Finite Group Databasebeta

← #15685164

Subgroups — #15685164

Order 2944.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093229C211yesmaximal, characteristic, complemented
2#13093224C211yesmaximal, characteristic, complemented
3#13093222C211yesmaximal, characteristic, complemented
4#13093219C211yesmaximal, characteristic, complemented
5#13092806C211yesmaximal, characteristic, complemented
6#13092688C211yesmaximal, characteristic, complemented
7#13092687C211yesmaximal, characteristic, complemented
8#13092681C211yesmaximal, characteristic, complemented
9#13092680C211yesmaximal, characteristic, complemented
10#13092596C211yesmaximal, characteristic, complemented
11#13092591C211yesmaximal, characteristic, complemented
12#13092586C211yesmaximal, characteristic, complemented
13#13092586C211yesmaximal, characteristic, complemented
14#13092540C211yesmaximal, characteristic, complemented
15C23×#444C211yesmaximal, characteristic, complemented
16#10625161C2211yescharacteristic, complemented
17#10625160C2211yescharacteristic
18#10625160C2211yescharacteristic, complemented
19#10625160C2211yescharacteristic, complemented
20C23×#135C2211yescharacteristic
21C23×#131C2211yescharacteristic, complemented
22C23×#131C2211yescharacteristic, complemented
23#10625122C2211yescharacteristic, complemented
24#10625120C2211yescharacteristic
25#10625120C2211yescharacteristic, complemented
26#10625120C2211yescharacteristic, complemented
27#10625090—21no—
28#10625089—21no—
29#10625087—21no—
30#10625085—21no—
31#10625085—21no—
32SD16×D23—21no—
33#10625082—21no—
34D8×D23—21no—
35#10625080—21no—
36#10625080C2211yescharacteristic, complemented
37#10625079—21no—
38#10625079—21no—
39#10625079—21no—
40#10625079C2211yescharacteristic
41#10625079C2211yescharacteristic, complemented
42#10625079C2211yescharacteristic, complemented
43#10625075—21no—
44#10625075—21no—
45#10625075C2211yescharacteristic
46C2×D184—21no—
47C2×D184C2211yescharacteristic, complemented
48C2×D184C2211yescharacteristic, complemented
49C2×#67263—21no—
50C2×#67263C2211yescharacteristic, complemented
51C2×#67263C2211yescharacteristic, complemented
52#10625072C2211yescharacteristic, complemented
53#10625072C2211yescharacteristic, complemented
54#10625046C2211yescharacteristic, complemented
55#10625045C2211yescharacteristic, complemented
56C23×#108C2211yescharacteristic, complemented
57C23×#104C2211yescharacteristic, complemented
58C23×#104C2211yescharacteristic, complemented
59C23×#97C2211yescharacteristic, complemented
60#10625006C2211yescharacteristic, complemented
61#10625005C2211yescharacteristic, complemented
62#10625005C2211yescharacteristic, complemented
63#10625005C2211yescharacteristic, complemented
64#10625001C2211yescharacteristic, complemented
65#10624987C2211yescharacteristic, complemented
66#10624987C2211yescharacteristic, complemented
67#41×C23C2311yescharacteristic
68#41×C23C2311yescharacteristic
69#67292—21no—
70#67292—21no—
71#67292—21no—
72Q8×D23—21no—
73#67290—21no—
74#67290—41no—
75D4×D23—21no—
76D4×D23—21no—
77D4×D23—21no—
78D4×D23—41no—
79D4×D23—41no—
80D4×D23—41no—
81#67288—21no—
