Finite Group Databasebeta

← #15684878

Subgroups — #15684878

Order 2944.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625120C211yesmaximal, characteristic, complemented
2C22×#67272C211yesmaximal, characteristic, complemented
3D4×D92C211yesmaximal, characteristic, complemented
4#13092807C211yesmaximal, characteristic, complemented
5#13092668C211yesmaximal, characteristic, complemented
6#13092648C211yesmaximal, characteristic, complemented
7#13092629C211yesmaximal, characteristic, complemented
8#13092612C211yesmaximal, characteristic, complemented
9#13092567C211yesmaximal, characteristic, complemented
10#13092562C211yesmaximal, characteristic, complemented
11#13092551C211yesmaximal, characteristic, complemented
12#13092550C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14#13092489C211yesmaximal, characteristic, complemented
15C23×#546C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic, complemented
17C22×D4×C23C2211yescharacteristic, complemented
18C2×D4×D23—21no—
19C22×D92C2211yescharacteristic
20C22×D92C2211yescharacteristic, complemented
21C23×#124C2211yescharacteristic, complemented
22C23×#123—21no—
23C23×C22⋊Q8C2211yescharacteristic, complemented
24C23×#121—21no—
25C23×#121C2211yescharacteristic, complemented
26C23×#120—21no—
27C4×D4×C23C2211yescharacteristic
28C4×D4×C23C2211yescharacteristic, complemented
29C2×C22⋊C4×C23—21no—
30#10625120—24no—
31C2×#67274C2211yescharacteristic, complemented
32C2×#67274C2211yescharacteristic, complemented
33C2×#67274C2211yescharacteristic, complemented
34C2×#67272—24no—
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37C2×#67272C2211yescharacteristic, complemented
38C2×#67272C2211yescharacteristic, complemented
39C2×#67272C2211yescharacteristic, complemented
40C2×#67272C2211yescharacteristic, complemented
41#10625101C2211yescharacteristic
42#10625101C2211yescharacteristic, complemented
43C2×#67267C2211yescharacteristic, complemented
44C22×C23⋊C8C2211yescharacteristic, complemented
45#10625066—21no—
46#10625053—21no—
47#10625053—21no—
48#10625045C2211yescharacteristic, complemented
49C4×D92C2211yescharacteristic, complemented
50#10625017C2211yescharacteristic, complemented
51#10625014C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic, complemented
53C22⋊(C23⋊C8)C2211yescharacteristic, complemented
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic, complemented
56#10624991C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58#10624990C2211yescharacteristic, complemented
59C4⋊(C23⋊C8)C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C24×C23—21no—
62C23×D23—21no—
63C23×D23—21no—
64#41×C23—22no—
65#41×C23—41no—
66C2×Q8×C23C2311yescharacteristic
67C2×D4×C23—22no—
68C2×D4×C23—21no—
69C2×D4×C23—21no—
70C2×D4×C23—21no—
71C2×D4×C23—41no—
72C2×D4×C23D411yescharacteristic
73C2×D4×C23C2311yescharacteristic
74C2×D4×C23C2311yescharacteristic
75C22×C4×C23—21no—
76C22×C4×C23—21no—
77C22×C4×C23C2311yescharacteristic
78C22×C4×C23C2311yescharacteristic
79C2×C22⋊D23—21no—
80C2×C22⋊D23—21no—
81D4×D23—44no—
82C2×D92—22no—
83C2×D92—22no—
84C2×D92—21no—
85C2×D92—21no—
86C2×D92—21no—
87C2×D92—21no—
88C2×D92—41no—
89C2×D92—41no—
90C2×D92C2311yescharacteristic
91C2×D92C2311yescharacteristic
92C2×D92C2311yescharacteristic
93C2×C4×D23—21no—
94C4⋊C4×C23—21no—
95C4⋊C4×C23D411yescharacteristic
96C4⋊C4×C23C2311yescharacteristic
97C22⋊C4×C23—21no—
98C22⋊C4×C23—21no—
99C22⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C22⋊C4×C23—21no—
102C22⋊C4×C23D411yescharacteristic
103C22⋊C4×C23D411yescharacteristic
104C42×C23C2311yescharacteristic
105#67274—22no—
106#67274—22no—
107#67274—41no—
108#67272—22no—
109#67272—22no—
110#67272—22no—
111#67272—22no—
112#67272—41no—
113#67272D414yescomplemented
114(C2×D23)⋊C4—21no—
115(C2×D23)⋊C4—21no—
116(C2×D23)⋊C4—21no—
117C4⋊Dic23C2311yescharacteristic
118#67267—22no—
119C2×C23⋊C8—22no—
