Finite Group Databasebeta

← #123606

Subgroups — #123606

Order 512.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#419C211yesmaximal, characteristic
2C22×#419C211yesmaximal, characteristic
3C2×#2310C211yesmaximal, characteristic
4C22×#344C211yesmaximal, characteristic
5C2×#1740C211yesmaximal, characteristic
6#20347C211yesmaximal, characteristic
7C2×#1733C211yesmaximal, characteristic
8C24×Q8C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C2×#419—22no—
16C2×#419—22no—
17C2×#419—22no—
18C2×#419—22no—
19C2×#419—22no—
20C2×#419—22no—
21C2×#419—22no—
22C2×#419—22no—
23C2×#419—22no—
24C2×#419—22no—
25C2×#419C414yescomplemented
26C2×#419C414yescomplemented
27C22×#103—22no—
28C22×#103—22no—
29#2310—22no—
30#2310—22no—
31#2310—22no—
32#2310C414yescomplemented
33C2×#391—22no—
34C2×#391—22no—
35C2×#381—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—
48C23×Q8—21no—
49C23×Q8—21no—
50C23×Q8—21no—
51C23×Q8—21no—
52C23×Q8—21no—
53C23×Q8—21no—
54C23×Q8—21no—
55C23×Q8—21no—
56C23×Q8—21no—
57C23×Q8—21no—
58C23×Q8—21no—
59C23×Q8—21no—
60C23×Q8—21no—
61C23×Q8—21no—
62C23×Q8—21no—
63C23×Q8—21no—
64C23×Q8—21no—
65C23×Q8—21no—
66C23×Q8—21no—
67C23×Q8—21no—
68C23×Q8—21no—
69C23×Q8—21no—
70C23×Q8—21no—
71C23×Q8C2×C412yes—
72C23×Q8C2×C412yes—
73C23×Q8C2×C412yes—
74C23×Q8D412yes—
75C23×Q8D412yes—
76C23×Q8D412yes—
77C23×Q8Q812yes—
78C24×C4—21no—
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⋊C4D412yes—
166C22×C42—21no—
167C22×C42—21no—
168C22×C42—21no—
169C22×C42—21no—
170#419—28no—
171#419—28no—
172#419—28no—
173#419—28no—
174#419—28no—
175#419—28no—
176#419—28no—
177#419—28no—
178C2×#103—28no—
179C2×#103—28no—
180C2×#103—28no—
181C2×#103—28no—
182C2×#103—28no—
183C2×#103—28no—
184#391—28no—
185#391—28no—
186#391—28no—
187#391—28no—
188#381—28no—
189#381—28no—
190C2×#95—28no—
191#344—28no—
192#342—28no—
193#340—28no—
194#339—28no—
195C25C2×D411yescharacteristic
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—22no—
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—41no—
274C22×Q8—41no—
275C22×Q8—41no—
276C22×Q8—41no—
277C22×Q8—41no—
278C22×Q8—41no—
279C22×Q8—41no—
280C22×Q8—41no—
281C22×Q8—41no—
282C22×Q8—41no—
283C22×Q8—41no—
284C22×Q8—41no—
285C22×Q8—41no—
286C22×Q8—41no—
287C22×Q8—41no—
288C22×Q8—41no—
289C22×Q8—41no—
290C22×Q8—41no—
291C22×Q8—41no—
292C22×Q8—41no—
293C22×Q8—41no—
294C22×Q8—41no—
295C22×Q8—41no—
296C22×Q8—41no—
297C22×Q8—41no—
298C22×Q8—41no—
299C22×Q8—41no—
300C22×Q8—41no—
301C22×Q8—41no—
302C22×Q8—41no—
303C22×Q8—41no—
304C22×Q8—41no—
305C22×Q8—41no—
306C22×Q8—41no—
307C22×Q8—41no—
308C22×Q8—41no—
309C22×Q8—41no—
310C22×Q8—41no—
311C22×Q8—41no—
312C22×Q8—41no—
313C22×Q8—41no—
314C22×Q8—41no—
315C22×Q8—41no—
316C22×Q8—41no—
317C22×Q8—41no—
318C22×Q8—41no—
319C22×Q8—41no—
320C22×Q8—41no—
321C22×Q8—41no—
322C22×Q8—41no—
323C22×Q8—41no—
324C22×Q8—41no—
325C22×Q8—41no—
326C22×Q8—41no—
327C22×Q8—41no—
328C22×Q8—41no—
329C22×Q8C4214yes—
330C22×Q8C22⋊C414yes—
331C22×Q8C22⋊C414yes—
332C22×Q8C22⋊C414yes—
333C22×Q8C4⋊C414yes—
