Finite Group Databasebeta

← #15684892

Subgroups — #15684892

Order 2944.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625085C211yesmaximal, characteristic, complemented
2#13093078C211yesmaximal, characteristic, complemented
3D4×C22⋊D23C211yesmaximal, characteristic, complemented
4#13092803C211yesmaximal, characteristic, complemented
5#13092660C211yesmaximal, characteristic, complemented
6#13092653C211yesmaximal, characteristic, complemented
7#13092634C211yesmaximal, characteristic, complemented
8#13092615C211yesmaximal, characteristic, complemented
9#13092566C211yesmaximal, characteristic, complemented
10#13092561C211yesmaximal, characteristic, complemented
11#13092556C211yesmaximal, characteristic, complemented
12#13092551C211yesmaximal, characteristic, complemented
13#13092518C211yesmaximal, characteristic, complemented
14#13092488C211yesmaximal, characteristic, complemented
15C22×SD16×C23C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic, complemented
17C22×D4×C23C2211yescharacteristic
18C22×C22⋊D23—21no—
19C2×#67292C2211yescharacteristic, complemented
20C2×D4×D23C2211yescharacteristic
21C2×SD16×C23—24no—
22C2×SD16×C23C2211yescharacteristic
23C2×SD16×C23C2211yescharacteristic
24C2×SD16×C23C2211yescharacteristic, complemented
25C2×SD16×C23C2211yescharacteristic, complemented
26C22×C8×C23C2211yescharacteristic, complemented
27#10625124—21no—
28#10625118—21no—
29#10625118C2211yescharacteristic, complemented
30#10625117—21no—
31#10625117C2211yescharacteristic, complemented
32Q8×Dic23C2211yescharacteristic, complemented
33C2×#67274C2211yescharacteristic, complemented
34C2×#67274C2211yescharacteristic, complemented
35#10625111C2211yescharacteristic
36#10625110—21no—
37#10625109C2211yescharacteristic
38#10625108—21no—
39D4×Dic23C2211yescharacteristic
40C2×#67272C2211yescharacteristic
41C2×#67272C2211yescharacteristic, complemented
42#10625101—21no—
43#10625101C2211yescharacteristic
44#10625101C2211yescharacteristic, complemented
45C4×C22⋊D23—21no—
46C4×C22⋊D23C2211yescharacteristic
47#10625085—24no—
48C2×D184C2211yescharacteristic, complemented
49C2×#67262C2211yescharacteristic, complemented
50#10625017C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic
53#10625014C2211yescharacteristic, complemented
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic, complemented
56#10625003C2211yescharacteristic, complemented
57(C2×D23)⋊C8C2211yescharacteristic, complemented
58#10625000C2211yescharacteristic, complemented
59#10624997C2211yescharacteristic, complemented
60Dic23⋊C8C2211yescharacteristic, complemented
61C24×C23—21no—
62C23×D23—21no—
63C2×Q8×C23—21no—
64C2×Q8×C23—22no—
65C2×Q8×C23—41no—
66C2×Q8×C23C2311yescharacteristic
67C2×Q8×C23C2311yescharacteristic
68C2×D4×C23—22no—
69C2×D4×C23—21no—
70C2×D4×C23—41no—
71C2×D4×C23C2311yescharacteristic
72C2×D4×C23C2311yescharacteristic
73C22×C4×C23—21no—
74C22×C4×C23C2311yescharacteristic
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C2×C22⋊D23—21no—
78C2×C22⋊D23—21no—
79C2×C22⋊D23—21no—
80C2×C22⋊D23—21no—
81C2×C22⋊D23—44no—
82C2×C22⋊D23D411yescharacteristic
83C22×Dic23—21no—
84#67292—22no—
85#67292—41no—
86D4×D23—22no—
87D4×D23—41no—
88C2×D92—21no—
89C2×D92C2311yescharacteristic
90C2×D92C2311yescharacteristic
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93SD16×C23—22no—
94SD16×C23—22no—
95SD16×C23—22no—
96SD16×C23D414yescomplemented
97C2×C8×C23—22no—
98C2×C8×C23C2311yescharacteristic
99C2×C8×C23C2311yescharacteristic
100C22⋊Dic23—21no—
101C22⋊Dic23—21no—
102C22⋊Dic23D411yescharacteristic
103#67274—22no—
104#67274—41no—
105#67272—22no—
106#67272—41no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4D411yescharacteristic
113C4⋊Dic23—21no—
114C4⋊Dic23C2311yescharacteristic
115C4⋊Dic23C2311yescharacteristic
