Finite Group Databasebeta

← C2×#31394 #7504591

Subgroups — C2×#31394 #7504591

Order 512.

2540 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic
2C2×#2417C211yesmaximal, characteristic, complemented
3#31394C2116yesmaximal, direct product factor
4C2×#2101C211yesmaximal, characteristic, complemented
5C2×#2076C211yesmaximal, characteristic, complemented
6C2×#2074C211yesmaximal, characteristic, complemented
7C2×#2036C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#1893C211yesmaximal, characteristic, complemented
11C2×#1892C211yesmaximal, characteristic, complemented
12C2×#1877C211yesmaximal, characteristic, complemented
13C2×#1874C211yesmaximal, characteristic, complemented
14C2×#1869C211yesmaximal, characteristic, complemented
15C2×#1862C211yesmaximal, characteristic, complemented
16C2×#1823C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C22×#107C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2211yescharacteristic
35C22×C22⋊C8C2211yescharacteristic
36#2535—24no—
37#2535C2218yes—
38#2417—24no—
39#2417C2218yescomplemented
40C2×#398—21no—
41C2×#397—21no—
42C2×#396—21no—
43C2×#392—21no—
44C2×#391C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#386—21no—
47C2×#386—21no—
48C2×#386—21no—
49C2×#382C2211yescharacteristic
50C2×#380—21no—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54#2101C2218yescomplemented
55#2076C2218yescomplemented
56#2074C2218yescomplemented
57#2036C2218yescomplemented
58#2000C2218yescomplemented
59#2000C2218yescomplemented
60#1893C2218yescomplemented
61#1892C2218yescomplemented
62#1877C2218yescomplemented
63#1874C2218yescomplemented
64#1869C2218yescomplemented
65#1862C2218yescomplemented
66#1823C2218yescomplemented
67C2×#340C2211yescharacteristic
68C2×#340C2211yescharacteristic
69C2×#340C2211yescharacteristic
70C2×#340C2211yescharacteristic
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#336C2211yescharacteristic
76C2×#336C2211yescharacteristic
77C23×Q8C2311yescharacteristic
78C23×D4—21no—
79C23×D4—21no—
80C23×D4D411yescharacteristic
81C23×D4C2311yescharacteristic
82C24×C4—21no—
83C24×C4—21no—
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C22×SD16—24no—
87C22×SD16—42no—
88C22×SD16—42no—
89C22×SD16C2314yes—
90C23×C8—42no—
91C23×C8—42no—
92C23×C8—42no—
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2314yes—
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—42no—
102C2×C22⋊Q8—42no—
103C2×C22⋊Q8—42no—
104C2×C22⋊Q8C2314yes—
105C2×C22⋊Q8C2314yes—
106C2×#121—22no—
107C2×#121—22no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—42no—
111C2×#121—42no—
112C2×#121C2314yes—
113C2×#121C2314yes—
114C2×C4×D4—22no—
115C2×C4×D4—42no—
116C2×C4×D4—42no—
117C2×C4×D4—42no—
118C2×C4×D4—42no—
119C2×C4×D4D414yes—
120C2×C4×D4C2314yes—
121C2×C4×D4C2314yes—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—22no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—42no—
129C22×C4⋊C4D411yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4D411yescharacteristic
146C22×C22⋊C4D411yescharacteristic
147C22×C42C2311yescharacteristic
148C2×#107—42no—
149C2×#107C2314yes—
150C2×#103—42no—
151C2×#103—42no—
152C2×#103—42no—
153C2×#103C2314yes—
154C2×#103C2314yes—
155C2×#103C2314yes—
156C2×#102—24no—
157C2×#102—42no—
158C2×#102—42no—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×C22⋊C8—42no—
163C2×C22⋊C8—42no—
164C2×C22⋊C8—42no—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C2×C22⋊C8C2314yes—
168#398—28no—
169#397—28no—
170#396—28no—
171#392—28no—
172#391—22no—
173#391C2314yes—
174#389—22no—
175#389C2314yes—
176#386—28no—
177#386—28no—
178#386—28no—
179#382—22no—
180#382C2314yes—
181#380—22no—
182#380—22no—
183#380—22no—
184#380—28no—
185#380C2314yes—
186#380C2314yes—
187#380C2314yes—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196#340C2314yes—
197#340C2314yes—
198#340C2314yes—
199#340C2314yes—
200#340C2314yes—
201#340C2314yes—
202#340C2314yes—
203#340C2314yes—
204#336C2314yes—
205#336C2314yes—
206C25—21no—
207C25C2×D411yescharacteristic
208C25C2×D411yescharacteristic
209C22×Q8—21no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8C2412yes—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—21no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—42no—
228C22×D4—44no—
229C22×D4—44no—
230C22×D4—44no—
231C22×D4—44no—
232C22×D4—82no—
233C22×D4—82no—
234C22×D4C2×D414yes—
235C22×D4#4114yes—
236C22×D4C2412yes—
237C23×C4—21no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4—44no—
261C23×C4—82no—
262C23×C4—82no—
263C23×C4—82no—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C2×SD16—28no—
274C2×SD16—44no—
275C2×SD16—44no—
276C2×SD16—416no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—44no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8—416no—
293C22×C8C2412yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22⋊Q8—28no—
298C22⋊Q8—44no—
299C22⋊Q8—44no—
300C22⋊Q8—44no—
301C22⋊Q8—48no—
302C22⋊Q8—48no—
303#121—28no—
304#121—28no—
305#121—44no—
306#121—44no—
307#121—48no—
308#121—48no—
309C4×D4—44no—
310C4×D4—44no—
311C4×D4—48no—
312C4×D4—44no—
313C4×D4—44no—
314C4×D4—48no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
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—28no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—48no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—82no—
344C2×C4⋊C4C2×D414yes—
345C2×C4⋊C4#4114yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—82no—
368C2×C22⋊C4—82no—
369C2×C22⋊C4—82no—
