Finite Group Databasebeta

← C2×#25938 #6447664

Subgroups — C2×#25938 #6447664

Order 512.

3562 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C22×#488C211yesmaximal, characteristic, complemented
3C22×#463C211yesmaximal, characteristic
4C2×#2592C211yesmaximal, characteristic, complemented
5#25938C2116yesmaximal, direct product factor
6C2×#2026C211yesmaximal, characteristic, complemented
7C2×#2024C211yesmaximal, characteristic, complemented
8C2×#2025C211yesmaximal, characteristic, complemented
9C2×#2023C211yesmaximal, characteristic, complemented
10C2×#1989C211yesmaximal, characteristic, complemented
11C2×#1984C211yesmaximal, characteristic, complemented
12C2×#1879C211yesmaximal, characteristic
13C2×#1879C211yesmaximal, characteristic
14C2×#1877C211yesmaximal, characteristic, complemented
15C2×#1877C211yesmaximal, characteristic, complemented
16C2×C4×#102C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C2×#554—28no—
20C2×#554—24no—
21C2×#554—28no—
22C2×#554C2218yescomplemented
23C22×C4⋊Q8C2211yescharacteristic
24C22×#125C2211yescharacteristic
25C22×#125C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8—21no—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8—21no—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C23×C4⋊C4—21no—
35C2×#488—28no—
36C2×#488C2218yescomplemented
37C2×#463—28no—
38C2×#463C2218yes—
39C22×C4⋊C8C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×C4×C8C2211yescharacteristic
49#2592—24no—
50#2592C2218yescomplemented
51C2×#397—21no—
52C2×#393—21no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#388—21no—
58C2×#388—21no—
59C2×C4×C4⋊C4C2211yescharacteristic
60#2026C2218yescomplemented
61#2025C2218yescomplemented
62#2024C2218yescomplemented
63#2023C2218yescomplemented
64#1989C2218yescomplemented
65#1984C2218yescomplemented
66#1879C2218yes—
67#1879C2218yes—
68#1877C2218yescomplemented
69#1877C2218yescomplemented
70C4×#102C2218yescomplemented
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8D411yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4—21no—
88C24×C4—21no—
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16C2314yes—
93C22×D8—24no—
94C22×D8—24no—
95C22×D8—24no—
96C22×D8C2314yes—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101#554—264no—
102#554—232no—
103#554—232no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—22no—
107C2×C4⋊Q8C2314yes—
108C2×#125—24no—
109C2×#125—24no—
110C2×#125—22no—
111C2×#125—22no—
112C2×#125—24no—
113C2×#125D418yes—
114C2×#125C2314yes—
115C2×#125C2314yes—
116C2×#124—22no—
117C2×#124—24no—
118C2×#124—24no—
119C2×#124C2314yes—
120C2×C22⋊Q8—216no—
121C2×C22⋊Q8—216no—
122C2×C22⋊Q8—216no—
123C2×C22⋊Q8—28no—
124C2×C22⋊Q8—28no—
125C2×C22⋊Q8—28no—
126C2×C4×Q8—24no—
127C2×C4×Q8—24no—
128C2×C4×Q8D414yes—
129C2×C4×Q8C2314yes—
130C2×C4×D4—24no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4—24no—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—22no—
137C2×C4×D4—24no—
138C2×C4×D4D418yes—
139C2×C4×D4C2314yes—
140C2×C4×D4C2314yes—
141C2×C4×D4C2314yes—
142C22×C4⋊C4—216no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—28no—
149C22×C4⋊C4D411yescharacteristic
150C22×C4⋊C4D411yescharacteristic
151C22×C4⋊C4D411yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C42—21no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#488—232no—
171#463—232no—
172C2×C4⋊C8—24no—
173C2×C4⋊C8C2314yes—
174C2×#103—24no—
175C2×#103—24no—
176C2×#103—24no—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#102—24no—
181C2×#102—24no—
182C2×#102—24no—
183C2×#102—24no—
184C2×#102—24no—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×C4×C8—24no—
191C2×C4×C8C2314yes—
192#397—28no—
193#393—28no—
194#391—22no—
195#391—22no—
196#391C2314yes—
197#391C2314yes—
198#390—22no—
199#390—22no—
200#390C2314yes—
