Finite Group Databasebeta

← #123644

Subgroups — #123644

Order 512.

2978 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#418C211yesmaximal, characteristic
2C22×#418C211yesmaximal, characteristic
3C23×#100C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C2×#1733C211yesmaximal, characteristic, complemented
6C22×#338C211yesmaximal, characteristic, complemented
7#20335C211yesmaximal, characteristic, complemented
8C24×D4C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
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×#418—22no—
26C2×#418C414yescomplemented
27C22×#102—22no—
28C22×#102C414yescomplemented
29C22×#100—22no—
30C22×#100—22no—
31C22×#100—22no—
32C22×#100—22no—
33C22×#100—22no—
34C22×#100—22no—
35C22×#100C414yescomplemented
36C2×#344—22no—
37C2×#344—22no—
38C2×#344—22no—
39#1733—22no—
40#1733—22no—
41C2×#339—22no—
42C2×#338—22no—
43C2×#338—22no—
44C2×#338—22no—
45#1729—22no—
46#1729—22no—
47#1728—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×M16—21no—
104C22×M16—21no—
105C22×M16—21no—
106C22×M16—21no—
107C22×M16—21no—
108C22×M16—21no—
109C22×M16—21no—
110C22×M16—21no—
111C22×M16—21no—
112C22×M16—21no—
113C22×M16—21no—
114C22×M16—21no—
115C22×M16—21no—
116C22×M16—21no—
117C22×M16—21no—
118C22×M16—21no—
119C22×M16—21no—
120C22×M16—21no—
121C22×M16—21no—
122C22×M16—21no—
123C22×M16—21no—
124C22×M16—21no—
125C22×M16—21no—
126C22×M16C2×C412yes—
127C22×M16C2×C412yes—
128C22×M16C2×C412yes—
129C22×M16D412yes—
130C22×M16D412yes—
131C22×M16D412yes—
132C22×M16D412yes—
133C22×M16D412yes—
134C22×M16D412yes—
135C22×M16D412yes—
136C23×C8—21no—
137C23×C8—21no—
138C23×C8C2×C412yes—
139C23×C8D412yes—
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×#117—21no—
150C2×#117—21no—
151C2×#117—21no—
152C2×#117—21no—
153C2×#117—21no—
154C2×#117—21no—
155C2×#117—21no—
156C2×#117—21no—
157C2×#117—21no—
158C2×#117—21no—
159C2×#117C2×C412yes—
160C2×#117D412yes—
161C2×#117D412yes—
162C2×#117D412yes—
163C2×#117D412yes—
164C22×C4⋊C4—21no—
165C22×C4⋊C4C2×C412yes—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C42—21no—
169C22×C42—21no—
170#418—28no—
171#418—28no—
172#418—28no—
173#418—28no—
174#418—28no—
175#418—28no—
176#418—28no—
177#418—28no—
178C2×#102—28no—
179C2×#102—28no—
180C2×#102—28no—
181C2×#102—28no—
182C2×#102—28no—
183C2×#102—28no—
184C2×#100—28no—
185C2×#100—28no—
186C2×#100—28no—
187C2×#100—28no—
188C2×#100—28no—
189C2×#100—28no—
190C2×#100—28no—
191#344—28no—
192#339—28no—
193#338—28no—
194#336—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—
211C25#4111yescharacteristic
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—41no—
354C23×C4C22×C411yescharacteristic
355C23×C4C22×C411yescharacteristic
356C23×C4C22×C411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
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×Q811yescharacteristic
373C23×C4#4111yescharacteristic
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
384C2×M16—22no—
385C2×M16—22no—
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—22no—
414C2×M16—22no—
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—22no—
418C2×M16—22no—
419C2×M16—22no—
420C2×M16—22no—
421C2×M16—22no—
422C2×M16—22no—
423C2×M16—22no—
424C2×M16—22no—
425C2×M16—22no—
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—22no—
429C2×M16—22no—
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—22no—
434C2×M16—22no—
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—22no—
438C2×M16—41no—
439C2×M16—41no—
440C2×M16—41no—
