Finite Group Databasebeta

← #123609

Subgroups — #123609

Order 512.

2478 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#421C211yesmaximal, characteristic
2C22×#421C211yesmaximal, characteristic
3C2×#2879C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic, complemented
5C2×#1742C211yesmaximal, characteristic, complemented
6C2×#1738C211yesmaximal, characteristic, complemented
7C2×#1733C211yesmaximal, characteristic, complemented
8C23×#41C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C2×#421—22no—
16C2×#421—22no—
17C2×#421—22no—
18C2×#421—22no—
19C2×#421—22no—
20C2×#421—22no—
21C2×#421—22no—
22C2×#421—22no—
23C2×#421—22no—
24C2×#421—22no—
25C2×#421C414yescomplemented
26C2×#421C414yescomplemented
27C22×#104—22no—
28C22×#104—22no—
29#2879—22no—
30#2879—22no—
31#2879—22no—
32#2879C414yescomplemented
33C2×#408—22no—
34C2×#408—22no—
35C2×#407—22no—
36C2×#344—22no—
37C2×#344—22no—
38C2×#344—22no—
39#1742—22no—
40#1742—22no—
41C2×#343—22no—
42#1738—22no—
43#1738—22no—
44C2×#341—22no—
45#1733—22no—
46#1733—22no—
47C2×#339—22no—
48C22×#41—21no—
49C22×#41—21no—
50C22×#41—21no—
51C22×#41—21no—
52C22×#41—21no—
53C22×#41—21no—
54C22×#41—21no—
55C22×#41—21no—
56C22×#41—21no—
57C22×#41—21no—
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×#41C2×C412yes—
71C22×#41C2×C412yes—
72C22×#41C2×C412yes—
73C22×#41D412yes—
74C22×#41D412yes—
75C22×#41D412yes—
76C23×Q8Q811yescharacteristic
77C23×D4—21no—
78C23×D4Q811yescharacteristic
79C24×C4—21no—
80C24×C4C2311yescharacteristic
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×M16C2×C412yes—
126C22×M16C2×C412yes—
127C22×M16C2×C412yes—
128C22×M16C2×C412yes—
129C22×M16D412yes—
130C22×M16D412yes—
131C22×M16D412yes—
132C22×M16D412yes—
133C22×M16D412yes—
134C22×M16D412yes—
135C22×M16D412yes—
136C22×M16D412yes—
137C23×C8—21no—
138C23×C8—21no—
139C23×C8—21no—
140C23×C8—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×#117—21no—
160C2×#117C2×C412yes—
161C2×#117C2×C412yes—
162C2×#117D412yes—
163C2×#117D412yes—
164C2×#117D412yes—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C42—21no—
170C22×C42D412yes—
171#421—28no—
172#421—28no—
173#421—28no—
174#421—28no—
175#421—28no—
176#421—28no—
177#421—28no—
178#421—28no—
179C2×#104—28no—
180C2×#104—28no—
181C2×#104—28no—
182C2×#104—28no—
183C2×#104—28no—
184C2×#104—28no—
185#408—28no—
186#408—28no—
187#408—28no—
188#408—28no—
189#407—28no—
190#407—28no—
191C2×C22⋊C8—28no—
192#344—28no—
193#343—28no—
194#341—28no—
195#339—28no—
196C25—21no—
197C25#4111yescharacteristic
198C2×#41—22no—
199C2×#41—22no—
200C2×#41—22no—
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—22no—
210C2×#41—22no—
211C2×#41—22no—
212C2×#41—22no—
213C2×#41—22no—
214C2×#41—22no—
215C2×#41—22no—
216C2×#41—22no—
217C2×#41—22no—
218C2×#41—22no—
219C2×#41—22no—
220C2×#41—22no—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41—22no—
224C2×#41—22no—
225C2×#41—22no—
226C2×#41—22no—
227C2×#41—22no—
228C2×#41—22no—
229C2×#41—22no—
230C2×#41—22no—
231C2×#41—22no—
232C2×#41—22no—
233C2×#41—22no—
234C2×#41—22no—
235C2×#41—22no—
236C2×#41—22no—
