Finite Group Databasebeta

← #15685188

Subgroups — #15685188

Order 2944.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093228C211yesmaximal, characteristic, complemented
2#13093225C211yesmaximal, characteristic, complemented
3#13093224C211yesmaximal, characteristic, complemented
4#13092788C211yesmaximal, characteristic, complemented
5#13092682C211yesmaximal, characteristic, complemented
6#13092680C211yesmaximal, characteristic, complemented
7#13092678C211yesmaximal, characteristic, complemented
8#13092677C211yesmaximal, characteristic, complemented
9#13092600C211yesmaximal, characteristic, complemented
10#13092598C211yesmaximal, characteristic, complemented
11#13092585C211yesmaximal, characteristic, complemented
12#13092583C211yesmaximal, characteristic, complemented
13#13092534C211yesmaximal, characteristic, complemented
14#13092532C211yesmaximal, characteristic, complemented
15C23×#577C211yesmaximal, characteristic, complemented
16C23×2−1+4C2211yescharacteristic
17C23×H(5,𝔽2)C2211yescharacteristic, complemented
18#10625161C2211yescharacteristic
19#10625160C2211yescharacteristic, complemented
20C23×#137—21no—
21C23×#137C2211yescharacteristic, complemented
22C23×AGL(1,ℤ/8)—21no—
23C23×AGL(1,ℤ/8)C2211yescharacteristic
24C23×#135—21no—
25C23×#135C2211yescharacteristic
26C2×SD16×C23—21no—
27C2×SD16×C23C2211yescharacteristic, complemented
28C23×#131C2211yescharacteristic, complemented
29#10625122—21no—
30#10625122C2211yescharacteristic, complemented
31#10625122C2211yescharacteristic, complemented
32#10625121—21no—
33#10625121—21no—
34#10625121C2211yescharacteristic
35#10625120—21no—
36#10625120C2211yescharacteristic
37#10625120C2211yescharacteristic
38#10625119C2211yescharacteristic, complemented
39#10625119C2211yescharacteristic, complemented
40#10625115C2211yescharacteristic, complemented
41#10625113—21no—
42#10625113C2211yescharacteristic, complemented
43C2×#67274—21no—
44C2×#67274C2211yescharacteristic, complemented
45#10625111C2211yescharacteristic
46C2×#67273—21no—
47C2×#67273C2211yescharacteristic, complemented
48#10625103—21no—
49#10625103C2211yescharacteristic
50#10625089—21no—
51#10625087—21no—
52SD16×D23—21no—
53#10625082—21no—
54C2×#67263C2211yescharacteristic, complemented
55#10625072C2211yescharacteristic, complemented
56#10625019C2211yescharacteristic, complemented
57#10625019C2211yescharacteristic, complemented
58#10625019C2211yescharacteristic, complemented
59#10625018C2211yescharacteristic, complemented
60#10625015C2211yescharacteristic, complemented
61#10625007C2211yescharacteristic, complemented
62#10625006C2211yescharacteristic, complemented
63#10625005C2211yescharacteristic, complemented
64#10625004C2211yescharacteristic, complemented
65#10625001C2211yescharacteristic, complemented
66C8×Dic23C2211yescharacteristic, complemented
67#41×C23—21no—
68#41×C23—21no—
69#41×C23—21no—
70#41×C23—21no—
71#41×C23—41no—
72#41×C23C2311yescharacteristic
73#41×C23C2311yescharacteristic
74#41×C23C2311yescharacteristic
