Finite Group Databasebeta

← C2×#28746 #6466801

Subgroups — C2×#28746 #6466801

Order 512.

2694 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#496C211yesmaximal, characteristic
2C22×#446C211yesmaximal, characteristic, complemented
3C2×#2548C211yesmaximal, characteristic, complemented
4C2×#2592C211yesmaximal, characteristic, complemented
5#28746C2116yesmaximal, direct product factor
6C2×#2055C211yesmaximal, characteristic, complemented
7C2×#2055C211yesmaximal, characteristic, complemented
8C2×#2054C211yesmaximal, characteristic, complemented
9C2×#2054C211yesmaximal, characteristic, complemented
10C2×#1983C211yesmaximal, characteristic, complemented
11C2×#1982C211yesmaximal, characteristic, complemented
12C2×#1973C211yesmaximal, characteristic, complemented
13C2×#1972C211yesmaximal, characteristic, complemented
14C2×#1970C211yesmaximal, characteristic, complemented
15C2×#1968C211yesmaximal, characteristic, complemented
16C2×#1776C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C23×D8C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#124—21no—
23C22×#124C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C2×#496—28no—
26C2×#496C2218yes—
27C2×#446—28no—
28C2×#446C2218yescomplemented
29C22×#107C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#97C2211yescharacteristic
43C22×#97C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#2592—24no—
46#2592C2218yescomplemented
47#2548—24no—
48#2548C2218yescomplemented
49C2×#397—21no—
50C2×#394—21no—
51C2×#394—21no—
52C2×#393—21no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#390—21no—
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#388—21no—
63C2×#388—21no—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66#2055C2218yescomplemented
67#2055C2218yescomplemented
68#2054C2218yescomplemented
69#2054C2218yescomplemented
70#1983C2218yescomplemented
71#1982C2218yescomplemented
72#1973C2218yescomplemented
73#1972C2218yescomplemented
74#1970C2218yescomplemented
75#1968C2218yescomplemented
76#1776C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8D411yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4—21no—
83C23×D4C2311yescharacteristic
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C22×SD16—24no—
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—42no—
91C22×SD16—42no—
92C22×SD16C2314yes—
93C22×SD16C2314yes—
94C22×D8—24no—
95C22×D8—24no—
96C22×D8—24no—
97C22×D8—24no—
98C22×D8—42no—
99C22×D8—42no—
100C22×D8C2314yes—
101C22×D8C2314yes—
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106C2×#127—24no—
107C2×#127—22no—
108C2×#127—24no—
109C2×#127C2314yes—
110C2×#124—28no—
111C2×#124—22no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—48no—
115C2×#124C2314yes—
116C2×C4×Q8—24no—
117C2×C4×Q8—24no—
118C2×C4×Q8D414yes—
119C2×C4×Q8C2314yes—
120C22×C4⋊C4D411yescharacteristic
121C22×C4⋊C4D411yescharacteristic
122C22×C4⋊C4D411yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146#496—232no—
147#446—232no—
148C2×#107—24no—
149C2×#107C2314yes—
150C2×#106—24no—
151C2×#106C2314yes—
152C2×C4⋊C8—24no—
153C2×C4⋊C8—24no—
154C2×C4⋊C8—24no—
155C2×C4⋊C8C2314yes—
156C2×C4⋊C8C2314yes—
157C2×C4⋊C8C2314yes—
158C2×#103—42no—
159C2×#103—42no—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#102—42no—
163C2×#102—42no—
164C2×#102—42no—
165C2×#102—42no—
166C2×#102—42no—
167C2×#102—42no—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#97—24no—
175C2×#97D418yes—
176C2×#97C2314yes—
177C2×#97C2314yes—
178C2×C4×C8—24no—
179C2×C4×C8C2314yes—
180#397—28no—
181#394—28no—
182#394—28no—
183#393—28no—
184#391—22no—
185#391—22no—
186#391C2314yes—
187#391C2314yes—
188#390—28no—
189#390—22no—
190#390—22no—
191#390—22no—
192#390—22no—
193#390—22no—
194#390—22no—
195#390C2314yes—
196#390C2314yes—
197#390C2314yes—
198#390C2314yes—
199#390C2314yes—
200#390C2314yes—
201#388—28no—
202#388—28no—
203C4×C4⋊C4—22no—
204C4×C4⋊C4—22no—
205C4×C4⋊C4C2314yes—
206C4×C4⋊C4C2314yes—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213#340C2314yes—
214#340C2314yes—
215C25—21no—
216C25—21no—
217C25—21no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—21no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—42no—
228C22×Q8C2×D414yes—
229C22×Q8C2412yes—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—82no—
258C22×D4—82no—
259C22×D4C2412yes—
260C22×D4C2412yes—
261C22×D4C2412yes—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2411yescharacteristic
274C2×SD16—28no—
275C2×SD16—28no—
276C2×SD16—28no—
277C2×SD16—28no—
278C2×SD16—44no—
279C2×SD16—44no—
280C2×SD16—416no—
281C2×SD16—416no—
282C2×D8—28no—
283C2×D8—28no—
284C2×D8—28no—
285C2×D8—28no—
286C2×D8—44no—
287C2×D8—44no—
288C2×D8—416no—
289C2×D8—416no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8C2×D414yes—
299C22×C8C2×D414yes—
300C22×C8#4114yes—
301C22×C8#4114yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306#127—28no—
307#127—28no—
308#127—48no—
309#124—28no—
310#124—28no—
311#124—432no—
312#124—48no—
313C4×Q8—216no—
314C4×Q8—28no—
315C4×Q8—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2412yes—
335C2×C4⋊C4C2412yes—
336C2×C4⋊C4C2412yes—
