Finite Group Databasebeta

← C22⋊C4×#102 #356089

Subgroups — C22⋊C4×#102 #356089

Order 512.

3466 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#102C211yesmaximal, characteristic
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C2×#1786C211yesmaximal, characteristic
4C2×C4×#102C212yesmaximal, complemented
5C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
6C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
7#10931C212yesmaximal, complemented
8#10925C212yesmaximal, complemented
9#10788C212yesmaximal, complemented
10#10730C211yesmaximal, characteristic, complemented
11#10721C211yesmaximal, characteristic, complemented
12C24×D4C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C22×C4×D4C2212yes—
15C23×C4⋊C4C2211yescharacteristic
16C23×C22⋊C4—21no—
17C22×#102—28no—
18C22×#102C418yescomplemented
19C22×#102C2211yescharacteristic
20C22×#102C2212yes—
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2212yes—
24C22×#102C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C4×C8C2212yescomplemented
27D4×C22⋊C4—24no—
28D4×C22⋊C4C418yescomplemented
29C2×#390C2212yes—
30C2×#386—22no—
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#379—21no—
34C2×C4×C4⋊C4C2212yescomplemented
35C2×C4×C22⋊C4—21no—
36C2×C4×C22⋊C4C2211yescharacteristic
37#1786C418yescomplemented
38C4×#102—28no—
39C8×C22⋊C4—24no—
40C2×#340C2212yescomplemented
41C2×#340C2212yescomplemented
42C2×#340C2212yescomplemented
43C2×#340C2212yescomplemented
44C2×#336C2212yescomplemented
45#1436—22no—
46C4⋊#95C2212yescomplemented
47C22⋊#95—21no—
48C26—21no—
49C23×D4—24no—
50C23×D4—24no—
51C23×D4—22no—
52C23×D4—21no—
53C23×D4—22no—
54C23×D4—22no—
55C23×D4—42no—
56C23×D4—42no—
57C23×D4C2×C414yes—
58C23×D4C2×C414yes—
59C23×D4C2×C414yes—
60C23×D4C2311yescharacteristic
61C23×D4C2311yescharacteristic
62C24×C4—21no—
63C24×C4—22no—
64C24×C4C2311yescharacteristic
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—24no—
68C23×C8—42no—
69C23×C8C2×C414yescomplemented
70C23×C8C2312yes—
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C2×C4×D4—24no—
74C2×C4×D4—24no—
75C2×C4×D4—24no—
76C2×C4×D4—42no—
77C2×C4×D4—42no—
78C2×C4×D4C2×C418yescomplemented
79C22×C4⋊C4—24no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—42no—
83C22×C4⋊C4C2×C414yescomplemented
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2312yes—
86C22×C4⋊C4C2312yes—
87C22×C4⋊C4C2311yescharacteristic
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4—22no—
91C22×C22⋊C4—22no—
92C22×C22⋊C4—22no—
93C22×C22⋊C4—28no—
94C22×C22⋊C4—44no—
95C22×C22⋊C4—44no—
96C22×C22⋊C4D411yescharacteristic
97C22×C22⋊C4D411yescharacteristic
98C22×C42—22no—
99C22×C42C2312yes—
100C2×#102—24no—
101C2×#102—24no—
102C2×#102—24no—
103C2×#102—24no—
104C2×#102—24no—
105C2×#102—232no—
106C2×#102—42no—
107C2×#102—42no—
108C2×#102C2×C414yes—
109C2×#102C2×C414yes—
110C2×#102C2×C414yescomplemented
111C2×#102C2×C414yescomplemented
112C2×#102C2×C418yescomplemented
113C2×#102C2×C418yescomplemented
114C2×#102D418yes—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8C2×C414yescomplemented
118C2×C4×C8—24no—
119C2×C4×C8—24no—
120C2×C4×C8—42no—
121#390—24no—
122#390C2×C418yescomplemented
123#386—216no—
124#380—22no—
125#380—22no—
126#380C2×C414yes—
127#380C2×C414yescomplemented
128#379—28no—
129C4×C4⋊C4—24no—
130C4×C4⋊C4—42no—
131C4×C22⋊C4—44no—
132C4×C22⋊C4C2×C414yes—
133C4×C22⋊C4D414yes—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—22no—
137C2×#95—22no—
138C2×#95—22no—
139C2×#95D412yes—
140#340—24no—
141#340—24no—
142#340—42no—
143#340—42no—
144#336—24no—
145C25—21no—
