Finite Group Databasebeta

← #464×D37 #18004036

Subgroups — #464×D37 #18004036

Order 4736.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D37C211yesmaximal, characteristic, complemented
2C2×SD16×D37C211yesmaximal, characteristic
3#124×D37C211yesmaximal, characteristic
4C4×Q8×D37C211yesmaximal, characteristic, complemented
5#14557758C211yesmaximal, characteristic, complemented
6#14557757C211yesmaximal, characteristic, complemented
7#14557756C211yesmaximal, characteristic, complemented
8#14557755C211yesmaximal, characteristic, complemented
9#14557754C211yesmaximal, characteristic, complemented
10#14557753C211yesmaximal, characteristic, complemented
11#14557752C211yesmaximal, characteristic, complemented
12C4⋊C8×D37C211yesmaximal, characteristic, complemented
13#103×D37C211yesmaximal, characteristic, complemented
14#102×D37C211yesmaximal, characteristic
15C37×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19C2×Dic148C2211yescharacteristic, complemented
20C2×#10596942C2211yescharacteristic, complemented
21C2×#10596942C2211yescharacteristic, complemented
22Q16×D37—24no—
23C2×#10596930C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596941C2211yescharacteristic
26SD16×D37—24no—
27C2×C8×D37C2211yescharacteristic
28C2×C8×D37C2211yescharacteristic
29#11924525C2211yescharacteristic
30#11924524C2211yescharacteristic
31#11924523C2211yescharacteristic
32#11924522—21no—
33#11924522—21no—
34Q8×Dic37C2211yescharacteristic, complemented
35C4×Dic74—21no—
36C4×Dic74C2211yescharacteristic, complemented
37#11924501—21no—
38#11924501C2211yescharacteristic, complemented
39C4⋊C4×D37—21no—
40C4⋊C4×D37C2211yescharacteristic
41C22⋊C4×D37—21no—
42C22⋊C4×D37—21no—
43C42×D37—21no—
44C42×D37C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic, complemented
46#11924465C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924460C2211yescharacteristic, complemented
50#11924459C2211yescharacteristic, complemented
51#11924458C2211yescharacteristic
52#11924457C2211yescharacteristic
53#11924456C2211yescharacteristic
54C2×Q16×C37C2211yescharacteristic, complemented
55C2×SD16×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic
57C4×Q8×C37C2211yescharacteristic, complemented
58C4⋊C8×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#102×C37C2211yescharacteristic
61C23×D37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66Q8×D37—22no—
67Q8×D37—22no—
68Q8×D37—22no—
69Q8×D37D414yes—
70D4×D37—22no—
71D4×D37—22no—
72C2×D148C2311yescharacteristic
73C2×C4×D37—21no—
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37D411yescharacteristic
77C2×C4×D37D411yescharacteristic
78C2×C4×D37C2311yescharacteristic
79C2×Dic74—21no—
80C2×Dic74—21no—
81C2×Dic74C2311yescharacteristic
82C2×Dic74C2311yescharacteristic
83Q16×C37—22no—
84SD16×C37—22no—
85C2×C8×C37C2311yescharacteristic
86C2×C8×C37C2311yescharacteristic
87C4⋊C4×C37—21no—
88C4⋊C4×C37C2311yescharacteristic
89C22⋊C4×C37—21no—
90C22⋊C4×C37—21no—
91C42×C37—21no—
92C42×C37C2311yescharacteristic
93C22⋊Dic37—21no—
94C22⋊Dic37—21no—
95#10596942—22no—
96#10596942—22no—
97#10596941—22no—
98#10596940—22no—
99#10596938—21no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103C4⋊Dic37—21no—
104C4⋊Dic37C2311yescharacteristic
105#10596936—21no—
106#10596936—21no—
107#10596936—21no—
