Finite Group Databasebeta

← #360137

Subgroups — #360137

Order 512.

2342 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D8C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#1879C212yesmaximal
4C2×#1802C211yesmaximal, characteristic, complemented
5C2×#1802C211yesmaximal, characteristic, complemented
6#13906C211yesmaximal, characteristic, complemented
7#11219C212yesmaximal, complemented
8#11066C212yesmaximal, complemented
9#10841C211yesmaximal, characteristic, complemented
10#10834C211yesmaximal, characteristic, complemented
11#10788C212yesmaximal, complemented
12C23×D8C2211yescharacteristic
13C22×C4×D4C2211yescharacteristic
14C22×C4×D4C2212yes—
15C22×C4×D4C2211yescharacteristic
16C23×C4⋊C4—21no—
17C2×C4×D8—24no—
18C2×C4×D8—24no—
19C2×C4×D8C418yescomplemented
20C22×#107C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#102C2212yes—
23C22×#102C2212yes—
24C22×#102C2211yescharacteristic
25C22×#102C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27D4×C4⋊C4—24no—
28D4×C4⋊C4—24no—
29C2×#390C2212yes—
30C2×#389C2212yes—
31C2×#385—22no—
32C2×#384C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#380—21no—
35C2×#380—21no—
36C2×#380—21no—
37C2×C4×C4⋊C4C2211yescharacteristic
38#1879—28no—
39#1802—24no—
40#1802—24no—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#336C2212yes—
46C2×#336C2212yes—
47#1439—22no—
48C4⋊#95C2212yes—
49C23×D4C2311yescharacteristic
50C23×D4C2311yescharacteristic
51C24×C4—21no—
52C24×C4—21no—
53C24×C4—22no—
54C22×D8—22no—
55C22×D8—22no—
56C22×D8—22no—
57C22×D8—22no—
58C22×D8C2×C414yes—
59C22×D8D414yes—
60C22×D8Q814yes—
61C23×C8C2312yes—
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C2×C4×D4—24no—
65C2×C4×D4—24no—
66C2×C4×D4—24no—
67C2×C4×D4—24no—
68C2×C4×D4—22no—
69C2×C4×D4—22no—
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—42no—
77C2×C4×D4—42no—
78C2×C4×D4C2×C414yes—
79C2×C4×D4C2×C414yescomplemented
80C2×C4×D4D414yes—
81C2×C4×D4D414yes—
82C22×C4⋊C4—28no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—44no—
89C22×C4⋊C4—44no—
90C22×C4⋊C4D411yescharacteristic
91C22×C4⋊C4D411yescharacteristic
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4—22no—
100C22×C22⋊C4—22no—
101C22×C42C2312yes—
102C22×C42C2311yescharacteristic
103C4×D8—232no—
104C2×#107—22no—
105C2×#107—22no—
106C2×#107C2×C414yescomplemented
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—22no—
113C2×#102—22no—
114C2×#102—24no—
115C2×#102—24no—
116C2×#102—24no—
117C2×#102—24no—
118C2×#102—24no—
119C2×#102—42no—
120C2×#102C2×C414yes—
121C2×#102C2×C414yescomplemented
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124C2×C4×C8C2×C414yescomplemented
125#390—24no—
126#390—42no—
127#389—24no—
128#389—24no—
129#385—216no—
130#384—22no—
131#384—22no—
132#384—22no—
133#384D414yes—
134#380—28no—
135#380—44no—
136#380—44no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C2×#95—22no—
140C2×#95—22no—
141C2×#95—22no—
142C2×#95D412yes—
143#340—24no—
144#340—24no—
145#340—24no—
146#340—42no—
147#336—24no—
148#336—42no—
149C25—21no—
150C25—21no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4—21no—
154C22×D4—21no—
155C22×D4—21no—
156C22×D4—21no—
157C22×D4—21no—
158C22×D4—21no—
159C22×D4—21no—
160C22×D4—21no—
161C22×D4—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4C22×C412yes—
170C22×D4C22×C412yes—
171C22×D4C2×D412yes—
172C22×D4C2×D412yes—
173C22×D4C2×D412yes—
174C22×D4C2×D412yes—
175C22×D4C2×Q812yes—
176C22×D4C2×Q812yes—
177C22×D4#4112yes—
178C22×D4#4112yes—
179C23×C4—21no—
180C23×C4—24no—
181C23×C4—24no—
182C23×C4—24no—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—28no—
186C23×C4—24no—
187C23×C4—22no—
188C23×C4—44no—
189C23×C4—44no—
190C23×C4—44no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4—44no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—82no—
203C23×C4—82no—
204C23×C4C2×D412yes—
205C23×C4C2×D412yes—
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2411yescharacteristic
209C2×D8—28no—
210C2×D8—28no—
211C2×D8—28no—
212C2×D8—28no—
213C2×D8—28no—
214C2×D8—28no—
215C2×D8C4⋊C4116yescomplemented
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—22no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8C22×C412yes—
234C22×C8C22×C412yes—
