Finite Group Databasebeta

← #11660910

Subgroups — #11660910

Order 768.

1914 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85776C211yesmaximal, characteristic
2C2×C3×C8×D4C211yesmaximal, characteristic, complemented
3#83734C212yesmaximal, complemented
4C2×#5111C212yesmaximal, complemented
5#82302C211yesmaximal, characteristic, complemented
6#79429C214yesmaximal, complemented
7#79423C214yesmaximal, complemented
8#79409C214yesmaximal, complemented
9#79402C214yesmaximal, complemented
10#79016C212yesmaximal, complemented
11#78604C212yesmaximal, complemented
12#78601C212yesmaximal, complemented
13#78448C212yesmaximal, complemented
14#60310—31nomaximal, Sylow
15C23×C3×C8C2211yescharacteristic
16C23×C3×C8C2211yescharacteristic, complemented
17C2×C3×C4×D4C2211yescharacteristic
18#5804C412yes—
19#5791C2212yes—
20C2×C4×#67C2212yes—
21C2×#901C2212yescomplemented
22C22×ΓL(1,𝔽25)C2212yescomplemented
23#5564C414yes—
24#5560C414yes—
25#5547C2214yes—
26#5538C2214yes—
27#5515C412yes—
28#5494C412yes—
29#5493C411yescharacteristic
30#5483C411yescharacteristic
31#5479C2212yes—
32C3×C8×D4C2214yescomplemented
33C3×C8×D4C2214yescomplemented
34C2×C3×C4⋊C8C2211yescharacteristic, complemented
35C2×C3×C22⋊C8C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic, complemented
37C2×C3×C4×C8C2211yescharacteristic, complemented
38#5207C2212yescomplemented
39C2×#830C2212yes—
40#5111C2214yescomplemented
41#5111C2214yescomplemented
42#5111C2214yescomplemented
43#5111C2214yescomplemented
44#5111C2214yescomplemented
45#5110C2212yescomplemented
46C8×#67C2214yescomplemented
47C8×#67C2214yescomplemented
48C8×#67C2214yescomplemented
49C2×(C2×D3)⋊C8C2212yescomplemented
50#5102C2212yescomplemented
51#5101C2212yescomplemented
52C2×#815C2212yescomplemented
53C2×Dic3⋊C8C2212yescomplemented
54#5011C2214yescomplemented
55#5011C2214yescomplemented
56#4926C2212yescomplemented
57#4840C2214yescomplemented
58#4839C2214yescomplemented
59#4836C2214yescomplemented
60#4828C2214yescomplemented
61#4729C2214yescomplemented
62#4728C2214yescomplemented
63#4727C2214yescomplemented
64#67⋊C8C2214yescomplemented
65#67⋊C8C2214yescomplemented
66D3×C22⋊C8C2214yescomplemented
67#4720C2214yescomplemented
68#4718C2214yescomplemented
69#4690C2214yescomplemented
70#4689C2214yescomplemented
71#4688C2212yescomplemented
72C8×D12C2212yescomplemented
73#4679C2212yescomplemented
74C8×Dic6C2212yescomplemented
75#3459—31no—
76#2994—34no—
77#2992—32no—
78#2977—34no—
79#2976—32no—
80#2973—31no—
81#2972—32no—
82#2968—34no—
83#2966—32no—
84#2933—34no—
85#2929—32no—
86C2×#435—32no—
87C2×C8×D4D311yescharacteristic, complemented
88C22×C3×D4C2×C411yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C22×#67C2×C412yes—
