Finite Group Databasebeta

← C2×#10778 #353363

Subgroups — C2×#10778 #353363

Order 512.

4022 conjugacy classes of subgroups.

The subgroup lattice has 1441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#568C211yesmaximal, characteristic
2C22×#421C211yesmaximal, characteristic
3C2×#2896C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C22×#344C211yesmaximal, characteristic, complemented
6C2×#1738C211yesmaximal, characteristic, complemented
7C2×#1733C211yesmaximal, characteristic, complemented
8#10778C218yesmaximal, direct product factor
9C23×#41C2211yescharacteristic
10C2×#568—22no—
11C2×#568—22no—
12C2×#568—22no—
13C2×#568—22no—
14C2×#568—22no—
15C2×#568—22no—
16C2×#568—22no—
17C2×#568—22no—
18C2×#568—22no—
19C2×#568—22no—
20C2×#568C414yescomplemented
21C2×#568C2214yes—
22C22×#131—22no—
23C22×#131C414yescomplemented
24C23×M16—22no—
25C23×M16C2211yescharacteristic
26C23×M16C2211yescharacteristic
27C23×M16C2211yescharacteristic
28C23×M16C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C2×#421—22no—
32C2×#421—22no—
33C2×#421—22no—
34C2×#421C414yescomplemented
35C2×#421C414yescomplemented
36C2×#421C2214yes—
37C22×#104—22no—
38#2896—22no—
39#2896—22no—
40#2896C414yescomplemented
41#2896C2214yes—
42C2×#417—22no—
43C2×#419C412yescomplemented
44C2×#418C412yescomplemented
45C2×#416—22no—
46C2×#344—22no—
47C2×#344—22no—
48C2×#344—22no—
49C2×#344—22no—
50C2×#344C2214yescomplemented
51C2×#344C2214yescomplemented
52#1738—22no—
53#1738C2214yescomplemented
54C2×#341—22no—
55#1733—22no—
56#1733C2214yescomplemented
57C2×#339—22no—
58C22×#41—21no—
59C22×#41—21no—
60C22×#41—21no—
61C22×#41—21no—
62C22×#41—21no—
63C22×#41—21no—
64C22×#41—21no—
65C22×#41—21no—
66C22×#41—21no—
67C22×#41—21no—
68C22×#41—21no—
69C22×#41—21no—
70C22×#41—21no—
71C22×#41—21no—
72C22×#41C2×C412yes—
73C22×#41C2×C412yes—
74C22×#41C2×C412yes—
75C22×#41C2×C412yes—
76C22×#41C2×C412yes—
77C22×#41D412yes—
78C22×#41D412yes—
79C22×#41D412yes—
80C22×#41D412yes—
81C22×#41D412yes—
82C22×#41D412yes—
83C22×#41Q812yes—
84C22×#41Q812yes—
85C22×#41C2312yes—
86C23×Q8C2×C411yescharacteristic
87C23×D4—21no—
88C23×D4C2×C411yescharacteristic
89C24×C4—21no—
90C24×C4C2311yescharacteristic
91#568—28no—
92#568—28no—
93#568—28no—
94#568—28no—
95#568—28no—
96#568—28no—
97#568—28no—
98#568—28no—
99#568—28no—
100#568—28no—
101#568—28no—
102#568—28no—
103#568—28no—
104#568—28no—
105#568—28no—
106#568—28no—
107C2×#131—28no—
108C2×#131—28no—
109C2×#131—28no—
110C2×#131—28no—
111C2×#131—28no—
112C2×#131—28no—
113C2×#131—28no—
114C2×#131—28no—
115C2×#131—28no—
116C2×#131—28no—
117C2×#131—28no—
118C2×#131C2×C4116yescomplemented
119C22×M16—28no—
120C22×M16—28no—
121C22×M16—28no—
122C22×M16—28no—
123C22×M16—21no—
124C22×M16—21no—
125C22×M16—21no—
126C22×M16—21no—
127C22×M16—21no—
128C22×M16—21no—
129C22×M16—21no—
130C22×M16—21no—
131C22×M16—21no—
132C22×M16—21no—
133C22×M16—21no—
134C22×M16—21no—
135C22×M16—21no—
136C22×M16—21no—
137C22×M16—21no—
138C22×M16—28no—
139C22×M16—28no—
140C22×M16—21no—
141C22×M16—21no—
142C22×M16—21no—
143C22×M16—21no—
144C22×M16—21no—
145C22×M16—21no—
146C22×M16—24no—
147C22×M16—21no—
148C22×M16—21no—
149C22×M16—21no—
150C22×M16—21no—
151C22×M16—21no—
152C22×M16—21no—
153C22×M16—21no—
154C22×M16—21no—
155C22×M16—21no—
