Finite Group Databasebeta

← #18004049

Subgroups — #18004049

Order 4736.

496 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×#11924558C211yesmaximal, characteristic, complemented
2C2×#11924556C211yesmaximal, characteristic, complemented
3#14558079C211yesmaximal, characteristic, complemented
4#14558001C211yesmaximal, characteristic, complemented
5#14557758C211yesmaximal, characteristic, complemented
6#14557754C211yesmaximal, characteristic, complemented
7#14557751C211yesmaximal, characteristic, complemented
8#14557747C211yesmaximal, characteristic, complemented
9#14557742C211yesmaximal, characteristic, complemented
10#14557737C211yesmaximal, characteristic, complemented
11#14557732C211yesmaximal, characteristic, complemented
12#14557727C211yesmaximal, characteristic, complemented
13C2×#11924465C211yesmaximal, characteristic, complemented
14#14557527C211yesmaximal, characteristic, complemented
15C37×#416C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18#11924558—24no—
19#11924556—24no—
20C2×Dic148C2211yescharacteristic
21C2×#10596942C2211yescharacteristic
22C2×#10596930C2211yescharacteristic
23C2×#10596930C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596941C2211yescharacteristic
26C2×D296C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C22×#64436C2211yescharacteristic
29#11924534C2211yescharacteristic
30#11924532C2211yescharacteristic
31#11924525C2211yescharacteristic
32#11924523C2211yescharacteristic
33#11924508—21no—
34#11924508—21no—
35#11924501C2211yescharacteristic
36#11924501C2211yescharacteristic
37#11924498C2211yescharacteristic
38#11924498C2211yescharacteristic
39C4×C22⋊D37—21no—
40C4×C22⋊D37—21no—
41#11924496—21no—
42#11924496—21no—
43#11924493—21no—
44C2×C4×Dic37C2211yescharacteristic
45C42×D37—21no—
46#11924465C2211yescharacteristic
47#11924465C2211yescharacteristic
48#11924465C2211yescharacteristic
49#11924465C2211yescharacteristic
50#11924459C2211yescharacteristic
51#11924459C2211yescharacteristic
52#11924456C2211yescharacteristic
53#11924456C2211yescharacteristic
54C2×#41×C37C2211yescharacteristic
55C22×C8×C37C2211yescharacteristic
56#117×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59#102×C37C2211yescharacteristic
60#102×C37C2211yescharacteristic
61#41×C37—22no—
62#41×C37—22no—
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37—21no—
65C2×D4×C37C2311yescharacteristic
66C22×C4×C37—21no—
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—21no—
69C2×C22⋊D37—21no—
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C22×Dic37D411yescharacteristic
73C22×Dic37D411yescharacteristic
74#10596962—22no—
75#10596962—22no—
76#10596962—22no—
77#10596962D414yescomplemented
78C2×D148C2311yescharacteristic
79C2×D148C2311yescharacteristic
80C2×C4×D37—21no—
81C2×C4×D37—21no—
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×Dic74C2311yescharacteristic
85C2×Dic74C2311yescharacteristic
86C2×C8×C37—22no—
87C2×C8×C37C2311yescharacteristic
88C2×C8×C37C2311yescharacteristic
89C4⋊C4×C37C2311yescharacteristic
90C4⋊C4×C37C2311yescharacteristic
91C22⋊C4×C37—21no—
92C42×C37—21no—
93C22⋊Dic37—21no—
94C22⋊Dic37—21no—
95#10596942—22no—
96#10596941—22no—
97#10596940—22no—
98#10596939—22no—