82#67288—21no—
83#67288—21no—
84#67288—21no—
85#67288C2311yescharacteristic
86#67288C2311yescharacteristic
87C2×D92—21no—
88C2×D92—21no—
89C2×D92—21no—
90C2×D92—41no—
91C2×D92C2311yescharacteristic
92C2×D92C2311yescharacteristic
93C2×D92C2311yescharacteristic
94C2×Dic46—21no—
95C2×Dic46C2311yescharacteristic
96Q16×C23D411yescharacteristic, complemented
97SD16×C23D411yescharacteristic, complemented
98SD16×C23D411yescharacteristic, complemented
99D8×C23D411yescharacteristic, complemented
100M16×C23—21no—
101M16×C23—21no—
102M16×C23C2311yescharacteristic
103M16×C23C2311yescharacteristic
104C2×C8×C23—21no—
105C2×C8×C23—21no—
106C2×C8×C23C2311yescharacteristic
107C2×C8×C23C2311yescharacteristic
108C42×C23C2311yescharacteristic
109#67275—21no—
110#67274—21no—
111#67274—21no—
112#67274—21no—
113#67273—21no—
114#67272—21no—
115#67272—21no—
116#67272—21no—
117(C2×D23)⋊C4—41no—
118#67267C2311yescharacteristic
119#67267C2311yescharacteristic
120Dic92—21no—
121Dic92D411yescharacteristic, complemented
122D184—21no—
123D184—21no—
124D184—21no—
125D184—21no—
126D184—21no—
127D184—21no—
128D184—21no—
129D184D411yescharacteristic, complemented
130#67263—21no—
131#67263—21no—
132#67263—21no—
133#67263—21no—
134#67263—21no—
135#67263—21no—
136#67263—21no—
137#67263—21no—
138#67263D411yescharacteristic, complemented
139#67263D411yescharacteristic, complemented
140#67262—21no—
141#67262—21no—
142C8×D23—21no—
143C8×D23—21no—
144C22×D23—21no—
145C22×D23—21no—
146C22×D23—21no—
147C22×D23—41no—
148C22×D23—41no—
149C22×D23—41no—
150Q8×C23C2×D411yescharacteristic
151Q8×C23C2×D411yescharacteristic
152D4×C23—21no—
153D4×C23—21no—
154D4×C23C2×D411yescharacteristic
155D4×C23C2×D411yescharacteristic
156C2×C4×C23—21no—
157C2×C4×C23—21no—
158C2×C4×C23—21no—
159C2×C4×C23C2411yescharacteristic
160C22⋊D23—21no—
161C22⋊D23—21no—
162C22⋊D23—41no—
163C22⋊D23—41no—
164C22⋊D23—41no—
165C22⋊D23—41no—
166C2×Dic23—21no—
167C2×Dic23—41no—
168D92—21no—
169D92—21no—
170D92—21no—
171D92—21no—
172D92—21no—
173D92—21no—
174D92—41no—
175D92—41no—
176D92—41no—
177D92—82no—
178D92C2×D411yescharacteristic
179D92C2×D411yescharacteristic
180C4×D23—21no—
181C4×D23—21no—
182C4×D23—41no—
183C4×D23—41no—
184C4×D23—41no—
185C4×D23—41no—
186Dic46—21no—
187Dic46—21no—
188Dic46—41no—
189Dic46C2×D411yescharacteristic
190Dic46C2×D411yescharacteristic
191C8×C23—21no—
192C8×C23—21no—
193C8×C23C2×D411yescharacteristic
194C8×C23C2×D411yescharacteristic
195C8×C23C2×D411yescharacteristic
196C8×C23C2×D411yescharacteristic
197C23⋊C8—21no—
198C23⋊C8—21no—
199#3288—231nomaximal, Sylow
200C22×C23—21no—
201C22×C23—21no—
202C22×C23H(5,𝔽2)11yescharacteristic
203C2×D23—21no—
204C2×D23—21no—
205C2×D23—41no—
206C2×D23—41no—
207C2×D23—41no—
208C2×D23—81no—
209C2×D23—81no—
210C2×D23—81no—
211C2×D23—161no—
212C2×D23—161no—
213C2×D23—161no—
214C4×C23—21no—
215C4×C23—21no—
216C4×C23—41no—
217C4×C23C22×D411yescharacteristic
218C4×C23C22×D411yescharacteristic
219Dic23—21no—
220Dic23—21no—
221Dic23—41no—
222#577—231no—
223#577—231no—
224#576—231no—
225#576—231no—
226#496—231no—
227#472—231no—
228#472—231no—
229#471—231no—
230#471—231no—
