Finite Group Databasebeta

← #357843

Subgroups — #357843

Order 512.

2730 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic, complemented
2C2×#2896C211yesmaximal, characteristic
3C22×#417C211yesmaximal, characteristic
4C22×#413C211yesmaximal, characteristic
5C22×#343C211yesmaximal, characteristic, complemented
6C2×#1738C211yesmaximal, characteristic, complemented
7#20335C211yesmaximal, characteristic, complemented
8#11145C214yesmaximal, complemented
9#11144C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C23×M16C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C2×#428—24no—
18C2×#428—22no—
19C2×#428—24no—
20C2×#428C2214yes—
21C22×#107—21no—
22C22×#106—21no—
23#2896—24no—
24#2896—24no—
25C2×#417—24no—
26C2×#417—22no—
27C2×#417—22no—
28C2×#417—24no—
29C2×#417—21no—
30C2×#417—21no—
31C2×#419C2212yes—
32C2×#418C2212yes—
33C2×#416—22no—
34C22×#103C2212yes—
35C22×#102C2212yes—
36C2×#413—24no—
37C2×#413—24no—
38C2×#413C418yescomplemented
39C22×#101C2212yes—
40C22×#100C2212yes—
41C2×#343—24no—
42C2×#343C2214yes—
43#1738—24no—
44C2×#341C2214yes—
45#1729—22no—
46#1729C2214yes—
47#1728—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—21no—
52C22×#41—21no—
53C22×#41—22no—
54C22×#41—21no—
55C22×#41—21no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41C2×C414yes—
62C22×#41D414yes—
63C22×#41Q814yes—
64C23×Q8C2311yescharacteristic
65C23×D4—21no—
66C23×D4C2311yescharacteristic
67C24×C4—21no—
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C22×M16—22no—
71C22×M16—21no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—21no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16—21no—
79C22×M16—22no—
80C22×M16—22no—
81C22×M16—22no—
82C22×M16—22no—
83C22×M16—22no—
84C22×M16—22no—
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16C2×C414yes—
93C22×M16C2×C414yes—
94C22×M16D414yes—
95C22×M16D414yes—
96C22×M16D414yes—
97C22×M16D412yes—
98C22×M16D412yes—
99C22×M16C2312yes—
100C22×M16C2312yes—
101C22×M16C2312yes—
102C23×C8—21no—
103C23×C8—21no—
104C23×C8—21no—
105C23×C8C2312yes—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—22no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—22no—
112C2×#117D412yes—
113C2×#117C2312yes—
114C22×C4⋊C4—22no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—22no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—22no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4D411yescharacteristic
123C22×C4⋊C4D411yescharacteristic
124C22×C4⋊C4D414yes—
125C22×C4⋊C4C2312yes—
126C22×C22⋊C4—21no—
127C22×C42—21no—
128#428—216no—
129#428—28no—
130#428—28no—
131C2×#107—28no—
132C2×#107—24no—
133C2×#106—28no—
134C2×#106—24no—
135#419—24no—
136#419—24no—
137#418—24no—
138#418—24no—
139#417—216no—
140#417—216no—
141#417—28no—
142#417—28no—
143#416—216no—
144C2×#103—24no—
145C2×#103—24no—
146C2×#103—24no—
147C2×#103—22no—
148C2×#103—22no—
149C2×#102—24no—
150C2×#102—24no—
151C2×#102—24no—
152C2×#102—22no—
153C2×#102—22no—
154#413—232no—
155C2×#101—24no—
156C2×#101—24no—
157C2×#101C2×C418yescomplemented
158C2×#100—24no—
159C2×#100—24no—
160C2×#100C2×C418yescomplemented
161#343—28no—
162#341—28no—
163#336—28no—
164C25—21no—
165C25#4111yescharacteristic
166C2×#41—28no—
167C2×#41—28no—
168C2×#41—28no—
169C2×#41—24no—
170C2×#41—24no—
171C2×#41—28no—
172C2×#41—24no—
173C2×#41—24no—
