Finite Group Databasebeta

← #10826307

Subgroups — #10826307

Order 768.

1956 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5831C211yesmaximal, characteristic, complemented
2C22×D3×SD16C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5C2×#5156C211yesmaximal, characteristic, complemented
6#82640C211yesmaximal, characteristic, complemented
7#72048C211yesmaximal, characteristic, complemented
8#72045C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#70266C211yesmaximal, characteristic, complemented
11#70240C211yesmaximal, characteristic, complemented
12#70214C211yesmaximal, characteristic, complemented
13#70202C211yesmaximal, characteristic, complemented
14#69962C211yesmaximal, characteristic, complemented
15#69957C211yesmaximal, characteristic, complemented
16#23858—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic, complemented
18C22×D3×Q8C2211yescharacteristic
19C22×D3×D4C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23#5831—24no—
24#5831—24no—
25C2×Q8×Dic3C2211yescharacteristic, complemented
26C22×#215C2211yescharacteristic
27C2×#938—21no—
28C2×#938C2211yescharacteristic
29C2×#937—21no—
30C2×#936—21no—
31C2×#936C2211yescharacteristic, complemented
32C22×#214C2211yescharacteristic
33C22×#213C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×C4×#67—21no—
36C2×C4×#67C2211yescharacteristic
37C2×#924—21no—
38C2×#924C2211yescharacteristic, complemented
39C2×D3×SD16—24no—
40C2×D3×SD16—24no—
41C2×D3×SD16—24no—
42C22×#204C2211yescharacteristic
43C22×D3×C8C2211yescharacteristic
44C3×#449—24no—
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×C22⋊C8C2211yescharacteristic, complemented
48#5238—24no—
49C2×#835C2211yescharacteristic, complemented
50#5223—21no—
51#5221C2211yescharacteristic
52C2×#832C2211yescharacteristic
53C2×#832C2211yescharacteristic, complemented
54C2×#830C2211yescharacteristic, complemented
55#5156—24no—
56C2×#821C2211yescharacteristic
57C2×(C2×D3)⋊C8C2211yescharacteristic
58C2×#816C2211yescharacteristic, complemented
59#4988C2211yescharacteristic
60#4987C2211yescharacteristic
61C2×#810C2211yescharacteristic, complemented
62#4959—21no—
63#4955—21no—
64#4551C2211yescharacteristic, complemented
65#4550C2211yescharacteristic, complemented
66#4550C2211yescharacteristic, complemented
67#4529C2211yescharacteristic, complemented
68C23×SD16—31no—
69C2×#548—31no—
70C2×#449—31no—
71C2×#449D311yescharacteristic, complemented
72C2×#447—31no—
73#2408—31no—
74#2012—31no—
75#2012—31no—
76#2000—31no—
77#2000—31no—
78#1893—31no—
79#1880—31no—
80#1880—31no—
81#1869—31no—
82#1787—31no—
83C24×D3—21no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4C2311yescharacteristic
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—21no—
96C23×C3×C4C2311yescharacteristic
97C22×#67—21no—
98C22×#67—21no—
99C22×#67—21no—
100C22×#67D411yescharacteristic
101C2×D3×Q8—22no—
102C2×D3×Q8—22no—
103C2×D3×Q8—22no—
104C2×D3×Q8—41no—
105C2×D3×Q8—41no—
106C2×D3×Q8D414yescomplemented
107C2×D3×D4—22no—
108C2×D3×D4—22no—
109C2×D3×D4—22no—
110C2×D3×D4—22no—
111C2×D3×D4—41no—
