Finite Group Databasebeta

← #357955

Subgroups — #357955

Order 512.

3006 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#417C211yesmaximal, characteristic
2C22×#417C211yesmaximal, characteristic
3C2×#2297C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic, complemented
5C2×#1736C211yesmaximal, characteristic, complemented
6C2×#1728C211yesmaximal, characteristic, complemented
7C2×C4⋊#95C211yesmaximal, characteristic, complemented
8#11190C214yesmaximal, complemented
9#11189C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×#417—24no—
18C2×#417—24no—
19C2×#417—24no—
20C2×#417—24no—
21C2×#417—24no—
22C2×#417C418yescomplemented
23C22×#103C2212yes—
24C22×#103C2212yes—
25C22×#102C2212yes—
26C22×#102C2212yes—
27#2297—24no—
28#2297—24no—
29C2×#391C2212yes—
30C2×#390C2212yes—
31C2×#386—22no—
32C2×C4×C22⋊C4—21no—
33C2×C4×C22⋊C4—21no—
34C22×#95—22no—
35#1736—24no—
36#1736—24no—
37C2×#340C2214yes—
38C2×#340C2214yes—
39#1728—24no—
40C2×#336C2214yes—
41C4⋊#95—21no—
42C4⋊#95—21no—
43C4⋊#95C2214yes—
44C22×#41—22no—
45C22×#41—22no—
46C22×#41—22no—
47C22×#41—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41C2×C414yes—
56C22×#41D414yes—
57C22×#41D414yes—
58C23×Q8C2311yescharacteristic
59C23×D4—21no—
60C23×D4C2311yescharacteristic
61C24×C4—21no—
62C24×C4—21no—
63C24×C4—21no—
64C24×C4D412yes—
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16—22no—
78C22×M16C2×C414yes—
79C22×M16D414yes—
80C23×C8C2312yes—
81C23×C8C2312yes—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117D414yes—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4C2×C414yes—
101C22×C4⋊C4D414yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—22no—
107C22×C22⋊C4—22no—
108C22×C42—22no—
109C22×C42—22no—
110C22×C42—22no—
111C22×C42—21no—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—22no—
115C22×C42D411yescharacteristic
116C22×C42D411yescharacteristic
117C22×C42C2312yes—
118#417—232no—
119#417—232no—
120C2×#103—24no—
121C2×#103—24no—
122C2×#103—24no—
123C2×#103—24no—
124C2×#103—24no—
125C2×#103C2×C418yescomplemented
126C2×#102—24no—
127C2×#102—24no—
128C2×#102—24no—
129C2×#102—24no—
130C2×#102—24no—
131C2×#102C2×C418yescomplemented
132#391—24no—
133#391—24no—
134#390—24no—
135#390—24no—
136#386—216no—
137C4×C22⋊C4—28no—
138C4×C22⋊C4—28no—
139C2×#95—22no—
140C2×#95—22no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—48no—
144#340—28no—
145#340—28no—
146#336—28no—
147C25—21no—
148C25C2×D411yescharacteristic
149C2×#41—28no—
150C2×#41—28no—
151C2×#41—28no—
152C2×#41—28no—
153C2×#41—28no—
154C2×#41—28no—
155C2×#41—28no—
156C2×#41—28no—
157C2×#41—28no—
158C2×#41—28no—
159C2×#41—28no—
160C2×#41—28no—
161C2×#41—28no—
162C2×#41—28no—
163C2×#41—28no—
164C2×#41—44no—
165C2×#41—44no—
166C2×#41—44no—
167C2×#41—44no—
168C2×#41—44no—
169C2×#41—44no—
170C2×#41—44no—
171C2×#41—44no—
172C2×#41—44no—
173C2×#41—44no—
174C2×#41—44no—
175C2×#41—44no—
176C2×#41C22⋊C4116yes—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8C22×C412yes—
189C22×Q8C2×D412yes—
190C22×Q8C2×D412yes—
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—24no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—42no—
206C22×D4—42no—
207C22×D4—42no—
208C22×D4—42no—
209C22×D4C22×C412yes—
210C22×D4C2×D412yes—
211C22×D4C2×D412yes—
212C23×C4—24no—
213C23×C4—21no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—44no—
233C23×C4—44no—
234C23×C4—44no—
235C23×C4—44no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4C22×C412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D412yes—
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D412yes—
247C23×C4C2×D412yes—
248C23×C4C2×D412yes—
249C23×C4#4112yes—
250C23×C4#4112yes—
251C23×C4#4112yes—
252C23×C4#4112yes—
253C23×C4#4112yes—
254C23×C4#4112yes—
