Finite Group Databasebeta

← #18006111

Subgroups — #18006111

Order 4736.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924569C211yesmaximal, characteristic, complemented
2C22×#10596930C211yesmaximal, characteristic, complemented
3D4×Dic74C211yesmaximal, characteristic, complemented
4#14558179C211yesmaximal, characteristic
5#14557927C211yesmaximal, characteristic, complemented
6#14557779C211yesmaximal, characteristic, complemented
7#14557774C211yesmaximal, characteristic, complemented
8#14557756C211yesmaximal, characteristic, complemented
9#14557739C211yesmaximal, characteristic, complemented
10#14557697C211yesmaximal, characteristic, complemented
11#14557691C211yesmaximal, characteristic, complemented
12#14557686C211yesmaximal, characteristic, complemented
13#14557674C211yesmaximal, characteristic, complemented
14#14557635C211yesmaximal, characteristic, complemented
15C37×#435C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18C22×Dic74C2211yescharacteristic, complemented
19C22×D148C2211yescharacteristic
20#11924569—24no—
21C2×Dic148C2211yescharacteristic, complemented
22C2×Dic148C2211yescharacteristic, complemented
23C2×Dic148C2211yescharacteristic, complemented
24C2×#10596930—24no—
25C2×#10596930C2211yescharacteristic
26C2×#10596930C2211yescharacteristic
27C2×#10596930C2211yescharacteristic
28C2×#10596930C2211yescharacteristic
29C2×#10596930C2211yescharacteristic
30C2×#10596930C2211yescharacteristic
31#11924536C2211yescharacteristic, complemented
32#11924535—21no—
33#11924524C2211yescharacteristic
34#11924521—21no—
35#11924515C2211yescharacteristic
36#11924515C2211yescharacteristic
37#11924515C2211yescharacteristic, complemented
38#11924513—21no—
39#11924513—21no—
40#11924510C2211yescharacteristic
41#11924509—21no—
42#11924504—21no—
43C4×Dic74C2211yescharacteristic, complemented
44C4×D148C2211yescharacteristic
45D4×Dic37—21no—
46C22⋊C4×D37—21no—
47#11924470C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924461C2211yescharacteristic, complemented
50#11924461C2211yescharacteristic, complemented
51#11924461C2211yescharacteristic, complemented
52#11924458C2211yescharacteristic
53#11924458C2211yescharacteristic
54C2×M16×C37C2211yescharacteristic, complemented
55C22×C8×C37C2211yescharacteristic
56C4×D4×C37C2211yescharacteristic
57C4⋊C8×C37C2211yescharacteristic, complemented
58C22⋊C8×C37C2211yescharacteristic
59C22⋊C8×C37C2211yescharacteristic, complemented
60#97×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×D4×C37D411yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C22×Dic37—21no—
69#10596962—22no—
70#10596962—41no—
71C2×D148—22no—
72C2×D148—21no—
73C2×D148—41no—
74C2×D148C2311yescharacteristic
75C2×D148C2311yescharacteristic
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×Dic74—22no—
79C2×Dic74—22no—
80C2×Dic74—21no—
81C2×Dic74—21no—
82C2×Dic74—41no—
83C2×Dic74—41no—
84C2×Dic74C2311yescharacteristic
85C2×Dic74C2311yescharacteristic
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88M16×C37—22no—
89C2×C8×C37—22no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C4⋊C4×C37D411yescharacteristic
95C22⋊C4×C37D411yescharacteristic
96C22⋊C4×C37D411yescharacteristic
97C42×C37C2311yescharacteristic
98C22⋊Dic37—21no—
99C22⋊Dic37—21no—
100C22⋊Dic37—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105C4⋊Dic37—21no—
106C4⋊Dic37—21no—
107C4⋊Dic37C2311yescharacteristic
108C4⋊Dic37C2311yescharacteristic
