Finite Group Databasebeta

← #15684891

Subgroups — #15684891

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×#10625082C211yesmaximal, characteristic, complemented
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3#13093075C211yesmaximal, characteristic, complemented
4#13093052C211yesmaximal, characteristic, complemented
5#13092660C211yesmaximal, characteristic, complemented
6#13092650C211yesmaximal, characteristic, complemented
7#13092629C211yesmaximal, characteristic, complemented
8#13092614C211yesmaximal, characteristic, complemented
9#13092566C211yesmaximal, characteristic, complemented
10#13092559C211yesmaximal, characteristic, complemented
11#13092554C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092519C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#496C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic, complemented
17C2×#67290C2211yescharacteristic, complemented
18C2×D4×D23—21no—
19C2×D4×D23C2211yescharacteristic
20C2×D4×D23C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic, complemented
22C2×SD16×C23C2211yescharacteristic, complemented
23C2×D8×C23C2211yescharacteristic, complemented
24C2×D8×C23C2211yescharacteristic, complemented
25C23×#127C2211yescharacteristic
26C23×#124C2211yescharacteristic, complemented
27#10625117C2211yescharacteristic, complemented
28C2×#67274C2211yescharacteristic
29#10625109—21no—
30#10625109C2211yescharacteristic
31#10625109C2211yescharacteristic
32#10625109C2211yescharacteristic, complemented
33#10625108—21no—
34#10625108—21no—
35C2×#67273C2211yescharacteristic, complemented
36C2×#67273C2211yescharacteristic, complemented
37C2×#67272C2211yescharacteristic
38SD16×D23—24no—
39#10625082—24no—
40C2×#67263C2211yescharacteristic
41C2×#67262C2211yescharacteristic, complemented
42C2×C8×D23C2211yescharacteristic, complemented
43#10625056—21no—
44#10625055—21no—
45(C22⋊D23)⋊C4—21no—
46#10625049—21no—
47C4×D92C2211yescharacteristic
48C4×D92C2211yescharacteristic
49C4×Dic46C2211yescharacteristic, complemented
50C23×#97C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic, complemented
54#10625014C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57(C2×D23)⋊C8C2211yescharacteristic, complemented
58#10625000C2211yescharacteristic, complemented
59#10624998C2211yescharacteristic, complemented
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23—21no—
65C2×D4×C23—21no—
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C2×D4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C22×Dic23—21no—
76Q8×D23—22no—
77Q8×D23—41no—
78#67290—22no—
79#67290—41no—
80D4×D23—22no—
81D4×D23—22no—
82D4×D23—41no—
83D4×D23—41no—
84D4×D23—44no—
85C2×D92D411yescharacteristic
86C2×D92C2311yescharacteristic
87C2×C4×D23—21no—
88C2×C4×D23—21no—
89C2×C4×D23C2311yescharacteristic
90C2×C4×D23C2311yescharacteristic
91C2×Dic46—21no—
92C2×Dic46C2311yescharacteristic
93SD16×C23—22no—
94SD16×C23—41no—
95D8×C23—22no—
96D8×C23—41no—
97C2×C8×C23C2311yescharacteristic
98C2×C8×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C42×C23C2311yescharacteristic
102C22⋊Dic23—21no—
103C22⋊Dic23—21no—
104C22⋊Dic23—21no—
105#67274—22no—
106#67273—22no—
107#67273—22no—
108#67272—22no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4D411yescharacteristic
112(C2×D23)⋊C4D411yescharacteristic
113C4⋊Dic23D411yescharacteristic
114C4⋊Dic23C2311yescharacteristic
115C4⋊Dic23C2311yescharacteristic
116Dic23⋊C4—21no—
117Dic23⋊C4—21no—
