Finite Group Databasebeta

← #15685180

Subgroups — #15685180

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#13093229C211yesmaximal, characteristic, complemented
3#13093223C211yesmaximal, characteristic, complemented
4#13093221C211yesmaximal, characteristic, complemented
5#13092798C211yesmaximal, characteristic, complemented
6#13092691C211yesmaximal, characteristic, complemented
7#13092686C211yesmaximal, characteristic, complemented
8#13092681C211yesmaximal, characteristic, complemented
9#13092597C211yesmaximal, characteristic, complemented
10#13092593C211yesmaximal, characteristic, complemented
11#13092592C211yesmaximal, characteristic, complemented
12#13092588C211yesmaximal, characteristic, complemented
13#13092533C211yesmaximal, characteristic, complemented
14#13092532C211yesmaximal, characteristic, complemented
15C23×#471C211yesmaximal, characteristic, complemented
16#10625161C2211yescharacteristic, complemented
17#10625160C2211yescharacteristic
18#10625158C2211yescharacteristic, complemented
19#10625155C2211yescharacteristic
20C23×#137C2211yescharacteristic, complemented
21C23×AGL(1,ℤ/8)C2211yescharacteristic
22C2×SD16×C23C2211yescharacteristic, complemented
23C23×#131C2211yescharacteristic, complemented
24#10625121C2211yescharacteristic
25#10625118C2211yescharacteristic, complemented
26C2×#67275C2211yescharacteristic, complemented
27#10625113C2211yescharacteristic
28#10625107C2211yescharacteristic, complemented
29#10625103C2211yescharacteristic, complemented
30C2×#67272C2211yescharacteristic
31#10625089—21no—
32Q16×D23—21no—
33#10625087—21no—
34#10625087—21no—
35#10625087—21no—
36#10625086—21no—
37#10625086—21no—
38#10625085—21no—
39#10625085—21no—
40SD16×D23—21no—
41#10625082—21no—
42D8×D23—21no—
43#10625080—21no—
44#10625080C2211yescharacteristic
45#10625080C2211yescharacteristic, complemented
46#10625079—21no—
47#10625079C2211yescharacteristic
48#10625079C2211yescharacteristic, complemented
49#10625078C2211yescharacteristic
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
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—
71#67292—21no—
72#67292—21no—
73#67292—21no—
74Q8×D23—21no—
75Q8×D23—21no—
76Q8×D23—21no—
77#67290—21no—
78#67290—21no—
79#67290—21no—
80#67290—41no—
81D4×D23—21no—
82D4×D23—21no—
83D4×D23—21no—
84D4×D23—41no—
85#67288—21no—
86#67288—21no—
87#67288—41no—
88#67288C2311yescharacteristic
89#67288C2311yescharacteristic
90#67288C2311yescharacteristic
91C2×D92—21no—
92C2×D92C2311yescharacteristic
93C2×Dic46—21no—
94C2×Dic46C2311yescharacteristic
95Q16×C23—21no—
96SD16×C23—21no—
97SD16×C23—21no—
98SD16×C23—21no—
99SD16×C23—21no—
100D8×C23—21no—
101M16×C23—21no—
102M16×C23C2311yescharacteristic
103M16×C23C2311yescharacteristic
104M16×C23C2311yescharacteristic
105C2×C8×C23—21no—
106C2×C8×C23C2311yescharacteristic
107C22⋊Dic23—41no—
108#67275—21no—
109#67275—21no—
110#67275—21no—
111#67275D411yescharacteristic
112#67274—21no—
113#67274D411yescharacteristic
114#67273—21no—
115#67273D411yescharacteristic
116#67272—21no—
117#67272—21no—
118#67272—21no—
119#67272D411yescharacteristic
120(C2×D23)⋊C4—41no—
121C4×Dic23C2311yescharacteristic
122#67267C2311yescharacteristic
123C2×C23⋊C8C2311yescharacteristic
124Dic92—21no—
125Dic92—21no—
126Dic92D411yescharacteristic
127D184—21no—