201#390C2314yes—
202#388—28no—
203#388—28no—
204C4×C4⋊C4—22no—
205C4×C4⋊C4C2314yes—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214#340C2314yes—
215#340C2314yes—
216#340C2314yes—
217#336C2314yes—
218#336C2314yes—
219#336C2314yes—
220#336C2314yes—
221C25—21no—
222C25—21no—
223C22×Q8—28no—
224C22×Q8—24no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—21no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—42no—
235C22×Q8—82no—
236C22×Q8—82no—
237C22×Q8C2×D414yes—
238C22×Q8C2412yes—
239C22×D4—21no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—21no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4C2×D414yes—
251C22×D4#4114yes—
252C22×D4#4114yes—
253C22×D4C2412yes—
254C22×D4C2412yes—
255C23×C4—28no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—28no—
260C23×C4—24no—
261C23×C4—28no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—82no—
270C23×C4—82no—
271C23×C4—82no—
272C23×C4—82no—
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2411yescharacteristic
280C2×SD16—28no—
281C2×SD16—28no—
282C2×SD16—28no—
283C2×SD16—416no—
284C2×D8—28no—
285C2×D8—28no—
286C2×D8—28no—
287C2×D8—416no—
288C22×C8—22no—
289C22×C8—22no—
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×C8—22no—
299C22×C8—22no—
300C22×C8C2412yes—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C4⋊Q8—216no—
305C4⋊Q8—28no—
306C4⋊Q8—28no—
307#125—216no—
308#125—28no—
309#125—28no—
310#125—216no—
311#125—28no—
312#125C2×D4116yes—
313#124—28no—
314#124—28no—
315#124—48no—
316C22⋊Q8—264no—
317C22⋊Q8—264no—
318C22⋊Q8—264no—
319C4×Q8—216no—
320C4×Q8—28no—
321C4×Q8—28no—
322C4×D4—216no—
323C4×D4—216no—
324C4×D4—28no—
325C4×D4—28no—
326C4×D4—28no—
327C4×D4—28no—
328C4×D4—216no—
329C4×D4—28no—
330C4×D4C2×D4116yes—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—264no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—24no—
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—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—82no—
385C2×C22⋊C4—82no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—82no—
392C2×C42C2×D412yes—
393C2×C42C2×D412yes—
394C2×C42C2×D412yes—
395C2×C42C2×D414yes—
396C2×C42C2×D414yes—
397C2×C42C2412yes—
398C2×C42C2412yes—
399C2×C42C2412yes—
400C4⋊C8—28no—
401#103—28no—
402#103—28no—
403#103—28no—
404#102—28no—
405#102—28no—
406#102—28no—
407#102—28no—
408#102—28no—
409C4×C8—28no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24C22×D411yescharacteristic
432C2×Q8—216no—
433C2×Q8—28no—
434C2×Q8—28no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—44no—
442C2×Q8—416no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—84no—
451C2×Q8—84no—
452C2×Q8—816no—
453C2×D4—24no—
454C2×D4—28no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4#124116yes—
476C2×D4C22×D414yes—
477C2×D4C2×#4114yes—
478C2×D4C2×#4114yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—216no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
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—216no—
502C22×C4—216no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—432no—
507C22×C4—48no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—48no—
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—816no—
525C22×C4—84no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—816no—
530C22×C4#12014yes—
531C22×C4#12014yes—
532C22×C4#13514yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C42−1+412yes—
545C22×C42−1+412yes—
546C22×C4C2511yescharacteristic
547SD16—416no—
548D8—416no—
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—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—44no—
562C2×C8—44no—
563C2×C8—44no—
564C2×C8—44no—
565C4⋊C4—216no—
566C4⋊C4—216no—
567C4⋊C4—216no—
568C4⋊C4—28no—
569C4⋊C4—216no—
570C4⋊C4—216no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—28no—
