Finite Group Databasebeta

← #10944033

Subgroups — #10944033

Order 768.

1894 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic
3C2×#5153C211yesmaximal, characteristic, complemented
4C2×#4787C211yesmaximal, characteristic, complemented
5C2×#4776C211yesmaximal, characteristic, complemented
6#76474C211yesmaximal, characteristic, complemented
7C3×#1879C211yesmaximal, characteristic, complemented
8#71612C211yesmaximal, characteristic, complemented
9#70200C211yesmaximal, characteristic, complemented
10#70154C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68878C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68662C211yesmaximal, characteristic, complemented
16#32908—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C23×C4×D3—21no—
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#936C2211yescharacteristic, complemented
23C2×D4×Dic3C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×C4×#67—21no—
27C22×#204C2211yescharacteristic
28C4×D3×D4—24no—
29C4×D3×D4—24no—
30C2×#897C2211yescharacteristic
31C2×#893C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C4×D12C2211yescharacteristic
36C2×C42×D3C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic, complemented
39C3×#390C2211yescharacteristic, complemented
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic, complemented
42#5156—24no—
43#5153—24no—
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic, complemented
48C2×Dic3⋊C8C2211yescharacteristic, complemented
49C2×Dic3⋊C8C2211yescharacteristic, complemented
50#4977C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic
53#4956—21no—
54#4956—21no—
55#4951—21no—
56#4951—21no—
57#4929C2211yescharacteristic, complemented
58#4787—24no—
59#4776—24no—
60C3×#340C2211yescharacteristic, complemented
61C3×#336C2211yescharacteristic, complemented
62#4551C2211yescharacteristic, complemented
63#4529C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4524C2211yescharacteristic, complemented
66C22×C4×D4—31no—
67C2×#463—31no—
68C2×#463—31no—
69C2×#450—31no—
70C2×#447—31no—
71#2850—31no—
72#1879—31no—
73#1879D311yescharacteristic, complemented
74#1877—31no—
75#1877—31no—
76#1874—31no—
77#1872—31no—
78#1804—31no—
79#1804—31no—
80#1797—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4D414yes—
94C22×D12C2311yescharacteristic
95C22×C4×D3—28no—
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3—44no—
100C22×C4×D3—44no—
101C22×C4×D3D411yescharacteristic
102C22×C4×D3D411yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C2×C3×D8—22no—
106C2×C3×D8—22no—
107C2×C3×D8—22no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C42C2311yescharacteristic
118C2×#217—21no—
119C2×#217—21no—
120C2×#217—21no—
121C2×#217—21no—
122#938—22no—
123#938—22no—
124#936—22no—
125#936—22no—
126D4×Dic3—22no—
127D4×Dic3D414yescomplemented
128C2×#214—22no—
129C2×#214—22no—
130C2×#214—22no—
131C2×#213—22no—
132C2×#213—22no—
133C2×#213—22no—
134C4×#67—28no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3D411yescharacteristic
143C2×C4×Dic3D411yescharacteristic
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C2×#204—22no—
148C2×#204—22no—
149C2×#204—22no—
150#897—22no—
151#897—22no—
152#893—22no—
153#893D414yescomplemented
154D3×C4⋊C4—22no—
155D3×C4⋊C4—22no—
156#67⋊C4—28no—
157D3×C22⋊C4—28no—
158C4×D12—22no—
159C4×D12—22no—
160C42×D3—22no—
161C42×D3—22no—
162C3×#102—22no—
163C3×#102—22no—
164#832—22no—
165#832—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#821—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—22no—
173#816—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176#810—22no—
177#809—22no—
178C23×D4—31no—
179C24×C4—61no—
180C22×SD16—31no—
181C22×SD16—31no—
182C22×D8—31no—
183C22×D8C2×D311yescharacteristic
184C2×#124—31no—