337C2×C4⋊C4C2412yes—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—82no—
361C2×C22⋊C4—82no—
362C2×C22⋊C4—82no—
363C2×C22⋊C4—82no—
364C2×C22⋊C4—82no—
365C2×C22⋊C4—82no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—44no—
373C2×C42—82no—
374C2×C42C2×D412yes—
375C2×C42C2×D412yes—
376C2×C42C2×D412yes—
377C2×C42C2×D414yes—
378C2×C42#4114yes—
379C2×C42C2412yes—
380C2×C42C2412yes—
381C2×C42C2412yes—
382#107—28no—
383#106—28no—
384C4⋊C8—28no—
385C4⋊C8—28no—
386C4⋊C8—28no—
387#103—44no—
388#103—44no—
389#102—44no—
390#102—44no—
391#102—44no—
392#102—44no—
393#102—44no—
394#102—44no—
395#97—28no—
396#97C2×D4116yes—
397C4×C8—28no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24C22×D411yescharacteristic
429C2×Q8—28no—
430C2×Q8—28no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—44no—
438C2×Q8—416no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—42no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—84no—
490C2×D4—84no—
491C2×D4—816no—
492C2×D4—816no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
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—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4#12114yes—
529C22×C4#12114yes—
530C22×C4AGL(1,ℤ/8)14yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D412yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4C2511yescharacteristic
545SD16—416no—
546SD16—416no—
547D8—416no—
548D8—416no—
549C2×C8—28no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—44no—
559C2×C8—44no—
560C2×C8#124116yescomplemented
561C2×C8C22×D414yes—
562C2×C8C22×D414yes—
563C2×C8C2×#4114yes—
564C2×C8C2×#4114yes—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—84no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C22⋊C4—84no—
593C22⋊C4—84no—
594C42—24no—
595C42—24no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—48no—
601C42—84no—
602C42#12118yes—
603C42C22×D414yes—
604C42C2×#4114yes—
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—42no—
624C23—42no—
625C23—42no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23—84no—
630C23—84no—
631C23—84no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23—84no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23C2×#12112yes—
648C23#55012yes—
649C23#55012yes—
650C23C2×AGL(1,ℤ/8)12yes—
651C23#57512yes—
652C23#57612yes—
653C23#57712yes—
654C23C23×D411yescharacteristic
655Q8—416no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—84no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—816no—
674D4—816no—
675D4—84no—
676D4—84no—
677D4—84no—
678C2×C4—22no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4C2×#12114yes—
720C2×C4C2×#12114yes—
721C2×C4C2×#12112yes—
722C2×C4C2×#12414yes—
723C2×C4#53514yes—
724C2×C4#55012yes—
725C2×C4#55012yes—
726C2×C4#55914yes—
727C2×C4#55914yes—
728C2×C4C2×AGL(1,ℤ/8)14yes—
729C2×C4C23×D411yescharacteristic
730C2×C4C22×#4111yescharacteristic
731C2×C4C22×#4111yescharacteristic
732C2×C4C22×#4111yescharacteristic
733C2×C4C2×H(5,𝔽2)11yescharacteristic
734C2×C4C2×H(5,𝔽2)11yescharacteristic
735C8—24no—
736C8—42no—
737C8—42no—
738C8C2×#12418yescomplemented
739C22—82no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—168no—
761C22—168no—
762C22—168no—
763C22#254814yes—
764C22#305514yes—
765C22#306214yes—
766C22#339714yes—
767C22#339914yes—
768C22#340114yes—
769C22#340314yes—
770C22C22×#12111yescharacteristic
771C22C2×#55011yescharacteristic
772C22C2×#55011yescharacteristic
773C22C22×AGL(1,ℤ/8)11yescharacteristic
774C22C2×#57511yescharacteristic
775C22C2×#57611yescharacteristic
776C22C2×#57711yescharacteristic
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#254814yes—
789C4C22×#12411yescharacteristic
790C4C2×#53511yescharacteristic
791C4C2×#55911yescharacteristic
792C4C2×#55911yescharacteristic
793C2—162no—
794C2—162no—
795C2—162no—
796C2#2874618yesdirect product factor
797C2C2×#254811yescharacteristic
798C2C2×#305511yescharacteristic
799C2C2×#306211yescharacteristic
800C2C2×#339711yescharacteristic
801C2C2×#339911yescharacteristic
802C2C2×#340111yescharacteristic
803C2C2×#340311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#496C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#446C2semidirect
3. C2×#2548C2semidirect
4. C2×#2592C2semidirect
5. #28746C2direct (N × H)
6. C2×#2055C2semidirect
7. C2×#2055C2semidirect
8. C2×#2054C2semidirect
9. C2×#2054C2semidirect
10. C2×#1983C2semidirect
11. C2×#1982C2semidirect
12. C2×#1973C2semidirect
13. C2×#1972C2semidirect
14. C2×#1970C2semidirect
15. C2×#1968C2semidirect
16. C2×#1776C2semidirect
28. C2×#446C22semidirect
46. #2592C22semidirect
48. #2548C22semidirect
66. #2055C22semidirect
67. #2055C22semidirect
68. #2054C22semidirect
69. #2054C22semidirect
70. #1983C22semidirect
71. #1982C22semidirect
72. #1973C22semidirect
73. #1972C22semidirect
74. #1970C22semidirect
75. #1968C22semidirect
76. #1776C22semidirect
560. C2×C8#124semidirect
738. C8C2×#124semidirect
796. C2#28746direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4962
C22×#4462
C2×#25482
C2×#25922
#287462
C2×#20552
C2×#20542
C2×#19832
C2×#19822
C2×#19732
C2×#19722
C2×#19702
C2×#19682
C2×#17762