Finite Group Databasebeta

← #354077

Subgroups — #354077

Order 512.

3138 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#417C211yesmaximal, characteristic
2C22×#416C211yesmaximal, characteristic
3C22×#405C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic, complemented
7#13795C211yesmaximal, characteristic, complemented
8#10928C212yesmaximal, complemented
9#10927C212yesmaximal, complemented
10#10926C212yesmaximal, complemented
11#10925C212yesmaximal, complemented
12C23×#41C2211yescharacteristic
13C23×M16C2211yescharacteristic
14C24×C8C2211yescharacteristic
15C22×#117C2211yescharacteristic
16C22×#117C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C2×#417—24no—
20C2×#417—24no—
21C2×#417C418yescomplemented
22C2×#416—24no—
23C2×#416—24no—
24C2×#416C418yescomplemented
25C22×#103C2211yescharacteristic
26C22×#103C2212yes—
27C22×#103C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2212yes—
30C22×#102C2211yescharacteristic
31C2×#405—24no—
32C2×#405—24no—
33C2×#405—24no—
34C22×#97C2212yes—
35C22×C4×C8C2212yes—
36#2311—24no—
37#2311C418yescomplemented
38C2×#391C2212yes—
39C2×#390C2212yes—
40C2×#386—22no—
41C2×#380—22no—
42#1736—24no—
43C2×#340—24no—
44C2×#340C2212yes—
45C2×#340C2212yes—
46C2×#340C2212yes—
47C2×#340C2212yes—
48C4⋊#95—22no—
49C4⋊#95C2212yes—
50C4⋊#95C2212yes—
51C22⋊#95—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41—22no—
62C22×#41—22no—
63C22×#41C2×C414yes—
64C22×#41C2×C414yes—
65C22×#41C2×C414yes—
66C23×Q8C2311yescharacteristic
67C23×D4—21no—
68C23×D4C2311yescharacteristic
69C24×C4—21no—
70C24×C4—21no—
71C24×C4—21no—
72C24×C4C2311yescharacteristic
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—22no—
77C22×M16C2×C414yes—
78C22×M16D414yes—
79C22×M16D414yes—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8C2×C414yes—
85C23×C8D414yes—
86C23×C8D414yes—
87C23×C8C2311yescharacteristic
88C23×C8C2312yes—
89C23×C8C2311yescharacteristic
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117C2×C414yes—
100C2×#117C2×C414yes—
101C2×#117D414yes—
102C22×C4⋊C4—22no—
103C22×C4⋊C4—22no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—22no—
107C22×C4⋊C4—22no—
108C22×C4⋊C4—22no—
109C22×C4⋊C4—22no—
110C22×C4⋊C4—22no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—22no—
114C22×C4⋊C4C2×C414yes—
115C22×C4⋊C4C2×C414yes—
116C22×C4⋊C4D412yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4D412yes—
124C22×C42—21no—
125C22×C42C2312yes—
126#417—232no—
127#416—232no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—24no—
133C2×#103—24no—
134C2×#103C2×C414yescomplemented
135C2×#103C2×C414yescomplemented
136C2×#103C2×C418yescomplemented
137C2×#102—22no—
138C2×#102—22no—
139C2×#102—22no—
140C2×#102—22no—
141C2×#102—24no—
142C2×#102—24no—
143C2×#102C2×C414yescomplemented
144C2×#102C2×C414yescomplemented
145C2×#102C2×C418yescomplemented
146#405—232no—
147C2×#97—24no—
148C2×#97—24no—
149C2×#97—24no—
150C2×C4×C8—24no—
151C2×C4×C8—24no—
152C2×C4×C8—24no—
153#391—24no—
154#391C2×C418yescomplemented
155#390—24no—
156#390C2×C418yescomplemented
157#386—216no—
