Finite Group Databasebeta

← #116801

Subgroups — #116801

Order 512.

1112 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1948C211yesmaximal, characteristic, complemented
2C2×#1802C211yesmaximal, characteristic
3C22×D4⋊C8C211yesmaximal, characteristic
4#13906C211yesmaximal, characteristic
5#10841C211yesmaximal, characteristic, complemented
6C2×#1296C211yesmaximal, characteristic, complemented
7C2×#1279C211yesmaximal, characteristic, complemented
8C22×C4×D4C2211yescharacteristic
9C22×#106—21no—
10C22×C4⋊C8C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×#102—21no—
13C22×C4×C8C2211yescharacteristic
14C2×#390—21no—
15C2×#384C2211yescharacteristic
16C2×#384C2211yescharacteristic
17C2×#380—21no—
18C2×#380—21no—
19C2×C4×C4⋊C4C2211yescharacteristic
20#1948—22no—
21#1948—22no—
22#1802—22no—
23#1802—22no—
24C2×#340—21no—
25C2×#340—21no—
26C2×#340—22no—
27C2×D4⋊C8—22no—
28C2×D4⋊C8—22no—
29C2×D4⋊C8C414yescomplemented
30#1439—22no—
31C4⋊#95—21no—
32#1296—22no—
33#1279—22no—
34C23×D4D411yescharacteristic
35C24×C4—21no—
36C23×C8—21no—
37C23×C8—21no—
38C23×C8—21no—
39C2×C4×D4—21no—
40C2×C4×D4—21no—
41C2×C4×D4—21no—
42C2×C4×D4—21no—
43C2×C4×D4—21no—
44C2×C4×D4—21no—
45C2×C4×D4—21no—
46C2×C4×D4—21no—
47C2×C4×D4—21no—
48C2×C4×D4—21no—
49C2×C4×D4C2×C412yes—
50C2×C4×D4Q812yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4D411yescharacteristic
57C22×C4⋊C4D411yescharacteristic
58C22×C4⋊C4D411yescharacteristic
59C22×C4⋊C4D412yes—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—22no—
63C22×C42—21no—
64C22×C42C2311yescharacteristic
65C2×#106—24no—
66C2×#106—42no—
67C2×#106—42no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8C2×C412yes—
77C2×C4⋊C8D412yes—
78C2×C4⋊C8D412yes—
79C2×C4⋊C8D412yes—
80C2×#102—24no—
81C2×#102—42no—
82C2×#102—42no—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8—21no—
87C2×C4×C8—21no—
88C2×C4×C8C2×C412yes—
89#390—42no—
90#390—42no—
91#384—21no—
92#384—21no—
93#384—21no—
94#384—21no—
95#384—21no—
96#384—21no—
97#384—21no—
98#384D412yes—
99#380—42no—
100#380—42no—
101#380—42no—
102#380—42no—
103C4×C4⋊C4—21no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4—21no—
106C4×C4⋊C4—21no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—21no—
110#340—24no—
111#340—24no—
112#340—44no—
113D4⋊C8—28no—
114C25—21no—
115C22×D4—21no—
116C22×D4—21no—
117C22×D4—21no—
118C22×D4—21no—
119C22×D4—21no—
120C22×D4—21no—
121C22×D4—21no—
122C22×D4—21no—
123C22×D4—21no—
124C22×D4—21no—
125C22×D4—21no—
126C22×D4C4⋊C412yes—
127C22×D4SD1612yes—
128C22×D4SD1612yes—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—41no—
136C23×C4—41no—
137C23×C4—41no—
138C23×C4—41no—
139C23×C4—41no—
140C23×C4—41no—
141C23×C4—41no—
142C23×C4—41no—
143C23×C4—41no—
144C23×C4—41no—
145C23×C4—41no—
146C23×C4—41no—
147C23×C4—41no—
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—41no—
159C22×C8—41no—
160C22×C8—41no—
161C22×C8—41no—
162C22×C8—41no—
163C22×C8—41no—
164C22×C8—41no—
165C22×C8—41no—
166C22×C8—41no—
167C22×C8—41no—
168C22×C8—41no—
169C22×C8—41no—
170C22×C8—41no—
171C22×C8—41no—
172C4×D4—22no—
173C4×D4—22no—
174C4×D4—22no—
175C4×D4—22no—
176C4×D4—22no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—22no—
180C4×D4—41no—
181C4×D4—41no—
182C4×D4—41no—
183C4×D4—41no—
184C4×D4—41no—
185C4×D4—41no—
186C4×D4—41no—