174C2×#41—28no—
175C2×#41—24no—
176C2×#41—24no—
177C2×#41—24no—
178C2×#41—24no—
179C2×#41—24no—
180C2×#41—24no—
181C2×#41—28no—
182C2×#41—24no—
183C2×#41—24no—
184C2×#41—28no—
185C2×#41—28no—
186C2×#41—28no—
187C2×#41—42no—
188C2×#41—42no—
189C2×#41—42no—
190C2×#41—42no—
191C2×#41—44no—
192C2×#41—42no—
193C2×#41—42no—
194C2×#41—44no—
195C2×#41—42no—
196C2×#41—42no—
197C2×#41—44no—
198C2×#41—44no—
199C2×#41—42no—
200C2×#41—42no—
201C2×#41—44no—
202C2×#41—44no—
203C2×#41—42no—
204C2×#41—42no—
205C2×#41C4⋊C4116yes—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8C22×C412yes—
218C22×Q8C2×D412yes—
219C22×Q8C2×Q812yes—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—42no—
235C22×D4—41no—
236C22×D4—41no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4C22×C412yes—
240C22×D4C2×D412yes—
241C22×D4C2×Q812yes—
242C23×C4—21no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—42no—
251C23×C4—41no—
252C23×C4—41no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4—84no—
259C23×C4C22×C412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D412yes—
268C23×C4C2×D411yescharacteristic
269C23×C4C2×Q812yes—
270C23×C4#4111yescharacteristic
271C23×C4#4112yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C23×C4#4112yes—
276C23×C4C2411yescharacteristic
277C2×M16—24no—
278C2×M16—28no—
279C2×M16—24no—
280C2×M16—24no—
281C2×M16—28no—
282C2×M16—28no—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—24no—
287C2×M16—24no—
288C2×M16—24no—
289C2×M16—24no—
290C2×M16—24no—
291C2×M16—24no—
292C2×M16—24no—
293C2×M16—24no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—28no—
297C2×M16—28no—
298C2×M16—28no—
299C2×M16—28no—
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—44no—
309C2×M16—44no—
310C2×M16—42no—
311C2×M16—42no—
312C2×M16—44no—
313C2×M16—44no—
314C2×M16—44no—
315C2×M16—44no—
316C2×M16—44no—
317C2×M16—42no—
318C2×M16—44no—
319C2×M16—42no—
320C2×M16C22⋊C4116yes—
321C2×M16C22×C414yes—
322C2×M16C22×C414yes—
323C2×M16C2×D414yes—
324C2×M16C2×D414yes—
325C2×M16C2×D414yes—
326C22×C8—24no—
327C22×C8—24no—
328C22×C8—24no—
329C22×C8—22no—
330C22×C8—24no—
331C22×C8—24no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8—42no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8—42no—
344C22×C8C2×D414yes—
345#117—24no—
346#117—24no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351#117—42no—
352#117—42no—
353#117—42no—
354#117—42no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D412yes—
380C2×C4⋊C4C2×D412yes—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—42no—
388C2×C42—42no—
389#107—216no—
390#106—216no—
391#103—216no—
392#103—28no—
393#103—28no—
394#102—216no—
395#102—28no—
396#102—28no—
397#101—216no—
398#100—216no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—42no—
403C24—42no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—41no—
408C24—82no—
409C24—82no—
410C24#11712yes—
411C24#12111yescharacteristic
412C24#12111yescharacteristic
413C24#12112yes—
414C24#12112yes—
415C24C22⋊Q812yes—
416C24#12612yes—
417C24#12612yes—
418C24C2×#4111yescharacteristic
419#41—216no—
420#41—216no—
421#41—216no—
422#41—216no—
423#41—48no—
424#41—48no—
425#41—48no—
426#41—48no—
427#41—48no—
428#41—48no—
429#41—48no—
430#41—48no—
431#41—48no—
432#41—48no—
433#41—48no—
434#41—48no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8C2×C4⋊C414yes—