441C2×M16—41no—
442C2×M16—41no—
443C2×M16—41no—
444C2×M16—41no—
445C2×M16—41no—
446C2×M16—41no—
447C2×M16—41no—
448C2×M16—41no—
449C2×M16—41no—
450C2×M16—41no—
451C2×M16—41no—
452C2×M16—41no—
453C2×M16—41no—
454C2×M16—41no—
455C2×M16—41no—
456C2×M16—41no—
457C2×M16—41no—
458C2×M16—41no—
459C2×M16—41no—
460C2×M16—41no—
461C2×M16—41no—
462C2×M16—41no—
463C2×M16—41no—
464C2×M16—41no—
465C2×M16—41no—
466C2×M16—41no—
467C2×M16—41no—
468C2×M16—41no—
469C2×M16—41no—
470C2×M16—41no—
471C2×M16—41no—
472C2×M16—41no—
473C2×M16—41no—
474C2×M16—41no—
475C2×M16—41no—
476C2×M16—41no—
477C2×M16—41no—
478C2×M16—41no—
479C2×M16—41no—
480C2×M16—41no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—41no—
484C2×M16—41no—
485C2×M16—41no—
486C2×M16—41no—
487C2×M16—41no—
488C2×M16—41no—
489C2×M16—41no—
490C2×M16—41no—
491C2×M16—41no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16C22⋊C414yes—
495C2×M16C22⋊C414yes—
496C22×C8—22no—
497C22×C8—22no—
498C22×C8—22no—
499C22×C8—22no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8—22no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8—41no—
522C22×C8C22⋊C414yes—
523C22×C8C22⋊C414yes—
524#117—22no—
525#117—22no—
526#117—22no—
527#117—22no—
528#117—22no—
529#117—22no—
530#117—22no—
531#117—22no—
532#117—22no—
533#117—22no—
534#117—22no—
535#117—22no—
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540#117—22no—
541#117—41no—
542#117—41no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117—41no—
547#117—41no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552#117—41no—
553#117—41no—
554#117—41no—
555#117C22⋊C414yes—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4C22⋊C414yes—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—41no—
589C2×C42—41no—
590C2×C42—41no—
591C2×C42—41no—
592#102—232no—
593#102—232no—
594#100—232no—
595C24—24no—
596C24—24no—
597C24—24no—
598C24—24no—
599C24—24no—
600C24—24no—
601C24—24no—
602C24—44no—
603C24—42no—
604C24—42no—
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—88no—
632C24—88no—
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#11711yescharacteristic
647C24C4×D411yescharacteristic
648C24C4×D411yescharacteristic
649C24#12111yescharacteristic
650C24#12111yescharacteristic
651C24#12111yescharacteristic
652C24C22⋊Q811yescharacteristic
653C24#12311yescharacteristic
654C24#12311yescharacteristic
655C24#12311yescharacteristic
656C24#12311yescharacteristic
657C24#12411yescharacteristic
658C24#12411yescharacteristic
659C24#12611yescharacteristic
660C24#12611yescharacteristic
661C2×D4—24no—
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—42no—
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#9518yes—
781C22×C4—24no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—84no—
788C22×C4—84no—
789C22×C4C2×C4211yescharacteristic
790C22×C4C2×C22⋊C411yescharacteristic
791C22×C4C2×C22⋊C411yescharacteristic
792C22×C4C2×C22⋊C411yescharacteristic
793C22×C4C2×C22⋊C411yescharacteristic
794C22×C4C2×C22⋊C411yescharacteristic
795C22×C4C2×C22⋊C411yescharacteristic
796C22×C4C2×C22⋊C411yescharacteristic
797C22×C4C2×C22⋊C411yescharacteristic
798C22×C4C2×C22⋊C411yescharacteristic
799C22×C4C2×C4⋊C411yescharacteristic
800C22×C4C2×C4⋊C411yescharacteristic
801C22×C4C2×C4⋊C411yescharacteristic
802C22×C4#11711yescharacteristic
803C22×C4#11711yescharacteristic
804C22×C4#11711yescharacteristic
805C22×C4#11711yescharacteristic
806C22×C4#11711yescharacteristic
807C22×C4C4×D411yescharacteristic
808C22×C4C4×D411yescharacteristic
809C22×C4C4×D411yescharacteristic