92C2×#235C2312yes—
93C22×C4×D3C2312yes—
94C22×C3×C8—42no—
95C22×C3×C8—42no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2312yes—
98C22×C3×C8C2312yes—
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2312yes—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2312yes—
103C22×C3×C8C2311yescharacteristic
104C3×C4×D4C2×C414yes—
105C3×C4×D4C2314yes—
106C2×C3×C4⋊C4C2×C411yescharacteristic
107C2×C3×C22⋊C4C2×C411yescharacteristic
108C2×C3×C22⋊C4C2×C411yescharacteristic
109C2×C3×C42C2311yescharacteristic
110#953C2×C414yes—
111C2×#217C2×C412yes—
112#939C2×C414yes—
113#939C2×C414yes—
114#937C2×C414yes—
115#935C2×C414yes—
116#930C2×C412yes—
117#930C2×C412yes—
118#930C2×C412yes—
119#929C2×C414yes—
120#929C2×C414yes—
121C4×#67C2×C414yes—
122C4×#67C2×C414yes—
123C4×#67C2314yes—
124C4×#67C2314yes—
125C4×#67C2314yes—
126C2×(C2×D3)⋊C4C2×C412yes—
127#926C2312yes—
128#924C2×C412yes—
129#924C2×C412yes—
130#924C2×C412yes—
131C2×Dic3⋊C4C2×C412yes—
132C2×C4×Dic3C2312yes—
133C2×#208C2312yes—
134C2×#208C2312yes—
135C22×C3⋊C8C2312yes—
136C22×C3⋊C8C2312yes—
137#901—44no—
138C2×ΓL(1,𝔽25)—44no—
139C2×ΓL(1,𝔽25)C2314yes—
140C2×ΓL(1,𝔽25)C2314yes—
141C2×D3×C8C2314yes—
142C2×D3×C8C2314yes—
143#898C2×C414yes—
144#896C2×C414yes—
145#894C2×C414yes—
146#889C2×C414yes—
147#886C2×C414yes—
148#885C2×C414yes—
149#884C2×C414yes—
150#883C2×C414yes—
151#882C2×C414yes—
152#879C2×C414yes—
153#878C2×C414yes—
154#878C2×C414yes—
155#876C2×C414yes—
156#875C2×C412yes—
157C4×D12C2312yes—
158#872C2314yes—
159#870C2×C412yes—
160C4×Dic6C2312yes—
161C3×C4⋊C8C2314yes—
162C3×C22⋊C8C2314yes—
163C3×C22⋊C8C2314yes—
164C3×C4×C8C2312yes—
165C3×C4×C8C2312yes—
166#830C2314yes—
167#830C2314yes—
168#830C2314yes—
169(C2×D3)⋊C8C2314yes—
170(C2×D3)⋊C8C2314yes—
171(C2×D3)⋊C8C2314yes—
172(C2×D3)⋊C8C2314yes—
173#815C2314yes—
174#815C2314yes—
175Dic3⋊C8C2314yes—
176Dic3⋊C8C2314yes—
177Dic3⋊C8C2314yes—
178Dic3⋊C8C2314yes—
179C8×Dic3C2314yes—
180C8×Dic3C2314yes—
181C4⋊(C3⋊C8)C2312yes—
182C4⋊(C3⋊C8)C2312yes—
183#803C2314yes—
184C2×#131—32no—
185C22×M16—32no—
186C23×C8C2×D311yescharacteristic
187C23×C8C2×D311yescharacteristic, complemented
188#543—31no—
189#539—34no—
190#539—32no—
191#538—34no—
192#538—32no—
193#534—32no—
194#534—31no—
195#529—34no—
196#529—32no—
197#525—32no—
198#525—34no—
199C2×C4×D4—32no—
200C2×C4×D4C2×D311yescharacteristic
201#446—34no—
202#446—32no—
203C8×Q8—32no—
204#436—34no—
205#436—32no—
206#435—34no—
207#435—34no—
208#435—34no—
209#435—34no—
210#435—34no—
211#435—34no—
212#435—34no—
213#435—34no—
214#435—34no—
215C8×D4—34no—
216C8×D4—34no—
217C8×D4—34no—
218C8×D4—34no—
219C8×D4—34no—
220C8×D4—32no—
221C8×D4C2×D314yescomplemented