158#380—216no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162#340—24no—
163#340—24no—
164#340—24no—
165#340—24no—
166C25—21no—
167C25C2×D411yescharacteristic
168C2×#41—28no—
169C2×#41—28no—
170C2×#41—28no—
171C2×#41—28no—
172C2×#41—28no—
173C2×#41—28no—
174C2×#41—28no—
175C2×#41—28no—
176C2×#41—28no—
177C2×#41—28no—
178C2×#41—28no—
179C2×#41—28no—
180C2×#41—28no—
181C2×#41—28no—
182C2×#41—28no—
183C2×#41—44no—
184C2×#41—44no—
185C2×#41—44no—
186C2×#41—44no—
187C2×#41—44no—
188C2×#41—44no—
189C2×#41—44no—
190C2×#41—44no—
191C2×#41—44no—
192C2×#41—44no—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41C42116yes—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8C22×C412yes—
208C22×Q8C22×C412yes—
209C22×Q8C22×C412yes—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4C22×C412yes—
229C22×D4C22×C412yes—
230C22×D4C22×C412yes—
231C23×C4—21no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—82no—
250C23×C4—82no—
251C23×C4—82no—
252C23×C4—82no—
253C23×C4C22×C412yes—
254C23×C4C22×C412yes—
255C23×C4C22×C412yes—
256C23×C4C2×D414yes—
257C23×C4C2×D412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4#4112yes—
264C23×C4#4112yes—
265C23×C4#4112yes—
266C23×C4#4112yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4C2411yescharacteristic
270C2×M16—28no—
271C2×M16—28no—
272C2×M16—28no—
273C2×M16—28no—
274C2×M16—28no—
275C2×M16—28no—
276C2×M16C22⋊C4116yescomplemented
277C22×C8—28no—
278C22×C8—28no—
279C22×C8—28no—
280C22×C8—28no—
281C22×C8—28no—
282C22×C8—28no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8C22⋊C4116yescomplemented
296C22×C8C22×C412yes—
297C22×C8C22×C412yes—
298C22×C8C22×C414yes—
299C22×C8C2×D412yes—
300C22×C8C2×D412yes—
301C22×C8C2×D412yes—
302C22×C8C2×D412yes—
303C22×C8C2×D414yes—
304C22×C8C2×D414yes—
305#117—28no—
306#117—28no—
307#117—28no—
308#117—28no—
309#117—28no—
310#117—28no—
311#117—44no—
312#117—44no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4C22⋊C418yes—
350C2×C4⋊C4C22×C414yes—
351C2×C4⋊C4C22×C414yes—
352C2×C4⋊C4C22×C412yes—
353C2×C4⋊C4C22×C412yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—216no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—84no—
361C2×C22⋊C4—84no—
362C2×C22⋊C4C22⋊C418yes—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42C22×C414yes—
371C2×C42C2×D414yes—
372#103—28no—
373#103—28no—
374#103—216no—
375#102—28no—
376#102—28no—
377#102—216no—
378#97—216no—
379C4×C8—216no—
380#95—216no—
381#95—84no—
382#95—84no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24C2×C22⋊C412yes—
399C24C4×D412yes—
400C24C4×D412yes—
401C24#12112yes—
402C24#12112yes—
403C24#12412yes—
404C24#12712yes—
405C24C22×D411yescharacteristic
406#41—232no—
407#41—232no—
408#41—416no—
409#41—416no—
410#41—416no—
411#41—416no—
412#41—416no—
413#41—416no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8C2×C4214yes—
442C2×D4—216no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×C4214yes—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—216no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—88no—
520C22×C4—88no—
521C22×C4—88no—
522C22×C4—84no—
523C22×C4—84no—
524C22×C4—84no—