810C22×C4C4×D411yescharacteristic
811C22×C4C4×D411yescharacteristic
812C22×C4C4×D411yescharacteristic
813C22×C4C4×D411yescharacteristic
814C22×C4C4×D411yescharacteristic
815C22×C4C4×D411yescharacteristic
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×C4#12011yescharacteristic
830C22×C4#12011yescharacteristic
831C22×C4#12011yescharacteristic
832C22×C4#12011yescharacteristic
833C22×C4#12011yescharacteristic
834C22×C4#12011yescharacteristic
835C22×C4#12011yescharacteristic
836C22×C4#12011yescharacteristic
837C22×C4#12011yescharacteristic
838C22×C4#12011yescharacteristic
839C22×C4#12011yescharacteristic
840C22×C4#12011yescharacteristic
841C22×C4#12011yescharacteristic
842C22×C4#12011yescharacteristic
843C22×C4#12011yescharacteristic
844C22×C4#12011yescharacteristic
845C22×C4#12111yescharacteristic
846C22×C4#12111yescharacteristic
847C22×C4#12111yescharacteristic
848C22×C4#12111yescharacteristic
849C22×C4#12111yescharacteristic
850C22×C4#12111yescharacteristic
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×C4C22⋊Q811yescharacteristic
879C22×C4C22⋊Q811yescharacteristic
880C22×C4C22⋊Q811yescharacteristic
881C22×C4C22⋊Q811yescharacteristic
882C22×C4C22⋊Q811yescharacteristic
883C22×C4C22⋊Q811yescharacteristic
884C22×C4C22⋊Q811yescharacteristic
885C22×C4C22⋊Q811yescharacteristic
886C22×C4C22⋊Q811yescharacteristic
887C22×C4C22⋊Q811yescharacteristic
888C22×C4C22⋊Q811yescharacteristic
889C22×C4#12311yescharacteristic
890C22×C4#12311yescharacteristic
891C22×C4#12311yescharacteristic
892C22×C4#12311yescharacteristic
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#12411yescharacteristic
910C22×C4#12411yescharacteristic
911C22×C4#12411yescharacteristic
912C22×C4#12411yescharacteristic
913C22×C4#12411yescharacteristic
914C22×C4#12411yescharacteristic
915C22×C4#12411yescharacteristic
916C22×C4#12411yescharacteristic
917C22×C4#12411yescharacteristic
918C22×C4#12411yescharacteristic
919C22×C4#12611yescharacteristic
920C22×C4#12611yescharacteristic
921C22×C4#12611yescharacteristic
922C22×C4#12611yescharacteristic
923C22×C4#12611yescharacteristic
924C22×C4#12611yescharacteristic
925C22×C4#12711yescharacteristic
926C22×C4#12711yescharacteristic
927C22×C4#12711yescharacteristic
928C22×C4#12711yescharacteristic
929M16—24no—
930M16—24no—
931M16—24no—
932M16—24no—
933M16—42no—
934M16—42no—
935M16—42no—
936M16—42no—
937M16—42no—
938M16—42no—
939M16—42no—
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—
954M16—42no—
955M16—42no—
956M16—42no—
957M16—42no—
958M16—42no—
959M16—42no—
960M16—42no—
961C2×C8—24no—
962C2×C8—24no—
963C2×C8—24no—
964C2×C8—24no—
965C2×C8—24no—
966C2×C8—24no—
967C2×C8—24no—
968C2×C8—24no—
969C2×C8—42no—
970C2×C8—42no—
971C2×C8—42no—
972C2×C8—42no—
973C2×C8—42no—
974C2×C8—42no—
975C2×C8—42no—
976C2×C8—42no—
977C2×C8—42no—
978C2×C8—42no—
979C2×C8—42no—
980C2×C8—42no—
981C2×C8—42no—
982C2×C8—42no—
983C2×C8—42no—
984C2×C8—42no—
985C2×C8—42no—
986C2×C8—42no—
987C2×C8—42no—
988C2×C8—42no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C22⋊C4—24no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C42—24no—
1006C42—42no—
1007C42—42no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—42no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—28no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—44no—
1030C23—44no—
1031C23—44no—
1032C23—44no—
1033C23—44no—
1034C23—44no—
1035C23—44no—
1036C23—44no—
1037C23—44no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—88no—
1044C23—88no—