222C8×D4C2×D314yescomplemented
223#433—34no—
224#433—34no—
225#433—34no—
226#432—32no—
227#431—34no—
228#424—32no—
229#424—34no—
230C2×C4⋊C8—32no—
231C2×C4⋊C8C2×D311yescharacteristic, complemented
232#408—32no—
233#408—34no—
234#407—32no—
235C2×C22⋊C8—32no—
236C2×C22⋊C8—32no—
237C2×C22⋊C8—34no—
238C2×C22⋊C8C2×D311yescharacteristic
239C2×C22⋊C8C2×D311yescharacteristic, complemented
240#405—32no—
241#405—34no—
242C2×#97—32no—
243C2×C4×C8C2×D311yescharacteristic, complemented
244C24×C3C22×C411yescharacteristic
245C24×C3C22×C411yescharacteristic
246C23×D3C22×C412yes—
247C2×C3×D4—24no—
248C2×C3×D4C22×C414yes—
249C22×C3×C4—41no—
250C22×C3×C4—41no—
251C22×C3×C4—41no—
252C22×C3×C4—41no—
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C22×C412yes—
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C22×C412yes—
258C22×C3×C4C22×C411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C2×#67—28no—
263C2×#67C22×C414yes—
264C2×#67C22×C414yes—
265C2×#67C22×C414yes—
266C2×#67C22×C414yes—
267C22×Dic3C22×C412yes—
268C22×Dic3C22×C412yes—
269C22×Dic3C22×C412yes—
270#235—42no—
271#235—42no—
272C2×D12C22×C412yes—
273C2×D12C22×C412yes—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C2×C4×D3C22×C414yes—
277C2×C4×D3C2414yes—
278C2×Dic6C22×C412yes—
279C2×Dic6C22×C412yes—
280C2×C3×C8—24no—
281C2×C3×C8—24no—
282C2×C3×C8—22no—
283C2×C3×C8—41no—
284C2×C3×C8—42no—
285C2×C3×C8—41no—
286C2×C3×C8—42no—
287C2×C3×C8—41no—
288C2×C3×C8C2412yes—
289C2×C3×C8C2412yes—
290C2×C3×C8C2411yescharacteristic
291C2×C3×C8C2412yes—
292C2×C3×C8C2411yescharacteristic
293C3×C4⋊C4C22×C414yes—
294C3×C22⋊C4C22×C414yes—
295C3×C22⋊C4C22×C414yes—
296C3×C42C22×C412yes—
297C3×C42C2412yes—
298#217C22×C414yes—
299#217C22×C414yes—
300#217C22×C414yes—
301#217C22×C414yes—
302(C2×D3)⋊C4C22×C414yes—
303(C2×D3)⋊C4C22×C414yes—
304(C2×D3)⋊C4C22×C414yes—
305(C2×D3)⋊C4C22×C414yes—
306(C2×D3)⋊C4C22×C414yes—
307(C2×D3)⋊C4C22×C414yes—
308C4⋊Dic3C22×C412yes—
309C4⋊Dic3C22×C412yes—
310C4⋊Dic3C22×C412yes—
311C4⋊Dic3C22×C412yes—
312Dic3⋊C4C22×C414yes—
313Dic3⋊C4C22×C414yes—
314Dic3⋊C4C22×C414yes—
315Dic3⋊C4C22×C414yes—
316Dic3⋊C4C22×C414yes—
317Dic3⋊C4C22×C414yes—
318C4×Dic3C22×C414yes—
319C4×Dic3C2414yes—
320#208—42no—
321#208—42no—
322C2×C3⋊C8—42no—
323C2×C3⋊C8—42no—
324C2×C3⋊C8C2414yes—
325C2×C3⋊C8C2414yes—
326ΓL(1,𝔽25)—28no—
327ΓL(1,𝔽25)—44no—
328D3×C8—44no—
329D3×C8—44no—
330C2×#41—32no—
331C22×D4—32no—
332C22×D4C4×D311yescharacteristic
333C23×C4—32no—
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336#131—124no—
337C2×M16—32no—
338C2×M16—32no—
339C2×M16—34no—
340C2×M16—34no—
341C2×M16—124no—
342C22×C8—32no—
343C22×C8—32no—
344C22×C8—34no—
345C22×C8—34no—
