Finite Group Databasebeta

← #15685189

Subgroups — #15685189

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#13093229C211yesmaximal, characteristic, complemented
2#13093227C211yesmaximal, characteristic, complemented
3#13093226C211yesmaximal, characteristic, complemented
4#13093223C211yesmaximal, characteristic, complemented
5#13092788C211yesmaximal, characteristic, complemented
6#13092683C211yesmaximal, characteristic, complemented
7#13092681C211yesmaximal, characteristic, complemented
8#13092679C211yesmaximal, characteristic, complemented
9#13092602C211yesmaximal, characteristic, complemented
10#13092598C211yesmaximal, characteristic, complemented
11#13092587C211yesmaximal, characteristic, complemented
12#13092583C211yesmaximal, characteristic, complemented
13#13092533C211yesmaximal, characteristic, complemented
14#13092532C211yesmaximal, characteristic, complemented
15C23×#471C211yesmaximal, characteristic, complemented
16#10625161C2211yescharacteristic
17#10625160C2211yescharacteristic, complemented
18#10625158C2211yescharacteristic
19#10625155C2211yescharacteristic, complemented
20C23×#137C2211yescharacteristic, complemented
21C23×AGL(1,ℤ/8)C2211yescharacteristic
22C2×SD16×C23C2211yescharacteristic, complemented
23C23×#131C2211yescharacteristic, complemented
24#10625121C2211yescharacteristic
25#10625115C2211yescharacteristic, complemented
26#10625113C2211yescharacteristic, complemented
27C2×#67274C2211yescharacteristic, complemented
28#10625111C2211yescharacteristic
29C2×#67273C2211yescharacteristic, complemented
30#10625103C2211yescharacteristic
31#10625090—21no—
32#10625089—21no—
33#10625087—21no—
34#10625086—21no—
35#10625086—21no—
36#10625085—21no—
37#10625085—21no—
38SD16×D23—21no—
39SD16×D23—21no—
40SD16×D23—21no—
41#10625083—21no—
42#10625082—21no—
43#10625080—21no—
44#10625080C2211yescharacteristic, complemented
45#10625080C2211yescharacteristic, complemented
46#10625079—21no—
47#10625079C2211yescharacteristic
48#10625079C2211yescharacteristic
49#10625078C2211yescharacteristic, complemented
50#10625078C2211yescharacteristic, complemented
51#10625075—21no—
52#10625075C2211yescharacteristic
53C2×#67263—21no—
54C2×#67263C2211yescharacteristic, complemented
55#10625072C2211yescharacteristic, complemented
56C23×#108C2211yescharacteristic, complemented
57C23×#101C2211yescharacteristic, complemented
58C23×#100C2211yescharacteristic, complemented
59#10625019C2211yescharacteristic, complemented
60#10625007C2211yescharacteristic, complemented
61#10625007C2211yescharacteristic, complemented
62#10625007C2211yescharacteristic, complemented
63#10625006C2211yescharacteristic, complemented
64#10625005C2211yescharacteristic, complemented
65#10625004C2211yescharacteristic, complemented
66C8×Dic23C2211yescharacteristic, complemented
67#41×C23C2311yescharacteristic
68C2×Q8×C23C2311yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C2×C22⋊D23—41no—
71C2×C22⋊D23—41no—
72#67292—21no—
73#67292—21no—
74#67292—21no—
75Q8×D23—21no—
76Q8×D23—21no—
77Q8×D23—21no—
78#67290—21no—
79#67290—21no—
80#67290—21no—
81#67290—41no—
82D4×D23—21no—
83D4×D23—21no—
84D4×D23—21no—
85D4×D23—41no—
86#67288—21no—
87#67288—21no—
88#67288—41no—
89#67288C2311yescharacteristic
90#67288C2311yescharacteristic
91#67288C2311yescharacteristic
92C2×D92—21no—
93C2×D92C2311yescharacteristic
94C2×Dic46—21no—
95C2×Dic46C2311yescharacteristic
96Q16×C23—21no—
97SD16×C23—21no—
98SD16×C23—21no—
99SD16×C23—21no—
100SD16×C23—21no—
101D8×C23—21no—
102M16×C23—21no—
103M16×C23C2311yescharacteristic
104M16×C23C2311yescharacteristic
105M16×C23C2311yescharacteristic
106C2×C8×C23—21no—
107C2×C8×C23C2311yescharacteristic
108#67275—21no—
109#67275D411yescharacteristic, complemented
110#67274—21no—
111#67274—21no—
112#67274—21no—
113#67274D411yescharacteristic, complemented
