Finite Group Databasebeta

← C2×#11109 #357697

Subgroups — C2×#11109 #357697

Order 512.

2658 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2911C211yesmaximal, characteristic, complemented
2C22×#421C212yesmaximal
3C2×#2879C211yesmaximal, characteristic
4C22×#344C212yesmaximal, complemented
5C22×#338C211yesmaximal, characteristic, complemented
6#11109C218yesmaximal, direct product factor
7C23×#41C2211yescharacteristic
8C23×M16C2212yes—
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2212yes—
12#2911—22no—
13#2911—24no—
14#2911C2214yescomplemented
15C2×#428—24no—
16C2×#427—22no—
17C2×#421—24no—
18C2×#421—24no—
19C2×#421—24no—
20C2×#421—24no—
21C2×#421—24no—
22C2×#421C2218yes—
23C22×#104—24no—
24#2879—22no—
25#2879—22no—
26#2879C414yescomplemented
27#2879C2214yes—
28C2×#408—22no—
29C2×#408C414yescomplemented
30C2×#407—22no—
31C2×#344—24no—
32C2×#344—24no—
33C2×#344C2218yescomplemented
34C2×#338—22no—
35C2×#338—22no—
36C2×#338C2214yescomplemented
37C22×#41—21no—
38C22×#41—21no—
39C22×#41—21no—
40C22×#41—21no—
41C22×#41—21no—
42C22×#41—21no—
43C22×#41—22no—
44C22×#41—22no—
45C22×#41—22no—
46C22×#41—22no—
47C22×#41—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41C2×C412yes—
52C22×#41C2×C412yes—
53C22×#41D412yes—
54C22×#41D412yes—
55C22×#41Q812yes—
56C22×#41C2312yes—
57C23×Q8Q811yescharacteristic
58C23×D4—21no—
59C23×D4Q811yescharacteristic
60C24×C4—21no—
61C24×C4C2311yescharacteristic
62C22×M16—22no—
63C22×M16—22no—
64C22×M16—22no—
65C22×M16—22no—
66C22×M16—21no—
67C22×M16—21no—
68C22×M16—21no—
69C22×M16—21no—
70C22×M16—22no—
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×M16C2×C412yes—
86C22×M16C2×C412yes—
87C22×M16C2×C412yes—
88C22×M16D414yes—
89C22×M16D414yes—
90C22×M16D412yes—
91C22×M16D412yes—
92C22×M16D412yes—
93C22×M16C2314yes—
94C22×M16C2312yes—
95C22×M16C2312yes—
96C23×C8—22no—
97C23×C8C2×C412yes—
98C23×C8D412yes—
99C2×#117—22no—
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×#117D414yes—
109C2×#117D414yes—
110C2×#117C2314yes—
111C22×C4⋊C4—22no—
112C22×C22⋊C4—22no—
113C22×C42—22no—
114#428—216no—
115#428—216no—
116#427—28no—
117#427—28no—
118C2×#107—24no—
119C2×#106—24no—
120#421—216no—
121#421—216no—
122#421—216no—
123#421—216no—
124C2×#104—216no—
125C2×#104—216no—
126C2×#104—216no—
127#408—28no—
128#408—28no—
129#408—28no—
130#408C2×C4116yescomplemented
131#407—28no—
132#407—28no—
133C2×C22⋊C8—28no—
134#344—216no—
135#338—28no—
136C25—21no—
137C25#4111yescharacteristic
138C2×#41—22no—
139C2×#41—22no—
140C2×#41—22no—
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—24no—
151C2×#41—24no—
152C2×#41—24no—
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—41no—
175C2×#41—42no—
176C2×#41—41no—
177C2×#41—42no—
178C2×#41—42no—
179C2×#41—42no—
180C2×#41—42no—
181C2×#41—42no—
182C2×#41—42no—
183C2×#41—41no—
184C2×#41—41no—
185C2×#41—42no—
186C2×#41—42no—
187C2×#41—42no—
188C2×#41—42no—
189C2×#41—42no—
190C2×#41—41no—
191C2×#41—42no—
192C2×#41—41no—
193C2×#41—42no—
194C2×#41—42no—
195C2×#41—42no—
196C2×#41—42no—
197C2×#41—42no—
198C2×#41—42no—
199C2×#41—42no—
200C2×#41—41no—
201C2×#41—41no—
202C2×#41C4⋊C414yes—
203C2×#41C4⋊C414yes—
204C2×#41C22×C414yes—
205C2×#41C2×D414yes—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8C4⋊C412yes—
214C22×Q8C4⋊C412yes—
215C22×Q8C2×Q812yes—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4C4⋊C412yes—
234C22×D4C4⋊C412yes—
235C22×D4C2×Q812yes—
236C23×C4—21no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4C2×Q811yescharacteristic