116Dic23⋊C4—21no—
117Dic23⋊C4D411yescharacteristic
118C4×Dic23—21no—
119C4×Dic23C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122D184—22no—
123#67262—22no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—42no—
127C23×C23—42no—
128C23×C23—81no—
129C23×C23C2×D411yescharacteristic
130C22×D23—21no—
131C22×D23—21no—
132C22×D23—42no—
133C22×D23—42no—
134C22×D23—81no—
135C22×D23C2×D411yescharacteristic
136Q8×C23—21no—
137Q8×C23—21no—
138Q8×C23—21no—
139Q8×C23—42no—
140Q8×C23C2×D412yescomplemented
141D4×C23—21no—
142D4×C23—21no—
143D4×C23—21no—
144D4×C23—42no—
145D4×C23C2×D412yes—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—42no—
151C2×C4×C23C2×D411yescharacteristic
152C2×C4×C23C2411yescharacteristic
153C22⋊D23—22no—
154C22⋊D23—42no—
155C22⋊D23—42no—
156C22⋊D23—42no—
157C22⋊D23—42no—
158C22⋊D23—42no—
159C22⋊D23—81no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23—42no—
163C2×Dic23C2×D411yescharacteristic
164C2×Dic23C2×D411yescharacteristic
165C2×Dic23C2×D411yescharacteristic
166D92—21no—
167D92—21no—
168D92—21no—
169D92—21no—
170D92—42no—
171C4×D23—21no—
172C4×D23—21no—
173C4×D23—42no—
174C8×C23—21no—
175C8×C23C2×D412yescomplemented
176C23⋊C8—21no—
177C23⋊C8—21no—
178#3265—231nomaximal, Sylow
179C22×C23—21no—
180C22×C23—21no—
181C22×C23—22no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—84no—
188C22×C23AGL(1,ℤ/8)12yescomplemented
189C22×C23C22×D411yescharacteristic
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—21no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—41no—
198C2×D23—41no—
199C2×D23—84no—
200C4×C23—22no—
201C4×C23—21no—
202C4×C23—41no—
203C4×C23C22×D411yescharacteristic
204C4×C23H(5,𝔽2)11yescharacteristic
205Dic23—21no—
206Dic23—21no—
207Dic23—21no—
208Dic23—41no—
209Dic23—41no—
210C2×AGL(1,ℤ/8)—231no—
211C22×SD16D2311yescharacteristic, complemented
212#548—231no—
213D42—231no—
214#496—231no—
215#468—231no—
216#466—231no—
217#463—231no—
218#460—231no—
219#450—231no—
220#449—231no—
221#448—231no—
222#447—231no—
223#440—231no—
224#435—231no—
225C2×C23—22no—
226C2×C23—42no—
227C2×C23—81no—
228C2×C23D4211yescharacteristic
229C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C23#57711yescharacteristic
231D23—41no—
232D23—81no—
233D23—81no—
234C2×#41—231no—
235C22×Q8C2×D2311yescharacteristic, complemented
236C22×D4—231no—
237C22×D4—461no—
238C22×D4C2×D2311yescharacteristic
239AGL(1,ℤ/8)—464no—
240C2×SD16—24no—
241C2×SD16—231no—
242C2×SD16—231no—
243C2×SD16C2×D2311yescharacteristic
244C2×SD16C2×D2311yescharacteristic
245C2×SD16C2×D2311yescharacteristic, complemented
246C2×SD16C2×D2311yescharacteristic, complemented
247C2×D8—231no—
248C2×D8—231no—
249C2×D8—231no—
250C2×M16—231no—
251C22×C8C2×D2311yescharacteristic, complemented
252#127—231no—
253#124—231no—
254#124—461no—
255C22⋊Q8—231no—
256C22⋊Q8—461no—
257#121—231no—
258#121—231no—
259#121—231no—
260#121—461no—
261#121—461no—
262#120—461no—
263#120—461no—
264C4×Q8—231no—
265C4×D4—231no—
266C4×D4—231no—
267C4×D4—461no—
268#107—231no—
269C4⋊C8—231no—
270#103—231no—
271#103—231no—
272#102—231no—
273#102—231no—
274#102—231no—
275#102—231no—
276C22⋊C8—231no—
277C22⋊C8—231no—
278#97—231no—
279C23#326511yescharacteristic, complemented, Sylow
280C24—21no—
281C24—461no—
282#41—462no—
283#41—921no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D2311yescharacteristic
288C2×Q8C22×D2311yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—231no—
293C2×D4—231no—
294C2×D4—231no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—462no—
300C2×D4—461no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—921no—
304C2×D4—924no—
305C2×D4C22×D2311yescharacteristic
306C2×D4C22×D2311yescharacteristic
307C22×C4—21no—
308C22×C4—231no—
309C22×C4—461no—
310C22×C4—461no—