99#10596938—21no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106#10596936—21no—
107C4×Dic37—21no—
108C4×Dic37—21no—
109C4×Dic37D411yescharacteristic
110C4×Dic37D411yescharacteristic
111C4×Dic37C2311yescharacteristic
112C4×Dic37C2311yescharacteristic
113C2×#64436—22no—
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116Dic148—22no—
117D296—22no—
118#10596930—22no—
119#10596930—22no—
120C23×C37—21no—
121C23×C37C2×D411yescharacteristic
122C22×D37—21no—
123C22×D37—21no—
124Q8×C37—21no—
125Q8×C37—21no—
126D4×C37—21no—
127D4×C37—21no—
128D4×C37—42no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—42no—
133C2×C4×C37C2×D412yes—
134C2×C4×C37C2×D411yescharacteristic
135C2×C4×C37#4112yes—
136C2×C4×C37C2411yescharacteristic
137C22⋊D37—24no—
138C22⋊D37—42no—
139C22⋊D37—42no—
140C22⋊D37—42no—
141C2×Dic37—21no—
142C2×Dic37—22no—
143C2×Dic37—21no—
144C2×Dic37—41no—
145C2×Dic37C2×D411yescharacteristic
146C2×Dic37C2×D411yescharacteristic
147C2×Dic37C2×D411yescharacteristic
148C2×Dic37C2×D411yescharacteristic
149D148—21no—
150D148—21no—
151D148—21no—
152D148C2×D412yes—
153C4×D37—24no—
154C4×D37—42no—
155C4×D37—42no—
156C4×D37—42no—
157Dic74—21no—
158Dic74—21no—
159Dic74—21no—
160Dic74C2×D412yes—
161C8×C37—21no—
162C8×C37—21no—
163#64436—21no—
164#64436—21no—
165C22×C37—21no—
166C22×C37—21no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—41no—
170C22×C37#12112yes—
171C22×C37C22×D411yescharacteristic
172C2×D37—22no—
173C2×D37—41no—
174C2×D37—41no—
175C2×D37—41no—
176C2×D37—41no—
177C2×D37—41no—
178C4×C37—41no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37#12112yes—
182C4×C37C22×D411yescharacteristic
183C4×C37C2×#4111yescharacteristic
184Dic37—22no—
185Dic37—21no—
186Dic37—21no—
187Dic37—21no—
188Dic37—41no—
189Dic37#13512yescomplemented
190#3035—371nomaximal, Sylow
191C2×C37—22no—
192C2×C37—81no—
193C2×C37C2×#12111yescharacteristic
194C2×C37C2×#13511yescharacteristic
195C2×C37#57511yescharacteristic
196D37—42no—
197D37—81no—
198C2×#135—371no—
199C2×#135—371no—
200#532—371no—
201C4×#41—371no—
202#464—371no—
203#464—371no—
204#463—371no—
205#463—371no—
206#462—371no—
207#461—371no—
208#460—371no—
209#459—371no—
210C2×C4⋊C8—371no—
211#416—371no—
212#416D3711yescharacteristic, complemented
213C37#303511yescharacteristic, complemented, Sylow
214C2×#41—371no—
215C2×#41—371no—
216C2×#41C2×D3711yescharacteristic
217#135—744no—
218#135—744no—
219C2×Q16—371no—
220C2×Q16—371no—
221C2×SD16—371no—
222C2×SD16—371no—
223C2×SD16—371no—
224C2×SD16—371no—
225C2×D8—371no—
226C2×D8—371no—
227C22×C8—371no—
228C22×C8C2×D3711yescharacteristic
229C4⋊Q8—371no—
230#127—371no—
231#124—371no—
232#124—371no—
233#121—741no—
234#121—741no—
235C4×Q8—371no—
236C4×Q8—371no—
237C4×D4—371no—
238C4×D4—371no—
239C4×D4—741no—
240C4×D4—741no—
241C4×D4—741no—
242C4×D4—741no—
243#117—741no—
244#117C2×D3711yescharacteristic
245C2×C42—371no—
246C2×C42—741no—
247C4⋊C8—371no—
248C4⋊C8—371no—
249C4⋊C8—371no—
250C4⋊C8—371no—
251#103—371no—
252#103—371no—
253#103C2×D3711yescharacteristic
254#103C2×D3711yescharacteristic
255#102—371no—
256#102—371no—
257#102C2×D3711yescharacteristic
258#102C2×D3711yescharacteristic
259#41—22no—
260#41—22no—
261#41—374no—