235C22×C8C2×D412yes—
236C22×C8C2×Q812yes—
237C4×D4—28no—
238C4×D4—28no—
239C4×D4—28no—
240C4×D4—28no—
241C4×D4—28no—
242C4×D4—48no—
243C4×D4—48no—
244C4×D4—48no—
245C4×D4—48no—
246C4×D4—44no—
247C4×D4—44no—
248C4×D4C22⋊C4116yescomplemented
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—432no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4—44no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4—81no—
287C2×C4⋊C4—81no—
288C2×C4⋊C4—81no—
289C2×C4⋊C4D814yescomplemented
290C2×C4⋊C4C22×C412yes—
291C2×C4⋊C4C22×C412yes—
292C2×C4⋊C4C2×D414yes—
293C2×C4⋊C4C2×D412yes—
294C2×C4⋊C4C2×D412yes—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—44no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—44no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4—44no—
308C2×C22⋊C4—82no—
309C2×C22⋊C4—82no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42C22×C412yes—
317C2×C42C2×D412yes—
318C2×C42C2×D412yes—
319C2×C42C2×D412yes—
320C2×C42#4112yes—
321C2×C42#4112yes—
322#107—28no—
323C4⋊C8—44no—
324#102—28no—
325#102—28no—
326#102—48no—
327#102—48no—
328C4×C8—28no—
329#95—28no—
330#95—24no—
331#95—44no—
332#95—44no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—22no—
341C24—22no—
342C24—22no—
343C24—41no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—41no—
350C24—41no—
351C24—41no—
352C24—41no—
353C24—41no—
354C24—41no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24C22×D411yescharacteristic
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4C2×C22⋊C414yes—
413C2×D4C2×C4⋊C414yes—
414C2×D4C2×C4⋊C414yescomplemented
415C2×D4#11714yes—
416C2×D4#12114yes—
417C2×D4#12114yes—
418C2×D4C22⋊Q814yes—
419C2×D4C22⋊Q814yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—216no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—416no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—48no—
449C22×C4—48no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—48no—
454C22×C4—416no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—41no—
460C22×C4—42no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—48no—
468C22×C4—48no—
469C22×C4—48no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—88no—
478C22×C4—88no—
479C22×C4—88no—
480C22×C4—88no—
481C22×C4—88no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4—84no—
485C22×C4—84no—
486C22×C4C4×D412yes—
487C22×C4C4×D412yes—
488C22×C4#12012yes—
489C22×C4#12012yes—
490C22×C4#12112yes—
491C22×C4#12112yes—
492C22×C4C2×D814yes—
493C22×C4C2×D812yes—
494C22×C4#13512yes—
495C22×C4AGL(1,ℤ/8)12yes—
496C22×C4AGL(1,ℤ/8)12yes—
497C22×C4C23×C411yescharacteristic
498C22×C4C22×D411yescharacteristic
499C22×C4C22×D411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×Q811yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4H(5,𝔽2)11yescharacteristic
508C22×C4H(5,𝔽2)11yescharacteristic
509C22×C42−1+411yescharacteristic
510C22×C42−1+411yescharacteristic
511D8—232no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—42no—
526C2×C8—42no—
527C2×C8—42no—
528C2×C8—42no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8C2×C4⋊C414yescomplemented
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—28no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—416no—
542C4⋊C4—42no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—42no—
546C4⋊C4—48no—
547C4⋊C4—44no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—84no—
553C4⋊C4—84no—
554C4⋊C4—84no—
555C4⋊C4C2×C22⋊C414yes—
556C22⋊C4—216no—
557C22⋊C4—416no—
558C22⋊C4—48no—
559C22⋊C4—88no—
560C22⋊C4—88no—
561C42—42no—
562C42—42no—
563C42—42no—
564C42—42no—
565C42C2×C22⋊C414yes—
566C42C4×D414yes—
567C42#12114yes—
568C42#12314yes—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23C2×C4×D411yescharacteristic
640C23C2×#12011yescharacteristic
641C23C2×#12111yescharacteristic
642C23D4211yescharacteristic
643C23#54611yescharacteristic
644C23#54811yescharacteristic
645C23D4×Q811yescharacteristic
646C23C22×D811yescharacteristic
647C23C2×#13511yescharacteristic
648C23C2×AGL(1,ℤ/8)11yescharacteristic
649C23C2×AGL(1,ℤ/8)11yescharacteristic
650C23#57611yescharacteristic
651C23#57711yescharacteristic
652C23#57711yescharacteristic
653C23#57811yescharacteristic
654D4—24no—
655D4—24no—
656D4—24no—
657D4—24no—
658D4—24no—
