Finite Group Databasebeta

← #18006166

Subgroups — #18006166

Order 4736.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924568C211yesmaximal, characteristic, complemented
2Q8×C22⋊D37C211yesmaximal, characteristic, complemented
3#14558194C211yesmaximal, characteristic
4#14557926C211yesmaximal, characteristic, complemented
5#14557788C211yesmaximal, characteristic, complemented
6#14557762C211yesmaximal, characteristic, complemented
7#14557757C211yesmaximal, characteristic, complemented
8#14557741C211yesmaximal, characteristic, complemented
9#14557694C211yesmaximal, characteristic, complemented
10#14557689C211yesmaximal, characteristic, complemented
11#14557687C211yesmaximal, characteristic, complemented
12#14557672C211yesmaximal, characteristic, complemented
13#14557640C211yesmaximal, characteristic, complemented
14#14557604C211yesmaximal, characteristic, complemented
15C22×Q16×C37C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18#11924568—24no—
19C2×#10596942C2211yescharacteristic
20C2×#10596942C2211yescharacteristic
21C2×#10596930C2211yescharacteristic
22C2×#10596941C2211yescharacteristic
23C2×#10596941C2211yescharacteristic
24C2×#10596929C2211yescharacteristic
25#11924534—21no—
26#11924534C2211yescharacteristic
27#11924525—21no—
28#11924525C2211yescharacteristic
29#11924515—21no—
30#11924515C2211yescharacteristic
31#11924512—21no—
32#11924512—21no—
33#11924512C2211yescharacteristic
34#11924512C2211yescharacteristic
35#11924510—21no—
36#11924510C2211yescharacteristic
37Q8×Dic37C2211yescharacteristic
38Q8×Dic37C2211yescharacteristic
39C4×C22⋊D37—21no—
40C4×C22⋊D37—21no—
41C4×C22⋊D37C2211yescharacteristic
42#11924468C2211yescharacteristic
43#11924465C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924460C2211yescharacteristic
47#11924460C2211yescharacteristic
48#11924460C2211yescharacteristic
49#11924458C2211yescharacteristic
50C22⋊#64436C2211yescharacteristic
51#11924448C2211yescharacteristic
52#11924446C2211yescharacteristic
53C22×Q8×C37C2211yescharacteristic
54C22×Q8×C37C2211yescharacteristic
55C2×Q16×C37—24no—
56C2×Q16×C37C2211yescharacteristic
57C2×Q16×C37C2211yescharacteristic
58C2×Q16×C37C2211yescharacteristic
59C2×Q16×C37C2211yescharacteristic
60C22×C8×C37C2211yescharacteristic
61C2×Q8×C37—21no—
62C2×Q8×C37—21no—
63C2×Q8×C37—22no—
64C2×Q8×C37—22no—
65C2×Q8×C37—41no—
66C2×Q8×C37—41no—
67C2×Q8×C37C2311yescharacteristic
68C2×Q8×C37C2311yescharacteristic
69C2×Q8×C37C2311yescharacteristic
70C2×Q8×C37C2311yescharacteristic
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37C2311yescharacteristic
74C2×C22⋊D37—21no—
75C2×C22⋊D37D411yescharacteristic
76#10596966—22no—
77#10596966—41no—
78Q8×D37—22no—
79Q8×D37—41no—
80C2×D148—21no—
81C2×D148C2311yescharacteristic
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×C4×D37C2311yescharacteristic
85C2×Dic74—21no—
86C2×Dic74C2311yescharacteristic
87Q16×C37—22no—
88Q16×C37—22no—
89Q16×C37—22no—
90Q16×C37D414yescomplemented
91C2×C8×C37—22no—
92C2×C8×C37C2311yescharacteristic
93C2×C8×C37C2311yescharacteristic
94C22⋊Dic37—21no—
95C22⋊Dic37D411yescharacteristic
96#10596942—22no—
97#10596942—41no—
98#10596941—22no—