334C22×Q8C4⋊C414yes—
335C22×Q8C4⋊C414yes—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—41no—
347C23×C4—41no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4—41no—
352C23×C4—41no—
353C23×C4—41no—
354C23×C4—41no—
355C23×C4C22×C411yescharacteristic
356C23×C4C22×C411yescharacteristic
357C23×C4C22×C411yescharacteristic
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
384C23×C4#4111yescharacteristic
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—41no—
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×M16C22⋊C414yes—
441C22×C8—22no—
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—41no—
451C22×C8—41no—
452C22×C8—41no—
453C22×C8—41no—
454C22×C8C22⋊C414yes—
455#117—22no—
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—41no—
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#117C22⋊C414yes—
519C2×C4⋊C4—22no—
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—41no—
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⋊C4C22⋊C414yes—
542C2×C4⋊C4C22⋊C414yes—
543C2×C22⋊C4—22no—
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—41no—
556C2×C22⋊C4—41no—
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⋊C4C22⋊C414yes—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—41no—
577C2×C42—41no—
578C2×C42—41no—
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—
591#103—232no—
592#103—232no—
593#95—232no—
594C24—44no—
595C24C2×C22⋊C411yescharacteristic
596C24C4×D411yescharacteristic
597C24C4×D411yescharacteristic
598C24#12011yescharacteristic
599C24#12011yescharacteristic
600C24#12011yescharacteristic
601C24#12111yescharacteristic
602C24#12111yescharacteristic
603C24#12111yescharacteristic
604C24#12111yescharacteristic
605C24#12111yescharacteristic
606C24C22⋊Q811yescharacteristic
607C24#12311yescharacteristic
608C24#12411yescharacteristic
609C24#12711yescharacteristic
610C2×Q8—24no—
611C2×Q8—24no—
612C2×Q8—24no—
613C2×Q8—24no—
614C2×Q8—24no—
615C2×Q8—24no—
616C2×Q8—24no—
617C2×Q8—24no—
618C2×Q8—24no—
619C2×Q8—24no—
620C2×Q8—24no—
621C2×Q8—24no—
622C2×Q8—24no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—24no—
626C2×Q8—24no—
627C2×Q8—24no—
628C2×Q8—24no—
629C2×Q8—24no—
630C2×Q8—24no—
631C2×Q8—24no—
632C2×Q8—24no—
633C2×Q8—24no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—24no—
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—24no—
645C2×Q8—42no—
646C2×Q8—42no—
647C2×Q8—42no—
648C2×Q8—42no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8—42no—
652C2×Q8—42no—
653C2×Q8—42no—
654C2×Q8—42no—
655C2×Q8—42no—
656C2×Q8—42no—
657C2×Q8—42no—
658C2×Q8—42no—
659C2×Q8—42no—
660C2×Q8—42no—
661C2×Q8—42no—
662C2×Q8—42no—
663C2×Q8—42no—
664C2×Q8—42no—
665C2×Q8—42no—
666C2×Q8—42no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—42no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8—42no—
678C2×Q8—42no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8—42no—
684C2×Q8—42no—
685C2×Q8—42no—
686C2×Q8—42no—
687C2×Q8—42no—
688C2×Q8—42no—
