Finite Group Databasebeta

← #365610

Subgroups — #365610

Order 512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 805 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×#1944C211yesmaximal, characteristic, complemented
5C2×#1863C211yesmaximal, characteristic, complemented
6C2×#1862C211yesmaximal, characteristic
7C2×#1845C211yesmaximal, characteristic, complemented
8#13977C211yesmaximal, characteristic
9#13976C211yesmaximal, characteristic, complemented
10#11124C211yesmaximal, characteristic, complemented
11#11123C211yesmaximal, characteristic
12#11050C211yesmaximal, characteristic, complemented
13#11049C211yesmaximal, characteristic
14#10863C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#440—24no—
20C2×#440—24no—
21C2×#440—24no—
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×#97C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#385—22no—
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45#1973—24no—
46#1968C418yescomplemented
47#1944—24no—
48#1863—24no—
49#1862—24no—
50#1845—24no—
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1444—22no—
59#1439—22no—
60#1436—22no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4×#95C2211yescharacteristic
64C23×Q8C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C22×SD16—22no—
68C22×SD16—22no—
69C22×SD16—22no—
70C22×SD16—22no—
71C22×SD16C2×C414yes—
72C22×SD16D414yes—
73C22×SD16Q814yes—
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—41no—
83C2×C4×Q8—41no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—41no—
89C2×C4×D4—41no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C22⋊C4—22no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—22no—
104C22×C42—21no—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108#440—232no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—22no—
117C2×#107—22no—
118C2×#107—41no—
119C2×#107—41no—
120C2×#107D414yes—
121C2×#106—22no—
122C2×#106—22no—
123C2×#106C2×C414yescomplemented
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—41no—
132C2×#103C2×C414yescomplemented
133C2×#102—22no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#102—22no—
138C2×#102—22no—
139C2×#102—22no—
140C2×#102—41no—
141C2×#102C2×C414yes—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97D414yes—
148C2×C4×C8—22no—
149C2×C4×C8—22no—
150C2×C4×C8C2×C414yescomplemented
151#391—22no—
152#391—22no—
153#391—41no—
154#391C2×C414yescomplemented
155#390—22no—
156#390—22no—
157#390—41no—
158#390C2×C414yes—
159#389—22no—
160#389—22no—
161#389—22no—
162#389—22no—
163#385—48no—
164#384—22no—
165#384—22no—
166#384—41no—
167#384—41no—
168C2×#95—22no—
169C2×#95—22no—
170C2×#95—21no—
171C2×#95—22no—
172C2×#95—21no—
173C2×#95—22no—
174C2×#95D412yes—
175C2×#95D412yes—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#336—22no—
181#336—22no—
182#336D414yes—
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×Q8C2×D412yes—
197C22×Q8C2×Q812yes—
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×D4C2×D412yes—
211C22×D4C2×Q812yes—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—44no—
222C23×C4—42no—
223C23×C4—82no—
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×SD16C4⋊C4116yescomplemented
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×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
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×C8C2×Q812yes—
261C22×C8#4112yes—
262C22×C8#4112yes—
263C22×C8#4112yes—
264C4×Q8—28no—
265C4×Q8—44no—
266C4×Q8—44no—
267C4×Q8—44no—
268C4×D4—28no—
269C4×D4—44no—
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—21no—
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—21no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—82no—
315C2×C4⋊C4—82no—
316C2×C4⋊C4—82no—
317C2×C4⋊C4C22×C412yes—
318C2×C4⋊C4C22×C412yes—
319C2×C4⋊C4C2×D412yes—
320C2×C4⋊C4C2×D412yes—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—82no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—42no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42C22×C412yes—
348C2×C42C2×D412yes—
349C2×C42C2×D412yes—
350C2×C42#4112yes—
351#107—28no—
352#107—44no—
353#107—44no—
354#107—44no—
355#106—28no—
356#103—28no—
357#103—28no—
358#103—44no—
359#102—28no—
360#102—28no—
361#102—44no—
362#97—28no—
363#97—44no—
364C4×C8—28no—
365#95—28no—
366#95—24no—
367#95—24no—
368#95—44no—
369#95—44no—
370#95—42no—
371#95—42no—
372#95—82no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—42no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24C22×D411yescharacteristic
385C2×Q8—22no—
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—41no—
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×Q8C2×C4⋊C414yes—
413C2×D4—22no—
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—41no—
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×D4C2×C4⋊C414yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
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—22no—
466C22×C4—22no—
467C22×C4—48no—
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—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—84no—
499C22×C4—84no—
