Finite Group Databasebeta

← #123605

Subgroups — #123605

Order 512.

3118 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#418C211yesmaximal, characteristic
2C22×#418C211yesmaximal, characteristic
3C2×#2309C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C2×#1740C211yesmaximal, characteristic, complemented
6#20347C211yesmaximal, characteristic, complemented
7C2×#1733C211yesmaximal, characteristic, complemented
8C24×D4C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C2×#418—22no—
16C2×#418—22no—
17C2×#418—22no—
18C2×#418—22no—
19C2×#418—22no—
20C2×#418—22no—
21C2×#418—22no—
22C2×#418—22no—
23C2×#418—22no—
24C2×#418—22no—
25C2×#418C414yescomplemented
26C2×#418C414yescomplemented
27C22×#102—22no—
28C22×#102—22no—
29#2309—22no—
30#2309—22no—
31#2309—22no—
32#2309C414yescomplemented
33C2×#390—22no—
34C2×#390—22no—
35C2×#379—22no—
36C2×#344—22no—
37C2×#344—22no—
38C2×#344—22no—
39#1740—22no—
40#1740—22no—
41C2×#342—22no—
42#1736—22no—
43#1736—22no—
44#1735—22no—
45#1733—22no—
46#1733—22no—
47C2×#339—22no—
48C26—21no—
49C23×D4—21no—
50C23×D4—21no—
51C23×D4—21no—
52C23×D4—21no—
53C23×D4—21no—
54C23×D4—21no—
55C23×D4—21no—
56C23×D4—21no—
57C23×D4—21no—
58C23×D4—21no—
59C23×D4—21no—
60C23×D4—21no—
61C23×D4—21no—
62C23×D4—21no—
63C23×D4—21no—
64C23×D4—21no—
65C23×D4—21no—
66C23×D4—21no—
67C23×D4—21no—
68C23×D4—21no—
69C23×D4—21no—
70C23×D4—21no—
71C23×D4—21no—
72C23×D4C2×C412yes—
73C23×D4C2×C412yes—
74C23×D4C2×C412yes—
75C23×D4D412yes—
76C23×D4D412yes—
77C23×D4D412yes—
78C23×D4Q812yes—
79C24×C4C2311yescharacteristic
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16—21no—
89C22×M16—21no—
90C22×M16—21no—
91C22×M16—21no—
92C22×M16—21no—
93C22×M16—21no—
94C22×M16—21no—
95C22×M16—21no—
96C22×M16—21no—
97C22×M16—21no—
98C22×M16—21no—
99C22×M16—21no—
100C22×M16—21no—
101C22×M16—21no—
102C22×M16—21no—
103C22×M16C2×C412yes—
104C22×M16C2×C412yes—
105C22×M16D412yes—
106C22×M16D412yes—
107C22×M16D412yes—
108C23×C8—21no—
109C23×C8D412yes—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—21no—
131C2×#117—21no—
132C2×#117—21no—
133C2×#117—21no—
134C2×#117—21no—
135C2×#117—21no—
136C2×#117—21no—
137C2×#117—21no—
138C2×#117—21no—
139C2×#117—21no—
140C2×#117—21no—
141C2×#117—21no—
142C2×#117—21no—
143C2×#117—21no—
144C2×#117—21no—
145C2×#117—21no—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—21no—
149C2×#117C2×C412yes—
150C2×#117C2×C412yes—
151C2×#117C2×C412yes—
152C2×#117C2×C412yes—
153C2×#117D412yes—
154C2×#117D412yes—
155C2×#117D412yes—
156C2×#117D412yes—
157C2×#117D412yes—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4D412yes—
161C22×C4⋊C4D412yes—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—28no—
166C22×C22⋊C4D412yes—
167C22×C42—21no—
168C22×C42—21no—
169C22×C42—21no—
170C22×C42—21no—
171#418—28no—
172#418—28no—
173#418—28no—
174#418—28no—
175#418—28no—
176#418—28no—
177#418—28no—
178#418—28no—
179C2×#102—28no—
180C2×#102—28no—
181C2×#102—28no—
182C2×#102—28no—
183C2×#102—28no—
184C2×#102—28no—
185#390—28no—
186#390—28no—
187#390—28no—
188#390—28no—
189#379—28no—
190#379—28no—
191#344—28no—
192#342—28no—
193#340—28no—
194#339—28no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—41no—
203C25—41no—