237C2×#41—22no—
238C2×#41—22no—
239C2×#41—22no—
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—41no—
259C2×#41—41no—
260C2×#41—41no—
261C2×#41—41no—
262C2×#41—41no—
263C2×#41—41no—
264C2×#41—41no—
265C2×#41—41no—
266C2×#41—41no—
267C2×#41—41no—
268C2×#41—41no—
269C2×#41—41no—
270C2×#41—41no—
271C2×#41—41no—
272C2×#41—41no—
273C2×#41—41no—
274C2×#41—41no—
275C2×#41—41no—
276C2×#41—41no—
277C2×#41—41no—
278C2×#41—41no—
279C2×#41—41no—
280C2×#41—41no—
281C2×#41—41no—
282C2×#41—41no—
283C2×#41—41no—
284C2×#41—41no—
285C2×#41—41no—
286C2×#41—41no—
287C2×#41—41no—
288C2×#41—41no—
289C2×#41—41no—
290C2×#41—41no—
291C2×#41—41no—
292C2×#41—41no—
293C2×#41—41no—
294C2×#41—41no—
295C2×#41—41no—
296C2×#41—41no—
297C2×#41—41no—
298C2×#41—41no—
299C2×#41—41no—
300C2×#41—41no—
301C2×#41—41no—
302C2×#41—41no—
303C2×#41—41no—
304C2×#41—41no—
305C2×#41—41no—
306C2×#41C4214yes—
307C2×#41C22⋊C414yes—
308C2×#41C22⋊C414yes—
309C2×#41C22⋊C414yes—
310C22×Q8—21no—
311C22×Q8—21no—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8—21no—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8—21no—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8C4⋊C412yes—
322C22×Q8C4⋊C412yes—
323C22×Q8C4⋊C412yes—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4C4⋊C412yes—
350C22×D4C4⋊C412yes—
351C22×D4C4⋊C412yes—
352C23×C4—21no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4C22×C411yescharacteristic
370C23×C4C22×C411yescharacteristic
371C23×C4C22×C411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2×D411yescharacteristic
376C23×C4C2×D411yescharacteristic
377C23×C4C2×D411yescharacteristic
378C23×C4C2×D411yescharacteristic
379C23×C4C2×D411yescharacteristic
380C23×C4C2×D411yescharacteristic
381C23×C4C2×D411yescharacteristic
382C23×C4C2×D411yescharacteristic
383C23×C4C2×D411yescharacteristic
384C23×C4C2×D411yescharacteristic
385C23×C4C2×D411yescharacteristic
386C23×C4C2×D411yescharacteristic
387C23×C4C2×Q811yescharacteristic
388C23×C4#4111yescharacteristic
389C23×C4#4111yescharacteristic
390C23×C4#4111yescharacteristic
391C23×C4#4111yescharacteristic
392C23×C4#4111yescharacteristic
393C23×C4#4111yescharacteristic
394C23×C4#4111yescharacteristic
395C23×C4#4111yescharacteristic
396C23×C4#4111yescharacteristic
397C23×C4#4111yescharacteristic
398C23×C4#4111yescharacteristic
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—22no—
439C2×M16—22no—
440C2×M16—22no—
441C2×M16—22no—
442C2×M16—22no—
443C2×M16—22no—
444C2×M16—22no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—22no—
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×M16—41no—
495C2×M16—41no—
496C2×M16—41no—
497C2×M16—41no—
498C2×M16—41no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16—41no—
502C2×M16—41no—
503C2×M16—41no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16C22⋊C414yes—
508C2×M16C22⋊C414yes—
509C2×M16C22⋊C414yes—
510C2×M16C22⋊C414yes—
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—22no—
515C22×C8—22no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—22no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—22no—