109#10596936—21no—
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113C4×Dic37—21no—
114Dic148—22no—
115Dic148—22no—
116Dic148—41no—
117#10596930—22no—
118#10596930—22no—
119#10596930—22no—
120#10596930—22no—
121#10596930—41no—
122#10596930D414yescomplemented
123C23×C37C2×D411yescharacteristic
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—42no—
128C22×D37—42no—
129C22×D37—81no—
130D4×C37—22no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2×D411yescharacteristic
138C2×C4×C37C2×D411yescharacteristic
139C2×C4×C37C2411yescharacteristic
140C22⋊D37—42no—
141C22⋊D37—81no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—42no—
149C2×Dic37—42no—
150D148—21no—
151D148—21no—
152D148—21no—
153D148—42no—
154D148C2×D412yes—
155C4×D37—42no—
156C4×D37—81no—
157Dic74—21no—
158Dic74—21no—
159Dic74—21no—
160Dic74—21no—
161Dic74—21no—
162Dic74—21no—
163Dic74—21no—
164Dic74—42no—
165Dic74—42no—
166Dic74C2×D412yes—
167C8×C37—21no—
168C8×C37—21no—
169C8×C37—21no—
170C8×C37C2×D412yes—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—21no—
175C22×C37—21no—
176C22×C37#13712yescomplemented
177C22×C37C22×D411yescharacteristic
178C2×D37—22no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—84no—
185C4×C37—21no—
186C4×C37—21no—
187C4×C37—21no—
188C4×C37—21no—
189C4×C37C22×D411yescharacteristic
190C4×C37H(5,𝔽2)11yescharacteristic
191Dic37—22no—
192Dic37—41no—
193Dic37—41no—
194Dic37—41no—
195Dic37—41no—
196Dic37—41no—
197#3266—371nomaximal, Sylow
198C2×C37—22no—
199C2×C37—41no—
200C2×C37D4211yescharacteristic
201C2×C37C2×#13711yescharacteristic
202C2×C37#57711yescharacteristic
203D37—42no—
204D37—81no—
205C2×#137—371no—
206C22×SD16—371no—
207D4×Q8—371no—
208#546—371no—
209#497—371no—
210#468—371no—
211#467—371no—
212#464—371no—
213#461—371no—
214#452—371no—
215#451—371no—
216#450—371no—
217#448—371no—
218#440—371no—
219#435D3711yescharacteristic, complemented
220C37#326611yescharacteristic, complemented, Sylow
221C2×#41—371no—
222C22×Q8—371no—
223C22×Q8—371no—
224C22×D4—371no—
225#137—744no—
226C2×Q16—371no—
227C2×Q16—371no—
228C2×Q16—371no—
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—744no—
236C2×M16C2×D3711yescharacteristic, complemented
237C22×C8C2×D3711yescharacteristic
238C4⋊Q8—371no—
239C4⋊Q8—741no—
240#124—371no—
241#123—741no—
242C22⋊Q8—371no—
243C22⋊Q8—371no—
244C22⋊Q8—371no—
245C22⋊Q8—741no—
246C22⋊Q8—741no—
247#121—371no—
248#121—741no—
249#120—741no—
250C4×Q8—371no—
251C4×D4—371no—
252C4×D4—741no—
253C4×D4C2×D3711yescharacteristic
254C2×C22⋊C4—741no—
255#107—371no—
256C4⋊C8C2×D3711yescharacteristic, complemented
257#103—371no—
258#103—371no—
259#103—371no—
260#103—371no—
261#102—371no—
262#102—371no—
263C22⋊C8C2×D3711yescharacteristic
264C22⋊C8C2×D3711yescharacteristic, complemented
265#97C2×D3711yescharacteristic, complemented
266C24—741no—
267#41—742no—
268#41—1481no—
269C2×Q8—371no—
270C2×Q8—371no—
271C2×Q8—371no—
272C2×Q8—371no—
273C2×Q8—742no—
274C2×Q8—742no—
275C2×Q8—741no—
276C2×Q8—741no—
277C2×Q8—1481no—
278C2×Q8—1481no—
279C2×D4—371no—
280C2×D4—371no—
281C2×D4—742no—
282C2×D4—741no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4—1481no—
286C2×D4D14811yescharacteristic
287C22×C4—741no—
288C22×C4—741no—
289C22×C4—741no—
290C22×C4—741no—
291C22×C4C22×D3711yescharacteristic
292C22×C4C22×D3711yescharacteristic
293Q16—742no—
294Q16—742no—
295Q16—1481no—
296SD16—374no—
297SD16—742no—
