Finite Group Databasebeta

← #10831001

Subgroups — #10831001

Order 768.

1608 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#84097C211yesmaximal, characteristic, complemented
3#84053C211yesmaximal, characteristic, complemented
4C2×#5174C211yesmaximal, characteristic, complemented
5C2×#5159C211yesmaximal, characteristic, complemented
6C2×#5128C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72128C211yesmaximal, characteristic, complemented
9#72054C211yesmaximal, characteristic, complemented
10#72051C211yesmaximal, characteristic, complemented
11#72049C211yesmaximal, characteristic, complemented
12#72043C211yesmaximal, characteristic, complemented
13#72040C211yesmaximal, characteristic, complemented
14#72038C211yesmaximal, characteristic, complemented
15#71988C211yesmaximal, characteristic, complemented
16#24277—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)—24no—
20C2×C3×AGL(1,ℤ/8)—24no—
21C2×C3×AGL(1,ℤ/8)—24no—
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C22×C3×D8C2211yescharacteristic
25C22×C3×D8C2211yescharacteristic
26C22×C3×M16C2211yescharacteristic
27C2×#953—21no—
28C2×#946C2211yescharacteristic, complemented
29C2×#938C2211yescharacteristic
30C2×#938C2211yescharacteristic
31C2×#938C2211yescharacteristic, complemented
32C2×C4×#67C2211yescharacteristic
33C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34#5247—21no—
35#5229C2211yescharacteristic, complemented
36C2×#835C2211yescharacteristic, complemented
37C2×#835C2211yescharacteristic, complemented
38#5223—21no—
39#5223—21no—
40#5222—21no—
41#5222—21no—
42#5221C2211yescharacteristic
43#5221C2211yescharacteristic
44#5221C2211yescharacteristic, complemented
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#832C2211yescharacteristic
48C2×#832C2211yescharacteristic
49C2×#832C2211yescharacteristic, complemented
50C2×#832C2211yescharacteristic, complemented
51#5213—21no—
52#5212C2211yescharacteristic
53#5212C2211yescharacteristic
54#5210—21no—
55C2×#830C2211yescharacteristic
56#5174—24no—
57#5159—24no—
58#5128—24no—
59C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C2×#818C2211yescharacteristic, complemented
61C2×#817C2211yescharacteristic, complemented
62C2×Dic3⋊C8C2211yescharacteristic, complemented
63C2×C8×Dic3C2211yescharacteristic, complemented
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)D311yescharacteristic, complemented
67C2×#469—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2408—31no—
71#2407—31no—
72#2055—31no—
73#2054—31no—
74#2000—31no—
75#1999—31no—
76#1970—31no—
77#1968—31no—
78#1809—31no—
79#1788—31no—
80#1786—31no—
81C25×C3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—21no—
92C22×C3×D4—22no—
93C22×C3×D4—21no—
94C22×C3×D4—22no—
95C22×C3×D4—41no—
96C22×C3×D4—41no—
97C22×C3×D4C2311yescharacteristic
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4—21no—
101C23×C3×C4C2311yescharacteristic
102C22×#67—21no—
103C22×#67—21no—
104C22×#67—21no—
105C22×#67D411yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C3×AGL(1,ℤ/8)—232no—
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16D414yescomplemented
114C2×C3×D8—22no—
115C2×C3×D8—22no—
116C2×C3×D8—22no—
117C2×C3×D8—22no—
118C2×C3×D8—22no—
119C2×C3×D8D414yescomplemented
120C2×C3×M16—22no—
121C2×C3×M16—22no—
122C2×C3×M16D414yescomplemented
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125#953—44no—
126C2×#217—21no—
127C2×#217—21no—
128C2×#217—21no—
129C2×#217—21no—
130C2×#217—21no—
131C2×#217—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#217—21no—
136C2×#217—21no—
137C2×#217D411yescharacteristic
138#946—22no—
139#946—41no—
140#938—22no—
141#938—22no—
142#938—22no—
143#938—41no—
144#938—41no—
145#938—41no—
146C4×#67—22no—