261C23×C4C2×Q811yescharacteristic
262C23×C4#4111yescharacteristic
263C23×C4#4111yescharacteristic
264C23×C4#4111yescharacteristic
265C23×C4#4112yes—
266C23×C4#4112yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4C2411yescharacteristic
270C2×M16—24no—
271C2×M16—24no—
272C2×M16—24no—
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—22no—
283C2×M16—22no—
284C2×M16—24no—
285C2×M16—24no—
286C2×M16—24no—
287C2×M16—24no—
288C2×M16—24no—
289C2×M16—24no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—24no—
293C2×M16—24no—
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—42no—
306C2×M16—42no—
307C2×M16—42no—
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—41no—
322C2×M16—42no—
323C2×M16—41no—
324C2×M16—42no—
325C2×M16—41no—
326C2×M16—41no—
327C2×M16C22⋊C414yes—
328C2×M16C22⋊C414yes—
329C2×M16C22×C414yes—
330C2×M16C2×D418yes—
331C2×M16C2×D414yes—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—24no—
339C22×C8—24no—
340C22×C8—24no—
341C22×C8—24no—
342C22×C8—24no—
343C22×C8—42no—
344C22×C8—42no—
345C22×C8—42no—
346C22×C8—42no—
347C22×C8C22⋊C414yes—
348C22×C8C22⋊C414yes—
349C22×C8C22×C414yes—
350C22×C8C2×D414yes—
351#117—24no—
352#117—24no—
353#117—24no—
354#117—24no—
355#117—24no—
356#117—24no—
357#117—24no—
358#117—24no—
359#117—24no—
360#117—42no—
361#117—42no—
362#117—42no—
363#117—42no—
364#117—42no—
365#117—42no—
366#117C2×D418yes—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385#107—216no—
386#106—216no—
387#104—264no—
388C22⋊C8—232no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—82no—
395C24—84no—
396C24#11711yescharacteristic
397C24#11711yescharacteristic
398C24#12111yescharacteristic
399C24#12112yes—
400C24#12111yescharacteristic
401C24#12112yes—
402C24C22⋊Q811yescharacteristic
403C24C22⋊Q811yescharacteristic
404C24#12612yes—
405C24#12612yes—
406C24C2×#4111yescharacteristic
407#41—28no—
408#41—28no—
409#41—28no—
410#41—28no—
411#41—28no—
412#41—28no—
413#41—28no—
414#41—28no—
415#41—42no—
416#41—44no—
417#41—42no—
418#41—44no—
419#41—42no—
420#41—42no—
421#41—42no—
422#41—42no—
423#41—44no—
424#41—44no—
425#41—44no—
426#41—44no—
427#41—44no—
428#41—44no—
429#41—42no—
430#41—42no—
431#41—42no—
432#41—44no—
433#41—42no—
434#41—42no—
435#41—44no—
436#41—42no—
437#41—44no—
438#41—44no—
439#41—44no—
440#41—44no—
441#41—44no—
442#41—42no—
443#41—42no—
444#41—42no—
445#41—44no—
446#41—42no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—24no—
451C2×Q8—24no—
452C2×Q8—24no—
453C2×Q8—24no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—42no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—41no—
462C2×Q8—42no—
463C2×Q8—41no—
464C2×Q8C2×C4⋊C414yes—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—24no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—41no—
498C2×D4—42no—
499C2×D4—41no—
500C2×D4C2×C4⋊C414yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—44no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—42no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—88no—
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4C2×C4⋊C411yescharacteristic
533C22×C4C2×C4⋊C411yescharacteristic
534C22×C4C2×C4⋊C411yescharacteristic
535C22×C4C2×C4⋊C411yescharacteristic
536C22×C4#11711yescharacteristic
537C22×C4#11711yescharacteristic
538C22×C4C4×D412yes—
539C22×C4C4×D412yes—
540C22×C4C4×D412yes—
541C22×C4C4×D412yes—
542C22×C4C4×D412yes—
543C22×C4C4×D412yes—
544C22×C4C4×D412yes—
545C22×C4C4×D412yes—
546C22×C4#12012yes—
