Finite Group Databasebeta

← C2×#11185 #357940

Subgroups — C2×#11185 #357940

Order 512.

2582 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#421C211yesmaximal, characteristic
2C22×#417C211yesmaximal, characteristic
3C2×#2879C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C22×#343C211yesmaximal, characteristic, complemented
6C2×#1736C211yesmaximal, characteristic, complemented
7C22×#338C211yesmaximal, characteristic, complemented
8#11185C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C2×#421—22no—
17C2×#421—24no—
18C2×#421—24no—
19C2×#421C2214yes—
20C22×#104—22no—
21C2×#417—22no—
22C2×#417—22no—
23C2×#417—22no—
24C2×#417—22no—
25C2×#417C414yescomplemented
26C2×#417C2214yes—
27C22×#103C412yescomplemented
28C22×#102C412yescomplemented
29#2879—22no—
30#2879—22no—
31#2879—22no—
32#2879C2214yes—
33C2×#408—22no—
34C2×#408—22no—
35C2×#407—22no—
36C2×#344—24no—
37C2×#344C2214yescomplemented
38C2×#343—22no—
39C2×#343—22no—
40C2×#343C2214yescomplemented
41#1736—22no—
42#1736C2214yescomplemented
43C2×#340—22no—
44C2×#338—24no—
45C2×#338C2214yescomplemented
46C22×#41—21no—
47C22×#41—21no—
48C22×#41—21no—
49C22×#41—21no—
50C22×#41—21no—
51C22×#41—21no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41C2×C412yes—
61C22×#41D412yes—
62C22×#41D412yes—
63C22×#41D412yes—
64C22×#41D412yes—
65C22×#41C2312yes—
66C23×Q8C2×C411yescharacteristic
67C23×D4—21no—
68C23×D4C2×C411yescharacteristic
69C24×C4—21no—
70C24×C4—21no—
71C24×C4C2311yescharacteristic
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16—21no—
93C22×M16—21no—
94C22×M16—21no—
95C22×M16—22no—
96C22×M16—21no—
97C22×M16—21no—
98C22×M16—22no—
99C22×M16—22no—
100C22×M16—22no—
101C22×M16—22no—
102C22×M16—22no—
103C22×M16C2×C412yes—
104C22×M16D412yes—
105C22×M16D412yes—
106C22×M16D414yes—
107C22×M16D412yes—
108C22×M16C2312yes—
109C22×M16C2312yes—
110C22×M16C2312yes—
111C22×M16C2312yes—
112C23×C8—21no—
113C23×C8—21no—
114C23×C8C2×C412yes—
115C23×C8D412yes—
116C2×#117—22no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—22no—
120C2×#117—21no—
121C2×#117—22no—
122C2×#117D414yes—
123C2×#117C2312yes—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2×C412yes—
137C22×C4⋊C4C2×C412yes—
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4—21no—
140C22×C42—21no—
141#421—216no—
142#421—28no—
143#421—28no—
144C2×#104—216no—
145C2×#104—28no—
146#417—28no—
147#417—28no—
148#417—28no—
149#417—28no—
150C2×#103—24no—
151C2×#103—24no—
152C2×#103C2×C418yescomplemented
153C2×#102—24no—
154C2×#102—24no—
155C2×#102C2×C418yescomplemented
156#408—28no—
157#408—28no—
158#408—28no—
159#408—28no—
160#407—28no—
161#407—28no—
162C2×C22⋊C8—28no—
163#344—28no—
164#343—28no—
165#340—28no—
166#338—28no—
167C25—21no—
168C25#4111yescharacteristic
169C2×#41—22no—
170C2×#41—22no—
171C2×#41—22no—
172C2×#41—22no—
173C2×#41—22no—
174C2×#41—22no—
175C2×#41—22no—
176C2×#41—22no—
177C2×#41—22no—
178C2×#41—22no—
179C2×#41—22no—
180C2×#41—22no—
181C2×#41—24no—
182C2×#41—24no—
183C2×#41—24no—
184C2×#41—24no—
185C2×#41—24no—
186C2×#41—24no—
187C2×#41—24no—
188C2×#41—24no—
189C2×#41—24no—