147C4×#67—22no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4D411yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×Dic3⋊C4—21no—
155C2×Dic3⋊C4D411yescharacteristic
156C2×C4×Dic3C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159C2×ΓL(1,𝔽25)—22no—
160C2×ΓL(1,𝔽25)—22no—
161C2×ΓL(1,𝔽25)—22no—
162#835—22no—
163#835—41no—
164#832—22no—
165#832—22no—
166#832—22no—
167#832—41no—
168#832—41no—
169#832—41no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173C3⋊#95—21no—
174#830—22no—
175(C2×D3)⋊C8—22no—
176#818—22no—
177#817—22no—
178Dic3⋊C8—22no—
179C8×Dic3—22no—
180C22×#41C2×D311yescharacteristic
181C23×D4C2×D311yescharacteristic
182C2×AGL(1,ℤ/8)—24no—
183C2×AGL(1,ℤ/8)—24no—
184C2×AGL(1,ℤ/8)—24no—
185C22×SD16C2×D311yescharacteristic
186C22×SD16C2×D311yescharacteristic
187C22×D8C2×D311yescharacteristic
188C22×D8C2×D311yescharacteristic
189C22×M16—31no—
190C22×M16C2×D311yescharacteristic
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#120—61no—
196C2×C4×D4—31no—
197#469—64no—
198#468—64no—
199#436—64no—
200C2×#107—31no—
201C2×#106—31no—
202C2×C4⋊C8—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C4×C8—31no—
214#394—61no—
215#394—61no—
216#392—61no—
217#392—61no—
218#391—31no—
219#390—31no—
220#390—31no—
221#390—31no—
222#386—61no—
223#385—61no—
224#380—31no—
225#380—31no—
226#379—61no—
227#340—31no—
228#340—31no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—42no—
233C24×C3—42no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—81no—
238C24×C3—81no—
239C24×C3C2×D411yescharacteristic
240C23×D3C2×D411yescharacteristic
241C3×#41—28no—
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8C2×D412yes—
251C2×C3×D4—28no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—44no—
268C2×C3×D4—44no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—44no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4C2×D412yes—
277C2×C3×D4C2×D412yes—
278C2×C3×D4C2×D412yes—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—42no—
285C22×C3×C4—42no—
286C22×C3×C4—42no—
287C22×C3×C4C2×D411yescharacteristic
288C22×C3×C4C2×D412yes—
289C22×C3×C4#4112yes—
290C22×C3×C4C2411yescharacteristic
291C2×#67—22no—
292C2×#67—22no—
293C2×#67—41no—
294C2×#67—42no—
295C2×#67—42no—
296C2×#67—42no—
297C2×#67—42no—
298C2×#67—42no—
299C2×#67—42no—
300C2×#67—81no—
301C2×#67—81no—
302C2×#67—81no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3C2×D411yescharacteristic
308C22×Dic3C2×D411yescharacteristic
309C22×Dic3C2×D411yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C3×SD16—28no—
317C3×SD16—28no—
318C3×D8—28no—
319C3×D8—28no—
320C3×M16—28no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8C2×D412yes—
324C2×C3×C8C2×D412yes—
325C2×C3×C8C2×D412yes—
326C2×C3×C8C2×D412yes—
327#217—22no—
328#217—42no—
329#217—42no—
330#217—42no—
331#217—42no—
332#217—42no—
333#217—42no—
334#217—42no—
335#217—81no—
336#217—81no—
337#217—81no—
338#217—81no—
339(C2×D3)⋊C4—22no—
340(C2×D3)⋊C4—42no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349Dic3⋊C4—22no—
350Dic3⋊C4—42no—
351C4×Dic3—21no—
352C4×Dic3—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359ΓL(1,𝔽25)—44no—
360C25—21no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—41no—
366C2×#41—41no—
367C22×Q8C22×D311yescharacteristic
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—31no—
375C22×D4—41no—
376C22×D4—41no—
377C22×D4—61no—
378C22×D4—61no—
379C22×D4—61no—
380C22×D4C22×D311yescharacteristic
381C22×D4C22×D311yescharacteristic
382C22×D4C22×D311yescharacteristic
383C23×C4—21no—
384C23×C4—31no—
385C23×C4C22×D311yescharacteristic
386AGL(1,ℤ/8)—232no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16#6714yescomplemented
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8—22no—