204C25—41no—
205C25—41no—
206C25—41no—
207C25—41no—
208C25—41no—
209C25—41no—
210C25—88no—
211C25C2×D411yescharacteristic
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
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—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
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—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—41no—
290C22×D4—41no—
291C22×D4—41no—
292C22×D4—41no—
293C22×D4—41no—
294C22×D4—41no—
295C22×D4—41no—
296C22×D4—41no—
297C22×D4—41no—
298C22×D4—41no—
299C22×D4—41no—
300C22×D4—41no—
301C22×D4—41no—
302C22×D4—41no—
303C22×D4—41no—
304C22×D4—41no—
305C22×D4—41no—
306C22×D4—41no—
307C22×D4—41no—
308C22×D4—41no—
309C22×D4—41no—
310C22×D4—41no—
311C22×D4—41no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4—41no—
315C22×D4—41no—
316C22×D4—41no—
317C22×D4—41no—
318C22×D4—41no—
319C22×D4—41no—
320C22×D4—41no—
321C22×D4—41no—
322C22×D4—41no—
323C22×D4—41no—
324C22×D4—41no—
325C22×D4—41no—
326C22×D4—41no—
327C22×D4—41no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4C4214yes—
346C22×D4C22⋊C414yes—
347C22×D4C22⋊C414yes—
348C22×D4C22⋊C414yes—
349C22×D4C4⋊C414yes—
350C22×D4C4⋊C414yes—
351C22×D4C4⋊C414yes—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—41no—
356C23×C4C22×C411yescharacteristic
357C23×C4C22×C411yescharacteristic
358C23×C4C22×C411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2×Q811yescharacteristic
374C23×C4#4111yescharacteristic
375C23×C4#4111yescharacteristic
376C23×C4#4111yescharacteristic
377C23×C4#4111yescharacteristic
378C23×C4#4111yescharacteristic
379C23×C4#4111yescharacteristic
380C23×C4#4111yescharacteristic
381C23×C4#4111yescharacteristic
382C23×C4#4111yescharacteristic
383C23×C4#4111yescharacteristic
384C23×C4#4111yescharacteristic
385C23×C4#4111yescharacteristic
386C2×M16—22no—
387C2×M16—22no—
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—22no—
394C2×M16—22no—
395C2×M16—22no—
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—22no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—41no—
414C2×M16—41no—
415C2×M16—41no—
416C2×M16—41no—
417C2×M16—41no—
418C2×M16—41no—
419C2×M16—41no—
420C2×M16—41no—
421C2×M16—41no—
422C2×M16—41no—
423C2×M16—41no—
424C2×M16—41no—
425C2×M16—41no—
426C2×M16—41no—
427C2×M16—41no—
428C2×M16—41no—
429C2×M16—41no—
430C2×M16—41no—
431C2×M16—41no—
432C2×M16—41no—
433C2×M16—41no—
434C2×M16—41no—
435C2×M16—41no—
436C2×M16—41no—
437C2×M16—41no—
438C2×M16—41no—
439C2×M16—41no—
440C2×M16—41no—
441C2×M16C22⋊C414yescomplemented
442C22×C8—22no—
443C22×C8—22no—
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—22no—
447C22×C8—22no—
448C22×C8—22no—
449C22×C8—22no—
450C22×C8—22no—
451C22×C8—41no—
452C22×C8—41no—
453C22×C8—41no—
454C22×C8—41no—
455C22×C8C22⋊C414yescomplemented
456#117—22no—
457#117—22no—
458#117—22no—
459#117—22no—
460#117—22no—
461#117—22no—
462#117—22no—
463#117—22no—
464#117—22no—
465#117—22no—
466#117—22no—
467#117—22no—
468#117—22no—
469#117—22no—
470#117—22no—
471#117—22no—
472#117—22no—
473#117—22no—
474#117—22no—
475#117—22no—
476#117—22no—
477#117—22no—
478#117—22no—
479#117—22no—
480#117—22no—
481#117—22no—
482#117—22no—
483#117—22no—
484#117—22no—