522C22×C8—22no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8—41no—
539#117—22no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—22no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—22no—
549#117—22no—
550#117—22no—
551#117—22no—
552#117—22no—
553#117—22no—
554#117—22no—
555#117—22no—
556#117—41no—
557#117—41no—
558#117—41no—
559#117—41no—
560#117—41no—
561#117—41no—
562#117—41no—
563#117—41no—
564#117—41no—
565#117—41no—
566#117—41no—
567#117—41no—
568#117—41no—
569#117—41no—
570#117C22⋊C414yes—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42C22⋊C414yes—
607#104—232no—
608#104—232no—
609C22⋊C8—232no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—41no—
614C24—41no—
615C24—41no—
616C24—41no—
617C24—82no—
618C24—84no—
619C24#11711yescharacteristic
620C24C4×D411yescharacteristic
621C24C4×D411yescharacteristic
622C24#12111yescharacteristic
623C24#12111yescharacteristic
624C24#12111yescharacteristic
625C24C22⋊Q811yescharacteristic
626C24#12311yescharacteristic
627C24#12311yescharacteristic
628C24#12311yescharacteristic
629C24#12311yescharacteristic
630C24#12411yescharacteristic
631C24#12411yescharacteristic
632C24#12611yescharacteristic
633C24#12611yescharacteristic
634#41—24no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—24no—
639#41—24no—
640#41—24no—
641#41—24no—
642#41—24no—
643#41—24no—
644#41—24no—
645#41—24no—
646#41—24no—
647#41—24no—
648#41—24no—
649#41—24no—
650#41—42no—
651#41—42no—
652#41—42no—
653#41—42no—
654#41—42no—
655#41—42no—
656#41—42no—
657#41—42no—
658#41—42no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41—42no—
668#41—42no—
669#41—42no—
670#41—42no—
671#41—42no—
672#41—42no—
673#41—42no—
674#41—42no—
675#41—42no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—42no—
680#41—42no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41—42no—
690#41—42no—
691#41—42no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—22no—
702C2×Q8—22no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—22no—
708C2×Q8—22no—
709C2×Q8—22no—
710C2×Q8—22no—
711C2×Q8—22no—
712C2×Q8—22no—
713C2×Q8—41no—
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8—41no—
720C2×Q8—41no—
721C2×Q8—41no—
722C2×Q8—41no—
723C2×Q8—41no—
724C2×Q8—41no—
725C2×Q8#9514yes—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—24no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
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—41no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—41no—
775C2×D4—41no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4#9514yes—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—41no—
791C22×C4—41no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—84no—
824C22×C4—84no—
825C22×C4C2×C4211yescharacteristic
826C22×C4C2×C22⋊C411yescharacteristic
827C22×C4C2×C22⋊C411yescharacteristic
828C22×C4C2×C22⋊C411yescharacteristic
829C22×C4C2×C22⋊C411yescharacteristic
830C22×C4C2×C22⋊C411yescharacteristic
831C22×C4C2×C22⋊C411yescharacteristic
832C22×C4C2×C22⋊C411yescharacteristic
833C22×C4C2×C22⋊C411yescharacteristic
834C22×C4C2×C22⋊C411yescharacteristic
835C22×C4C2×C4⋊C411yescharacteristic