156C22×M16—21no—
157C22×M16—21no—
158C22×M16—21no—
159C22×M16—21no—
160C22×M16—21no—
161C22×M16—21no—
162C22×M16—21no—
163C22×M16C2×C412yes—
164C22×M16C2×C412yes—
165C22×M16C2×C412yes—
166C22×M16C2×C412yes—
167C22×M16C2×C412yes—
168C22×M16C2×C412yes—
169C22×M16C2×C412yes—
170C22×M16D412yes—
171C22×M16D412yes—
172C22×M16D412yes—
173C22×M16D412yes—
174C22×M16D412yes—
175C22×M16D412yes—
176C22×M16D412yes—
177C22×M16D412yes—
178C22×M16C2312yes—
179C22×M16C2312yes—
180C22×M16C2312yes—
181C22×M16C2312yes—
182C23×C8—21no—
183C23×C8—24no—
184C23×C8—21no—
185C23×C8—21no—
186C23×C8C2×C412yes—
187C2×#117—21no—
188C2×#117—21no—
189C2×#117—21no—
190C2×#117—21no—
191C2×#117—21no—
192C2×#117—21no—
193C2×#117—21no—
194C2×#117—21no—
195C2×#117—21no—
196C2×#117—21no—
197C2×#117—21no—
198C2×#117—21no—
199C2×#117—21no—
200C2×#117—21no—
201C2×#117—21no—
202C2×#117—21no—
203C2×#117—21no—
204C2×#117—21no—
205C2×#117C2×C412yes—
206C2×#117C2×C412yes—
207C2×#117C2×C412yes—
208C2×#117C2×C412yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C22×C4⋊C4—21no—
212C22×C4⋊C4—21no—
213C22×C22⋊C4—21no—
214C22×C22⋊C4—21no—
215C22×C42—21no—
216C22×C42—21no—
217#421—28no—
218#421—28no—
219#421—28no—
220#421C2×C4116yescomplemented
221C2×#104—28no—
222C2×#104—28no—
223C2×#104—28no—
224#419—24no—
225#419C2×C418yescomplemented
226#418—24no—
227#418C2×C418yescomplemented
228#417—28no—
229#417—28no—
230#416—28no—
231#416—28no—
232C2×#103—24no—
233C2×#102—24no—
234#344—28no—
235#344—28no—
236#341—28no—
237#339—28no—
238C25—21no—
239C25#4111yescharacteristic
240C2×#41—22no—
241C2×#41—22no—
242C2×#41—22no—
243C2×#41—22no—
244C2×#41—22no—
245C2×#41—22no—
246C2×#41—22no—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41—22no—
250C2×#41—22no—
251C2×#41—22no—
252C2×#41—22no—
253C2×#41—22no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—22no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41C4214yes—
325C2×#41C4214yes—
326C2×#41C22⋊C414yes—
327C2×#41C22⋊C414yes—
328C2×#41C22⋊C414yes—
329C2×#41C22⋊C414yes—
330C2×#41C22⋊C414yes—
331C2×#41C22⋊C414yes—
332C2×#41C22⋊C414yes—
333C2×#41C22⋊C414yes—
334C2×#41C22⋊C414yes—
335C2×#41C22⋊C414yes—
336C2×#41C4⋊C414yes—
337C2×#41C4⋊C414yes—
338C2×#41C4⋊C414yes—
339C2×#41C4⋊C414yes—
340C2×#41C4⋊C414yes—
341C2×#41C4⋊C414yes—
342C2×#41C4⋊C414yes—
343C2×#41C4⋊C414yes—
344C2×#41C4⋊C414yes—
345C2×#41C4⋊C414yes—
346C2×#41C22×C414yes—
347C2×#41C22×C414yes—
348C2×#41C2×D414yes—
349C2×#41C2×D414yes—
350C2×#41C2×D414yes—
351C2×#41C2×Q814yes—
352C22×Q8—21no—
353C22×Q8—21no—
354C22×Q8—21no—
355C22×Q8—21no—
356C22×Q8—21no—
357C22×Q8—21no—
358C22×Q8—21no—
359C22×Q8C4212yes—
360C22×Q8C4212yes—
361C22×Q8C22⋊C412yes—
362C22×Q8C22⋊C412yes—
363C22×Q8C4⋊C412yes—
364C22×Q8C4⋊C412yes—
365C22×Q8C22×C412yes—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4C4212yes—
388C22×D4C4212yes—
389C22×D4C22⋊C412yes—
390C22×D4C22⋊C412yes—
391C22×D4C4⋊C412yes—
392C22×D4C4⋊C412yes—
393C22×D4C22×C412yes—
394C23×C4—21no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—41no—
410C23×C4—41no—
411C23×C4C22×C411yescharacteristic
412C23×C4C22×C411yescharacteristic
413C23×C4C22×C411yescharacteristic
414C23×C4C22×C411yescharacteristic
415C23×C4C22×C411yescharacteristic
416C23×C4C22×C411yescharacteristic
417C23×C4C2×D411yescharacteristic