187C4×D4—41no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—42no—
209C2×C4⋊C4—42no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—41no—
235C2×C4⋊C4C4⋊C412yes—
236C2×C4⋊C4D812yes—
237C2×C4⋊C4SD1612yes—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—41no—
242C2×C22⋊C4—41no—
243C2×C22⋊C4—41no—
244C2×C22⋊C4—44no—
245C2×C22⋊C4—44no—
246C2×C22⋊C4—44no—
247C2×C22⋊C4—44no—
248C2×C22⋊C4—82no—
249C2×C22⋊C4—82no—
250C2×C42—41no—
251C2×C42—41no—
252C2×C42—41no—
253C2×C42—41no—
254C2×C42—41no—
255C2×C42—41no—
256C2×C42C22×C411yescharacteristic
257C2×C42C2×D411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42C2×D411yescharacteristic
260C2×C42C2×D411yescharacteristic
261C2×C42C2×Q811yescharacteristic
262C2×C42#4111yescharacteristic
263C2×C42#4111yescharacteristic
264C2×C42#4111yescharacteristic
265C2×C42#4111yescharacteristic
266C2×C42#4111yescharacteristic
267C2×C42#4111yescharacteristic
268#106—48no—
269C4⋊C8—22no—
270C4⋊C8—22no—
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—22no—
274C4⋊C8—41no—
275C4⋊C8—41no—
276C4⋊C8C22⋊C414yescomplemented
277#102—48no—
278C4×C8—22no—
279C4×C8—22no—
280C4×C8—41no—
281C4×C8—41no—
282#95—44no—
283#95—44no—
284#95—41no—
285#95—41no—
286C24—22no—
287C24—22no—
288C24—22no—
289C24—41no—
290C24—41no—
291C24—41no—
292C24—41no—
293C24—41no—
294C24—41no—
295C24—41no—
296C24—41no—
297C24—41no—
298C24—41no—
299C24—41no—
300C24—41no—
301C24#12011yescharacteristic
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4#10614yescomplemented
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—81no—
376C22×C4—81no—
377C22×C4—81no—
378C22×C4—81no—
379C22×C4—81no—
380C22×C4—81no—
381C22×C4—81no—
382C22×C4—81no—
383C22×C4—81no—
384C22×C4—81no—
385C22×C4—81no—
386C22×C4—81no—
387C22×C4—81no—
388C22×C4—81no—
389C22×C4—81no—
390C22×C4—81no—
391C22×C4—81no—
392C22×C4—81no—
393C22×C4—81no—
394C22×C4—81no—
395C22×C4—81no—
396C22×C4—81no—
397C22×C4C2×C4⋊C411yescharacteristic
398C22×C4C4×D411yescharacteristic
399C22×C4C4×D411yescharacteristic
400C22×C4#12011yescharacteristic
401C22×C4#12011yescharacteristic
402C22×C4#12111yescharacteristic
403C22×C4#12111yescharacteristic
404C22×C4#12111yescharacteristic
405C22×C4#12111yescharacteristic
406C22×C4#12111yescharacteristic
407C22×C4#12111yescharacteristic
408C22×C4C22⋊Q811yescharacteristic
409C22×C4C22⋊Q811yescharacteristic
410C22×C4#12311yescharacteristic
411C22×C4#12311yescharacteristic
412C22×C4#12311yescharacteristic
413C22×C4#12411yescharacteristic
414C22×C4#12711yescharacteristic
415C22×C4C2×D811yescharacteristic
416C22×C4C2×SD1611yescharacteristic
417C22×C4C2×SD1611yescharacteristic
418C22×C4C2×SD1611yescharacteristic
419C22×C4#13511yescharacteristic
420C22×C4#13511yescharacteristic
421C22×C4#13511yescharacteristic
422C22×C4#13511yescharacteristic
423C22×C4AGL(1,ℤ/8)11yescharacteristic
424C22×C4AGL(1,ℤ/8)11yescharacteristic
425C22×C4AGL(1,ℤ/8)11yescharacteristic
426C22×C4AGL(1,ℤ/8)11yescharacteristic
427C22×C4AGL(1,ℤ/8)11yescharacteristic
428C22×C4#13711yescharacteristic
429C22×C4#13711yescharacteristic
430C22×C4#13711yescharacteristic
431C2×C8—24no—
432C2×C8—24no—
433C2×C8—42no—
434C2×C8—42no—
435C2×C8—42no—
436C2×C8—42no—
437C2×C8—42no—
438C2×C8—42no—
439C2×C8—42no—
440C2×C8—42no—
441C2×C8—42no—
442C2×C8—42no—
443C2×C8—42no—
444C2×C8—42no—
445C2×C8—42no—
446C2×C8—42no—