75C2×Q8×C23—21no—
76C2×Q8×C23—21no—
77C2×Q8×C23C2311yescharacteristic
78C2×D4×C23—21no—
79C2×D4×C23—21no—
80C2×D4×C23—41no—
81C2×D4×C23C2311yescharacteristic
82C2×C22⋊D23—41no—
83#67292—21no—
84Q8×D23—21no—
85#67290—21no—
86#67290—41no—
87D4×D23—21no—
88D4×D23—41no—
89#67288—21no—
90#67288—21no—
91#67288C2311yescharacteristic
92C2×D92—21no—
93C2×D92C2311yescharacteristic
94C2×Dic46—21no—
95C2×Dic46C2311yescharacteristic
96Q16×C23—21no—
97Q16×C23D411yescharacteristic, complemented
98SD16×C23—21no—
99SD16×C23—21no—
100SD16×C23—21no—
101SD16×C23—21no—
102SD16×C23D411yescharacteristic, complemented
103SD16×C23D411yescharacteristic, complemented
104D8×C23—21no—
105D8×C23D411yescharacteristic, complemented
106M16×C23—21no—
107M16×C23C2311yescharacteristic
108C2×C8×C23—21no—
109C2×C8×C23C2311yescharacteristic
110#67275—21no—
111#67275—21no—
112#67275—21no—
113#67275D411yescharacteristic, complemented
114#67274—21no—
115#67274—21no—
116#67274—21no—
117#67274—21no—
118#67274—21no—
119#67274D411yescharacteristic, complemented
120#67273—21no—
121#67273—21no—
122#67273—21no—
123#67273—21no—
124#67273—21no—
125#67273D411yescharacteristic, complemented
126#67272—21no—
127#67272—21no—
128#67272—21no—
129#67272D411yescharacteristic, complemented
130Dic23⋊C4—41no—
131C4×Dic23C2311yescharacteristic
132#67267—21no—
133#67267—21no—
134#67267C2311yescharacteristic
135#67267C2311yescharacteristic
136#67267C2311yescharacteristic
137C2×C23⋊C8—21no—
138C2×C23⋊C8—21no—
139C2×C23⋊C8C2311yescharacteristic
140#67263—21no—
141#67263—21no—
142#67262—21no—
143C8×D23—21no—
144C23×C23—21no—
145C23×C23—41no—
146C22×D23—21no—
147C22×D23—41no—
148Q8×C23—21no—
149Q8×C23—21no—
150Q8×C23—41no—
151Q8×C23C2×D411yescharacteristic
152Q8×C23C2×D411yescharacteristic
153Q8×C23C2×D411yescharacteristic
154D4×C23—21no—
155D4×C23—21no—
156D4×C23—21no—
157D4×C23—21no—
158D4×C23—21no—
159D4×C23—41no—
160D4×C23—41no—
161D4×C23—41no—
162D4×C23C2×D411yescharacteristic
163D4×C23C2×D411yescharacteristic
164D4×C23C2×D411yescharacteristic
165C2×C4×C23—21no—
166C2×C4×C23—21no—
167C2×C4×C23—21no—
168C2×C4×C23—21no—
169C2×C4×C23—41no—
170C2×C4×C23—41no—
171C2×C4×C23—41no—
172C2×C4×C23C2411yescharacteristic
173C22⋊D23—21no—
174C22⋊D23—41no—
175C22⋊D23—41no—
176C22⋊D23—82no—
177C2×Dic23—21no—
178C2×Dic23—21no—
179C2×Dic23—41no—
180D92—21no—
181D92—21no—
182D92—41no—
183D92C2×D411yescharacteristic
184C4×D23—21no—
185C4×D23—41no—
186C4×D23—41no—
187Dic46—21no—
188Dic46—21no—
189Dic46—41no—
190Dic46C2×D411yescharacteristic
191C8×C23—21no—
192C8×C23C2×D411yescharacteristic
193C8×C23C2×D411yescharacteristic
194C23⋊C8—21no—
195C23⋊C8—21no—
196C23⋊C8—21no—
197C23⋊C8C2×D411yescharacteristic
198C23⋊C8C2×D411yescharacteristic
199#3291—231nomaximal, Sylow
200C22×C23—21no—
201C22×C23—21no—
202C22×C23—21no—
203C22×C23—41no—
204C22×C23—81no—
205C22×C23—161no—
206C22×C23H(5,𝔽2)11yescharacteristic
207C2×D23—21no—
208C2×D23—41no—
209C2×D23—81no—
210C2×D23—161no—
211C4×C23—21no—