485#117—22no—
486#117—22no—
487#117—22no—
488#117—22no—
489#117—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494#117—41no—
495#117—41no—
496#117—41no—
497#117—41no—
498#117—41no—
499#117—41no—
500#117—41no—
501#117—41no—
502#117—41no—
503#117—41no—
504#117—41no—
505#117—41no—
506#117—41no—
507#117—41no—
508#117—41no—
509#117—41no—
510#117—41no—
511#117—41no—
512#117—41no—
513#117—41no—
514#117—41no—
515#117—41no—
516#117—41no—
517#117—41no—
518#117—41no—
519#117C22⋊C414yescomplemented
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4C22⋊C414yes—
543C2×C4⋊C4C22⋊C414yescomplemented
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—232no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—816no—
569C2×C22⋊C4C22⋊C414yes—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—41no—
580C2×C42—41no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—41no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—41no—
589C2×C42—41no—
590C2×C42—41no—
591C2×C42—41no—
592C2×C42—41no—
593C2×C42—41no—
594#102—232no—
595#102—232no—
596C24—24no—
597C24—24no—
598C24—24no—
599C24—24no—
600C24—24no—
601C24—24no—
602C24—24no—
603C24—44no—
604C24—416no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—42no—
620C24—42no—
621C24—42no—
622C24—42no—
623C24—42no—
624C24—42no—
625C24—42no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—88no—
634C24—88no—
635C24—88no—
636C24—88no—
637C24—88no—
638C24—88no—
639C24—88no—
640C24—88no—
641C24—88no—
642C24—88no—
643C24—88no—
644C24—88no—
645C24—88no—
646C24—88no—
647C24C2×C22⋊C411yescharacteristic
648C24C4×D411yescharacteristic
649C24C4×D411yescharacteristic
650C24#12011yescharacteristic
651C24#12011yescharacteristic
652C24#12011yescharacteristic
653C24#12111yescharacteristic
654C24#12111yescharacteristic
655C24#12111yescharacteristic
656C24#12111yescharacteristic
657C24#12111yescharacteristic
658C24C22⋊Q811yescharacteristic
659C24#12311yescharacteristic
660C24#12411yescharacteristic
661C24#12711yescharacteristic
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—42no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4#9518yes—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—84no—
797C22×C4—84no—
798C22×C4C2×C4211yescharacteristic
799C22×C4C2×C22⋊C411yescharacteristic
800C22×C4C2×C22⋊C411yescharacteristic
801C22×C4C2×C22⋊C411yescharacteristic
802C22×C4C2×C22⋊C411yescharacteristic
803C22×C4C2×C22⋊C411yescharacteristic
804C22×C4C2×C22⋊C411yescharacteristic
805C22×C4C2×C22⋊C411yescharacteristic
806C22×C4C2×C22⋊C411yescharacteristic
807C22×C4C2×C4⋊C411yescharacteristic
808C22×C4C2×C4⋊C411yescharacteristic
809C22×C4C2×C4⋊C411yescharacteristic
810C22×C4#11711yescharacteristic
811C22×C4#11711yescharacteristic
812C22×C4#11711yescharacteristic
813C22×C4#11711yescharacteristic
814C22×C4#11711yescharacteristic
815C22×C4#11711yescharacteristic
816C22×C4C4×D411yescharacteristic
817C22×C4C4×D411yescharacteristic
818C22×C4C4×D411yescharacteristic
819C22×C4C4×D411yescharacteristic
820C22×C4C4×D411yescharacteristic
821C22×C4C4×D411yescharacteristic
822C22×C4C4×D411yescharacteristic
823C22×C4C4×D411yescharacteristic
824C22×C4C4×D411yescharacteristic
825C22×C4C4×D411yescharacteristic
826C22×C4C4×D411yescharacteristic