128D184—21no—
129D184D411yescharacteristic
130#67263—21no—
131#67263—21no—
132#67263—21no—
133#67263—21no—
134#67263—21no—
135#67263—21no—
136#67263D411yescharacteristic
137#67263D411yescharacteristic
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—
165C2×Dic23—21no—
166C2×Dic23—21no—
167C2×Dic23—41no—
168C2×Dic23—41no—
169D92—21no—
170D92—21no—
171D92—41no—
172D92—41no—
173D92C2×D411yescharacteristic
174D92C2×D411yescharacteristic
175D92C2×D411yescharacteristic
176C4×D23—21no—
177C4×D23—21no—
178C4×D23—21no—
179C4×D23—41no—
180C4×D23—41no—
181C4×D23—41no—
182C4×D23—41no—
183Dic46—21no—
184Dic46—21no—
185Dic46—41no—
186Dic46—41no—
187Dic46C2×D411yescharacteristic
188Dic46C2×D411yescharacteristic
189Dic46C2×D411yescharacteristic
190C8×C23—21no—
191C8×C23—21no—
192C8×C23—21no—
193C8×C23C2×D411yescharacteristic
194C8×C23C2×D411yescharacteristic
195C23⋊C8—21no—
196C23⋊C8C2×D411yescharacteristic
197C23⋊C8C2×D411yescharacteristic
198#3290—231nomaximal, Sylow
199C22×C23—21no—
200C22×C23—41no—
201C22×C23—81no—
202C22×C23H(5,𝔽2)11yescharacteristic
203C2×D23—21no—
204C2×D23—21no—
205C2×D23—21no—
206C2×D23—41no—
207C2×D23—81no—
208C2×D23—161no—
209C2×D23—161no—
210C4×C23—21no—
211C4×C23—41no—
212C4×C23C22×D411yescharacteristic
213C4×C23C22×D411yescharacteristic
214Dic23—21no—
215Dic23—21no—
216Dic23—21no—
217Dic23—41no—
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#471D2311yescharacteristic, complemented
228#455—231no—
229#455—231no—
230#454—231no—
231#454—231no—
232#443—231no—
233#443—231no—
234C2×C23—21no—
235C2×C23—41no—
236C2×C23—81no—
237C2×C23D4211yescharacteristic
238D23—41no—
239D23—41no—
240D23—41no—
241D23—81no—
2422−1+4—231no—
2432−1+4—231no—
244H(5,𝔽2)—231no—
245H(5,𝔽2)—231no—
246#137—231no—
247#137—231no—
248#137—231no—
249#137—461no—
250#137—461no—
251#137—461no—
252#137—461no—
253#137C2×D2311yescharacteristic, complemented
254AGL(1,ℤ/8)—231no—
255AGL(1,ℤ/8)—231no—
256AGL(1,ℤ/8)—231no—
257AGL(1,ℤ/8)—461no—
258AGL(1,ℤ/8)—461no—
259AGL(1,ℤ/8)—461no—
260AGL(1,ℤ/8)—461no—
261AGL(1,ℤ/8)C2×D2311yescharacteristic
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—461no—
272C2×SD16—461no—
273C2×SD16C2×D2311yescharacteristic, complemented
274C2×D8—231no—
275C2×D8—461no—
276#131—231no—
277#131—231no—
278#131—231no—
279#131C2×D2311yescharacteristic, complemented
280#124—231no—
281#124—231no—
282#108—231no—
283#108C2×D2311yescharacteristic, complemented
284#104—231no—
285#104—231no—
286#104—231no—
287#104—231no—
288#101—231no—
289#101C2×D2311yescharacteristic, complemented
290#100—231no—
291#100C2×D2311yescharacteristic, complemented
292C4×C8—231no—
293C23#329011yescharacteristic, complemented, Sylow
294#41—231no—
295#41—231no—
296#41—231no—
297#41—461no—
298#41—461no—
299#41—461no—
300#41—461no—
301#41—461no—
302#41—461no—
303#41—461no—
304#41—461no—
305#41—921no—
306#41—921no—
307#41C22×D2311yescharacteristic
308C2×Q8—231no—
309C2×Q8—461no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8C22×D2311yescharacteristic
314C2×D4—231no—
315C2×D4—461no—
316C2×D4—461no—
317C2×D4—461no—
318C2×D4—461no—
319C2×D4—921no—
320C2×D4—921no—
321C2×D4C22×D2311yescharacteristic
322Q16—21no—
323Q16—231no—
324Q16—231no—
325Q16—461no—
326Q16—461no—
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—