311C22×C4C22×D2311yescharacteristic
312SD16—22no—
313SD16—22no—
314SD16—22no—
315SD16—462no—
316SD16—921no—
317SD16C22⋊D2314yescomplemented
318D8—462no—
319D8—462no—
320D8—921no—
321M16—462no—
322C2×C8—22no—
323C2×C8—231no—
324C2×C8—231no—
325C2×C8C22×D2311yescharacteristic
326C2×C8C22×D2311yescharacteristic
327C4⋊C4—231no—
328C4⋊C4—231no—
329C4⋊C4—231no—
330C4⋊C4—461no—
331C4⋊C4—461no—
332C22⋊C4—231no—
333C22⋊C4—231no—
334C22⋊C4—461no—
335C22⋊C4—461no—
336C22⋊C4—461no—
337C22⋊C4—461no—
338C22⋊C4—461no—
339C22⋊C4—461no—
340C22⋊C4—461no—
341C42—231no—
342C42—461no—
343C23—21no—
344C23—21no—
345C23—42no—
346C23—42no—
347C23—81no—
348C23—231no—
349C23—461no—
350C23—461no—
351C23—922no—
352C23—922no—
353C23—1841no—
354C23D4×D2311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8C2×C22⋊D2312yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—462no—
365D4—461no—
366D4—461no—
367D4—461no—
368D4—461no—
369D4—922no—
370D4—922no—
371D4—922no—
372D4—922no—
373D4—922no—
374D4—922no—
375D4—1841no—
376D4C2×C22⋊D2312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—231no—
383C2×C4—231no—
384C2×C4—231no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—461no—
389C2×C4—922no—
390C2×C4—922no—
391C2×C4D4×D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—21no—
394C8—461no—
395C8—461no—
396C8C2×C22⋊D2312yescomplemented
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—84no—
406C22—461no—
407C22—461no—
408C22—461no—
409C22—921no—
410C22—921no—
411C22—921no—
412C22—921no—
413C22—921no—
414C22—921no—
415C22—1844no—
416C22#1062508512yescomplemented
417C22C2×D4×D2311yescharacteristic
418C4—21no—
419C4—22no—
420C4—41no—
421C4—461no—
422C4—461no—
423C4—461no—
424C4—921no—
425C4—921no—
426C4#1062515511yescharacteristic
427C4C22×C22⋊D2311yescharacteristic
428C2—22no—
429C2—42no—
430C2—81no—
431C2—921no—
432C2—1841no—
433C2—1841no—
434C2D4×C22⋊D2311yescharacteristic
435C2C2×#1062508511yescharacteristic
436C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC22×SD16×C23C2
socleC22×C23C22×D4
hypercenterC22×SD16D23
hypocenterC23#3265
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. #13093078C2semidirect
3. D4×C22⋊D23C2semidirect
4. #13092803C2semidirect
5. #13092660C2semidirect
6. #13092653C2semidirect
7. #13092634C2semidirect
8. #13092615C2semidirect
9. #13092566C2semidirect
10. #13092561C2semidirect
11. #13092556C2semidirect
12. #13092551C2semidirect
13. #13092518C2semidirect
14. #13092488C2semidirect
15. C22×SD16×C23C2semidirect
16. C22×Q8×C23C22semidirect
19. C2×#67292C22semidirect
24. C2×SD16×C23C22semidirect
25. C2×SD16×C23C22semidirect
26. C22×C8×C23C22semidirect
29. #10625118C22semidirect
31. #10625117C22semidirect
32. Q8×Dic23C22semidirect
33. C2×#67274C22semidirect
34. C2×#67274C22semidirect
41. C2×#67272C22semidirect
44. #10625101C22semidirect
48. C2×D184C22semidirect
49. C2×#67262C22semidirect
50. #10625017C22semidirect
51. #10625017C22semidirect
53. #10625014C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
55. #10625003C22semidirect
56. #10625003C22semidirect
57. (C2×D23)⋊C8C22semidirect
58. #10625000C22semidirect
59. #10624997C22semidirect
60. Dic23⋊C8C22semidirect
96. SD16×C23D4semidirect
140. Q8×C23C2×D4semidirect
175. C8×C23C2×D4semidirect
188. C22×C23AGL(1,ℤ/8)semidirect
211. C22×SD16D23semidirect
235. C22×Q8C2×D23semidirect
245. C2×SD16C2×D23semidirect
246. C2×SD16C2×D23semidirect
251. C22×C8C2×D23semidirect
279. C23#3265semidirect
317. SD16C22⋊D23semidirect
359. Q8C2×C22⋊D23semidirect
396. C8C2×C22⋊D23semidirect
416. C22#10625085semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
#130930782
D4×C22⋊D232
#130928032
#130926602
#130926532
#130926342
#130926152
#130925662
#130925612
#130925562
#130925512
#130925182
#130924882
C22×SD16×C232
#326523