112C2×D3×D4—41no—
113C22×D12C2311yescharacteristic
114C22×C4×D3—21no—
115C22×C4×D3C2311yescharacteristic
116C22×Dic6—21no—
117C22×Dic6C2311yescharacteristic
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16D414yescomplemented
121C2×C3×D8—22no—
122C2×C3×D8—22no—
123C2×C3×D8—41no—
124C22×C3×C8C2311yescharacteristic
125C22×C3×C8C2311yescharacteristic
126C3×#121—22no—
127C3×#121—41no—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×#217—21no—
131C2×#217—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135C2×#217—21no—
136C2×#217D411yescharacteristic
137Q8×Dic3—22no—
138Q8×Dic3—22no—
139C2×#215—22no—
140C2×#215—22no—
141C2×#215D414yescomplemented
142#938—28no—
143#938—22no—
144#938D414yescomplemented
145#937—44no—
146#936—28no—
147#936—22no—
148#936—22no—
149C2×#214—22no—
150C2×#214—22no—
151C2×#214—22no—
152C2×#213—22no—
153C2×#213—22no—
154C2×#213—41no—
155#930—22no—
156#930—41no—
157C4×#67—28no—
158C4×#67—22no—
159C4×#67—22no—
160C2×(C2×D3)⋊C4—21no—
161C2×(C2×D3)⋊C4—21no—
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164C2×(C2×D3)⋊C4D411yescharacteristic
165C2×C4⋊Dic3—21no—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2311yescharacteristic
168#924—28no—
169#924—22no—
170#924—22no—
171C2×Dic3⋊C4—21no—
172C2×Dic3⋊C4D411yescharacteristic
173C2×C4×Dic3—21no—
174C2×C4×Dic3C2311yescharacteristic
175C22×C3⋊C8C2311yescharacteristic
176C22×C3⋊C8C2311yescharacteristic
177D3×SD16—232no—
178C2×#204—22no—
179C2×#204—22no—
180C2×#204—22no—
181C2×D3×C8—22no—
182C2×D3×C8—22no—
183C2×D3×C8—22no—
184C3×#103—22no—
185C3×#102—22no—
186C3×C22⋊C8—22no—
187#835—22no—
188#832—22no—
189#832—22no—
190C3⋊#95—21no—
191#830—22no—
192#821—22no—
193(C2×D3)⋊C8—22no—
194#816—41no—
195#810—41no—
196C22×#41C2×D311yescharacteristic, complemented
197C23×Q8—31no—
198C23×D4—31no—
199C22×SD16—31no—
200C22×SD16—31no—
201C22×SD16—31no—
202C22×SD16—64no—
203C22×SD16—64no—
204C22×SD16—64no—
205C22×SD16C2×D311yescharacteristic
206C22×D8—31no—
207C22×D8C2×D311yescharacteristic
208C23×C8—31no—
209#548—64no—
210#548—64no—
211C2×#124—31no—
212C2×#124—61no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8—61no—
215C2×#121—31no—
216C2×#121—31no—
217C2×#121—61no—
218C2×#121C2×D311yescharacteristic
219C2×#120—61no—
220C2×C4×Q8—31no—
221C2×C4×D4—31no—
222C2×C4×D4—61no—
223#449—24no—
224#449—64no—
225#447—64no—
226C2×#103—31no—
227C2×#103—31no—
228C2×#103—31no—
229C2×#103C2×D311yescharacteristic, complemented
230C2×#102—31no—
231C2×#102—31no—
232C2×#102—31no—
233C2×#102C2×D311yescharacteristic, complemented
234C2×C22⋊C8—31no—
235C2×C22⋊C8—31no—
236C2×C22⋊C8C2×D311yescharacteristic, complemented
237#394—61no—
238#392—61no—
239#390—31no—
240#390—31no—
241#380—31no—
242#379—61no—
243#340—31no—
244#340—31no—
245#336—31no—
246#336—31no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3C2×D411yescharacteristic
250C23×D3—21no—
251C23×D3—42no—
252C23×D3—42no—
253C23×D3—42no—
254C23×D3—42no—
255C23×D3—42no—
256C23×D3—81no—
257C23×D3—81no—
258C23×D3C2×D411yescharacteristic
259C3×#41—44no—
