Finite Group Databasebeta

← #18006446

Subgroups — #18006446

Order 4736.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 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#14557866C211yesmaximal, characteristic, complemented
4#14557854C211yesmaximal, characteristic, complemented
5#14557833C211yesmaximal, characteristic, complemented
6#14557767C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557745C211yesmaximal, characteristic, complemented
9#14557678C211yesmaximal, characteristic, complemented
10#14557667C211yesmaximal, characteristic, complemented
11C4×#10596939C211yesmaximal, characteristic, complemented
12D4×#64436C211yesmaximal, characteristic, complemented
13#14557529C211yesmaximal, characteristic, complemented
14C2×#11924457C211yesmaximal, characteristic, complemented
15C37×#546C211yesmaximal, characteristic, complemented
16C2×#10596941C2211yescharacteristic, complemented
17C2×#10596939C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C22×#64436C2211yescharacteristic
20C22×#64436C2211yescharacteristic, complemented
21#11924531—21no—
22#11924528C2211yescharacteristic, complemented
23#11924518—21no—
24#11924510C2211yescharacteristic
25#11924510C2211yescharacteristic, complemented
26#11924508—21no—
27C4×D148C2211yescharacteristic, complemented
28#11924496—21no—
29#11924495C2211yescharacteristic, complemented
30C2×C4⋊Dic37C2211yescharacteristic
31#11924469C2211yescharacteristic, complemented
32#11924469C2211yescharacteristic, complemented
33#11924467C2211yescharacteristic, complemented
34C4⋊#64436C2211yescharacteristic, complemented
35#11924460C2211yescharacteristic, complemented
36#11924460C2211yescharacteristic, complemented
37#11924460C2211yescharacteristic, complemented
38#11924457C2211yescharacteristic
39#11924457C2211yescharacteristic
40#11924457C2211yescharacteristic
41#11924457C2211yescharacteristic
42#11924457C2211yescharacteristic
43#11924457C2211yescharacteristic
44#11924456C2211yescharacteristic, complemented
45C22⋊#64436C2211yescharacteristic
46C22⋊#64436C2211yescharacteristic, complemented
47C4×#64436C2211yescharacteristic, complemented
48C2×#41×C37C2211yescharacteristic
49C22×D4×C37C2211yescharacteristic
50#124×C37C2211yescharacteristic
51#123×C37—21no—
52C22⋊Q8×C37C2211yescharacteristic
53#121×C37—21no—
54#121×C37C2211yescharacteristic
55#120×C37—21no—
56C4×D4×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58C2×C22⋊C4×C37—21no—
59C24×C37—21no—
60#41×C37—22no—
61#41×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37—22no—
64C2×D4×C37—21no—
65C2×D4×C37—21no—
66C2×D4×C37—21no—
67C2×D4×C37—41no—
68C2×D4×C37D411yescharacteristic
69C2×D4×C37C2311yescharacteristic
70C2×D4×C37C2311yescharacteristic
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37C2311yescharacteristic
74C22×C4×C37C2311yescharacteristic
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C22×Dic37—21no—
78C2×D148C2311yescharacteristic
79C2×C4×D37—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×C37—21no—
88C22⋊C4×C37D411yescharacteristic
89C22⋊C4×C37D411yescharacteristic
90C42×C37C2311yescharacteristic
91C22⋊Dic37—21no—
92#10596941—41no—
93#10596939—22no—
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×C37—21no—
113C23×C37—42no—
114C23×C37—42no—
115C23×C37—81no—
116C23×C37C2×D411yescharacteristic
117C23×C37C2×D411yescharacteristic
118C22×D37—21no—
119Q8×C37—21no—
120Q8×C37—21no—
121D4×C37—22no—
122D4×C37—21no—
123D4×C37—21no—
124D4×C37—21no—
125D4×C37—42no—
126D4×C37—42no—
127D4×C37—81no—
128D4×C37#4112yes—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—42no—
136C2×C4×C37—81no—
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2×D411yescharacteristic
140C2×C4×C37C2×D411yescharacteristic
141C2×C4×C37C2411yescharacteristic
142C22⋊D37—42no—
143C22⋊D37—81no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—81no—
148D148—21no—
149D148—21no—
150C4×D37—81no—
151#64436—21no—
152#64436—21no—
153#64436—21no—
154#64436—21no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—22no—
159C22×C37—21no—
160C22×C37—21no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—84no—
167C22×C37#13512yes—
168C22×C37C22×D411yescharacteristic
169C2×D37—41no—
170C2×D37—41no—
171C2×D37—41no—
172C4×C37—21no—
173C4×C37—21no—
174C4×C37—21no—
175C4×C37—21no—
176C4×C37—41no—
177C4×C37—41no—
178C4×C37C2×#4111yescharacteristic
179C4×C37H(5,𝔽2)11yescharacteristic
180Dic37—41no—
181Dic37—41no—
182Dic37—41no—
183#3297—371nomaximal, Sylow
184C2×C37—22no—
185C2×C37—41no—
186C2×C37—42no—