99#10596941—41no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104#10596938—21no—
105#10596938D411yescharacteristic
106C4⋊Dic37—21no—
107C4⋊Dic37—21no—
108C4⋊Dic37C2311yescharacteristic
109C4⋊Dic37C2311yescharacteristic
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113#10596936—21no—
114#10596936—21no—
115#10596936D411yescharacteristic
116C4×Dic37—21no—
117C4×Dic37—21no—
118C4×Dic37C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121#10596930—22no—
122#10596929—22no—
123C23×C37C2×D411yescharacteristic
124C22×D37—21no—
125C22×D37C2×D411yescharacteristic
126Q8×C37—21no—
127Q8×C37—21no—
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37—21no—
131Q8×C37—21no—
132Q8×C37—42no—
133Q8×C37—42no—
134Q8×C37C2×D412yes—
135Q8×C37C2×D412yes—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—42no—
143C2×C4×C37—42no—
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2411yescharacteristic
146C22⋊D37—22no—
147C22⋊D37—42no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37—21no—
151C2×Dic37C2×D411yescharacteristic
152C2×Dic37C2×D411yescharacteristic
153C2×Dic37C2×D411yescharacteristic
154D148—21no—
155D148—21no—
156D148—42no—
157C4×D37—21no—
158C4×D37—21no—
159C4×D37—42no—
160C4×D37—42no—
161Dic74—21no—
162Dic74—21no—
163Dic74—42no—
164C8×C37—21no—
165C8×C37C2×D412yes—
166#64436—21no—
167#64436—21no—
168C22×C37—21no—
169C22×C37—21no—
170C22×C37#13712yescomplemented
171C22×C37C22×D411yescharacteristic
172C2×D37—21no—
173C2×D37—21no—
174C2×D37—21no—
175C2×D37—41no—
176C2×D37—41no—
177C2×D37—41no—
178C4×C37—22no—
179C4×C37—22no—
180C4×C37—21no—
181C4×C37—41no—
182C4×C37—41no—
183C4×C37C22×D411yescharacteristic
184C4×C37H(5,𝔽2)11yescharacteristic
185Dic37—21no—
186Dic37—21no—
187Dic37—21no—
188Dic37—41no—
189Dic37—41no—
190Dic37—41no—
191#3270—371nomaximal, Sylow
192C2×C37—22no—
193C2×C37D4211yescharacteristic
194C2×C37C2×#13711yescharacteristic
195C2×C37#57811yescharacteristic
196D37—41no—
197D37—81no—
198C2×#137—371no—
199C22×Q16D3711yescharacteristic, complemented
200D4×Q8—371no—
201#548—371no—
202#497—371no—
203#470—371no—
204#465—371no—
205#464—371no—
206#462—371no—
207#452—371no—
208#451—371no—
209#451—371no—
210#448—371no—
211#441—371no—
212#435—371no—
213C37#327011yescharacteristic, complemented, Sylow
214C2×#41—371no—
215C22×Q8—371no—
216C22×Q8C2×D3711yescharacteristic
217C22×Q8C2×D3711yescharacteristic
218#137—744no—
219C2×Q16—24no—
220C2×Q16—371no—
221C2×Q16—371no—
222C2×Q16C2×D3711yescharacteristic
223C2×Q16C2×D3711yescharacteristic
224C2×Q16C2×D3711yescharacteristic
225C2×Q16C2×D3711yescharacteristic
226C2×SD16—371no—
227C2×SD16—371no—
228C2×SD16—371no—
229C2×M16—371no—
230C22×C8C2×D3711yescharacteristic
231C4⋊Q8—371no—
232C4⋊Q8—741no—
233#124—371no—
234#124—741no—
235C22⋊Q8—371no—
236C22⋊Q8—371no—
237C22⋊Q8—371no—
238C22⋊Q8—741no—
239C22⋊Q8—741no—
240C22⋊Q8—741no—
241#121—371no—
242#121—741no—
243C4×Q8—371no—
244C4×Q8—371no—
245C4×D4—371no—
246C4×D4—741no—
247C4×D4—741no—
248#106—371no—
249C4⋊C8—371no—
250#103—371no—
251#103—371no—
252#103—371no—
253#103—371no—
254#103—371no—
255#102—371no—
256C22⋊C8—371no—
257C22⋊C8—371no—
258#97—371no—
259#41—742no—
