Finite Group Databasebeta

← #15685181

Subgroups — #15685181

Order 2944.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093233C211yesmaximal, characteristic, complemented
2#13093228C211yesmaximal, characteristic, complemented
3#13093226C211yesmaximal, characteristic, complemented
4#13093220C211yesmaximal, characteristic, complemented
5#13092799C211yesmaximal, characteristic, complemented
6#13092690C211yesmaximal, characteristic, complemented
7#13092686C211yesmaximal, characteristic, complemented
8#13092682C211yesmaximal, characteristic, complemented
9#13092679C211yesmaximal, characteristic, complemented
10#13092596C211yesmaximal, characteristic, complemented
11#13092591C211yesmaximal, characteristic, complemented
12#13092589C211yesmaximal, characteristic, complemented
13#13092531C211yesmaximal, characteristic, complemented
14#13092531C211yesmaximal, characteristic, complemented
15C23×#455C211yesmaximal, characteristic, complemented
16C23×H(5,𝔽2)C2211yescharacteristic
17#10625161C2211yescharacteristic, complemented
18#10625160C2211yescharacteristic
19#10625158C2211yescharacteristic, complemented
20C23×#137C2211yescharacteristic
21C23×#137C2211yescharacteristic, complemented
22C23×#124C2211yescharacteristic, complemented
23#10625122—21no—
24#10625122C2211yescharacteristic
25#10625121—21no—
26#10625121—21no—
27#10625121C2211yescharacteristic
28#10625121C2211yescharacteristic
29#10625120—21no—
30#10625120C2211yescharacteristic
31#10625119C2211yescharacteristic
32#10625119C2211yescharacteristic, complemented
33C2×#67275C2211yescharacteristic, complemented
34C2×#67274C2211yescharacteristic, complemented
35C2×#67273—21no—
36C2×#67273C2211yescharacteristic, complemented
37#10625103—21no—
38#10625103—21no—
39#10625103C2211yescharacteristic
40#10625103C2211yescharacteristic, complemented
41C2×#67272—21no—
42C2×#67272C2211yescharacteristic
43#10625090—21no—
44#10625089—21no—
45#10625089—21no—
46Q16×D23—21no—
47#10625087—21no—
48#10625086—21no—
49#10625085—21no—
50SD16×D23—21no—
51#10625080C2211yescharacteristic, complemented
52#10625079C2211yescharacteristic, complemented
53#10625078C2211yescharacteristic, complemented
54#10625078C2211yescharacteristic, complemented
55#10625046C2211yescharacteristic, complemented
56C23×#104C2211yescharacteristic
57C23×#104C2211yescharacteristic, complemented
58C23×#100C2211yescharacteristic, complemented
59#10625018C2211yescharacteristic, complemented
60#10625006C2211yescharacteristic, complemented
61#10625005C2211yescharacteristic, complemented
62#10625004C2211yescharacteristic, complemented
63#10625004C2211yescharacteristic, complemented
64#10624987C2211yescharacteristic, complemented
65#10624987C2211yescharacteristic, complemented
66C4×C23⋊C8C2211yescharacteristic, complemented
67#41×C23—21no—
68#41×C23—21no—
69#41×C23C2311yescharacteristic
70#41×C23C2311yescharacteristic
71C2×Q8×C23C2311yescharacteristic
72C2×D4×C23—21no—
73C2×D4×C23—21no—
74C2×D4×C23—41no—
75C2×D4×C23C2311yescharacteristic
76#67292—21no—
77#67292—21no—
78#67292—21no—
79Q8×D23—21no—
80Q8×D23—21no—
81Q8×D23—21no—
82#67290—21no—
83#67290—41no—
84D4×D23—21no—
85D4×D23—41no—
86#67288—21no—
87#67288—21no—
88#67288—41no—
89#67288C2311yescharacteristic
90#67288C2311yescharacteristic
91C2×D92—21no—
92C2×D92C2311yescharacteristic
93C2×Dic46—21no—
94C2×Dic46C2311yescharacteristic
95Q16×C23—21no—
96Q16×C23—21no—
97SD16×C23—21no—
98SD16×C23—21no—
99M16×C23C2311yescharacteristic
100M16×C23C2311yescharacteristic
101C22⋊C4×C23—41no—
102C42×C23C2311yescharacteristic
103#67275—21no—
104#67275—21no—
105#67275—21no—
106#67275D411yescharacteristic
107#67275D411yescharacteristic
108#67274—21no—
109#67274—21no—