398C2×D8#6714yescomplemented
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—62no—
402C2×M16—62no—
403C2×M16—62no—
404C2×M16#6714yescomplemented
405C22×C8—31no—
406C22×C8—31no—
407C22×C8C22×D311yescharacteristic
408C22×C8C22×D311yescharacteristic
409C22⋊Q8—62no—
410C22⋊Q8—121no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#121—121no—
417#120—124no—
418C4×D4—62no—
419C4×D4—62no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—61no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C42—31no—
441#107—62no—
442#106—62no—
443C4⋊C8—62no—
444#103—62no—
445#103—121no—
446#102—62no—
447#102—62no—
448#102—62no—
449#102—121no—
450#102—121no—
451#102—121no—
452C22⋊C8—62no—
453C22⋊C8—62no—
454C4×C8—62no—
455#95—61no—
456#95—61no—
457#95—61no—
458#95—61no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—48no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—84no—
488C23×C3—84no—
489C23×C3—84no—
490C23×C3—84no—
491C23×C3—84no—
492C23×C3—84no—
493C23×C3#12112yes—
494C23×C3C22×D411yescharacteristic
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—48no—
513C3×D4—48no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—41no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—48no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4#12112yes—
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C2×#4111yescharacteristic
535C2×C3×C4H(5,𝔽2)11yescharacteristic
536C2×C3×C4H(5,𝔽2)11yescharacteristic
537#67—44no—
538#67—84no—
539#67—84no—
540#67—84no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3AGL(1,ℤ/8)12yescomplemented
562C4×D3—41no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C3×C8—22no—
567C3×C8#12014yescomplemented
568C3⋊C8—41no—
569C3⋊C8—41no—
570C24—21no—
571C24—21no—
572C24—21no—
573C24—31no—
574C24—42no—
575C24—42no—
576C24—42no—
577C24—42no—
578C24—42no—
579C24—81no—
580C24—81no—
581C24D3×D411yescharacteristic
582#41—28no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8C2×#6712yes—
592C2×D4—28no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—62no—
618C2×D4—62no—
619C2×D4—121no—
620C2×D4—122no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—241no—
627C2×D4—241no—
628C2×D4—241no—
629C2×D4C2×#6712yes—
630C2×D4C2×#6712yes—
631C2×D4C2×#6712yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4D3×D411yescharacteristic
654C22×C4#23712yes—
655C22×C4C2×#6712yes—
656C22×C4C23×D311yescharacteristic
657SD16—28no—
658SD16—28no—
659D8—28no—
660D8—28no—
661M16—28no—
662M16—124no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—61no—
666C2×C8—61no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—61no—
670C2×C8—61no—
671C2×C8C2×#6712yes—
672C2×C8C2×#6712yes—
673C2×C8C2×#6712yes—
674C2×C8C2×#6712yes—
675C4⋊C4—62no—
676C4⋊C4—61no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—122no—
685C22⋊C4—62no—
686C22⋊C4—62no—
687C22⋊C4—122no—
688C22⋊C4—122no—
689C22⋊C4—122no—
690C22⋊C4—122no—
691C22⋊C4—122no—
692C22⋊C4—122no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—241no—
696C22⋊C4—241no—
697C22⋊C4—241no—
698C22⋊C4—241no—
699C42—61no—
700C42—61no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—816no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3C2×#12111yescharacteristic
731C22×C3D4211yescharacteristic
732C22×C3D4211yescharacteristic
733C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
734C22×C3#57511yescharacteristic
735C22×C3#57611yescharacteristic
736C22×C3#57711yescharacteristic
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C3×C4—22no—
745C3×C4—42no—
746C3×C4C2×#12011yescharacteristic
747C3×C4#53511yescharacteristic
748C3×C4#54611yescharacteristic
749C3×C4#54611yescharacteristic
750Dic3—22no—
751Dic3—41no—
752Dic3—41no—
753Dic3—81no—
754Dic3—81no—
755Dic3—81no—