298SD16—742no—
299SD16—742no—
300SD16—742no—
301SD16—1481no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D3711yescharacteristic
305C2×C8C22×D3711yescharacteristic
306C2×C8C22×D3711yescharacteristic
307C2×C8C22×D3711yescharacteristic
308C4⋊C4—371no—
309C4⋊C4—371no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4—741no—
314C4⋊C4—741no—
315C4⋊C4—741no—
316C4⋊C4D14811yescharacteristic
317C22⋊C4—741no—
318C22⋊C4—741no—
319C22⋊C4—741no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4D14811yescharacteristic
325C22⋊C4D14811yescharacteristic
326C42—741no—
327C42C22×D3711yescharacteristic
328C23—2961no—
329C23—741no—
330C23—741no—
331C23—1482no—
332C23—1482no—
333C23C2×D14811yescharacteristic
334C23C2×D14811yescharacteristic
335Q8—372no—
336Q8—741no—
337Q8—741no—
338Q8—741no—
339Q8—741no—
340Q8—741no—
341Q8—741no—
342Q8—741no—
343Q8—1482no—
344Q8—1482no—
345D4—22no—
346D4—372no—
347D4—2961no—
348D4—741no—
349D4—741no—
350D4—741no—
351D4—1482no—
352D4—1482no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—2961no—
358C2×C4—741no—
359C2×C4—741no—
360C2×C4—741no—
361C2×C4—741no—
362C2×C4—741no—
363C2×C4—741no—
364C2×C4—1482no—
365C2×C4—1482no—
366C2×C4—1482no—
367C2×C4C2×D14811yescharacteristic
368C2×C4C2×D14811yescharacteristic
369C2×C4C2×D14811yescharacteristic
370C2×C4C2×D14811yescharacteristic
371C2×C4C23×D3711yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D3712yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—2964no—
382C22—742no—
383C22—1481no—
384C22—1481no—
385C22—1481no—
386C22—1481no—
387C22—1481no—
388C22#1192456912yescomplemented
389C22C22×D14811yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—742no—
395C4—1481no—
396C4—1481no—
397C4—1481no—
398C4—1481no—
399C4—1481no—
400C4C2×D4×D3711yescharacteristic
401C4#1192458211yescharacteristic
402C2—22no—
403C2—41no—
404C2—2961no—
405C2—1482no—
406C2D4×D14811yescharacteristic
407C2C2×#1192456911yescharacteristic
408C2#1455834511yescharacteristic
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#435C2
socleC22×C37C22×D4
prime radical#14558179C2
hypercenter#435D37
hypocenterC37#3266
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. C2×#11924569C2semidirect
2. C22×#10596930C2semidirect
3. D4×Dic74C2semidirect
5. #14557927C2semidirect
6. #14557779C2semidirect
7. #14557774C2semidirect
8. #14557756C2semidirect
9. #14557739C2semidirect
10. #14557697C2semidirect
11. #14557691C2semidirect
12. #14557686C2semidirect
13. #14557674C2semidirect
14. #14557635C2semidirect
15. C37×#435C2semidirect
18. C22×Dic74C22semidirect
21. C2×Dic148C22semidirect
22. C2×Dic148C22semidirect
23. C2×Dic148C22semidirect
31. #11924536C22semidirect
37. #11924515C22semidirect
43. C4×Dic74C22semidirect
47. #11924470C22semidirect
48. #11924461C22semidirect
49. #11924461C22semidirect
50. #11924461C22semidirect
51. #11924461C22semidirect
54. C2×M16×C37C22semidirect
57. C4⋊C8×C37C22semidirect
59. C22⋊C8×C37C22semidirect
60. #97×C37C22semidirect
122. #10596930D4semidirect
176. C22×C37#137semidirect
219. #435D37semidirect
220. C37#3266semidirect
236. C2×M16C2×D37semidirect
256. C4⋊C8C2×D37semidirect
264. C22⋊C8C2×D37semidirect
265. #97C2×D37semidirect
388. C22#11924569semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C22×#105969302
D4×Dic742
#145581792
#145579272
#145577792
#145577742
#145577562
#145577392
#145576972
#145576912
#145576862
#145576742
#145576352
C37×#4352
#326637