146C25—21no—
147C25—24no—
148C25—24no—
149C25—24no—
150C25—44no—
151C25—44no—
152C25—42no—
153C25—42no—
154C25—42no—
155C25—42no—
156C25—82no—
157C25—82no—
158C25C2×D411yescharacteristic
159C22×D4—28no—
160C22×D4—28no—
161C22×D4—216no—
162C22×D4—216no—
163C22×D4—24no—
164C22×D4—28no—
165C22×D4—28no—
166C22×D4—28no—
167C22×D4—24no—
168C22×D4—24no—
169C22×D4—21no—
170C22×D4—22no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C22×D4—22no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—22no—
178C22×D4—22no—
179C22×D4—22no—
180C22×D4—22no—
181C22×D4—44no—
182C22×D4—44no—
183C22×D4—48no—
184C22×D4—48no—
185C22×D4—48no—
186C22×D4—48no—
187C22×D4—48no—
188C22×D4—48no—
189C22×D4—48no—
190C22×D4—48no—
191C22×D4—44no—
192C22×D4—44no—
193C22×D4C42116yescomplemented
194C22×D4C22×C412yes—
195C22×D4C22×C412yes—
196C22×D4C22×C412yes—
197C22×D4C22×C412yes—
198C22×D4C22×C412yes—
199C22×D4C22×C412yes—
200C22×D4C2×D414yes—
201C22×D4#4114yes—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—24no—
211C23×C4—28no—
212C23×C4—44no—
213C23×C4—44no—
214C23×C4—44no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—44no—
218C23×C4—44no—
219C23×C4—82no—
220C23×C4—82no—
221C23×C4—82no—
222C23×C4C22×C412yes—
223C23×C4C22×C412yes—
224C23×C4C22×C412yes—
225C23×C4C2×D412yes—
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D412yes—
228C23×C4C2×D412yes—
229C23×C4#4112yes—
230C23×C4#4112yes—
231C23×C4C2411yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—22no—
235C22×C8—28no—
236C22×C8—21no—
237C22×C8—22no—
238C22×C8—22no—
239C22×C8—22no—
240C22×C8—21no—
241C22×C8—22no—
242C22×C8—22no—
243C22×C8—22no—
244C22×C8—22no—
245C22×C8—22no—
246C22×C8—28no—
247C22×C8—44no—
248C22×C8—48no—
249C22×C8—48no—
250C22×C8C22×C412yes—
251C22×C8C22×C414yes—
252C22×C8C22×C412yes—
253C22×C8C2×D414yes—
254C4×D4—216no—
255C4×D4—48no—
256C4×D4—48no—
257C4×D4—48no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4—48no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4C22×C412yes—
279C2×C4⋊C4C22×C414yes—
280C2×C4⋊C4C22×C414yes—
281C2×C4⋊C4C22×C412yes—
282C2×C4⋊C4C2×D414yes—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—28no—
288C2×C22⋊C4—28no—
289C2×C22⋊C4—28no—
290C2×C22⋊C4—44no—
291C2×C22⋊C4—44no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—44no—
297C2×C22⋊C4—44no—
298C2×C22⋊C4—432no—
299C2×C22⋊C4—82no—
300C2×C22⋊C4—82no—
301C2×C22⋊C4C22⋊C414yes—
302C2×C22⋊C4C22⋊C414yes—
303C2×C22⋊C4D814yes—
304C2×C22⋊C4SD1614yes—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—44no—
310C2×C42—44no—
311C2×C42—82no—
312C2×C42C22×C414yes—
313C2×C42C2×D414yes—
314#102—28no—
315#102—216no—
316#102—28no—
317#102—28no—
318#102—48no—
319#102C22⋊C4116yesdirect product factor
320C22⋊C8—28no—
321C4×C8—48no—
322#95—24no—
323#95—24no—
324#95—44no—
325#95—44no—
326#95—82no—
327#95C22⋊C418yes—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24—24no—
336C24—24no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—216no—
341C24—48no—
342C24—416no—
343C24—48no—
344C24—416no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—42no—
350C24—42no—
351C24—42no—
352C24—42no—
353C24—41no—
354C24—41no—
355C24—41no—
356C24—41no—
357C24—42no—
358C24—42no—
359C24—48no—
360C24—48no—
361C24—48no—
362C24—48no—
363C24—48no—
364C24—48no—
365C24—88no—
366C24—88no—
367C24—84no—
368C24—84no—
369C24—88no—
370C24—88no—
371C24—88no—
372C24—88no—
373C24—88no—
374C24—88no—
375C24—88no—
376C24—88no—
377C24C2×C22⋊C412yes—
378C24C4×D412yes—
379C24C4×D412yes—
380C24C2×D812yes—
381C24C2×SD1612yes—
382C24#13512yes—
383C24#13512yes—
384C24C22×D411yescharacteristic