418C23×C4C2×D411yescharacteristic
419C23×C4C2×D411yescharacteristic
420C23×C4C2×D411yescharacteristic
421C23×C4C2×D411yescharacteristic
422C23×C4C2×D411yescharacteristic
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D411yescharacteristic
425C23×C4C2×D411yescharacteristic
426C23×C4C2×D411yescharacteristic
427C23×C4C2×D411yescharacteristic
428C23×C4C2×D411yescharacteristic
429C23×C4C2×D411yescharacteristic
430C23×C4C2×D411yescharacteristic
431C23×C4C2×Q811yescharacteristic
432C23×C4C2×Q811yescharacteristic
433C23×C4#4111yescharacteristic
434C23×C4#4111yescharacteristic
435C23×C4#4111yescharacteristic
436C23×C4#4111yescharacteristic
437C23×C4#4111yescharacteristic
438C23×C4#4111yescharacteristic
439C23×C4#4111yescharacteristic
440C23×C4C2411yescharacteristic
441#131—232no—
442#131—232no—
443#131—232no—
444#131—232no—
445#131—232no—
446#131—232no—
447#131—232no—
448#131—232no—
449C2×M16—216no—
450C2×M16—216no—
451C2×M16—232no—
452C2×M16—232no—
453C2×M16—232no—
454C2×M16—232no—
455C2×M16—22no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—22no—
466C2×M16—22no—
467C2×M16—22no—
468C2×M16—22no—
469C2×M16—22no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—22no—
484C2×M16—22no—
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—22no—
488C2×M16—22no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—22no—
493C2×M16—22no—
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—22no—
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—216no—
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—22no—
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16C22⋊C414yes—
556C2×M16C22⋊C414yes—
557C2×M16C22⋊C414yes—
558C2×M16C22⋊C414yes—
559C2×M16C22⋊C414yes—
560C2×M16C22⋊C414yes—
561C2×M16C22×C414yes—
562C2×M16C22×C414yes—
563C2×M16C22×C414yes—
564C2×M16C2×D414yes—
565C2×M16C2×D414yes—
566C2×M16C2×D414yes—
567C2×M16C2×D414yes—
568C22×C8—216no—
569C22×C8—216no—
570C22×C8—22no—
571C22×C8—22no—
572C22×C8—22no—
573C22×C8—22no—
574C22×C8—22no—
575C22×C8—22no—
576C22×C8—22no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—22no—
581C22×C8—216no—
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—41no—
589C22×C8—41no—
590C22×C8—41no—
591C22×C8—41no—
592C22×C8—41no—
593C22×C8—41no—
594C22×C8—41no—
595C22×C8—41no—
596C22×C8C22⋊C414yes—
597C22×C8C22⋊C414yes—
598C22×C8C22×C414yes—
599#117—22no—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—22no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—41no—
627#117—41no—
628#117—41no—
629#117C22×C414yes—
630#117C22×C414yes—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—41no—
650C2×C22⋊C4—41no—
651C2×C22⋊C4—41no—
652C2×C22⋊C4—41no—
653C2×C22⋊C4—41no—
654C2×C22⋊C4—41no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—22no—
658C2×C42—22no—
659C2×C42—22no—
660C2×C42—22no—
661C2×C42—41no—
662C2×C42—41no—
663C2×C42—41no—
664C2×C42—41no—
665C2×C42—41no—
666C2×C42—41no—
667#104—232no—
668#103—216no—
669#102—216no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—82no—
678C24—84no—
679C24#11711yescharacteristic
680C24#11711yescharacteristic
681C24C4×D411yescharacteristic
682C24C4×D411yescharacteristic
683C24C4×D411yescharacteristic
684C24C4×D411yescharacteristic
685C24#12111yescharacteristic
686C24#12111yescharacteristic
