Finite Group Databasebeta

← #11867110

Subgroups — #11867110

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64123C211yesmaximal, characteristic, complemented
2C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596098C211yesmaximal, characteristic, complemented
4C3⋊D3×#121C211yesmaximal, characteristic, complemented
5C32×#468C211yesmaximal, characteristic, complemented
6#10592870C211yesmaximal, characteristic, complemented
7#10592834C211yesmaximal, characteristic, complemented
8#10592748C211yesmaximal, characteristic, complemented
9#10592738C211yesmaximal, characteristic, complemented
10#10592582C211yesmaximal, characteristic, complemented
11#10592580C211yesmaximal, characteristic, complemented
12#10592506C211yesmaximal, characteristic, complemented
13#10592502C211yesmaximal, characteristic, complemented
14#10592474C211yesmaximal, characteristic, complemented
15#10592469C211yesmaximal, characteristic, complemented
16#80805—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22C2×C32×M16C2211yescharacteristic, complemented
23C32×C22⋊Q8C2211yescharacteristic, complemented
24C32×#121C2211yescharacteristic
25#64155C2211yescharacteristic, complemented
26C2×#3755C2211yescharacteristic, complemented
27#64148—21no—
28#64147C2211yescharacteristic
29C2×#3753C2211yescharacteristic, complemented
30#64139C2211yescharacteristic
31#64139C2211yescharacteristic, complemented
32C2×#3748C2211yescharacteristic, complemented
33#64123—24no—
34M16×C3⋊D3—24no—
35C2×#3745C2211yescharacteristic, complemented
36C2×#3743C2211yescharacteristic
37C2×#3743C2211yescharacteristic
38C2×C8×C3⋊D3C2211yescharacteristic, complemented
39C2×C8×C3⋊D3C2211yescharacteristic, complemented
40#64104C2211yescharacteristic
41#64104C2211yescharacteristic, complemented
42#64103—21no—
43#64102—21no—
44#64101C2211yescharacteristic
45C4⋊C4×C3⋊D3C2211yescharacteristic
46#64093—21no—
47#64091—21no—
48#64090—21no—
49C22⋊C4×C3⋊D3—21no—
50C32×#107C2211yescharacteristic, complemented
51C32×#103C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63648C2211yescharacteristic, complemented
56#63648C2211yescharacteristic, complemented
57#63644C2211yescharacteristic, complemented
58#63636C2211yescharacteristic, complemented
59#63636C2211yescharacteristic, complemented
60#63635C2211yescharacteristic, complemented
61#63634C2211yescharacteristic, complemented
62C2×#914—34no—
63C2×D3×M16—34no—
64#5627—34no—
65D3×#121—34no—
66C3×#468D314yescomplemented
67#5171—34no—
68#5135—34no—
69#5049—34no—
70#5039—34no—
71#4883—34no—
72#4881—34no—
73#4807—34no—
74#4803—34no—
75#4775—34no—
76#4770—34no—
77C23×C3⋊D3—21no—
78C23×C3⋊D3D411yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×D4—21no—
81C2×C32×D4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C2×#638—21no—
87C22×C3⋊Dic3D411yescharacteristic
88#3832—22no—
89#3832—22no—
90D4×C3⋊D3—22no—
91D4×C3⋊D3—22no—
92D4×C3⋊D3—44no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3D411yescharacteristic
103C2×C4×C3⋊D3D411yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C32×SD16—22no—
107C32×M16—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115#3757—21no—
116#3755—22no—
117#3753—22no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3750—21no—
128C4×C3⋊Dic3—21no—
129#3748—22no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3745—22no—
133#3743—22no—
134#3743D414yescomplemented
135C8×C3⋊D3—22no—
136C8×C3⋊D3—22no—
137#3055—91noSylow
138C2×#239—34no—
139C2×D3×D4—34no—
140C2×D3×D4—64no—
141C22×C4×D3—34no—
142C2×C3×SD16C2×D314yescomplemented