260C3×#41—44no—
261C3×#41—44no—
262C3×#41—44no—
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8C2×D412yes—
267C2×C3×Q8C2×D412yes—
268C2×C3×Q8C2×D412yes—
269C2×C3×D4—24no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—81no—
285C2×C3×D4C2×D412yes—
286C2×C3×D4C2×D412yes—
287C22×C3×C4—21no—
288C22×C3×C4—24no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C2×#67—22no—
301C2×#67—24no—
302C2×#67—22no—
303C2×#67—22no—
304C2×#67—42no—
305C2×#67—42no—
306C2×#67—42no—
307C2×#67—42no—
308C2×#67—42no—
309C2×#67—42no—
310C2×#67—42no—
311C2×#67—81no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3C2×D411yescharacteristic
316C22×Dic3C2×D411yescharacteristic
317C22×Dic3C2×D411yescharacteristic
318D3×Q8—28no—
319D3×Q8—44no—
320D3×Q8—44no—
321D3×Q8—44no—
322D3×D4—28no—
323D3×D4—44no—
324D3×D4—44no—
325D3×D4—44no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12C2×D412yes—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—24no—
337C2×C4×D3—42no—
338C2×C4×D3—42no—
339C2×C4×D3C2×D412yes—
340C2×C4×D3C2×D412yes—
341C2×Dic6—21no—
342C2×Dic6—21no—
343C2×Dic6—21no—
344C2×Dic6—21no—
345C2×Dic6—21no—
346C2×Dic6—24no—
347C2×Dic6—42no—
348C2×Dic6—42no—
349C2×Dic6C2×D412yes—
350C3×SD16—28no—
351C3×D8—44no—
352C2×C3×C8—21no—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—21no—
357C2×C3×C8C2×D412yes—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C22⋊C4—42no—
361#217—24no—
362#217—24no—
363#217—24no—
364#217—24no—
365#217—22no—
366#217—42no—
367#217—81no—
368#215—28no—
369#214—28no—
370#213—44no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—42no—
373(C2×D3)⋊C4—42no—
374(C2×D3)⋊C4—42no—
375(C2×D3)⋊C4—81no—
376C4⋊Dic3—24no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3C2×D412yes—
381Dic3⋊C4—24no—
382Dic3⋊C4—22no—
383C4×Dic3—24no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C2×C3⋊C8—21no—
387C2×C3⋊C8—21no—
388C2×C3⋊C8—21no—
389C2×C3⋊C8—21no—
390C2×C3⋊C8—21no—
391C2×C3⋊C8C2×D412yes—
392#204—28no—
393D3×C8—28no—
394C25—61no—
395C2×#41—22no—
396C2×#41—22no—
397C2×#41—22no—
398C2×#41—22no—
399C2×#41—41no—
400C2×#41—41no—
401C22×Q8—34no—
402C22×Q8—31no—
403C22×Q8—61no—
404C22×Q8—62no—
405C22×Q8—62no—
406C22×Q8—62no—
407C22×Q8—121no—
408C22×Q8—121no—
409C22×Q8C22×D311yescharacteristic
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—31no—
413C22×D4—31no—
414C22×D4—62no—
415C22×D4—62no—
416C22×D4—61no—
417C22×D4—62no—
418C22×D4—62no—
419C22×D4—61no—
420C22×D4—61no—
421C22×D4—121no—
422C22×D4—121no—
423C22×D4C22×D311yescharacteristic
424C22×D4C22×D311yescharacteristic
425C23×C4—21no—
426C23×C4—31no—
427C23×C4—61no—
428C23×C4C22×D311yescharacteristic
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—34no—
432C2×SD16—62no—
433C2×SD16—62no—
434C2×SD16—62no—
435C2×SD16—632no—
436C2×SD16—62no—
437C2×SD16—62no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16#6714yescomplemented
442C2×D8—22no—
443C2×D8—22no—
444C2×D8—41no—
445C2×D8—62no—
446C2×D8—62no—
447C2×D8—121no—
448C22×C8—31no—
449C22×C8—31no—
450C22×C8—62no—
451C22×C8—62no—
452C22×C8—62no—