231#455—231no—
232#454—231no—
233#453—231no—
234#453—231no—
235#444—231no—
236#444D2311yescharacteristic, complemented
237C2×C23—21no—
238C2×C23—41no—
239C2×C23—41no—
240C2×C23D4211yescharacteristic
241D23—41no—
242D23—41no—
243D23—81no—
244D23—81no—
245D23—81no—
2462−1+4—231no—
247H(5,𝔽2)—231no—
248H(5,𝔽2)—231no—
249H(5,𝔽2)—231no—
250#137—231no—
251#137—231no—
252#137—461no—
253#137—461no—
254AGL(1,ℤ/8)—231no—
255AGL(1,ℤ/8)—231no—
256AGL(1,ℤ/8)—231no—
257AGL(1,ℤ/8)—231no—
258AGL(1,ℤ/8)—231no—
259AGL(1,ℤ/8)—231no—
260AGL(1,ℤ/8)—461no—
261AGL(1,ℤ/8)—461no—
262AGL(1,ℤ/8)—461no—
263AGL(1,ℤ/8)—461no—
264AGL(1,ℤ/8)—461no—
265AGL(1,ℤ/8)—461no—
266#135—231no—
267#135—461no—
268#135—461no—
269#135—461no—
270#135—461no—
271#135C2×D2311yescharacteristic
272C2×SD16—231no—
273C2×SD16—231no—
274C2×SD16—461no—
275C2×SD16—461no—
276C2×D8—231no—
277C2×D8—231no—
278C2×D8—461no—
279C2×D8—461no—
280#131—231no—
281#131—231no—
282#131C2×D2311yescharacteristic, complemented
283#131C2×D2311yescharacteristic, complemented
284#127—231no—
285#124—231no—
286#108—231no—
287#108C2×D2311yescharacteristic, complemented
288#104—231no—
289#104—231no—
290#104C2×D2311yescharacteristic, complemented
291#104C2×D2311yescharacteristic, complemented
292#101—231no—
293#100—231no—
294#100—231no—
295#100—231no—
296#97C2×D2311yescharacteristic, complemented
297C23#328811yescharacteristic, complemented, Sylow
298#41—231no—
299#41—231no—
300#41—461no—
301#41—461no—
302#41—461no—
303#41—461no—
304#41—461no—
305#41—461no—
306#41—461no—
307#41—461no—
308#41—921no—
309#41C22×D2311yescharacteristic
310#41C22×D2311yescharacteristic
311C2×Q8—231no—
312C2×Q8—461no—
313C2×Q8—461no—
314C2×D4—231no—
315C2×D4—231no—
316C2×D4—231no—
317C2×D4—461no—
318C2×D4—461no—
319C2×D4—461no—
320C2×D4—461no—
321C2×D4—461no—
322C2×D4—461no—
323C2×D4—921no—
324C2×D4—921no—
325C2×D4—921no—
326C2×D4—921no—
327Q16—231no—
328Q16—461no—
329Q16—461no—
330Q16D9211yescharacteristic, complemented
331SD16—231no—
332SD16—231no—
333SD16—461no—
334SD16—461no—
335SD16—461no—
336SD16—461no—
337SD16—461no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16D9211yescharacteristic, complemented
346SD16D9211yescharacteristic, complemented
347D8—231no—
348D8—461no—
349D8—461no—
350D8—461no—
351D8—461no—
352D8—461no—
353D8—461no—
354D8—461no—
355D8—461no—
356D8—461no—
357D8—461no—
358D8D9211yescharacteristic, complemented
359M16—21no—
360M16—21no—
361M16—231no—
362M16—231no—
363M16—461no—
364M16—461no—
365M16C22×D2311yescharacteristic
366M16C22×D2311yescharacteristic
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—461no—
370C2×C8—461no—
371C2×C8C22×D2311yescharacteristic
372C2×C8C22×D2311yescharacteristic
373C22⋊C4—921no—
374C42C22×D2311yescharacteristic
375C23—461no—
376C23—461no—
377C23—461no—
378C23—921no—
379C23—921no—
380C23—921no—
381Q8—231no—
382Q8—231no—
383Q8—461no—
384Q8—461no—
385Q8—921no—
386Q8C2×D9211yescharacteristic
387Q8C2×D9211yescharacteristic
388D4—21no—
389D4—21no—
390D4—231no—
391D4—231no—
392D4—461no—
393D4—461no—
394D4—461no—
395D4—461no—
396D4—461no—
397D4—461no—
398D4—461no—
399D4—461no—
400D4—921no—
401D4—921no—
