Finite Group Databasebeta

← #15676374

Subgroups — #15676374

Order 2944.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625108C211yesmaximal, characteristic
2C2×C4×C22⋊D23C211yesmaximal, characteristic, complemented
3C22×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D23C211yesmaximal, characteristic, complemented
5#13092317C211yesmaximal, characteristic, complemented
6#13092308C211yesmaximal, characteristic, complemented
7#13092307C211yesmaximal, characteristic, complemented
8#13092297C211yesmaximal, characteristic, complemented
9#13092296C211yesmaximal, characteristic, complemented
10#13092293C211yesmaximal, characteristic, complemented
11#13092290C211yesmaximal, characteristic, complemented
12#13092288C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic23C211yesmaximal, characteristic, complemented
14C4×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×D4×C23C211yesmaximal, characteristic, complemented
16C24×D23C2211yescharacteristic
17C22×D4×C23C2211yescharacteristic
18C23×C4×C23C2211yescharacteristic
19C23×C4×C23C2211yescharacteristic, complemented
20C22×C22⋊D23C2211yescharacteristic
21C22×C22⋊D23C2211yescharacteristic
22C23×Dic23C2211yescharacteristic
23C22×C4×D23C2211yescharacteristic
24C22×C4×D23C2211yescharacteristic
25C4×D4×C23—24no—
26C2×C4⋊C4×C23C2211yescharacteristic, complemented
27C2×C22⋊C4×C23C2211yescharacteristic
28C2×C22⋊C4×C23C2211yescharacteristic, complemented
29C2×C42×C23C2211yescharacteristic, complemented
30C2×C22⋊Dic23C2211yescharacteristic
31C2×C22⋊Dic23C2211yescharacteristic
32C2×C22⋊Dic23C2211yescharacteristic, complemented
33C2×C22⋊Dic23C2211yescharacteristic, complemented
34#10625108C418yescomplemented
35C4×C22⋊D23—24no—
36C2×(C2×D23)⋊C4—24no—
37C2×(C2×D23)⋊C4C2211yescharacteristic
38C2×(C2×D23)⋊C4C2211yescharacteristic
39C2×(C2×D23)⋊C4C2211yescharacteristic
40C2×(C2×D23)⋊C4C2211yescharacteristic
41C2×(C2×D23)⋊C4C2211yescharacteristic
42C2×(C2×D23)⋊C4C2211yescharacteristic
43C2×(C2×D23)⋊C4C2211yescharacteristic
44C2×(C2×D23)⋊C4C2211yescharacteristic
45C2×Dic23⋊C4C2211yescharacteristic, complemented
46C2×Dic23⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic23C2211yescharacteristic, complemented
48C2×C4×Dic23C2211yescharacteristic, complemented
49C22⋊C4×D23—24no—
50C23⋊#95C2211yescharacteristic, complemented
51C23⋊#95C2211yescharacteristic, complemented
52C23⋊#95C2211yescharacteristic, complemented
53C23⋊#95C2211yescharacteristic, complemented
54C23⋊#95C2211yescharacteristic, complemented
55C23⋊#95C2211yescharacteristic, complemented
56C24×C23C2311yescharacteristic
57C24×C23C2311yescharacteristic
58C23×D23—22no—
59C23×D23—22no—
60C23×D23—22no—
61C23×D23—22no—
62C23×D23—41no—
63C23×D23—41no—
64C23×D23C2×C414yescomplemented
65C23×D23C2311yescharacteristic
66C23×D23C2311yescharacteristic
67C2×D4×C23—22no—
68C2×D4×C23—22no—
69C2×D4×C23C2×C414yescomplemented
70C22×C4×C23—22no—
71C22×C4×C23—22no—
72C22×C4×C23—22no—
73C22×C4×C23—22no—
74C22×C4×C23—41no—
75C22×C4×C23—41no—
76C22×C4×C23C2311yescharacteristic
77C22×C4×C23C2311yescharacteristic
78C22×C4×C23C2311yescharacteristic
79C22×C4×C23C2311yescharacteristic
80C22×C4×C23C2311yescharacteristic
81C2×C22⋊D23—22no—
82C2×C22⋊D23—22no—
83C2×C22⋊D23—41no—
84C2×C22⋊D23—41no—
85C2×C22⋊D23C2×C414yescomplemented