463C2×D4—216no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4C2×C4⋊C414yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—216no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—48no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—48no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—48no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—88no—
532C22×C4—84no—
533C22×C4—88no—
534C22×C4C2×C22⋊C414yes—
535C22×C4C2×C4⋊C414yes—
536C22×C4#11712yes—
537C22×C4C4×D412yes—
538C22×C4C4×D412yes—
539C22×C4C4×D414yes—
540C22×C4C4×D412yes—
541C22×C4C4×D412yes—
542C22×C4C4×D414yes—
543C22×C4#12012yes—
544C22×C4#12012yes—
545C22×C4#12012yes—
546C22×C4#12012yes—
547C22×C4#12012yes—
548C22×C4#12012yes—
549C22×C4#12114yes—
550C22×C4#12112yes—
551C22×C4#12112yes—
552C22×C4#12114yes—
553C22×C4#12112yes—
554C22×C4#12112yes—
555C22×C4#12114yes—
556C22×C4#12112yes—
557C22×C4#12112yes—
558C22×C4#12111yescharacteristic
559C22×C4#12111yescharacteristic
560C22×C4C22⋊Q814yes—
561C22×C4C22⋊Q812yes—
562C22×C4C22⋊Q812yes—
563C22×C4C22⋊Q814yes—
564C22×C4C22⋊Q812yes—
565C22×C4C22⋊Q812yes—
566C22×C4C22⋊Q814yes—
567C22×C4C22⋊Q812yes—
568C22×C4#12314yes—
569C22×C4#12314yes—
570C22×C4#12314yes—
571C22×C4#12312yes—
572C22×C4#12312yes—
573C22×C4#12314yes—
574C22×C4#12412yes—
575C22×C4#12412yes—
576C22×C4#12414yes—
577C22×C4#12414yes—
578C22×C4#12612yes—
579C22×C4#12612yes—
580C22×C4#12712yes—
581C22×C4#12712yes—
582C22×C4C23×C411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×Q811yescharacteristic
591C22×C4C2×#4111yescharacteristic
592C22×C4C2×#4111yescharacteristic
593C22×C4C2×#4111yescharacteristic
594C22×C4C2×#4111yescharacteristic
595C22×C4C2×#4111yescharacteristic
596M16—24no—
597M16—24no—
598M16—24no—
599M16—216no—
600M16—24no—
601M16—24no—
602M16—24no—
603M16—24no—
604M16—42no—
605M16—42no—
606M16—42no—
607M16—42no—
608M16—48no—
609M16—48no—
610M16—48no—
611M16—48no—
612M16C2×C22⋊C418yes—
613C2×C8—24no—
614C2×C8—24no—
615C2×C8—24no—
616C2×C8—216no—
617C2×C8—24no—
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—24no—
622C2×C8—42no—
623C2×C8—42no—
624C2×C8—42no—
625C2×C8—42no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8—42no—
629C2×C8—42no—
630C2×C8—48no—
631C2×C8—48no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—44no—
647C42—42no—
648C42—42no—
649C42—44no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—42no—
658C23—42no—
659C23—44no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—84no—
672C23—84no—
673C23—82no—
674C23—82no—
675C23—84no—
676C23—84no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23—82no—
681C23#38014yes—
682C23#38812yes—
683C23#38812yes—
684C23#38814yes—
685C23#39212yes—
686C23#39212yes—
687C23#39612yes—
688C23#39612yes—
689C23#39614yes—
690C23#39714yes—
691C23C2×#11711yescharacteristic
692C23C2×#12111yescharacteristic
693C23C2×#12111yescharacteristic
694C23C2×#12111yescharacteristic
695C23C2×C22⋊Q811yescharacteristic
696C23C2×#12611yescharacteristic
697C23C2×#12611yescharacteristic
698Q8—24no—
699Q8—24no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704Q8—42no—
705Q8—42no—
706D4—24no—
707D4—24no—
708D4—416no—
709D4—416no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716C2×C4—24no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—416no—
