Finite Group Databasebeta

← #364990

Subgroups — #364990

Order 512.

1996 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2354C211yesmaximal, characteristic
3C2×#1954C211yesmaximal, characteristic
4C2×#1873C212yesmaximal, complemented
5C2×#1803C211yesmaximal, characteristic, complemented
6C2×C4×#103C211yesmaximal, characteristic, complemented
7#11199C212yesmaximal, complemented
8#10970C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10841C211yesmaximal, characteristic, complemented
11#10731C212yesmaximal, complemented
12C22×C22⋊Q8C2212yes—
13C22×C4×Q8C2211yescharacteristic
14C22×C4×D4C2211yescharacteristic
15C22×#117C2212yes—
16C22×C4⋊C8C2211yescharacteristic
17C22×#103C2211yescharacteristic
18C22×#103C2212yes—
19C22×#103C2211yescharacteristic
20C22×C22⋊C8C2212yes—
21C22×C22⋊C8C2212yes—
22C22×C4×C8C2211yescharacteristic
23#2538—24no—
24#2538C418yescomplemented
25C2×#396—22no—
26#2354—24no—
27#2354—24no—
28C2×#390—21no—
29C2×#390—21no—
30C2×#389—21no—
31C2×#388—22no—
32C2×#384C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#380C2212yes—
35C2×#380C2212yes—
36C2×C4×C4⋊C4—21no—
37C2×C4×C4⋊C4C2211yescharacteristic
38#1954—24no—
39#1873—28no—
40#1803—24no—
41C4×#103—24no—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2212yes—
48C2×#340C2212yes—
49C23×Q8C2311yescharacteristic
50C23×D4D411yescharacteristic
51C24×C4C2312yes—
52C23×C8C2312yes—
53C23×C8C2311yescharacteristic
54C23×C8C2311yescharacteristic
55C2×C22⋊Q8—24no—
56C2×C22⋊Q8—24no—
57C2×C22⋊Q8—24no—
58C2×C22⋊Q8—42no—
59C2×C22⋊Q8—42no—
60C2×C22⋊Q8C2×C418yes—
61C2×C4×Q8—22no—
62C2×C4×Q8—22no—
63C2×C4×Q8—22no—
64C2×C4×Q8—22no—
65C2×C4×Q8—22no—
66C2×C4×Q8C2×C414yes—
67C2×C4×D4—22no—
68C2×C4×D4—22no—
69C2×C4×D4—22no—
70C2×C4×D4—22no—
71C2×C4×D4C2×C414yes—
72C2×C4×D4D414yes—
73C2×#117—24no—
74C2×#117—24no—
75C2×#117—24no—
76C2×#117—24no—
77C2×#117—42no—
78C2×#117—42no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4D411yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2312yes—
88C22×C4⋊C4C2312yes—
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C22⋊C4—22no—
92C22×C22⋊C4—22no—
93C22×C22⋊C4—22no—
94C22×C22⋊C4—22no—
95C22×C22⋊C4D412yes—
96C22×C42—22no—
97C22×C42—21no—
98C22×C42—21no—
99C22×C42C2311yescharacteristic
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×#103—22no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—24no—
109C2×#103—24no—
110C2×#103—42no—
111C2×#103D414yescomplemented
112C2×C22⋊C8—24no—
113C2×C22⋊C8—24no—
114C2×C22⋊C8—24no—
115C2×C22⋊C8—24no—
116C2×C22⋊C8—42no—
117C2×C22⋊C8—42no—
118C2×C4×C8—22no—
119C2×C4×C8—22no—
120C2×C4×C8—22no—
121#396—216no—
122#390—28no—
123#390—28no—
124#389—28no—
125#388—216no—
126#384—22no—
127#384—22no—
128#384C2×C414yes—
129#384D414yes—
130#380—24no—
131#380—24no—
132#380—24no—
133#380C2×C418yes—
134C4×C4⋊C4—28no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4D414yes—
137C2×#95—22no—
138C2×#95—22no—
139C2×#95—21no—
140#340—24no—
141#340—24no—
142#340—24no—
143#340—22no—
144#340—22no—
145#340—42no—
146#340—42no—
147C25C2×D412yes—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—21no—
152C22×Q8—21no—
153C22×Q8—21no—
154C22×Q8—21no—
155C22×Q8—21no—
156C22×Q8—21no—
157C22×Q8—21no—
158C22×Q8—21no—
159C22×Q8C22×C412yes—
160C22×Q8C2×D412yes—
161C22×Q8#4112yes—
162C22×D4—22no—
163C22×D4—22no—
164C22×D4—22no—
165C22×D4—22no—
166C22×D4—22no—
167C22×D4—22no—
168C22×D4C22⋊C414yes—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C22×C414yes—
188C23×C4C2×D412yes—
189C23×C4C2×D414yes—
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2411yescharacteristic
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—22no—
206C22×C8—22no—
207C22×C8—22no—
208C22×C8—22no—
209C22×C8—22no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8C2×D412yes—
213C22×C8#4112yes—