143C2×C3×M16C2×D314yescomplemented
144C3×C22⋊Q8C2×D314yescomplemented
145C3×#121C2×D314yes—
146#946—34no—
147C2×#215—34no—
148#939—64no—
149#938—34no—
150C2×#213—34no—
151#930—34no—
152#930—34no—
153C2×#208—34no—
154#914—616no—
155D3×M16—616no—
156C2×D24—34no—
157C2×ΓL(1,𝔽25)—34no—
158C2×ΓL(1,𝔽25)—34no—
159C2×D3×C8—34no—
160C2×D3×C8—34no—
161#895—34no—
162#895—34no—
163#894—64no—
164#893—64no—
165#892—34no—
166D3×C4⋊C4—34no—
167#884—64no—
168#882—64no—
169#67⋊C4—64no—
170D3×C22⋊C4—64no—
171C3×#107C2×D314yescomplemented
172C3×#103C2×D314yescomplemented
173C3×#102C2×D314yescomplemented
174#835—34no—
175#832—34no—
176#821—34no—
177#821—34no—
178#817—34no—
179#809—34no—
180#809—34no—
181#808—34no—
182#807—34no—
183C23×C32—21no—
184C23×C32C2×D411yescharacteristic
185C22×C3⋊D3—22no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3—41no—
190C22×C3⋊D3—42no—
191C22×C3⋊D3—42no—
192C22×C3⋊D3—42no—
193C22×C3⋊D3C2×D411yescharacteristic
194C22×C3⋊D3C2×D411yescharacteristic
195C32×Q8—21no—
196C32×Q8—21no—
197C32×D4—21no—
198C32×D4—21no—
199C32×D4—42no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2411yescharacteristic
207#638—42no—
208#638—42no—
209#638—42no—
210#638—42no—
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3C2×D411yescharacteristic
215C2×C3⋊Dic3C2×D411yescharacteristic
216C4⋊(C3⋊D3)—21no—
217C4⋊(C3⋊D3)—21no—
218C4⋊(C3⋊D3)—21no—
219C4⋊(C3⋊D3)—21no—
220C4⋊(C3⋊D3)—42no—
221C4⋊(C3⋊D3)—42no—
222C4⋊(C3⋊D3)—42no—
223C4×C3⋊D3—22no—
224C4×C3⋊D3—21no—
225C4×C3⋊D3—21no—
226C4×C3⋊D3—22no—
227C4×C3⋊D3—42no—
228C4×C3⋊D3—42no—
229C4×C3⋊D3C2×D412yes—
230C4×C3⋊D3#4112yes—
231C32×C8—21no—
232C32×C8C2×D412yescomplemented
233C3⋊(C3⋊C8)—21no—
234C3⋊(C3⋊C8)C2×D412yescomplemented
235C2×AGL(1,ℤ/8)—91no—
236C22×M16—91no—
237#525—91no—
238C2×#121—91no—
239#469—91no—
240#469—91no—
241#468—91no—
242#468C3⋊D311yescharacteristic, complemented
243#466—91no—
244#466—91no—
245#465—91no—
246#465—91no—
247#428—91no—
248#418—91no—
249#417—91no—
250C23×D3—34no—
251C23×D3—64no—
252C2×C3×Q8C22×D314yes—
253C2×C3×D4—24no—
254C2×C3×D4C22×D314yes—
255C22×C3×C4C22×D314yes—
256C2×#67—64no—
257C2×#67—64no—
258C2×#67—64no—
259C2×#67—64no—
260C22×Dic3—34no—
261#239—68no—
262#239—68no—
263D3×D4—68no—
264D3×D4—68no—
265D3×D4—1216no—
266C2×D12—34no—
267C2×D12—34no—
268C2×D12—64no—
269C2×D12—64no—
270C2×D12—64no—
271C2×C4×D3—34no—
272C2×C4×D3—34no—
273C2×C4×D3—34no—
274C2×C4×D3—34no—
275C2×C4×D3—68no—
276C2×C4×D3—68no—
277C2×C4×D3—64no—
278C2×C4×D3—64no—
279C3×SD16—28no—
280C3×M16—28no—
281C2×C3×C8C22×D314yes—
282C2×C3×C8C22×D314yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4C22×D314yes—
285C3×C4⋊C4C22×D314yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288#217—64no—
289#215—68no—
290#213—68no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297C4⋊Dic3—34no—
298C4⋊Dic3—34no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301C4×Dic3—64no—
302#208—68no—
303C2×C3⋊C8—34no—
304C2×C3⋊C8—34no—
305D24—68no—
306ΓL(1,𝔽25)—316no—
307ΓL(1,𝔽25)—68no—
308D3×C8—68no—
309D3×C8—68no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32C22×D411yescharacteristic
317C2×C3⋊D3—21no—
318C2×C3⋊D3—21no—
319C2×C3⋊D3—21no—
320C2×C3⋊D3—21no—
321C2×C3⋊D3—44no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3—84no—
329C2×C3⋊D3#12112yes—
330C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
331C32×C4—21no—
332C32×C4—41no—
333C32×C4—41no—
334C32×C4—41no—
335C32×C4C22×D411yescharacteristic
336C32×C4C2×#4111yescharacteristic
337C3⋊Dic3—21no—
338C3⋊Dic3—41no—
339C3⋊Dic3—41no—
340C3⋊Dic3#12112yes—