260#41—1481no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—371no—
268C2×Q8—741no—
269C2×Q8—742no—
270C2×Q8—1481no—
271C2×Q8C22×D3711yescharacteristic
272C2×Q8C22×D3711yescharacteristic
273C2×Q8C22×D3711yescharacteristic
274C2×Q8C22×D3711yescharacteristic
275C2×D4—371no—
276C2×D4—371no—
277C2×D4—741no—
278C2×D4—741no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—371no—
282C22×C4—741no—
283C22×C4—741no—
284C22×C4C22×D3711yescharacteristic
285Q16—22no—
286Q16—22no—
287Q16—22no—
288Q16—742no—
289Q16—1481no—
290Q16C22⋊D3714yescomplemented
291SD16—742no—
292SD16—742no—
293SD16—1481no—
294M16—742no—
295C2×C8—22no—
296C2×C8—371no—
297C2×C8—371no—
298C2×C8C22×D3711yescharacteristic
299C2×C8C22×D3711yescharacteristic
300C4⋊C4—371no—
301C4⋊C4—371no—
302C4⋊C4—371no—
303C4⋊C4—741no—
304C4⋊C4—741no—
305C4⋊C4—741no—
306C4⋊C4—741no—
307C4⋊C4—741no—
308C4⋊C4—741no—
309C4⋊C4—741no—
310C22⋊C4—371no—
311C22⋊C4—371no—
312C22⋊C4—741no—
313C22⋊C4—741no—
314C22⋊C4—741no—
315C22⋊C4—741no—
316C22⋊C4—741no—
317C22⋊C4—741no—
318C42—371no—
319C42—741no—
320C42—741no—
321C23—371no—
322C23—741no—
323C23D4×D3711yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—42no—
331Q8—42no—
332Q8—741no—
333Q8—741no—
334Q8—1482no—
335Q8C2×C22⋊D3712yes—
336Q8C2×C22⋊D3712yes—
337D4—742no—
338D4—741no—
339D4—741no—
340D4—1482no—
341D4—1482no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—371no—
351C2×C4—371no—
352C2×C4—371no—
353C2×C4—741no—
354C2×C4—741no—
355C2×C4—741no—
356C2×C4—741no—
357C2×C4—741no—
358C2×C4—1482no—
359C2×C4—1482no—
360C2×C4D4×D3711yescharacteristic
361C2×C4C23×D3711yescharacteristic
362C8—21no—
363C8—741no—
364C8—741no—
365C8C2×C22⋊D3712yes—
366C22—21no—
367C22—21no—
368C22—741no—
369C22—741no—
370C22—741no—
371C22—1481no—
372C22—1481no—
373C22—1481no—
374C22#1192456812yescomplemented
375C22C2×D4×D3711yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—741no—
382C4—741no—
383C4—741no—
384C4—1481no—
385C4—1481no—
386C4—1481no—
387C4C22×C22⋊D3711yescharacteristic
388C4#1192458111yescharacteristic
389C2—22no—
390C2—2961no—
391C2—1481no—
392C2D4×C22⋊D3711yescharacteristic
393C2C2×#1192456811yescharacteristic
394C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×Q16×C37C2
socleC22×C37C22×D4
prime radical#14558194C2
hypercenterC22×Q16D37
hypocenterC37#3270
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#11924568C2semidirect
2. Q8×C22⋊D37C2semidirect
4. #14557926C2semidirect
5. #14557788C2semidirect
6. #14557762C2semidirect
7. #14557757C2semidirect
8. #14557741C2semidirect
9. #14557694C2semidirect
10. #14557689C2semidirect
11. #14557687C2semidirect
12. #14557672C2semidirect
13. #14557640C2semidirect
14. #14557604C2semidirect
15. C22×Q16×C37C2semidirect
90. Q16×C37D4semidirect
170. C22×C37#137semidirect
199. C22×Q16D37semidirect
213. C37#3270semidirect
290. Q16C22⋊D37semidirect
374. C22#11924568semidirect

Maximal subgroups

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

subgroupindex
C2×#119245682
Q8×C22⋊D372
#145581942
#145579262
#145577882
#145577622
#145577572
#145577412
#145576942
#145576892
#145576872
#145576722
#145576402
#145576042
C22×Q16×C372
#327037