Finite Group Databasebeta

← #18006498

Subgroups — #18006498

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#14558229C211yesmaximal, characteristic, complemented
2#14557887C211yesmaximal, characteristic, complemented
3#14557871C211yesmaximal, characteristic, complemented
4#14557849C211yesmaximal, characteristic, complemented
5#14557840C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557745C211yesmaximal, characteristic, complemented
9#14557678C211yesmaximal, characteristic, complemented
10#14557672C211yesmaximal, characteristic, complemented
11C4×#10596941C211yesmaximal, characteristic, complemented
12D4×#64436C211yesmaximal, characteristic, complemented
13#14557529C211yesmaximal, characteristic, complemented
14C2×#11924460C211yesmaximal, characteristic, complemented
15C37×#548C211yesmaximal, characteristic, complemented
16C2×#10596941C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C22×#64436C2211yescharacteristic
20C22×#64436C2211yescharacteristic
21#11924531—21no—
22#11924528C2211yescharacteristic
23#11924518—21no—
24#11924510C2211yescharacteristic
25#11924510C2211yescharacteristic
26#11924508—21no—
27C4×D148C2211yescharacteristic
28#11924496—21no—
29#11924495C2211yescharacteristic
30C2×C4⋊Dic37C2211yescharacteristic
31#11924469C2211yescharacteristic
32#11924467C2211yescharacteristic
33#11924467C2211yescharacteristic
34C4⋊#64436C2211yescharacteristic
35#11924460C2211yescharacteristic
36#11924460C2211yescharacteristic
37#11924460C2211yescharacteristic
38#11924460C2211yescharacteristic
39#11924460C2211yescharacteristic
40#11924460C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924457C2211yescharacteristic
43#11924457C2211yescharacteristic
44#11924456C2211yescharacteristic
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic
47C4×#64436C2211yescharacteristic
48C2×#41×C37C2211yescharacteristic
49C22×Q8×C37C2211yescharacteristic
50#124×C37—21no—
51#124×C37C2211yescharacteristic
52C22⋊Q8×C37—21no—
53C22⋊Q8×C37C2211yescharacteristic
54#121×C37—21no—
55#121×C37C2211yescharacteristic
56C4×Q8×C37C2211yescharacteristic
57C4×D4×C37—21no—
58C4×D4×C37C2211yescharacteristic
59#41×C37—22no—
60#41×C37—41no—
61C2×Q8×C37—21no—
62C2×Q8×C37—22no—
63C2×Q8×C37—41no—
64C2×Q8×C37C2311yescharacteristic
65C2×Q8×C37C2311yescharacteristic
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37D411yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C22×C4×C37—21no—
71C22×C4×C37—21no—
72C22×C4×C37C2311yescharacteristic
73C22×C4×C37C2311yescharacteristic
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C22×Dic37—21no—
77C2×D148C2311yescharacteristic
78C2×C4×D37—21no—
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37D411yescharacteristic
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×C37—21no—
90C42×C37C2311yescharacteristic
91C22⋊Dic37—21no—
92#10596941—22no—
93#10596941—41no—
94#10596939—41no—
95#10596938—21no—
96#10596938—21no—
97#10596938—21no—
98C4⋊Dic37—21no—
99C4⋊Dic37C2311yescharacteristic
100C4⋊Dic37C2311yescharacteristic
101C4⋊Dic37C2311yescharacteristic
102#10596936—21no—
103#10596936—21no—
104C4×Dic37—21no—
105C2×#64436—41no—
106C2×#64436—41no—
107C2×#64436C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C2×#64436C2311yescharacteristic
111C23×C37—21no—
112C23×C37C2×D411yescharacteristic
113C23×C37C2×D411yescharacteristic
114C22×D37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—21no—
118Q8×C37—42no—
119Q8×C37#4112yes—
120D4×C37—22no—
121D4×C37—21no—
122D4×C37—21no—
123D4×C37—42no—
124D4×C37—42no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—42no—
133C2×C4×C37—42no—
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2411yescharacteristic
139C22⋊D37—42no—
140C22⋊D37—81no—
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—81no—
145D148—21no—
146D148—21no—
147C4×D37—81no—
148#64436—21no—
149#64436—21no—
150#64436—21no—
151#64436—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—41no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37#13512yes—
161C22×C37C22×D411yescharacteristic
162C2×D37—41no—
163C2×D37—41no—
164C2×D37—41no—
165C4×C37—21no—
166C4×C37—21no—