341C2×#41—91no—
342C22×D4—91no—
343C22×D4—181no—
344C23×C4—91no—
345AGL(1,ℤ/8)—184no—
346C2×SD16—91no—
347C2×SD16C2×C3⋊D311yescharacteristic, complemented
348C2×D8—91no—
349C2×D8—91no—
350C2×M16—91no—
351C2×M16—91no—
352C2×M16—91no—
353C2×M16—184no—
354C2×M16C2×C3⋊D311yescharacteristic, complemented
355C22×C8—91no—
356C22×C8—91no—
357#123—181no—
358C22⋊Q8—91no—
359C22⋊Q8C2×C3⋊D311yescharacteristic, complemented
360#121—91no—
361#121—91no—
362#121—91no—
363#121—91no—
364#121—91no—
365#121—181no—
366#121—181no—
367#121C2×C3⋊D311yescharacteristic
368#120—181no—
369C4×D4—181no—
370C4×D4—181no—
371#117—91no—
372C2×C4⋊C4—91no—
373C2×C22⋊C4—181no—
374#107—91no—
375#107C2×C3⋊D311yescharacteristic, complemented
376#106—91no—
377#106—91no—
378#103—91no—
379#103C2×C3⋊D311yescharacteristic, complemented
380#102—91no—
381#102—91no—
382#102—91no—
383#102—91no—
384#102—91no—
385#102C2×C3⋊D311yescharacteristic, complemented
386C23×C3—24no—
387C23×C3D3×D414yes—
388C22×D3—34no—
389C22×D3—34no—
390C22×D3—68no—
391C22×D3—68no—
392C22×D3—64no—
393C22×D3—64no—
394C22×D3—128no—
395C22×D3—124no—
396C22×D3—128no—
397C22×D3—128no—
398C3×Q8—24no—
399C3×Q8—24no—
400C3×D4—24no—
401C3×D4—24no—
402C3×D4—48no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4D3×D414yes—
409C2×C3×C4C23×D314yes—
410#67—128no—
411#67—128no—
412#67—128no—
413#67—128no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—68no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419D12—64no—
420D12—64no—
421D12—64no—
422D12—64no—
423D12—128no—
424D12—128no—
425D12—128no—
426C4×D3—38no—
427C4×D3—38no—
428C4×D3—68no—
429C4×D3—68no—
430C4×D3—64no—
431C4×D3—64no—
432C4×D3—128no—
433C4×D3—128no—
434C3×C8—24no—
435C3×C8D3×D418yescomplemented
436C3⋊C8—38no—
437C3⋊C8—64no—
438C2×C32—41no—
439C2×C32—81no—
440C2×C32C2×#12111yescharacteristic
441C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
442C2×C32#57511yescharacteristic
443C3⋊D3—22no—
444C3⋊D3—22no—
445C3⋊D3—81no—
446C3⋊D3—81no—
447C24—91no—
448C24—181no—
449#41—182no—
450#41—182no—
451C2×Q8C22×C3⋊D311yescharacteristic
452C2×D4—21no—
453C2×D4—91no—
454C2×D4—91no—
455C2×D4—181no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—182no—
459C2×D4—182no—
460C2×D4—181no—
461C2×D4—181no—
462C2×D4—181no—
463C2×D4—181no—
464C2×D4—364no—
465C2×D4C22×C3⋊D311yescharacteristic
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—91no—
471C22×C4—182no—
472C22×C4—182no—
473C22×C4—181no—
474C22×C4—181no—
475C22×C4C22×C3⋊D311yescharacteristic
476SD16—22no—
477SD16—182no—
478D8—182no—
479D8—182no—
480M16—22no—
481M16—94no—
482M16—182no—
483M16—182no—
484C2×C8—91no—
485C2×C8—91no—
486C2×C8—182no—
487C2×C8—182no—
488C2×C8C22×C3⋊D311yescharacteristic
489C2×C8C22×C3⋊D311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—91no—
492C4⋊C4—91no—
493C4⋊C4—181no—
494C4⋊C4—181no—
495C4⋊C4C22×C3⋊D311yescharacteristic
496C4⋊C4C22×C3⋊D311yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C22⋊C4—181no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C42—181no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—24no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3C2×D3×D414yes—
514C2×D3—38no—
515C2×D3—38no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—64no—
520C2×D3—1216no—
521C2×D3—124no—
522C2×D3—124no—
523C2×D3—124no—
524C2×D3—124no—
525C2×D3—124no—
526C2×D3—124no—
527C2×D3—2416no—
528C3×C4—24no—
529C3×C4—44no—
530C3×C4—44no—
531C3×C4—44no—
532C3×C4C2×D3×D414yes—
533C3×C4D3×#4114yes—
534Dic3—38no—
535Dic3—64no—
536Dic3—124no—
537Dic3—124no—
