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—741no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4C22×D3711yescharacteristic
282C4⋊C4C22×D3711yescharacteristic
283C22⋊C4—371no—
284C22⋊C4—371no—
285C22⋊C4—741no—
286C22⋊C4—741no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C42—371no—
294C42—741no—
295C42—741no—
296C23—371no—
297C23—741no—
298C23—741no—
299C23D4×D3711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1059696212yes—
305D4—2961no—
306D4—742no—
307D4—741no—
308D4—741no—
309D4—741no—
310D4—741no—
311D4—1482no—
312D4—1482no—
313D4—1482no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—371no—
323C2×C4—371no—
324C2×C4—371no—
325C2×C4—2961no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—741no—
330C2×C4—1482no—
331C2×C4D4×D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—741no—
340C22—741no—
341C22—741no—
342C22—1481no—
343C22—1481no—
344C22—1481no—
345C22—1481no—
346C22—1481no—
347C22—1481no—
348C22#1192455912yes—
349C22C2×D4×D3711yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—741no—
356C4—741no—
357C4—741no—
358C4—1481no—
359C4—1481no—
360C4C2×#1059696211yescharacteristic
361C4#1192458111yescharacteristic
362C2—22no—
363C2—2961no—
364C2—2961no—
365C2—1481no—
366C2#1455817311yescharacteristic
367C2C2×#1192455911yescharacteristic
368C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#103×C37C2
socleC22×C37C22×D4
hypercenterC2×#103D37
hypocenterC37#3301
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #14558231C2semidirect
2. #14558194C2semidirect
3. #14557889C2semidirect
4. #14557873C2semidirect
5. #14557851C2semidirect
6. #14557842C2semidirect
7. #14557769C2semidirect
8. #14557765C2semidirect
9. #14557751C2semidirect
10. #14557681C2semidirect
11. #14557672C2semidirect
12. #14557618C2semidirect
13. C8×C22⋊D37C2semidirect
14. #14557528C2semidirect
15. C2×#103×C37C2semidirect
199. C2×#103D37semidirect
200. C37#3301semidirect

Maximal subgroups

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

subgroupindex
#145582312
#145581942
#145578892
#145578732
#145578512
#145578422
#145577692
#145577652
#145577512
#145576812
#145576722
#145576182
C8×C22⋊D372
#145575282
C2×#103×C372
#330137