167C4×C37—22no—
168C4×C37—21no—
169C4×C37—21no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37C2×#4111yescharacteristic
173C4×C37H(5,𝔽2)11yescharacteristic
174Dic37—41no—
175Dic37—41no—
176Dic37—41no—
177#3301—371nomaximal, Sylow
178C2×C37—22no—
179C2×C37—41no—
180C2×C37—81no—
181C2×C37#54611yescharacteristic
182C2×C37C2×#13511yescharacteristic
183C2×C37#57711yescharacteristic
184D37—81no—
185#553—371no—
186#548D3711yescharacteristic, complemented
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×#103—371no—
200C37#330111yescharacteristic, complemented, Sylow
201C2×#41C2×D3711yescharacteristic
202C22×Q8C2×D3711yescharacteristic
203C2×SD16—371no—
204C2×SD16—371no—
205C2×D8—371no—
206C22×C8—371no—
207C22×C8—371no—
208#126—741no—
209#125—371no—
210#124—21no—
211#124C2×D3711yescharacteristic
212#123—741no—
213C22⋊Q8—21no—
214C22⋊Q8C2×D3711yescharacteristic
215#121—21no—
216#121—371no—
217#121—371no—
218#121—741no—
219#121C2×D3711yescharacteristic
220C4×Q8C2×D3711yescharacteristic
221C4×D4—21no—
222C4×D4—371no—
223C4×D4—741no—
224C4×D4C2×D3711yescharacteristic
225#117—371no—
226C2×C4⋊C4—371no—
227#107—371no—
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#103—371no—
237#102—371no—
238#102—371no—
239#102—371no—
240#102—371no—
241C22⋊C8—371no—
242C22⋊C8—371no—
243C4×C8—371no—
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D3711yescharacteristic
250C2×Q8C22×D3711yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—371no—
254C2×D4—741no—
255C2×D4—741no—
256C2×D4C22⋊D3711yescharacteristic
257C2×D4C22×D3711yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—741no—
261C22×C4—741no—
262C22×C4C22×D3711yescharacteristic
263C22×C4C22×D3711yescharacteristic
264SD16—742no—
265SD16—1481no—
266D8—1481no—
267C2×C8—371no—
268C2×C8—371no—
269C2×C8—371no—
270C2×C8—371no—
271C2×C8—1481no—
272C2×C8—1481no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—371no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4C22⋊D3711yescharacteristic
282C4⋊C4C22×D3711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—741no—
288C22⋊C4—741no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4C22⋊D3711yescharacteristic
292C22⋊C4C22⋊D3711yescharacteristic
293C42—21no—
294C42—741no—
295C42C22×D3711yescharacteristic
296C23—21no—
297C23—741no—
298C23C2×C22⋊D3711yescharacteristic
299C23C2×C22⋊D3711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1059696412yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—42no—
310D4—2961no—
311D4—741no—
312D4—741no—
313D4—1482no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—2961no—
324C2×C4—2961no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4C2×C22⋊D3711yescharacteristic
329C2×C4C2×C22⋊D3711yescharacteristic
330C2×C4C2×C22⋊D3711yescharacteristic
331C2×C4C2×C22⋊D3711yescharacteristic
332C2×C4C23×D3711yescharacteristic
333C8—741no—
334C8—741no—
335C8—741no—
336C8—741no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1481no—
346C22—1481no—
347C22—1481no—
348C22#1192455612yes—
349C22C22×C22⋊D3711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—1481no—
358C4—1481no—
359C4—1481no—
360C4C2×#1059696411yescharacteristic
361C4#1192458111yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—2961no—
366C2#1455817711yescharacteristic
367C2C2×#1192455611yescharacteristic
368C2#1455834111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#548C2
socleC22×C37C22×D4
hypercenter#548D37
hypocenterC37#3301
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14558229C2semidirect
2. #14557887C2semidirect
3. #14557871C2semidirect
4. #14557849C2semidirect
5. #14557840C2semidirect
6. #14557767C2semidirect
7. #14557764C2semidirect
8. #14557745C2semidirect
9. #14557678C2semidirect
10. #14557672C2semidirect
11. C4×#10596941C2semidirect
12. D4×#64436C2semidirect
13. #14557529C2semidirect
14. C2×#11924460C2semidirect
15. C37×#548C2semidirect
186. #548D37semidirect
200. C37#3301semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145578872
#145578712
#145578492
#145578402
#145577672
#145577642
#145577452
#145576782
#145576722
C4×#105969412
D4×#644362
#145575292
C2×#119244602
C37×#5482
#330137