346C22×C8—42no—
347C22×C8—42no—
348C22×C8C22×D311yescharacteristic
349C22×C8C22×D312yes—
350C22×C8C22×D312yes—
351C22×C8C22×D312yes—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354C22×C8C22×D312yes—
355C22×C8C22×D311yescharacteristic
356#126—34no—
357#126—34no—
358#126—34no—
359#125—34no—
360#125—32no—
361#124—34no—
362#124—32no—
363#123—34no—
364#123—34no—
365#123—34no—
366#123—34no—
367#123—34no—
368#123—34no—
369C22⋊Q8—32no—
370C22⋊Q8—32no—
371C22⋊Q8—32no—
372C22⋊Q8—34no—
373C22⋊Q8—34no—
374C22⋊Q8—34no—
375#121—34no—
376#121—34no—
377#121—32no—
378#121—32no—
379#121—32no—
380#121—34no—
381#120—34no—
382#120—34no—
383#120—34no—
384C4×Q8—32no—
385C4×D4—34no—
386C4×D4—34no—
387C4×D4—34no—
388C4×D4—34no—
389C4×D4—34no—
390C4×D4—32no—
391C4×D4C4×D314yes—
392C4×D4C22×D314yes—
393#117—32no—
394#117—34no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4C4×D311yescharacteristic
397C2×C22⋊C4—32no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4C4×D311yescharacteristic
400C2×C22⋊C4C4×D311yescharacteristic
401C2×C42—32no—
402C2×C42C22×D311yescharacteristic
403C4⋊C8—34no—
404C4⋊C8—34no—
405C4⋊C8—34no—
406C4⋊C8—34no—
407C4⋊C8—32no—
408C4⋊C8—32no—
409C4⋊C8C22×D314yes—
410C22⋊C8—34no—
411C22⋊C8—34no—
412C22⋊C8—34no—
413C22⋊C8—34no—
414C22⋊C8—34no—
415C22⋊C8—34no—
416C22⋊C8—34no—
417C22⋊C8C22×D314yes—
418C22⋊C8C22×D314yes—
419#97—34no—
420#97—34no—
421#97—34no—
422C4×C8—34no—
423C4×C8—34no—
424C4×C8C22×D312yes—
425C4×C8C22×D312yes—
426C23×C3—22no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3#13114yescomplemented
432C23×C3C23×C412yes—
433C23×C3C23×C411yescharacteristic
434C23×C3C23×C412yes—
435C22×D3—24no—
436C22×D3—42no—
437C22×D3—42no—
438C22×D3C23×C414yes—
439C3×D4—28no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—41no—
448C2×C3×C4—42no—
449C2×C3×C4—41no—
450C2×C3×C4—42no—
451C2×C3×C4—41no—
452C2×C3×C4C23×C412yes—
453C2×C3×C4C23×C411yescharacteristic
454C2×C3×C4C23×C412yes—
455C2×C3×C4C23×C412yes—
456C2×C3×C4C23×C412yes—
457C2×C3×C4C2511yescharacteristic
458#67—28no—
459#67—28no—
460#67—44no—
461#67—44no—
462C2×Dic3—24no—
463C2×Dic3—42no—
464C2×Dic3—42no—
465C2×Dic3C23×C414yes—
466C2×Dic3C23×C414yes—
467C2×Dic3C23×C414yes—
468D12—42no—
469D12—42no—
470C4×D3—24no—
471C4×D3—24no—
472C4×D3—44no—
473Dic6—42no—
474Dic6—42no—
475C3×C8—22no—
476C3×C8—22no—
477C3×C8—21no—
478C3×C8—22no—
479C3×C8H(5,𝔽2)12yes—
480C3⋊C8—24no—
481C3⋊C8—24no—
482C24—32no—
483C24C2×C4×D311yescharacteristic
484C24C2×C4×D311yescharacteristic
485#41—122no—
486#41—122no—
487C2×Q8—32no—
488C2×Q8—32no—
489C2×D4—24no—
490C2×D4—34no—
491C2×D4—34no—
492C2×D4—34no—
493C2×D4—34no—
494C2×D4—32no—
495C2×D4—32no—
496C2×D4—68no—