214C22⋊Q8—216no—
215C22⋊Q8—48no—
216C22⋊Q8—48no—
217C22⋊Q8—48no—
218C4×Q8—28no—
219C4×Q8—28no—
220C4×Q8—44no—
221C4×Q8—44no—
222C4×D4—28no—
223C4×D4—28no—
224C4×D4—28no—
225C4×D4—28no—
226#117—48no—
227#117—48no—
228#117—48no—
229#117—48no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—44no—
262C2×C4⋊C4—44no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—81no—
270C2×C4⋊C4—81no—
271C2×C4⋊C4—81no—
272C2×C4⋊C4—81no—
273C2×C4⋊C4C22⋊C414yes—
274C2×C4⋊C4C22×C412yes—
275C2×C4⋊C4C22×C414yes—
276C2×C4⋊C4C2×D414yes—
277C2×C4⋊C4C2×D412yes—
278C2×C4⋊C4C2×D412yes—
279C2×C4⋊C4C2×D412yes—
280C2×C4⋊C4#4112yes—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—28no—
284C2×C22⋊C4—28no—
285C2×C22⋊C4—28no—
286C2×C22⋊C4—28no—
287C2×C22⋊C4—44no—
288C2×C22⋊C4—44no—
289C2×C22⋊C4—44no—
290C2×C22⋊C4—44no—
291C2×C22⋊C4—82no—
292C2×C22⋊C4—82no—
293C2×C22⋊C4—82no—
294C2×C22⋊C4—82no—
295C2×C22⋊C4C22⋊C418yes—
296C2×C42—28no—
297C2×C42—24no—
298C2×C42—24no—
299C2×C42—44no—
300C2×C42—44no—
301C2×C42—42no—
302C2×C42—42no—
303C2×C42—42no—
304C2×C42—42no—
305C2×C42C22×C412yes—
306C2×C42C2×D412yes—
307C2×C42C2×D412yes—
308C2×C42C2×D412yes—
309C2×C42#4112yes—
310C2×C42#4112yes—
311C4⋊C8—44no—
312#103—28no—
313#103—28no—
314#103—48no—
315C22⋊C8—48no—
316C22⋊C8—48no—
317C4×C8—44no—
318#95—28no—
319#95—28no—
320#95—24no—
321C24—22no—
322C24—22no—
323C24—22no—
324C24—22no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24C2×C22⋊C414yes—
336C24C22×D411yescharacteristic
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8C4×D414yes—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—44no—
371C2×D4—44no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—41no—
441C22×C4—42no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C2×C22⋊C414yes—
453C22×C4C2×C22⋊C412yes—
454C22×C4C2×C22⋊C412yes—
455C22×C4#12012yes—
456C22×C4#12012yes—
457C22×C4#12312yes—
458C22×C4#12312yes—
459C22×C4#13512yes—
460C22×C4#13512yes—
461C22×C4#13712yes—
462C22×C4#13712yes—
463C22×C4C23×C411yescharacteristic
464C22×C4C22×D411yescharacteristic
465C22×C4C22×D411yescharacteristic
466C22×C4C22×D411yescharacteristic
467C22×C4C22×D411yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4C2×#4111yescharacteristic
473C22×C4H(5,𝔽2)11yescharacteristic
474C22×C4H(5,𝔽2)11yescharacteristic
475C22×C4H(5,𝔽2)11yescharacteristic
476C22×C42−1+411yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—42no—
492C2×C8—42no—
493C2×C8—42no—
494C2×C8—42no—
495C2×C8—42no—
496C2×C8—42no—
497C2×C8—42no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—28no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—416no—
511C4⋊C4—42no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—48no—
520C4⋊C4—48no—
521C4⋊C4—48no—
522C4⋊C4—84no—
523C4⋊C4—84no—
524C4⋊C4#12114yes—
525C22⋊C4—216no—
526C22⋊C4—416no—
527C22⋊C4—416no—
528C22⋊C4—88no—
529C22⋊C4—88no—
530C42—416no—
531C42—48no—
532C42—48no—
533C42C4×D414yes—
534C42C4×D414yes—
535C42#12114yes—
536C42#12114yes—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23C22×C22⋊C411yescharacteristic
573C23C2×#12011yescharacteristic
574C23C2×#12311yescharacteristic
575C23D4211yescharacteristic
576C23#54611yescharacteristic
577C23#54611yescharacteristic
578C23#54711yescharacteristic
579C23C2×#13511yescharacteristic
580C23C2×#13511yescharacteristic
581C23C2×#13711yescharacteristic
582C23C2×#13711yescharacteristic
583C23#57611yescharacteristic
584C23#57711yescharacteristic
585C23#57711yescharacteristic
586C23#57811yescharacteristic
587Q8—24no—
588Q8—24no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595D4—416no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—44no—
631C2×C4—44no—
632C2×C4—44no—
633C2×C4—42no—
634C2×C4—44no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—44no—
642C2×C4—42no—
643C2×C4—81no—
