Finite Group Databasebeta

← #375934

Subgroups — #375934

Order 512.

1193 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2962C211yesmaximal, characteristic, complemented
2#23451C211yesmaximal, characteristic
3C2×#1866C211yesmaximal, characteristic
4#20838C211yesmaximal, characteristic
5C2×#1764C211yesmaximal, characteristic
6#11386C211yesmaximal, characteristic, complemented
7#11329C211yesmaximal, characteristic, complemented
8#11068C211yesmaximal, characteristic
9#10934C211yesmaximal, characteristic
10#10933C211yesmaximal, characteristic
11#10911C211yesmaximal, characteristic, complemented
12#10887C211yesmaximal, characteristic, complemented
13#10882C211yesmaximal, characteristic, complemented
14#10876C211yesmaximal, characteristic, complemented
15#10809C211yesmaximal, characteristic, complemented
16C22×#131C2211yescharacteristic
17C2×#533C2211yescharacteristic
18#2962—24no—
19#2962—24no—
20C2×#446—21no—
21C2×#446—21no—
22C2×#446—21no—
23C2×C8×Q8—21no—
24C22×#108C2211yescharacteristic
25C2×#424C2211yescharacteristic
26C2×#424C2211yescharacteristic
27C2×#424C2211yescharacteristic
28C22×C4⋊C8C2211yescharacteristic
29C22×#104C2211yescharacteristic
30C22×#104C2211yescharacteristic
31C2×#416C2211yescharacteristic
32C2×#416C2211yescharacteristic
33C2×#408C2211yescharacteristic
34C2×#405C2211yescharacteristic
35C2×#405C2211yescharacteristic
36C2×C4×M16C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38#2297C2211yescharacteristic
39#2026C411yescharacteristic, complemented
40#2026C411yescharacteristic, complemented
41#2025C411yescharacteristic, complemented
42#2025C411yescharacteristic, complemented
43#2024C411yescharacteristic, complemented
44#2024C411yescharacteristic, complemented
45#2023C411yescharacteristic, complemented
46#2023C411yescharacteristic, complemented
47#1866—24no—
48#1851—21no—
49#1851—21no—
50#1850—21no—
51#1850—21no—
52#1764—24no—
53C2×#341C2211yescharacteristic
54C2×#341C2211yescharacteristic
55C2×#341C2211yescharacteristic
56#1735C2211yescharacteristic
57#1735C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64#1729C2211yescharacteristic
65#1728C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C2×#131—22no—
73C2×#131—22no—
74C2×#131—22no—
75C2×#131—22no—
76C2×#131—41no—
77C2×#131—41no—
78C22×M16—21no—
79C22×M16C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C22×M16C2311yescharacteristic
82C22×M16C2311yescharacteristic
83C23×C8—21no—
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88#533—22no—
89#533—22no—
90#533—22no—
91#533—22no—
92C2×C4⋊Q8C2×C411yescharacteristic
93C2×C4⋊Q8C2×C411yescharacteristic
94C2×#125C2×C411yescharacteristic
95C2×#125C2×C411yescharacteristic
96C2×C22⋊Q8—21no—
97C2×C22⋊Q8—21no—
98C2×C4×Q8—21no—
99C2×C4×Q8—21no—
100C2×#117C2311yescharacteristic
101C2×#117C2311yescharacteristic
102C2×#117C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106#446—28no—
107#446—28no—
108#446—28no—
109C8×Q8—28no—
110C2×#108—22no—
111C2×#108—22no—
112C2×#108—41no—
113#424—22no—
114#424—22no—
115#424—22no—
116#424—22no—
117#424—41no—
118#424D414yes—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8D411yescharacteristic
128C2×C4⋊C8D411yescharacteristic
129C2×C4⋊C8D411yescharacteristic
130C2×C4⋊C8D411yescharacteristic
131C2×#104—22no—
132C2×#104—22no—
133C2×#104—22no—
134C2×#104—22no—
135C2×#104—41no—
136C2×#104Q814yescomplemented
137#416—22no—
138#416—22no—
139#416—22no—
140#416—22no—
141C2×#103C2×C411yescharacteristic
142C2×#103C2×C411yescharacteristic
143C2×#103C2×C411yescharacteristic
144C2×#103C2×C411yescharacteristic
145C2×#102C2×C411yescharacteristic
146C2×#102C2×C411yescharacteristic
147C2×#102C2×C411yescharacteristic
148C2×#102C2×C411yescharacteristic
149#408—22no—
150#408—41no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153#405—22no—
154#405—22no—
155#405—22no—
156#405D414yes—
157C4×M16—22no—
158C4×M16—22no—
159C2×#97—21no—
160C2×#97—21no—
161C2×#97—21no—
162C2×C4×C8—21no—
163C2×C4×C8—21no—
164C2×C4×C8—21no—
165C2×C4×C8—22no—
166C2×C4×C8—41no—
167C2×C4×C8—41no—