689C2×Q8—42no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8—42no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—42no—
698C2×Q8—42no—
699C2×Q8—42no—
700C2×Q8—42no—
701C2×Q8—42no—
702C2×Q8—42no—
703C2×Q8—42no—
704C2×Q8—42no—
705C2×Q8—42no—
706C2×Q8—42no—
707C2×Q8—42no—
708C2×Q8—42no—
709C2×Q8—42no—
710C2×Q8—42no—
711C2×Q8—42no—
712C2×Q8—42no—
713C2×Q8—42no—
714C2×Q8—42no—
715C2×Q8—42no—
716C2×Q8—42no—
717C2×Q8—42no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8—42no—
722C2×Q8—42no—
723C2×Q8—42no—
724C2×Q8—42no—
725C2×Q8—42no—
726C2×Q8—42no—
727C2×Q8—42no—
728C2×Q8—42no—
729C2×Q8#9518yes—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—84no—
780C22×C4—84no—
781C22×C4C2×C4211yescharacteristic
782C22×C4C2×C22⋊C411yescharacteristic
783C22×C4C2×C22⋊C411yescharacteristic
784C22×C4C2×C22⋊C411yescharacteristic
785C22×C4C2×C22⋊C411yescharacteristic
786C22×C4C2×C22⋊C411yescharacteristic
787C22×C4C2×C22⋊C411yescharacteristic
788C22×C4C2×C22⋊C411yescharacteristic
789C22×C4C2×C22⋊C411yescharacteristic
790C22×C4C2×C4⋊C411yescharacteristic
791C22×C4C2×C4⋊C411yescharacteristic
792C22×C4C2×C4⋊C411yescharacteristic
793C22×C4#11711yescharacteristic
794C22×C4#11711yescharacteristic
795C22×C4#11711yescharacteristic
796C22×C4#11711yescharacteristic
797C22×C4#11711yescharacteristic
798C22×C4#11711yescharacteristic
799C22×C4C4×D411yescharacteristic
800C22×C4C4×D411yescharacteristic
801C22×C4C4×D411yescharacteristic
802C22×C4C4×D411yescharacteristic
803C22×C4C4×D411yescharacteristic
804C22×C4C4×D411yescharacteristic
805C22×C4C4×D411yescharacteristic
806C22×C4C4×D411yescharacteristic
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×C4#12011yescharacteristic
822C22×C4#12011yescharacteristic
823C22×C4#12011yescharacteristic
824C22×C4#12011yescharacteristic
825C22×C4#12011yescharacteristic
826C22×C4#12011yescharacteristic
827C22×C4#12011yescharacteristic
828C22×C4#12011yescharacteristic
829C22×C4#12011yescharacteristic
830C22×C4#12011yescharacteristic
831C22×C4#12011yescharacteristic
832C22×C4#12011yescharacteristic
833C22×C4#12011yescharacteristic
834C22×C4#12111yescharacteristic
835C22×C4#12111yescharacteristic
836C22×C4#12111yescharacteristic
837C22×C4#12111yescharacteristic
838C22×C4#12111yescharacteristic
839C22×C4#12111yescharacteristic
840C22×C4#12111yescharacteristic
841C22×C4#12111yescharacteristic
842C22×C4#12111yescharacteristic
843C22×C4#12111yescharacteristic
844C22×C4#12111yescharacteristic
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×C4C22⋊Q811yescharacteristic
866C22×C4C22⋊Q811yescharacteristic
867C22×C4C22⋊Q811yescharacteristic
868C22×C4C22⋊Q811yescharacteristic
869C22×C4C22⋊Q811yescharacteristic
870C22×C4C22⋊Q811yescharacteristic
871C22×C4C22⋊Q811yescharacteristic
872C22×C4C22⋊Q811yescharacteristic
873C22×C4C22⋊Q811yescharacteristic
874C22×C4C22⋊Q811yescharacteristic
875C22×C4C22⋊Q811yescharacteristic
876C22×C4#12311yescharacteristic
877C22×C4#12311yescharacteristic
878C22×C4#12311yescharacteristic
879C22×C4#12311yescharacteristic
880C22×C4#12311yescharacteristic
