Finite Group Databasebeta

← #367050

Subgroups — #367050

Order 512.

2002 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#466C211yesmaximal, characteristic
2C2×#1970C211yesmaximal, characteristic, complemented
3C2×#1970C211yesmaximal, characteristic, complemented
4C2×#1942C211yesmaximal, characteristic, complemented
5C2×#1808C211yesmaximal, characteristic, complemented
6C2×C4×#107C211yesmaximal, characteristic, complemented
7C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
8#13998C212yesmaximal, complemented
9#11066C212yesmaximal, complemented
10#10969C212yesmaximal, complemented
11#10931C212yesmaximal, complemented
12C23×D8C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C22×#121C2212yes—
15C2×#466—24no—
16C2×#466—24no—
17C2×#466C418yescomplemented
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#102C2212yes—
22C22×#102C2212yes—
23C22×#102C2212yes—
24C22×C22⋊C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27C2×#390—22no—
28C2×#390C2212yes—
29C2×#390C2212yes—
30C2×#389C2212yes—
31C2×#380C2212yes—
32C2×C4×C4⋊C4C2212yes—
33C2×C4×C22⋊C4C2211yescharacteristic
34#1970—24no—
35#1970—24no—
36#1942—24no—
37#1808—24no—
38C4×#107—24no—
39C8×C22⋊C4—24no—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45#1439—22no—
46#1438—22no—
47#1437—22no—
48C23×D4—22no—
49C23×D4C2312yes—
50C24×C4C2311yescharacteristic
51C22×D8—22no—
52C22×D8—22no—
53C22×D8—22no—
54C22×D8—22no—
55C22×D8—22no—
56C22×D8—22no—
57C22×D8C2×C414yes—
58C23×C8—22no—
59C23×C8—22no—
60C23×C8—22no—
61C23×C8—22no—
62C23×C8—22no—
63C23×C8—22no—
64C23×C8C2×C414yes—
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×#121—24no—
70C2×#121—24no—
71C2×#121—24no—
72C2×#121—42no—
73C2×#121—42no—
74C2×#121C2×C418yes—
75C22×C4⋊C4—22no—
76C22×C4⋊C4C2312yes—
77C22×C4⋊C4C2312yes—
78C22×C4⋊C4C2312yes—
79C22×C22⋊C4—22no—
80C22×C22⋊C4—22no—
81C22×C22⋊C4—22no—
82C22×C22⋊C4—22no—
83C22×C22⋊C4—22no—
84C22×C22⋊C4—22no—
85C22×C22⋊C4D411yescharacteristic
86C22×C22⋊C4D411yescharacteristic
87C22×C42—22no—
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90#466—232no—
91C2×#107—22no—
92C2×#107—22no—
93C2×#107—22no—
94C2×#107—22no—
95C2×#107—22no—
96C2×#107C2×C414yes—
97C2×#107D414yes—
98C2×#107D414yes—
99C2×#107D414yescomplemented
100C2×#102—24no—
101C2×#102—24no—
102C2×#102—24no—
103C2×#102—24no—
104C2×#102—24no—
105C2×#102—42no—
106C2×#102—42no—
107C2×#102—42no—
108C2×#102C2×C418yes—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—22no—
112C2×C4×C8—22no—
113C2×C4×C8—22no—
114C2×C4×C8—22no—
115C2×C4×C8—22no—
116C2×C4×C8—22no—
117C2×C4×C8D414yescomplemented
118#390—24no—
119#390—24no—
120#390—24no—
121#390—42no—
122#390—48no—
123#389—24no—
124#389—42no—
125#380—24no—
126#380—42no—
127C4×C4⋊C4—24no—
128C4×C4⋊C4—42no—
129C4×C22⋊C4—22no—
130C4×C22⋊C4—22no—
131C2×#95—22no—
132C2×#95—22no—
133C2×#95—22no—
134C2×#95D411yescharacteristic
135C2×#95D411yescharacteristic
136#340—24no—
137#340—24no—
138#340—24no—
139#336—22no—
140#336—22no—
141C25—22no—
142C25C2×D411yescharacteristic
143C22×D4—28no—
144C22×D4—22no—
145C22×D4—22no—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4—22no—