453C22×C8C22×D311yescharacteristic
454C22×C8C22×D311yescharacteristic
455#124—62no—
456#124—68no—
457#124—62no—
458C22⋊Q8—62no—
459C22⋊Q8—62no—
460C22⋊Q8—68no—
461#121—22no—
462#121—34no—
463#121—41no—
464#121—62no—
465#121—68no—
466#121—62no—
467#121—121no—
468#120—124no—
469C4×Q8—62no—
470C4×Q8—62no—
471C4×D4—62no—
472C4×D4—62no—
473C4×D4—68no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—61no—
478C2×C4⋊C4—61no—
479C2×C4⋊C4C22×D311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—61no—
484C2×C22⋊C4—61no—
485C2×C22⋊C4—61no—
486C2×C22⋊C4—61no—
487C2×C22⋊C4—61no—
488C2×C22⋊C4—61no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C22⋊C4—61no—
492C2×C22⋊C4—61no—
493C2×C42—31no—
494C2×C42—61no—
495#103—22no—
496#103—62no—
497#103—121no—
498#103—121no—
499#102—22no—
500#102—62no—
501#102—62no—
502#102—62no—
503C22⋊C8—22no—
504C22⋊C8—62no—
505C22⋊C8—62no—
506#95—61no—
507C23×C3—21no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3C22×D411yescharacteristic
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—22no—
534C22×D3—48no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—84no—
542C22×D3—84no—
543C22×D3—84no—
544C22×D3—84no—
545C22×D3—84no—
546C22×D3—84no—
547C22×D3#12012yes—
548C22×D3#13512yes—
549C22×D3AGL(1,ℤ/8)12yes—
550C3×Q8—22no—
551C3×Q8—22no—
552C3×Q8—22no—
553C3×Q8#12014yescomplemented
554C3×D4—22no—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—22no—
558C3×D4—48no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—84no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—48no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4H(5,𝔽2)11yescharacteristic
583C2×C3×C4H(5,𝔽2)11yescharacteristic
584#67—48no—
585#67—44no—
586#67—48no—
587#67—84no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3#12012yes—
606D12—22no—
607D12—22no—
608D12—41no—
609D12—41no—
610C4×D3—22no—
611C4×D3—22no—
612C4×D3—22no—
613C4×D3—22no—
614C4×D3—48no—
615Dic6—22no—
616Dic6—22no—
617Dic6—48no—
618Dic6—41no—
619Dic6—41no—
620C3×C8—22no—
621C3×C8—41no—
622C3⋊C8—22no—
623C3⋊C8—41no—
624C24—21no—
625C24—21no—
626C24—31no—
627C24—61no—
628C24—122no—
629C24—122no—
630C24—122no—
631C24—122no—
632C24—122no—
633C24—241no—
634C24—241no—
635C24D3×D411yescharacteristic
636#41—44no—
637#41—44no—
638#41—44no—
639#41—44no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—32no—
644C2×Q8—64no—
645C2×Q8—61no—
646C2×Q8—68no—
647C2×Q8—61no—
648C2×Q8—61no—
649C2×Q8—61no—
650C2×Q8—61no—
651C2×Q8—122no—
652C2×Q8—122no—
653C2×Q8—124no—
654C2×Q8—124no—
655C2×Q8—124no—
656C2×Q8D3×D412yes—
657C2×Q8D3×D412yes—
658C2×Q8C2×#6712yes—
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—32no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—68no—
676C2×D4—64no—
677C2×D4—62no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—81no—
686C2×D4—122no—
687C2×D4—124no—
688C2×D4—124no—
689C2×D4—124no—
690C2×D4—122no—
691C2×D4—122no—
692C2×D4—122no—
693C2×D4—122no—
694C2×D4—122no—
695C2×D4—122no—
696C2×D4—241no—
697C2×D4D3×D412yes—