827C22×C4C4×D411yescharacteristic
828C22×C4C4×D411yescharacteristic
829C22×C4C4×D411yescharacteristic
830C22×C4C4×D411yescharacteristic
831C22×C4C4×D411yescharacteristic
832C22×C4C4×D411yescharacteristic
833C22×C4C4×D411yescharacteristic
834C22×C4C4×D411yescharacteristic
835C22×C4C4×D411yescharacteristic
836C22×C4C4×D411yescharacteristic
837C22×C4C4×D411yescharacteristic
838C22×C4#12011yescharacteristic
839C22×C4#12011yescharacteristic
840C22×C4#12011yescharacteristic
841C22×C4#12011yescharacteristic
842C22×C4#12011yescharacteristic
843C22×C4#12011yescharacteristic
844C22×C4#12011yescharacteristic
845C22×C4#12011yescharacteristic
846C22×C4#12011yescharacteristic
847C22×C4#12011yescharacteristic
848C22×C4#12011yescharacteristic
849C22×C4#12011yescharacteristic
850C22×C4#12011yescharacteristic
851C22×C4#12111yescharacteristic
852C22×C4#12111yescharacteristic
853C22×C4#12111yescharacteristic
854C22×C4#12111yescharacteristic
855C22×C4#12111yescharacteristic
856C22×C4#12111yescharacteristic
857C22×C4#12111yescharacteristic
858C22×C4#12111yescharacteristic
859C22×C4#12111yescharacteristic
860C22×C4#12111yescharacteristic
861C22×C4#12111yescharacteristic
862C22×C4#12111yescharacteristic
863C22×C4#12111yescharacteristic
864C22×C4#12111yescharacteristic
865C22×C4#12111yescharacteristic
866C22×C4#12111yescharacteristic
867C22×C4#12111yescharacteristic
868C22×C4#12111yescharacteristic
869C22×C4#12111yescharacteristic
870C22×C4#12111yescharacteristic
871C22×C4#12111yescharacteristic
872C22×C4#12111yescharacteristic
873C22×C4#12111yescharacteristic
874C22×C4#12111yescharacteristic
875C22×C4#12111yescharacteristic
876C22×C4#12111yescharacteristic
877C22×C4#12111yescharacteristic
878C22×C4#12111yescharacteristic
879C22×C4#12111yescharacteristic
880C22×C4#12111yescharacteristic
881C22×C4#12111yescharacteristic
882C22×C4C22⋊Q811yescharacteristic
883C22×C4C22⋊Q811yescharacteristic
884C22×C4C22⋊Q811yescharacteristic
885C22×C4C22⋊Q811yescharacteristic
886C22×C4C22⋊Q811yescharacteristic
887C22×C4C22⋊Q811yescharacteristic
888C22×C4C22⋊Q811yescharacteristic
889C22×C4C22⋊Q811yescharacteristic
890C22×C4C22⋊Q811yescharacteristic
891C22×C4C22⋊Q811yescharacteristic
892C22×C4C22⋊Q811yescharacteristic
893C22×C4#12311yescharacteristic
894C22×C4#12311yescharacteristic
895C22×C4#12311yescharacteristic
896C22×C4#12311yescharacteristic
897C22×C4#12311yescharacteristic
898C22×C4#12311yescharacteristic
899C22×C4#12311yescharacteristic
900C22×C4#12311yescharacteristic
901C22×C4#12311yescharacteristic
902C22×C4#12311yescharacteristic
903C22×C4#12311yescharacteristic
904C22×C4#12311yescharacteristic
905C22×C4#12311yescharacteristic
906C22×C4#12311yescharacteristic
907C22×C4#12311yescharacteristic
908C22×C4#12311yescharacteristic
909C22×C4#12311yescharacteristic
910C22×C4#12311yescharacteristic
911C22×C4#12311yescharacteristic
912C22×C4#12311yescharacteristic
913C22×C4#12311yescharacteristic
914C22×C4#12311yescharacteristic
915C22×C4#12311yescharacteristic
916C22×C4#12411yescharacteristic
917C22×C4#12411yescharacteristic
918C22×C4#12411yescharacteristic
919C22×C4#12411yescharacteristic
920C22×C4#12411yescharacteristic
921C22×C4#12411yescharacteristic