212C4×C23—21no—
213C4×C23—21no—
214C4×C23—41no—
215C4×C23C22×D411yescharacteristic
216C4×C23C22×D411yescharacteristic
217Dic23—22no—
218Dic23—21no—
219Dic23—41no—
220#577—231no—
221#577—231no—
222#577—231no—
223#577D2311yescharacteristic, complemented
224#492—231no—
225#471—231no—
226#471—231no—
227#471—231no—
228#471—231no—
229#456—231no—
230#456—231no—
231#453—231no—
232#453—231no—
233#443—231no—
234#443—231no—
235C2×C23—21no—
236C2×C23—41no—
237C2×C23—41no—
238C2×C23—41no—
239C2×C23—81no—
240C2×C23D4211yescharacteristic
241D23—41no—
242D23—81no—
2432−1+4—231no—
2442−1+4C2×D2311yescharacteristic
245H(5,𝔽2)—231no—
246H(5,𝔽2)C2×D2311yescharacteristic, complemented
247#137—21no—
248#137—231no—
249#137—231no—
250#137—231no—
251#137—461no—
252#137—461no—
253#137—461no—
254#137C2×D2311yescharacteristic, complemented
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—231no—
257AGL(1,ℤ/8)—231no—
258AGL(1,ℤ/8)—231no—
259AGL(1,ℤ/8)—461no—
260AGL(1,ℤ/8)—461no—
261AGL(1,ℤ/8)—461no—
262AGL(1,ℤ/8)C2×D2311yescharacteristic
263#135—21no—
264#135—231no—
265#135—461no—
266#135—461no—
267#135—461no—
268#135C2×D2311yescharacteristic
269C2×SD16—21no—
270C2×SD16—231no—
271C2×SD16—231no—
272C2×SD16—231no—
273C2×SD16—461no—
274C2×SD16—461no—
275C2×SD16—461no—
276C2×SD16C2×D2311yescharacteristic, complemented
277#131—231no—
278#131—231no—
279#131—231no—
280#131C2×D2311yescharacteristic, complemented
281C4⋊Q8—231no—
282#127—231no—
283#108—231no—
284#108—231no—
285#104—231no—
286#104—231no—
287#104—231no—
288#104—231no—
289#101—231no—
290#101—231no—
291#100—231no—
292#100—231no—
293C4×C8—231no—
294C23#329111yescharacteristic, complemented, Sylow
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—231no—
301#41—461no—
302#41—461no—
303#41—461no—
304#41—461no—
305#41—921no—
306#41C22×D2311yescharacteristic
307#41C22×D2311yescharacteristic
308#41C22×D2311yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—231no—
312C2×Q8—461no—
313C2×Q8—461no—
314C2×Q8C22×D2311yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—231no—
319C2×D4—461no—
320C2×D4—461no—
321C2×D4—921no—
322C2×D4—921no—
323C2×D4C22×D2311yescharacteristic
324Q16—21no—
325Q16—231no—
326Q16—461no—
327Q16—461no—
328Q16—461no—
329Q16C22⋊D2311yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—231no—
335SD16—231no—
336SD16—461no—
337SD16—461no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16—461no—
346SD16—461no—
347SD16—461no—
348SD16C22⋊D2311yescharacteristic, complemented
349SD16C22⋊D2311yescharacteristic, complemented
350D8—21no—
351D8—231no—
352D8—461no—
353D8—461no—
354D8—461no—
355D8C22⋊D2311yescharacteristic, complemented
356M16—21no—
357M16—231no—
358M16—231no—
359M16—231no—
360M16—461no—
361M16—461no—
362M16—461no—
363M16C22×D2311yescharacteristic
364C2×C8—21no—
365C2×C8—231no—
366C2×C8—461no—
367C2×C8—461no—
368C2×C8—461no—
369C2×C8C22×D2311yescharacteristic
370C4⋊C4—921no—
371C42—231no—
372C23—21no—
373C23—41no—
374C23—461no—