262#41—742no—
263#41—742no—
264#41—742no—
265C2×Q8—371no—
266C2×Q8—371no—
267C2×Q8C22×D3711yescharacteristic
268C2×D4—21no—
269C2×D4—371no—
270C2×D4—371no—
271C2×D4—741no—
272C2×D4—741no—
273C2×D4—741no—
274C2×D4—741no—
275C2×D4C22×D3711yescharacteristic
276C22×C4—21no—
277C22×C4—371no—
278C22×C4—371no—
279C22×C4—741no—
280C22×C4—741no—
281C22×C4—741no—
282C22×C4—741no—
283C22×C4C22×D3711yescharacteristic
284Q16—742no—
285Q16—742no—
286SD16—742no—
287SD16—742no—
288SD16—742no—
289SD16—742no—
290D8—742no—
291D8—742no—
292C2×C8—22no—
293C2×C8—371no—
294C2×C8—371no—
295C2×C8—742no—
296C2×C8C22×D3711yescharacteristic
297C2×C8C22×D3711yescharacteristic
298C4⋊C4—741no—
299C4⋊C4—741no—
300C4⋊C4—741no—
301C4⋊C4—741no—
302C4⋊C4C22×D3711yescharacteristic
303C4⋊C4C22×D3711yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—741no—
306C22⋊C4—741no—
307C22⋊C4—741no—
308C22⋊C4—741no—
309C22⋊C4—741no—
310C22⋊C4—741no—
311C42—21no—
312C42—371no—
313C42—371no—
314C42—371no—
315C42—371no—
316C42—741no—
317C42—741no—
318C23—21no—
319C23—741no—
320C23—741no—
321C23D4×D3711yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—372no—
325Q8—741no—
326Q8—741no—
327Q8—741no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—372no—
332D4—744no—
333D4—741no—
334D4—741no—
335D4—741no—
336D4—1482no—
337D4—1482no—
338D4—1482no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—371no—
344C2×C4—371no—
345C2×C4—371no—
346C2×C4—371no—
347C2×C4—742no—
348C2×C4—741no—
349C2×C4—744no—
350C2×C4—741no—
351C2×C4—1482no—
352C2×C4—1482no—
353C2×C4—1481no—
354C2×C4—1482no—
355C2×C4#1059696212yes—
356C2×C4D4×D3712yes—
357C2×C4D4×D3711yescharacteristic
358C2×C4C23×D3711yescharacteristic
359C8—21no—
360C8—21no—
361C8—741no—
362C8—741no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—742no—
369C22—1481no—
370C22—1481no—
371C22—1481no—
372C22—1481no—
373C22—1481no—
374C22#1192450912yes—
375C22C2×D4×D3711yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—372no—
380C4—742no—
381C4—741no—
382C4—741no—
383C4—741no—
384C4—1481no—
385C4#1192450912yes—
386C4C2×D4×D3711yescharacteristic
387C4C2×#1059696211yescharacteristic
388C2—22no—
389C2—81no—
390C2—2961no—
391C2—1482no—
392C2C2×#1192450911yescharacteristic
393C2#135×D3711yescharacteristic
394C2#1455833011yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#416C2
socleC22×C37C22×D4
hypercenter#416D37
hypocenterC37#3035
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#11924558C2semidirect
2. C2×#11924556C2semidirect
3. #14558079C2semidirect
4. #14558001C2semidirect
5. #14557758C2semidirect
6. #14557754C2semidirect
7. #14557751C2semidirect
8. #14557747C2semidirect
9. #14557742C2semidirect
10. #14557737C2semidirect
11. #14557732C2semidirect
12. #14557727C2semidirect
13. C2×#11924465C2semidirect
14. #14557527C2semidirect
15. C37×#416C2semidirect
77. #10596962D4semidirect
189. Dic37#135semidirect
212. #416D37semidirect
213. C37#3035semidirect

Maximal subgroups

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

subgroupindex
C2×#119245582
C2×#119245562
#145580792
#145580012
#145577582
#145577542
#145577512
#145577472
#145577422
#145577372
#145577322
#145577272
C2×#119244652
#145575272
C37×#4162
#303537