190C2×#41—24no—
191C2×#41—24no—
192C2×#41—24no—
193C2×#41—24no—
194C2×#41—24no—
195C2×#41—24no—
196C2×#41—24no—
197C2×#41—24no—
198C2×#41—24no—
199C2×#41—24no—
200C2×#41—24no—
201C2×#41—22no—
202C2×#41—22no—
203C2×#41—22no—
204C2×#41—22no—
205C2×#41—22no—
206C2×#41—22no—
207C2×#41—22no—
208C2×#41—22no—
209C2×#41—42no—
210C2×#41—42no—
211C2×#41—42no—
212C2×#41—42no—
213C2×#41—42no—
214C2×#41—42no—
215C2×#41—42no—
216C2×#41—42no—
217C2×#41—42no—
218C2×#41—42no—
219C2×#41—42no—
220C2×#41—42no—
221C2×#41—42no—
222C2×#41—42no—
223C2×#41—42no—
224C2×#41—42no—
225C2×#41—42no—
226C2×#41—42no—
227C2×#41—42no—
228C2×#41—42no—
229C2×#41—42no—
230C2×#41—42no—
231C2×#41—42no—
232C2×#41—42no—
233C2×#41C22⋊C414yes—
234C2×#41C22⋊C414yes—
235C2×#41C2×D414yes—
236C2×#41C2×D414yes—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8C22⋊C412yes—
245C22×Q8C22⋊C412yes—
246C22×Q8C22×C412yes—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4C22⋊C412yes—
265C22×D4C22⋊C412yes—
266C22×D4C22×C412yes—
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—41no—
286C23×C4—84no—
287C23×C4C22×C411yescharacteristic
288C23×C4C22×C411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4#4112yes—
300C23×C4#4112yes—
301C23×C4#4112yes—
302C23×C4#4112yes—
303C23×C4#4111yescharacteristic
304C23×C4#4112yes—
305C23×C4#4112yes—
306C23×C4#4111yescharacteristic
307C23×C4#4111yescharacteristic
308C23×C4C2411yescharacteristic
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—24no—
312C2×M16—24no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—22no—
321C2×M16—22no—
322C2×M16—22no—
323C2×M16—22no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—22no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—24no—
335C2×M16—24no—
336C2×M16—24no—
337C2×M16—24no—
338C2×M16—24no—
339C2×M16—24no—
340C2×M16—24no—
341C2×M16—24no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—42no—
351C2×M16—42no—
352C2×M16—42no—
353C2×M16—41no—
354C2×M16—41no—
355C2×M16—42no—
356C2×M16—42no—
357C2×M16—42no—
358C2×M16—42no—
359C2×M16—42no—
360C2×M16—42no—
361C2×M16—42no—
362C2×M16—42no—
363C2×M16—42no—
364C2×M16—42no—
365C2×M16—42no—
366C2×M16—42no—
367C2×M16—42no—
368C2×M16—42no—
369C2×M16—42no—
370C2×M16—42no—
371C2×M16—42no—
372C2×M16—42no—
373C2×M16—42no—
374C2×M16—42no—
375C2×M16—42no—
376C2×M16—42no—
377C2×M16—42no—
378C2×M16—42no—
379C2×M16C2×D414yes—
380C2×M16C2×D414yes—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—24no—
384C22×C8—24no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—24no—
390C22×C8—24no—
391C22×C8—24no—
392C22×C8—22no—
393C22×C8—22no—
394C22×C8—42no—
395C22×C8—41no—
396C22×C8—41no—
397C22×C8—42no—
398C22×C8—42no—
399C22×C8C22×C414yes—
400C22×C8C2×D414yes—
401#117—24no—
402#117—22no—
403#117—24no—
404#117—22no—
405#117—24no—
406#117—22no—
407#117—42no—
408#117—42no—
409#117—42no—
410#117C2×D414yes—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4C22×C414yes—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—42no—
447C2×C42—24no—
448C2×C42—22no—
449C2×C42—41no—
450C2×C42—42no—
451#104—232no—
452#103—216no—
453#102—216no—