86C2×C22⋊D23C2×C414yescomplemented
87C22×Dic23—22no—
88C22×Dic23—22no—
89C22×Dic23—41no—
90C22×Dic23C2311yescharacteristic
91C22×Dic23C2311yescharacteristic
92C22×Dic23C2311yescharacteristic
93C22×Dic23C2311yescharacteristic
94C22×Dic23C2311yescharacteristic
95C22×Dic23C2311yescharacteristic
96C2×C4×D23—22no—
97C2×C4×D23—22no—
98C2×C4×D23—22no—
99C2×C4×D23—22no—
100C2×C4×D23—41no—
101C2×C4×D23—41no—
102C4⋊C4×C23—22no—
103C22⋊C4×C23—22no—
104C22⋊C4×C23D414yescomplemented
105C42×C23—22no—
106C22⋊Dic23—22no—
107C22⋊Dic23—22no—
108C22⋊Dic23—41no—
109C22⋊Dic23C2×C414yescomplemented
110(C2×D23)⋊C4—22no—
111(C2×D23)⋊C4—22no—
112(C2×D23)⋊C4—22no—
113(C2×D23)⋊C4—22no—
114(C2×D23)⋊C4—22no—
115(C2×D23)⋊C4C2×C414yescomplemented
116(C2×D23)⋊C4C2×C414yescomplemented
117(C2×D23)⋊C4D414yescomplemented
118Dic23⋊C4—22no—
119Dic23⋊C4—41no—
120C4×Dic23—22no—
121C4×Dic23—41no—
122C23×C23—21no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—21no—
127C23×C23—21no—
128C23×C23—21no—
129C23×C23—21no—
130C23×C23—21no—
131C23×C23—21no—
132C23×C23C22×C412yes—
133C23×C23C22×C412yes—
134C23×C23C2×D412yes—
135C23×C23#4112yes—
136C23×C23C2411yescharacteristic
137C22×D23—21no—
138C22×D23—21no—
139C22×D23—21no—
140C22×D23—21no—
141C22×D23—28no—
142C22×D23—21no—
143C22×D23—21no—
144C22×D23—21no—
145C22×D23—21no—
146C22×D23—21no—
147C22×D23—21no—
148C22×D23—28no—
149C22×D23—44no—
150C22×D23—44no—
151C22×D23—44no—
152C22×D23—44no—
153C22×D23—44no—
154C22×D23C22×C412yes—
155C22×D23C22×C412yes—
156C22×D23C2×D412yes—
157C22×D23#4112yes—
158D4×C23—28no—
159C2×C4×C23—21no—
160C2×C4×C23—21no—
161C2×C4×C23—21no—
162C2×C4×C23—21no—
163C2×C4×C23—21no—
164C2×C4×C23—21no—
165C2×C4×C23—21no—
166C2×C4×C23—21no—
167C2×C4×C23—21no—
168C2×C4×C23—21no—
169C2×C4×C23—21no—
170C2×C4×C23—44no—
171C2×C4×C23—44no—
172C2×C4×C23C22×C412yes—
173C2×C4×C23C2×D412yes—
174C2×C4×C23C2×D412yes—
175C2×C4×C23C2×D412yes—
176C22⋊D23—28no—
177C22⋊D23—44no—
178C2×Dic23—21no—
179C2×Dic23—21no—
180C2×Dic23—21no—
181C2×Dic23—21no—
182C2×Dic23—21no—
183C2×Dic23—21no—
184C2×Dic23—21no—
185C2×Dic23—21no—
186C2×Dic23—21no—
187C2×Dic23—21no—
188C2×Dic23—21no—
189C2×Dic23—21no—
190C2×Dic23—21no—
191C2×Dic23—21no—
192C2×Dic23—21no—
193C2×Dic23—44no—
194C2×Dic23C22×C412yes—
195C2×Dic23C22×C412yes—
196C2×Dic23C2×D412yes—
197C4×D23—44no—
198C4×D23—44no—
199#2358—231nomaximal, Sylow
200C22×C23—22no—
201C22×C23—22no—
202C22×C23—22no—
203C22×C23—22no—
204C22×C23—22no—
205C22×C23—22no—
206C22×C23—22no—
207C22×C23—22no—
208C22×C23—22no—
209C22×C23—41no—
210C22×C23—41no—
211C22×C23—41no—
212C22×C23—41no—
213C22×C23C4×D414yescomplemented
214C22×C23C23×C411yescharacteristic
215C22×C23C22×D411yescharacteristic
216C22×C23C22×D411yescharacteristic
217C22×C23C2×#4111yescharacteristic
218C22×C23C2×#4111yescharacteristic
219C22×C23H(5,𝔽2)11yescharacteristic
220C22×C23H(5,𝔽2)11yescharacteristic
221C2×D23—22no—
222C2×D23—22no—
223C2×D23—22no—
224C2×D23—22no—
225C2×D23—22no—
226C2×D23—22no—
227C2×D23—22no—
228C2×D23—22no—
229C2×D23—22no—
230C2×D23—416no—
231C2×D23—41no—
232C2×D23—41no—
233C2×D23—41no—
234C2×D23—41no—
235C2×D23C4×D414yescomplemented
236C4×C23—22no—
237C4×C23—22no—
238C4×C23—22no—
239C4×C23—22no—
240C4×C23—41no—
241Dic23—22no—
242Dic23—22no—
243Dic23—22no—
244Dic23—41no—