447C2×C8—42no—
448C2×C8—81no—
449C2×C8—81no—
450C2×C8—81no—
451C2×C8—81no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—44no—
459C4⋊C4—44no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—82no—
471C4⋊C4—82no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—88no—
489C22⋊C4—88no—
490C42—81no—
491C42—81no—
492C42—81no—
493C42—81no—
494C42C2×C22⋊C411yescharacteristic
495C42#11711yescharacteristic
496C42C4×D411yescharacteristic
497C42C4×D411yescharacteristic
498C42#12111yescharacteristic
499C42#12111yescharacteristic
500C42C22⋊Q811yescharacteristic
501C42C22⋊Q811yescharacteristic
502C42C22⋊Q811yescharacteristic
503C42C22⋊Q811yescharacteristic
504C42#12311yescharacteristic
505C42#12311yescharacteristic
506C42#12411yescharacteristic
507C42#12411yescharacteristic
508C42#12611yescharacteristic
509C42#12611yescharacteristic
510C23—24no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—81no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23—81no—
541C23—81no—
542C23—81no—
543C23—81no—
544C23—81no—
545C23#38511yescharacteristic
546C23#39211yescharacteristic
547C23#39411yescharacteristic
548C23#44711yescharacteristic
549C23#44811yescharacteristic
550C23#44911yescharacteristic
551C23#44911yescharacteristic
552C23#45011yescharacteristic
553C23#45011yescharacteristic
554C23#45211yescharacteristic
555C23#45211yescharacteristic
556C23#45311yescharacteristic
557C23#45411yescharacteristic
558C23#45511yescharacteristic
559C23#45611yescharacteristic
560D4—24no—
561D4—24no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4—81no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—82no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4—82no—
614C2×C4—82no—
615C2×C4—82no—
616C2×C4—82no—
617C2×C4—82no—
618C2×C4—82no—
619C2×C4—161no—
620C2×C4—161no—
621C2×C4—161no—
622C2×C4—161no—
623C2×C4#38011yescharacteristic
624C2×C4#38511yescharacteristic
625C2×C4#38611yescharacteristic
626C2×C4#38811yescharacteristic
627C2×C4#38811yescharacteristic
628C2×C4#39011yescharacteristic
629C2×C4#39311yescharacteristic
630C2×C4#39411yescharacteristic
631C2×C4#39611yescharacteristic
632C2×C4#39611yescharacteristic
633C2×C4#39711yescharacteristic
634C2×C4#39911yescharacteristic
635C2×C4C2×#10611yescharacteristic
636C2×C4#42711yescharacteristic
637C2×C4#42811yescharacteristic
638C2×C4#42811yescharacteristic
639C2×C4C4×D811yescharacteristic
640C2×C4C4×SD1611yescharacteristic
641C2×C4#44011yescharacteristic
642C2×C4#44211yescharacteristic
643C2×C4#44711yescharacteristic
644C2×C4#44811yescharacteristic
645C2×C4#44811yescharacteristic
646C2×C4#44911yescharacteristic
647C2×C4#44911yescharacteristic
648C2×C4#44911yescharacteristic
649C2×C4#45011yescharacteristic
650C2×C4#45211yescharacteristic
651C2×C4#45911yescharacteristic
652C2×C4#46011yescharacteristic
653C2×C4#46311yescharacteristic
654C2×C4#46411yescharacteristic
655C2×C4#46511yescharacteristic
656C2×C4#46511yescharacteristic
657C2×C4#46511yescharacteristic
658C2×C4#46511yescharacteristic
659C2×C4#46511yescharacteristic
660C2×C4#46611yescharacteristic
661C2×C4#46811yescharacteristic
662C2×C4#46811yescharacteristic
663C2×C4#46811yescharacteristic
664C2×C4#46911yescharacteristic
665C2×C4#46911yescharacteristic
666C2×C4#47011yescharacteristic
667C2×C4#47411yescharacteristic
668C2×C4#47611yescharacteristic