187C2×C37—81no—
188C2×C37#54611yescharacteristic
189C2×C37C2×#13511yescharacteristic
190C2×C37#57611yescharacteristic
191D37—81no—
192#553—371no—
193#546D3711yescharacteristic, complemented
194#488—371no—
195#484—371no—
196#482—371no—
197#478—371no—
198#466—371no—
199#465—371no—
200#463—371no—
201#449—371no—
202#447—371no—
203C4×D8—371no—
204C8×D4—371no—
205#416—371no—
206C2×#102—371no—
207C37#329711yescharacteristic, complemented, Sylow
208C2×#41C2×D3711yescharacteristic
209C22×D4C2×D3711yescharacteristic
210C2×SD16—371no—
211C2×D8—371no—
212C2×D8—371no—
213C22×C8—371no—
214C22×C8—371no—
215#126—741no—
216#125—371no—
217#124C2×D3711yescharacteristic
218#123—21no—
219#123—741no—
220C22⋊Q8C2×D3711yescharacteristic
221#121—21no—
222#121—371no—
223#121—371no—
224#121—741no—
225#121C2×D3711yescharacteristic
226#120—21no—
227C4×D4—371no—
228C4×D4—741no—
229C4×D4C2×D3711yescharacteristic
230C4×D4C2×D3711yescharacteristic
231#117—371no—
232C2×C4⋊C4—371no—
233C2×C22⋊C4—21no—
234#107—371no—
235#107—371no—
236#106—371no—
237C4⋊C8—371no—
238#103—371no—
239#103—371no—
240#103—371no—
241#102—371no—
242#102—371no—
243#102—371no—
244#102—371no—
245#102—371no—
246#102—371no—
247#102—371no—
248C22⋊C8—371no—
249C22⋊C8—371no—
250C4×C8—371no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D3711yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—371no—
261C2×D4—741no—
262C2×D4—741no—
263C2×D4C22⋊D3711yescharacteristic
264C2×D4C22×D3711yescharacteristic
265C2×D4C22×D3711yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—741no—
269C22×C4—741no—
270C22×C4C22×D3711yescharacteristic
271C22×C4C22×D3711yescharacteristic
272SD16—1481no—
273D8—742no—
274D8—1481no—
275C2×C8—371no—
276C2×C8—371no—
277C2×C8—371no—
278C2×C8—371no—
279C2×C8—1481no—
280C2×C8—1481no—
281C4⋊C4—21no—
282C4⋊C4—371no—
283C4⋊C4—371no—
284C4⋊C4—371no—
285C4⋊C4—741no—
286C4⋊C4—741no—
287C4⋊C4—741no—
288C4⋊C4C22⋊D3711yescharacteristic
289C4⋊C4C22×D3711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—741no—
296C22⋊C4—741no—
297C22⋊C4—741no—
298C22⋊C4—741no—
299C22⋊C4C22⋊D3711yescharacteristic
300C22⋊C4C22⋊D3711yescharacteristic
301C42—741no—
302C42C22×D3711yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—741no—
309C23C2×C22⋊D3711yescharacteristic
310C23C2×C22⋊D3711yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—2961no—
321D4—741no—
322D4—741no—
323D4—1482no—
324D4#1059696412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—2961no—
334C2×C4—2961no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4C2×C22⋊D3711yescharacteristic
339C2×C4C2×C22⋊D3711yescharacteristic
340C2×C4C2×C22⋊D3711yescharacteristic
341C2×C4C2×C22⋊D3711yescharacteristic
342C2×C4C23×D3711yescharacteristic
343C8—741no—
344C8—741no—
345C8—741no—
346C8—741no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—1481no—
360C22—1481no—
361C22—1481no—
362C22#1192455612yes—
363C22C22×C22⋊D3711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—1481no—
371C4—1481no—
372C4—1481no—
373C4C2×#1059696411yescharacteristic
374C4#1192458111yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—2961no—
380C2#1455817711yescharacteristic
381C2C2×#1192455611yescharacteristic
382C2#1455833611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#546C2
socleC22×C37C22×D4
hypercenter#546D37
hypocenterC37#3297
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14558229C2semidirect
2. #14557887C2semidirect
3. #14557866C2semidirect
4. #14557854C2semidirect
5. #14557833C2semidirect
6. #14557767C2semidirect
7. #14557764C2semidirect
8. #14557745C2semidirect
9. #14557678C2semidirect
10. #14557667C2semidirect
11. C4×#10596939C2semidirect
12. D4×#64436C2semidirect
13. #14557529C2semidirect
14. C2×#11924457C2semidirect
15. C37×#546C2semidirect
16. C2×#10596941C22semidirect
20. C22×#64436C22semidirect
22. #11924528C22semidirect
25. #11924510C22semidirect
27. C4×D148C22semidirect
29. #11924495C22semidirect
31. #11924469C22semidirect
32. #11924469C22semidirect
33. #11924467C22semidirect
34. C4⋊#64436C22semidirect
35. #11924460C22semidirect
36. #11924460C22semidirect
37. #11924460C22semidirect
44. #11924456C22semidirect
46. C22⋊#64436C22semidirect
47. C4×#64436C22semidirect
193. #546D37semidirect
207. C37#3297semidirect

Maximal subgroups

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

subgroupindex
#145582292
#145578872
#145578662
#145578542
#145578332
#145577672
#145577642
#145577452
#145576782
#145576672
C4×#105969392
D4×#644362
#145575292
C2×#119244572
C37×#5462
#329737