114#67273—21no—
115#67273—21no—
116#67273—21no—
117#67273D411yescharacteristic, complemented
118#67272—21no—
119#67272D411yescharacteristic, complemented
120Dic23⋊C4—41no—
121C4×Dic23C2311yescharacteristic
122#67267C2311yescharacteristic
123C2×C23⋊C8C2311yescharacteristic
124Dic92—21no—
125Dic92—21no—
126Dic92D411yescharacteristic, complemented
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#67263D411yescharacteristic, complemented
137#67263D411yescharacteristic, complemented
138#67262—21no—
139#67262—21no—
140#67262—21no—
141C8×D23—21no—
142C8×D23—21no—
143C8×D23—21no—
144C23×C23—21no—
145C22×D23—21no—
146C22×D23—41no—
147C22×D23—41no—
148Q8×C23—21no—
149Q8×C23—21no—
150Q8×C23C2×D411yescharacteristic
151D4×C23—21no—
152D4×C23—21no—
153D4×C23—21no—
154D4×C23C2×D411yescharacteristic
155C2×C4×C23—21no—
156C2×C4×C23—21no—
157C2×C4×C23C2411yescharacteristic
158C22⋊D23—21no—
159C22⋊D23—21no—
160C22⋊D23—21no—
161C22⋊D23—41no—
162C22⋊D23—41no—
163C22⋊D23—41no—
164C22⋊D23—41no—
165C22⋊D23—82no—
166C2×Dic23—21no—
167C2×Dic23—21no—
168C2×Dic23—41no—
169C2×Dic23—41no—
170D92—21no—
171D92—21no—
172D92—41no—
173D92—41no—
174D92C2×D411yescharacteristic
175D92C2×D411yescharacteristic
176D92C2×D411yescharacteristic
177C4×D23—21no—
178C4×D23—21no—
179C4×D23—21no—
180C4×D23—41no—
181C4×D23—41no—
182C4×D23—41no—
183C4×D23—41no—
184Dic46—21no—
185Dic46—21no—
186Dic46—41no—
187Dic46—41no—
188Dic46C2×D411yescharacteristic
189Dic46C2×D411yescharacteristic
190Dic46C2×D411yescharacteristic
191C8×C23—21no—
192C8×C23—21no—
193C8×C23—21no—
194C8×C23C2×D411yescharacteristic
195C8×C23C2×D411yescharacteristic
196C23⋊C8—21no—
197C23⋊C8C2×D411yescharacteristic
198C23⋊C8C2×D411yescharacteristic
199#3291—231nomaximal, Sylow
200C22×C23—21no—
201C22×C23—41no—
202C22×C23—81no—
203C22×C23H(5,𝔽2)11yescharacteristic
204C2×D23—21no—
205C2×D23—21no—
206C2×D23—21no—
207C2×D23—41no—
208C2×D23—81no—
209C2×D23—161no—
210C2×D23—161no—
211C4×C23—21no—
212C4×C23—41no—
213C4×C23C22×D411yescharacteristic
214C4×C23C22×D411yescharacteristic
215Dic23—22no—
216Dic23—21no—
217Dic23—21no—
218Dic23—21no—
219Dic23—41no—
220#577—231no—
221#577—231no—
222#577—231no—
223#577—231no—
224#492—231no—
225#471—231no—
226#471—231no—
227#471—231no—
228#471D2311yescharacteristic, complemented
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—81no—
238C2×C23D4211yescharacteristic
239D23—41no—
240D23—41no—
241D23—41no—
242D23—81no—
2432−1+4—231no—
2442−1+4—231no—
245H(5,𝔽2)—231no—
246H(5,𝔽2)—231no—
247#137—231no—
248#137—231no—
249#137—231no—
250#137—461no—
251#137—461no—
252#137—461no—
253#137—461no—
254#137C2×D2311yescharacteristic, complemented
255AGL(1,ℤ/8)—231no—
256AGL(1,ℤ/8)—231no—
257AGL(1,ℤ/8)—231no—
258AGL(1,ℤ/8)—461no—
259AGL(1,ℤ/8)—461no—
260AGL(1,ℤ/8)—461no—
261AGL(1,ℤ/8)—461no—
262AGL(1,ℤ/8)C2×D2311yescharacteristic
263#135—231no—
264#135—231no—
265#135—461no—
266#135—461no—
267#135—461no—
268#135—461no—
269C2×SD16—231no—
270C2×SD16—231no—
271C2×SD16—231no—
272C2×SD16—461no—
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#108C2×D2311yescharacteristic, complemented
285#104—231no—
286#104—231no—
287#104—231no—
288#104—231no—
289#101—231no—
290#101C2×D2311yescharacteristic, complemented
291#100—231no—
292#100C2×D2311yescharacteristic, complemented
293C4×C8—231no—
294C23#329111yescharacteristic, complemented, Sylow
295#41—231no—
296#41—231no—
297#41—231no—
298#41—461no—
299#41—461no—
300#41—461no—
301#41—461no—
302#41—461no—
303#41—461no—
304#41—461no—
305#41—461no—
306#41—921no—
307#41—921no—
308#41C22×D2311yescharacteristic
309C2×Q8—231no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8—461no—
314C2×Q8C22×D2311yescharacteristic
315C2×D4—231no—
316C2×D4—461no—
317C2×D4—461no—
318C2×D4—461no—
319C2×D4—461no—
320C2×D4—921no—
321C2×D4—921no—
322C2×D4—921no—