1045C23—88no—
1046C23—88no—
1047C23—88no—
1048C23—88no—
1049C23—88no—
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—
1078C23C4×C22⋊C411yescharacteristic
1079C23#38011yescharacteristic
1080C23#38111yescharacteristic
1081C23#38511yescharacteristic
1082C23#38511yescharacteristic
1083C23#38611yescharacteristic
1084C23#38611yescharacteristic
1085C23#38611yescharacteristic
1086C23#38611yescharacteristic
1087C23#38811yescharacteristic
1088C23#38811yescharacteristic
1089C23#38811yescharacteristic
1090C23#38811yescharacteristic
1091C23#38811yescharacteristic
1092C23#38811yescharacteristic
1093C23#38811yescharacteristic
1094C23#38811yescharacteristic
1095C23#39011yescharacteristic
1096C23#39011yescharacteristic
1097C23#39211yescharacteristic
1098C23#39311yescharacteristic
1099C23#39411yescharacteristic
1100C23#39411yescharacteristic
1101C23#39411yescharacteristic
1102C23#39411yescharacteristic
1103C23#39411yescharacteristic
1104C23#39411yescharacteristic
1105C23#39611yescharacteristic
1106C23#39611yescharacteristic
1107C23#39711yescharacteristic
1108C23#39711yescharacteristic
1109C23#39711yescharacteristic
1110C23#39711yescharacteristic
1111C23#39711yescharacteristic
1112C23#39911yescharacteristic
1113D4—28no—
1114D4—28no—
1115D4—44no—
1116D4—44no—
1117D4—44no—
1118D4—44no—
1119D4—44no—
1120D4—44no—
1121D4—44no—
1122D4—44no—
1123D4—44no—
1124D4—44no—
1125D4—44no—
1126D4—44no—
1127D4—44no—
1128D4—44no—
1129C2×C4—48no—
1130C2×C4—44no—
1131C2×C4—44no—
1132C2×C4—84no—
1133C2×C4—84no—
1134C2×C4—84no—
1135C2×C4—84no—
1136C2×C4—84no—
1137C2×C4C2×#9511yescharacteristic
1138C2×C4C4×C22⋊C411yescharacteristic
1139C2×C4C4×C22⋊C411yescharacteristic
1140C2×C4C4×C22⋊C411yescharacteristic
1141C2×C4C4×C22⋊C411yescharacteristic
1142C2×C4C4×C22⋊C411yescharacteristic
1143C2×C4#37911yescharacteristic
1144C2×C4#37911yescharacteristic
1145C2×C4#37911yescharacteristic
1146C2×C4#38011yescharacteristic
1147C2×C4#38011yescharacteristic
1148C2×C4#38011yescharacteristic
1149C2×C4#38011yescharacteristic
1150C2×C4#38011yescharacteristic
1151C2×C4#38111yescharacteristic
1152C2×C4#38111yescharacteristic
1153C2×C4#38511yescharacteristic
1154C2×C4#38511yescharacteristic
1155C2×C4#38511yescharacteristic
1156C2×C4#38511yescharacteristic
1157C2×C4#38511yescharacteristic
1158C2×C4#38511yescharacteristic
1159C2×C4#38511yescharacteristic
1160C2×C4#38511yescharacteristic
1161C2×C4#38511yescharacteristic
1162C2×C4#38511yescharacteristic
1163C2×C4#38611yescharacteristic
1164C2×C4#38611yescharacteristic
1165C2×C4#38611yescharacteristic
1166C2×C4#38611yescharacteristic
1167C2×C4#38611yescharacteristic
1168C2×C4#38611yescharacteristic
1169C2×C4#38611yescharacteristic
1170C2×C4#38611yescharacteristic
1171C2×C4#38611yescharacteristic
1172C2×C4#38611yescharacteristic
1173C2×C4#38611yescharacteristic
1174C2×C4#38611yescharacteristic
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#38811yescharacteristic
1184C2×C4#38811yescharacteristic
1185C2×C4#38811yescharacteristic
1186C2×C4#38811yescharacteristic
1187C2×C4#38811yescharacteristic
1188C2×C4#38811yescharacteristic
1189C2×C4#38811yescharacteristic
1190C2×C4#38811yescharacteristic
1191C2×C4#38811yescharacteristic
1192C2×C4#38811yescharacteristic
1193C2×C4#38811yescharacteristic
1194C2×C4#38811yescharacteristic
1195C2×C4#38811yescharacteristic
1196C2×C4#38811yescharacteristic
1197C2×C4#38811yescharacteristic
1198C2×C4#38811yescharacteristic
1199C2×C4#39011yescharacteristic
1200C2×C4#39011yescharacteristic