922C22×C4#12411yescharacteristic
923C22×C4#12411yescharacteristic
924C22×C4#12411yescharacteristic
925C22×C4#12411yescharacteristic
926C22×C4#12411yescharacteristic
927C22×C4#12611yescharacteristic
928C22×C4#12611yescharacteristic
929C22×C4#12611yescharacteristic
930C22×C4#12611yescharacteristic
931C22×C4#12611yescharacteristic
932C22×C4#12611yescharacteristic
933C22×C4#12611yescharacteristic
934C22×C4#12611yescharacteristic
935C22×C4#12711yescharacteristic
936C22×C4#12711yescharacteristic
937C22×C4#12711yescharacteristic
938M16—24no—
939M16—24no—
940M16—42no—
941M16—42no—
942M16—42no—
943M16—42no—
944M16—42no—
945M16—42no—
946M16—42no—
947M16—42no—
948M16—42no—
949M16—42no—
950M16—42no—
951M16—42no—
952M16—42no—
953M16—42no—
954C2×C8—24no—
955C2×C8—24no—
956C2×C8—24no—
957C2×C8—24no—
958C2×C8—42no—
959C2×C8—42no—
960C2×C8—42no—
961C2×C8—42no—
962C2×C8—42no—
963C2×C8—42no—
964C2×C8—42no—
965C2×C8—42no—
966C2×C8—42no—
967C2×C8—42no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—832no—
1001C42—24no—
1002C42—42no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—42no—
1013C42—42no—
1014C42—42no—
1015C42—42no—
1016C42—42no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—28no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—416no—
1034C23—416no—
1035C23—416no—
1036C23—44no—
1037C23—44no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—44no—
1044C23—44no—
1045C23—44no—
1046C23—44no—
1047C23—44no—
1048C23—44no—
1049C23—44no—
1050C23—88no—
1051C23—88no—
1052C23—88no—
1053C23—88no—
1054C23—88no—
1055C23—88no—
1056C23—88no—
1057C23—88no—
1058C23—88no—
1059C23—88no—
1060C23—88no—
1061C23—88no—
1062C23—88no—
1063C23—88no—
1064C23—88no—
1065C23—88no—
1066C23—88no—
1067C23—88no—
1068C23—88no—
1069C23—88no—
1070C23—88no—
1071C23—88no—
1072C23—88no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23—88no—
1077C23—88no—
1078C23—88no—
1079C23—88no—
1080C23—88no—
1081C23—88no—
1082C23C4×C22⋊C411yescharacteristic
1083C23#37911yescharacteristic
1084C23#38011yescharacteristic
1085C23#38511yescharacteristic
1086C23#38511yescharacteristic
1087C23#38611yescharacteristic
1088C23#38611yescharacteristic
1089C23#38611yescharacteristic
1090C23#38611yescharacteristic
1091C23#38611yescharacteristic
1092C23#38611yescharacteristic
1093C23#38811yescharacteristic
1094C23#38811yescharacteristic
1095C23#38811yescharacteristic
1096C23#38811yescharacteristic
1097C23#39011yescharacteristic
1098C23#39011yescharacteristic
1099C23#39011yescharacteristic
1100C23#39011yescharacteristic
1101C23#39211yescharacteristic
1102C23#39211yescharacteristic
1103C23#39211yescharacteristic
1104C23#39211yescharacteristic
1105C23#39211yescharacteristic
1106C23#39311yescharacteristic
1107C23#39411yescharacteristic
1108C23#39411yescharacteristic
1109C23#39411yescharacteristic
1110C23#39411yescharacteristic
1111C23#39411yescharacteristic
1112C23#39411yescharacteristic
1113C23#39611yescharacteristic
1114C23#39611yescharacteristic
1115C23#39711yescharacteristic
1116C23#39911yescharacteristic
1117D4—28no—
1118D4—28no—
1119D4—44no—
1120D4—44no—
1121D4—44no—
1122D4—44no—
1123D4—44no—
1124D4—44no—
1125D4—44no—
1126D4—44no—
1127D4—44no—
1128D4—44no—
1129D4—44no—
1130D4—44no—
