Finite Group Databasebeta

← #11867171

Subgroups — #11867171

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2#10595034C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4C2×#63818C211yesmaximal, characteristic, complemented
5C3×#4966C211yesmaximal, characteristic, complemented
6C3×#4964C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10590523C212yesmaximal, complemented
9#10590522C212yesmaximal, complemented
10#10590509C212yesmaximal, complemented
11#10590508C212yesmaximal, complemented
12#79211—31nomaximal
13#78888—31nomaximal
14C22×C4⋊(C3⋊D3)—21no—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752—21no—
20#64104—21no—
21#64104—21no—
22#64104C2212yes—
23#64104C2212yes—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63981—21no—
28#63962—21no—
29#63916C2211yescharacteristic, complemented
30#63916C2211yescharacteristic, complemented
31C4×#626—21no—
32C4×#626—21no—
33#63871C2211yescharacteristic, complemented
34#63871C2211yescharacteristic, complemented
35C2×#3717C2212yescomplemented
36#63825—24no—
37C2×#3714C2212yescomplemented
38C2×#3712C2212yescomplemented
39#63818—24no—
40C2×#3710C2212yescomplemented
41C3×#810C2212yescomplemented
42C3×#809C2212yescomplemented
43C3×#808C2212yescomplemented
44C3×#807C2212yescomplemented
45#63564C2212yescomplemented
46#63564C2212yescomplemented
47#5828—31no—
48C2×#949—31no—
49C2×#908—31no—
50C2×D3×M16—31no—
51C2×D3×M16—31no—
52#5524—31no—
53C2×#895—31no—
54C2×#895—31no—
55C2×#895—61no—
56C3×#428—31no—
57C3×#417—31no—
58#5131—31no—
59#5001—31no—
60#4966D311yescharacteristic, complemented
61#4964D311yescharacteristic, complemented
62#4886—32no—
63#4883—32no—
64#4865—32no—
65#4864—32no—
66#4812—32no—
67#4807—32no—
68#4782—32no—
69#4775—32no—
70C23×C3⋊D3—21no—
71C23×C3⋊D3D411yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3D411yescharacteristic
75C2×C4⋊(C3⋊D3)—22no—
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4⋊(C3⋊D3)—22no—
78C2×C4⋊(C3⋊D3)—22no—
79C2×C4⋊(C3⋊D3)—21no—
80C2×C4⋊(C3⋊D3)—44no—
81C2×C4⋊(C3⋊D3)C2312yes—
82C2×C4×C3⋊D3—22no—
83C2×C4×C3⋊D3—22no—
84C2×C4×C3⋊D3D411yescharacteristic
85C2×C4×C3⋊D3D411yescharacteristic
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×C4×C3⋊D3C2311yescharacteristic
88C2×C3×#67—21no—
89C3×#235—22no—
90C3×#235—22no—
91C2×C3×D12C2311yescharacteristic
92C2×C3×C4×D3—21no—
93C2×C3×Dic6C2311yescharacteristic
94C2×#626—21no—
95C2×#626—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2312yes—
98#3752—22no—
99#3752—22no—
100C3×#217—21no—
101C3×C4⋊Dic3C2311yescharacteristic
102C3×C4⋊Dic3C2311yescharacteristic
103C3×C4×Dic3—21no—
104C3×#208—22no—
105C3×#208D414yescomplemented
106C2×C3×C3⋊C8C2312yes—
107C2×C3×C3⋊C8C2312yes—
108Dic3⋊Dic3—21no—
109Dic3⋊Dic3—21no—
110#3722—21no—
111#3722—21no—
112(C2×D3)⋊Dic3—21no—
113(C2×D3)⋊Dic3—21no—
114#3717—24no—
115#3714—24no—
116#3712—24no—
117#3710—24no—
118#3055—91noSylow
119C2×C3×#41—31no—
120C2×#235C2×D311yescharacteristic
121C22×D12—31no—
122C22×D12—31no—
123C22×D12—61no—
124C22×D12—61no—
125C22×D12—61no—