385C2×D4—232no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—24no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—216no—
411C2×D4—416no—
412C2×D4—416no—
413C2×D4—432no—
414C2×D4—416no—
415C2×D4—432no—
416C2×D4—48no—
417C2×D4—416no—
418C2×D4—48no—
419C2×D4—416no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4C2×C4214yes—
427C2×D4C2×C4214yes—
428C2×D4C2×C22⋊C414yes—
429C2×D4#11714yes—
430C2×D4C4×D418yes—
431C2×D4C4×D418yes—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—48no—
464C22×C4—416no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—41no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—48no—
485C22×C4—416no—
486C22×C4—88no—
487C22×C4—88no—
488C22×C4—88no—
489C22×C4—88no—
490C22×C4—88no—
491C22×C4—84no—
492C22×C4—88no—
493C22×C4—88no—
494C22×C4C2×C4214yes—
495C22×C4C2×C22⋊C414yes—
496C22×C4C2×C22⋊C412yes—
497C22×C4C2×C22⋊C414yes—
498C22×C4#11714yes—
499C22×C4C4×D414yes—
500C22×C4C4×D414yes—
501C22×C4C4×D412yes—
502C22×C4C4×D412yes—
503C22×C4C2×D814yes—
504C22×C4C2×SD1614yes—
505C22×C4C23×C411yescharacteristic
506C22×C4C23×C411yescharacteristic
507C22×C4C23×C411yescharacteristic
508C22×C4C22×D412yes—
509C22×C4C22×D411yescharacteristic
510C22×C4C2×#4112yes—
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4H(5,𝔽2)12yes—
514C22×C4H(5,𝔽2)12yes—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—24no—
518C2×C8—24no—
519C2×C8—22no—
520C2×C8—24no—
521C2×C8—24no—
522C2×C8—22no—
523C2×C8—24no—
524C2×C8—22no—
525C2×C8—416no—
526C2×C8—42no—
527C2×C8—42no—
528C2×C8—42no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
532C2×C8C2×C22⋊C414yescomplemented
533C4⋊C4—22no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—24no—
541C4⋊C4—48no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4C2×C22⋊C414yescomplemented
548C22⋊C4—28no—
549C22⋊C4—416no—
550C22⋊C4—48no—
551C22⋊C4—48no—
552C22⋊C4—416no—
553C22⋊C4—88no—
554C22⋊C4#102116yesdirect product factor
555C42—24no—
556C42—24no—
557C42—24no—
558C42—24no—
559C42—88no—
560C23—22no—
561C23—24no—
562C23—22no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—22no—
567C23—22no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—28no—
577C23—24no—
578C23—24no—
579C23—28no—
580C23—24no—
581C23—24no—
582C23—432no—
583C23—42no—
584C23—42no—
585C23—44no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—44no—
591C23—42no—
592C23—42no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—42no—
603C23—42no—
604C23—44no—
605C23—42no—
606C23—42no—
607C23—44no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—44no—
613C23—42no—
614C23—42no—
615C23—432no—
616C23—816no—
617C23—816no—
618C23—816no—
619C23—832no—
620C23—832no—
621C23—832no—
622C23—832no—
623C23—816no—
624C23—816no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—82no—
629C23—82no—
630C23—82no—
631C23—82no—
632C23—82no—
633C23C4×C22⋊C414yes—
634C23C2×#10214yes—
635C23#41614yes—
636C23C4×D814yes—
637C23C4×D814yes—
638C23C4×SD1614yes—
639C23C4×SD1614yes—
640C23C22×C22⋊C411yescharacteristic
641C23C2×C4×D411yescharacteristic
642C23C2×C4×D411yescharacteristic
643C23D4212yes—
644C23#54612yes—
645C23C22×D811yescharacteristic
646C23C22×SD1611yescharacteristic
647C23C2×#13511yescharacteristic
648C23C2×#13511yescharacteristic
649C23#57612yes—
650C23#57712yes—
651D4—24no—
652D4—24no—
653D4—28no—
654D4—28no—
655D4—24no—
656D4—24no—
657D4—24no—
658D4—432no—
659D4—42no—
660D4—42no—
661D4—44no—
662D4—44no—
663D4C4×C22⋊C418yescomplemented
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—28no—
676C2×C4—24no—