500C22×C4—88no—
501C22×C4—88no—
502C22×C4C4×D414yes—
503C22×C4#12712yes—
504C22×C4#12712yes—
505C22×C4AGL(1,ℤ/8)14yes—
506C22×C4#13714yes—
507C22×C4C23×C411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×Q811yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4H(5,𝔽2)11yescharacteristic
518C22×C4H(5,𝔽2)11yescharacteristic
519C22×C42−1+411yescharacteristic
520C22×C42−1+411yescharacteristic
521SD16—232no—
522C2×C8—22no—
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—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8C2×C4⋊C414yes—
543C2×C8C4×D414yes—
544C2×C8C4×D414yes—
545C2×C8C4×D414yes—
546C2×C8#12014yes—
547C2×C8C22⋊Q814yes—
548C2×C8C22⋊Q814yes—
549C2×C8#12314yes—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—48no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
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—88no—
576C4⋊C4—88no—
577C4⋊C4—84no—
578C4⋊C4—84no—
579C22⋊C4—48no—
580C22⋊C4—416no—
581C22⋊C4—88no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—48no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C23—24no—
596C23—42no—
597C23—42no—
598C23—44no—
599C23—44no—
600C23—42no—
601C23—44no—
602C23—42no—
603C23—44no—
604C23—42no—
605C23—44no—
606C23—44no—
607C23—42no—
608C23—82no—
609C23—82no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23C2×C4×D411yescharacteristic
619C23C2×#12711yescharacteristic
620C23#53211yescharacteristic
621C23D4211yescharacteristic
622C23D4211yescharacteristic
623C23#54711yescharacteristic
624C23D4×Q811yescharacteristic
625C23C2×AGL(1,ℤ/8)12yes—
626C23C2×#13712yes—
627C23#57612yes—
628C23#57812yes—
629Q8—24no—
630Q8—24no—
631Q8—42no—
632Q8—42no—
633Q8—42no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637D4—24no—
638D4—24no—
639D4—42no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—42no—
644D4—42no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
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—44no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—816no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—82no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#44018yescomplemented
707C2×C4C22×C4⋊C411yescharacteristic
708C2×C4C2×C4×D411yescharacteristic
709C2×C4C2×C4×D411yescharacteristic
710C2×C4C2×C4×D411yescharacteristic
711C2×C4#52011yescharacteristic
712C2×C4#52011yescharacteristic
713C2×C4C2×#12011yescharacteristic
714C2×C4C2×C22⋊Q811yescharacteristic
715C2×C4C2×C22⋊Q811yescharacteristic
716C2×C4C2×#12311yescharacteristic
717C2×C4#53211yescharacteristic
718C2×C4#53211yescharacteristic
719C2×C4#53511yescharacteristic
720C2×C4#53611yescharacteristic
721C2×C4#54211yescharacteristic
722C2×C4#54211yescharacteristic
723C2×C4D4211yescharacteristic
724C2×C4D4211yescharacteristic
725C2×C4#54711yescharacteristic
726C2×C4#54711yescharacteristic
727C2×C4#54711yescharacteristic
728C2×C4#54811yescharacteristic
729C2×C4#54811yescharacteristic
730C2×C4D4×Q811yescharacteristic
731C2×C4#55311yescharacteristic
732C2×C4#55311yescharacteristic
733C2×C4#55411yescharacteristic
734C2×C4#55411yescharacteristic
735C8—24no—
736C8—42no—
737C8—42no—
738C8#38518yescomplemented
739C22—48no—
740C22—44no—
741C22—84no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—84no—
749C22—84no—
750C22C4×#12711yescharacteristic
751C22D4×C4⋊C411yescharacteristic
752C22#236111yescharacteristic
753C22#242211yescharacteristic
754C22#243311yescharacteristic
755C22#245211yescharacteristic
756C22#254211yescharacteristic
757C22C2×#44012yes—
758C22#295112yes—
759C22#315111yescharacteristic
760C22#315211yescharacteristic
761C22#315511yescharacteristic
762C22#315611yescharacteristic
763C22#317512yes—
764C22#318212yes—
765C22#326412yes—
766C22#327012yes—
767C22#327412yes—
768C22#327612yes—
769C22#334312yes—
770C22#334612yes—
771C22#338512yes—
772C22#338612yes—
773C4—28no—
774C4—44no—
775C4—42no—
776C4—42no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4—161no—
783C4—161no—
784C4C2×#38511yescharacteristic
785C4#232611yescharacteristic
786C4D4×C4⋊C411yescharacteristic
787C4#236111yescharacteristic
788C4#242211yescharacteristic
789C4#243211yescharacteristic
790C4#245211yescharacteristic
791C4#256611yescharacteristic
792C2—84no—
793C2#1397711yescharacteristic
794C2#2169211yescharacteristic
795C2#2169611yescharacteristic
796C2#2267112yes—
797C2#2303212yes—
798C2#2504512yes—
799C2#2579411yescharacteristic
800C2#2579511yescharacteristic
801C2#2649512yes—
802C2#2854311yescharacteristic
803C2#2854511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1944C2semidirect
5. C2×#1863C2semidirect
7. C2×#1845C2semidirect
9. #13976C2semidirect
10. #11124C2semidirect
12. #11050C2semidirect
14. #10863C2semidirect
15. #10696C2semidirect
46. #1968C4semidirect
123. C2×#106C2×C4semidirect
132. C2×#103C2×C4semidirect
150. C2×C4×C8C2×C4semidirect
154. #391C2×C4semidirect
235. C2×SD16C4⋊C4semidirect
706. C2×C4#440semidirect
738. C8#385semidirect

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×#19442
C2×#18632
C2×#18622
C2×#18452
#139772
#139762
#111242
#111232
#110502
#110492
#108632
#106962