836C22×C4C2×C4⋊C411yescharacteristic
837C22×C4C2×C4⋊C411yescharacteristic
838C22×C4#11711yescharacteristic
839C22×C4#11711yescharacteristic
840C22×C4#11711yescharacteristic
841C22×C4#11711yescharacteristic
842C22×C4#11711yescharacteristic
843C22×C4C4×D411yescharacteristic
844C22×C4C4×D411yescharacteristic
845C22×C4C4×D411yescharacteristic
846C22×C4C4×D411yescharacteristic
847C22×C4C4×D411yescharacteristic
848C22×C4C4×D411yescharacteristic
849C22×C4C4×D411yescharacteristic
850C22×C4C4×D411yescharacteristic
851C22×C4C4×D411yescharacteristic
852C22×C4C4×D411yescharacteristic
853C22×C4C4×D411yescharacteristic
854C22×C4C4×D411yescharacteristic
855C22×C4C4×D411yescharacteristic
856C22×C4C4×D411yescharacteristic
857C22×C4C4×D411yescharacteristic
858C22×C4C4×D411yescharacteristic
859C22×C4C4×D411yescharacteristic
860C22×C4C4×D411yescharacteristic
861C22×C4C4×D411yescharacteristic
862C22×C4C4×D411yescharacteristic
863C22×C4C4×D411yescharacteristic
864C22×C4C4×D411yescharacteristic
865C22×C4#12011yescharacteristic
866C22×C4#12011yescharacteristic
867C22×C4#12011yescharacteristic
868C22×C4#12011yescharacteristic
869C22×C4#12011yescharacteristic
870C22×C4#12011yescharacteristic
871C22×C4#12011yescharacteristic
872C22×C4#12011yescharacteristic
873C22×C4#12011yescharacteristic
874C22×C4#12011yescharacteristic
875C22×C4#12011yescharacteristic
876C22×C4#12011yescharacteristic
877C22×C4#12011yescharacteristic
878C22×C4#12011yescharacteristic
879C22×C4#12011yescharacteristic
880C22×C4#12011yescharacteristic
881C22×C4#12111yescharacteristic
882C22×C4#12111yescharacteristic
883C22×C4#12111yescharacteristic
884C22×C4#12111yescharacteristic
885C22×C4#12111yescharacteristic
886C22×C4#12111yescharacteristic
887C22×C4#12111yescharacteristic
888C22×C4#12111yescharacteristic
889C22×C4#12111yescharacteristic
890C22×C4#12111yescharacteristic
891C22×C4#12111yescharacteristic
892C22×C4#12111yescharacteristic
893C22×C4#12111yescharacteristic
894C22×C4#12111yescharacteristic
895C22×C4#12111yescharacteristic
896C22×C4#12111yescharacteristic
897C22×C4#12111yescharacteristic
898C22×C4#12111yescharacteristic
899C22×C4#12111yescharacteristic
900C22×C4#12111yescharacteristic
901C22×C4#12111yescharacteristic
902C22×C4#12111yescharacteristic
903C22×C4#12111yescharacteristic
904C22×C4#12111yescharacteristic
905C22×C4#12111yescharacteristic
906C22×C4#12111yescharacteristic
907C22×C4#12111yescharacteristic
908C22×C4#12111yescharacteristic
909C22×C4#12111yescharacteristic
910C22×C4#12111yescharacteristic
911C22×C4#12111yescharacteristic
912C22×C4#12111yescharacteristic
913C22×C4#12111yescharacteristic
914C22×C4C22⋊Q811yescharacteristic
915C22×C4C22⋊Q811yescharacteristic
916C22×C4C22⋊Q811yescharacteristic
917C22×C4C22⋊Q811yescharacteristic
918C22×C4C22⋊Q811yescharacteristic
919C22×C4C22⋊Q811yescharacteristic
920C22×C4C22⋊Q811yescharacteristic
921C22×C4C22⋊Q811yescharacteristic
922C22×C4C22⋊Q811yescharacteristic
923C22×C4C22⋊Q811yescharacteristic
924C22×C4C22⋊Q811yescharacteristic
925C22×C4#12311yescharacteristic
926C22×C4#12311yescharacteristic
