Finite Group Databasebeta

← #18006167

Subgroups — #18006167

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×#11924567C211yesmaximal, characteristic, complemented
2C22×#10596942C211yesmaximal, characteristic, complemented
3#14558192C211yesmaximal, characteristic
4#14557925C211yesmaximal, characteristic, complemented
5#14557789C211yesmaximal, characteristic, complemented
6#14557764C211yesmaximal, characteristic, complemented
7#14557755C211yesmaximal, characteristic, complemented
8#14557740C211yesmaximal, characteristic, complemented
9#14557693C211yesmaximal, characteristic, complemented
10#14557689C211yesmaximal, characteristic, complemented
11#14557688C211yesmaximal, characteristic, complemented
12#14557672C211yesmaximal, characteristic, complemented
13#14557638C211yesmaximal, characteristic, complemented
14#14557605C211yesmaximal, characteristic, complemented
15D4×Q8×C37C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18#11924567—24no—
19C2×#10596942—24no—
20C2×#10596942C2211yescharacteristic
21C2×#10596942C2211yescharacteristic
22C2×#10596942C2211yescharacteristic
23C2×#10596942C2211yescharacteristic
24C2×#10596942C2211yescharacteristic
25C2×#10596942C2211yescharacteristic
26C2×#10596941C2211yescharacteristic
27C2×#10596941C2211yescharacteristic
28C2×#10596941C2211yescharacteristic
29C2×#10596934C2211yescharacteristic
30C22×#64436C2211yescharacteristic
31#11924524C2211yescharacteristic
32#11924522—21no—
33#11924515C2211yescharacteristic
34#11924514—21no—
35#11924510C2211yescharacteristic
36#11924508—21no—
37C4×Dic74C2211yescharacteristic
38#11924496—21no—
39#11924467C2211yescharacteristic
40C4⋊#64436C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924459C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924456C2211yescharacteristic
47C22⋊#64436C2211yescharacteristic
48C22⋊#64436C2211yescharacteristic
49#11924447C2211yescharacteristic
50C22×Q8×C37C2211yescharacteristic
51C22×Q8×C37C2211yescharacteristic
52C4⋊Q8×C37—21no—
53C4⋊Q8×C37C2211yescharacteristic
54C22⋊Q8×C37—21no—
55C22⋊Q8×C37—21no—
56C22⋊Q8×C37C2211yescharacteristic
57C22⋊Q8×C37C2211yescharacteristic
58C4×Q8×C37C2211yescharacteristic
59C4×D4×C37—21no—
60C4×D4×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×D4×C37D411yescharacteristic
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—
78#10596962—22no—
79#10596962—41no—
80C2×D148C2311yescharacteristic
81C2×C4×D37—21no—
82C2×Dic74—22no—
83C2×Dic74—21no—
84C2×Dic74—41no—
85C2×Dic74C2311yescharacteristic
86C2×Dic74C2311yescharacteristic
87C4⋊C4×C37—21no—
88C4⋊C4×C37—21no—
89C4⋊C4×C37—21no—
90C4⋊C4×C37—21no—
91C4⋊C4×C37—21no—
92C4⋊C4×C37D411yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊C4×C37D411yescharacteristic
97C22⋊C4×C37D411yescharacteristic
98C42×C37—21no—
99C42×C37C2311yescharacteristic
100C22⋊Dic37—21no—
101#10596942—22no—
102#10596942—22no—
103#10596942—22no—
104#10596942—22no—
105#10596942—41no—
106#10596942D414yescomplemented
107#10596941—22no—
108#10596941—22no—
109#10596941—41no—
110#10596938—21no—
111#10596938—21no—
112#10596938—21no—
113C4⋊Dic37C2311yescharacteristic
114#10596936—21no—
115#10596936—21no—
116C4×Dic37—21no—
117#10596934—22no—
118C2×#64436—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C23×C37C2×D411yescharacteristic
124C23×C37C2×D411yescharacteristic
125C22×D37—21no—
126Q8×C37—21no—
127Q8×C37—21no—
128Q8×C37—21no—
129Q8×C37—21no—
130Q8×C37—21no—
131Q8×C37—42no—
132Q8×C37—42no—
133Q8×C37C2×D412yes—
134D4×C37—22no—
135C2×C4×C37—21no—
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—21no—
143C2×C4×C37—42no—
144C2×C4×C37—42no—
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2×D411yescharacteristic
147C2×C4×C37C2×D411yescharacteristic
148C2×C4×C37C2×D411yescharacteristic
149C2×C4×C37C2411yescharacteristic
150C22⋊D37—42no—
151C22⋊D37—42no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—42no—
156D148—21no—
157D148—21no—
158C4×D37—42no—
159Dic74—21no—
160Dic74—21no—
161Dic74—21no—
162Dic74—42no—
163Dic74C2×D412yes—
164#64436—21no—
165#64436—21no—
166#64436—21no—
167#64436C2×D412yes—
168C22×C37—21no—
169C22×C37—21no—
170C22×C37—21no—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37#13712yescomplemented
174C22×C37C22×D411yescharacteristic