687C24C22⋊Q811yescharacteristic
688C24C22⋊Q811yescharacteristic
689C24#12311yescharacteristic
690C24#12311yescharacteristic
691C24#12311yescharacteristic
692C24#12311yescharacteristic
693C24C2×#4111yescharacteristic
694#41—24no—
695#41—24no—
696#41—24no—
697#41—24no—
698#41—24no—
699#41—24no—
700#41—24no—
701#41—24no—
702#41—24no—
703#41—24no—
704#41—24no—
705#41—24no—
706#41—24no—
707#41—24no—
708#41—24no—
709#41—24no—
710#41—24no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—24no—
716#41—24no—
717#41—24no—
718#41—24no—
719#41—24no—
720#41—24no—
721#41—24no—
722#41—24no—
723#41—24no—
724#41—24no—
725#41—24no—
726#41—24no—
727#41—24no—
728#41—24no—
729#41—24no—
730#41—24no—
731#41—24no—
732#41—24no—
733#41—24no—
734#41—24no—
735#41—24no—
736#41—24no—
737#41—24no—
738#41—24no—
739#41—24no—
740#41—24no—
741#41—24no—
742#41—24no—
743#41—24no—
744#41—24no—
745#41—24no—
746#41—24no—
747#41—24no—
748#41—24no—
749#41—24no—
750#41#9518yes—
751#41#9518yes—
752#41#9518yes—
753#41#9518yes—
754#41C2×C22⋊C418yes—
755#41C2×C22⋊C418yes—
756#41C2×C4⋊C418yes—
757#41C2×C4⋊C418yes—
758C2×Q8—22no—
759C2×Q8—22no—
760C2×Q8—22no—
761C2×Q8—22no—
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8#9514yes—
780C2×Q8#9514yes—
781C2×Q8#9514yes—
782C2×Q8#9514yes—
783C2×Q8C2×C4214yes—
784C2×Q8C2×C22⋊C414yes—
785C2×Q8C2×C4⋊C414yes—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4#9514yes—
836C2×D4#9514yes—
837C2×D4#9514yes—
838C2×D4#9514yes—
839C2×D4C2×C4214yes—
840C2×D4C2×C22⋊C414yes—
841C2×D4C2×C4⋊C414yes—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4C2×C4211yescharacteristic
886C22×C4C2×C4211yescharacteristic
887C22×C4C2×C4211yescharacteristic
888C22×C4C2×C4211yescharacteristic
889C22×C4C2×C22⋊C411yescharacteristic
890C22×C4C2×C22⋊C411yescharacteristic
891C22×C4C2×C22⋊C411yescharacteristic
892C22×C4C2×C22⋊C411yescharacteristic
893C22×C4C2×C22⋊C411yescharacteristic
894C22×C4C2×C22⋊C411yescharacteristic
895C22×C4C2×C22⋊C411yescharacteristic
896C22×C4C2×C22⋊C411yescharacteristic
897C22×C4C2×C22⋊C411yescharacteristic
898C22×C4C2×C22⋊C411yescharacteristic
899C22×C4C2×C22⋊C411yescharacteristic
900C22×C4C2×C22⋊C411yescharacteristic
901C22×C4C2×C22⋊C411yescharacteristic
902C22×C4C2×C22⋊C411yescharacteristic
903C22×C4C2×C22⋊C411yescharacteristic
904C22×C4C2×C22⋊C411yescharacteristic
905C22×C4C2×C22⋊C411yescharacteristic
906C22×C4C2×C22⋊C411yescharacteristic
907C22×C4C2×C22⋊C411yescharacteristic
908C22×C4C2×C22⋊C411yescharacteristic
909C22×C4C2×C4⋊C411yescharacteristic
910C22×C4C2×C4⋊C411yescharacteristic
911C22×C4C2×C4⋊C411yescharacteristic
912C22×C4C2×C4⋊C411yescharacteristic
913C22×C4C2×C4⋊C411yescharacteristic
914C22×C4C2×C4⋊C411yescharacteristic
915C22×C4C2×C4⋊C411yescharacteristic
916C22×C4C2×C4⋊C411yescharacteristic
917C22×C4C2×C4⋊C411yescharacteristic
918C22×C4C2×C4⋊C411yescharacteristic
919C22×C4C2×C4⋊C411yescharacteristic
920C22×C4C2×C4⋊C411yescharacteristic
921C22×C4#11711yescharacteristic
922C22×C4#11711yescharacteristic
923C22×C4#11711yescharacteristic
924C22×C4#11711yescharacteristic
925C22×C4#11711yescharacteristic
926C22×C4#11711yescharacteristic
927C22×C4C4×D411yescharacteristic
928C22×C4C4×D411yescharacteristic
929C22×C4C4×D411yescharacteristic
930C22×C4C4×D411yescharacteristic