110#67274—21no—
111#67274D411yescharacteristic
112#67274D411yescharacteristic
113#67273—21no—
114#67273—21no—
115#67273—21no—
116#67273—21no—
117#67273—21no—
118#67273D411yescharacteristic
119#67273D411yescharacteristic
120#67272—21no—
121#67272—21no—
122#67272—21no—
123#67272—21no—
124#67272—21no—
125#67272D411yescharacteristic
126#67272D411yescharacteristic
127(C2×D23)⋊C4—41no—
128#67267—21no—
129#67267—21no—
130#67267C2311yescharacteristic
131#67267C2311yescharacteristic
132C2×C23⋊C8—21no—
133C2×C23⋊C8—21no—
134C2×C23⋊C8C2311yescharacteristic
135C2×C23⋊C8C2311yescharacteristic
136Dic92—21no—
137D184—21no—
138#67263—21no—
139#67263—21no—
140#67262—21no—
141#67262—21no—
142C8×D23—21no—
143C8×D23—21no—
144C23×C23—21no—
145C23×C23—41no—
146C22×D23—21no—
147C22×D23—41no—
148Q8×C23—21no—
149Q8×C23—21no—
150Q8×C23C2×D411yescharacteristic
151Q8×C23C2×D411yescharacteristic
152D4×C23—21no—
153D4×C23—21no—
154D4×C23—21no—
155D4×C23—21no—
156D4×C23—41no—
157D4×C23—41no—
158D4×C23C2×D411yescharacteristic
159D4×C23C2×D411yescharacteristic
160C2×C4×C23—21no—
161C2×C4×C23—21no—
162C2×C4×C23—21no—
163C2×C4×C23—21no—
164C2×C4×C23—41no—
165C2×C4×C23C2411yescharacteristic
166C22⋊D23—21no—
167C22⋊D23—21no—
168C22⋊D23—41no—
169C22⋊D23—41no—
170C2×Dic23—21no—
171C2×Dic23—41no—
172D92—21no—
173D92—21no—
174D92—41no—
175D92—41no—
176D92C2×D411yescharacteristic
177D92C2×D411yescharacteristic
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
190C8×C23—21no—
191C8×C23—21no—
192C23⋊C8—21no—
193C23⋊C8—21no—
194C23⋊C8C2×D411yescharacteristic
195C23⋊C8C2×D411yescharacteristic
196C23⋊C8C2×D411yescharacteristic
197C23⋊C8C2×D411yescharacteristic
198#3290—231nomaximal, Sylow
199C22×C23—21no—
200C22×C23—21no—
201C22×C23—41no—
202C22×C23—81no—
203C22×C23—161no—
204C22×C23H(5,𝔽2)11yescharacteristic
205C2×D23—21no—
206C2×D23—21no—
207C2×D23—41no—
208C2×D23—81no—
209C2×D23—161no—
210C4×C23—21no—
211C4×C23—21no—
212C4×C23—41no—
213C4×C23—41no—
214C4×C23C22×D411yescharacteristic
215C4×C23C22×D411yescharacteristic
216Dic23—21no—
217Dic23—21no—
218Dic23—41no—
219#578—231no—
220#577—231no—
221#577—231no—
222#576—231no—
223#495—231no—
224#473—231no—
225#472—231no—
226#471—231no—
227#471—231no—
228#455—231no—
229#455D2311yescharacteristic, complemented
230#454—231no—
231#454—231no—
232#443—231no—
233#443—231no—
234C2×C23—21no—
235C2×C23—41no—
236C2×C23—41no—
237C2×C23—81no—
238C2×C23D4211yescharacteristic
239D23—41no—
240D23—41no—
241D23—81no—
2422−1+4—231no—
2432−1+4—231no—
244H(5,𝔽2)—231no—
245H(5,𝔽2)C2×D2311yescharacteristic
246#137—231no—
247#137—231no—
248#137—461no—
249#137—461no—
250#137—461no—
251#137—461no—
252#137C2×D2311yescharacteristic
253#137C2×D2311yescharacteristic, complemented
254AGL(1,ℤ/8)—231no—
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—
262#135—231no—
263#135—231no—
264#135—461no—
265#135—461no—
266#135—461no—
267#135—461no—
268C2×Q16—231no—
269C2×Q16—461no—
270C2×SD16—231no—
271C2×SD16—231no—
272C2×SD16—461no—
273C2×SD16—461no—
274C2×D8—231no—
275C2×D8—461no—
276#131—231no—
277#131—231no—
278#131—231no—
279#131—231no—
280#124—231no—
281#124C2×D2311yescharacteristic, complemented
282#108—231no—
283#108—231no—
284#104—231no—
285#104—231no—
286#104C2×D2311yescharacteristic
287#104C2×D2311yescharacteristic, complemented
288#101—231no—
289#101—231no—
290#100—231no—
291#100C2×D2311yescharacteristic, complemented
292C4×C8—231no—
293C23#329011yescharacteristic, complemented, Sylow
294#41—21no—
295#41—21no—
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—921no—
305#41—921no—
306#41C22×D2311yescharacteristic
307#41C22×D2311yescharacteristic
308C2×Q8—231no—