185C2×C22⋊Q8—31no—
186C2×#121—31no—
187C2×C4×D4—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×C4×D4—64no—
193C2×C4×D4—64no—
194C2×C4×D4C2×D311yescharacteristic
195C22×C4⋊C4—31no—
196C22×C22⋊C4—61no—
197C22×C42—31no—
198#463—64no—
199#463—64no—
200#450—64no—
201#447—64no—
202C2×C4⋊C8—31no—
203C2×C4⋊C8—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102C2×D311yescharacteristic
211C2×#102C2×D311yescharacteristic, complemented
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214#391—31no—
215#390C2×D311yescharacteristic, complemented
216#388—61no—
217#388—61no—
218#386—61no—
219#386—61no—
220#382—31no—
221#340—31no—
222#340—31no—
223#340—31no—
224#340C2×D311yescharacteristic, complemented
225#336—31no—
226#336C2×D311yescharacteristic, complemented
227C24×C3—21no—
228C24×C3—21no—
229C23×D3—24no—
230C23×D3—24no—
231C23×D3—21no—
232C23×D3—24no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3C2×D411yescharacteristic
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4C2×D412yes—
248C2×C3×D4C2×D412yes—
249C2×C3×D4#4112yes—
250C22×C3×C4—24no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C2×#67—24no—
259C2×#67—24no—
260C2×#67—24no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C22×Dic3—21no—
265C22×Dic3—24no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—42no—
269C22×Dic3—42no—
270C22×Dic3C2×D411yescharacteristic
271C22×Dic3C2×D411yescharacteristic
272C22×Dic3C2×D411yescharacteristic
273D3×D4—28no—
274D3×D4—28no—
275D3×D4—28no—
276D3×D4—28no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12C2×D412yes—
281C2×D12C2×D412yes—
282C2×D12#4112yes—
283C2×C4×D3—22no—
284C2×C4×D3—22no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—22no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—22no—
293C2×C4×D3—22no—
294C2×C4×D3—24no—
295C2×C4×D3—432no—
296C2×C4×D3—41no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×C4×D3C2×D412yes—
304C2×C4×D3#4112yes—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C3×D8—44no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4C2×D412yes—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C42—21no—
326C3×C42—21no—
327#217—24no—
328#217—42no—
329#217—42no—
330#217—42no—
331#214—44no—
332#213—44no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—42no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—42no—
340C4⋊Dic3C2×D412yes—
341Dic3⋊C4—24no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3C2×D412yes—
345C4×Dic3C2×D412yes—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352#204—44no—
353C25—61no—
354C22×Q8—31no—
355C22×D4—34no—
356C22×D4—31no—
357C22×D4—62no—
358C22×D4—61no—
359C22×D4—62no—
360C22×D4—62no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—61no—
364C22×D4C22×D311yescharacteristic
365C22×D4C22×D311yescharacteristic
366C23×C4—21no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—61no—
371C23×C4—61no—
372C23×C4—68no—
373C23×C4—61no—
374C23×C4—61no—
375C23×C4—124no—
376C23×C4—124no—
377C2×SD16—62no—
378C2×SD16—62no—
379C2×SD16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—22no—
386C2×D8—62no—
387C2×D8—62no—
388C2×D8—62no—
389C22×C8—31no—
390C22×C8—31no—
391C22×C8C22×D311yescharacteristic
392C22×C8C22×D311yescharacteristic
393#124—62no—
394#124—62no—
395C22⋊Q8—62no—
396C22⋊Q8—62no—
397#121—62no—
398#121—62no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—34no—
402C4×D4—34no—
403C4×D4—62no—
404C4×D4—62no—
405C4×D4—62no—
406C4×D4—62no—
407C4×D4—68no—
408C4×D4—68no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—68no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—62no—
432C2×C42—62no—
433C2×C42C22×D311yescharacteristic
434C4⋊C8—62no—
435C4⋊C8—62no—
436#103—62no—
437#103—62no—
438#102—22no—
439#102—22no—
440#102—62no—
441#102—62no—