168#391C2×C411yescharacteristic
169#391C2×C411yescharacteristic
170#390C2×C411yescharacteristic
171#390C2×C411yescharacteristic
172#386—21no—
173#386—21no—
174C4×C22⋊C4—21no—
175C4×C22⋊C4—21no—
176C2×#95—21no—
177C2×#95—21no—
178#341—22no—
179#341—22no—
180#341—41no—
181#340C2×C411yescharacteristic
182#340C2×C411yescharacteristic
183#340C2×C411yescharacteristic
184#340C2×C411yescharacteristic
185#340C2×C411yescharacteristic
186#340C2×C411yescharacteristic
187#340C2×C411yescharacteristic
188#340C2×C411yescharacteristic
189#339—22no—
190#339—22no—
191#339—22no—
192#339—22no—
193#339—22no—
194#339—41no—
195#336—21no—
196#336—21no—
197#336—22no—
198#336—21no—
199#336—21no—
200#336—41no—
201#336—41no—
202#336C2×C411yescharacteristic
203#336C2×C411yescharacteristic
204#336C2×C411yescharacteristic
205#336C2×C411yescharacteristic
206C2×#41—21no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—21no—
212C2×#41—21no—
213C2×#41—21no—
214C2×#41—21no—
215C2×#41—21no—
216C2×#41C2×Q812yes—
217C2×#41#4112yes—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8C22×C411yescharacteristic
221C22×D4—21no—
222C22×D4C22×C411yescharacteristic
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4#4111yescharacteristic
227C23×C4#4111yescharacteristic
228C23×C4C2411yescharacteristic
229#131—28no—
230#131—44no—
231#131—44no—
232#131—44no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—42no—
253C2×M16—42no—
254C2×M16—42no—
255C2×M16C2×D412yes—
256C2×M16C2×D412yes—
257C2×M16C2×Q812yes—
258C2×M16#4112yes—
259C2×M16#4112yes—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—42no—
287C22×C8—42no—
288C22×C8—42no—
289C22×C8C22×C411yescharacteristic
290C22×C8C22×C411yescharacteristic
291C22×C8C22×C411yescharacteristic
292C22×C8C22×C411yescharacteristic
293C22×C8C2×D411yescharacteristic
294C22×C8C2×D411yescharacteristic
295C22×C8C2×D412yes—
296C22×C8C2×D412yes—
297C22×C8C2×D411yescharacteristic
298C22×C8C2×D411yescharacteristic
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303#125—22no—
304#125—22no—
305#125—22no—
306#125—22no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—24no—
311C4×Q8—24no—
312C4×Q8—24no—
313C4×Q8—24no—
314C4×Q8—24no—
315#117—21no—
316#117—21no—
317#117—21no—
318#117—21no—
319#117—21no—
320#117—21no—
321#117—21no—
322#117—21no—
323#117C2×D412yes—
324#117C2×D412yes—
325#117#4112yes—
326#117#4112yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C22×C411yescharacteristic
334C2×C4⋊C4C22×C411yescharacteristic
335C2×C4⋊C4C22×C411yescharacteristic
336C2×C4⋊C4C22×C411yescharacteristic
337C2×C4⋊C4C22×C411yescharacteristic
338C2×C4⋊C4C22×C411yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42C22×C411yescharacteristic
365C2×C42C22×C411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2×D411yescharacteristic
368C2×C42C2×Q812yes—
369#108—44no—
370C4⋊C8—24no—
371C4⋊C8—24no—
372C4⋊C8—22no—
373C4⋊C8—22no—
374C4⋊C8—22no—
375C4⋊C8—22no—
376C4⋊C8—24no—
377C4⋊C8—24no—
378C4⋊C8—42no—
379C4⋊C8—42no—
380#104—28no—
381#104—44no—
382#103—22no—
383#103—22no—
384#103—22no—
385#103—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390C22⋊C8—42no—
391C22⋊C8—42no—
392#97—24no—
393#97—24no—
394#97—24no—
395C4×C8—24no—
396C4×C8—24no—
397C4×C8—24no—
398C4×C8—44no—
399#95—24no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—42no—
405C24—21no—
406C24C2×#4111yescharacteristic
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423C2×Q8—24no—
424C2×Q8—24no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×Q8—81no—
434C2×Q8C4×Q812yes—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4C4×Q812yes—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4C4×D411yescharacteristic
483C22×C4C4×D411yescharacteristic
484C22×C4C4×D411yescharacteristic
485C22×C4C4×D411yescharacteristic
486C22×C4C23×C411yescharacteristic
487C22×C4C22×D411yescharacteristic
488C22×C4C22×D411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C22×Q811yescharacteristic
491C22×C4C2×#4111yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4H(5,𝔽2)11yescharacteristic