927C22×C4#12311yescharacteristic
928C22×C4#12311yescharacteristic
929C22×C4#12311yescharacteristic
930C22×C4#12311yescharacteristic
931C22×C4#12311yescharacteristic
932C22×C4#12311yescharacteristic
933C22×C4#12311yescharacteristic
934C22×C4#12311yescharacteristic
935C22×C4#12311yescharacteristic
936C22×C4#12311yescharacteristic
937C22×C4#12311yescharacteristic
938C22×C4#12311yescharacteristic
939C22×C4#12311yescharacteristic
940C22×C4#12311yescharacteristic
941C22×C4#12311yescharacteristic
942C22×C4#12311yescharacteristic
943C22×C4#12311yescharacteristic
944C22×C4#12311yescharacteristic
945C22×C4#12411yescharacteristic
946C22×C4#12411yescharacteristic
947C22×C4#12411yescharacteristic
948C22×C4#12411yescharacteristic
949C22×C4#12411yescharacteristic
950C22×C4#12411yescharacteristic
951C22×C4#12411yescharacteristic
952C22×C4#12411yescharacteristic
953C22×C4#12411yescharacteristic
954C22×C4#12411yescharacteristic
955C22×C4#12611yescharacteristic
956C22×C4#12611yescharacteristic
957C22×C4#12611yescharacteristic
958C22×C4#12611yescharacteristic
959C22×C4#12611yescharacteristic
960C22×C4#12611yescharacteristic
961C22×C4#12711yescharacteristic
962C22×C4#12711yescharacteristic
963C22×C4#12711yescharacteristic
964C22×C4#12711yescharacteristic
965M16—24no—
966M16—24no—
967M16—24no—
968M16—24no—
969M16—24no—
970M16—24no—
971M16—24no—
972M16—24no—
973M16—42no—
974M16—42no—
975M16—42no—
976M16—42no—
977M16—42no—
978M16—42no—
979M16—42no—
980M16—42no—
981M16—42no—
982M16—42no—
983M16—42no—
984M16—42no—
985M16—42no—
986M16—42no—
987M16—42no—
988M16—42no—
989M16—42no—
990M16—42no—
991M16—42no—
992M16—42no—
993M16—42no—
994M16—42no—
995M16—42no—
996M16—42no—
997C2×C8—24no—
998C2×C8—24no—
999C2×C8—24no—
1000C2×C8—24no—
1001C2×C8—42no—
1002C2×C8—42no—
1003C2×C8—42no—
1004C2×C8—42no—
1005C2×C8—42no—
1006C2×C8—42no—
1007C2×C8—42no—
1008C2×C8—42no—
1009C2×C8—42no—
1010C2×C8—42no—
1011C2×C8—42no—
1012C2×C8—42no—
1013C2×C8—42no—
1014C2×C8—42no—
1015C2×C8—42no—
1016C2×C8—42no—
1017C2×C8—42no—
1018C2×C8—42no—
1019C2×C8—42no—
1020C2×C8—42no—
1021C2×C8—42no—
1022C2×C8—42no—
1023C2×C8—42no—
1024C2×C8—42no—
1025C4⋊C4—24no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C22⋊C4—24no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C42—24no—
1042C42—24no—
1043C42—24no—
1044C42—42no—
1045C42—42no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C23—24no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—48no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—84no—
1065C23—84no—
1066C23—81no—
1067C23—81no—
1068C23—81no—
1069C23—81no—
1070C23—81no—
1071C23—81no—
1072C23—81no—
1073C23—81no—
1074C23—84no—
1075C23—84no—
1076C23—84no—
1077C23—84no—
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
1113Q8—24no—
1114Q8—24no—
1115Q8—42no—
1116Q8—42no—
1117Q8—42no—
1118Q8—42no—
1119Q8—42no—
1120Q8—42no—
1121D4—24no—
1122D4—24no—
1123D4—44no—
1124D4—44no—
1125D4—44no—
1126D4—44no—
1127D4—44no—
1128D4—44no—
1129D4—44no—
1130D4—44no—
1131D4—42no—
1132D4—42no—
1133D4—42no—
1134D4—42no—
1135D4—42no—
1136D4—42no—
