Finite Group Databasebeta

← C2×#11110 #357698

Subgroups — C2×#11110 #357698

Order 512.

2658 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#430C211yesmaximal, characteristic, complemented
2C2×#2896C212yesmaximal
3C2×#2879C211yesmaximal, characteristic
4C22×#344C212yesmaximal, complemented
5C22×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6#11110C218yesmaximal, direct product factor
7C23×#41C2211yescharacteristic
8C23×M16C2212yes—
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2212yes—
12C2×#430—24no—
13C2×#430—24no—
14C2×#430—22no—
15C2×#430C2214yescomplemented
16C22×#108—22no—
17#2896—24no—
18#2896—24no—
19#2896—24no—
20#2896C2218yes—
21C2×#417—24no—
22C2×#419—22no—
23C2×#418—22no—
24C2×#416—24no—
25#2879—22no—
26#2879—22no—
27#2879C414yescomplemented
28#2879C2214yes—
29C2×#408—22no—
30C2×#408C414yescomplemented
31C2×#407—22no—
32C2×#344—24no—
33C2×#344—24no—
34C2×#344C2218yescomplemented
35C2×H(3,ℤ/4)—22no—
36C2×H(3,ℤ/4)—22no—
37C2×H(3,ℤ/4)C2214yescomplemented
38C22×#41—21no—
39C22×#41—21no—
40C22×#41—21no—
41C22×#41—21no—
42C22×#41—21no—
43C22×#41—21no—
44C22×#41—22no—
45C22×#41—22no—
46C22×#41—22no—
47C22×#41—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41C2×C412yes—
53C22×#41C2×C412yes—
54C22×#41D412yes—
55C22×#41Q812yes—
56C22×#41Q812yes—
57C22×#41C2312yes—
58C23×Q8D411yescharacteristic
59C23×D4—21no—
60C23×D4D411yescharacteristic
61C24×C4—21no—
62C24×C4C2311yescharacteristic
63C22×M16—22no—
64C22×M16—22no—
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—21no—
68C22×M16—21no—
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—22no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16C2×C412yes—
87C22×M16C2×C412yes—
88C22×M16C2×C412yes—
89C22×M16D414yes—
90C22×M16D414yes—
91C22×M16D412yes—
92C22×M16D412yes—
93C22×M16D412yes—
94C22×M16C2314yes—
95C22×M16C2312yes—
96C22×M16C2312yes—
97C23×C8—22no—
98C23×C8C2×C412yes—
99C23×C8D412yes—
100C2×#117—22no—
101C2×#117—22no—
102C2×#117—22no—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117—22no—
107C2×#117—22no—
108C2×#117—22no—
109C2×#117D414yes—
110C2×#117D414yes—
111C2×#117C2314yes—
112C22×C4⋊C4—22no—
113C22×C22⋊C4—22no—
114C22×C42—22no—
115#430—216no—
116#430—216no—
117C2×#108—28no—
118C2×#108—28no—
119C2×#108—28no—
120#419—28no—
121#419—28no—
122#418—28no—
123#418—28no—
124#417—216no—
125#417—216no—
126#416—216no—
127#416—216no—
128C2×#103—28no—
129C2×#102—28no—
130#408—28no—
131#408—28no—
132#408—28no—
133#408C2×C4116yescomplemented
134#407—28no—
135#407—28no—
136C2×C22⋊C8—28no—
137#344—216no—
138H(3,ℤ/4)—28no—
139C25—21no—
140C25#4111yescharacteristic
141C2×#41—22no—
142C2×#41—22no—
143C2×#41—22no—
144C2×#41—22no—
145C2×#41—22no—
146C2×#41—22no—
147C2×#41—22no—
148C2×#41—22no—
149C2×#41—22no—
150C2×#41—22no—
151C2×#41—22no—
152C2×#41—22no—
153C2×#41—24no—
154C2×#41—24no—
155C2×#41—24no—
156C2×#41—24no—
157C2×#41—24no—
158C2×#41—24no—
159C2×#41—24no—
160C2×#41—24no—
161C2×#41—24no—
162C2×#41—24no—
163C2×#41—24no—
164C2×#41—24no—
165C2×#41—24no—
166C2×#41—24no—
167C2×#41—24no—