126C22×D12—62no—
127C22×C4×D3—31no—
128C22×C4×D3—31no—
129C22×C4×D3—61no—
130C2×C3×M16—31no—
131C2×C3×M16—31no—
132C3×#117—31no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C4⋊C4C2×D311yescharacteristic
136#949—64no—
137#946—31no—
138#946—31no—
139C2×#215—32no—
140#938—31no—
141#938—31no—
142#937—61no—
143#935—61no—
144C2×#213—32no—
145C4×#67—61no—
146C4×#67—61no—
147C2×(C2×D3)⋊C4—61no—
148C2×(C2×D3)⋊C4—61no—
149C2×(C2×D3)⋊C4—62no—
150#926C2×D311yescharacteristic
151C2×#208C2×D311yescharacteristic
152C2×#208C2×D311yescharacteristic
153#908—64no—
154D3×M16—64no—
155D3×M16—64no—
156C2×D24—32no—
157C2×#204—32no—
158C2×ΓL(1,𝔽25)—32no—
159C2×ΓL(1,𝔽25)—32no—
160C2×D3×C8—32no—
161C2×D3×C8—32no—
162#897—31no—
163#897—31no—
164#895—31no—
165#895—31no—
166#895—32no—
167#895—32no—
168#895—32no—
169#895—32no—
170#895—62no—
171#895—62no—
172#895—61no—
173#895—61no—
174#895—61no—
175#895—61no—
176#895—62no—
177#895—62no—
178#886—61no—
179#882—61no—
180C4×D12—61no—
181C4×D12—61no—
182C3×#107—32no—
183C3×#106—32no—
184C3×#103—32no—
185C3×#102—32no—
186#821—32no—
187#821—32no—
188#810C2×D312yescomplemented
189#809—32no—
190#809—32no—
191#809C2×D312yescomplemented
192#808C2×D312yescomplemented
193#807C2×D312yescomplemented
194C23×C32C2×D411yescharacteristic
195C22×C3⋊D3—22no—
196C22×C3⋊D3—22no—
197C22×C3⋊D3—22no—
198C22×C3⋊D3—41no—
199C22×C3⋊D3—42no—
200C22×C3⋊D3—42no—
201C22×C3⋊D3—42no—
202C22×C3⋊D3C2×D411yescharacteristic
203C22×C3⋊D3C2×D411yescharacteristic
204C22×C3×D3—21no—
205C2×C32×C4—22no—
206C2×C32×C4—42no—
207C2×C32×C4C2×D412yes—
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4#4112yes—
210C2×C32×C4C2411yescharacteristic
211C2×C3⋊Dic3—22no—
212C2×C3⋊Dic3C2×D411yescharacteristic
213C2×C3⋊Dic3C2×D411yescharacteristic
214C4⋊(C3⋊D3)—22no—
215C4⋊(C3⋊D3)—22no—
216C4⋊(C3⋊D3)—44no—
217C4⋊(C3⋊D3)—44no—
218C4⋊(C3⋊D3)—42no—
219C4×C3⋊D3—22no—
220C4×C3⋊D3—22no—
221C4×C3⋊D3—21no—
222C4×C3⋊D3—21no—
223C4×C3⋊D3—21no—
224C4×C3⋊D3—21no—
225C3×#67—42no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C3×D12—21no—
230C3×D12—21no—
231C3×C4×D3—42no—
232C3×Dic6—21no—
233C3×Dic6—21no—
234#626—42no—
235#626—42no—
236C3×C3⋊C8—22no—
237C3×C3⋊C8C2×D414yescomplemented
238C2×AGL(1,ℤ/8)—91no—
239C22×M16—91no—
240#525—91no—
241C2×#121—91no—
242#469—92no—
243#468—92no—
244#466—92no—
245#465—92no—
246#428—31no—
247#418—91no—
248#417—31no—
249C23×D3—31no—
250C23×D3—31no—
251C23×D3—61no—
252C23×D3—62no—
253C23×D3—61no—
254C23×D3—61no—
255C3×#41—62no—
256C3×#41—62no—
257C2×C3×Q8—31no—
258C2×C3×D4—31no—
259C2×C3×D4—61no—
260C22×C3×C4—22no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—61no—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C2×#67—21no—
268C2×#67—61no—
269C2×#67—61no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—61no—
273#235—22no—
274#235—22no—
275C2×D12—32no—
276C2×D12—32no—
277C2×D12—62no—
278C2×D12—62no—
279C2×D12—62no—
280C2×D12—62no—
281C2×D12—62no—
282C2×D12—62no—
283C2×D12—62no—
284C2×D12—62no—
285C2×D12—62no—
286C2×D12—64no—