454C22⋊C8—232no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—82no—
463C24—82no—
464C24C4×D411yescharacteristic
465C24C4×D411yescharacteristic
466C24#12111yescharacteristic
467C24#12111yescharacteristic
468C24#12311yescharacteristic
469C24#12311yescharacteristic
470C24#12312yes—
471C24#12412yes—
472C24#12612yes—
473C24#12612yes—
474C24C2×#4111yescharacteristic
475#41—24no—
476#41—24no—
477#41—24no—
478#41—24no—
479#41—24no—
480#41—24no—
481#41—24no—
482#41—24no—
483#41—28no—
484#41—28no—
485#41—28no—
486#41—28no—
487#41—42no—
488#41—42no—
489#41—42no—
490#41—42no—
491#41—42no—
492#41—42no—
493#41—42no—
494#41—42no—
495#41—44no—
496#41—44no—
497#41—44no—
498#41—44no—
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503#41—44no—
504#41—44no—
505#41—44no—
506#41—44no—
507#41—44no—
508#41—44no—
509#41—44no—
510#41—44no—
511#41—44no—
512#41—44no—
513#41—44no—
514#41—44no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—24no—
523C2×Q8—24no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8C2×C22⋊C414yes—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C2×C22⋊C414yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4C2×C22⋊C411yescharacteristic
611C22×C4C2×C22⋊C411yescharacteristic
612C22×C4C2×C22⋊C411yescharacteristic
613C22×C4C2×C22⋊C411yescharacteristic
614C22×C4#11712yes—
615C22×C4#11712yes—
616C22×C4#11712yes—
617C22×C4#11712yes—
618C22×C4C4×D412yes—
619C22×C4C4×D412yes—
620C22×C4C4×D412yes—
621C22×C4C4×D412yes—
622C22×C4C4×D411yescharacteristic
623C22×C4C4×D411yescharacteristic
624C22×C4C4×D411yescharacteristic
625C22×C4C4×D411yescharacteristic
626C22×C4C4×D411yescharacteristic
627C22×C4C4×D411yescharacteristic
628C22×C4#12012yes—
629C22×C4#12012yes—
630C22×C4#12011yescharacteristic
631C22×C4#12011yescharacteristic
632C22×C4#12011yescharacteristic
633C22×C4#12011yescharacteristic
634C22×C4#12112yes—
635C22×C4#12112yes—
636C22×C4#12112yes—
637C22×C4#12112yes—
638C22×C4#12111yescharacteristic
639C22×C4#12111yescharacteristic
640C22×C4#12111yescharacteristic
641C22×C4#12111yescharacteristic
642C22×C4#12112yes—
643C22×C4#12112yes—
644C22×C4#12112yes—
645C22×C4#12112yes—
646C22×C4#12112yes—
647C22×C4#12112yes—
648C22×C4#12112yes—
649C22×C4#12112yes—
650C22×C4#12111yescharacteristic
651C22×C4#12111yescharacteristic
652C22×C4#12312yes—
653C22×C4#12312yes—
654C22×C4#12312yes—
655C22×C4#12312yes—
656C22×C4#12312yes—
657C22×C4#12312yes—
658C22×C4#12312yes—
659C22×C4#12312yes—
660C22×C4#12312yes—
661C22×C4#12312yes—
662C22×C4#12312yes—
663C22×C4#12312yes—
664C22×C4#12312yes—
665C22×C4#12312yes—
666C22×C4#12312yes—
667C22×C4#12312yes—
668C22×C4#12311yescharacteristic
669C22×C4#12311yescharacteristic
670C22×C4#12312yes—
671C22×C4#12412yes—
672C22×C4#12412yes—
673C22×C4#12412yes—
674C22×C4#12412yes—
675C22×C4#12412yes—
676C22×C4#12412yes—
677C22×C4#12412yes—
678C22×C4#12612yes—
679C22×C4#12612yes—
680C22×C4#12612yes—
681C22×C4#12612yes—
682C22×C4#12612yes—
683C22×C4#12612yes—
684C22×C4C23×C411yescharacteristic
685C22×C4C22×D411yescharacteristic
686C22×C4C22×D411yescharacteristic
687C22×C4C22×D411yescharacteristic