168C2×#41—24no—
169C2×#41—24no—
170C2×#41—24no—
171C2×#41—24no—
172C2×#41—24no—
173C2×#41—24no—
174C2×#41—24no—
175C2×#41—24no—
176C2×#41—24no—
177C2×#41—41no—
178C2×#41—41no—
179C2×#41—42no—
180C2×#41—42no—
181C2×#41—42no—
182C2×#41—42no—
183C2×#41—42no—
184C2×#41—42no—
185C2×#41—42no—
186C2×#41—42no—
187C2×#41—42no—
188C2×#41—41no—
189C2×#41—41no—
190C2×#41—42no—
191C2×#41—42no—
192C2×#41—42no—
193C2×#41—41no—
194C2×#41—42no—
195C2×#41—41no—
196C2×#41—42no—
197C2×#41—42no—
198C2×#41—42no—
199C2×#41—42no—
200C2×#41—42no—
201C2×#41—42no—
202C2×#41—42no—
203C2×#41—41no—
204C2×#41—41no—
205C2×#41C4⋊C414yes—
206C2×#41C4⋊C414yes—
207C2×#41C22×C414yes—
208C2×#41C2×Q814yes—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8C4⋊C412yes—
217C22×Q8C4⋊C412yes—
218C22×Q8C2×D412yes—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4C4⋊C412yes—
237C22×D4C4⋊C412yes—
238C22×D4C2×D412yes—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4C22×C411yescharacteristic
252C23×C4C22×C411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×Q811yescharacteristic
264C23×C4C2×Q811yescharacteristic
265C23×C4#4111yescharacteristic
266C23×C4#4111yescharacteristic
267C23×C4#4111yescharacteristic
268C23×C4#4112yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
271C23×C4#4112yes—
272C23×C4C2411yescharacteristic
273C2×M16—24no—
274C2×M16—24no—
275C2×M16—24no—
276C2×M16—24no—
277C2×M16—24no—
278C2×M16—24no—
279C2×M16—24no—
280C2×M16—24no—
281C2×M16—24no—
282C2×M16—24no—
283C2×M16—24no—
284C2×M16—24no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—24no—
288C2×M16—24no—
289C2×M16—24no—
290C2×M16—24no—
291C2×M16—24no—
292C2×M16—22no—
293C2×M16—22no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16—24no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—24no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—24no—
308C2×M16—42no—
309C2×M16—42no—
310C2×M16—42no—
311C2×M16—42no—
312C2×M16—42no—
313C2×M16—42no—
314C2×M16—42no—
315C2×M16—42no—
316C2×M16—42no—
317C2×M16—42no—
318C2×M16—42no—
319C2×M16—42no—
320C2×M16—42no—
321C2×M16—42no—
322C2×M16—41no—
323C2×M16—42no—
324C2×M16—41no—
325C2×M16—42no—
326C2×M16—42no—
327C2×M16—42no—
328C2×M16—41no—
329C2×M16—41no—
330C2×M16C22⋊C414yes—
331C2×M16C22⋊C414yes—
332C2×M16C22×C414yes—
333C2×M16C2×D418yes—
334C2×M16C2×D414yes—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—24no—
342C22×C8—24no—
343C22×C8—24no—
344C22×C8—24no—
345C22×C8—24no—
346C22×C8—42no—
347C22×C8—42no—
348C22×C8—42no—
349C22×C8—42no—
350C22×C8C22⋊C414yes—
351C22×C8C22⋊C414yes—
352C22×C8C22×C414yes—
353C22×C8C2×D414yes—
354#117—24no—
355#117—24no—
356#117—24no—
357#117—24no—
358#117—24no—
359#117—24no—
360#117—24no—
361#117—24no—
362#117—24no—
363#117—42no—
364#117—42no—
365#117—42no—
366#117—42no—
367#117—42no—
368#117—42no—
369#117C2×D418yes—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388#108—232no—
389#103—232no—
390#102—232no—
391C22⋊C8—232no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—42no—
396C24—42no—
397C24—82no—
398C24—84no—