547C22×C4#12012yes—
548C22×C4#12012yes—
549C22×C4#12012yes—
550C22×C4#12011yescharacteristic
551C22×C4#12012yes—
552C22×C4#12011yescharacteristic
553C22×C4#12111yescharacteristic
554C22×C4#12111yescharacteristic
555C22×C4#12111yescharacteristic
556C22×C4#12111yescharacteristic
557C22×C4#12112yes—
558C22×C4#12112yes—
559C22×C4#12112yes—
560C22×C4#12112yes—
561C22×C4#12112yes—
562C22×C4#12112yes—
563C22×C4#12112yes—
564C22×C4#12112yes—
565C22×C4#12111yescharacteristic
566C22×C4#12111yescharacteristic
567C22×C4#12112yes—
568C22×C4#12112yes—
569C22×C4C22⋊Q811yescharacteristic
570C22×C4C22⋊Q811yescharacteristic
571C22×C4C22⋊Q811yescharacteristic
572C22×C4C22⋊Q811yescharacteristic
573C22×C4C22⋊Q812yes—
574C22×C4C22⋊Q812yes—
575C22×C4C22⋊Q812yes—
576C22×C4C22⋊Q812yes—
577C22×C4C22⋊Q812yes—
578C22×C4C22⋊Q812yes—
579C22×C4C22⋊Q812yes—
580C22×C4C22⋊Q812yes—
581C22×C4C22⋊Q811yescharacteristic
582C22×C4C22⋊Q811yescharacteristic
583C22×C4#12312yes—
584C22×C4#12312yes—
585C22×C4#12312yes—
586C22×C4#12312yes—
587C22×C4#12311yescharacteristic
588C22×C4#12311yescharacteristic
589C22×C4#12312yes—
590C22×C4#12312yes—
591C22×C4#12312yes—
592C22×C4#12312yes—
593C22×C4#12312yes—
594C22×C4#12412yes—
595C22×C4#12412yes—
596C22×C4#12412yes—
597C22×C4#12412yes—
598C22×C4#12411yescharacteristic
599C22×C4#12412yes—
600C22×C4#12411yescharacteristic
601C22×C4#12612yes—
602C22×C4#12612yes—
603C22×C4#12712yes—
604C22×C4#12711yescharacteristic
605C22×C4#12711yescharacteristic
606C22×C4C23×C411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×Q811yescharacteristic
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4111yescharacteristic
616M16—28no—
617M16—28no—
618M16—28no—
619M16—28no—
620M16—28no—
621M16—28no—
622M16—44no—
623M16—44no—
624M16—44no—
625M16—42no—
626M16—42no—
627M16—44no—
628M16—42no—
629M16—42no—
630M16—44no—
631M16—44no—
632M16—44no—
633M16—44no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—28no—
642C2×C8—28no—
643C2×C8—44no—
644C2×C8—44no—
645C2×C8—42no—
646C2×C8—44no—
647C2×C8—42no—
648C2×C8—44no—
649C2×C8—44no—
650C2×C8—44no—
651C2×C8—44no—
652C2×C8C2×C22⋊C418yes—
653C4⋊C4—28no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C22⋊C4—28no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C42—28no—
662C42—44no—
663C42—44no—
664C42—44no—
665C23—24no—
666C23—44no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—48no—
672C23—44no—
673C23—42no—
674C23—44no—
675C23—42no—
676C23—88no—
677C23—81no—
678C23—82no—
679C23—81no—
680C23—81no—
681C23—82no—
682C23—81no—
683C23—84no—
684C23—84no—
685C23—88no—
686C23#38011yescharacteristic
687C23#38011yescharacteristic
688C23#38011yescharacteristic
689C23#38011yescharacteristic
690C23#38812yes—
691C23#38812yes—
692C23#38812yes—
693C23#38812yes—
694C23#39211yescharacteristic
695C23#39211yescharacteristic
696C23#39212yes—
697C23#39612yes—
698C23#39612yes—
699C23#39612yes—
700C23#39612yes—
701C23#39711yescharacteristic
702C23#39712yes—
703C23#39711yescharacteristic
704C23C2×#11711yescharacteristic
705C23C2×#12112yes—
706C23C2×#12111yescharacteristic
707C23C2×C22⋊Q811yescharacteristic
708C23C2×#12612yes—
709Q8—28no—
710Q8—42no—
711Q8—42no—
712Q8—42no—
713Q8—42no—
714Q8—44no—
715D4—28no—
716D4—44no—
717D4—44no—
718D4—44no—
719D4—44no—
720D4—48no—
721D4—48no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—44no—
727C2×C4—24no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—48no—
733C2×C4—44no—
734C2×C4—48no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—48no—