575C4⋊C4—28no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4C22×D414yes—
586C4⋊C4C22×D414yes—
587C4⋊C4C22×D414yes—
588C22⋊C4—216no—
589C22⋊C4—216no—
590C22⋊C4—216no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C42—24no—
598C42—24no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—84no—
604C42#12018yes—
605C42C22×D414yes—
606C42C22×D414yes—
607C23—24no—
608C23—216no—
609C23—24no—
610C23—24no—
611C23—48no—
612C23—48no—
613C23—48no—
614C23—48no—
615C23—48no—
616C23—48no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—84no—
629C23—84no—
630C23—84no—
631C23—84no—
632C23—84no—
633C23—84no—
634C23—84no—
635C23C2×#12012yes—
636C23#54812yes—
637C23#54812yes—
638C23C2×#13512yes—
639C23#57512yes—
640C23#57612yes—
641C23#57712yes—
642C23C23×D411yescharacteristic
643Q8—416no—
644Q8—42no—
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—816no—
649Q8—84no—
650D4—24no—
651D4—216no—
652D4—24no—
653D4—24no—
654D4—42no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—84no—
659D4C2×#12418yes—
660C2×C4—22no—
661C2×C4—28no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—432no—
682C2×C4—44no—
683C2×C4—48no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—48no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—816no—
704C2×C4—816no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4C2×#12014yes—
709C2×C4C2×#12014yes—
710C2×C4C2×#12012yes—
711C2×C4C2×#12414yes—
712C2×C4#53614yes—
713C2×C4#54812yes—
714C2×C4#54812yes—
715C2×C4#54814yes—
716C2×C4#54814yes—
717C2×C4C2×#13514yes—
718C2×C4C23×D411yescharacteristic
719C2×C4C23×D411yescharacteristic
720C2×C4C22×#4111yescharacteristic
721C2×C4C22×#4111yescharacteristic
722C2×C4C2×2−1+411yescharacteristic
723C2×C4C2×2−1+411yescharacteristic
724C8—42no—
725C8—42no—
726C8—42no—
727C8—42no—
728C22—28no—
729C22—432no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—168no—
744C22#243614yes—
745C22#300214yes—
746C22#301214yes—
747C22#336014yes—
748C22#336114yes—
749C22#337014yes—
750C22#337614yes—
751C22C22×#12011yescharacteristic
752C22C2×#54811yescharacteristic
753C22C2×#54811yescharacteristic
754C22C22×#13511yescharacteristic
755C22C2×#57511yescharacteristic
756C22C2×#57611yescharacteristic
757C22C2×#57711yescharacteristic
758C4—24no—
759C4—24no—
760C4—24no—
761C4—42no—
762C4—44no—
763C4—42no—
764C4—42no—
765C4—44no—
766C4—44no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4#243614yes—
771C4C22×#12411yescharacteristic
772C4C2×#53611yescharacteristic
773C4C2×#54811yescharacteristic
774C4C2×#54811yescharacteristic
775C2—48no—
776C2—162no—
777C2#2593818yesdirect product factor
778C2C2×#243611yescharacteristic
779C2C2×#300211yescharacteristic
780C2C2×#301211yescharacteristic
781C2C2×#336011yescharacteristic
782C2C2×#336111yescharacteristic
783C2C2×#337011yescharacteristic
784C2C2×#337611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D8C22
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
1. C22×#554C2semidirect
2. C22×#488C2semidirect
4. C2×#2592C2semidirect
5. #25938C2direct (N × H)
6. C2×#2026C2semidirect
7. C2×#2024C2semidirect
8. C2×#2025C2semidirect
9. C2×#2023C2semidirect
10. C2×#1989C2semidirect
11. C2×#1984C2semidirect
14. C2×#1877C2semidirect
15. C2×#1877C2semidirect
16. C2×C4×#102C2semidirect
22. C2×#554C22semidirect
36. C2×#488C22semidirect
50. #2592C22semidirect
60. #2026C22semidirect
61. #2025C22semidirect
62. #2024C22semidirect
63. #2023C22semidirect
64. #1989C22semidirect
65. #1984C22semidirect
68. #1877C22semidirect
69. #1877C22semidirect
70. C4×#102C22semidirect
777. C2#25938direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5542
C22×#4882
C22×#4632
C2×#25922
#259382
C2×#20262
C2×#20242
C2×#20252
C2×#20232
C2×#19892
C2×#19842
C2×#18792
C2×#18772
C2×C4×#1022