1137C2×C4—24no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—84no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—84no—
1158C2×C4—84no—
1159C2×C4—84no—
1160C2×C4C2×#9511yescharacteristic
1161C2×C4C4×C22⋊C411yescharacteristic
1162C2×C4C4×C22⋊C411yescharacteristic
1163C2×C4C4×C22⋊C411yescharacteristic
1164C2×C4C4×C22⋊C411yescharacteristic
1165C2×C4C4×C22⋊C411yescharacteristic
1166C2×C4#37911yescharacteristic
1167C2×C4#37911yescharacteristic
1168C2×C4#37911yescharacteristic
1169C2×C4#38011yescharacteristic
1170C2×C4#38011yescharacteristic
1171C2×C4#38011yescharacteristic
1172C2×C4#38011yescharacteristic
1173C2×C4#38011yescharacteristic
1174C2×C4#38111yescharacteristic
1175C2×C4#38111yescharacteristic
1176C2×C4#38511yescharacteristic
1177C2×C4#38511yescharacteristic
1178C2×C4#38511yescharacteristic
1179C2×C4#38511yescharacteristic
1180C2×C4#38511yescharacteristic
1181C2×C4#38511yescharacteristic
1182C2×C4#38511yescharacteristic
1183C2×C4#38511yescharacteristic
1184C2×C4#38511yescharacteristic
1185C2×C4#38511yescharacteristic
1186C2×C4#38611yescharacteristic
1187C2×C4#38611yescharacteristic
1188C2×C4#38611yescharacteristic
1189C2×C4#38611yescharacteristic
1190C2×C4#38611yescharacteristic
1191C2×C4#38611yescharacteristic
1192C2×C4#38611yescharacteristic
1193C2×C4#38611yescharacteristic
1194C2×C4#38611yescharacteristic
1195C2×C4#38611yescharacteristic
1196C2×C4#38611yescharacteristic
1197C2×C4#38611yescharacteristic
1198C2×C4#38611yescharacteristic
1199C2×C4#38611yescharacteristic
1200C2×C4#38611yescharacteristic
1201C2×C4#38611yescharacteristic
1202C2×C4#38611yescharacteristic
1203C2×C4#38611yescharacteristic
1204C2×C4#38611yescharacteristic
1205C2×C4#38611yescharacteristic
1206C2×C4#38811yescharacteristic
1207C2×C4#38811yescharacteristic
1208C2×C4#38811yescharacteristic
1209C2×C4#38811yescharacteristic
1210C2×C4#38811yescharacteristic
1211C2×C4#38811yescharacteristic
1212C2×C4#38811yescharacteristic
1213C2×C4#38811yescharacteristic
1214C2×C4#38811yescharacteristic
1215C2×C4#38811yescharacteristic
1216C2×C4#38811yescharacteristic
1217C2×C4#38811yescharacteristic
1218C2×C4#38811yescharacteristic
1219C2×C4#38811yescharacteristic
1220C2×C4#38811yescharacteristic
1221C2×C4#38811yescharacteristic
1222C2×C4#39011yescharacteristic
1223C2×C4#39011yescharacteristic
1224C2×C4#39011yescharacteristic
1225C2×C4#39011yescharacteristic
1226C2×C4#39011yescharacteristic
1227C2×C4#39011yescharacteristic
1228C2×C4#39011yescharacteristic
1229C2×C4#39011yescharacteristic
1230C2×C4#39011yescharacteristic
1231C2×C4#39011yescharacteristic
1232C2×C4#39211yescharacteristic
1233C2×C4#39211yescharacteristic
1234C2×C4#39211yescharacteristic
1235C2×C4#39211yescharacteristic
1236C2×C4#39211yescharacteristic
1237C2×C4#39211yescharacteristic
1238C2×C4#39211yescharacteristic
1239C2×C4#39211yescharacteristic
1240C2×C4#39211yescharacteristic
1241C2×C4#39211yescharacteristic
1242C2×C4#39211yescharacteristic
1243C2×C4#39311yescharacteristic
1244C2×C4#39311yescharacteristic
1245C2×C4#39311yescharacteristic
1246C2×C4#39411yescharacteristic
1247C2×C4#39411yescharacteristic
