Finite Group Databasebeta

← #354597

Subgroups — #354597

Order 512.

1954 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#440C211yesmaximal, characteristic
2C2×#1973C211yesmaximal, characteristic
3C2×#1968C211yesmaximal, characteristic
4C2×#1776C211yesmaximal, characteristic, complemented
5C2×#1763C211yesmaximal, characteristic, complemented
6C2×#1762C211yesmaximal, characteristic
7C2×C4×#97C211yesmaximal, characteristic, complemented
8C4×#391C211yesmaximal, characteristic, complemented
9C4×#390C211yesmaximal, characteristic
10#10928C211yesmaximal, characteristic, complemented
11#10927C211yesmaximal, characteristic
12#10926C211yesmaximal, characteristic, complemented
13#10925C211yesmaximal, characteristic
14#10863C211yesmaximal, characteristic, complemented
15#10862C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#440—24no—
20C2×#440—24no—
21C2×#440C418yescomplemented
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×#97C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4—22no—
44C2×C43C2211yescharacteristic
45#1973C418yescomplemented
46#1968C418yescomplemented
47#1776—24no—
48#1763—24no—
49#1762—24no—
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C4×#97—24no—
57#1437—22no—
58#1436—22no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4×#95—22no—
64C23×Q8C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C22×SD16—22no—
68C22×SD16—22no—
69C22×SD16—22no—
70C22×SD16—22no—
71C22×SD16C2×C414yes—
72C22×SD16C2×C414yes—
73C22×SD16C2×C414yes—
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—22no—
83C2×C4×Q8C2×C414yes—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4C2×C414yes—
90C22×C4⋊C4—21no—
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4—22no—
100C22×C42—21no—
101C22×C42—21no—
102C22×C42—21no—
103C22×C42D412yes—
104C22×C42D412yes—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108#440—232no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—22no—
113C2×#107C2×C414yes—
114C2×#107C2×C414yescomplemented
115C2×#106—22no—
116C2×#106—22no—
117C2×#106C2×C414yescomplemented
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103C2×C414yes—
125C2×#103C2×C414yescomplemented
126C2×#103C2×C414yescomplemented
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102—22no—
132C2×#102—22no—
133C2×#102C2×C414yes—
134C2×#102C2×C414yes—
135C2×#102C2×C414yes—
136C2×#97—22no—
137C2×#97—22no—
138C2×#97—22no—
139C2×#97—22no—
140C2×#97—22no—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97C2×C414yes—
144C2×#97C2×C414yescomplemented
145C2×#97D414yes—
146C2×#97D414yes—
147C2×#97D414yes—
148C2×C4×C8—22no—
149C2×C4×C8—22no—
150C2×C4×C8—22no—
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153C2×C4×C8C2×C414yescomplemented
154#391—22no—
155#391—22no—
156#391C2×C414yescomplemented
157#391C2×C414yescomplemented
158#390—22no—
159#390—22no—
160#390C2×C414yes—
161#390C2×C414yes—
162C4×C4⋊C4—22no—
163C4×C4⋊C4—22no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C4×C22⋊C4—48no—
167C2×#95—22no—
168C2×#95—22no—
169C2×#95—22no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95—22no—
173C2×#95—21no—
174C2×#95—21no—
175C43—22no—
176C43—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182#340—22no—
183C25—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8C22×C412yes—
196C22×Q8C22×C412yes—
197C22×Q8C22×C412yes—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×D4C22×C412yes—
210C22×D4C22×C412yes—
211C22×D4C22×C412yes—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—24no—