931C22×C4C4×D411yescharacteristic
932C22×C4C4×D411yescharacteristic
933C22×C4C4×D411yescharacteristic
934C22×C4C4×D411yescharacteristic
935C22×C4C4×D411yescharacteristic
936C22×C4C4×D411yescharacteristic
937C22×C4C4×D411yescharacteristic
938C22×C4C4×D411yescharacteristic
939C22×C4C4×D411yescharacteristic
940C22×C4C4×D411yescharacteristic
941C22×C4C4×D411yescharacteristic
942C22×C4C4×D411yescharacteristic
943C22×C4C4×D411yescharacteristic
944C22×C4C4×D411yescharacteristic
945C22×C4C4×D411yescharacteristic
946C22×C4C4×D411yescharacteristic
947C22×C4C4×D411yescharacteristic
948C22×C4C4×D411yescharacteristic
949C22×C4C4×D411yescharacteristic
950C22×C4C4×D411yescharacteristic
951C22×C4C4×D411yescharacteristic
952C22×C4C4×D411yescharacteristic
953C22×C4C4×D411yescharacteristic
954C22×C4C4×D411yescharacteristic
955C22×C4#12011yescharacteristic
956C22×C4#12011yescharacteristic
957C22×C4#12011yescharacteristic
958C22×C4#12011yescharacteristic
959C22×C4#12011yescharacteristic
960C22×C4#12011yescharacteristic
961C22×C4#12011yescharacteristic
962C22×C4#12011yescharacteristic
963C22×C4#12011yescharacteristic
964C22×C4#12011yescharacteristic
965C22×C4#12011yescharacteristic
966C22×C4#12011yescharacteristic
967C22×C4#12011yescharacteristic
968C22×C4#12011yescharacteristic
969C22×C4#12011yescharacteristic
970C22×C4#12011yescharacteristic
971C22×C4#12111yescharacteristic
972C22×C4#12111yescharacteristic
973C22×C4#12111yescharacteristic
974C22×C4#12111yescharacteristic
975C22×C4#12111yescharacteristic
976C22×C4#12111yescharacteristic
977C22×C4#12111yescharacteristic
978C22×C4#12111yescharacteristic
979C22×C4#12111yescharacteristic
980C22×C4#12111yescharacteristic
981C22×C4#12111yescharacteristic
982C22×C4#12111yescharacteristic
983C22×C4#12111yescharacteristic
984C22×C4#12111yescharacteristic
985C22×C4C22⋊Q811yescharacteristic
986C22×C4C22⋊Q811yescharacteristic
987C22×C4C22⋊Q811yescharacteristic
988C22×C4C22⋊Q811yescharacteristic
989C22×C4C22⋊Q811yescharacteristic
990C22×C4C22⋊Q811yescharacteristic
991C22×C4C22⋊Q811yescharacteristic
992C22×C4C22⋊Q811yescharacteristic
993C22×C4C22⋊Q811yescharacteristic
994C22×C4C22⋊Q811yescharacteristic
995C22×C4C22⋊Q811yescharacteristic
996C22×C4C22⋊Q811yescharacteristic
997C22×C4C22⋊Q811yescharacteristic
998C22×C4C22⋊Q811yescharacteristic
999C22×C4#12311yescharacteristic
1000C22×C4#12311yescharacteristic
1001C22×C4#12311yescharacteristic
1002C22×C4#12311yescharacteristic
1003C22×C4#12311yescharacteristic
1004C22×C4#12311yescharacteristic
1005C22×C4#12311yescharacteristic
1006C22×C4#12311yescharacteristic
1007C22×C4#12311yescharacteristic
1008C22×C4#12311yescharacteristic
1009C22×C4#12311yescharacteristic
1010C22×C4#12311yescharacteristic
1011C22×C4C23×C411yescharacteristic
1012C22×C4C23×C411yescharacteristic
1013C22×C4C23×C411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C22×D411yescharacteristic
1018C22×C4C22×D411yescharacteristic
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C22×Q811yescharacteristic
1022C22×C4C2×#4111yescharacteristic
1023C22×C4C2×#4111yescharacteristic
1024C22×C4C2×#4111yescharacteristic
1025M16—264no—
1026M16—24no—
1027M16—24no—
1028M16—24no—
1029M16—24no—
1030M16—24no—
1031M16—24no—
1032M16—24no—
1033M16—24no—
1034M16—24no—
1035M16—24no—