442#102—62no—
443#102—62no—
444C22⋊C8—62no—
445C22⋊C8—62no—
446#95—61no—
447#95—61no—
448#95—61no—
449#95—61no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3C22×D411yescharacteristic
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—216no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—48no—
474C22×D3—48no—
475C22×D3—48no—
476C22×D3—48no—
477C22×D3—48no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—48no—
483C22×D3#12112yes—
484C22×D3#13512yes—
485C22×D3AGL(1,ℤ/8)12yes—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4#12114yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—48no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4AGL(1,ℤ/8)12yes—
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512C2×C3×C4C2×#4111yescharacteristic
513#67—216no—
514#67—84no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—22no—
522C2×Dic3—48no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3#12012yes—
532C2×Dic3#12012yes—
533C2×Dic3#12112yes—
534D12—22no—
535D12—22no—
536D12—22no—
537D12#12114yes—
538C4×D3—28no—
539C4×D3—22no—
540C4×D3—22no—
541C4×D3—22no—
542C4×D3—22no—
543C4×D3—44no—
544C4×D3—48no—
545C4×D3—48no—
546C4×D3—48no—
547Dic6—41no—
548Dic6—41no—
549Dic6—41no—
550Dic6—41no—
551C3×C8—41no—
552C3×C8—41no—
553C3⋊C8—41no—
554C3⋊C8—41no—
555C24—21no—
556C24—21no—
557C24—31no—
558C24—64no—
559C24—64no—
560C24—64no—
561C24—61no—
562C24—122no—
563C24—122no—
564C24—122no—
565C24—122no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—61no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—32no—
582C2×D4—32no—
583C2×D4—32no—
584C2×D4—64no—
585C2×D4—68no—
586C2×D4—68no—
587C2×D4—68no—
588C2×D4—64no—
589C2×D4—64no—
590C2×D4—68no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—122no—
595C2×D4—122no—
596C2×D4—122no—
597C2×D4#23512yes—
598C2×D4D3×D412yes—
599C2×D4D3×D412yes—
600C22×C4—24no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—64no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—64no—
616C22×C4—64no—
617C22×C4—64no—
618C22×C4—62no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—121no—
627C22×C4—122no—
628C22×C4—1232no—
629C22×C4—122no—
630C22×C4—122no—
631C22×C4—122no—
632C22×C4—122no—
633C22×C4—122no—
634C22×C4—122no—
635C22×C4—122no—
636C22×C4D3×D411yescharacteristic
637C22×C4D3×D411yescharacteristic
638C22×C4C23×D311yescharacteristic
639SD16—124no—
640SD16—124no—
641D8—44no—
642D8—124no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—61no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—32no—
659C4⋊C4—64no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—122no—
664C4⋊C4D3×D412yes—
665C22⋊C4—24no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—64no—
669C22⋊C4—64no—
670C22⋊C4—64no—
671C22⋊C4—122no—
672C22⋊C4—122no—
673C22⋊C4—122no—
674C22⋊C4—122no—
675C42—21no—
676C42—21no—
677C42—32no—
678C42—32no—
679C42—62no—
680C42—62no—
681C22×C3—24no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3C2×#12011yescharacteristic
696C22×C3C2×#12111yescharacteristic
697C22×C3#52511yescharacteristic
698C22×C3C2×#13511yescharacteristic
699C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
700C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
701C22×C3#57511yescharacteristic
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—24no—
709C2×D3—432no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3#46314yescomplemented
717C3×C4—22no—
718C3×C4—41no—
719C3×C4—42no—
720C3×C4—81no—
721C3×C4C2×#12111yescharacteristic
722C3×C4C2×#12111yescharacteristic
723C3×C4#52511yescharacteristic
724C3×C4#52511yescharacteristic
725Dic3—22no—
726Dic3—22no—
727Dic3—22no—
728Dic3—42no—
729Dic3—81no—
730Dic3—81no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—32no—
735C23—32no—