881C22×C4#12311yescharacteristic
882C22×C4#12311yescharacteristic
883C22×C4#12311yescharacteristic
884C22×C4#12311yescharacteristic
885C22×C4#12311yescharacteristic
886C22×C4#12311yescharacteristic
887C22×C4#12311yescharacteristic
888C22×C4#12311yescharacteristic
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#12411yescharacteristic
900C22×C4#12411yescharacteristic
901C22×C4#12411yescharacteristic
902C22×C4#12411yescharacteristic
903C22×C4#12411yescharacteristic
904C22×C4#12411yescharacteristic
905C22×C4#12411yescharacteristic
906C22×C4#12411yescharacteristic
907C22×C4#12411yescharacteristic
908C22×C4#12411yescharacteristic
909C22×C4#12411yescharacteristic
910C22×C4#12611yescharacteristic
911C22×C4#12611yescharacteristic
912C22×C4#12611yescharacteristic
913C22×C4#12611yescharacteristic
914C22×C4#12611yescharacteristic
915C22×C4#12611yescharacteristic
916C22×C4#12611yescharacteristic
917C22×C4#12611yescharacteristic
918C22×C4#12711yescharacteristic
919C22×C4#12711yescharacteristic
920C22×C4#12711yescharacteristic
921M16—24no—
922M16—24no—
923M16—42no—
924M16—42no—
925M16—42no—
926M16—42no—
927M16—42no—
928M16—42no—
929M16—42no—
930M16—42no—
931M16—42no—
932M16—42no—
933M16—42no—
934M16—42no—
935M16—42no—
936M16—42no—
937C2×C8—24no—
938C2×C8—24no—
939C2×C8—24no—
940C2×C8—24no—
941C2×C8—42no—
942C2×C8—42no—
943C2×C8—42no—
944C2×C8—42no—
945C2×C8—42no—
946C2×C8—42no—
947C2×C8—42no—
948C2×C8—42no—
949C2×C8—42no—
950C2×C8—42no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C42—24no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—42no—
993C42—42no—
994C42—42no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—42no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23C4×C22⋊C411yescharacteristic
1015C23#37911yescharacteristic
1016C23#38011yescharacteristic
1017C23#38511yescharacteristic
1018C23#38511yescharacteristic
1019C23#38611yescharacteristic
1020C23#38611yescharacteristic
1021C23#38611yescharacteristic
1022C23#38611yescharacteristic
1023C23#38611yescharacteristic
1024C23#38611yescharacteristic
1025C23#38811yescharacteristic
1026C23#38811yescharacteristic
1027C23#38811yescharacteristic
1028C23#38811yescharacteristic
1029C23#39011yescharacteristic
1030C23#39011yescharacteristic
1031C23#39011yescharacteristic
1032C23#39011yescharacteristic
1033C23#39211yescharacteristic
1034C23#39211yescharacteristic
1035C23#39211yescharacteristic
1036C23#39211yescharacteristic
1037C23#39211yescharacteristic
1038C23#39311yescharacteristic
1039C23#39411yescharacteristic
1040C23#39411yescharacteristic
1041C23#39411yescharacteristic
1042C23#39411yescharacteristic
1043C23#39411yescharacteristic
1044C23#39411yescharacteristic
1045C23#39611yescharacteristic
1046C23#39611yescharacteristic
1047C23#39711yescharacteristic
1048C23#39911yescharacteristic
1049Q8—28no—
1050Q8—28no—
1051Q8—44no—
1052Q8—44no—
1053Q8—44no—
1054Q8—44no—
1055Q8—44no—
1056Q8—44no—
1057Q8—44no—
1058Q8—44no—
1059Q8—44no—
1060Q8—44no—
1061Q8—44no—
1062Q8—44no—
1063Q8—44no—