1036M16—24no—
1037M16—24no—
1038M16—24no—
1039M16—24no—
1040M16—24no—
1041M16—24no—
1042M16—24no—
1043M16—24no—
1044M16—24no—
1045M16—42no—
1046M16—42no—
1047M16—42no—
1048M16—42no—
1049M16—42no—
1050M16—42no—
1051M16—42no—
1052M16—42no—
1053M16—42no—
1054M16—42no—
1055M16—42no—
1056M16—42no—
1057M16C2×C22⋊C418yes—
1058C2×C8—264no—
1059C2×C8—24no—
1060C2×C8—24no—
1061C2×C8—24no—
1062C2×C8—24no—
1063C2×C8—24no—
1064C2×C8—24no—
1065C2×C8—24no—
1066C2×C8—24no—
1067C2×C8—24no—
1068C2×C8—24no—
1069C2×C8—24no—
1070C2×C8—24no—
1071C2×C8—24no—
1072C2×C8—24no—
1073C2×C8—24no—
1074C2×C8—42no—
1075C2×C8—42no—
1076C2×C8—42no—
1077C2×C8—42no—
1078C2×C8—42no—
1079C2×C8—42no—
1080C2×C8—42no—
1081C2×C8—42no—
1082C2×C8—42no—
1083C2×C8—42no—
1084C2×C8—42no—
1085C2×C8—42no—
1086C2×C8C2×C22⋊C418yes—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C22⋊C4—24no—
1096C22⋊C4—24no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C42—24no—
1104C42—24no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C23—24no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—42no—
1125C23—48no—
1126C23—84no—
1127C23—84no—
1128C23—81no—
1129C23—81no—
1130C23—81no—
1131C23—81no—
1132C23—81no—
1133C23—81no—
1134C23—81no—
1135C23—81no—
1136C23—84no—
1137C23—84no—
1138C23—84no—
1139C23—84no—
1140C23C4×C22⋊C411yescharacteristic
1141C23C4×C22⋊C411yescharacteristic
1142C23C4×C22⋊C411yescharacteristic
1143C23C4×C22⋊C411yescharacteristic
1144C23#38011yescharacteristic
1145C23#38011yescharacteristic
1146C23#38011yescharacteristic
1147C23#38011yescharacteristic
1148C23#38111yescharacteristic
1149C23#38111yescharacteristic
1150C23#38111yescharacteristic
1151C23#38111yescharacteristic
1152C23#38511yescharacteristic
1153C23#38511yescharacteristic
1154C23#38511yescharacteristic
1155C23#38511yescharacteristic
1156C23#38511yescharacteristic
1157C23#38511yescharacteristic
1158C23#38511yescharacteristic
1159C23#38511yescharacteristic
1160C23#38611yescharacteristic
1161C23#38611yescharacteristic
1162C23#38611yescharacteristic
1163C23#38611yescharacteristic
1164C23#38611yescharacteristic
1165C23#38611yescharacteristic
1166C23#38611yescharacteristic
1167C23#38611yescharacteristic
1168C23C2×#11711yescharacteristic
1169C23C2×C4×D411yescharacteristic
1170C23C2×C4×D411yescharacteristic
1171C23C2×#12111yescharacteristic
1172C23C2×C22⋊Q811yescharacteristic
1173C23C2×#12311yescharacteristic
1174C23C2×#12311yescharacteristic
1175Q8—24no—
1176Q8—24no—
1177Q8—24no—
1178Q8—24no—
1179Q8—24no—
1180Q8—24no—
1181Q8—24no—
1182Q8C2×#9518yes—
1183D4—28no—
1184D4—28no—
1185D4—28no—
1186D4—28no—
1187D4—28no—
1188D4—28no—
1189D4—28no—
1190D4—28no—
1191D4—24no—
1192D4—24no—
1193D4—24no—
1194D4—24no—
1195D4—24no—
1196D4—24no—
1197D4—24no—
1198D4C2×#9518yes—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—28no—
1207C2×C4—28no—
1208C2×C4—28no—
1209C2×C4—28no—
1210C2×C4—28no—
1211C2×C4—28no—
1212C2×C4—28no—
1213C2×C4—28no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—84no—
1217C2×C4—84no—
1218C2×C4—84no—
1219C2×C4—84no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4C2×#9511yescharacteristic
1223C2×C4C2×#9511yescharacteristic
1224C2×C4C2×#9511yescharacteristic
1225C2×C4C2×#9511yescharacteristic
1226C2×C4C2×#9511yescharacteristic
1227C2×C4C2×#9511yescharacteristic