149C22×D4—22no—
150C22×D4—22no—
151C22×D4—22no—
152C22×D4—22no—
153C22×D4—22no—
154C22×D4—22no—
155C22×D4—22no—
156C22×D4—22no—
157C22×D4—44no—
158C22×D4—44no—
159C22×D4—44no—
160C22×D4—44no—
161C22×D4—82no—
162C22×D4—82no—
163C22×D4C22×C414yes—
164C23×C4—22no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4C22×C412yes—
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4#4112yes—
186C23×C4C2411yescharacteristic
187C2×D8—28no—
188C2×D8—28no—
189C2×D8—28no—
190C2×D8—44no—
191C2×D8—44no—
192C2×D8—44no—
193C2×D8—44no—
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—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—28no—
213C22×C8—28no—
214C22×C8—28no—
215C22×C8—44no—
216C22×C8—44no—
217C22×C8—44no—
218C22×C8—44no—
219C22×C8C22×C412yes—
220C22×C8C22×C412yes—
221C22×C8C2×D412yes—
222C22×C8C2×D412yes—
223C22×C8C2×D412yes—
224C22×C8C2×D412yes—
225C22×C8C2×D412yes—
226C22×C8#4112yes—
227C22×C8#4112yes—
228C22×C8#4112yes—
229#121—216no—
230#121—48no—
231#121—48no—
232#121—48no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—82no—
250C2×C4⋊C4C22×C414yes—
251C2×C4⋊C4C2×D414yes—
252C2×C4⋊C4C2×D414yes—
253C2×C4⋊C4C2×D414yes—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—28no—
260C2×C22⋊C4—44no—
261C2×C22⋊C4—44no—
262C2×C22⋊C4—44no—
263C2×C22⋊C4—44no—
264C2×C22⋊C4—44no—
265C2×C22⋊C4—44no—
266C2×C22⋊C4—44no—
267C2×C22⋊C4—44no—
268C2×C22⋊C4—44no—
269C2×C22⋊C4—44no—
270C2×C22⋊C4—44no—
271C2×C22⋊C4—44no—
272C2×C22⋊C4—82no—
273C2×C22⋊C4—82no—
274C2×C22⋊C4—82no—
275C2×C22⋊C4—82no—
276C2×C22⋊C4—82no—
277C2×C22⋊C4D814yescomplemented
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—44no—
289C2×C42—44no—
290C2×C42—82no—
291C2×C42C2×D412yes—
292C2×C42#4112yes—
293#107—28no—
294#107—44no—
295#107C22⋊C4116yescomplemented
296#102—216no—
297#102—48no—
298#102—48no—
299C22⋊C8—28no—
300C4×C8—28no—
301C4×C8—44no—
302#95—22no—
303#95—22no—
304#95—44no—
305#95—44no—
306#95—44no—
307C24—21no—
308C24—21no—
309C24—21no—
310C24—21no—
311C24—21no—
312C24—21no—
313C24—21no—
314C24—21no—
315C24—21no—
316C24—21no—
317C24—21no—
318C24—21no—
319C24—24no—
320C24—42no—
321C24—42no—
322C24—42no—
323C24—42no—
324C24—42no—
325C24—42no—
326C24—42no—
327C24—42no—
328C24—42no—
329C24—42no—
330C24—42no—
331C24—42no—
332C24—42no—
333C24—42no—
334C24C4×D412yes—
335C24C2×D812yes—
336C24#13512yes—
337C24C22×D411yescharacteristic
338C2×D4—24no—
339C2×D4—24no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—416no—
345C2×D4—416no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—42no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—88no—
369C2×D4—88no—
370C2×D4—88no—
371C2×D4—88no—
372C2×D4—88no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—24no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4C4×D412yes—
451C22×C4#12112yes—
452C22×C4#12112yes—
453C22×C4C2×D812yes—
454C22×C4C2×D812yes—
455C22×C4#13512yes—
456C22×C4#13512yes—
457C22×C4C23×C411yescharacteristic
458C22×C4C22×D411yescharacteristic
459C22×C4C22×D411yescharacteristic
460C22×C4C22×D411yescharacteristic
461C22×C4C22×D411yescharacteristic