1131D4—44no—
1132D4—44no—
1133C2×C4—48no—
1134C2×C4—48no—
1135C2×C4—44no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—84no—
1140C2×C4—84no—
1141C2×C4—84no—
1142C2×C4—84no—
1143C2×C4—84no—
1144C2×C4—84no—
1145C2×C4—84no—
1146C2×C4—84no—
1147C2×C4—84no—
1148C2×C4—84no—
1149C2×C4C2×#9511yescharacteristic
1150C2×C4C4×C22⋊C411yescharacteristic
1151C2×C4C4×C22⋊C411yescharacteristic
1152C2×C4C4×C22⋊C411yescharacteristic
1153C2×C4C4×C22⋊C411yescharacteristic
1154C2×C4C4×C22⋊C411yescharacteristic
1155C2×C4#37911yescharacteristic
1156C2×C4#37911yescharacteristic
1157C2×C4#38011yescharacteristic
1158C2×C4#38011yescharacteristic
1159C2×C4#38011yescharacteristic
1160C2×C4#38011yescharacteristic
1161C2×C4#38011yescharacteristic
1162C2×C4#38111yescharacteristic
1163C2×C4#38111yescharacteristic
1164C2×C4#38111yescharacteristic
1165C2×C4#38511yescharacteristic
1166C2×C4#38511yescharacteristic
1167C2×C4#38511yescharacteristic
1168C2×C4#38511yescharacteristic
1169C2×C4#38511yescharacteristic
1170C2×C4#38511yescharacteristic
1171C2×C4#38511yescharacteristic
1172C2×C4#38511yescharacteristic
1173C2×C4#38511yescharacteristic
1174C2×C4#38511yescharacteristic
1175C2×C4#38611yescharacteristic
1176C2×C4#38611yescharacteristic
1177C2×C4#38611yescharacteristic
1178C2×C4#38611yescharacteristic
1179C2×C4#38611yescharacteristic
1180C2×C4#38611yescharacteristic
1181C2×C4#38611yescharacteristic
1182C2×C4#38611yescharacteristic
1183C2×C4#38611yescharacteristic
1184C2×C4#38611yescharacteristic
1185C2×C4#38611yescharacteristic
1186C2×C4#38611yescharacteristic
1187C2×C4#38611yescharacteristic
1188C2×C4#38611yescharacteristic
1189C2×C4#38611yescharacteristic
1190C2×C4#38611yescharacteristic
1191C2×C4#38611yescharacteristic
1192C2×C4#38611yescharacteristic
1193C2×C4#38811yescharacteristic
1194C2×C4#38811yescharacteristic
1195C2×C4#38811yescharacteristic
1196C2×C4#38811yescharacteristic
1197C2×C4#38811yescharacteristic
1198C2×C4#38811yescharacteristic
1199C2×C4#38811yescharacteristic
1200C2×C4#38811yescharacteristic
1201C2×C4#38811yescharacteristic
1202C2×C4#38811yescharacteristic
1203C2×C4#38811yescharacteristic
1204C2×C4#38811yescharacteristic
1205C2×C4#38811yescharacteristic
1206C2×C4#38811yescharacteristic
1207C2×C4#38811yescharacteristic
1208C2×C4#38811yescharacteristic
1209C2×C4#38811yescharacteristic
1210C2×C4#38811yescharacteristic
1211C2×C4#38811yescharacteristic
1212C2×C4#38811yescharacteristic
1213C2×C4#39011yescharacteristic
1214C2×C4#39011yescharacteristic
1215C2×C4#39011yescharacteristic
1216C2×C4#39011yescharacteristic
1217C2×C4#39011yescharacteristic
1218C2×C4#39011yescharacteristic
1219C2×C4#39011yescharacteristic
1220C2×C4#39011yescharacteristic
1221C2×C4#39211yescharacteristic
1222C2×C4#39211yescharacteristic
1223C2×C4#39211yescharacteristic
1224C2×C4#39211yescharacteristic
1225C2×C4#39211yescharacteristic
1226C2×C4#39211yescharacteristic
1227C2×C4#39211yescharacteristic
1228C2×C4#39311yescharacteristic
1229C2×C4#39311yescharacteristic
1230C2×C4#39311yescharacteristic
1231C2×C4#39411yescharacteristic
1232C2×C4#39411yescharacteristic
1233C2×C4#39411yescharacteristic
1234C2×C4#39411yescharacteristic
1235C2×C4#39411yescharacteristic