538C32#305511yescharacteristic, complemented, Sylow
539C23—21no—
540C23—91no—
541C23—91no—
542C23—182no—
543C23—182no—
544C23—181no—
545C23—181no—
546C23—361no—
547C23—362no—
548C23—362no—
549C23—362no—
550C23D4×C3⋊D311yescharacteristic
551Q8—21no—
552Q8—21no—
553D4—21no—
554D4—21no—
555D4—42no—
556D4—181no—
557D4—181no—
558D4—181no—
559D4—181no—
560D4—362no—
561D4—362no—
562D4—362no—
563D4—362no—
564D4—362no—
565D4—362no—
566D4—362no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—91no—
573C2×C4—92no—
574C2×C4—92no—
575C2×C4—91no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—362no—
584C2×C4—362no—
585C2×C4D4×C3⋊D311yescharacteristic
586C2×C4C23×C3⋊D311yescharacteristic
587C8—21no—
588C8—92no—
589C8—181no—
590C8D4×C3⋊D312yescomplemented
591C2×C3—44no—
592C2×C3—84no—
593C2×C3D3×#12114yes—
594C2×C3D3×AGL(1,ℤ/8)14yes—
595C2×C3#577714yes—
596D3—68no—
597D3—68no—
598D3—244no—
599D3—244no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—92no—
607C22—92no—
608C22—181no—
609C22—181no—
610C22—181no—
611C22—181no—
612C22—364no—
613C22—361no—
614C22—361no—
615C22—361no—
616C22—361no—
617C22—361no—
618C22—361no—
619C22—724no—
620C22C2×D4×C3⋊D311yescharacteristic
621C4—21no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—92no—
626C4—181no—
627C4—361no—
628C4—361no—
629C4C2×D4×C3⋊D311yescharacteristic
630C4#41×C3⋊D311yescharacteristic
631C3#8080514yescomplemented
632C2—41no—
633C2—81no—
634C2—182no—
635C2—182no—
636C2—721no—
637C2—721no—
638C2C3⋊D3×#12111yescharacteristic
639C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
640C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#468C2
socleC22×C32C22×D4
hypercenter#468C3⋊D3
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#64123C2semidirect
2. C2×M16×C3⋊D3C2semidirect
3. #10596098C2semidirect
4. C3⋊D3×#121C2semidirect
5. C32×#468C2semidirect
6. #10592870C2semidirect
7. #10592834C2semidirect
8. #10592748C2semidirect
9. #10592738C2semidirect
10. #10592582C2semidirect
11. #10592580C2semidirect
12. #10592506C2semidirect
13. #10592502C2semidirect
14. #10592474C2semidirect
15. #10592469C2semidirect
21. C2×C32×SD16C22semidirect
22. C2×C32×M16C22semidirect
23. C32×C22⋊Q8C22semidirect
25. #64155C22semidirect
26. C2×#3755C22semidirect
29. C2×#3753C22semidirect
31. #64139C22semidirect
32. C2×#3748C22semidirect
35. C2×#3745C22semidirect
38. C2×C8×C3⋊D3C22semidirect
39. C2×C8×C3⋊D3C22semidirect
41. #64104C22semidirect
50. C32×#107C22semidirect
51. C32×#103C22semidirect
52. C32×#102C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63648C22semidirect
56. #63648C22semidirect
57. #63644C22semidirect
58. #63636C22semidirect
59. #63636C22semidirect
60. #63635C22semidirect
61. #63634C22semidirect
66. C3×#468D3semidirect
134. #3743D4semidirect
142. C2×C3×SD16C2×D3semidirect
143. C2×C3×M16C2×D3semidirect
144. C3×C22⋊Q8C2×D3semidirect
171. C3×#107C2×D3semidirect
172. C3×#103C2×D3semidirect
173. C3×#102C2×D3semidirect
232. C32×C8C2×D4semidirect
234. C3⋊(C3⋊C8)C2×D4semidirect
242. #468C3⋊D3semidirect
330. C2×C3⋊D3AGL(1,ℤ/8)semidirect
347. C2×SD16C2×C3⋊D3semidirect
354. C2×M16C2×C3⋊D3semidirect
359. C22⋊Q8C2×C3⋊D3semidirect
375. #107C2×C3⋊D3semidirect
379. #103C2×C3⋊D3semidirect
385. #102C2×C3⋊D3semidirect
435. C3×C8D3×D4semidirect
538. C32#3055semidirect
590. C8D4×C3⋊D3semidirect
631. C3#80805semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
C2×M16×C3⋊D32
#105960982
C3⋊D3×#1212
C32×#4682
#105928702
#105928342
#105927482
#105927382
#105925822
#105925802
#105925062
#105925022
#105924742
#105924692
#808053