644C2×C4—82no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—82no—
652C2×C4—82no—
653C2×C4—82no—
654C2×C4—82no—
655C2×C4—82no—
656C2×C4—82no—
657C2×C4—81no—
658C2×C4—82no—
659C2×C4#38614yes—
660C2×C4#38614yes—
661C2×C4#41614yes—
662C2×C4#41914yes—
663C2×C4#45214yes—
664C2×C4#45214yes—
665C2×C4#48514yes—
666C2×C4#48514yes—
667C2×C4C2×C4×D411yescharacteristic
668C2×C4C2×C4×D411yescharacteristic
669C2×C4C2×C4×D411yescharacteristic
670C2×C4C4×#4111yescharacteristic
671C2×C4#51811yescharacteristic
672C2×C4#52011yescharacteristic
673C2×C4C2×#12111yescharacteristic
674C2×C4C2×#12111yescharacteristic
675C2×C4C2×#12111yescharacteristic
676C2×C4#52511yescharacteristic
677C2×C4#52911yescharacteristic
678C2×C4#53211yescharacteristic
679C2×C4#53511yescharacteristic
680C2×C4#53711yescharacteristic
681C2×C4#54011yescharacteristic
682C2×C4#54211yescharacteristic
683C2×C4D4211yescharacteristic
684C2×C4D4211yescharacteristic
685C2×C4#54611yescharacteristic
686C2×C4#54611yescharacteristic
687C2×C4#54611yescharacteristic
688C2×C4#54711yescharacteristic
689C2×C4#54711yescharacteristic
690C2×C4#54811yescharacteristic
691C2×C4#55011yescharacteristic
692C2×C4#55311yescharacteristic
693C2×C4#55311yescharacteristic
694C2×C4#55511yescharacteristic
695C8—42no—
696C8—42no—
697C8—82no—
698C22—44no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—82no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22C2×#38611yescharacteristic
714C22D4×C22⋊C411yescharacteristic
715C22#233911yescharacteristic
716C22#240711yescharacteristic
717C22#240811yescharacteristic
718C22#242011yescharacteristic
719C22#242211yescharacteristic
720C22C2×#41611yescharacteristic
721C22C2×#41911yescharacteristic
722C22#289711yescharacteristic
723C22#289811yescharacteristic
724C22C2×#45211yescharacteristic
725C22C2×#45211yescharacteristic
726C22#301211yescharacteristic
727C22#301311yescharacteristic
728C22C2×#48511yescharacteristic
729C22C2×#48511yescharacteristic
730C22#309811yescharacteristic
731C22#309911yescharacteristic
732C22#327611yescharacteristic
733C22#327811yescharacteristic
734C22#328411yescharacteristic
735C22#328711yescharacteristic
736C22#330211yescharacteristic
737C22#330411yescharacteristic
738C22#330411yescharacteristic
739C22#330511yescharacteristic
740C22#332811yescharacteristic
741C22#332911yescharacteristic
742C22#333111yescharacteristic
743C22#333311yescharacteristic
744C22#334011yescharacteristic
745C22#334211yescharacteristic
746C22#335611yescharacteristic
747C22#335711yescharacteristic
748C4—24no—
749C4—44no—
750C4—44no—
751C4—44no—
752C4—82no—
753C4—84no—
754C4—84no—
755C4—82no—
756C4#187318yescomplemented
757C4C4×#12111yescharacteristic
758C4#232411yescharacteristic
759C4#236111yescharacteristic
760C4#236311yescharacteristic
761C4#242711yescharacteristic
762C4#242811yescharacteristic
763C4#253511yescharacteristic
764C4#253711yescharacteristic
765C2—84no—
766C2#1397011yescharacteristic
767C2C2×#187311yescharacteristic
768C2#2091511yescharacteristic
769C2#2241811yescharacteristic
770C2#2243011yescharacteristic
771C2#2249011yescharacteristic
772C2#2250211yescharacteristic
773C2#2412111yescharacteristic
774C2#2412311yescharacteristic
775C2#2424111yescharacteristic
776C2#2424211yescharacteristic
777C2#2497011yescharacteristic
778C2#2497211yescharacteristic
779C2#2501511yescharacteristic
780C2#2501711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1873C2semidirect
5. C2×#1803C2semidirect
6. C2×C4×#103C2semidirect
7. #11199C2semidirect
8. #10970C2semidirect
9. #10849C2semidirect
10. #10841C2semidirect
11. #10731C2semidirect
24. #2538C4semidirect
111. C2×#103D4semidirect
756. C4#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#23542
C2×#19542
C2×#18732
C2×#18032
C2×C4×#1032
#111992
#109702
#108492
#108412
#107312