497C22×C4H(5,𝔽2)11yescharacteristic
498C22×C42−1+411yescharacteristic
499C22×C42−1+411yescharacteristic
500M16—22no—
501M16—22no—
502M16—22no—
503M16—22no—
504M16—22no—
505M16—22no—
506M16—22no—
507M16—48no—
508M16—41no—
509M16—41no—
510M16—41no—
511M16—41no—
512M16—41no—
513M16—41no—
514M16—41no—
515M16—41no—
516M16C22⋊Q814yes—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—22no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—22no—
548C2×C8—48no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8#12012yes—
569C2×C8#12012yes—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4C4×D412yes—
585C4⋊C4C4×D412yes—
586C4⋊C4C4×D412yes—
587C4⋊C4C4×D412yes—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—42no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—22no—
604C42—22no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23C2×C4×D411yescharacteristic
632C23#52511yescharacteristic
633C23#52511yescharacteristic
634C23#55211yescharacteristic
635C23#55411yescharacteristic
636C23#55611yescharacteristic
637C23#55911yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—48no—
641Q8—41no—
642Q8—41no—
643Q8—84no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—41no—
651D4—41no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4#44312yes—
707C2×C4C2×C4×D411yescharacteristic
708C2×C4C2×C4×D411yescharacteristic
709C2×C4C2×C4×Q811yescharacteristic
710C2×C4C4×#4111yescharacteristic
711C2×C4#52011yescharacteristic
712C2×C4#52011yescharacteristic
713C2×C4C2×#12011yescharacteristic
714C2×C4C2×C22⋊Q811yescharacteristic
715C2×C4#52511yescharacteristic
716C2×C4#52511yescharacteristic
717C2×C4#52911yescharacteristic
718C2×C4#53311yescharacteristic
719C2×C4#53511yescharacteristic
720C2×C4#53611yescharacteristic
721C2×C4#54211yescharacteristic
722C2×C4#54211yescharacteristic
723C2×C4#54611yescharacteristic
724C2×C4#54611yescharacteristic
725C2×C4#54611yescharacteristic
726C2×C4#54611yescharacteristic
727C2×C4#54811yescharacteristic
728C2×C4#54811yescharacteristic
729C2×C4D4×Q811yescharacteristic
730C2×C4D4×Q811yescharacteristic
731C2×C4#55211yescharacteristic
732C2×C4#55411yescharacteristic
733C2×C4#55611yescharacteristic
734C2×C4#55911yescharacteristic
735C8—22no—
736C8—22no—
737C8—24no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—42no—
745C8—42no—
746C8—81no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22C4×#12011yescharacteristic
767C22#236011yescharacteristic
768C22#236711yescharacteristic
769C22#245811yescharacteristic
770C22#246511yescharacteristic
771C22#258011yescharacteristic
772C22#259911yescharacteristic
773C22C2×#44311yescharacteristic
774C22#295511yescharacteristic
775C22#295611yescharacteristic
776C22#295711yescharacteristic
777C4—22no—
778C4—44no—
779C4—42no—
780C4—41no—
781C4—42no—
782C4—42no—
783C4—41no—
784C4—41no—
785C4—42no—
786C4—42no—
787C4—82no—
788C4—81no—
789C4—81no—
790C4C4×C22⋊Q811yescharacteristic
791C4#232611yescharacteristic
792C4#236011yescharacteristic
793C4#236711yescharacteristic
794C4#240411yescharacteristic
795C4#240911yescharacteristic
796C4#245811yescharacteristic
797C4#246511yescharacteristic
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—82no—
803C2#1417211yescharacteristic
804C2#2146611yescharacteristic
805C2#2146811yescharacteristic
806C2#2298211yescharacteristic
807C2#2298411yescharacteristic
808C2#2323411yescharacteristic
809C2#2323611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C4⋊C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2962C2semidirect
6. #11386C2semidirect
7. #11329C2semidirect
11. #10911C2semidirect
12. #10887C2semidirect
13. #10882C2semidirect
14. #10876C2semidirect
15. #10809C2semidirect
39. #2026C4semidirect
40. #2026C4semidirect
41. #2025C4semidirect
42. #2025C4semidirect
43. #2024C4semidirect
44. #2024C4semidirect
45. #2023C4semidirect
46. #2023C4semidirect
136. C2×#104Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#29622
#234512
C2×#18662
#208382
C2×#17642
#113862
#113292
#110682
#109342
#109332
#109112
#108872
#108822
#108762
#108092