497C2×D4C2×C4×D314yes—
498C22×C4—32no—
499C22×C4—32no—
500C22×C4—32no—
501C22×C4—34no—
502C22×C4—34no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—122no—
508C22×C4—122no—
509C22×C4C2×C4×D311yescharacteristic
510C22×C4C2×C4×D311yescharacteristic
511C22×C4C2×C4×D312yes—
512C22×C4C2×C4×D311yescharacteristic
513C22×C4C2×C4×D311yescharacteristic
514C22×C4C2×C4×D312yes—
515C22×C4C23×D311yescharacteristic
516C22×C4C23×D312yes—
517C22×C4C23×D312yes—
518M16—68no—
519M16—124no—
520M16—122no—
521M16—122no—
522C2×C8—22no—
523C2×C8—24no—
524C2×C8—24no—
525C2×C8—34no—
526C2×C8—34no—
527C2×C8—42no—
528C2×C8—42no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—124no—
533C2×C8—124no—
534C2×C8—122no—
535C2×C8—122no—
536C2×C8C23×D312yes—
537C2×C8C23×D312yes—
538C2×C8C23×D311yescharacteristic
539C2×C8C23×D312yes—
540C2×C8C23×D311yescharacteristic
541C4⋊C4—34no—
542C4⋊C4—34no—
543C4⋊C4—34no—
544C4⋊C4—32no—
545C4⋊C4—34no—
546C4⋊C4—32no—
547C4⋊C4—34no—
548C4⋊C4—32no—
549C4⋊C4—34no—
550C4⋊C4—32no—
551C4⋊C4C2×C4×D314yes—
552C22⋊C4—34no—
553C22⋊C4—34no—
554C22⋊C4—34no—
555C22⋊C4—34no—
556C22⋊C4—34no—
557C22⋊C4—34no—
558C22⋊C4—34no—
559C22⋊C4—34no—
560C22⋊C4—34no—
561C22⋊C4—34no—
562C22⋊C4C2×C4×D314yes—
563C22⋊C4C2×C4×D314yes—
564C42—34no—
565C42—34no—
566C42C2×C4×D312yes—
567C42C23×D312yes—
568C22×C3—22no—
569C22×C3—21no—
570C22×C3—22no—
571C22×C3—21no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3C2×#13114yes—
578C22×C3C2×#13112yes—
579C22×C3C24×C411yescharacteristic
580C2×D3—24no—
581C2×D3—24no—
582C2×D3—24no—
583C2×D3—84no—
584C3×C4—22no—
585C3×C4—22no—
586C3×C4—21no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4C2×H(5,𝔽2)11yescharacteristic
590C3×C4#58511yescharacteristic
591Dic3—24no—
592Dic3—24no—
593Dic3—24no—
594C23—22no—
595C23—34no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—64no—
601C23—122no—
602C23—122no—
603C23#90114yescomplemented
604C23C22×C4×D312yes—
605C23C22×C4×D311yescharacteristic
606C23C22×C4×D312yes—
607Q8—122no—
608Q8—122no—
609D4—28no—
610D4—68no—
611D4—68no—
612D4—122no—
613D4—122no—
614D4—124no—
615D4—124no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—34no—
624C2×C4—34no—
625C2×C4—34no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—64no—
632C2×C4—64no—
633C2×C4—64no—
634C2×C4—124no—
635C2×C4—122no—
636C2×C4—122no—
637C2×C4C22×C4×D312yes—
638C2×C4C22×C4×D311yescharacteristic
639C2×C4C22×C4×D312yes—
640C2×C4C22×C4×D312yes—
641C2×C4C22×C4×D312yes—
642C2×C4C24×D311yescharacteristic
643C8—21no—
644C8—22no—
645C8—22no—
646C8—22no—
647C8—64no—
648C8—64no—
649C8#100412yes—
650C2×C3—24no—
651C2×C3—22no—
652C2×C3—42no—
653C2×C3C4×H(5,𝔽2)11yescharacteristic
654C2×C3C22×#13111yescharacteristic