287C2×D12—64no—
288C2×D12—62no—
289C2×D12—61no—
290C2×D12—61no—
291C2×D12—61no—
292C2×D12—61no—
293C2×D12—122no—
294C2×D12—122no—
295C2×D12—124no—
296C2×D12—124no—
297C2×D12—128no—
298C2×D12C22×D311yescharacteristic
299C2×C4×D3—21no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—31no—
304C2×C4×D3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—62no—
315C2×C4×D3—62no—
316C2×C4×D3—122no—
317C2×C4×D3—122no—
318C2×Dic6C22×D311yescharacteristic
319C3×M16—34no—
320C3×M16—62no—
321C2×C3×C8—32no—
322C2×C3×C8—32no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4C22×D312yes—
330C3×C4⋊C4C22×D312yes—
331C3×C22⋊C4—61no—
332C3×C42—61no—
333#217—21no—
334#217—61no—
335#217—61no—
336#215—64no—
337#213—64no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344(C2×D3)⋊C4—62no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—64no—
349(C2×D3)⋊C4—64no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356C4×Dic3—21no—
357#208—22no—
358#208D1214yescomplemented
359C2×C3⋊C8C22×D312yes—
360C2×C3⋊C8C22×D312yes—
361D24—64no—
362#204—64no—
363ΓL(1,𝔽25)—64no—
364ΓL(1,𝔽25)—64no—
365D3×C8—64no—
366D3×C8—64no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32#12112yes—
370C22×C32C22×D411yescharacteristic
371C2×C3⋊D3—21no—
372C2×C3⋊D3—21no—
373C2×C3⋊D3—21no—
374C2×C3⋊D3—21no—
375C2×C3⋊D3—21no—
376C2×C3⋊D3—44no—
377C2×C3⋊D3—42no—
378C2×C3⋊D3—42no—
379C2×C3⋊D3—42no—
380C2×C3⋊D3—84no—
381C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
382C2×C3×D3—41no—
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C32×C4—42no—
386C32×C4#12112yes—
387C32×C4C22×D411yescharacteristic
388C32×C4C2×#4111yescharacteristic
389C3⋊Dic3—21no—
390C3⋊Dic3—21no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C2×#41—31no—
395C22×D4—91no—
396C22×D4—181no—
397C23×C4—91no—
398AGL(1,ℤ/8)—184no—
399C2×SD16—92no—
400C2×D8—92no—
401C2×M16—31no—
402C2×M16—31no—
403C2×M16—92no—
404C2×M16—184no—
405C22×C8—92no—
406#123—181no—
407C22⋊Q8—91no—
408C22⋊Q8—91no—
409#121—91no—
410#121—91no—
411#121—92no—
412#121—92no—
413#121—181no—
414#121—181no—
415#120—181no—
416C4×D4—181no—
417C4×D4—181no—
418#117—31no—
419C2×C4⋊C4D3211yescharacteristic
420C2×C22⋊C4—181no—
421#107—32no—
422#106—32no—
423#103—32no—
424#102—32no—
425#102—92no—
426#102—92no—
427C23×C3—21no—
428C23×C3—61no—
429C23×C3D3×D411yescharacteristic
430C23×C3D3×D411yescharacteristic
431C22×D3—21no—
432C22×D3—31no—
433C22×D3—31no—
434C22×D3—31no—
435C22×D3—31no—
436C22×D3—61no—
437C22×D3—61no—
438C22×D3—62no—
439C22×D3—62no—
440C22×D3—64no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—64no—
444C22×D3—62no—
445C22×D3—62no—
446C22×D3—122no—
447C22×D3—121no—
448C22×D3—121no—
449C22×D3—122no—
450C22×D3—124no—
451C22×D3—122no—
452C22×D3—122no—
453C22×D3—124no—
454C22×D3—124no—
455C22×D3—122no—
456C22×D3—122no—
457C22×D3—122no—
458C22×D3—122no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×D4—61no—
462C3×D4—61no—
463C3×D4—122no—
464C2×C3×C4—24no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—44no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—122no—
