Finite Group Databasebeta

← #15676376

Subgroups — #15676376

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×#10625124C211yesmaximal, characteristic
2C2×C4×C22⋊D23C211yesmaximal, characteristic, complemented
3C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic23C211yesmaximal, characteristic, complemented
5#13092317C211yesmaximal, characteristic, complemented
6#13092311C211yesmaximal, characteristic, complemented
7#13092305C211yesmaximal, characteristic, complemented
8#13092296C211yesmaximal, characteristic, complemented
9#13092294C211yesmaximal, characteristic, complemented
10#13092293C211yesmaximal, characteristic, complemented
11#13092290C211yesmaximal, characteristic, complemented
12#13092289C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic23C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic23C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C23C211yesmaximal, characteristic, complemented
16C25×C23C2211yescharacteristic
17C23×C4×C23C2211yescharacteristic
18C23×C4×C23C2211yescharacteristic
19C22×C22⋊D23C2211yescharacteristic
20C22×C22⋊D23C2211yescharacteristic
21C22×C22⋊D23C2211yescharacteristic
22C23×Dic23C2211yescharacteristic
23C23×Dic23C2211yescharacteristic
24C22×C4×D23C2211yescharacteristic, complemented
25C2×C22⋊C4×C23—24no—
26C2×C22⋊C4×C23C2211yescharacteristic
27C2×C22⋊C4×C23C2211yescharacteristic
28C2×C22⋊C4×C23C2211yescharacteristic
29C2×C22⋊C4×C23C2211yescharacteristic
30#10625124C418yescomplemented
31C2×C22⋊Dic23—24no—
32C2×C22⋊Dic23C2211yescharacteristic
33C2×C22⋊Dic23C2211yescharacteristic
34C2×C22⋊Dic23C2211yescharacteristic
35C2×C22⋊Dic23C2211yescharacteristic
36C2×C22⋊Dic23C2211yescharacteristic
37C2×C22⋊Dic23C2211yescharacteristic
38C2×C22⋊Dic23C2211yescharacteristic
39C4×C22⋊D23—24no—
40C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D23)⋊C4C2211yescharacteristic, complemented
43C2×Dic23⋊C4C2211yescharacteristic, complemented
44C2×Dic23⋊C4C2211yescharacteristic, complemented
45C2×Dic23⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic23C2211yescharacteristic, complemented
47C2×C4×Dic23C2211yescharacteristic, complemented
48C2×C4×Dic23C2211yescharacteristic, complemented
49(C22⋊D23)⋊C4—24no—
50C23⋊#95C2211yescharacteristic, complemented
51C23⋊#95C2211yescharacteristic, complemented
52C23⋊#95C2211yescharacteristic, complemented
53C23⋊#95C2211yescharacteristic, complemented
54C23⋊#95C2211yescharacteristic, complemented
55C23⋊#95C2211yescharacteristic, complemented
56C24×C23—22no—
57C24×C23—22no—
58C24×C23—22no—
59C24×C23—22no—
60C24×C23—41no—
61C24×C23—41no—
62C24×C23C2×C414yescomplemented
63C24×C23C2311yescharacteristic
64C24×C23C2311yescharacteristic
65C24×C23C2311yescharacteristic
66C23×D23C2311yescharacteristic
67C22×C4×C23—22no—
68C22×C4×C23—22no—
69C22×C4×C23—22no—
70C22×C4×C23—22no—
71C22×C4×C23—41no—
72C22×C4×C23—41no—
73C22×C4×C23C2311yescharacteristic