399C24#11711yescharacteristic
400C24#11711yescharacteristic
401C24#12111yescharacteristic
402C24#12111yescharacteristic
403C24C22⋊Q811yescharacteristic
404C24C22⋊Q811yescharacteristic
405C24#12312yes—
406C24#12312yes—
407C24#12412yes—
408C24#12412yes—
409C24C2×#4111yescharacteristic
410#41—28no—
411#41—28no—
412#41—28no—
413#41—28no—
414#41—28no—
415#41—28no—
416#41—28no—
417#41—28no—
418#41—42no—
419#41—44no—
420#41—42no—
421#41—42no—
422#41—44no—
423#41—42no—
424#41—42no—
425#41—42no—
426#41—44no—
427#41—44no—
428#41—44no—
429#41—44no—
430#41—44no—
431#41—44no—
432#41—42no—
433#41—42no—
434#41—42no—
435#41—44no—
436#41—42no—
437#41—42no—
438#41—44no—
439#41—42no—
440#41—44no—
441#41—44no—
442#41—44no—
443#41—44no—
444#41—44no—
445#41—42no—
446#41—42no—
447#41—42no—
448#41—44no—
449#41—42no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—24no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8—24no—
459C2×Q8—41no—
460C2×Q8—42no—
461C2×Q8—41no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8C2×C4⋊C414yes—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—22no—
474C2×D4—24no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—41no—
496C2×D4—42no—
497C2×D4—41no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—41no—
502C2×D4—41no—
503C2×D4C2×C4⋊C414yes—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—42no—
519C22×C4—44no—
520C22×C4—42no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—88no—
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C22⋊C411yescharacteristic
533C22×C4C2×C22⋊C411yescharacteristic
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C4⋊C411yescharacteristic
536C22×C4C2×C4⋊C411yescharacteristic
537C22×C4C2×C4⋊C411yescharacteristic
538C22×C4C2×C4⋊C411yescharacteristic
539C22×C4#11711yescharacteristic
540C22×C4#11711yescharacteristic
541C22×C4C4×D412yes—
542C22×C4C4×D412yes—
543C22×C4C4×D412yes—
544C22×C4C4×D412yes—
545C22×C4C4×D412yes—
546C22×C4C4×D412yes—
547C22×C4C4×D412yes—
548C22×C4C4×D412yes—
549C22×C4#12012yes—
550C22×C4#12012yes—
551C22×C4#12012yes—
552C22×C4#12012yes—
553C22×C4#12011yescharacteristic
554C22×C4#12011yescharacteristic
555C22×C4#12012yes—
556C22×C4#12111yescharacteristic
557C22×C4#12111yescharacteristic
558C22×C4#12111yescharacteristic
559C22×C4#12111yescharacteristic
560C22×C4#12112yes—
561C22×C4#12112yes—
562C22×C4#12112yes—
563C22×C4#12112yes—
564C22×C4#12112yes—
565C22×C4#12112yes—
566C22×C4#12112yes—
567C22×C4#12112yes—
568C22×C4#12112yes—
569C22×C4#12112yes—
570C22×C4#12112yes—
571C22×C4#12112yes—
572C22×C4#12111yescharacteristic
573C22×C4#12111yescharacteristic
574C22×C4C22⋊Q811yescharacteristic
575C22×C4C22⋊Q811yescharacteristic
576C22×C4C22⋊Q811yescharacteristic
577C22×C4C22⋊Q811yescharacteristic
578C22×C4C22⋊Q812yes—
579C22×C4C22⋊Q812yes—
580C22×C4C22⋊Q812yes—
581C22×C4C22⋊Q812yes—
582C22×C4C22⋊Q812yes—
583C22×C4C22⋊Q812yes—
584C22×C4C22⋊Q812yes—
585C22×C4C22⋊Q812yes—
586C22×C4C22⋊Q811yescharacteristic
587C22×C4C22⋊Q811yescharacteristic
588C22×C4#12312yes—
589C22×C4#12312yes—
590C22×C4#12312yes—