462C22×C4C2×#4111yescharacteristic
463C22×C4C2×#4111yescharacteristic
464C22×C4C2×#4111yescharacteristic
465C22×C4C2×#4111yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4H(5,𝔽2)11yescharacteristic
468C22×C4H(5,𝔽2)11yescharacteristic
469C22×C4H(5,𝔽2)11yescharacteristic
470C22×C42−1+411yescharacteristic
471D8—416no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—41no—
482C2×C8—41no—
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—41no—
492C2×C8—41no—
493C2×C8—416no—
494C2×C8C2×C22⋊C414yes—
495C2×C8C4×D414yes—
496C2×C8C4×D414yes—
497C2×C8#12114yes—
498C2×C8#12114yes—
499C2×C8#12414yes—
500C2×C8#12714yes—
501C4⋊C4—24no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—88no—
513C4⋊C4C2×C22⋊C418yes—
514C22⋊C4—28no—
515C22⋊C4—28no—
516C22⋊C4—416no—
517C22⋊C4—88no—
518C22⋊C4—88no—
519C22⋊C4—88no—
520C22⋊C4—88no—
521C22⋊C4—88no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—41no—
527C42—41no—
528C42—41no—
529C42—41no—
530C42—88no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—44no—
572C23—82no—
573C23—82no—
574C23—82no—
575C23—82no—
576C23—82no—
577C23—82no—
578C23—82no—
579C23—82no—
580C23—82no—
581C23—82no—
582C23—82no—
583C23—82no—
584C23—82no—
585C23—82no—
586C23—82no—
587C23—82no—
588C23—82no—
589C23—82no—
590C23—82no—
591C23—82no—
592C23—82no—
593C23—82no—
594C23—82no—
595C23—82no—
596C23—82no—
597C23—82no—
598C23—82no—
599C23—82no—
600C23C4×D814yes—
601C23C2×C4×D411yescharacteristic
602C23C2×#12111yescharacteristic
603C23#53211yescharacteristic
604C23D4211yescharacteristic
605C23D4211yescharacteristic
606C23D4211yescharacteristic
607C23#54711yescharacteristic
608C23C22×D811yescharacteristic
609C23C2×#13511yescharacteristic
610C23C2×#13511yescharacteristic
611C23C2×#13511yescharacteristic
612C23#57611yescharacteristic
613C23#57611yescharacteristic
614C23#57611yescharacteristic
615C23#57811yescharacteristic
616D4—44no—
617D4—44no—
618D4—44no—
619D4—44no—
620D4—832no—
621D4—82no—
622D4—82no—
623D4—82no—
624D4—82no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—28no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—44no—
648C2×C4—41no—
649C2×C4—44no—
650C2×C4—41no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—82no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4#46614yescomplemented
689C2×C4C22×C22⋊C411yescharacteristic
690C2×C4C2×C4×D411yescharacteristic
691C2×C4C2×C4×D411yescharacteristic
692C2×C4C4×#4111yescharacteristic
693C2×C4#51811yescharacteristic
694C2×C4#52011yescharacteristic
695C2×C4C2×#12111yescharacteristic
696C2×C4C2×#12111yescharacteristic
697C2×C4#52511yescharacteristic
698C2×C4C2×#12411yescharacteristic
699C2×C4#52911yescharacteristic
700C2×C4C2×#12711yescharacteristic
701C2×C4#53511yescharacteristic
702C2×C4#53711yescharacteristic
703C2×C4#54011yescharacteristic
704C2×C4#54211yescharacteristic
705C2×C4#54611yescharacteristic
706C2×C4#54611yescharacteristic
707C2×C4#54611yescharacteristic
708C2×C4#54811yescharacteristic
709C2×C4#54811yescharacteristic
710C2×C4#54811yescharacteristic
711C2×C4#55011yescharacteristic
712C2×C4#55011yescharacteristic
713C2×C4#55011yescharacteristic