478C2×C3×C4C2×D1212yes—
479C2×C3×C4#23512yes—
480C2×C3×C4D3×D412yes—
481C2×C3×C4D3×D411yescharacteristic
482C2×C3×C4D3×D411yescharacteristic
483C2×C3×C4#23912yes—
484C2×C3×C4C23×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486#67—42no—
487#67—122no—
488#67—122no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—122no—
501D12—21no—
502D12—21no—
503D12—62no—
504D12—62no—
505D12—62no—
506D12—62no—
507D12—122no—
508D12—122no—
509D12—124no—
510D12—124no—
511D12—124no—
512D12—128no—
513D12—128no—
514D12—124no—
515D12—124no—
516D12—122no—
517D12—122no—
518D12—122no—
519D12—122no—
520C4×D3—42no—
521C4×D3—62no—
522C4×D3—62no—
523C4×D3—62no—
524C4×D3—62no—
525C4×D3—61no—
526C4×D3—61no—
527C4×D3—61no—
528C4×D3—61no—
529C4×D3—61no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—61no—
533C4×D3—121no—
534C4×D3—121no—
535C4×D3—121no—
536C4×D3—121no—
537C4×D3—122no—
538C4×D3—122no—
539Dic6—21no—
540Dic6—21no—
541C3×C8—34no—
542C3×C8—62no—
543C3⋊C8—22no—
544C3⋊C8C2×D1214yescomplemented
545C2×C32—22no—
546C2×C32C2×#12111yescharacteristic
547C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
548C2×C32#57511yescharacteristic
549C3⋊D3—22no—
550C3⋊D3—41no—
551C3⋊D3—82no—
552C3×D3—81no—
553C24—91no—
554C24—181no—
555#41—62no—
556#41—62no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—61no—
560C2×D4—92no—
561C2×D4—182no—
562C2×D4—182no—
563C2×D4—181no—
564C2×D4—181no—
565C2×D4—182no—
566C2×D4—182no—
567C2×D4—181no—
568C2×D4—364no—
569C22×C4—21no—
570C22×C4—61no—
571C22×C4—91no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—91no—
576C22×C4—182no—
577C22×C4—182no—
578C22×C4C2×D3211yescharacteristic
579SD16—184no—
580D8—184no—
581M16—34no—
582M16—62no—
583M16—184no—
584C2×C8—32no—
585C2×C8—32no—
586C2×C8—184no—
587C4⋊C4—21no—
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4C2×D3212yes—
593C22⋊C4—61no—
594C22⋊C4—182no—
595C22⋊C4—182no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C22⋊C4—181no—
600C42—61no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—22no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3#88412yes—
613C22×C3#89512yes—
614C22×C3C2×D3×D411yescharacteristic
615C22×C3C2×D3×D411yescharacteristic
616C2×D3—32no—
617C2×D3—32no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—62no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—62no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3—124no—
638C2×D3—124no—
639C2×D3—128no—
640C2×D3—124no—
641C2×D3—124no—
642C2×D3—124no—
643C2×D3—122no—
644C2×D3—122no—
645C2×D3—122no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3—248no—
650C2×D3—244no—
651C2×D3—244no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—22no—
655C3×C4—44no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4#88412yes—
662C3×C4#89512yes—
663C3×C4C22×D1211yescharacteristic
664C3×C4C2×#23511yescharacteristic
665C3×C4C2×D3×D411yescharacteristic
666C3×C4C2×#23911yescharacteristic
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—121no—