108C4×Dic37—21no—
109C4×Dic37—21no—
110C4×Dic37—21no—
111C4×Dic37D411yescharacteristic
112C4×Dic37D411yescharacteristic
113C4×Dic37C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116Dic148—22no—
117#10596930—22no—
118C8×D37—22no—
119C8×D37—22no—
120C23×C37—21no—
121C22×D37—21no—
122C22×D37—42no—
123C22×D37—42no—
124C22×D37—42no—
125C22×D37C2×D411yescharacteristic
126Q8×C37—21no—
127Q8×C37—21no—
128Q8×C37—21no—
129Q8×C37C2×D412yes—
130D4×C37—21no—
131D4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37C2×D411yescharacteristic
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2411yescharacteristic
138C22⋊D37—42no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144C2×Dic37C2×D411yescharacteristic
145D148—21no—
146D148—21no—
147C4×D37—24no—
148C4×D37—22no—
149C4×D37—22no—
150C4×D37—42no—
151C4×D37—42no—
152C4×D37C2×D412yes—
153C4×D37#4112yes—
154Dic74—21no—
155Dic74—24no—
156Dic74—21no—
157Dic74—21no—
158Dic74—42no—
159Dic74C2×D412yes—
160C8×C37—21no—
161C8×C37—21no—
162#64436—21no—
163#64436—21no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37C22×D411yescharacteristic
168C2×D37—41no—
169C2×D37—41no—
170C2×D37—41no—
171C2×D37—84no—
172C2×D37#12112yes—
173C2×D37#13512yes—
174C2×D37#13712yes—
175C4×C37—22no—
176C4×C37—21no—
177C4×C37—21no—
178C4×C37—41no—
179C4×C37—41no—
180C4×C37C22×D411yescharacteristic
181C4×C37C2×#4111yescharacteristic
182Dic37—22no—
183Dic37—21no—
184Dic37—21no—
185Dic37—41no—
186Dic37—41no—
187Dic37#12112yes—
188C2×#464—371nomaximal, Sylow
189C2×C37—81no—
190C2×C37C2×#12111yescharacteristic
191C2×C37C2×#13511yescharacteristic
192C2×C37C2×#13711yescharacteristic
193D37—81no—
194D37#46414yesdirect product factor
195C22×Q16—371no—
196C22×SD16—371no—
197C2×#124—371no—
198C2×C4×Q8—371no—
199#464—371no—
200#464—371no—
201#464—371no—
202#464—371no—
203#464—371no—
204#464—371no—
205#464—371no—
206#464D3711yescharacteristic, direct product factor
207C2×C4⋊C8—371no—
208C2×#103—371no—
209C2×#102—371no—
210C37C2×#46411yescharacteristic, complemented, Sylow
211C22×Q8—371no—
212C22×Q8—371no—
213C22×D4—371no—
214C2×Q16—371no—
215C2×Q16—371no—
216C2×Q16—371no—
217C2×Q16—744no—
218C2×Q16C2×D3711yescharacteristic, complemented
219C2×SD16—371no—
220C2×SD16—371no—
221C2×SD16—371no—
222C2×SD16—744no—
223C2×SD16C2×D3711yescharacteristic
224C22×C8—371no—
225C22×C8—371no—
226#124—371no—
227#124—371no—
228#124—371no—
229#124—741no—
230#124—741no—
231#124C2×D3711yescharacteristic
232C4×Q8—371no—
233C4×Q8—371no—
234C4×Q8—371no—
235C4×Q8—741no—
236C4×Q8—741no—
237C4×Q8C2×D3711yescharacteristic, complemented
238C2×C4⋊C4—371no—
239C2×C4⋊C4—741no—
240C2×C22⋊C4—741no—
241C2×C22⋊C4—741no—
242C2×C42—371no—
243C2×C42—741no—
244C4⋊C8—371no—
245C4⋊C8—371no—
246C4⋊C8—371no—
247C4⋊C8C2×D3711yescharacteristic, complemented
248#103—371no—
249#103—371no—
250#103—371no—
251#103C2×D3711yescharacteristic, complemented
252#102—371no—
253#102—371no—
254#102—371no—
255#102C2×D3711yescharacteristic
256C24—741no—
257C2×Q8—374no—
258C2×Q8—371no—
259C2×Q8—371no—
260C2×Q8—741no—
261C2×Q8—741no—
262C2×Q8—742no—
263C2×Q8—742no—
264C2×Q8—742no—
265C2×Q8C22×D3711yescharacteristic
266C2×Q8C22×D3711yescharacteristic
267C2×D4—371no—
268C2×D4—742no—
269C2×D4—742no—
270C2×D4—741no—
271C2×D4C22×D3711yescharacteristic