525C22×C4—84no—
526C22×C4—88no—
527C22×C4C2×C4214yes—
528C22×C4C2×C22⋊C418yes—
529C22×C4C2×C22⋊C414yes—
530C22×C4C2×C22⋊C414yes—
531C22×C4C2×C22⋊C412yes—
532C22×C4#11714yes—
533C22×C4#11714yes—
534C22×C4#11714yes—
535C22×C4C4×D414yes—
536C22×C4C4×D414yes—
537C22×C4C4×D414yes—
538C22×C4C4×D414yes—
539C22×C4C4×D414yes—
540C22×C4C4×D414yes—
541C22×C4C4×D414yes—
542C22×C4C4×D414yes—
543C22×C4C4×D414yes—
544C22×C4C4×D414yes—
545C22×C4C4×D412yes—
546C22×C4C4×D412yes—
547C22×C4#12014yes—
548C22×C4#12114yes—
549C22×C4#12114yes—
550C22×C4#12114yes—
551C22×C4#12114yes—
552C22×C4#12112yes—
553C22×C4#12112yes—
554C22×C4#12314yes—
555C22×C4#12314yes—
556C22×C4#12314yes—
557C22×C4#12414yes—
558C22×C4#12414yes—
559C22×C4#12412yes—
560C22×C4#12614yes—
561C22×C4#12614yes—
562C22×C4#12712yes—
563C22×C4C23×C411yescharacteristic
564C22×C4C23×C411yescharacteristic
565C22×C4C23×C411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C2×#4111yescharacteristic
572C22×C4C2×#4111yescharacteristic
573C22×C4C2×#4111yescharacteristic
574C22×C4C2×#4111yescharacteristic
575C22×C4C2×#4111yescharacteristic
576C22×C4C2×#4111yescharacteristic
577M16—232no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—22no—
585C2×C8—24no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—24no—
596C2×C8—232no—
597C2×C8C2×C22⋊C414yes—
598C2×C8C2×C22⋊C414yes—
599C2×C8C2×C22⋊C418yes—
600C4⋊C4—216no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—42no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C22⋊C4—216no—
620C22⋊C4—48no—
621C22⋊C4—816no—
622C42—24no—
623C42—24no—
624C42—24no—
625C42—24no—
626C42—48no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—82no—
657C23—82no—
658C23—81no—
659C23—81no—
660C23—81no—
661C23—81no—
662C23—82no—
663C23—82no—
664C23—82no—
665C23—82no—
666C23C4×C22⋊C414yes—
667C23#38614yes—
668C23#38814yes—
669C23#38814yes—
670C23#39014yes—
671C23#39014yes—
672C23#39014yes—
673C23C22×C22⋊C411yescharacteristic
674C23C2×C4×D411yescharacteristic
675C23C2×C4×D411yescharacteristic
676C23C2×#12111yescharacteristic
677C23C2×#12111yescharacteristic
678C23C2×#12411yescharacteristic
679C23C2×#12711yescharacteristic
680C23#57612yes—
681C23#57712yes—
682C23#57712yes—
683C23#57812yes—
684Q8—24no—
685Q8—24no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—42no—
691Q8—42no—
692D4—24no—
693D4—24no—
694D4—432no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—432no—
716C2×C4—48no—
717C2×C4—48no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—816no—
725C2×C4—816no—
726C2×C4—84no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—81no—
735C2×C4—82no—
736C2×C4—82no—
737C2×C4—84no—
738C2×C4C4×C22⋊C414yes—
739C2×C4C4×C22⋊C418yes—
740C2×C4C4×C22⋊C418yes—
741C2×C4#38614yes—
742C2×C4#38618yes—
743C2×C4#38618yes—
744C2×C4#38814yes—
745C2×C4#38814yes—
746C2×C4#38818yes—
747C2×C4#38818yes—
748C2×C4#38818yes—
749C2×C4#38818yes—
750C2×C4#39014yes—
751C2×C4#39014yes—
752C2×C4#39014yes—
753C2×C4C22×C4211yescharacteristic
754C2×C4C22×C22⋊C411yescharacteristic
755C2×C4C22×C22⋊C411yescharacteristic
756C2×C4C2×#11711yescharacteristic
757C2×C4C2×#11711yescharacteristic