736C23—32no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—616no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—128no—
757C23—128no—
758C23—128no—
759C23—128no—
760C23—128no—
761C23—128no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23C2×D3×D411yescharacteristic
767Q8—121no—
768Q8—121no—
769Q8—121no—
770Q8—121no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—34no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—616no—
780D4—62no—
781D4—62no—
782D4—62no—
783D4—244no—
784D4#88414yes—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—22no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—48no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—68no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—62no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—128no—
813C2×C4—124no—
814C2×C4—128no—
815C2×C4—128no—
816C2×C4—128no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4#91112yes—
826C2×C4C2×#23511yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4D3×#4111yescharacteristic
831C2×C4D3×#4111yescharacteristic
832C8—41no—
833C8—41no—
834C8—121no—
835C8—121no—
836C2×C3—44no—
837C2×C3—161no—
838C2×C3#284711yescharacteristic
839C2×C3#300211yescharacteristic
840C2×C3#300311yescharacteristic
841C2×C3C2×#46311yescharacteristic
842C2×C3#303611yescharacteristic
843C2×C3#310511yescharacteristic
844C2×C3#311411yescharacteristic
845D3—24no—
846D3—44no—
847C22—24no—
848C22—34no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—64no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—1232no—
870C22—122no—
871C22—122no—
872C22—122no—
873C22—122no—
874C22—122no—
875C22—122no—
876C22#554711yescharacteristic
877C22D3×#12011yescharacteristic
878C22D3×#12111yescharacteristic
879C22C2×#91111yescharacteristic
880C22D3×#13511yescharacteristic
881C22D3×AGL(1,ℤ/8)11yescharacteristic
882C22#577311yescharacteristic
883C4—22no—
884C4—42no—
885C4—41no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—81no—
890C4—122no—
891C4—241no—
892C4—241no—
893C4C2×#88411yescharacteristic
894C4#554711yescharacteristic
895C4D3×#12111yescharacteristic
896C4#565611yescharacteristic
897C3#3290811yescharacteristic, complemented, Sylow
898C2—44no—
899C2—64no—
900C2—124no—
901C2—161no—
902C2#7493511yescharacteristic
903C2#7959211yescharacteristic
904C2#7987111yescharacteristic
905C2#8000211yescharacteristic
906C2#8008211yescharacteristic
907C2#8033211yescharacteristic
908C2D3×#46311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1879C2
socleC23×C3C22×D4
prime radicalC2×#5156C2
hypercenter#1879D3
hypocenterC3#32908
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D4C2semidirect
3. C2×#5153C2semidirect
4. C2×#4787C2semidirect
5. C2×#4776C2semidirect
6. #76474C2semidirect
7. C3×#1879C2semidirect
8. #71612C2semidirect
9. #70200C2semidirect
10. #70154C2semidirect
11. #69657C2semidirect
12. #68893C2semidirect
13. #68878C2semidirect
14. #68672C2semidirect
15. #68662C2semidirect
22. C2×#936C22semidirect
38. C2×C3×#102C22semidirect
39. C3×#390C22semidirect
41. C2×#832C22semidirect
47. C2×#816C22semidirect
48. C2×Dic3⋊C8C22semidirect
49. C2×Dic3⋊C8C22semidirect
50. #4977C22semidirect
51. C2×#810C22semidirect
57. #4929C22semidirect
60. C3×#340C22semidirect
61. C3×#336C22semidirect
62. #4551C22semidirect
63. #4529C22semidirect
64. #4529C22semidirect
65. #4524C22semidirect
73. #1879D3semidirect
127. D4×Dic3D4semidirect
153. #893D4semidirect
211. C2×#102C2×D3semidirect
215. #390C2×D3semidirect
224. #340C2×D3semidirect
226. #336C2×D3semidirect
716. C2×D3#463semidirect
897. C3#32908semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D42
C2×#51562
C2×#51532
C2×#47872
C2×#47762
#764742
C3×#18792
#716122
#702002
#701542
#696572
#688932
#688782
#686722
#686622
#329083