724C2×C4—416no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—88no—
733C2×C4—88no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4#38014yes—
738C2×C4#38514yes—
739C2×C4#38514yes—
740C2×C4#38514yes—
741C2×C4#38514yes—
742C2×C4#38614yes—
743C2×C4#38614yes—
744C2×C4#38814yes—
745C2×C4#38812yes—
746C2×C4#38812yes—
747C2×C4#39014yes—
748C2×C4#39014yes—
749C2×C4#39212yes—
750C2×C4#39212yes—
751C2×C4#39314yes—
752C2×C4#39314yes—
753C2×C4#39414yes—
754C2×C4#39414yes—
755C2×C4#39414yes—
756C2×C4#39414yes—
757C2×C4#39614yes—
758C2×C4#39612yes—
759C2×C4#39612yes—
760C2×C4#39714yes—
761C2×C4#39914yes—
762C2×C4#39914yes—
763C2×C4C22×C22⋊C411yescharacteristic
764C2×C4C22×C4⋊C411yescharacteristic
765C2×C4C2×C4×D411yescharacteristic
766C2×C4C2×C4×D411yescharacteristic
767C2×C4C2×C4×D411yescharacteristic
768C2×C4C2×C4×D411yescharacteristic
769C2×C4C2×#12011yescharacteristic
770C2×C4C2×#12011yescharacteristic
771C2×C4C2×#12011yescharacteristic
772C2×C4C2×#12111yescharacteristic
773C2×C4C2×#12111yescharacteristic
774C2×C4C2×#12111yescharacteristic
775C2×C4C2×#12111yescharacteristic
776C2×C4C2×#12111yescharacteristic
777C2×C4C2×C22⋊Q811yescharacteristic
778C2×C4C2×C22⋊Q811yescharacteristic
779C2×C4C2×C22⋊Q811yescharacteristic
780C2×C4C2×C22⋊Q811yescharacteristic
781C2×C4C2×C22⋊Q811yescharacteristic
782C2×C4C2×#12311yescharacteristic
783C2×C4C2×#12311yescharacteristic
784C2×C4C2×#12311yescharacteristic
785C2×C4C2×#12311yescharacteristic
786C2×C4C2×#12311yescharacteristic
787C2×C4C2×#12411yescharacteristic
788C2×C4C2×#12411yescharacteristic
789C2×C4C2×#12411yescharacteristic
790C2×C4C2×#12711yescharacteristic
791C8—28no—
792C8—44no—
793C8—44no—
794C8—44no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—24no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—22no—
804C22—21no—
805C22—21no—
806C22—22no—
807C22—22no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—84no—
817C22—84no—
818C22—84no—
819C22—84no—
820C22—84no—
821C22—84no—
822C22—82no—
823C22—82no—
824C22#143914yes—
825C22#143914yes—
826C22C2×#38011yescharacteristic
827C22C2×#38811yescharacteristic
828C22C2×#38811yescharacteristic
829C22C2×#39211yescharacteristic
830C22C2×#39611yescharacteristic
831C22C2×#39611yescharacteristic
832C22C2×#39711yescharacteristic
833C22#306812yes—
834C22#306912yes—
835C4—44no—
836C4—82no—
837C4—84no—
838C4—82no—
839C4#143914yes—
840C4#143914yes—
841C4C2×#38511yescharacteristic
842C4C2×#38511yescharacteristic
843C4C2×#38611yescharacteristic
844C4C2×#39011yescharacteristic
845C4C2×#39311yescharacteristic
846C4C2×#39411yescharacteristic
847C4C2×#39411yescharacteristic
848C4C2×#39911yescharacteristic
849C2—21no—
850C2—21no—
851C2—21no—
852C2—21no—
853C2—24no—
854C2—24no—
855C2—84no—
856C2C2×#143911yescharacteristic
857C2#2107612yes—
858C2#2343911yescharacteristic
859C2#2344011yescharacteristic
860C2#2360412yes—
subgroupG/H
center, socleC23C2×#121
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#428C2semidirect
5. C22×#343C2semidirect
6. C2×#1738C2semidirect
7. #20335C2semidirect
8. #11145C2semidirect
9. #11144C2semidirect
38. C2×#413C4semidirect
157. C2×#101C2×C4semidirect
160. C2×#100C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C2×#28962
C22×#4172
C22×#4132
C22×#3432
C2×#17382
#203352
#111452
#111442