675Dic3—121no—
676C32#305511yescharacteristic, complemented, Sylow
677C23—61no—
678C23—91no—
679C23—91no—
680C23—182no—
681C23—182no—
682C23—182no—
683C23—361no—
684C23—362no—
685C23—362no—
686C23—362no—
687C23#381111yescharacteristic
688Q8—61no—
689Q8—61no—
690D4—61no—
691D4—61no—
692D4—122no—
693D4—182no—
694D4—182no—
695D4—364no—
696D4—364no—
697D4—362no—
698D4—362no—
699D4—362no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—122no—
708C2×C4—182no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—182no—
714C2×C4—182no—
715C2×C4#379912yes—
716C2×C4D3×D1212yes—
717C2×C4#381111yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—34no—
720C8—62no—
721C2×C3—24no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—241no—
728C2×C3C2×#88411yescharacteristic
729C2×C3C2×#89511yescharacteristic
730C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
731C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
732C2×C3#577711yescharacteristic
733C2×C3#577711yescharacteristic
734D3—62no—
735D3—62no—
736D3—81no—
737D3—122no—
738D3—122no—
739D3—121no—
740D3—121no—
741D3—244no—
742D3—242no—
743D3—242no—
744C22—21no—
745C22—21no—
746C22—92no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—181no—
751C22—181no—
752C22—181no—
753C22—181no—
754C22—181no—
755C22—364no—
756C22—362no—
757C22—362no—
758C22—362no—
759C22—724no—
760C22#6391012yes—
761C22C2×#381111yescharacteristic
762C4—42no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4#6391012yes—
769C4C2×#379911yescharacteristic
770C4C2×D3×D1211yescharacteristic
771C3—21no—
772C3#7888811yescharacteristic, complemented
773C3#7921111yescharacteristic, complemented
774C2—22no—
775C2—182no—
776C2—241no—
777C2—361no—
778C2—722no—
779C2C2×#6391011yescharacteristic
780C2#1059510011yescharacteristic
781C2#1059532311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64104C2semidirect
2. #10595034C2semidirect
3. C2×#63825C2semidirect
4. C2×#63818C2semidirect
5. C3×#4966C2semidirect
6. C3×#4964C2semidirect
7. #10591096C2semidirect
8. #10590523C2semidirect
9. #10590522C2semidirect
10. #10590509C2semidirect
11. #10590508C2semidirect
29. #63916C22semidirect
30. #63916C22semidirect
33. #63871C22semidirect
34. #63871C22semidirect
35. C2×#3717C22semidirect
37. C2×#3714C22semidirect
38. C2×#3712C22semidirect
40. C2×#3710C22semidirect
41. C3×#810C22semidirect
42. C3×#809C22semidirect
43. C3×#808C22semidirect
44. C3×#807C22semidirect
45. #63564C22semidirect
46. #63564C22semidirect
60. #4966D3semidirect
61. #4964D3semidirect
105. C3×#208D4semidirect
188. #810C2×D3semidirect
191. #809C2×D3semidirect
192. #808C2×D3semidirect
193. #807C2×D3semidirect
237. C3×C3⋊C8C2×D4semidirect
358. #208D12semidirect
381. C2×C3⋊D3AGL(1,ℤ/8)semidirect
544. C3⋊C8C2×D12semidirect
676. C32#3055semidirect
772. C3#78888semidirect
773. C3#79211semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
#105950342
C2×#638252
C2×#638182
C3×#49662
C3×#49642
#105910962
#105905232
#105905222
#105905092
#105905082
#792113
#788883