758C2×C4C2×#11711yescharacteristic
759C2×C4C2×C4×D411yescharacteristic
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C2×C4×D411yescharacteristic
762C2×C4C2×C4×D411yescharacteristic
763C2×C4C2×C4×D411yescharacteristic
764C2×C4C2×C4×D411yescharacteristic
765C2×C4C2×C4×D411yescharacteristic
766C2×C4C2×C4×D411yescharacteristic
767C2×C4C2×C4×D411yescharacteristic
768C2×C4C2×C4×D411yescharacteristic
769C2×C4C2×#12011yescharacteristic
770C2×C4C2×#12111yescharacteristic
771C2×C4C2×#12111yescharacteristic
772C2×C4C2×#12111yescharacteristic
773C2×C4C2×#12111yescharacteristic
774C2×C4C2×#12311yescharacteristic
775C2×C4C2×#12311yescharacteristic
776C2×C4C2×#12311yescharacteristic
777C2×C4C2×#12411yescharacteristic
778C2×C4C2×#12411yescharacteristic
779C2×C4C2×#12611yescharacteristic
780C2×C4C2×#12611yescharacteristic
781C8—24no—
782C8—24no—
783C8—28no—
784C22—28no—
785C22—28no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—28no—
792C22—24no—
793C22—24no—
794C22—48no—
795C22—44no—
796C22—84no—
797C22—84no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—84no—
803C22—82no—
804C22—82no—
805C22#143718yes—
806C22C2×C4×C22⋊C411yescharacteristic
807C22C2×#38611yescharacteristic
808C22C2×#38811yescharacteristic
809C22C2×#38811yescharacteristic
810C22C2×#39011yescharacteristic
811C22C2×#39011yescharacteristic
812C22C2×#39011yescharacteristic
813C22#289712yes—
814C22#289812yes—
815C22#294612yes—
816C22#294712yes—
817C22#295112yes—
818C22#295212yes—
819C22#306012yes—
820C22#306112yes—
821C22#306212yes—
822C22#306312yes—
823C22#313612yes—
824C22#313712yes—
825C22#315411yescharacteristic
826C22#315411yescharacteristic
827C22#315511yescharacteristic
828C22#315611yescharacteristic
829C4—44no—
830C4—48no—
831C4—84no—
832C4—82no—
833C4—82no—
834C4—84no—
835C4#143718yes—
836C4C2×C4×C22⋊C411yescharacteristic
837C4C2×C4×C22⋊C411yescharacteristic
838C4C2×#38611yescharacteristic
839C4C2×#38611yescharacteristic
840C4C2×#38811yescharacteristic
841C4C2×#38811yescharacteristic
842C4C2×#38811yescharacteristic
843C4C2×#38811yescharacteristic
844C2—28no—
845C2—84no—
846C2C2×#143711yescharacteristic
847C2#2041512yes—
848C2#2097612yes—
849C2#2108712yes—
850C2#2109212yes—
851C2#2120511yescharacteristic
852C2#2120611yescharacteristic
853C2#2122911yescharacteristic
854C2#2123011yescharacteristic
855C2#2123411yescharacteristic
856C2#2123511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#405C2semidirect
5. C2×#1736C2semidirect
6. C22×#340C2semidirect
7. #13795C2semidirect
8. #10928C2semidirect
9. #10927C2semidirect
10. #10926C2semidirect
11. #10925C2semidirect
21. C2×#417C4semidirect
24. C2×#416C4semidirect
37. #2311C4semidirect
134. C2×#103C2×C4semidirect
135. C2×#103C2×C4semidirect
136. C2×#103C2×C4semidirect
143. C2×#102C2×C4semidirect
144. C2×#102C2×C4semidirect
145. C2×#102C2×C4semidirect
154. #391C2×C4semidirect
156. #390C2×C4semidirect
276. C2×M16C22⋊C4semidirect
295. C22×C8C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4172
C22×#4162
C22×#4052
C2×#23112
C2×#17362
C22×#3402
#137952
#109282
#109272
#109262
#109252