118C4×Dic23—21no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121#67263D414yescomplemented
122#67262—22no—
123C8×D23—22no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—42no—
131C22×D23—42no—
132C22×D23—81no—
133C22×D23—81no—
134C22×D23C2×D411yescharacteristic
135C22×D23C2×D411yescharacteristic
136Q8×C23—21no—
137Q8×C23—21no—
138D4×C23—21no—
139D4×C23—21no—
140D4×C23—21no—
141D4×C23—21no—
142D4×C23—21no—
143D4×C23—21no—
144D4×C23—42no—
145D4×C23—81no—
146C2×C4×C23—21no—
147C2×C4×C23C2×D411yescharacteristic
148C2×C4×C23C2×D411yescharacteristic
149C2×C4×C23C2411yescharacteristic
150C22⋊D23—42no—
151C22⋊D23—42no—
152C22⋊D23—42no—
153C22⋊D23—42no—
154C22⋊D23—42no—
155C22⋊D23—42no—
156C2×Dic23—21no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159C2×Dic23—42no—
160C2×Dic23C2×D411yescharacteristic
161C2×Dic23C2×D411yescharacteristic
162D92—22no—
163D92—21no—
164D92C2×D412yes—
165C4×D23—21no—
166C4×D23—21no—
167C4×D23—21no—
168C4×D23—21no—
169C4×D23—42no—
170C4×D23—42no—
171Dic46—21no—
172Dic46—42no—
173Dic46C2×D412yescomplemented
174C8×C23—21no—
175C8×C23C2×D412yescomplemented
176C23⋊C8—21no—
177C23⋊C8—21no—
178#3265—231nomaximal, Sylow
179C22×C23—41no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23C22×D411yescharacteristic
189C2×D23—21no—
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—22no—
193C2×D23—21no—
194C2×D23—21no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—84no—
198C2×D23—84no—
199C2×D23AGL(1,ℤ/8)12yescomplemented
200C4×C23—21no—
201C4×C23—21no—
202C4×C23—41no—
203C4×C23C22×D411yescharacteristic
204C4×C23H(5,𝔽2)11yescharacteristic
205Dic23—22no—
206Dic23—21no—
207Dic23—21no—
208Dic23—41no—
209Dic23—41no—
210C2×AGL(1,ℤ/8)—231no—
211C22×SD16—231no—
212#548—231no—
213D42—231no—
214#496D2311yescharacteristic, complemented
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—81no—
226C2×C23—81no—
227C2×C23—81no—
228C2×C23D4211yescharacteristic
229C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C23#57711yescharacteristic
231D23—22no—
232D23—41no—
233D23—42no—
234C2×#41—231no—
235C22×Q8—231no—
236C22×D4—231no—
237C22×D4—231no—
238C22×D4—461no—
239AGL(1,ℤ/8)—464no—
240C2×SD16—231no—
241C2×SD16—231no—
242C2×SD16—231no—
243C2×SD16—231no—
244C2×SD16—464no—
245C2×SD16C2×D2311yescharacteristic, complemented
246C2×SD16C2×D2311yescharacteristic, complemented
247C2×D8—231no—
248C2×D8C2×D2311yescharacteristic, complemented
249C2×D8C2×D2311yescharacteristic, complemented
250C2×M16—231no—
251C22×C8—231no—
252#127C2×D2311yescharacteristic
253#124—461no—
254#124C2×D2311yescharacteristic, complemented
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#97C2×D2311yescharacteristic, complemented
279C23#326511yescharacteristic, complemented, Sylow
280C24—461no—
281C24—461no—
282#41—462no—
283#41—921no—
284C2×Q8—231no—
285C2×Q8—461no—
286C2×Q8—462no—
287C2×Q8—921no—
288C2×Q8C22×D2311yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—231no—
292C2×D4—231no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—462no—
296C2×D4—462no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—461no—
300C2×D4—461no—
301C2×D4—921no—
302C2×D4—921no—
303C2×D4—924no—
304C2×D4C22×D2311yescharacteristic
305C2×D4C22×D2311yescharacteristic
306C2×D4C22×D2311yescharacteristic
307C22×C4—231no—
308C22×C4—231no—
309C22×C4—461no—
310C22×C4—461no—
311C22×C4—461no—
312SD16—22no—
313SD16—41no—
314SD16—234no—
315SD16—462no—
316SD16—462no—
317SD16—462no—
318D8—22no—
319D8—41no—
320D8—462no—
321M16—462no—
322C2×C8—231no—