1228C2×C4C2×#9511yescharacteristic
1229C2×C4C2×#9511yescharacteristic
1230C2×C4C4×C22⋊C411yescharacteristic
1231C2×C4C4×C22⋊C411yescharacteristic
1232C2×C4C4×C22⋊C411yescharacteristic
1233C2×C4C4×C22⋊C411yescharacteristic
1234C2×C4C4×C22⋊C411yescharacteristic
1235C2×C4C4×C22⋊C411yescharacteristic
1236C2×C4C4×C22⋊C411yescharacteristic
1237C2×C4C4×C22⋊C411yescharacteristic
1238C2×C4C4×C22⋊C411yescharacteristic
1239C2×C4C4×C22⋊C411yescharacteristic
1240C2×C4C4×C22⋊C411yescharacteristic
1241C2×C4C4×C22⋊C411yescharacteristic
1242C2×C4#37911yescharacteristic
1243C2×C4#37911yescharacteristic
1244C2×C4#37911yescharacteristic
1245C2×C4#37911yescharacteristic
1246C2×C4#37911yescharacteristic
1247C2×C4#37911yescharacteristic
1248C2×C4#37911yescharacteristic
1249C2×C4#37911yescharacteristic
1250C2×C4#38011yescharacteristic
1251C2×C4#38011yescharacteristic
1252C2×C4#38011yescharacteristic
1253C2×C4#38011yescharacteristic
1254C2×C4#38011yescharacteristic
1255C2×C4#38011yescharacteristic
1256C2×C4#38011yescharacteristic
1257C2×C4#38011yescharacteristic
1258C2×C4#38011yescharacteristic
1259C2×C4#38011yescharacteristic
1260C2×C4#38011yescharacteristic
1261C2×C4#38011yescharacteristic
1262C2×C4#38111yescharacteristic
1263C2×C4#38111yescharacteristic
1264C2×C4#38111yescharacteristic
1265C2×C4#38111yescharacteristic
1266C2×C4#38511yescharacteristic
1267C2×C4#38511yescharacteristic
1268C2×C4#38511yescharacteristic
1269C2×C4#38511yescharacteristic
1270C2×C4#38511yescharacteristic
1271C2×C4#38511yescharacteristic
1272C2×C4#38511yescharacteristic
1273C2×C4#38511yescharacteristic
1274C2×C4#38511yescharacteristic
1275C2×C4#38511yescharacteristic
1276C2×C4#38511yescharacteristic
1277C2×C4#38511yescharacteristic
1278C2×C4#38511yescharacteristic
1279C2×C4#38511yescharacteristic
1280C2×C4#38511yescharacteristic
1281C2×C4#38511yescharacteristic
1282C2×C4#38511yescharacteristic
1283C2×C4#38511yescharacteristic
1284C2×C4#38511yescharacteristic
1285C2×C4#38511yescharacteristic
1286C2×C4#38511yescharacteristic
1287C2×C4#38511yescharacteristic
1288C2×C4#38511yescharacteristic
1289C2×C4#38511yescharacteristic
1290C2×C4#38611yescharacteristic
1291C2×C4#38611yescharacteristic
1292C2×C4#38611yescharacteristic
1293C2×C4#38611yescharacteristic
1294C2×C4#38611yescharacteristic
1295C2×C4#38611yescharacteristic
1296C2×C4#38611yescharacteristic
1297C2×C4#38611yescharacteristic
1298C2×C4#38611yescharacteristic
1299C2×C4#38611yescharacteristic
1300C2×C4#38611yescharacteristic
1301C2×C4#38611yescharacteristic
1302C2×C4#38611yescharacteristic
1303C2×C4#38611yescharacteristic
1304C2×C4#38611yescharacteristic
1305C2×C4#38611yescharacteristic
1306C2×C4#38611yescharacteristic
1307C2×C4#38611yescharacteristic
1308C2×C4#38611yescharacteristic
1309C2×C4#38611yescharacteristic
1310C2×C4#38611yescharacteristic
1311C2×C4#38611yescharacteristic
1312C2×C4#38611yescharacteristic
1313C2×C4#38611yescharacteristic
1314C2×C4C22×C4211yescharacteristic
1315C2×C4C22×C22⋊C411yescharacteristic
1316C2×C4C22×C22⋊C411yescharacteristic
1317C2×C4C22×C22⋊C411yescharacteristic
1318C2×C4C22×C22⋊C411yescharacteristic
1319C2×C4C22×C22⋊C411yescharacteristic
1320C2×C4C22×C4⋊C411yescharacteristic
1321C2×C4C22×C4⋊C411yescharacteristic
1322C2×C4C22×C4⋊C411yescharacteristic