1064Q8—44no—
1065C2×C4—28no—
1066C2×C4—44no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—48no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—84no—
1087C2×C4—84no—
1088C2×C4—84no—
1089C2×C4—84no—
1090C2×C4—84no—
1091C2×C4—84no—
1092C2×C4—84no—
1093C2×C4—84no—
1094C2×C4—84no—
1095C2×C4—84no—
1096C2×C4C2×#9511yescharacteristic
1097C2×C4C4×C22⋊C411yescharacteristic
1098C2×C4C4×C22⋊C411yescharacteristic
1099C2×C4C4×C22⋊C411yescharacteristic
1100C2×C4C4×C22⋊C411yescharacteristic
1101C2×C4C4×C22⋊C411yescharacteristic
1102C2×C4#37911yescharacteristic
1103C2×C4#37911yescharacteristic
1104C2×C4#38011yescharacteristic
1105C2×C4#38011yescharacteristic
1106C2×C4#38011yescharacteristic
1107C2×C4#38011yescharacteristic
1108C2×C4#38011yescharacteristic
1109C2×C4#38111yescharacteristic
1110C2×C4#38111yescharacteristic
1111C2×C4#38111yescharacteristic
1112C2×C4#38511yescharacteristic
1113C2×C4#38511yescharacteristic
1114C2×C4#38511yescharacteristic
1115C2×C4#38511yescharacteristic
1116C2×C4#38511yescharacteristic
1117C2×C4#38511yescharacteristic
1118C2×C4#38511yescharacteristic
1119C2×C4#38511yescharacteristic
1120C2×C4#38511yescharacteristic
1121C2×C4#38511yescharacteristic
1122C2×C4#38611yescharacteristic
1123C2×C4#38611yescharacteristic
1124C2×C4#38611yescharacteristic
1125C2×C4#38611yescharacteristic
1126C2×C4#38611yescharacteristic
1127C2×C4#38611yescharacteristic
1128C2×C4#38611yescharacteristic
1129C2×C4#38611yescharacteristic
1130C2×C4#38611yescharacteristic
1131C2×C4#38611yescharacteristic
1132C2×C4#38611yescharacteristic
1133C2×C4#38611yescharacteristic
1134C2×C4#38611yescharacteristic
1135C2×C4#38611yescharacteristic
1136C2×C4#38611yescharacteristic
1137C2×C4#38611yescharacteristic
1138C2×C4#38611yescharacteristic
1139C2×C4#38611yescharacteristic
1140C2×C4#38811yescharacteristic
1141C2×C4#38811yescharacteristic
1142C2×C4#38811yescharacteristic
1143C2×C4#38811yescharacteristic
1144C2×C4#38811yescharacteristic
1145C2×C4#38811yescharacteristic
1146C2×C4#38811yescharacteristic
1147C2×C4#38811yescharacteristic
1148C2×C4#38811yescharacteristic
1149C2×C4#38811yescharacteristic
1150C2×C4#38811yescharacteristic
1151C2×C4#38811yescharacteristic
1152C2×C4#38811yescharacteristic
1153C2×C4#38811yescharacteristic
1154C2×C4#38811yescharacteristic
1155C2×C4#38811yescharacteristic
1156C2×C4#38811yescharacteristic
1157C2×C4#38811yescharacteristic
1158C2×C4#38811yescharacteristic
1159C2×C4#38811yescharacteristic
1160C2×C4#39011yescharacteristic
1161C2×C4#39011yescharacteristic
1162C2×C4#39011yescharacteristic
1163C2×C4#39011yescharacteristic
1164C2×C4#39011yescharacteristic
1165C2×C4#39011yescharacteristic
1166C2×C4#39011yescharacteristic
1167C2×C4#39011yescharacteristic
1168C2×C4#39211yescharacteristic
1169C2×C4#39211yescharacteristic
1170C2×C4#39211yescharacteristic
1171C2×C4#39211yescharacteristic
1172C2×C4#39211yescharacteristic
1173C2×C4#39211yescharacteristic
1174C2×C4#39211yescharacteristic
1175C2×C4#39311yescharacteristic