74C22×C4×C23C2311yescharacteristic
75C22×C4×C23C2311yescharacteristic
76C22×C4×C23C2311yescharacteristic
77C2×C22⋊D23—22no—
78C2×C22⋊D23—22no—
79C2×C22⋊D23—22no—
80C2×C22⋊D23—22no—
81C2×C22⋊D23—41no—
82C2×C22⋊D23—41no—
83C2×C22⋊D23C2×C414yescomplemented
84C2×C22⋊D23C2×C414yescomplemented
85C2×C22⋊D23C2×C414yescomplemented
86C22×Dic23—22no—
87C22×Dic23—22no—
88C22×Dic23—22no—
89C22×Dic23—22no—
90C22×Dic23—41no—
91C22×Dic23—41no—
92C22×Dic23C2311yescharacteristic
93C22×Dic23C2311yescharacteristic
94C22×Dic23C2311yescharacteristic
95C22×Dic23C2311yescharacteristic
96C22×Dic23C2311yescharacteristic
97C22×Dic23C2311yescharacteristic
98C22×Dic23C2311yescharacteristic
99C2×C4×D23—22no—
100C2×C4×D23—22no—
101C2×C4×D23—41no—
102C22⋊C4×C23—22no—
103C22⋊C4×C23—22no—
104C22⋊C4×C23—22no—
105C22⋊C4×C23D414yescomplemented
106C22⋊Dic23—22no—
107C22⋊Dic23—22no—
108C22⋊Dic23—22no—
109C22⋊Dic23C2×C414yescomplemented
110C22⋊Dic23C2×C414yescomplemented
111C22⋊Dic23C2×C414yescomplemented
112C22⋊Dic23D414yescomplemented
113(C2×D23)⋊C4—22no—
114(C2×D23)⋊C4—22no—
115(C2×D23)⋊C4—41no—
116Dic23⋊C4—22no—
117Dic23⋊C4—22no—
118Dic23⋊C4—41no—
119C4×Dic23—22no—
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—28no—
131C23×C23—28no—
132C23×C23—21no—
133C23×C23—21no—
134C23×C23—21no—
135C23×C23—21no—
136C23×C23—21no—
137C23×C23—21no—
138C23×C23—44no—
139C23×C23—44no—
140C23×C23—44no—
141C23×C23—44no—
142C23×C23—44no—
143C23×C23C22×C412yes—
144C23×C23C22×C412yes—
145C23×C23C22×C412yes—
146C23×C23C2×D412yes—
147C23×C23C2×D412yes—
148C23×C23#4112yes—
149C23×C23#4112yes—
150C23×C23C2411yescharacteristic
151C22×D23—21no—
152C22×D23—21no—
153C22×D23—21no—
154C22×D23—21no—
155C22×D23—21no—
156C22×D23—21no—
157C22×D23C22×C412yes—
158C2×C4×C23—21no—
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—44no—
169C2×C4×C23—44no—
170C2×C4×C23C2×D412yes—
171C2×C4×C23C2×D412yes—
172C22⋊D23—28no—
173C22⋊D23—28no—
174C22⋊D23—44no—
175C2×Dic23—21no—
176C2×Dic23—21no—
177C2×Dic23—21no—
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—44no—
192C2×Dic23—44no—
193C2×Dic23C22×C412yes—
194C2×Dic23C22×C412yes—
195C2×Dic23C22×C412yes—
196C2×Dic23C2×D412yes—
197C2×Dic23C2×D412yes—
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—22no—
210C22×C23—22no—
211C22×C23—22no—
212C22×C23—22no—
213C22×C23—22no—
214C22×C23—22no—
215C22×C23—416no—
216C22×C23—41no—
217C22×C23—41no—
218C22×C23—41no—
219C22×C23—41no—
220C22×C23C4×D414yescomplemented
221C22×C23C4×D414yescomplemented
222C22×C23C23×C411yescharacteristic
223C22×C23C22×D411yescharacteristic
224C22×C23C22×D411yescharacteristic
225C22×C23C2×#4111yescharacteristic
226C22×C23C2×#4111yescharacteristic
227C22×C23H(5,𝔽2)11yescharacteristic
228C22×C23H(5,𝔽2)11yescharacteristic
229C2×D23—22no—
230C2×D23—22no—
231C2×D23—22no—
232C2×D23—41no—
233C2×D23—41no—
234C2×D23—41no—
235C2×D23—41no—
236C4×C23—22no—
