Finite Group Databasebeta

← C2×#23586 #6432025

Subgroups — C2×#23586 #6432025

Order 512.

3406 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#541C211yesmaximal, characteristic
2C22×#441C211yesmaximal, characteristic, complemented
3C22×C4×Q16C211yesmaximal, characteristic, complemented
4C2×#2323C211yesmaximal, characteristic
5#23586C2116yesmaximal, direct product factor
6C2×#2059C211yesmaximal, characteristic, complemented
7C2×#2043C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic
9C2×#2035C211yesmaximal, characteristic
10C2×#2026C211yesmaximal, characteristic, complemented
11C2×#2016C211yesmaximal, characteristic, complemented
12C2×#2001C211yesmaximal, characteristic
13C2×#2001C211yesmaximal, characteristic
14C2×#1763C211yesmaximal, characteristic, complemented
15C2×C4×#103C211yesmaximal, characteristic, complemented
16C2×#1750C211yesmaximal, characteristic
17C23×Q16C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C2×#541—28no—
20C2×#541—28no—
21C2×#541—24no—
22C2×#541C2218yes—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126—21no—
25C22×#126—21no—
26C22×#125—21no—
27C22×#125—21no—
28C22×#125C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#441—28no—
37C2×#441C2218yescomplemented
38C2×C4×Q16—28no—
39C2×C4×Q16C2218yescomplemented
40C22×#107C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#103C2211yescharacteristic
49C22×#103C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×#97C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2323—24no—
55#2323C2218yes—
56C2×#391C2211yescharacteristic
57C2×#389—21no—
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60C2×#388—21no—
61C2×#387—21no—
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2059C2218yescomplemented
65#2043C2218yescomplemented
66#2036C2218yes—
67#2035C2218yes—
68#2026C2218yescomplemented
69#2016C2218yescomplemented
70#2001C2218yes—
71#2001C2218yes—
72#1763C2218yescomplemented
73C4×#103C2218yescomplemented
74#1750C2218yes—
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C22×Q16—24no—
86C22×Q16—24no—
87C22×Q16—24no—
88C22×Q16—24no—
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16C2314yes—
92C22×Q16C2314yes—
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97#541—264no—
98#541—232no—
99#541—232no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—22no—
103C2×C4⋊Q8C2314yes—
104C2×#126—216no—
105C2×#126—216no—
106C2×#126—28no—
107C2×#126—28no—
108C2×#125—216no—
109C2×#125—216no—
110C2×#125—28no—
111C2×#125—28no—
112C2×#125—24no—
113C2×#125—24no—
114C2×#125—22no—
115C2×#125C2314yes—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8C2314yes—
126C2×C22⋊Q8C2314yes—
127C2×C22⋊Q8C2314yes—
128C2×C4×Q8—24no—
129C2×C4×Q8—24no—
130C2×C4×Q8—22no—
131C2×C4×Q8—22no—
132C2×C4×Q8—22no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8D418yes—
136C2×C4×Q8D418yes—
137C2×C4×Q8C2314yes—
138C2×C4×Q8C2314yes—
139C2×C4×Q8C2314yes—
140C2×#117—24no—
141C2×#117—24no—
142C2×#117D414yes—
143C2×#117C2314yes—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4D411yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4D411yescharacteristic
167C22×C22⋊C4D411yescharacteristic
168C22×C42—21no—
169C22×C42—21no—
170C22×C42—21no—
171C22×C42—21no—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#441—232no—
175C4×Q16—232no—
176C2×#107—24no—
177C2×#107C2314yes—
178C2×#106—24no—
179C2×#106C2314yes—
180C2×#103—24no—
181C2×#103—24no—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—24no—
187C2×#103—24no—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×C22⋊C8—24no—
197C2×C22⋊C8—24no—
198C2×C22⋊C8C2314yes—
199C2×C22⋊C8C2314yes—
200C2×#97—24no—
201C2×#97C2314yes—
202C2×C4×C8—24no—
203C2×C4×C8C2314yes—
204#391—22no—
205#391C2314yes—
206#389—28no—
207#389—22no—
208#389C2314yes—
209#388—28no—
210#388—28no—
211#387—28no—
212#380—22no—
213#380C2314yes—
214C4×C4⋊C4—22no—
215C4×C4⋊C4C2314yes—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221#340C2314yes—
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25C2×D411yescharacteristic
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8C2×D414yes—
247C22×Q8C2×D414yes—
248C22×Q8#4114yes—
249C22×Q8C2412yes—
250C22×Q8C2412yes—
251C22×Q8C2412yes—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C2×Q16—232no—
275C2×Q16—232no—
276C2×Q16—28no—
277C2×Q16—28no—
278C2×Q16—28no—
279C2×Q16—28no—
280C2×Q16—28no—
281C2×Q16—28no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8#4114yes—
293C22×C8#4114yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22×C8C2412yes—
298C4⋊Q8—216no—
299C4⋊Q8—28no—
300C4⋊Q8—28no—
301#126—264no—
302#126—264no—
303#125—264no—
304#125—264no—
305#125—216no—
306#125—28no—
307#125—28no—
308C22⋊Q8—216no—
309C22⋊Q8—216no—
310C22⋊Q8—216no—
311C22⋊Q8—28no—
312C22⋊Q8—28no—
313C22⋊Q8—28no—
314C22⋊Q8—28no—
315C22⋊Q8—28no—
316C22⋊Q8—28no—
317C4×Q8—216no—
