Finite Group Databasebeta

← #18006567

Subgroups — #18006567

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#14558235C211yesmaximal, characteristic, complemented
2#14558185C211yesmaximal, characteristic, complemented
3#14557900C211yesmaximal, characteristic, complemented
4#14557876C211yesmaximal, characteristic, complemented
5#14557861C211yesmaximal, characteristic, complemented
6#14557836C211yesmaximal, characteristic, complemented
7#14557761C211yesmaximal, characteristic, complemented
8#14557736C211yesmaximal, characteristic, complemented
9#14557677C211yesmaximal, characteristic, complemented
10#14557676C211yesmaximal, characteristic, complemented
11#14557642C211yesmaximal, characteristic, complemented
12#14557602C211yesmaximal, characteristic, complemented
13#14557535C211yesmaximal, characteristic, complemented
14#14557528C211yesmaximal, characteristic, complemented
15C37×#468C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924534C2211yescharacteristic
22#11924529—21no—
23#11924527C2211yescharacteristic
24#11924521—21no—
25#11924520—21no—
26#11924518—21no—
27#11924516C2211yescharacteristic
28#11924509—21no—
29#11924508—21no—
30#11924507C2211yescharacteristic
31D4×Dic37—21no—
32D4×Dic37C2211yescharacteristic
33#11924498C2211yescharacteristic
34C4×C22⋊D37C2211yescharacteristic
35#11924494C2211yescharacteristic
36C2×C4⋊Dic37C2211yescharacteristic
37C4⋊C4×D37—21no—
38#11924467C2211yescharacteristic
39#11924467C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924461C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51#11924446C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C2×M16×C37C2211yescharacteristic
54C22⋊Q8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#107×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37D411yescharacteristic
66C22×Dic37—21no—
67C22×Dic37—21no—
68#10596966—22no—
69#10596966—41no—
70#10596962—22no—
71#10596962—41no—
72C2×D148—21no—
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37C2311yescharacteristic
78C2×Dic74C2311yescharacteristic
79SD16×C37—41no—
80M16×C37—41no—
81C2×C8×C37C2311yescharacteristic
82C2×C8×C37C2311yescharacteristic
83C4⋊C4×C37—21no—
84C4⋊C4×C37C2311yescharacteristic
85C4⋊C4×C37C2311yescharacteristic
86C22⋊C4×C37—21no—
87C22⋊C4×C37—21no—
88C22⋊Dic37—21no—
89C22⋊Dic37—21no—
90C22⋊Dic37D411yescharacteristic
91#10596940—41no—
92#10596939—22no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96#10596938D411yescharacteristic
97C4⋊Dic37—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37—21no—
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104#10596936—21no—
105#10596936D411yescharacteristic
106C4×Dic37—21no—
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C8×D37—41no—
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117D4×C37—21no—
118D4×C37—21no—
119D4×C37—42no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2411yescharacteristic
127C22⋊D37—41no—
128C22⋊D37—42no—
129C22⋊D37—81no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—81no—
134C2×Dic37—81no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138D148—21no—
139D148—42no—
140D148#4112yes—
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—42no—
144C4×D37—42no—
145C4×D37—42no—
146Dic74—21no—
147Dic74—21no—
148C8×C37—21no—
149C8×C37—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—41no—
156C22×C37—41no—
157C22×C37—41no—
158C22×C37C22×D411yescharacteristic
159C2×D37—21no—
160C2×D37—22no—
161C2×D37—21no—
162C2×D37—21no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37C2×#4111yescharacteristic
170C4×C37H(5,𝔽2)11yescharacteristic
171Dic37—21no—
172Dic37—21no—
173Dic37—21no—
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3307—371nomaximal, Sylow
178C2×C37—41no—
179C2×C37—81no—
180C2×C37#54611yescharacteristic
181C2×C37#57511yescharacteristic