220C23×C4—44no—
221C23×C4—44no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4C2×D412yes—
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D412yes—
228C23×C4C2411yescharacteristic
229C2×SD16—28no—
230C2×SD16—28no—
231C2×SD16—28no—
232C2×SD16—28no—
233C2×SD16—28no—
234C2×SD16—28no—
235C2×SD16C42116yescomplemented
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8C22×C412yes—
249C22×C8C22×C412yes—
250C22×C8C22×C412yes—
251C22×C8C22×C412yes—
252C22×C8C22×C412yes—
253C22×C8C22×C412yes—
254C22×C8C2×D412yes—
255C22×C8C2×D412yes—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8C2×D412yes—
259C22×C8C2×D412yes—
260C22×C8#4112yes—
261C22×C8#4112yes—
262C22×C8#4112yes—
263C22×C8#4112yes—
264C4×Q8—28no—
265C4×Q8—28no—
266C4×Q8—44no—
267C4×Q8—44no—
268C4×D4—28no—
269C4×D4—28no—
270C4×D4—44no—
271C4×D4—44no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C22×C412yes—
310C2×C4⋊C4C22×C412yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42—42no—
337C2×C42—44no—
338C2×C42—44no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42C22×C412yes—
342C2×C42C22×C412yes—
343C2×C42C22×C412yes—
344C2×C42C2×D412yes—
345C2×C42C2×D412yes—
346C2×C42C2×D412yes—
347C2×C42#4112yes—
348C2×C42#4112yes—
349C2×C42#4112yes—
350C2×C42#4112yes—
351#107—28no—
352#107—28no—
353#106—28no—
354#103—28no—
355#103—28no—
356#103—28no—
357#102—28no—
358#102—28no—
359#102—28no—
360#97—28no—
361#97—28no—
362#97—28no—
363#97C22⋊C4116yescomplemented
364C4×C8—28no—
365C4×C8—28no—
366#95—28no—
367#95—28no—
368#95—44no—
369#95—44no—
370#95—42no—
371#95—42no—
372#95—44no—
373#95—44no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24C22×D411yescharacteristic
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8C2×C4214yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4C2×C4214yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—416no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—48no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4—88no—
498C22×C4C4×D414yes—
499C22×C4C4×D412yes—
500C22×C4C4×D412yes—
501C22×C4C4×D414yes—
502C22×C4#12112yes—
503C22×C4#12112yes—
504C22×C4#12712yes—
505C22×C4#12712yes—
506C22×C4AGL(1,ℤ/8)14yes—
507C22×C4#13714yes—
508C22×C4C23×C411yescharacteristic
509C22×C4C23×C411yescharacteristic
510C22×C4C23×C411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D411yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522SD16—232no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8C2×C4214yes—
542C2×C8C2×C22⋊C414yes—
543C2×C8C2×C22⋊C414yes—
544C2×C8#11714yes—
545C2×C8C4×D414yes—
546C2×C8C4×D414yes—
547C2×C8C4×D414yes—
548C2×C8C4×D414yes—
549C2×C8C4×D414yes—
550C2×C8C4×D414yes—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—48no—
576C22⋊C4—416no—
577C22⋊C4—48no—
578C22⋊C4—416no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—48no—
588C42—48no—
589C42—48no—
590C42—84no—
591C42—84no—
592C42C2×C22⋊C414yes—
593C42C4×D414yes—
594C42#12114yes—
595C42#12414yes—
596C23—24no—
597C23—42no—
598C23—42no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23—44no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23C2×C4×D411yescharacteristic
620C23C2×C4×D411yescharacteristic
621C23C2×C4×D411yescharacteristic
622C23C2×#12111yescharacteristic
623C23C2×#12711yescharacteristic
624C23#53211yescharacteristic
625C23#53211yescharacteristic
626C23C2×AGL(1,ℤ/8)12yes—
627C23C2×#13712yes—
628C23#57512yes—
629C23#57512yes—
630Q8—24no—