1236C2×C4#39411yescharacteristic
1237C2×C4#39411yescharacteristic
1238C2×C4#39411yescharacteristic
1239C2×C4#39411yescharacteristic
1240C2×C4#39411yescharacteristic
1241C2×C4#39411yescharacteristic
1242C2×C4#39411yescharacteristic
1243C2×C4#39411yescharacteristic
1244C2×C4#39411yescharacteristic
1245C2×C4#39411yescharacteristic
1246C2×C4#39411yescharacteristic
1247C2×C4#39411yescharacteristic
1248C2×C4#39411yescharacteristic
1249C2×C4#39611yescharacteristic
1250C2×C4#39611yescharacteristic
1251C2×C4#39611yescharacteristic
1252C2×C4#39611yescharacteristic
1253C2×C4#39611yescharacteristic
1254C2×C4#39611yescharacteristic
1255C2×C4#39711yescharacteristic
1256C2×C4#39711yescharacteristic
1257C2×C4#39711yescharacteristic
1258C2×C4#39711yescharacteristic
1259C2×C4#39711yescharacteristic
1260C2×C4#39711yescharacteristic
1261C2×C4#39711yescharacteristic
1262C2×C4#39711yescharacteristic
1263C2×C4#39711yescharacteristic
1264C2×C4#39711yescharacteristic
1265C2×C4#39711yescharacteristic
1266C2×C4#39911yescharacteristic
1267C2×C4#39911yescharacteristic
1268C2×C4#39911yescharacteristic
1269C8—44no—
1270C8—44no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—416no—
1306C22—48no—
1307C22—88no—
1308C22—88no—
1309C22—88no—
1310C22—88no—
1311C22—88no—
1312C22—88no—
1313C22—88no—
1314C22—88no—
1315C22—88no—
1316C22—88no—
1317C22—88no—
1318C22—88no—
1319C22—88no—
1320C22—88no—
1321C22C22⋊#9511yescharacteristic
1322C22#143711yescharacteristic
1323C22#143711yescharacteristic
1324C22#143811yescharacteristic
1325C22#143811yescharacteristic
1326C22#143811yescharacteristic
1327C22#143811yescharacteristic
1328C22#143911yescharacteristic
1329C22#143911yescharacteristic
1330C22#143911yescharacteristic
1331C22#143911yescharacteristic
1332C22#143911yescharacteristic
1333C22#143911yescharacteristic
1334C22#144011yescharacteristic
1335C22#144011yescharacteristic
1336C22#200814yes—
1337C4—84no—
1338C4—84no—
1339C4—84no—
1340C4—84no—
1341C4C22⋊#9511yescharacteristic
1342C4C22⋊#9511yescharacteristic
1343C4#143711yescharacteristic
1344C4#143711yescharacteristic
1345C4#143811yescharacteristic
1346C4#143811yescharacteristic
1347C4#143911yescharacteristic
1348C4#143911yescharacteristic
1349C4#143911yescharacteristic
1350C4#143911yescharacteristic
1351C4#143911yescharacteristic
1352C4#143911yescharacteristic
1353C4#144011yescharacteristic
1354C4#144011yescharacteristic
1355C4#144011yescharacteristic
1356C4#144011yescharacteristic
1357C2—21no—
1358C2—21no—
1359C2—21no—
1360C2—21no—
1361C2—21no—
1362C2—21no—
1363C2—21no—
1364C2—21no—
1365C2—21no—
1366C2—21no—
1367C2—21no—
1368C2—21no—
1369C2—88no—
1370C2#755511yescharacteristic
1371C2#1100412yes—
1372C2#1103012yes—
1373C2#1112912yes—
subgroupG/H
center, socleC23#392
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC24×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#344C2semidirect
5. C2×#1740C2semidirect
6. #20347C2semidirect
7. C2×#1733C2semidirect
25. C2×#418C4semidirect
26. C2×#418C4semidirect
32. #2309C4semidirect
441. C2×M16C22⋊C4semidirect
455. C22×C8C22⋊C4semidirect
519. #117C22⋊C4semidirect
543. C2×C4⋊C4C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4182
C2×#23092
C22×#3442
C2×#17402
#203472
C2×#17332