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122C2×C23⋊C8C2311yescharacteristic
123C2×C23⋊C8C2311yescharacteristic
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—42no—
127C23×C23—42no—
128C23×C23—81no—
129C23×C23C2×D411yescharacteristic
130C23×C23C2×D411yescharacteristic
131C22×D23—21no—
132C22×D23—21no—
133C22×D23—21no—
134C22×D23—42no—
135C22×D23—42no—
136C22×D23—42no—
137C22×D23—42no—
138C22×D23—81no—
139C22×D23—81no—
140Q8×C23—21no—
141Q8×C23—21no—
142D4×C23—22no—
143D4×C23—21no—
144D4×C23—21no—
145D4×C23—21no—
146D4×C23—42no—
147D4×C23—42no—
148D4×C23—81no—
149D4×C23C2×D412yescomplemented
150C2×C4×C23—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23—21no—
156C2×C4×C23—42no—
157C2×C4×C23—81no—
158C2×C4×C23C2×D411yescharacteristic
159C2×C4×C23C2×D411yescharacteristic
160C2×C4×C23C2×D411yescharacteristic
161C2×C4×C23C2×D411yescharacteristic
162C2×C4×C23C2411yescharacteristic
163C22⋊D23—42no—
164C22⋊D23—42no—
165C2×Dic23—21no—
166D92—21no—
167D92—21no—
168D92—21no—
169D92—21no—
170D92—21no—
171D92—42no—
172D92—42no—
173D92—42no—
174D92—81no—
175D92C2×D412yes—
176C4×D23—42no—
177C23⋊C8—21no—
178C23⋊C8—21no—
179C23⋊C8—21no—
180C23⋊C8C2×D412yescomplemented
181#3264—231nomaximal, Sylow
182C22×C23—21no—
183C22×C23—21no—
184C22×C23—21no—
185C22×C23—22no—
186C22×C23—21no—
187C22×C23—21no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23—41no—
192C22×C23—41no—
193C22×C23—84no—
194C22×C23AGL(1,ℤ/8)12yescomplemented
195C22×C23C22×D411yescharacteristic
196C2×D23—22no—
197C2×D23—41no—
198C2×D23—41no—
199C2×D23—41no—
200C2×D23—41no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—41no—
204C2×D23—41no—
205C2×D23—84no—
206C2×D23—84no—
207C4×C23—21no—
208C4×C23—21no—
209C4×C23—21no—
210C4×C23—21no—
211C4×C23—41no—
212C4×C23—41no—
213C4×C23C22×D411yescharacteristic
214C4×C23H(5,𝔽2)11yescharacteristic
215Dic23—41no—
216C2×AGL(1,ℤ/8)—231no—
217C22×D8—231no—
218#546D2311yescharacteristic, complemented
219D42—231no—
220#496—231no—
221#469—231no—
222#465—231no—
223#463—231no—
224#459—231no—
225#450—231no—
226#449—231no—
227#447—231no—
228#447—231no—
229#442—231no—
230#435—231no—
231C2×C23—22no—
232C2×C23—41no—
233C2×C23—42no—
234C2×C23—81no—
235C2×C23D4211yescharacteristic
236C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
237C2×C23#57611yescharacteristic
238D23—42no—
239D23—81no—
240D23—81no—
241C2×#41C2×D2311yescharacteristic, complemented
242C22×D4—231no—
243C22×D4—231no—
244C22×D4—461no—
245C22×D4C2×D2311yescharacteristic, complemented
246AGL(1,ℤ/8)—464no—
247C2×SD16—231no—
248C2×SD16—231no—
249C2×SD16—231no—
250C2×D8—231no—
251C2×D8—231no—
252C2×D8—231no—
253C2×D8—231no—
254C2×D8—231no—
255C2×D8—231no—
256C2×D8—464no—
257C2×M16—231no—
258C22×C8—231no—
259#127—231no—
260#124C2×D2311yescharacteristic, complemented
261#123—21no—
262C22⋊Q8C2×D2311yescharacteristic, complemented
263#121—21no—
264#121—231no—
265#121—231no—
266#121—461no—
267#121C2×D2311yescharacteristic, complemented
268#120—21no—
269#120—461no—
270#120—461no—
271C4×D4—231no—
272C4×D4C2×D2311yescharacteristic
273C4×D4C2×D2311yescharacteristic, complemented
274C2×C22⋊C4—21no—
275#106—231no—
276C4⋊C8—231no—
277#103—231no—
278#102—231no—
279#102—231no—
280#102—231no—
281#102—231no—
282#102—231no—
283C22⋊C8—231no—
284C22⋊C8—231no—
285#97—231no—
286C23#326411yescharacteristic, complemented, Sylow
287C24—21no—
288C24—461no—
289C24—461no—
290#41—22no—
291#41—41no—
292C2×Q8C22×D2311yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—231no—
299C2×D4—231no—
300C2×D4—231no—
301C2×D4—462no—
302C2×D4—462no—
303C2×D4—461no—
304C2×D4—461no—
305C2×D4—461no—
306C2×D4—461no—
307C2×D4—461no—
308C2×D4—461no—
309C2×D4—921no—
310C2×D4—921no—
311C2×D4—924no—
312C2×D4C22⋊D2311yescharacteristic
313C2×D4C22×D2311yescharacteristic
314C2×D4C22×D2311yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—461no—