245Dic23—41no—
246Dic23—41no—
247C2×#120—231no—
248C2×C4×D4—231no—
249C2×C4×D4D2311yescharacteristic, complemented
250C22×C22⋊C4—231no—
251C22×C22⋊C4—231no—
252#390—231no—
253#388—231no—
254#388—231no—
255#386—231no—
256#386—231no—
257#386—231no—
258#385—231no—
259#385—231no—
260C4×C22⋊C4—231no—
261C4×C22⋊C4—231no—
262C2×C23—24no—
263C2×C23—42no—
264C2×C23C2×C4×D411yescharacteristic
265C2×C23C2×C4×D411yescharacteristic
266C2×C23#51811yescharacteristic
267C2×C23D4211yescharacteristic
268C2×C23#54611yescharacteristic
269C2×C23#54611yescharacteristic
270C2×C23#55111yescharacteristic
271D23—24no—
272D23—42no—
273C25—231no—
274C22×D4—231no—
275C22×D4—231no—
276C22×D4C2×D2311yescharacteristic
277C23×C4—231no—
278C23×C4—231no—
279C23×C4—231no—
280C23×C4C2×D2311yescharacteristic
281C23×C4C2×D2311yescharacteristic, complemented
282#120—238no—
283C4×D4—24no—
284C4×D4—464no—
285C2×C4⋊C4—231no—
286C2×C4⋊C4—231no—
287C2×C4⋊C4C2×D2311yescharacteristic, complemented
288C2×C22⋊C4—231no—
289C2×C22⋊C4—231no—
290C2×C22⋊C4—231no—
291C2×C22⋊C4—231no—
292C2×C22⋊C4—231no—
293C2×C22⋊C4—231no—
294C2×C22⋊C4—231no—
295C2×C22⋊C4—231no—
296C2×C22⋊C4—231no—
297C2×C22⋊C4—231no—
298C2×C22⋊C4—231no—
299C2×C22⋊C4—231no—
300C2×C22⋊C4—464no—
301C2×C22⋊C4—464no—
302C2×C22⋊C4C2×D2311yescharacteristic
303C2×C22⋊C4C2×D2311yescharacteristic, complemented
304C2×C42—231no—
305C2×C42—231no—
306C2×C42C2×D2311yescharacteristic, complemented
307#95—231no—
308#95—231no—
309#95—231no—
310#95—231no—
311#95—231no—
312#95—231no—
313C23#235811yescharacteristic, complemented, Sylow
314C24—231no—
315C24—231no—
316C24—234no—
317C24—462no—
318C24—462no—
319C24—462no—
320C24—462no—
321C24—921no—
322C24—921no—
323C24C22×D2311yescharacteristic
324C24C22×D2311yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—234no—
328C2×D4—234no—
329C2×D4—462no—
330C2×D4—462no—
331C2×D4—921no—
332C2×D4—921no—
333C2×D4C4×D2314yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—231no—
341C22×C4—231no—
342C22×C4—231no—
343C22×C4—231no—
344C22×C4—231no—
345C22×C4—231no—
346C22×C4—462no—
347C22×C4—462no—
348C22×C4—462no—
349C22×C4—462no—
350C22×C4—462no—
351C22×C4—462no—
352C22×C4—921no—
353C22×C4—921no—
354C22×C4—921no—
355C22×C4C22×D2311yescharacteristic
356C22×C4C22×D2311yescharacteristic
357C22×C4C22×D2311yescharacteristic
358C22×C4C22×D2311yescharacteristic
359C22×C4C22×D2311yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—462no—
362C4⋊C4—921no—
363C22⋊C4—22no—
364C22⋊C4—234no—
365C22⋊C4—234no—
366C22⋊C4—234no—
367C22⋊C4—234no—
368C22⋊C4—462no—
369C22⋊C4—462no—
370C22⋊C4—462no—
371C22⋊C4—462no—
372C22⋊C4—462no—
373C22⋊C4—462no—
374C22⋊C4—462no—
375C22⋊C4—921no—
376C22⋊C4C22⋊D2314yescomplemented
377C42—22no—
378C42—462no—
379C42—921no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—232no—
391C23—232no—
392C23—232no—
393C23—232no—
394C23—468no—
395C23—461no—
396C23—461no—
397C23—461no—
398C23—461no—
399C23—468no—
400C23—461no—
401C23—461no—
402C23—461no—
403C23—461no—
404C23—461no—
405C23—461no—
406C23—924no—
407C23—924no—
408C23—924no—
409C23—924no—
410C23—924no—
411C23C2×C4×D2312yes—
412C23C2×C4×D2312yes—
413C23#6728812yes—
414C23C2×C22⋊D2312yes—
415C23C23×D2311yescharacteristic
416D4—28no—
417D4—468no—
418D4—924no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—44no—