323C2×C8—231no—
324C2×C8—462no—
325C2×C8C22×D2311yescharacteristic
326C2×C8C22×D2311yescharacteristic
327C4⋊C4—231no—
328C4⋊C4—231no—
329C4⋊C4—231no—
330C4⋊C4—461no—
331C4⋊C4—461no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—231no—
335C22⋊C4—231no—
336C22⋊C4—461no—
337C22⋊C4—461no—
338C22⋊C4—461no—
339C22⋊C4—461no—
340C22⋊C4—461no—
341C42—461no—
342C42C22×D2311yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—231no—
347C23—231no—
348C23—461no—
349C23—922no—
350C23—922no—
351C23—922no—
352C23—922no—
353C23—1841no—
354C23—1841no—
355Q8—21no—
356Q8—21no—
357Q8—232no—
358Q8—461no—
359Q8—922no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—81no—
368D4—232no—
369D4—462no—
370D4—461no—
371D4—922no—
372D4—922no—
373D4—922no—
374D4—922no—
375D4—922no—
376D4—922no—
377C2×C4—21no—
378C2×C4—231no—
379C2×C4—231no—
380C2×C4—461no—
381C2×C4—461no—
382C2×C4—461no—
383C2×C4—461no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—922no—
388C2×C4—922no—
389C2×C4—922no—
390C2×C4D4×D2311yescharacteristic
391C2×C4D4×D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—21no—
394C8—461no—
395C8—461no—
396C8D4×D2312yescomplemented
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—232no—
407C22—461no—
408C22—461no—
409C22—461no—
410C22—461no—
411C22—461no—
412C22—462no—
413C22—921no—
414C22—921no—
415C22—1844no—
416C22—1844no—
417C22C2×D4×D2311yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—461no—
422C4—461no—
423C4—462no—
424C4—921no—
425C4—921no—
426C4C2×D4×D2311yescharacteristic
427C4#1062515511yescharacteristic
428C2—81no—
429C2—81no—
430C2—81no—
431C2—462no—
432C2—921no—
433C2—922no—
434C2#1309305211yescharacteristic
435C2AGL(1,ℤ/8)×D2311yescharacteristic
436C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#496C2
socleC22×C23C22×D4
hypercenter#496D23
hypocenterC23#3265
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×SD16×D23C2semidirect
3. #13093075C2semidirect
4. #13093052C2semidirect
5. #13092660C2semidirect
6. #13092650C2semidirect
7. #13092629C2semidirect
8. #13092614C2semidirect
9. #13092566C2semidirect
10. #13092559C2semidirect
11. #13092554C2semidirect
12. #13092549C2semidirect
13. #13092519C2semidirect
14. #13092490C2semidirect
15. C23×#496C2semidirect
16. C2×Q8×D23C22semidirect
17. C2×#67290C22semidirect
21. C2×SD16×C23C22semidirect
22. C2×SD16×C23C22semidirect
23. C2×D8×C23C22semidirect
24. C2×D8×C23C22semidirect
26. C23×#124C22semidirect
27. #10625117C22semidirect
32. #10625109C22semidirect
35. C2×#67273C22semidirect
36. C2×#67273C22semidirect
41. C2×#67262C22semidirect
42. C2×C8×D23C22semidirect
49. C4×Dic46C22semidirect
50. C23×#97C22semidirect
51. #10625017C22semidirect
52. #10625014C22semidirect
53. #10625014C22semidirect
54. #10625014C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. (C2×D23)⋊C8C22semidirect
58. #10625000C22semidirect
59. #10624998C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
121. #67263D4semidirect
173. Dic46C2×D4semidirect
175. C8×C23C2×D4semidirect
199. C2×D23AGL(1,ℤ/8)semidirect
214. #496D23semidirect
245. C2×SD16C2×D23semidirect
246. C2×SD16C2×D23semidirect
248. C2×D8C2×D23semidirect
249. C2×D8C2×D23semidirect
254. #124C2×D23semidirect
278. #97C2×D23semidirect
279. C23#3265semidirect
396. C8D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C2×SD16×D232
#130930752
#130930522
#130926602
#130926502
#130926292
#130926142
#130925662
#130925592
#130925542
#130925492
#130925192
#130924902
C23×#4962
#326523