669C2×C4#47811yescharacteristic
670C2×C4#47811yescharacteristic
671C2×C4#48111yescharacteristic
672C2×C4#48111yescharacteristic
673C2×C4#48211yescharacteristic
674C2×C4#48211yescharacteristic
675C2×C4#48311yescharacteristic
676C2×C4#48311yescharacteristic
677C2×C4#48511yescharacteristic
678C2×C4#48511yescharacteristic
679C2×C4#48611yescharacteristic
680C2×C4#48811yescharacteristic
681C2×C4#48911yescharacteristic
682C2×C4#49011yescharacteristic
683C8—44no—
684C8—44no—
685C8—82no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—82no—
690C22—82no—
691C22—82no—
692C22—82no—
693C22—82no—
694C22—82no—
695C22—82no—
696C22—82no—
697C22—82no—
698C22—82no—
699C22—82no—
700C22—82no—
701C22#143911yescharacteristic
702C22#162111yescharacteristic
703C22#162211yescharacteristic
704C22#162711yescharacteristic
705C22#162811yescharacteristic
706C22#162911yescharacteristic
707C22#163411yescharacteristic
708C22#163511yescharacteristic
709C22#163511yescharacteristic
710C22#163911yescharacteristic
711C22#164211yescharacteristic
712C22#164311yescharacteristic
713C22#164611yescharacteristic
714C22#164711yescharacteristic
715C22#165011yescharacteristic
716C22#165111yescharacteristic
717C22#165411yescharacteristic
718C22#185311yescharacteristic
719C22#185411yescharacteristic
720C22#185911yescharacteristic
721C22#186011yescharacteristic
722C22#186211yescharacteristic
723C22#186411yescharacteristic
724C22#199911yescharacteristic
725C22#200011yescharacteristic
726C22#200011yescharacteristic
727C22#200011yescharacteristic
728C22#200611yescharacteristic
729C22#200711yescharacteristic
730C22#203411yescharacteristic
731C22#203511yescharacteristic
732C22#203711yescharacteristic
733C22#203811yescharacteristic
734C22#204111yescharacteristic
735C22#204211yescharacteristic
736C4—21no—
737C4—21no—
738C4—21no—
739C4—21no—
740C4—82no—
741C4—82no—
742C4—82no—
743C4—162no—
744C4—162no—
745C4#180711yescharacteristic
746C4#180911yescharacteristic
747C4#185311yescharacteristic
748C4#185411yescharacteristic
749C4#187911yescharacteristic
750C4#188011yescharacteristic
751C4#193411yescharacteristic
752C4#193611yescharacteristic
753C4#202311yescharacteristic
754C4#202511yescharacteristic
755C4#203411yescharacteristic
756C4#203511yescharacteristic
757C4#206511yescharacteristic
758C4#206711yescharacteristic
759C4#207711yescharacteristic
760C4#207711yescharacteristic
761C2—84no—
762C2#888511yescharacteristic
763C2#888611yescharacteristic
764C2#889311yescharacteristic
765C2#889411yescharacteristic
766C2#1022911yescharacteristic
767C2#1023111yescharacteristic
768C2#1023211yescharacteristic
769C2#1023511yescharacteristic
770C2#1040911yescharacteristic
771C2#1041211yescharacteristic
772C2#1041711yescharacteristic
773C2#1042011yescharacteristic
774C2#1106611yescharacteristic
775C2#1109511yescharacteristic
776C2#1111311yescharacteristic
subgroupG/H
center, socleC24#120
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC23×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1948C2semidirect
5. #10841C2semidirect
6. C2×#1296C2semidirect
7. C2×#1279C2semidirect
29. C2×D4⋊C8C4semidirect
276. C4⋊C8C22⋊C4semidirect
329. C2×D4#106semidirect

Maximal subgroups

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

subgroupindex
C2×#19482
C2×#18022
C22×D4⋊C82
#139062
#108412
C2×#12962
C2×#12792