272C22×C4—371no—
273C22×C4—371no—
274C22×C4—371no—
275C22×C4—741no—
276C22×C4—741no—
277C22×C4—741no—
278Q16—22no—
279Q16—742no—
280Q16—742no—
281Q16—742no—
282SD16—22no—
283SD16—742no—
284SD16—742no—
285SD16—742no—
286C2×C8—371no—
287C2×C8—371no—
288C2×C8—742no—
289C2×C8—742no—
290C2×C8C22×D3711yescharacteristic
291C2×C8C22×D3711yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—371no—
294C4⋊C4—741no—
295C4⋊C4—741no—
296C4⋊C4—741no—
297C4⋊C4—741no—
298C4⋊C4C22×D3711yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—741no—
302C22⋊C4—741no—
303C22⋊C4—741no—
304C22⋊C4—741no—
305C22⋊C4—741no—
306C22⋊C4—741no—
307C42—21no—
308C42—371no—
309C42—371no—
310C42—371no—
311C42—741no—
312C42—741no—
313C42—741no—
314C42C22×D3711yescharacteristic
315C23—21no—
316C23—371no—
317C23—741no—
318C23—1482no—
319C23—1482no—
320C23—1482no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—372no—
325Q8—744no—
326Q8—741no—
327Q8—741no—
328Q8—741no—
329Q8—1482no—
330Q8D4×D3712yes—
331D4—21no—
332D4—21no—
333D4—741no—
334D4—741no—
335D4—1482no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—371no—
340C2×C4—372no—
341C2×C4—372no—
342C2×C4—371no—
343C2×C4—371no—
344C2×C4—742no—
345C2×C4—742no—
346C2×C4—744no—
347C2×C4—741no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—1482no—
351C2×C4—1482no—
352C2×C4D4×D3711yescharacteristic
353C2×C4D4×D3711yescharacteristic
354C2×C4C23×D3711yescharacteristic
355C8—21no—
356C8—21no—
357C8—741no—
358C8—741no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—372no—
363C22—372no—
364C22—372no—
365C22—2964no—
366C22—1481no—
367C22—1481no—
368C22—1481no—
369C22C2×D4×D3711yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—372no—
376C4—742no—
377C4—741no—
378C4—741no—
379C4—1481no—
380C4—1481no—
381C4C2×D4×D3711yescharacteristic
382C4#41×D3711yescharacteristic
383C2—81no—
384C2—374no—
385C2—2961no—
386C2#121×D3711yescharacteristic
387C2#135×D3711yescharacteristic
388C2#137×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#464C2
socleC22×C37C22×D4
prime radicalC2×D4×D37C22
hypercenter#464D37
hypocenterC37C2×#464
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D37C2semidirect
4. C4×Q8×D37C2semidirect
5. #14557758C2semidirect
6. #14557757C2semidirect
7. #14557756C2semidirect
8. #14557755C2semidirect
9. #14557754C2semidirect
10. #14557753C2semidirect
11. #14557752C2semidirect
12. C4⋊C8×D37C2semidirect
13. #103×D37C2semidirect
15. C37×#464C2semidirect
19. C2×Dic148C22semidirect
20. C2×#10596942C22semidirect
21. C2×#10596942C22semidirect
34. Q8×Dic37C22semidirect
36. C4×Dic74C22semidirect
38. #11924501C22semidirect
45. C4⋊#64436C22semidirect
46. #11924465C22semidirect
47. #11924465C22semidirect
48. #11924461C22semidirect
49. #11924460C22semidirect
50. #11924459C22semidirect
54. C2×Q16×C37C22semidirect
57. C4×Q8×C37C22semidirect
58. C4⋊C8×C37C22semidirect
59. #103×C37C22semidirect
194. D37#464direct (N × H)
206. #464D37direct (N × H)
210. C37C2×#464semidirect
218. C2×Q16C2×D37semidirect
237. C4×Q8C2×D37semidirect
247. C4⋊C8C2×D37semidirect
251. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D372
C2×SD16×D372
#124×D372
C4×Q8×D372
#145577582
#145577572
#145577562
#145577552
#145577542
#145577532
#145577522
C4⋊C8×D372
#103×D372
#102×D372
C37×#4642
C2×#46437