655C2×C3#357311yescharacteristic
656D3—44no—
657C22—21no—
658C22—22no—
659C22—21no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—44no—
665C22—44no—
666C22—64no—
667C22—64no—
668C22—64no—
669C22—244no—
670C22C2×#90112yes—
671C22C2×#90114yes—
672C22C23×C4×D311yescharacteristic
673C4—22no—
674C4—22no—
675C4—21no—
676C4—22no—
677C4—22no—
678C4—64no—
679C4—64no—
680C4—64no—
681C4C2×#100411yescharacteristic
682C4#596411yescharacteristic
683C3#6031011yescharacteristic, complemented, Sylow
684C2—22no—
685C2—24no—
686C2—42no—
687C2—124no—
688C2C4×#100411yescharacteristic
689C2C22×#90111yescharacteristic
690C2#8716011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC2×C3×C8×D4C2
prime radical#85776C2
cosocleC2×C3×C4C25
hypercenterC2×C8×D4D3
hypocenterC3#60310
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C8×D4C2semidirect
3. #83734C2semidirect
4. C2×#5111C2semidirect
5. #82302C2semidirect
6. #79429C2semidirect
7. #79423C2semidirect
8. #79409C2semidirect
9. #79402C2semidirect
10. #79016C2semidirect
11. #78604C2semidirect
12. #78601C2semidirect
13. #78448C2semidirect
16. C23×C3×C8C22semidirect
21. C2×#901C22semidirect
22. C22×ΓL(1,𝔽25)C22semidirect
32. C3×C8×D4C22semidirect
33. C3×C8×D4C22semidirect
34. C2×C3×C4⋊C8C22semidirect
36. C2×C3×C22⋊C8C22semidirect
37. C2×C3×C4×C8C22semidirect
38. #5207C22semidirect
40. #5111C22semidirect
41. #5111C22semidirect
42. #5111C22semidirect
43. #5111C22semidirect
44. #5111C22semidirect
45. #5110C22semidirect
46. C8×#67C22semidirect
47. C8×#67C22semidirect
48. C8×#67C22semidirect
49. C2×(C2×D3)⋊C8C22semidirect
50. #5102C22semidirect
51. #5101C22semidirect
52. C2×#815C22semidirect
53. C2×Dic3⋊C8C22semidirect
54. #5011C22semidirect
55. #5011C22semidirect
56. #4926C22semidirect
57. #4840C22semidirect
58. #4839C22semidirect
59. #4836C22semidirect
60. #4828C22semidirect
61. #4729C22semidirect
62. #4728C22semidirect
63. #4727C22semidirect
64. #67⋊C8C22semidirect
65. #67⋊C8C22semidirect
66. D3×C22⋊C8C22semidirect
67. #4720C22semidirect
68. #4718C22semidirect
69. #4690C22semidirect
70. #4689C22semidirect
71. #4688C22semidirect
72. C8×D12C22semidirect
73. #4679C22semidirect
74. C8×Dic6C22semidirect
87. C2×C8×D4D3semidirect
187. C23×C8C2×D3semidirect
221. C8×D4C2×D3semidirect
222. C8×D4C2×D3semidirect
231. C2×C4⋊C8C2×D3semidirect
239. C2×C22⋊C8C2×D3semidirect
243. C2×C4×C8C2×D3semidirect
431. C23×C3#131semidirect
603. C23#901semidirect
683. C3#60310semidirect

Maximal subgroups

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

subgroupindex
#857762
C2×C3×C8×D42
#837342
C2×#51112
#823022
#794292
#794232
#794092
#794022
#790162
#786042
#786012
#784482
#603103