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4C2×D414yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42C2×D412yes—
375C2×C42C2412yes—
376#107—44no—
377#103—44no—
378#103—44no—
379#103—44no—
380#102—28no—
381#102—44no—
382#102—44no—
383C22⋊C8—44no—
384C22⋊C8—44no—
385C22⋊C8—44no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—22no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24#13514yes—
415C24#13714yes—
416C24C22×D412yes—
417C24C22×D412yes—
418C24C22×D411yescharacteristic
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—42no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—24no—
436C2×D4—28no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—44no—
443C2×D4—416no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4—44no—
452C2×D4—84no—
453C2×D4—84no—
454C2×D4—816no—
455C2×D4—816no—
456C2×D4C2×#4114yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
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—48no—
496C22×C4—48no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
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—48no—
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—84no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—816no—
530C22×C4—816no—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D411yescharacteristic
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4H(5,𝔽2)12yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C4C2511yescharacteristic
543SD16—416no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
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—416no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8—44no—
560C2×C8—44no—
561C4⋊C4—24no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—44no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—84no—
583C4⋊C4C2×#4114yes—
584C22⋊C4—44no—
585C22⋊C4—44no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—84no—
592C22⋊C4—84no—
593C22⋊C4—84no—
594C42—24no—
595C42—22no—
596C42—22no—
597C23—22no—
598C23—22no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—28no—
606C23—28no—
607C23—28no—
608C23—28no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—42no—
625C23—48no—
626C23—42no—
627C23—48no—
628C23—48no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—84no—
634C23—84no—
635C23—84no—
636C23—84no—
637C23#53412yes—
638C23#54612yes—
639C23#54612yes—
640C23C2×#13514yes—
641C23C2×#13512yes—
642C23C2×#13714yes—
643C23C2×#13712yes—
644C23#57612yes—
645C23#57712yes—
646C23C23×D411yescharacteristic
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—42no—
651Q8—84no—
652D4—24no—
653D4—24no—
654D4—416no—
655D4—42no—
656D4—48no—
657D4—42no—
658D4—816no—
659D4—816no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
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—48no—
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—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
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—816no—
709C2×C4—816no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4#53412yes—
717C2×C4#53814yes—
718C2×C4#54014yes—
719C2×C4#54612yes—
720C2×C4#54612yes—
721C2×C4#55314yes—
722C2×C4#56014yes—
723C2×C4C22×#4111yescharacteristic
724C2×C4C22×#4111yescharacteristic
725C2×C4C2×H(5,𝔽2)11yescharacteristic
726C2×C4C2×H(5,𝔽2)11yescharacteristic
727C2×C4C2×H(5,𝔽2)11yescharacteristic
728C2×C4C2×H(5,𝔽2)11yescharacteristic
729C8—42no—
730C8—42no—
731C8—42no—
732C8—42no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—416no—
744C22—416no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—82no—
753C22—82no—
754C22—816no—
755C22—82no—
756C22—82no—
757C22#268814yes—
758C22#319014yes—
759C22#319814yes—
760C22#329614yes—
761C22#329714yes—
762C22#331414yes—
763C22#332014yes—
764C22C2×#53411yescharacteristic
765C22C2×#54611yescharacteristic
766C22C2×#54611yescharacteristic
767C22C22×#13511yescharacteristic
768C22C22×#13711yescharacteristic
769C22C2×#57611yescharacteristic
770C22C2×#57711yescharacteristic
771C4—42no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—44no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4#268814yes—
783C4C2×#53811yescharacteristic
784C4C2×#54011yescharacteristic
785C4C2×#55311yescharacteristic
786C4C2×#56011yescharacteristic
787C2—44no—
788C2—44no—
789C2—84no—
790C2#3139418yesdirect product factor
791C2C2×#268811yescharacteristic
792C2C2×#319011yescharacteristic
793C2C2×#319811yescharacteristic
794C2C2×#329611yescharacteristic
795C2C2×#329711yescharacteristic
796C2C2×#331411yescharacteristic
797C2C2×#332011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2417C2semidirect
3. #31394C2direct (N × H)
4. C2×#2101C2semidirect
5. C2×#2076C2semidirect
6. C2×#2074C2semidirect
7. C2×#2036C2semidirect
8. C2×#2000C2semidirect
9. C2×#2000C2semidirect
10. C2×#1893C2semidirect
11. C2×#1892C2semidirect
12. C2×#1877C2semidirect
13. C2×#1874C2semidirect
14. C2×#1869C2semidirect
15. C2×#1862C2semidirect
16. C2×#1823C2semidirect
39. #2417C22semidirect
54. #2101C22semidirect
55. #2076C22semidirect
56. #2074C22semidirect
57. #2036C22semidirect
58. #2000C22semidirect
59. #2000C22semidirect
60. #1893C22semidirect
61. #1892C22semidirect
62. #1877C22semidirect
63. #1874C22semidirect
64. #1869C22semidirect
65. #1862C22semidirect
66. #1823C22semidirect
790. C2#31394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25352
C2×#24172
#313942
C2×#21012
C2×#20762
C2×#20742
C2×#20362
C2×#20002
C2×#18932
C2×#18922
C2×#18772
C2×#18742
C2×#18692
C2×#18622
C2×#18232