255C23×C4#4112yes—
256C23×C4#4112yes—
257C23×C4C2411yescharacteristic
258C2×M16—28no—
259C2×M16—28no—
260C2×M16—28no—
261C2×M16—28no—
262C2×M16—28no—
263C2×M16—28no—
264C2×M16—44no—
265C2×M16—44no—
266C2×M16—44no—
267C2×M16—44no—
268C2×M16—44no—
269C2×M16—44no—
270C2×M16—44no—
271C2×M16—44no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8C22×C414yes—
285C22×C8C2×D414yes—
286#117—28no—
287#117—28no—
288#117—44no—
289#117—44no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4C22×C414yes—
320C2×C4⋊C4C2×D414yes—
321C2×C4⋊C4C2×D414yes—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C42—24no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—42no—
345C2×C42—44no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42—42no—
349C2×C42—44no—
350#103—216no—
351#103—216no—
352#102—216no—
353#102—216no—
354#95—28no—
355#95—28no—
356#95—48no—
357#95—48no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—42no—
370C24—42no—
371C24—42no—
372C24—42no—
373C24C4×D412yes—
374C24#12012yes—
375C24#12112yes—
376C24#12112yes—
377C24#12112yes—
378C24#12312yes—
379C24#12412yes—
380C24C22×D411yescharacteristic
381#41—232no—
382#41—232no—
383#41—416no—
384#41—416no—
385#41—416no—
386#41—416no—
387#41—416no—
388#41—416no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8C2×C22⋊C414yes—
417C2×D4—216no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4C2×C22⋊C414yes—
452C22×C4—216no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—216no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—48no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—48no—
487C22×C4—48no—
488C22×C4—416no—
489C22×C4—416no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—88no—
507C22×C4—84no—
508C22×C4—84no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4—88no—
512C22×C4C2×C22⋊C414yes—
513C22×C4#11714yes—
514C22×C4#11714yes—
515C22×C4C4×D414yes—
516C22×C4C4×D414yes—
517C22×C4C4×D414yes—
518C22×C4C4×D412yes—
519C22×C4#12014yes—
520C22×C4#12012yes—
521C22×C4#12114yes—
522C22×C4#12114yes—
523C22×C4#12114yes—
524C22×C4#12114yes—
525C22×C4#12114yes—
526C22×C4#12112yes—
527C22×C4#12112yes—
528C22×C4#12112yes—
529C22×C4#12314yes—
530C22×C4#12314yes—
531C22×C4#12314yes—
532C22×C4#12314yes—
533C22×C4#12314yes—
534C22×C4#12314yes—
535C22×C4#12314yes—
536C22×C4#12314yes—
537C22×C4#12314yes—
538C22×C4#12312yes—
539C22×C4#12414yes—
540C22×C4#12414yes—
541C22×C4#12414yes—
542C22×C4#12412yes—
543C22×C4#12614yes—
544C22×C4#12614yes—
545C22×C4#12614yes—
546C22×C4#12614yes—
547C22×C4AGL(1,ℤ/8)14yes—
548C22×C4#13714yes—
549C22×C4C23×C411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C2×#4111yescharacteristic
556C22×C4C2×#4111yescharacteristic
557C22×C4C2×#4111yescharacteristic
558C22×C4C2×#4111yescharacteristic
559C22×C4C2×#4111yescharacteristic
560C22×C4C2×#4111yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563M16—416no—
564M16—416no—
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—42no—
572C2×C8—42no—
573C2×C8—42no—
574C2×C8—42no—
575C2×C8—42no—
576C2×C8—42no—
577C2×C8—42no—
578C2×C8—42no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C22⋊C4—416no—
594C22⋊C4—416no—
595C22⋊C4—48no—
596C42—42no—
597C42—42no—
598C42—42no—
599C42—42no—
600C42—44no—
601C42—44no—
602C42—48no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—82no—
639C23—82no—
640C23—82no—
641C23—82no—
642C23#38614yes—
643C23#38814yes—
644C23#38814yes—
645C23#39414yes—
646C23#39414yes—
647C23#39414yes—
648C23#39714yes—
649C23C2×C4×D411yescharacteristic
650C23C2×#12011yescharacteristic
651C23C2×#12111yescharacteristic
652C23C2×#12111yescharacteristic
653C23C2×#12111yescharacteristic
654C23C2×#12311yescharacteristic
655C23C2×#12411yescharacteristic
656C23C2×AGL(1,ℤ/8)12yes—
657C23C2×#13712yes—