346D8—21no—
347D8—231no—
348D8—231no—
349D8—461no—
350D8—461no—
351D8—461no—
352D8—461no—
353D8—461no—
354M16—21no—
355M16—231no—
356M16—461no—
357M16—461no—
358M16—461no—
359M16C22×D2311yescharacteristic
360M16C22×D2311yescharacteristic
361M16C22×D2311yescharacteristic
362C2×C8—21no—
363C2×C8—231no—
364C2×C8—461no—
365C2×C8—461no—
366C2×C8—461no—
367C2×C8C22×D2311yescharacteristic
368C22⋊C4—921no—
369C22⋊C4—921no—
370C42—231no—
371C23—21no—
372C23—461no—
373C23—921no—
374C23—921no—
375Q8—21no—
376Q8—21no—
377Q8—231no—
378Q8—231no—
379Q8—231no—
380Q8—461no—
381Q8—461no—
382Q8—921no—
383Q8—921no—
384Q8D4×D2311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—231no—
389D4—231no—
390D4—231no—
391D4—461no—
392D4—461no—
393D4—461no—
394D4—461no—
395D4—461no—
396D4—921no—
397D4—921no—
398D4—921no—
399D4—921no—
400D4—921no—
401D4—921no—
402D4D4×D2311yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—461no—
406C2×C4—461no—
407C2×C4—461no—
408C2×C4—461no—
409C2×C4—461no—
410C2×C4—921no—
411C2×C4—921no—
412C2×C4—921no—
413C2×C4—921no—
414C2×C4—921no—
415C2×C4—921no—
416C2×C4C23×D2311yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—231no—
421C8—231no—
422C8—461no—
423C8D4×D2311yescharacteristic
424C8D4×D2311yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—461no—
429C22—461no—
430C22—461no—
431C22—921no—
432C22—3681no—
433C22—3681no—
434C22—1841no—
435C22#1062516011yescharacteristic
436C4—21no—
437C4—41no—
438C4—461no—
439C4—461no—
440C4—461no—
441C4—921no—
442C4—921no—
443C4C2×D4×D2311yescharacteristic
444C4C2×D4×D2311yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—921no—
449C2—921no—
450C2—921no—
451C2—1841no—
452C2#1309305111yescharacteristic
subgroupG/H
centerC2#13093051
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#471C2
socleC2×C23D42
hypercenter#471D23
hypocenterC23#3290
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. #13093233C2semidirect
2. #13093229C2semidirect
3. #13093223C2semidirect
4. #13093221C2semidirect
5. #13092798C2semidirect
6. #13092691C2semidirect
7. #13092686C2semidirect
8. #13092681C2semidirect
9. #13092597C2semidirect
10. #13092593C2semidirect
11. #13092592C2semidirect
12. #13092588C2semidirect
13. #13092533C2semidirect
14. #13092532C2semidirect
15. C23×#471C2semidirect
16. #10625161C22semidirect
18. #10625158C22semidirect
20. C23×#137C22semidirect
22. C2×SD16×C23C22semidirect
23. C23×#131C22semidirect
25. #10625118C22semidirect
26. C2×#67275C22semidirect
28. #10625107C22semidirect
29. #10625103C22semidirect
45. #10625080C22semidirect
48. #10625079C22semidirect
50. #10625078C22semidirect
54. C2×#67263C22semidirect
55. #10625072C22semidirect
56. C23×#108C22semidirect
57. C23×#101C22semidirect
58. C23×#100C22semidirect
59. #10625019C22semidirect
61. #10625007C22semidirect
62. #10625007C22semidirect
63. #10625006C22semidirect
64. #10625005C22semidirect
65. #10625004C22semidirect
66. C8×Dic23C22semidirect
227. #471D23semidirect
253. #137C2×D23semidirect
273. C2×SD16C2×D23semidirect
279. #131C2×D23semidirect
283. #108C2×D23semidirect
289. #101C2×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
#130932292
#130932232
#130932212
#130927982
#130926912
#130926862
#130926812
#130925972
#130925932
#130925922
#130925882
#130925332
#130925322
C23×#4712
#329023