1248C2×C4#39411yescharacteristic
1249C2×C4#39411yescharacteristic
1250C2×C4#39411yescharacteristic
1251C2×C4#39411yescharacteristic
1252C2×C4#39411yescharacteristic
1253C2×C4#39411yescharacteristic
1254C2×C4#39411yescharacteristic
1255C2×C4#39411yescharacteristic
1256C2×C4#39411yescharacteristic
1257C2×C4#39411yescharacteristic
1258C2×C4#39411yescharacteristic
1259C2×C4#39411yescharacteristic
1260C2×C4#39411yescharacteristic
1261C2×C4#39411yescharacteristic
1262C2×C4#39411yescharacteristic
1263C2×C4#39411yescharacteristic
1264C2×C4#39611yescharacteristic
1265C2×C4#39611yescharacteristic
1266C2×C4#39611yescharacteristic
1267C2×C4#39611yescharacteristic
1268C2×C4#39611yescharacteristic
1269C2×C4#39611yescharacteristic
1270C2×C4#39711yescharacteristic
1271C2×C4#39711yescharacteristic
1272C2×C4#39711yescharacteristic
1273C2×C4#39711yescharacteristic
1274C2×C4#39711yescharacteristic
1275C2×C4#39711yescharacteristic
1276C2×C4#39711yescharacteristic
1277C2×C4#39911yescharacteristic
1278C2×C4#39911yescharacteristic
1279C2×C4#39911yescharacteristic
1280C8—44no—
1281C8—44no—
1282C8—44no—
1283C8—44no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
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—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—48no—
1320C22—44no—
1321C22—84no—
1322C22—84no—
1323C22—84no—
1324C22—84no—
1325C22—84no—
1326C22—84no—
1327C22C22⋊#9511yescharacteristic
1328C22#143711yescharacteristic
1329C22#143711yescharacteristic
1330C22#143811yescharacteristic
1331C22#143811yescharacteristic
1332C22#143911yescharacteristic
1333C22#143911yescharacteristic
1334C22#143911yescharacteristic
1335C22#143911yescharacteristic
1336C22#143911yescharacteristic
1337C22#143911yescharacteristic
1338C22#144011yescharacteristic
1339C22#144011yescharacteristic
1340C22#144011yescharacteristic
1341C22#144011yescharacteristic
1342C4—44no—
1343C4—84no—
1344C4—84no—
1345C4C22⋊#9511yescharacteristic
1346C4C22⋊#9511yescharacteristic
1347C4#143711yescharacteristic
1348C4#143711yescharacteristic
1349C4#143811yescharacteristic
1350C4#143811yescharacteristic
1351C4#143811yescharacteristic
1352C4#143811yescharacteristic
1353C4#143911yescharacteristic
1354C4#143911yescharacteristic
1355C4#143911yescharacteristic
1356C4#143911yescharacteristic
1357C4#143911yescharacteristic
1358C4#143911yescharacteristic
1359C4#144011yescharacteristic
1360C4#144011yescharacteristic
1361C2—21no—
1362C2—21no—
1363C2—21no—
1364C2—21no—
1365C2—21no—
1366C2—21no—
1367C2—21no—
1368C2—21no—
1369C2—21no—
1370C2—21no—
1371C2—21no—
1372C2—21no—
1373C2—21no—
1374C2—21no—
1375C2—84no—
1376C2#755511yescharacteristic
1377C2#1111812yes—
subgroupG/H
centerC2×C4#392
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC22#1439
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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×#1742C2semidirect
6. C2×#1738C2semidirect
7. C2×#1733C2semidirect
25. C2×#421C4semidirect
26. C2×#421C4semidirect
32. #2879C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4212
C2×#28792
C22×#3442
C2×#17422
C2×#17382
C2×#17332