756Dic3—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—61no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—84no—
793C23—84no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23#93812yes—
799C23C2×D3×D411yescharacteristic
800Q8—22no—
801Q8—22no—
802Q8—41no—
803Q8—41no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—22no—
809D4—22no—
810D4—48no—
811D4—48no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—41no—
816D4—41no—
817D4—41no—
818D4—124no—
819D4—244no—
820D4—244no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—32no—
830C2×C4—48no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—121no—
842C2×C4—121no—
843C2×C4—121no—
844C2×C4—121no—
845C2×C4—121no—
846C2×C4—121no—
847C2×C4—121no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4#93812yes—
858C2×C4C2×#23711yescharacteristic
859C2×C4#100411yescharacteristic
860C2×C4#100411yescharacteristic
861C2×C4C22×#6711yescharacteristic
862C2×C4C22×#6711yescharacteristic
863C2×C4C22×#6711yescharacteristic
864C8—22no—
865C8—121no—
866C8—121no—
867C8#95314yescomplemented
868C2×C3—42no—
869C2×C3—82no—
870C2×C3—82no—
871C2×C3—82no—
872C2×C3#240811yescharacteristic
873C2×C3#305511yescharacteristic
874C2×C3#306211yescharacteristic
875C2×C3#327211yescharacteristic
876C2×C3#327311yescharacteristic
877C2×C3#327411yescharacteristic
878C2×C3#327511yescharacteristic
879D3—81no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—816no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22D3×AGL(1,ℤ/8)11yescharacteristic
917C22#577311yescharacteristic
918C22#577411yescharacteristic
919C22#577511yescharacteristic
920C22C2×#93811yescharacteristic
921C22D4×#6711yescharacteristic
922C22D4×#6711yescharacteristic
923C4—22no—
924C4—42no—
925C4—62no—
926C4—121no—
927C4—121no—
928C4—241no—
929C4—241no—
930C4—241no—
931C4—241no—
932C4#580511yescharacteristic
933C4#580611yescharacteristic
934C4#580611yescharacteristic
935C4C2×#95311yescharacteristic
936C3#2427711yescharacteristic, complemented, Sylow
937C2—42no—
938C2—82no—
939C2—82no—
940C2—82no—
941C2—241no—
942C2#8395011yescharacteristic
943C2#8395111yescharacteristic
944C2#8395811yescharacteristic
945C2#8395911yescharacteristic
946C2#8396111yescharacteristic
947C2#8396211yescharacteristic
948C2#8405311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC22×C3×AGL(1,ℤ/8)C2
socleC23×C3C22×D4
hypercenterC22×AGL(1,ℤ/8)D3
hypocenterC3#24277
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×C3×AGL(1,ℤ/8)C2semidirect
2. #84097C2semidirect
3. #84053C2semidirect
4. C2×#5174C2semidirect
5. C2×#5159C2semidirect
6. C2×#5128C2semidirect
7. #72135C2semidirect
8. #72128C2semidirect
9. #72054C2semidirect
10. #72051C2semidirect
11. #72049C2semidirect
12. #72043C2semidirect
13. #72040C2semidirect
14. #72038C2semidirect
15. #71988C2semidirect
28. C2×#946C22semidirect
31. C2×#938C22semidirect
33. C22×ΓL(1,𝔽25)C22semidirect
35. #5229C22semidirect
36. C2×#835C22semidirect
37. C2×#835C22semidirect
44. #5221C22semidirect
49. C2×#832C22semidirect
50. C2×#832C22semidirect
59. C2×(C2×D3)⋊C8C22semidirect
60. C2×#818C22semidirect
61. C2×#817C22semidirect
62. C2×Dic3⋊C8C22semidirect
63. C2×C8×Dic3C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
66. C22×AGL(1,ℤ/8)D3semidirect
113. C2×C3×SD16D4semidirect
119. C2×C3×D8D4semidirect
122. C2×C3×M16D4semidirect
392. C2×SD16#67semidirect
398. C2×D8#67semidirect
404. C2×M16#67semidirect
561. C2×Dic3AGL(1,ℤ/8)semidirect
567. C3×C8#120semidirect
867. C8#953semidirect
936. C3#24277semidirect

Maximal subgroups

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

subgroupindex
C22×C3×AGL(1,ℤ/8)2
#840972
#840532
C2×#51742
C2×#51592
C2×#51282
#721352
#721282
#720542
#720512
#720492
#720432
#720402
#720382
#719882
#242773