698C2×D4C2×#6712yes—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—31no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—64no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—122no—
724C22×C4—122no—
725C22×C4D3×D411yescharacteristic
726C22×C4C23×D311yescharacteristic
727SD16—28no—
728SD16—68no—
729SD16—68no—
730SD16—68no—
731D8—44no—
732D8—124no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—32no—
739C2×C8—68no—
740C2×C8—61no—
741C2×C8—61no—
742C2×C8—61no—
743C2×C8—61no—
744C2×C8—61no—
745C2×C8C2×#6712yes—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—32no—
749C4⋊C4—62no—
750C4⋊C4—64no—
751C4⋊C4—64no—
752C4⋊C4—61no—
753C4⋊C4—61no—
754C4⋊C4—61no—
755C22⋊C4—42no—
756C22⋊C4—62no—
757C22⋊C4—62no—
758C22⋊C4—64no—
759C22⋊C4—64no—
760C22⋊C4—64no—
761C22⋊C4—64no—
762C22⋊C4—122no—
763C22⋊C4—122no—
764C22⋊C4—122no—
765C22⋊C4—122no—
766C22⋊C4—241no—
767C22⋊C4—241no—
768C42—64no—
769C42—61no—
770C42—61no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—42no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—42no—
779C22×C3—41no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—81no—
785C22×C3—81no—
786C22×C3—81no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—81no—
791C22×C3—81no—
792C22×C3C2×#12011yescharacteristic
793C22×C3D4211yescharacteristic
794C22×C3D4211yescharacteristic
795C22×C3C2×#13511yescharacteristic
796C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
797C22×C3#57711yescharacteristic
798C22×C3#57711yescharacteristic
799C2×D3—22no—
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—42no—
806C2×D3—42no—
807C2×D3—42no—
808C2×D3—816no—
809C2×D3—81no—
810C2×D3—81no—
811C2×D3—81no—
812C2×D3—81no—
813C2×D3#44914yescomplemented
814C3×C4—24no—
815C3×C4—41no—
816C3×C4—81no—
817C3×C4C2×#12011yescharacteristic
818C3×C4#53411yescharacteristic
819C3×C4D4211yescharacteristic
820C3×C4D4211yescharacteristic
821Dic3—22no—
822Dic3—42no—
823Dic3—41no—
824Dic3—42no—
825Dic3—41no—
826Dic3—81no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—22no—
832C23—21no—
833C23—21no—
834C23—22no—
835C23—21no—
836C23—32no—
837C23—32no—
838C23—32no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—62no—
856C23—128no—
857C23—121no—
858C23—121no—
859C23—121no—
860C23—121no—
861C23—121no—
862C23—121no—
863C23—244no—
864C23—244no—
865C23—244no—
866C23—244no—
867C23—244no—
868C23—244no—
869C23C2×D3×D411yescharacteristic
870Q8—22no—
871Q8—22no—
872Q8—22no—
873Q8—62no—
874Q8—62no—
875Q8—128no—
876Q8—121no—
877Q8—121no—
878Q8#93714yescomplemented
879D4—22no—
880D4—22no—
881D4—22no—
882D4—22no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—62no—
889D4—62no—
890D4—84no—
891D4—128no—
892D4—124no—
893D4—128no—
894D4—121no—
895D4—121no—
896D4—244no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—32no—
904C2×C4—48no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—62no—
924C2×C4—61no—
925C2×C4—62no—
926C2×C4—128no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4C2×D3×D411yescharacteristic
935C2×C4C2×D3×D411yescharacteristic
936C2×C4C2×D3×D411yescharacteristic
937C2×C4#100411yescharacteristic