677C2×C4—28no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—832no—
702C2×C4—816no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4C4×C22⋊C414yes—
714C2×C4C2×#10218yescomplemented
715C2×C4C22×C4211yescharacteristic
716C2×C4C22×C22⋊C411yescharacteristic
717C2×C4C2×#11711yescharacteristic
718C2×C4C2×#11711yescharacteristic
719C2×C4C2×C4×D411yescharacteristic
720C2×C4C2×C4×D412yes—
721C2×C4C2×C4×D411yescharacteristic
722C2×C4C2×C4×D412yes—
723C2×C4#51811yescharacteristic
724C2×C4#51812yes—
725C2×C4#51811yescharacteristic
726C2×C4#51812yes—
727C2×C4D4212yes—
728C2×C4#54612yes—
729C2×C4#54612yes—
730C2×C4#54612yes—
731C2×C4#55112yes—
732C2×C4#55112yes—
733C8—24no—
734C8—42no—
735C8—44no—
736C22—24no—
737C22—24no—
738C22—28no—
739C22—28no—
740C22—28no—
741C22—28no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—28no—
747C22—44no—
748C22—44no—
749C22—48no—
750C22—48no—
751C22—48no—
752C22—48no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—864no—
761C22—82no—
762C22—82no—
763C22—84no—
764C22—84no—
765C22—84no—
766C22—84no—
767C22—82no—
768C22—82no—
769C22C4×#10218yescomplemented
770C22C2×C4×C22⋊C411yescharacteristic
771C22D4×C22⋊C412yes—
772C22D4×C22⋊C411yescharacteristic
773C22#234211yescharacteristic
774C22#235812yes—
775C22C22×#10211yescharacteristic
776C22C2×#41611yescharacteristic
777C22#289712yes—
778C22C2×C4×D811yescharacteristic
779C22C2×C4×D811yescharacteristic
780C22C2×C4×SD1611yescharacteristic
781C22C2×C4×SD1611yescharacteristic
782C22#294612yes—
783C22#294811yescharacteristic
784C22#294911yescharacteristic
785C22D4×D812yes—
786C22#328012yes—
787C22D4×SD1612yes—
788C22#328212yes—
789C22#329412yes—
790C22#329512yes—
791C22#329612yes—
792C22#329712yes—
793C4—28no—
794C4—24no—
795C4—44no—
796C4—44no—
797C4—84no—
798C4—84no—
799C4—82no—
800C4C2×C4×C22⋊C411yescharacteristic
801C4#227311yescharacteristic
802C4D4×C22⋊C411yescharacteristic
803C4#234212yes—
804C4#234211yescharacteristic
805C4#235812yes—
806C2—28no—
807C2—48no—
808C2—84no—
809C2C22⋊C4211yescharacteristic
810C2C2×C4×#10211yescharacteristic
811C2#2041611yescharacteristic
812C2D4×#10212yes—
813C2#2241412yes—
814C2C22⋊C4×D811yescharacteristic
815C2C22⋊C4×SD1611yescharacteristic
816C2#2257011yescharacteristic
817C2#2257411yescharacteristic
818C2#2287012yes—
819C2#2287412yes—
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC24×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×C4×#102C2semidirect
5. C2×C8×C22⋊C4C2semidirect
6. C22⋊C4×C4⋊C4C2semidirect
7. #10931C2semidirect
8. #10925C2semidirect
9. #10788C2semidirect
10. #10730C2semidirect
11. #10721C2semidirect
18. C22×#102C4semidirect
26. C22×C4×C8C22semidirect
28. D4×C22⋊C4C4semidirect
34. C2×C4×C4⋊C4C22semidirect
37. #1786C4semidirect
40. C2×#340C22semidirect
41. C2×#340C22semidirect
42. C2×#340C22semidirect
43. C2×#340C22semidirect
44. C2×#336C22semidirect
46. C4⋊#95C22semidirect
69. C23×C8C2×C4semidirect
78. C2×C4×D4C2×C4semidirect
83. C22×C4⋊C4C2×C4semidirect
110. C2×#102C2×C4semidirect
111. C2×#102C2×C4semidirect
112. C2×#102C2×C4semidirect
113. C2×#102C2×C4semidirect
117. C2×C22⋊C8C2×C4semidirect
122. #390C2×C4semidirect
127. #380C2×C4semidirect
193. C22×D4C42semidirect
319. #102C22⋊C4direct (N × H)
532. C2×C8C2×C22⋊C4semidirect
547. C4⋊C4C2×C22⋊C4semidirect
554. C22⋊C4#102direct (N × H)
663. D4C4×C22⋊C4semidirect
714. C2×C4C2×#102semidirect
769. C22C4×#102semidirect

Maximal subgroups

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

subgroupindex
C23×#1022
C2×D4×C22⋊C42
C2×#17862
C2×C4×#1022
C2×C8×C22⋊C42
C22⋊C4×C4⋊C42
#109312
#109252
#107882
#107302
#107212