658C23#57512yes—
659C23#57512yes—
660Q8—24no—
661Q8—24no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—42no—
667Q8—42no—
668D4—24no—
669D4—24no—
670D4—432no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—42no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—432no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—432no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—48no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—48no—
706C2×C4—44no—
707C2×C4—816no—
708C2×C4—816no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—84no—
712C2×C4—82no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—84no—
719C2×C4#38118yes—
720C2×C4#38614yes—
721C2×C4#38618yes—
722C2×C4#38814yes—
723C2×C4#38814yes—
724C2×C4#38818yes—
725C2×C4#38818yes—
726C2×C4#39418yes—
727C2×C4#39414yes—
728C2×C4#39414yes—
729C2×C4#39414yes—
730C2×C4#39718yes—
731C2×C4#39718yes—
732C2×C4#39718yes—
733C2×C4#39714yes—
734C2×C4C22×C22⋊C411yescharacteristic
735C2×C4C2×#11711yescharacteristic
736C2×C4C2×#11711yescharacteristic
737C2×C4C2×C4×D411yescharacteristic
738C2×C4C2×C4×D411yescharacteristic
739C2×C4C2×C4×D411yescharacteristic
740C2×C4C2×#12011yescharacteristic
741C2×C4C2×#12111yescharacteristic
742C2×C4C2×#12111yescharacteristic
743C2×C4C2×#12111yescharacteristic
744C2×C4C2×#12111yescharacteristic
745C2×C4C2×#12111yescharacteristic
746C2×C4C2×#12311yescharacteristic
747C2×C4C2×#12311yescharacteristic
748C2×C4C2×#12311yescharacteristic
749C2×C4C2×#12311yescharacteristic
750C2×C4C2×#12311yescharacteristic
751C2×C4C2×#12311yescharacteristic
752C2×C4C2×#12311yescharacteristic
753C2×C4C2×#12311yescharacteristic
754C2×C4C2×#12311yescharacteristic
755C2×C4C2×#12411yescharacteristic
756C2×C4C2×#12411yescharacteristic
757C2×C4C2×#12411yescharacteristic
758C2×C4C2×#12611yescharacteristic
759C2×C4C2×#12611yescharacteristic
760C2×C4C2×#12611yescharacteristic
761C2×C4C2×#12611yescharacteristic
762C8—44no—
763C8—44no—
764C22—28no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—84no—
778C22—82no—
779C22—82no—
780C22—84no—
781C22—84no—
782C22—84no—
783C22—82no—
784C22—82no—
785C22#144018yes—
786C22C2×#38611yescharacteristic
787C22C2×#38811yescharacteristic
788C22C2×#38811yescharacteristic
789C22C2×#39411yescharacteristic
790C22C2×#39411yescharacteristic
791C22C2×#39411yescharacteristic
792C22C2×#39711yescharacteristic
793C22C4×AGL(1,ℤ/8)12yes—
794C22C4×#13712yes—
795C22#300612yes—
796C22#300712yes—
797C22#303612yes—
798C22#303712yes—
799C22#303811yescharacteristic
800C22#303911yescharacteristic
801C22#304011yescharacteristic
802C22#304011yescharacteristic
803C22#305512yes—
804C22#305612yes—
805C22#309212yes—
806C22#309312yes—
807C22#314112yes—
808C22#314212yes—
809C4—44no—
810C4—44no—
811C4—44no—
812C4—84no—
813C4—84no—
814C4—84no—
815C4#144018yes—
816C4C2×#38111yescharacteristic
817C4C2×#38611yescharacteristic
818C4C2×#38811yescharacteristic
819C4C2×#38811yescharacteristic
820C4C2×#39411yescharacteristic
821C4C2×#39711yescharacteristic
822C4C2×#39711yescharacteristic
823C4C2×#39711yescharacteristic
824C2—28no—
825C2—84no—
826C2C2×#144011yescharacteristic
827C2#2092711yescharacteristic
828C2#2092811yescharacteristic
829C2#2105912yes—
830C2#2109312yes—
831C2#2348212yes—
832C2#2350812yes—
833C2#2354611yescharacteristic
834C2#2354711yescharacteristic
835C2#2363011yescharacteristic
836C2#2363111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1736C2semidirect
5. C2×#1736C2semidirect
6. C2×#1728C2semidirect
7. C2×C4⋊#95C2semidirect
8. #11190C2semidirect
9. #11189C2semidirect
22. C2×#417C4semidirect
125. C2×#103C2×C4semidirect
131. C2×#102C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4172
C2×#22972
C2×#17362
C2×#17282
C2×C4⋊#952
#111902
#111892