318C22×C4C22×D2311yescharacteristic
319C22×C4C22×D2311yescharacteristic
320SD16—462no—
321SD16—462no—
322SD16—921no—
323D8—234no—
324D8—462no—
325D8—462no—
326D8—462no—
327D8—462no—
328D8—921no—
329M16—462no—
330C2×C8—231no—
331C2×C8—231no—
332C2×C8—231no—
333C2×C8—231no—
334C2×C8—462no—
335C4⋊C4—21no—
336C4⋊C4—231no—
337C4⋊C4C22⋊D2311yescharacteristic
338C4⋊C4C22×D2311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—461no—
345C22⋊C4—461no—
346C22⋊C4—461no—
347C22⋊C4C22⋊D2311yescharacteristic
348C22⋊C4C22⋊D2311yescharacteristic
349C42C22×D2311yescharacteristic
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—461no—
356C23—461no—
357C23—461no—
358C23—922no—
359C23—922no—
360C23—922no—
361C23—922no—
362C23—1841no—
363C23—1841no—
364C23C2×C22⋊D2311yescharacteristic
365C23C2×C22⋊D2311yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—42no—
374D4—81no—
375D4—232no—
376D4—461no—
377D4—461no—
378D4—461no—
379D4—461no—
380D4—461no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—922no—
385D4—922no—
386D4—1841no—
387D4D4×D2312yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—81no—
396C2×C4—461no—
397C2×C4—922no—
398C2×C4C2×C22⋊D2311yescharacteristic
399C2×C4C2×C22⋊D2311yescharacteristic
400C2×C4C2×C22⋊D2311yescharacteristic
401C2×C4C2×C22⋊D2311yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—232no—
404C8—461no—
405C8—461no—
406C8—461no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—462no—
420C22—921no—
421C22—921no—
422C22—921no—
423C22—921no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22—921no—
428C22—1844no—
429C22—1844no—
430C22#1062512012yescomplemented
431C22C22×C22⋊D2311yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062515511yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—922no—
446C2—1841no—
447C2—1841no—
448C2D4×C22⋊D2311yescharacteristic
449C2C2×#1062512011yescharacteristic
450C2#1309322011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#546C2
socleC22×C23C22×D4
hypercenter#546D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#10625120C2semidirect
2. C22×#67272C2semidirect
3. D4×D92C2semidirect
4. #13092807C2semidirect
5. #13092668C2semidirect
6. #13092648C2semidirect
7. #13092629C2semidirect
8. #13092612C2semidirect
9. #13092567C2semidirect
10. #13092562C2semidirect
11. #13092551C2semidirect
12. #13092550C2semidirect
13. #13092527C2semidirect
14. #13092489C2semidirect
15. C23×#546C2semidirect
16. C2×#41×C23C22semidirect
17. C22×D4×C23C22semidirect
20. C22×D92C22semidirect
21. C23×#124C22semidirect
23. C23×C22⋊Q8C22semidirect
25. C23×#121C22semidirect
28. C4×D4×C23C22semidirect
31. C2×#67274C22semidirect
32. C2×#67274C22semidirect
33. C2×#67274C22semidirect
37. C2×#67272C22semidirect
38. C2×#67272C22semidirect
39. C2×#67272C22semidirect
40. C2×#67272C22semidirect
42. #10625101C22semidirect
43. C2×#67267C22semidirect
44. C22×C23⋊C8C22semidirect
48. #10625045C22semidirect
49. C4×D92C22semidirect
50. #10625017C22semidirect
51. #10625014C22semidirect
52. #10625014C22semidirect
53. C22⋊(C23⋊C8)C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
55. #10624991C22semidirect
56. #10624991C22semidirect
57. #10624991C22semidirect
58. #10624990C22semidirect
59. C4⋊(C23⋊C8)C22semidirect
60. #10624985C22semidirect
113. #67272D4semidirect
149. D4×C23C2×D4semidirect
180. C23⋊C8C2×D4semidirect
194. C22×C23AGL(1,ℤ/8)semidirect
218. #546D23semidirect
241. C2×#41C2×D23semidirect
245. C22×D4C2×D23semidirect
260. #124C2×D23semidirect
262. C22⋊Q8C2×D23semidirect
267. #121C2×D23semidirect
273. C4×D4C2×D23semidirect
286. C23#3264semidirect
387. D4D4×D23semidirect
430. C22#10625120semidirect

Maximal subgroups

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

subgroupindex
C2×#106251202
C22×#672722
D4×D922
#130928072
#130926682
#130926482
#130926292
#130926122
#130925672
#130925622
#130925512
#130925502
#130925272
#130924892
C23×#5462
#326423