237C4×C23—22no—
238C4×C23—41no—
239C4×C23—41no—
240Dic23—22no—
241Dic23—22no—
242Dic23—22no—
243Dic23—22no—
244Dic23—22no—
245Dic23—41no—
246Dic23—41no—
247C2×#120—231no—
248C2×C4×D4—231no—
249C2×C4×D4—231no—
250C22×C22⋊C4—231no—
251C22×C22⋊C4D2311yescharacteristic, complemented
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—24no—
264C2×C23—42no—
265C2×C23C2×C4×D411yescharacteristic
266C2×C23C2×C4×D411yescharacteristic
267C2×C23#51811yescharacteristic
268C2×C23D4211yescharacteristic
269C2×C23#54611yescharacteristic
270C2×C23#54611yescharacteristic
271C2×C23#55111yescharacteristic
272D23—42no—
273C25C2×D2311yescharacteristic
274C22×D4—231no—
275C22×D4—231no—
276C22×D4—231no—
277C23×C4—231no—
278C23×C4—231no—
279C23×C4—231no—
280C23×C4C2×D2311yescharacteristic
281C23×C4C2×D2311yescharacteristic
282#120—238no—
283C4×D4—464no—
284C4×D4—464no—
285C2×C4⋊C4—231no—
286C2×C4⋊C4—231no—
287C2×C4⋊C4—231no—
288C2×C22⋊C4—24no—
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—464no—
300C2×C22⋊C4C2×D2311yescharacteristic
301C2×C22⋊C4C2×D2311yescharacteristic
302C2×C22⋊C4C2×D2311yescharacteristic
303C2×C22⋊C4C2×D2311yescharacteristic
304C2×C42—231no—
305C2×C42—231no—
306C2×C42—231no—
307#95—231no—
308#95—231no—
309#95—231no—
310#95—231no—
311#95—231no—
312#95—231no—
313C23#235811yescharacteristic, complemented, Sylow
314C24—22no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—231no—
321C24C4×D2314yescomplemented
322C24C22×D2311yescharacteristic
323C24C22×D2311yescharacteristic
324C24C22×D2311yescharacteristic
325C2×D4—234no—
326C2×D4—234no—
327C2×D4—234no—
328C2×D4—462no—
329C2×D4—462no—
330C2×D4—462no—
331C2×D4—462no—
332C2×D4—921no—
333C2×D4—921no—
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—231no—
347C22×C4—462no—
348C22×C4—462no—
349C22×C4—462no—
350C22×C4—462no—
351C22×C4—462no—
352C22×C4—462no—
353C22×C4—921no—
354C22×C4—921no—
355C22×C4—921no—
356C22×C4C22×D2311yescharacteristic
357C22×C4C22×D2311yescharacteristic
358C22×C4C22×D2311yescharacteristic
359C22×C4C22×D2311yescharacteristic
360C4⋊C4—462no—
361C4⋊C4—462no—
362C4⋊C4—921no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—234no—
367C22⋊C4—234no—
368C22⋊C4—234no—
369C22⋊C4—234no—
370C22⋊C4—462no—
371C22⋊C4—462no—
372C22⋊C4—462no—
373C22⋊C4—462no—
374C22⋊C4—462no—
375C22⋊C4—921no—
376C22⋊C4C22⋊D2314yescomplemented
377C42—462no—
378C42—462no—
379C42—921no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—28no—
389C23—28no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—44no—
397C23—44no—
398C23—44no—
399C23—44no—
400C23—44no—
401C23—232no—
402C23—461no—
403C23—461no—
404C23—461no—
405C23—461no—
406C23—461no—
407C23—461no—
408C23C2×C4×D2312yes—
409C23C2×C4×D2312yes—
410C23C2×C4×D2312yes—
411C23#6728812yes—
412C23D4×D2312yes—
413C23#6729012yes—
414C23C2×C22⋊D2312yes—
415C23C23×D2311yescharacteristic
416D4—468no—