1201C2×C4#39011yescharacteristic
1202C2×C4#39011yescharacteristic
1203C2×C4#39011yescharacteristic
1204C2×C4#39011yescharacteristic
1205C2×C4#39011yescharacteristic
1206C2×C4#39011yescharacteristic
1207C2×C4#39011yescharacteristic
1208C2×C4#39011yescharacteristic
1209C2×C4#39211yescharacteristic
1210C2×C4#39211yescharacteristic
1211C2×C4#39211yescharacteristic
1212C2×C4#39211yescharacteristic
1213C2×C4#39211yescharacteristic
1214C2×C4#39211yescharacteristic
1215C2×C4#39211yescharacteristic
1216C2×C4#39211yescharacteristic
1217C2×C4#39211yescharacteristic
1218C2×C4#39211yescharacteristic
1219C2×C4#39211yescharacteristic
1220C2×C4#39311yescharacteristic
1221C2×C4#39311yescharacteristic
1222C2×C4#39311yescharacteristic
1223C2×C4#39411yescharacteristic
1224C2×C4#39411yescharacteristic
1225C2×C4#39411yescharacteristic
1226C2×C4#39411yescharacteristic
1227C2×C4#39411yescharacteristic
1228C2×C4#39411yescharacteristic
1229C2×C4#39411yescharacteristic
1230C2×C4#39411yescharacteristic
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#39611yescharacteristic
1242C2×C4#39611yescharacteristic
1243C2×C4#39611yescharacteristic
1244C2×C4#39611yescharacteristic
1245C2×C4#39611yescharacteristic
1246C2×C4#39611yescharacteristic
1247C2×C4#39711yescharacteristic
1248C2×C4#39711yescharacteristic
1249C2×C4#39711yescharacteristic
1250C2×C4#39711yescharacteristic
1251C2×C4#39711yescharacteristic
1252C2×C4#39711yescharacteristic
1253C2×C4#39711yescharacteristic
1254C2×C4#39911yescharacteristic
1255C2×C4#39911yescharacteristic
1256C2×C4#39911yescharacteristic
1257C8—44no—
1258C8—44no—
1259C8—44no—
1260C8—44no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—48no—
1296C22—88no—
1297C22—88no—
1298C22—88no—
1299C22—88no—
1300C22—88no—
1301C22—88no—
1302C22—88no—
1303C22—88no—
1304C22—88no—
1305C22—88no—
1306C22—88no—
1307C22—88no—
1308C22—88no—
1309C22—88no—
1310C22—88no—
1311C22C22⋊#9511yescharacteristic
1312C22#143711yescharacteristic
1313C22#143711yescharacteristic
1314C22#143811yescharacteristic
1315C22#143811yescharacteristic
1316C22#143911yescharacteristic
1317C22#143911yescharacteristic
1318C22#143911yescharacteristic
1319C22#143911yescharacteristic
1320C22#143911yescharacteristic
1321C22#143911yescharacteristic
1322C22#144011yescharacteristic
1323C22#144011yescharacteristic
1324C22#144011yescharacteristic
1325C22#144011yescharacteristic
1326C22#190314yes—
1327C4—84no—
1328C4—84no—
1329C4C22⋊#9511yescharacteristic
1330C4C22⋊#9511yescharacteristic
1331C4#143711yescharacteristic
1332C4#143711yescharacteristic
1333C4#143811yescharacteristic
1334C4#143811yescharacteristic
1335C4#143811yescharacteristic
1336C4#143811yescharacteristic
1337C4#143911yescharacteristic
1338C4#143911yescharacteristic
1339C4#143911yescharacteristic
1340C4#143911yescharacteristic
1341C4#143911yescharacteristic
1342C4#143911yescharacteristic
1343C4#144011yescharacteristic
1344C4#144011yescharacteristic
1345C2—21no—
1346C2—21no—
1347C2—21no—
1348C2—21no—
1349C2—21no—
1350C2—21no—
1351C2—21no—
1352C2—21no—
1353C2—21no—
1354C2—21no—
1355C2—21no—
1356C2—21no—
1357C2—88no—
1358C2#755511yescharacteristic
1359C2#1095312yes—
1360C2#1101412yes—
1361C2#1105812yes—
subgroupG/H
center, socleC23#386
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×#1733C2semidirect
6. C22×#338C2semidirect
7. #20335C2semidirect
26. C2×#418C4semidirect
28. C22×#102C4semidirect
35. C22×#100C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4182
C23×#1002
C22×#3442
C2×#17332
C22×#3382
#203352