591C22×C4#12312yes—
592C22×C4#12311yescharacteristic
593C22×C4#12311yescharacteristic
594C22×C4#12312yes—
595C22×C4#12312yes—
596C22×C4#12312yes—
597C22×C4#12411yescharacteristic
598C22×C4#12412yes—
599C22×C4#12411yescharacteristic
600C22×C4#12412yes—
601C22×C4#12412yes—
602C22×C4#12612yes—
603C22×C4#12612yes—
604C22×C4#12612yes—
605C22×C4#12612yes—
606C22×C4#12712yes—
607C22×C4#12711yescharacteristic
608C22×C4#12711yescharacteristic
609C22×C4C23×C411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×Q811yescharacteristic
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4111yescharacteristic
619M16—28no—
620M16—28no—
621M16—28no—
622M16—28no—
623M16—28no—
624M16—28no—
625M16—44no—
626M16—44no—
627M16—44no—
628M16—42no—
629M16—42no—
630M16—44no—
631M16—42no—
632M16—42no—
633M16—44no—
634M16—44no—
635M16—44no—
636M16—44no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—24no—
644C2×C8—28no—
645C2×C8—28no—
646C2×C8—44no—
647C2×C8—44no—
648C2×C8—42no—
649C2×C8—44no—
650C2×C8—42no—
651C2×C8—44no—
652C2×C8—44no—
653C2×C8—44no—
654C2×C8—44no—
655C2×C8C2×C22⋊C418yes—
656C4⋊C4—28no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C22⋊C4—28no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C42—28no—
665C42—44no—
666C42—44no—
667C42—44no—
668C23—24no—
669C23—44no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—44no—
674C23—48no—
675C23—44no—
676C23—42no—
677C23—44no—
678C23—42no—
679C23—88no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—82no—
684C23—82no—
685C23—81no—
686C23—84no—
687C23—84no—
688C23—88no—
689C23#38011yescharacteristic
690C23#38011yescharacteristic
691C23#38011yescharacteristic
692C23#38011yescharacteristic
693C23#38812yes—
694C23#38812yes—
695C23#38812yes—
696C23#38812yes—
697C23#39311yescharacteristic
698C23#39311yescharacteristic
699C23#39312yes—
700C23#39412yes—
701C23#39412yes—
702C23#39412yes—
703C23#39412yes—
704C23#39911yescharacteristic
705C23#39911yescharacteristic
706C23#39912yes—
707C23C2×#11711yescharacteristic
708C23C2×#12111yescharacteristic
709C23C2×C22⋊Q811yescharacteristic
710C23C2×#12312yes—
711C23C2×#12412yes—
712Q8—28no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716Q8—42no—
717Q8—44no—
718D4—28no—
719D4—44no—
720D4—44no—
721D4—44no—
722D4—44no—
723D4—48no—
724D4—48no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—44no—
730C2×C4—24no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—48no—
736C2×C4—44no—
737C2×C4—48no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—48no—
742C2×C4—88no—
743C2×C4—88no—
744C2×C4—88no—
745C2×C4#38011yescharacteristic
746C2×C4#38011yescharacteristic
747C2×C4#38011yescharacteristic
748C2×C4#38011yescharacteristic
749C2×C4#38512yes—
750C2×C4#38512yes—
751C2×C4#38512yes—
752C2×C4#38512yes—
753C2×C4#38512yes—
754C2×C4#38512yes—
755C2×C4#38512yes—
756C2×C4#38512yes—
757C2×C4#38611yescharacteristic
758C2×C4#38611yescharacteristic
759C2×C4#38611yescharacteristic
760C2×C4#38611yescharacteristic
761C2×C4#38612yes—
762C2×C4#38612yes—
763C2×C4#38812yes—
764C2×C4#38812yes—