175C2×D37—41no—
176C2×D37—41no—
177C2×D37—41no—
178C4×C37—21no—
179C4×C37—21no—
180C4×C37—22no—
181C4×C37—21no—
182C4×C37—21no—
183C4×C37—41no—
184C4×C37—41no—
185C4×C37—41no—
186C4×C37C22×D411yescharacteristic
187C4×C37H(5,𝔽2)11yescharacteristic
188Dic37—22no—
189Dic37—41no—
190Dic37—41no—
191#3270—371nomaximal, Sylow
192C2×C37—22no—
193C2×C37—41no—
194C2×C37D4211yescharacteristic
195C2×C37C2×#13711yescharacteristic
196C2×C37#57811yescharacteristic
197D37—81no—
198C2×#137—371no—
199C22×Q16—371no—
200D4×Q8D3711yescharacteristic, complemented
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—371no—
220C2×Q16—371no—
221C2×Q16—371no—
222C2×Q16—371no—
223C2×Q16—371no—
224C2×Q16—371no—
225C2×Q16—744no—
226C2×SD16—371no—
227C2×SD16—371no—
228C2×SD16—371no—
229C2×M16—371no—
230C22×C8—371no—
231C4⋊Q8—21no—
232C4⋊Q8C2×D3711yescharacteristic
233#124—371no—
234#124—741no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—371no—
238C22⋊Q8—741no—
239C22⋊Q8C2×D3711yescharacteristic
240C22⋊Q8C2×D3711yescharacteristic
241#121—371no—
242#121—741no—
243C4×Q8—371no—
244C4×Q8C2×D3711yescharacteristic
245C4×D4—21no—
246C4×D4—741no—
247C4×D4C2×D3711yescharacteristic
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—371no—
269C2×Q8—742no—
270C2×Q8—741no—
271C2×Q8—1481no—
272C2×Q8C22×D3711yescharacteristic
273C2×Q8C22×D3711yescharacteristic
274C2×Q8C22×D3711yescharacteristic
275C2×D4—371no—
276C2×D4—741no—
277C2×D4—741no—
278C2×D4C22⋊D3711yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—741no—
282C22×C4—741no—
283C22×C4C22×D3711yescharacteristic
284C22×C4C22×D3711yescharacteristic
285Q16—374no—
286Q16—742no—
287Q16—742no—
288Q16—742no—
289Q16—742no—
290Q16—1481no—
291SD16—742no—
292SD16—742no—
293SD16—1481no—
294M16—742no—
295C2×C8—371no—
296C2×C8—371no—
297C2×C8—371no—
298C2×C8—371no—
299C2×C8—742no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—371no—
306C4⋊C4—741no—
307C4⋊C4—741no—
308C4⋊C4C22⋊D3711yescharacteristic
309C4⋊C4C22×D3711yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—741no—
313C22⋊C4—741no—
314C22⋊C4—741no—
315C22⋊C4—741no—
316C22⋊C4C22⋊D3711yescharacteristic
317C22⋊C4C22⋊D3711yescharacteristic
318C42—21no—
319C42—741no—
320C42C22×D3711yescharacteristic
321C23—741no—
322C23C2×C22⋊D3711yescharacteristic
323C23C2×C22⋊D3711yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—42no—
331Q8—372no—
332Q8—741no—
333Q8—741no—
334Q8—741no—
335Q8—1482no—
336Q8D4×D3712yes—
337D4—22no—
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—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—741no—
353C2×C4—741no—
354C2×C4—741no—
355C2×C4—1482no—
356C2×C4—1482no—
357C2×C4C2×C22⋊D3711yescharacteristic
358C2×C4C2×C22⋊D3711yescharacteristic
359C2×C4C2×C22⋊D3711yescharacteristic
360C2×C4C2×C22⋊D3711yescharacteristic
361C2×C4C23×D3711yescharacteristic
362C8—372no—
363C8—741no—
364C8—741no—
365C8—741no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—1481no—
372C22—1481no—
373C22—1481no—
374C22#1192456712yescomplemented
375C22C22×C22⋊D3711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—742no—
385C4—1481no—
386C4—1481no—
387C4C2×D4×D3711yescharacteristic
388C4#1192458111yescharacteristic
389C2—22no—
390C2—41no—
391C2—2961no—
392C2D4×C22⋊D3711yescharacteristic
393C2C2×#1192456711yescharacteristic
394C2#1455834811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingD4×Q8×C37C2
socleC22×C37C22×D4
prime radical#14558192C2
hypercenterD4×Q8D37
hypocenterC37#3270
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11924567C2semidirect
2. C22×#10596942C2semidirect
4. #14557925C2semidirect
5. #14557789C2semidirect
6. #14557764C2semidirect
7. #14557755C2semidirect
8. #14557740C2semidirect
9. #14557693C2semidirect
10. #14557689C2semidirect
11. #14557688C2semidirect
12. #14557672C2semidirect
13. #14557638C2semidirect
14. #14557605C2semidirect
15. D4×Q8×C37C2semidirect
106. #10596942D4semidirect
173. C22×C37#137semidirect
200. D4×Q8D37semidirect
213. C37#3270semidirect
374. C22#11924567semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
C22×#105969422
#145581922
#145579252
#145577892
#145577642
#145577552
#145577402
#145576932
#145576892
#145576882
#145576722
#145576382
#145576052
D4×Q8×C372
#327037