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—44no—
430C2×C4—44no—
431C2×C4—232no—
432C2×C4—232no—
433C2×C4—232no—
434C2×C4—232no—
435C2×C4—232no—
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—461no—
451C2×C4—461no—
452C2×C4—924no—
453C2×C4—924no—
454C2×C4—924no—
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—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—416no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—462no—
478C22—462no—
479C22—462no—
480C22—921no—
481C22—921no—
482C22—921no—
483C22—921no—
484C22(C22⋊D23)⋊C414yescomplemented
485C22C4×C22⋊D2314yescomplemented
486C22C22×C4×D2311yescharacteristic
487C22C2×#6728811yescharacteristic
488C22C2×D4×D2311yescharacteristic
489C22C2×#6729011yescharacteristic
490C22#1062515511yescharacteristic
491C22#1062515511yescharacteristic
492C22C22×C22⋊D2311yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—462no—
498C4—462no—
499C4—462no—
500C4—462no—
501C4—462no—
502C4—921no—
503C4—921no—
504C2—24no—
505C2—24no—
506C2—42no—
507C2—922no—
508C2C2×(C22⋊D23)⋊C411yescharacteristic
509C2C2×C4×C22⋊D2311yescharacteristic
510C2#1309289011yescharacteristic
511C2D4×C22⋊D2311yescharacteristic
512C2#1309305711yescharacteristic
513C2#1309306111yescharacteristic
514C2#1309309311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC22×C22⋊C4×C23C2
socle, cosocleC23×C23C24
prime radicalC2×#10625124C2
hypercenterC22×C22⋊C4D23
hypocenterC23#2358
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D23C2semidirect
3. C2×(C22⋊D23)⋊C4C2semidirect
4. C22×C22⋊Dic23C2semidirect
5. #13092317C2semidirect
6. #13092311C2semidirect
7. #13092305C2semidirect
8. #13092296C2semidirect
9. #13092294C2semidirect
10. #13092293C2semidirect
11. #13092290C2semidirect
12. #13092289C2semidirect
13. C22⋊C4×Dic23C2semidirect
14. C4×C22⋊Dic23C2semidirect
15. C22×C22⋊C4×C23C2semidirect
24. C22×C4×D23C22semidirect
30. #10625124C4semidirect
40. C2×(C2×D23)⋊C4C22semidirect
41. C2×(C2×D23)⋊C4C22semidirect
42. C2×(C2×D23)⋊C4C22semidirect
43. C2×Dic23⋊C4C22semidirect
44. C2×Dic23⋊C4C22semidirect
45. C2×Dic23⋊C4C22semidirect
46. C2×C4×Dic23C22semidirect
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
62. C24×C23C2×C4semidirect
83. C2×C22⋊D23C2×C4semidirect
84. C2×C22⋊D23C2×C4semidirect
85. C2×C22⋊D23C2×C4semidirect
105. C22⋊C4×C23D4semidirect
109. C22⋊Dic23C2×C4semidirect
110. C22⋊Dic23C2×C4semidirect
111. C22⋊Dic23C2×C4semidirect
112. C22⋊Dic23D4semidirect
220. C22×C23C4×D4semidirect
221. C22×C23C4×D4semidirect
251. C22×C22⋊C4D23semidirect
313. C23#2358semidirect
321. C24C4×D23semidirect
376. C22⋊C4C22⋊D23semidirect
484. C22(C22⋊D23)⋊C4semidirect
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×#106251242
C2×C4×C22⋊D232
C2×(C22⋊D23)⋊C42
C22×C22⋊Dic232
#130923172
#130923112
#130923052
#130922962
#130922942
#130922932
#130922902
#130922892
C22⋊C4×Dic232
C4×C22⋊Dic232
C22×C22⋊C4×C232
#235823