375C23—921no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—231no—
380Q8—461no—
381Q8—461no—
382Q8—921no—
383Q8D4×D2311yescharacteristic
384Q8C2×C22⋊D2311yescharacteristic
385Q8C2×C22⋊D2311yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—231no—
395D4—461no—
396D4—461no—
397D4—461no—
398D4—921no—
399D4—921no—
400D4—921no—
401D4—1842no—
402D4D4×D2311yescharacteristic
403D4C2×C22⋊D2311yescharacteristic
404D4C2×C22⋊D2311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—461no—
413C2×C4—461no—
414C2×C4—461no—
415C2×C4—921no—
416C2×C4—921no—
417C2×C4—921no—
418C2×C4C23×D2311yescharacteristic
419C8—21no—
420C8—231no—
421C8—231no—
422C8—461no—
423C8—461no—
424C8—461no—
425C8C2×C22⋊D2311yescharacteristic
426C8C2×C22⋊D2311yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—461no—
434C22—921no—
435C22—3681no—
436C22—1841no—
437C22#1062515511yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—462no—
443C4—461no—
444C4—921no—
445C4C2×D4×D2311yescharacteristic
446C4C22×C22⋊D2311yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—921no—
453C2—1841no—
454C2D4×C22⋊D2311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#577C2
socleC2×C23D42
hypercenter#577D23
hypocenterC23#3291
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #13093228C2semidirect
2. #13093225C2semidirect
3. #13093224C2semidirect
4. #13092788C2semidirect
5. #13092682C2semidirect
6. #13092680C2semidirect
7. #13092678C2semidirect
8. #13092677C2semidirect
9. #13092600C2semidirect
10. #13092598C2semidirect
11. #13092585C2semidirect
12. #13092583C2semidirect
13. #13092534C2semidirect
14. #13092532C2semidirect
15. C23×#577C2semidirect
17. C23×H(5,𝔽2)C22semidirect
19. #10625160C22semidirect
21. C23×#137C22semidirect
27. C2×SD16×C23C22semidirect
28. C23×#131C22semidirect
30. #10625122C22semidirect
31. #10625122C22semidirect
38. #10625119C22semidirect
39. #10625119C22semidirect
40. #10625115C22semidirect
42. #10625113C22semidirect
44. C2×#67274C22semidirect
47. C2×#67273C22semidirect
54. C2×#67263C22semidirect
55. #10625072C22semidirect
56. #10625019C22semidirect
57. #10625019C22semidirect
58. #10625019C22semidirect
59. #10625018C22semidirect
60. #10625015C22semidirect
61. #10625007C22semidirect
62. #10625006C22semidirect
63. #10625005C22semidirect
64. #10625004C22semidirect
65. #10625001C22semidirect
66. C8×Dic23C22semidirect
97. Q16×C23D4semidirect
102. SD16×C23D4semidirect
103. SD16×C23D4semidirect
105. D8×C23D4semidirect
113. #67275D4semidirect
119. #67274D4semidirect
125. #67273D4semidirect
129. #67272D4semidirect
223. #577D23semidirect
246. H(5,𝔽2)C2×D23semidirect
254. #137C2×D23semidirect
276. C2×SD16C2×D23semidirect
280. #131C2×D23semidirect
294. C23#3291semidirect
329. Q16C22⋊D23semidirect
348. SD16C22⋊D23semidirect
349. SD16C22⋊D23semidirect
355. D8C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130932282
#130932252
#130932242
#130927882
#130926822
#130926802
#130926782
#130926772
#130926002
#130925982
#130925852
#130925832
#130925342
#130925322
C23×#5772
#329123