402D4—921no—
403D4—921no—
404D4—921no—
405D4—921no—
406D4—921no—
407D4—1842no—
408D4C2×D9211yescharacteristic
409D4C2×D9211yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—461no—
414C2×C4—461no—
415C2×C4—461no—
416C2×C4—921no—
417C2×C4—921no—
418C2×C4—921no—
419C2×C4—921no—
420C2×C4—921no—
421C2×C4C23×D2311yescharacteristic
422C8—21no—
423C8—21no—
424C8—461no—
425C8—461no—
426C8C2×D9211yescharacteristic
427C8C2×D9211yescharacteristic
428C8D4×D2311yescharacteristic
429C8D4×D2311yescharacteristic
430C22—21no—
431C22—21no—
432C22—461no—
433C22—461no—
434C22—921no—
435C22—921no—
436C22—921no—
437C22—3681no—
438C22—3681no—
439C22—3681no—
440C22—1841no—
441C22—1841no—
442C22—1841no—
443C22#1062516011yescharacteristic
444C4—21no—
445C4—21no—
446C4—41no—
447C4—461no—
448C4—461no—
449C4—921no—
450C4C22×D9211yescharacteristic
451C4C2×D4×D2311yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—921no—
456C2—921no—
457C2—1841no—
458C2—1841no—
459C2—1841no—
460C2D4×D9211yescharacteristic
subgroupG/H
centerC2D4×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#444C2
socleC2×C23D42
hypercenter#444D23
hypocenterC23#3288
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #13093229C2semidirect
2. #13093224C2semidirect
3. #13093222C2semidirect
4. #13093219C2semidirect
5. #13092806C2semidirect
6. #13092688C2semidirect
7. #13092687C2semidirect
8. #13092681C2semidirect
9. #13092680C2semidirect
10. #13092596C2semidirect
11. #13092591C2semidirect
12. #13092586C2semidirect
13. #13092586C2semidirect
14. #13092540C2semidirect
15. C23×#444C2semidirect
16. #10625161C22semidirect
18. #10625160C22semidirect
19. #10625160C22semidirect
21. C23×#131C22semidirect
22. C23×#131C22semidirect
23. #10625122C22semidirect
25. #10625120C22semidirect
26. #10625120C22semidirect
36. #10625080C22semidirect
41. #10625079C22semidirect
42. #10625079C22semidirect
47. C2×D184C22semidirect
48. C2×D184C22semidirect
50. C2×#67263C22semidirect
51. C2×#67263C22semidirect
52. #10625072C22semidirect
53. #10625072C22semidirect
54. #10625046C22semidirect
55. #10625045C22semidirect
56. C23×#108C22semidirect
57. C23×#104C22semidirect
58. C23×#104C22semidirect
59. C23×#97C22semidirect
60. #10625006C22semidirect
61. #10625005C22semidirect
62. #10625005C22semidirect
63. #10625005C22semidirect
64. #10625001C22semidirect
65. #10624987C22semidirect
66. #10624987C22semidirect
96. Q16×C23D4semidirect
97. SD16×C23D4semidirect
98. SD16×C23D4semidirect
99. D8×C23D4semidirect
121. Dic92D4semidirect
129. D184D4semidirect
138. #67263D4semidirect
139. #67263D4semidirect
236. #444D23semidirect
282. #131C2×D23semidirect
283. #131C2×D23semidirect
287. #108C2×D23semidirect
290. #104C2×D23semidirect
291. #104C2×D23semidirect
296. #97C2×D23semidirect
297. C23#3288semidirect
330. Q16D92semidirect
345. SD16D92semidirect
346. SD16D92semidirect
358. D8D92semidirect

Maximal subgroups

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

subgroupindex
#130932292
#130932242
#130932222
#130932192
#130928062
#130926882
#130926872
#130926812
#130926802
#130925962
#130925912
#130925862
#130925402
C23×#4442
#328823