318C4×Q8—216no—
319C4×Q8—28no—
320C4×Q8—28no—
321C4×Q8—28no—
322C4×Q8—28no—
323C4×Q8—48no—
324C4×Q8C2×D4116yes—
325C4×Q8C2×D4116yes—
326#117—216no—
327#117—28no—
328#117—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—82no—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C4⋊C4#4114yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—82no—
385C2×C22⋊C4C2×D414yes—
386C2×C22⋊C4C2×D414yes—
387C2×C42—28no—
388C2×C42—28no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—44no—
396C2×C42—82no—
397C2×C42C2×D412yes—
398C2×C42C2×D412yes—
399C2×C42C2×D414yes—
400C2×C42C2×D414yes—
401C2×C42C2412yes—
402C2×C42C2412yes—
403#107—28no—
404#106—28no—
405#103—28no—
406#103—28no—
407#103—28no—
408#103—28no—
409#103—28no—
410#103—28no—
411#103—28no—
412#103—28no—
413C22⋊C8—28no—
414C22⋊C8—28no—
415#97—28no—
416C4×C8—28no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24C22×D412yes—
430C24C22×D411yescharacteristic
431C2×Q8—24no—
432C2×Q8—24no—
433C2×Q8—24no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—42no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8C22×D414yes—
468C2×Q8C22×D414yes—
469C2×Q8C2×#4114yes—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4#12014yes—
529C22×C4#12014yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C2×#4112yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2511yescharacteristic
543Q16—232no—
544Q16—232no—
545C2×C8—28no—
546C2×C8—28no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8C2×#4114yes—
560C2×C8C2×#4114yes—
561C4⋊C4—216no—
562C4⋊C4—216no—
563C4⋊C4—216no—
564C4⋊C4—216no—
565C4⋊C4—216no—
566C4⋊C4—216no—
567C4⋊C4—216no—
568C4⋊C4—216no—
569C4⋊C4—216no—
570C4⋊C4—28no—
571C4⋊C4—28no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—42no—
583C4⋊C4—48no—
584C4⋊C4—42no—
585C4⋊C4—84no—
586C4⋊C4C22×D414yes—
587C4⋊C4C22×D414yes—
588C4⋊C4C2×#4114yes—
589C22⋊C4—216no—
590C22⋊C4—216no—
591C22⋊C4—216no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—84no—
595C42—216no—
596C42—216no—
597C42—24no—
598C42—22no—
599C42—22no—
600C42—48no—
601C42—84no—
602C42#12018yes—
603C42C22×D414yes—
604C42C22×D414yes—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23C2×#12012yes—
620C23#52512yes—
621C23#53212yes—
622C23#57712yes—
623C23#57812yes—
624C23#57812yes—
625C23#57812yes—
626C23C23×D411yescharacteristic
627Q8—24no—
628Q8—24no—
629Q8—24no—
630Q8—24no—
631Q8—24no—
632Q8—24no—
633Q8—48no—
634Q8—48no—
635Q8—48no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—42no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—44no—
665C2×C4—48no—
666C2×C4—48no—
667C2×C4—48no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—48no—
676C2×C4—44no—
677C2×C4—48no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4C2×#12014yes—
698C2×C4C2×#12014yes—
699C2×C4C2×#12012yes—
700C2×C4#52512yes—
701C2×C4#52514yes—
702C2×C4#52514yes—
703C2×C4#53212yes—
704C2×C4#53214yes—
705C2×C4#53214yes—
706C2×C4C23×D411yescharacteristic
707C2×C4C23×D411yescharacteristic
708C2×C4C22×#4111yescharacteristic
709C2×C4C22×#4111yescharacteristic
710C2×C4C22×#4111yescharacteristic
711C2×C4C22×#4111yescharacteristic
712C8—24no—
713C8—24no—
714C8—42no—
715C8—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—88no—
724C22#238814yes—
725C22#301114yes—
726C22#301314yes—
727C22#312014yes—
728C22#312714yes—
729C22#317714yes—
730C22#317814yes—
731C22C22×#12011yescharacteristic
732C22C2×#52511yescharacteristic
733C22C2×#53211yescharacteristic
734C22C2×#57711yescharacteristic
735C22C2×#57811yescharacteristic
736C22C2×#57811yescharacteristic
737C22C2×#57811yescharacteristic
738C4—24no—
739C4—24no—
740C4—44no—
741C4—42no—
742C4—44no—
743C4—42no—
744C4—44no—
745C4—42no—
746C4—44no—
747C4—44no—
748C4—44no—
749C4—82no—
750C4—82no—
751C4#238814yes—
752C4C2×#52511yescharacteristic
753C4C2×#52511yescharacteristic
754C4C2×#53211yescharacteristic
755C4C2×#53211yescharacteristic
756C2—82no—
757C2#2358618yesdirect product factor
758C2C2×#238811yescharacteristic
759C2C2×#301111yescharacteristic
760C2C2×#301311yescharacteristic
761C2C2×#312011yescharacteristic
762C2C2×#312711yescharacteristic
763C2C2×#317711yescharacteristic
764C2C2×#317811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#441C2semidirect
3. C22×C4×Q16C2semidirect
5. #23586C2direct (N × H)
6. C2×#2059C2semidirect
7. C2×#2043C2semidirect
10. C2×#2026C2semidirect
11. C2×#2016C2semidirect
14. C2×#1763C2semidirect
15. C2×C4×#103C2semidirect
37. C2×#441C22semidirect
39. C2×C4×Q16C22semidirect
64. #2059C22semidirect
65. #2043C22semidirect
68. #2026C22semidirect
69. #2016C22semidirect
72. #1763C22semidirect
73. C4×#103C22semidirect
757. C2#23586direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5412
C22×#4412
C22×C4×Q162
C2×#23232
#235862
C2×#20592
C2×#20432
C2×#20362
C2×#20352
C2×#20262
C2×#20162
C2×#20012
C2×#17632
C2×C4×#1032
C2×#17502