688C22×C4C22×D411yescharacteristic
689C22×C4C22×D411yescharacteristic
690C22×C4C22×D411yescharacteristic
691C22×C4C2×#4111yescharacteristic
692C22×C4C2×#4111yescharacteristic
693C22×C4C2×#4111yescharacteristic
694C22×C4C2×#4111yescharacteristic
695C22×C4C2×#4111yescharacteristic
696C22×C4C2×#4111yescharacteristic
697C22×C4C2×#4111yescharacteristic
698M16—24no—
699M16—24no—
700M16—24no—
701M16—24no—
702M16—42no—
703M16—42no—
704M16—42no—
705M16—42no—
706M16—42no—
707M16—42no—
708M16—42no—
709M16—42no—
710M16—42no—
711M16—42no—
712M16—42no—
713M16—42no—
714M16—44no—
715M16—44no—
716M16—44no—
717M16—44no—
718M16—44no—
719M16—44no—
720M16—44no—
721M16—44no—
722C2×C8—24no—
723C2×C8—24no—
724C2×C8—24no—
725C2×C8—24no—
726C2×C8—24no—
727C2×C8—24no—
728C2×C8—24no—
729C2×C8—24no—
730C2×C8—42no—
731C2×C8—42no—
732C2×C8—42no—
733C2×C8—42no—
734C2×C8—44no—
735C2×C8—44no—
736C2×C8—44no—
737C2×C8—44no—
738C2×C8—44no—
739C2×C8—44no—
740C2×C8—44no—
741C2×C8—44no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—42no—
748C4⋊C4—42no—
749C4⋊C4—42no—
750C4⋊C4—42no—
751C4⋊C4—42no—
752C4⋊C4—44no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—44no—
756C42—24no—
757C42—42no—
758C42—44no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—24no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—41no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—42no—
783C23—42no—
784C23—82no—
785C23—82no—
786C23—82no—
787C23—82no—
788C23—88no—
789C23—88no—
790C23#38611yescharacteristic
791C23#38611yescharacteristic
792C23#38611yescharacteristic
793C23#38611yescharacteristic
794C23#38812yes—
795C23#38812yes—
796C23#38812yes—
797C23#38812yes—
798C23#39412yes—
799C23#39412yes—
800C23#39712yes—
801C23#39712yes—
802C23#39712yes—
803C23#39712yes—
804C23#39712yes—
805C23#39712yes—
806C23C2×C4×D411yescharacteristic
807C23C2×#12111yescharacteristic
808C23C2×#12311yescharacteristic
809C23C2×#12311yescharacteristic
810C23C2×#12411yescharacteristic
811C23C2×#12611yescharacteristic
812C23C2×#12611yescharacteristic
813Q8—24no—
814Q8—24no—
815Q8—44no—
816Q8—44no—
817Q8—42no—
818Q8—42no—
819D4—24no—
820D4—24no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—44no—
825D4—48no—
826D4—48no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—42no—
831C2×C4—24no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—48no—
841C2×C4—48no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—82no—
845C2×C4—82no—
846C2×C4—88no—
847C2×C4—84no—
848C2×C4—84no—
849C2×C4—84no—
850C2×C4—84no—
851C2×C4—84no—
852C2×C4—84no—
853C2×C4—84no—
854C2×C4#38112yes—
855C2×C4#38112yes—
856C2×C4#38112yes—
857C2×C4#38112yes—
858C2×C4#38611yescharacteristic
859C2×C4#38611yescharacteristic
860C2×C4#38611yescharacteristic
861C2×C4#38611yescharacteristic
862C2×C4#38612yes—
863C2×C4#38612yes—
864C2×C4#38612yes—
865C2×C4#38612yes—
866C2×C4#38812yes—
867C2×C4#38812yes—
868C2×C4#38812yes—
869C2×C4#38812yes—
870C2×C4#38812yes—
871C2×C4#38812yes—
872C2×C4#38812yes—
873C2×C4#38812yes—
874C2×C4#38812yes—
875C2×C4#38812yes—
876C2×C4#38812yes—
877C2×C4#38812yes—
878C2×C4#39412yes—
879C2×C4#39412yes—