938C2×C4#100411yescharacteristic
939C2×C4C22×#6711yescharacteristic
940C8—22no—
941C8—41no—
942C8—62no—
943C8—121no—
944C2×C3—82no—
945C2×C3—81no—
946C2×C3—82no—
947C2×C3#240311yescharacteristic
948C2×C3C2×#44911yescharacteristic
949C2×C3#301011yescharacteristic
950C2×C3#326511yescharacteristic
951C2×C3#326511yescharacteristic
952C2×C3#328211yescharacteristic
953C2×C3#328211yescharacteristic
954D3—24no—
955D3—82no—
956C22—34no—
957C22—42no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—41no—
970C22—62no—
971C22—62no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—81no—
977C22—81no—
978C22—81no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—122no—
985C22—122no—
986C22—122no—
987C22—2416no—
988C22—241no—
989C22—241no—
990C22—241no—
991C22—241no—
992C22D3×#12011yescharacteristic
993C22#559011yescharacteristic
994C22D3×#13511yescharacteristic
995C22#577011yescharacteristic
996C22D3×AGL(1,ℤ/8)11yescharacteristic
997C22#577511yescharacteristic
998C22D4×#6711yescharacteristic
999C4—24no—
1000C4—41no—
1001C4—62no—
1002C4—81no—
1003C4—122no—
1004C4—121no—
1005C4—122no—
1006C4—121no—
1007C4—241no—
1008C4#558911yescharacteristic
1009C4#559011yescharacteristic
1010C4C2×#93711yescharacteristic
1011C4D4×#6711yescharacteristic
1012C3#2385811yescharacteristic, complemented, Sylow
1013C2—64no—
1014C2—81no—
1015C2—82no—
1016C2—82no—
1017C2—242no—
1018C2D3×#44911yescharacteristic
1019C2#8008611yescharacteristic
1020C2#8012111yescharacteristic
1021C2#8012611yescharacteristic
1022C2#8260411yescharacteristic
1023C2#8391911yescharacteristic
1024C2#8395311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#23858
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5831C2semidirect
2. C22×D3×SD16C2semidirect
3. C2×C3×#449C2semidirect
4. C2×#5238C2semidirect
5. C2×#5156C2semidirect
6. #82640C2semidirect
7. #72048C2semidirect
8. #72045C2semidirect
9. #71685C2semidirect
10. #70266C2semidirect
11. #70240C2semidirect
12. #70214C2semidirect
13. #70202C2semidirect
14. #69962C2semidirect
15. #69957C2semidirect
17. C22×C3×#41C22semidirect
25. C2×Q8×Dic3C22semidirect
31. C2×#936C22semidirect
38. C2×#924C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#102C22semidirect
47. C2×C3×C22⋊C8C22semidirect
49. C2×#835C22semidirect
53. C2×#832C22semidirect
54. C2×#830C22semidirect
58. C2×#816C22semidirect
61. C2×#810C22semidirect
64. #4551C22semidirect
65. #4550C22semidirect
66. #4550C22semidirect
67. #4529C22semidirect
71. C2×#449D3semidirect
106. C2×D3×Q8D4semidirect
120. C2×C3×SD16D4semidirect
141. C2×#215D4semidirect
144. #938D4semidirect
196. C22×#41C2×D3semidirect
229. C2×#103C2×D3semidirect
233. C2×#102C2×D3semidirect
236. C2×C22⋊C8C2×D3semidirect
441. C2×SD16#67semidirect
553. C3×Q8#120semidirect
813. C2×D3#449semidirect
878. Q8#937semidirect
1012. C3#23858semidirect

Maximal subgroups

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

subgroupindex
C2×#58312
C22×D3×SD162
C2×C3×#4492
C2×#52382
C2×#51562
#826402
#720482
#720452
#716852
#702662
#702402
#702142
#702022
#699622
#699572
#238583