1176C2×C4#39311yescharacteristic
1177C2×C4#39311yescharacteristic
1178C2×C4#39411yescharacteristic
1179C2×C4#39411yescharacteristic
1180C2×C4#39411yescharacteristic
1181C2×C4#39411yescharacteristic
1182C2×C4#39411yescharacteristic
1183C2×C4#39411yescharacteristic
1184C2×C4#39411yescharacteristic
1185C2×C4#39411yescharacteristic
1186C2×C4#39411yescharacteristic
1187C2×C4#39411yescharacteristic
1188C2×C4#39411yescharacteristic
1189C2×C4#39411yescharacteristic
1190C2×C4#39411yescharacteristic
1191C2×C4#39411yescharacteristic
1192C2×C4#39411yescharacteristic
1193C2×C4#39411yescharacteristic
1194C2×C4#39411yescharacteristic
1195C2×C4#39411yescharacteristic
1196C2×C4#39611yescharacteristic
1197C2×C4#39611yescharacteristic
1198C2×C4#39611yescharacteristic
1199C2×C4#39611yescharacteristic
1200C2×C4#39611yescharacteristic
1201C2×C4#39611yescharacteristic
1202C2×C4#39711yescharacteristic
1203C2×C4#39711yescharacteristic
1204C2×C4#39711yescharacteristic
1205C2×C4#39711yescharacteristic
1206C2×C4#39711yescharacteristic
1207C2×C4#39711yescharacteristic
1208C2×C4#39711yescharacteristic
1209C2×C4#39711yescharacteristic
1210C2×C4#39711yescharacteristic
1211C2×C4#39711yescharacteristic
1212C2×C4#39711yescharacteristic
1213C2×C4#39911yescharacteristic
1214C2×C4#39911yescharacteristic
1215C2×C4#39911yescharacteristic
1216C8—44no—
1217C8—44no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22C22⋊#9511yescharacteristic
1253C22#143711yescharacteristic
1254C22#143711yescharacteristic
1255C22#143811yescharacteristic
1256C22#143811yescharacteristic
1257C22#143811yescharacteristic
1258C22#143811yescharacteristic
1259C22#143911yescharacteristic
1260C22#143911yescharacteristic
1261C22#143911yescharacteristic
1262C22#143911yescharacteristic
1263C22#143911yescharacteristic
1264C22#143911yescharacteristic
1265C22#144011yescharacteristic
1266C22#144011yescharacteristic
1267C22#200914yes—
1268C4—48no—
1269C4—84no—
1270C4—84no—
1271C4—84no—
1272C4—84no—
1273C4C22⋊#9511yescharacteristic
1274C4C22⋊#9511yescharacteristic
1275C4#143711yescharacteristic
1276C4#143711yescharacteristic
1277C4#143811yescharacteristic
1278C4#143811yescharacteristic
1279C4#143911yescharacteristic
1280C4#143911yescharacteristic
1281C4#143911yescharacteristic
1282C4#143911yescharacteristic
1283C4#143911yescharacteristic
1284C4#143911yescharacteristic
1285C4#144011yescharacteristic
1286C4#144011yescharacteristic
1287C4#144011yescharacteristic
1288C4#144011yescharacteristic
1289C2—21no—
1290C2—21no—
1291C2—21no—
1292C2—21no—
1293C2—21no—
1294C2—21no—
1295C2—21no—
1296C2—21no—
1297C2—21no—
1298C2—21no—
1299C2—21no—
1300C2—21no—
1301C2#755511yescharacteristic
1302C2#1100512yes—
1303C2#1103112yes—
1304C2#1113012yes—
subgroupG/H
center, socleC23#392
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
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
25. C2×#419C4semidirect
26. C2×#419C4semidirect
32. #2310C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4192
C2×#23102
C22×#3442
C2×#17402
#203472
C2×#17332