714C2×C4#55311yescharacteristic
715C2×C4#55311yescharacteristic
716C2×C4#55511yescharacteristic
717C8—42no—
718C8—42no—
719C8—42no—
720C8#39018yescomplemented
721C22—24no—
722C22—24no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—84no—
738C22—84no—
739C22—84no—
740C22—84no—
741C22—84no—
742C22—84no—
743C22—162no—
744C22—162no—
745C22—162no—
746C22—162no—
747C22—162no—
748C22—162no—
749C22—162no—
750C22—162no—
751C22C4×#12111yescharacteristic
752C22D4×C22⋊C411yescharacteristic
753C22#236111yescharacteristic
754C22#241611yescharacteristic
755C22#242811yescharacteristic
756C22#249111yescharacteristic
757C22#254111yescharacteristic
758C22C2×C4×D811yescharacteristic
759C22C4×#13511yescharacteristic
760C22#294811yescharacteristic
761C22#295111yescharacteristic
762C22C2×#46611yescharacteristic
763C22#305011yescharacteristic
764C22#305811yescharacteristic
765C22#306111yescharacteristic
766C22#316811yescharacteristic
767C22#316911yescharacteristic
768C22#317511yescharacteristic
769C22#317611yescharacteristic
770C22D4×D811yescharacteristic
771C22D4×D811yescharacteristic
772C22D4×D811yescharacteristic
773C22#328011yescharacteristic
774C22#328011yescharacteristic
775C22#328011yescharacteristic
776C22#328511yescharacteristic
777C22#328511yescharacteristic
778C22#328511yescharacteristic
779C22#328711yescharacteristic
780C22#328711yescharacteristic
781C22#328711yescharacteristic
782C22#333411yescharacteristic
783C22#333911yescharacteristic
784C22#333911yescharacteristic
785C22#334111yescharacteristic
786C4—24no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—48no—
791C4—42no—
792C4—84no—
793C4—162no—
794C4C2×#39011yescharacteristic
795C4#232411yescharacteristic
796C4#234111yescharacteristic
797C4#236311yescharacteristic
798C4#241411yescharacteristic
799C4#242611yescharacteristic
800C4#249011yescharacteristic
801C4#254011yescharacteristic
802C2—44no—
803C2—164no—
804C2#1399811yescharacteristic
805C2C4×#46611yescharacteristic
806C2#2152411yescharacteristic
807C2C22⋊C4×D811yescharacteristic
808C2#2245111yescharacteristic
809C2#2302511yescharacteristic
810C2#2302711yescharacteristic
811C2#2477811yescharacteristic
812C2#2478011yescharacteristic
813C2#2541211yescharacteristic
814C2#2541411yescharacteristic
815C2#2779011yescharacteristic
816C2#2779111yescharacteristic
817C2#2848411yescharacteristic
818C2#2848511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#466C2
LCSG ▷ C22×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
2. C2×#1970C2semidirect
3. C2×#1970C2semidirect
4. C2×#1942C2semidirect
5. C2×#1808C2semidirect
6. C2×C4×#107C2semidirect
7. C2×C8×C22⋊C4C2semidirect
8. #13998C2semidirect
9. #11066C2semidirect
10. #10969C2semidirect
11. #10931C2semidirect
17. C2×#466C4semidirect
99. C2×#107D4semidirect
117. C2×C4×C8D4semidirect
277. C2×C22⋊C4D8semidirect
295. #107C22⋊C4semidirect
688. C2×C4#466semidirect
720. C8#390semidirect

Maximal subgroups

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

subgroupindex
C22×#4662
C2×#19702
C2×#19422
C2×#18082
C2×C4×#1072
C2×C8×C22⋊C42
#139982
#110662
#109692
#109312