431C2×C4—44no—
432C2×C4—232no—
433C2×C4—232no—
434C2×C4—232no—
435C2×C4—461no—
436C2×C4—461no—
437C2×C4—461no—
438C2×C4—461no—
439C2×C4—461no—
440C2×C4—461no—
441C2×C4—461no—
442C2×C4—461no—
443C2×C4—461no—
444C2×C4—461no—
445C2×C4—461no—
446C2×C4—461no—
447C2×C4—461no—
448C2×C4—461no—
449C2×C4—461no—
450C2×C4—924no—
451C2×C4—924no—
452C2×C4—924no—
453C2×C4C2×C4×D2312yes—
454C2×C4D4×D2312yes—
455C2×C4C2×C22⋊D2312yes—
456C2×C4C2×C22⋊D2312yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—234no—
471C22—462no—
472C22—462no—
473C22—462no—
474C22—462no—
475C22—462no—
476C22—462no—
477C22—462no—
478C22—462no—
479C22—462no—
480C22—9216no—
481C22—921no—
482C22—921no—
483C22—921no—
484C22—921no—
485C22C4×C22⋊D2314yescomplemented
486C22C22×C4×D2311yescharacteristic
487C22C2×#6728811yescharacteristic
488C22C2×D4×D2311yescharacteristic
489C22#1062515511yescharacteristic
490C22#41×D2311yescharacteristic
491C22#1062516011yescharacteristic
492C22C22×C22⋊D2311yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—462no—
499C4—462no—
500C4—462no—
501C4—921no—
502C4—921no—
503C4—921no—
504C2—24no—
505C2—42no—
506C2—464no—
507C2—922no—
508C2C4×D4×D2311yescharacteristic
509C2C2×C4×C22⋊D2311yescharacteristic
510C2#1309288911yescharacteristic
511C2D4×C22⋊D2311yescharacteristic
512C2#1309305511yescharacteristic
513C2#1309306311yescharacteristic
514C2#1309309611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC2×C4×D4×C23C2
socle, cosocleC23×C23C24
prime radicalC2×#10625108C2
hypercenterC2×C4×D4D23
hypocenterC23#2358
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D23C2semidirect
3. C22×(C2×D23)⋊C4C2semidirect
4. C2×C22⋊C4×D23C2semidirect
5. #13092317C2semidirect
6. #13092308C2semidirect
7. #13092307C2semidirect
8. #13092297C2semidirect
9. #13092296C2semidirect
10. #13092293C2semidirect
11. #13092290C2semidirect
12. #13092288C2semidirect
13. C22⋊C4×Dic23C2semidirect
14. C4×(C2×D23)⋊C4C2semidirect
15. C2×C4×D4×C23C2semidirect
19. C23×C4×C23C22semidirect
26. C2×C4⋊C4×C23C22semidirect
28. C2×C22⋊C4×C23C22semidirect
29. C2×C42×C23C22semidirect
32. C2×C22⋊Dic23C22semidirect
33. C2×C22⋊Dic23C22semidirect
34. #10625108C4semidirect
45. C2×Dic23⋊C4C22semidirect
46. C2×Dic23⋊C4C22semidirect
47. C2×C4×Dic23C22semidirect
48. C2×C4×Dic23C22semidirect
50. C23⋊#95C22semidirect
51. C23⋊#95C22semidirect
52. C23⋊#95C22semidirect
53. C23⋊#95C22semidirect
54. C23⋊#95C22semidirect
55. C23⋊#95C22semidirect
64. C23×D23C2×C4semidirect
69. C2×D4×C23C2×C4semidirect
85. C2×C22⋊D23C2×C4semidirect
86. C2×C22⋊D23C2×C4semidirect
104. C22⋊C4×C23D4semidirect
109. C22⋊Dic23C2×C4semidirect
115. (C2×D23)⋊C4C2×C4semidirect
116. (C2×D23)⋊C4C2×C4semidirect
117. (C2×D23)⋊C4D4semidirect
213. C22×C23C4×D4semidirect
235. C2×D23C4×D4semidirect
249. C2×C4×D4D23semidirect
281. C23×C4C2×D23semidirect
287. C2×C4⋊C4C2×D23semidirect
303. C2×C22⋊C4C2×D23semidirect
306. C2×C42C2×D23semidirect
313. C23#2358semidirect
333. C2×D4C4×D23semidirect
376. C22⋊C4C22⋊D23semidirect
485. C22C4×C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251082
C2×C4×C22⋊D232
C22×(C2×D23)⋊C42
C2×C22⋊C4×D232
#130923172
#130923082
#130923072
#130922972
#130922962
#130922932
#130922902
#130922882
C22⋊C4×Dic232
C4×(C2×D23)⋊C42
C2×C4×D4×C232
#235823