659D4—24no—
660D4—24no—
661D4—24no—
662D4—24no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4#38018yescomplemented
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—432no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—832no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—816no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4#38614yes—
722C2×C4#38614yes—
723C2×C4C4×D814yes—
724C2×C4#44214yes—
725C2×C4#44714yes—
726C2×C4#44914yes—
727C2×C4#45914yes—
728C2×C4#46314yes—
729C2×C4C22×C22⋊C411yescharacteristic
730C2×C4C22×C4⋊C411yescharacteristic
731C2×C4C2×#11711yescharacteristic
732C2×C4C2×C4×D411yescharacteristic
733C2×C4#52011yescharacteristic
734C2×C4#52011yescharacteristic
735C2×C4C2×#12111yescharacteristic
736C2×C4C2×#12111yescharacteristic
737C2×C4C2×#12111yescharacteristic
738C2×C4C2×C22⋊Q811yescharacteristic
739C2×C4C2×C22⋊Q811yescharacteristic
740C2×C4C2×#12311yescharacteristic
741C2×C4#53511yescharacteristic
742C2×C4#53611yescharacteristic
743C2×C4#53711yescharacteristic
744C2×C4#53711yescharacteristic
745C2×C4D4211yescharacteristic
746C2×C4#54611yescharacteristic
747C2×C4#54711yescharacteristic
748C2×C4#54711yescharacteristic
749C2×C4#54811yescharacteristic
750C2×C4D4×Q811yescharacteristic
751C2×C4#55211yescharacteristic
752C2×C4#55211yescharacteristic
753C2×C4#55311yescharacteristic
754C2×C4#55311yescharacteristic
755C2×C4#55411yescharacteristic
756C2×C4#55411yescharacteristic
757C8—24no—
758C8—42no—
759C8—82no—
760C22—28no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22C2×#38611yescharacteristic
791C22D4×C4⋊C411yescharacteristic
792C22#235211yescharacteristic
793C22#240811yescharacteristic
794C22#240911yescharacteristic
795C22#241611yescharacteristic
796C22#241711yescharacteristic
797C22C2×C4×D811yescharacteristic
798C22C2×#44211yescharacteristic
799C22#295111yescharacteristic
800C22#295211yescharacteristic
801C22C2×#44711yescharacteristic
802C22C2×#44911yescharacteristic
803C22#301211yescharacteristic
804C22#301311yescharacteristic
805C22C2×#45911yescharacteristic
806C22C2×#46311yescharacteristic
807C22#304511yescharacteristic
808C22#304611yescharacteristic
809C22#327211yescharacteristic
810C22#327211yescharacteristic
811C22D4×D811yescharacteristic
812C22#328311yescharacteristic
813C22#329411yescharacteristic
814C22#330311yescharacteristic
815C22#332511yescharacteristic
816C22#333011yescharacteristic
817C22#335811yescharacteristic
818C22#336011yescharacteristic
819C22#336611yescharacteristic
820C22#336711yescharacteristic
821C22Q8×D811yescharacteristic
822C22#338011yescharacteristic
823C22#338411yescharacteristic
824C22#338411yescharacteristic
825C4—24no—
826C4—44no—
827C4—44no—
828C4—84no—
829C4—82no—
830C4—82no—
831C4—162no—
832C4#187918yescomplemented
833C4C2×#38011yescharacteristic
834C4#231111yescharacteristic
835C4D4×C4⋊C411yescharacteristic
836C4#235211yescharacteristic
837C4#241611yescharacteristic
838C4#241711yescharacteristic
839C4#248611yescharacteristic
840C4#248711yescharacteristic
841C2—48no—
842C2—84no—
843C2#1387211yescharacteristic
844C2C2×#187911yescharacteristic
845C2#2093711yescharacteristic
846C2#2267011yescharacteristic
847C2C4⋊C4×D811yescharacteristic
848C2#2275811yescharacteristic
849C2#2276611yescharacteristic
850C2#2423611yescharacteristic
851C2#2423711yescharacteristic
852C2#2432611yescharacteristic
853C2#2432711yescharacteristic
854C2#2472611yescharacteristic
855C2#2472711yescharacteristic
856C2#2481111yescharacteristic
857C2#2481211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×D4×C4⋊C4C2semidirect
4. C2×#1802C2semidirect
5. C2×#1802C2semidirect
6. #13906C2semidirect
7. #11219C2semidirect
8. #11066C2semidirect
9. #10841C2semidirect
10. #10834C2semidirect
11. #10788C2semidirect
19. C2×C4×D8C4semidirect
79. C2×C4×D4C2×C4semidirect
106. C2×#107C2×C4semidirect
121. C2×#102C2×C4semidirect
124. C2×C4×C8C2×C4semidirect
215. C2×D8C4⋊C4semidirect
248. C4×D4C22⋊C4semidirect
289. C2×C4⋊C4D8semidirect
414. C2×D4C2×C4⋊C4semidirect
532. C2×C8C2×C4⋊C4semidirect
669. D4#380semidirect
832. C4#1879semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D82
C2×D4×C4⋊C42
C2×#18792
C2×#18022
#139062
#112192
#110662
#108412
#108342
#107882