765C2×C4#38812yes—
766C2×C4#38812yes—
767C2×C4#39011yescharacteristic
768C2×C4#39012yes—
769C2×C4#39012yes—
770C2×C4#39011yescharacteristic
771C2×C4#39011yescharacteristic
772C2×C4#39011yescharacteristic
773C2×C4#39211yescharacteristic
774C2×C4#39211yescharacteristic
775C2×C4#39212yes—
776C2×C4#39212yes—
777C2×C4#39211yescharacteristic
778C2×C4#39211yescharacteristic
779C2×C4#39311yescharacteristic
780C2×C4#39312yes—
781C2×C4#39311yescharacteristic
782C2×C4#39412yes—
783C2×C4#39412yes—
784C2×C4#39412yes—
785C2×C4#39412yes—
786C2×C4#39612yes—
787C2×C4#39612yes—
788C2×C4#39612yes—
789C2×C4#39612yes—
790C2×C4#39612yes—
791C2×C4#39612yes—
792C2×C4#39612yes—
793C2×C4#39612yes—
794C2×C4#39712yes—
795C2×C4#39711yescharacteristic
796C2×C4#39711yescharacteristic
797C2×C4#39712yes—
798C2×C4#39711yescharacteristic
799C2×C4#39711yescharacteristic
800C2×C4#39911yescharacteristic
801C2×C4#39912yes—
802C2×C4#39911yescharacteristic
803C2×C4C22×C22⋊C411yescharacteristic
804C2×C4C22×C4⋊C411yescharacteristic
805C2×C4C2×C4×D412yes—
806C2×C4C2×C4×D412yes—
807C2×C4C2×#12012yes—
808C2×C4C2×#12011yescharacteristic
809C2×C4C2×#12112yes—
810C2×C4C2×#12111yescharacteristic
811C2×C4C2×#12112yes—
812C2×C4C2×#12112yes—
813C2×C4C2×C22⋊Q811yescharacteristic
814C2×C4C2×C22⋊Q812yes—
815C2×C4C2×C22⋊Q812yes—
816C2×C4C2×#12312yes—
817C2×C4C2×#12311yescharacteristic
818C2×C4C2×#12411yescharacteristic
819C2×C4C2×#12612yes—
820C2×C4C2×#12711yescharacteristic
821C8—28no—
822C8—48no—
823C8—44no—
824C22—24no—
825C22—22no—
826C22—24no—
827C22—22no—
828C22—22no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—48no—
848C22—44no—
849C22—84no—
850C22—88no—
851C22—88no—
852C22—84no—
853C22#143911yescharacteristic
854C22#143912yes—
855C22#143911yescharacteristic
856C22#143911yescharacteristic
857C22#143912yes—
858C22#143911yescharacteristic
859C22C2×#38011yescharacteristic
860C22C2×#38812yes—
861C22C2×#39311yescharacteristic
862C22C2×#39412yes—
863C22C2×#39911yescharacteristic
864C4—44no—
865C4—88no—
866C4#143911yescharacteristic
867C4#143912yes—
868C4#143911yescharacteristic
869C4#143911yescharacteristic
870C4#143911yescharacteristic
871C4#143912yes—
872C4C2×#38512yes—
873C4C2×#38611yescharacteristic
874C4C2×#39011yescharacteristic
875C4C2×#39211yescharacteristic
876C4C2×#39612yes—
877C4C2×#39711yescharacteristic
878C2—22no—
879C2—21no—
880C2—22no—
881C2—21no—
882C2—21no—
883C2—21no—
884C2—22no—
885C2—21no—
886C2—21no—
887C2—22no—
888C2—84no—
889C2#1111012yesdirect product factor
890C2C2×#143911yescharacteristic
subgroupG/H
centerC2×C4#390
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC22#1439
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#430C2semidirect
4. C22×#344C2semidirect
5. C22×H(3,ℤ/4)C2semidirect
6. #11110C2direct (N × H)
15. C2×#430C22semidirect
27. #2879C4semidirect
30. C2×#408C4semidirect
34. C2×#344C22semidirect
37. C2×H(3,ℤ/4)C22semidirect
133. #408C2×C4semidirect
889. C2#11110direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4302
C2×#28962
C2×#28792
C22×#3442
C22×H(3,ℤ/4)2
#111102