739C2×C4—88no—
740C2×C4—88no—
741C2×C4—88no—
742C2×C4#38011yescharacteristic
743C2×C4#38011yescharacteristic
744C2×C4#38011yescharacteristic
745C2×C4#38011yescharacteristic
746C2×C4#38512yes—
747C2×C4#38512yes—
748C2×C4#38512yes—
749C2×C4#38512yes—
750C2×C4#38512yes—
751C2×C4#38512yes—
752C2×C4#38512yes—
753C2×C4#38512yes—
754C2×C4#38611yescharacteristic
755C2×C4#38611yescharacteristic
756C2×C4#38611yescharacteristic
757C2×C4#38611yescharacteristic
758C2×C4#38612yes—
759C2×C4#38612yes—
760C2×C4#38812yes—
761C2×C4#38812yes—
762C2×C4#38812yes—
763C2×C4#38812yes—
764C2×C4#39011yescharacteristic
765C2×C4#39012yes—
766C2×C4#39012yes—
767C2×C4#39011yescharacteristic
768C2×C4#39011yescharacteristic
769C2×C4#39011yescharacteristic
770C2×C4#39211yescharacteristic
771C2×C4#39212yes—
772C2×C4#39211yescharacteristic
773C2×C4#39312yes—
774C2×C4#39311yescharacteristic
775C2×C4#39311yescharacteristic
776C2×C4#39311yescharacteristic
777C2×C4#39312yes—
778C2×C4#39311yescharacteristic
779C2×C4#39412yes—
780C2×C4#39412yes—
781C2×C4#39412yes—
782C2×C4#39412yes—
783C2×C4#39412yes—
784C2×C4#39412yes—
785C2×C4#39412yes—
786C2×C4#39412yes—
787C2×C4#39612yes—
788C2×C4#39612yes—
789C2×C4#39612yes—
790C2×C4#39612yes—
791C2×C4#39712yes—
792C2×C4#39711yescharacteristic
793C2×C4#39711yescharacteristic
794C2×C4#39911yescharacteristic
795C2×C4#39912yes—
796C2×C4#39911yescharacteristic
797C2×C4#39911yescharacteristic
798C2×C4#39912yes—
799C2×C4#39911yescharacteristic
800C2×C4C22×C22⋊C411yescharacteristic
801C2×C4C22×C4⋊C411yescharacteristic
802C2×C4C2×C4×D412yes—
803C2×C4C2×C4×D412yes—
804C2×C4C2×#12011yescharacteristic
805C2×C4C2×#12012yes—
806C2×C4C2×#12111yescharacteristic
807C2×C4C2×#12112yes—
808C2×C4C2×#12112yes—
809C2×C4C2×C22⋊Q811yescharacteristic
810C2×C4C2×C22⋊Q812yes—
811C2×C4C2×C22⋊Q812yes—
812C2×C4C2×#12312yes—
813C2×C4C2×#12312yes—
814C2×C4C2×#12311yescharacteristic
815C2×C4C2×#12412yes—
816C2×C4C2×#12411yescharacteristic
817C2×C4C2×#12711yescharacteristic
818C8—28no—
819C8—48no—
820C8—44no—
821C22—22no—
822C22—22no—
823C22—24no—
824C22—24no—
825C22—22no—
826C22—42no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—48no—
845C22—44no—
846C22—84no—
847C22—88no—
848C22—88no—
849C22—84no—
850C22#143911yescharacteristic
851C22#143912yes—
852C22#143911yescharacteristic
853C22#143911yescharacteristic
854C22#143912yes—
855C22#143911yescharacteristic
856C22C2×#38011yescharacteristic
857C22C2×#38812yes—
858C22C2×#39211yescharacteristic
859C22C2×#39612yes—
860C22C2×#39711yescharacteristic
861C4—44no—
862C4—88no—
863C4#143911yescharacteristic
864C4#143912yes—
865C4#143911yescharacteristic
866C4#143911yescharacteristic
867C4#143911yescharacteristic
868C4#143912yes—
869C4C2×#38512yes—
870C4C2×#38611yescharacteristic
871C4C2×#39011yescharacteristic
872C4C2×#39311yescharacteristic
873C4C2×#39412yes—
874C4C2×#39911yescharacteristic
875C2—21no—
876C2—21no—
877C2—22no—
878C2—21no—
879C2—22no—
880C2—21no—
881C2—21no—
882C2—22no—
883C2—21no—
884C2—22no—
885C2—84no—
886C2#1110912yesdirect product factor
887C2C2×#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. C2×#2911C2semidirect
4. C22×#344C2semidirect
5. C22×#338C2semidirect
6. #11109C2direct (N × H)
14. #2911C22semidirect
26. #2879C4semidirect
29. C2×#408C4semidirect
33. C2×#344C22semidirect
36. C2×#338C22semidirect
130. #408C2×C4semidirect
886. C2#11109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29112
C22×#4212
C2×#28792
C22×#3442
C22×#3382
#111092