323C2×D4C22×D2311yescharacteristic
324Q16—21no—
325Q16—231no—
326Q16—231no—
327Q16—461no—
328Q16—461no—
329Q16—461no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—231no—
335SD16—231no—
336SD16—231no—
337SD16—231no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16—461no—
346SD16—461no—
347SD16—461no—
348SD16—461no—
349SD16—461no—
350D8—21no—
351D8—231no—
352D8—231no—
353D8—461no—
354D8—461no—
355D8—461no—
356M16—21no—
357M16—231no—
358M16—461no—
359M16—461no—
360M16—461no—
361M16C22×D2311yescharacteristic
362M16C22×D2311yescharacteristic
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—461no—
374C23—921no—
375C23—921no—
376Q8—21no—
377Q8—21no—
378Q8—231no—
379Q8—231no—
380Q8—231no—
381Q8—461no—
382Q8—461no—
383Q8—921no—
384Q8—921no—
385Q8D4×D2311yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—231no—
390D4—231no—
391D4—231no—
392D4—461no—
393D4—461no—
394D4—461no—
395D4—461no—
396D4—461no—
397D4—921no—
398D4—921no—
399D4—921no—
400D4—921no—
401D4—921no—
402D4—921no—
403D4—1842no—
404D4D4×D2311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—461no—
408C2×C4—461no—
409C2×C4—461no—
410C2×C4—461no—
411C2×C4—461no—
412C2×C4—921no—
413C2×C4—921no—
414C2×C4—921no—
415C2×C4—921no—
416C2×C4—921no—
417C2×C4—921no—
418C2×C4C23×D2311yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—231no—
423C8—231no—
424C8—461no—
425C8D4×D2311yescharacteristic
426C8D4×D2311yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—461no—
431C22—461no—
432C22—461no—
433C22—921no—
434C22—3681no—
435C22—3681no—
436C22—1841no—
437C22#1062516011yescharacteristic
438C4—21no—
439C4—41no—
440C4—462no—
441C4—461no—
442C4—461no—
443C4—461no—
444C4—921no—
445C4C2×D4×D2311yescharacteristic
446C4C2×D4×D2311yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—921no—
451C2—921no—
452C2—921no—
453C2—1841no—
454C2#1309305111yescharacteristic
subgroupG/H
centerC2#13093051
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#471C2
socleC2×C23D42
hypercenter#471D23
hypocenterC23#3291
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #13093229C2semidirect
2. #13093227C2semidirect
3. #13093226C2semidirect
4. #13093223C2semidirect
5. #13092788C2semidirect
6. #13092683C2semidirect
7. #13092681C2semidirect
8. #13092679C2semidirect
9. #13092602C2semidirect
10. #13092598C2semidirect
11. #13092587C2semidirect
12. #13092583C2semidirect
13. #13092533C2semidirect
14. #13092532C2semidirect
15. C23×#471C2semidirect
17. #10625160C22semidirect
19. #10625155C22semidirect
20. C23×#137C22semidirect
22. C2×SD16×C23C22semidirect
23. C23×#131C22semidirect
25. #10625115C22semidirect
26. #10625113C22semidirect
27. C2×#67274C22semidirect
29. C2×#67273C22semidirect
44. #10625080C22semidirect
45. #10625080C22semidirect
49. #10625078C22semidirect
50. #10625078C22semidirect
54. C2×#67263C22semidirect
55. #10625072C22semidirect
56. C23×#108C22semidirect
57. C23×#101C22semidirect
58. C23×#100C22semidirect
59. #10625019C22semidirect
60. #10625007C22semidirect
61. #10625007C22semidirect
62. #10625007C22semidirect
63. #10625006C22semidirect
64. #10625005C22semidirect
65. #10625004C22semidirect
66. C8×Dic23C22semidirect
109. #67275D4semidirect
113. #67274D4semidirect
117. #67273D4semidirect
119. #67272D4semidirect
126. Dic92D4semidirect
129. D184D4semidirect
136. #67263D4semidirect
137. #67263D4semidirect
228. #471D23semidirect
254. #137C2×D23semidirect
276. C2×SD16C2×D23semidirect
280. #131C2×D23semidirect
284. #108C2×D23semidirect
290. #101C2×D23semidirect
292. #100C2×D23semidirect
294. C23#3291semidirect

Maximal subgroups

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

subgroupindex
#130932292
#130932272
#130932262
#130932232
#130927882
#130926832
#130926812
#130926792
#130926022
#130925982
#130925872
#130925832
#130925332
#130925322
C23×#4712
#329123