309C2×Q8—461no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8C22×D2311yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—231no—
318C2×D4—461no—
319C2×D4—461no—
320C2×D4—921no—
321C2×D4C22×D2311yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—231no—
325Q16—231no—
326Q16—461no—
327Q16—461no—
328Q16—461no—
329Q16—461no—
330SD16—21no—
331SD16—21no—
332SD16—231no—
333SD16—231no—
334SD16—231no—
335SD16—231no—
336SD16—461no—
337SD16—461no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16—461no—
346D8—231no—
347D8—231no—
348D8—461no—
349D8—461no—
350D8—461no—
351D8—461no—
352D8—461no—
353D8—461no—
354M16—231no—
355M16—231no—
356M16—461no—
357M16—461no—
358M16—461no—
359M16—461no—
360M16C22×D2311yescharacteristic
361M16C22×D2311yescharacteristic
362C2×C8—231no—
363C2×C8—231no—
364C2×C8—461no—
365C2×C8—461no—
366C2×C8—461no—
367C2×C8—461no—
368C22⋊C4—41no—
369C22⋊C4—921no—
370C42C22×D2311yescharacteristic
371C23—21no—
372C23—41no—
373C23—461no—
374C23—921no—
375Q8—21no—
376Q8—21no—
377Q8—231no—
378Q8—231no—
379Q8—461no—
380Q8—461no—
381Q8—921no—
382Q8—921no—
383Q8D4×D2311yescharacteristic
384Q8D4×D2311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—231no—
392D4—231no—
393D4—461no—
394D4—461no—
395D4—461no—
396D4—461no—
397D4—921no—
398D4—921no—
399D4—921no—
400D4—921no—
401D4D4×D2311yescharacteristic
402D4D4×D2311yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—461no—
409C2×C4—461no—
410C2×C4—461no—
411C2×C4—921no—
412C2×C4—921no—
413C2×C4—921no—
414C2×C4—921no—
415C2×C4—921no—
416C2×C4C23×D2311yescharacteristic
417C8—21no—
418C8—21no—
419C8—231no—
420C8—231no—
421C8—231no—
422C8—231no—
423C8—461no—
424C8—461no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—161no—
430C22—461no—
431C22—461no—
432C22—921no—
433C22—3681no—
434C22—1841no—
435C22#1062515511yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—461no—
441C4—461no—
442C4—921no—
443C4C2×D4×D2311yescharacteristic
444C4C2×D4×D2311yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—921no—
450C2—921no—
451C2—1841no—
452C2#1309304911yescharacteristic
subgroupG/H
centerC2#13093049
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#455C2
socleC2×C23D42
hypercenter#455D23
hypocenterC23#3290
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #13093233C2semidirect
2. #13093228C2semidirect
3. #13093226C2semidirect
4. #13093220C2semidirect
5. #13092799C2semidirect
6. #13092690C2semidirect
7. #13092686C2semidirect
8. #13092682C2semidirect
9. #13092679C2semidirect
10. #13092596C2semidirect
11. #13092591C2semidirect
12. #13092589C2semidirect
13. #13092531C2semidirect
14. #13092531C2semidirect
15. C23×#455C2semidirect
17. #10625161C22semidirect
19. #10625158C22semidirect
21. C23×#137C22semidirect
22. C23×#124C22semidirect
32. #10625119C22semidirect
33. C2×#67275C22semidirect
34. C2×#67274C22semidirect
36. C2×#67273C22semidirect
40. #10625103C22semidirect
51. #10625080C22semidirect
52. #10625079C22semidirect
53. #10625078C22semidirect
54. #10625078C22semidirect
55. #10625046C22semidirect
57. C23×#104C22semidirect
58. C23×#100C22semidirect
59. #10625018C22semidirect
60. #10625006C22semidirect
61. #10625005C22semidirect
62. #10625004C22semidirect
63. #10625004C22semidirect
64. #10624987C22semidirect
65. #10624987C22semidirect
66. C4×C23⋊C8C22semidirect
229. #455D23semidirect
253. #137C2×D23semidirect
281. #124C2×D23semidirect
287. #104C2×D23semidirect
291. #100C2×D23semidirect
293. C23#3290semidirect

Maximal subgroups

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

subgroupindex
#130932332
#130932282
#130932262
#130932202
#130927992
#130926902
#130926862
#130926822
#130926792
#130925962
#130925912
#130925892
#130925312
C23×#4552
#329023