182C2×C37#57711yescharacteristic
183D37—41no—
184D37—42no—
185#553—371no—
186#547—371no—
187#491—371no—
188#485—371no—
189#483—371no—
190#478—371no—
191#468D3711yescharacteristic, complemented
192#465—371no—
193#461—371no—
194#449—371no—
195#449—371no—
196#442—371no—
197#435—371no—
198#417—371no—
199#416—371no—
200C37#330711yescharacteristic, complemented, Sylow
201C2×#41—371no—
202C2×#41—371no—
203C2×SD16—371no—
204C2×SD16C2×D3711yescharacteristic
205C2×D8—371no—
206C2×M16C2×D3711yescharacteristic
207C22×C8—371no—
208C4⋊Q8—371no—
209#126—741no—
210#125—371no—
211#123—741no—
212#123—741no—
213#123—741no—
214C22⋊Q8—371no—
215C22⋊Q8C2×D3711yescharacteristic
216#121—371no—
217#121—741no—
218#121—741no—
219#121C2×D3711yescharacteristic
220C4×D4—371no—
221C4×D4—371no—
222C4×D4—371no—
223C4×D4—741no—
224#117—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—741no—
227#107C2×D3711yescharacteristic
228#106—371no—
229#106—371no—
230C4⋊C8—371no—
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103—371no—
236#103C2×D3711yescharacteristic
237#102—371no—
238#102—371no—
239#102—371no—
240#102C2×D3711yescharacteristic
241C22⋊C8—371no—
242C22⋊C8—371no—
243#97—371no—
244#41—742no—
245#41—742no—
246#41—1481no—
247#41—1481no—
248C2×Q8—371no—
249C2×Q8C22×D3711yescharacteristic
250C2×D4—21no—
251C2×D4—371no—
252C2×D4—371no—
253C2×D4—741no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4C22×D3711yescharacteristic
257C22×C4—371no—
258C22×C4—741no—
259C22×C4—741no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4C22×D3711yescharacteristic
264SD16—41no—
265SD16—1481no—
266D8—742no—
267M16—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⋊C4—741no—
282C4⋊C4—741no—
283C4⋊C4C22×D3711yescharacteristic
284C4⋊C4C22×D3711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—371no—
288C22⋊C4—371no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C42—371no—
295C42—741no—
296C23—21no—
297C23—371no—
298C23—741no—
299C23D4×D3711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—741no—
303Q8—741no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—372no—
308D4—2961no—
309D4—741no—
310D4—1482no—
311D4—1481no—
312D4—1482no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—371no—
319C2×C4—371no—
320C2×C4—371no—
321C2×C4—2961no—
322C2×C4—2961no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—1482no—
329C2×C4—1482no—
330C2×C4—1482no—
331C2×C4D4×D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—21no—
334C8—21no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—741no—
344C22—741no—
345C22—741no—
346C22—742no—
347C22—1481no—
348C22—1481no—
349C22C2×D4×D3711yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—741no—
355C4—741no—
356C4—741no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4#41×D3711yescharacteristic
361C4#1192458111yescharacteristic
362C2—41no—
363C2—81no—
364C2—1481no—
365C2—1482no—
366C2#1455817211yescharacteristic
367C2#1455832911yescharacteristic
368C2#1455834211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#468C2
socleC22×C37C22×D4
hypercenter#468D37
hypocenterC37#3307
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #14558235C2semidirect
2. #14558185C2semidirect
3. #14557900C2semidirect
4. #14557876C2semidirect
5. #14557861C2semidirect
6. #14557836C2semidirect
7. #14557761C2semidirect
8. #14557736C2semidirect
9. #14557677C2semidirect
10. #14557676C2semidirect
11. #14557642C2semidirect
12. #14557602C2semidirect
13. #14557535C2semidirect
14. #14557528C2semidirect
15. C37×#468C2semidirect
191. #468D37semidirect
200. C37#3307semidirect

Maximal subgroups

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

subgroupindex
#145582352
#145581852
#145579002
#145578762
#145578612
#145578362
#145577612
#145577362
#145576772
#145576762
#145576422
#145576022
#145575352
#145575282
C37×#4682
#330737