1323C2×C4C2×#11711yescharacteristic
1324C2×C4C2×C4×D411yescharacteristic
1325C2×C4C2×C4×D411yescharacteristic
1326C2×C4C2×C4×D411yescharacteristic
1327C2×C4C2×C4×D411yescharacteristic
1328C2×C4C2×C4×D411yescharacteristic
1329C2×C4C2×C4×D411yescharacteristic
1330C2×C4C2×#12011yescharacteristic
1331C2×C4C2×#12011yescharacteristic
1332C2×C4C2×#12011yescharacteristic
1333C2×C4C2×#12011yescharacteristic
1334C2×C4C2×#12111yescharacteristic
1335C2×C4C2×#12111yescharacteristic
1336C2×C4C2×#12111yescharacteristic
1337C2×C4C2×C22⋊Q811yescharacteristic
1338C2×C4C2×C22⋊Q811yescharacteristic
1339C2×C4C2×C22⋊Q811yescharacteristic
1340C2×C4C2×#12311yescharacteristic
1341C2×C4C2×#12311yescharacteristic
1342C8—28no—
1343C8—28no—
1344C8—44no—
1345C8—44no—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—28no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—41no—
1374C22—41no—
1375C22—41no—
1376C22—41no—
1377C22—41no—
1378C22—41no—
1379C22—41no—
1380C22—41no—
1381C22—41no—
1382C22—48no—
1383C22—48no—
1384C22—48no—
1385C22—84no—
1386C22—84no—
1387C22—84no—
1388C22—84no—
1389C22C22⋊#9511yescharacteristic
1390C22C22⋊#9511yescharacteristic
1391C22C22⋊#9511yescharacteristic
1392C22C22⋊#9511yescharacteristic
1393C22C22⋊#9511yescharacteristic
1394C22C22⋊#9511yescharacteristic
1395C22C22⋊#9511yescharacteristic
1396C22C22⋊#9511yescharacteristic
1397C22C2×C4×C22⋊C411yescharacteristic
1398C22C2×#38011yescharacteristic
1399C22C2×#38111yescharacteristic
1400C22C2×#38511yescharacteristic
1401C22C2×#38511yescharacteristic
1402C22C2×#38611yescharacteristic
1403C22C2×#38611yescharacteristic
1404C4—28no—
1405C4—84no—
1406C4—84no—
1407C4C22⋊#9511yescharacteristic
1408C4C22⋊#9511yescharacteristic
1409C4C22⋊#9511yescharacteristic
1410C4C22⋊#9511yescharacteristic
1411C4C22⋊#9511yescharacteristic
1412C4C22⋊#9511yescharacteristic
1413C4C22⋊#9511yescharacteristic
1414C4C22⋊#9511yescharacteristic
1415C4C22×#9511yescharacteristic
1416C4C2×C4×C22⋊C411yescharacteristic
1417C4C2×#37911yescharacteristic
1418C4C2×#38011yescharacteristic
1419C4C2×#38511yescharacteristic
1420C4C2×#38511yescharacteristic
1421C4C2×#38611yescharacteristic
1422C4C2×#38611yescharacteristic
1423C2—21no—
1424C2—21no—
1425C2—21no—
1426C2—21no—
1427C2—21no—
1428C2—21no—
1429C2—21no—
1430C2—21no—
1431C2—21no—
1432C2—21no—
1433C2—21no—
1434C2—21no—
1435C2—21no—
1436C2—21no—
1437C2—48no—
1438C2#1077812yesdirect product factor
1439C2C2×C22⋊#9511yescharacteristic
subgroupG/H
centerC2×C4#379
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC22C22⋊#95
prime radicalC23×#41C22
LCSG ▷ C2×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
4. C22×#344C2semidirect
5. C22×#344C2semidirect
6. C2×#1738C2semidirect
7. C2×#1733C2semidirect
8. #10778C2direct (N × H)
20. C2×#568C4semidirect
23. C22×#131C4semidirect
34. C2×#421C4semidirect
35. C2×#421C4semidirect
40. #2896C4semidirect
43. C2×#419C4semidirect
44. C2×#418C4semidirect
50. C2×#344C22semidirect
51. C2×#344C22semidirect
53. #1738C22semidirect
56. #1733C22semidirect
118. C2×#131C2×C4semidirect
220. #421C2×C4semidirect
225. #419C2×C4semidirect
227. #418C2×C4semidirect
1438. C2#10778direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5682
C22×#4212
C2×#28962
C22×#3442
C2×#17382
C2×#17332
#107782