880C2×C4#39412yes—
881C2×C4#39412yes—
882C2×C4#39412yes—
883C2×C4#39412yes—
884C2×C4#39412yes—
885C2×C4#39412yes—
886C2×C4#39412yes—
887C2×C4#39412yes—
888C2×C4#39412yes—
889C2×C4#39412yes—
890C2×C4#39412yes—
891C2×C4#39412yes—
892C2×C4#39712yes—
893C2×C4#39712yes—
894C2×C4#39712yes—
895C2×C4#39712yes—
896C2×C4#39712yes—
897C2×C4#39712yes—
898C2×C4#39712yes—
899C2×C4#39712yes—
900C2×C4#39712yes—
901C2×C4#39712yes—
902C2×C4C22×C22⋊C411yescharacteristic
903C2×C4C2×#11711yescharacteristic
904C2×C4C2×#11711yescharacteristic
905C2×C4C2×C4×D411yescharacteristic
906C2×C4C2×C4×D411yescharacteristic
907C2×C4C2×C4×D411yescharacteristic
908C2×C4C2×#12011yescharacteristic
909C2×C4C2×#12011yescharacteristic
910C2×C4C2×#12111yescharacteristic
911C2×C4C2×#12111yescharacteristic
912C2×C4C2×#12111yescharacteristic
913C2×C4C2×#12111yescharacteristic
914C2×C4C2×#12111yescharacteristic
915C2×C4C2×#12111yescharacteristic
916C2×C4C2×#12111yescharacteristic
917C2×C4C2×#12311yescharacteristic
918C2×C4C2×#12311yescharacteristic
919C2×C4C2×#12311yescharacteristic
920C2×C4C2×#12311yescharacteristic
921C2×C4C2×#12311yescharacteristic
922C2×C4C2×#12311yescharacteristic
923C2×C4C2×#12311yescharacteristic
924C2×C4C2×#12311yescharacteristic
925C2×C4C2×#12411yescharacteristic
926C2×C4C2×#12411yescharacteristic
927C2×C4C2×#12411yescharacteristic
928C2×C4C2×#12611yescharacteristic
929C2×C4C2×#12611yescharacteristic
930C8—44no—
931C8—44no—
932C8—44no—
933C8—44no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—44no—
963C22—44no—
964C22—44no—
965C22—88no—
966C22—84no—
967C22—84no—
968C22—88no—
969C22#144012yes—
970C22#144012yes—
971C22#144012yes—
972C22#144012yes—
973C22#190212yes—
974C22#190312yes—
975C22C2×#38611yescharacteristic
976C22C2×#38811yescharacteristic
977C22C2×#38811yescharacteristic
978C22C2×#39411yescharacteristic
979C22C2×#39711yescharacteristic
980C22C2×#39711yescharacteristic
981C22C2×#39711yescharacteristic
982C4—44no—
983C4—84no—
984C4—84no—
985C4#144012yes—
986C4#144012yes—
987C4#144012yes—
988C4#144012yes—
989C4C2×#38111yescharacteristic
990C4C2×#38611yescharacteristic
991C4C2×#38811yescharacteristic
992C4C2×#38811yescharacteristic
993C4C2×#39411yescharacteristic
994C4C2×#39411yescharacteristic
995C4C2×#39411yescharacteristic
996C4C2×#39711yescharacteristic
997C2—21no—
998C2—22no—
999C2—21no—
1000C2—21no—
1001C2—21no—
1002C2—21no—
1003C2—21no—
1004C2—22no—
1005C2—22no—
1006C2—84no—
1007C2#1118514yesdirect product factor
1008C2C2×#144011yescharacteristic
1009C2C2×#190211yescharacteristic
1010C2C2×#190311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#344C2semidirect
5. C22×#343C2semidirect
6. C2×#1736C2semidirect
7. C22×#338C2semidirect
8. #11185C2direct (N × H)
25. C2×#417C4semidirect
27. C22×#103C4semidirect
28. C22×#102C4semidirect
37. C2×#344C22semidirect
40. C2×#343C22semidirect
42. #1736C22semidirect
45. C2×#338C22semidirect
152. C2×#103C2×C4semidirect
155. C2×#102C2×C4semidirect
1007. C2#11185direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4212
C22×#4172
C2×#28792
C22×#3442
C22×#3432
C2×#17362
C22×#3382
#111852