631Q8—24no—
632Q8—42no—
633Q8—42no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638D4—24no—
639D4—24no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—816no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#39014yes—
706C2×C4#39014yes—
707C2×C4#44018yescomplemented
708C2×C4C22×C4211yescharacteristic
709C2×C4C22×C22⋊C411yescharacteristic
710C2×C4C2×#11711yescharacteristic
711C2×C4C2×C4×D411yescharacteristic
712C2×C4C2×C4×D411yescharacteristic
713C2×C4C2×C4×D411yescharacteristic
714C2×C4C2×C4×D411yescharacteristic
715C2×C4C2×C4×D411yescharacteristic
716C2×C4C2×C4×D411yescharacteristic
717C2×C4C2×C4×D411yescharacteristic
718C2×C4C4×#4111yescharacteristic
719C2×C4C4×#4111yescharacteristic
720C2×C4C4×#4111yescharacteristic
721C2×C4C4×#4111yescharacteristic
722C2×C4C4×#4111yescharacteristic
723C2×C4C4×#4111yescharacteristic
724C2×C4C2×#12111yescharacteristic
725C2×C4#52511yescharacteristic
726C2×C4#52511yescharacteristic
727C2×C4C2×#12411yescharacteristic
728C2×C4#52911yescharacteristic
729C2×C4#52911yescharacteristic
730C2×C4#52911yescharacteristic
731C2×C4#52911yescharacteristic
732C2×C4#53211yescharacteristic
733C2×C4#53211yescharacteristic
734C2×C4#53211yescharacteristic
735C2×C4#53211yescharacteristic
736C8—24no—
737C8—24no—
738C8—24no—
739C8C4×C22⋊C418yescomplemented
740C22—48no—
741C22—44no—
742C22—84no—
743C22—84no—
744C22—84no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22C42×D411yescharacteristic
752C22C2×#39011yescharacteristic
753C22#229311yescharacteristic
754C22C4×#12111yescharacteristic
755C22C4×#12111yescharacteristic
756C22C4×#12711yescharacteristic
757C22C4×#12711yescharacteristic
758C22C2×#44012yes—
759C22#294312yes—
760C22C4×AGL(1,ℤ/8)12yes—
761C22C4×AGL(1,ℤ/8)12yes—
762C22C4×#13712yes—
763C22C4×#13712yes—
764C22#305512yes—
765C22#305612yes—
766C22#315111yescharacteristic
767C22#315211yescharacteristic
768C22#315311yescharacteristic
769C22#315311yescharacteristic
770C22#318012yes—
771C22#318112yes—
772C22#318212yes—
773C22#318312yes—
774C4—28no—
775C4—24no—
776C4—24no—
777C4—44no—
778C4—44no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4C2×C4×C22⋊C411yescharacteristic
786C4C42×D411yescharacteristic
787C4#229311yescharacteristic
788C4#229711yescharacteristic
789C4C4×#12111yescharacteristic
790C4C4×#12111yescharacteristic
791C4C4×#12411yescharacteristic
792C4C4×#12411yescharacteristic
793C2—84no—
794C2C4×#39011yescharacteristic
795C2C4×#44012yes—
796C2#2123611yescharacteristic
797C2#2123711yescharacteristic
798C2#2128812yes—
799C2#2152812yes—
800C2#2154012yes—
801C2#2169211yescharacteristic
802C2#2169311yescharacteristic
803C2#2170111yescharacteristic
804C2#2170211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1776C2semidirect
5. C2×#1763C2semidirect
7. C2×C4×#97C2semidirect
8. C4×#391C2semidirect
10. #10928C2semidirect
12. #10926C2semidirect
14. #10863C2semidirect
15. #10862C2semidirect
21. C2×#440C4semidirect
45. #1973C4semidirect
46. #1968C4semidirect
114. C2×#107C2×C4semidirect
117. C2×#106C2×C4semidirect
125. C2×#103C2×C4semidirect
126. C2×#103C2×C4semidirect
144. C2×#97C2×C4semidirect
153. C2×C4×C8C2×C4semidirect
156. #391C2×C4semidirect
157. #391C2×C4semidirect
235. C2×SD16C42semidirect
363. #97C22⋊C4semidirect
707. C2×C4#440semidirect
739. C8C4×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4402
C2×#19732
C2×#19682
C2×#17762
C2×#17632
C2×#17622
C2×C4×#972
C4×#3912
C4×#3902
#109282
#109272
#109262
#109252
#108632
#108622