Finite Group Databasebeta

← C2×#28566 #6459477

Subgroups — C2×#28566 #6459477

Order 512.

2738 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×#465C211yesmaximal, characteristic, complemented
2C22×#435C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic, complemented
4C2×#2414C211yesmaximal, characteristic
5#28566C2116yesmaximal, direct product factor
6C2×#2088C211yesmaximal, characteristic, complemented
7C2×#2077C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#1936C211yesmaximal, characteristic, complemented
11C2×#1935C211yesmaximal, characteristic, complemented
12C2×#1895C211yesmaximal, characteristic, complemented
13C2×#1894C211yesmaximal, characteristic, complemented
14C2×#1875C211yesmaximal, characteristic, complemented
15C2×#1873C211yesmaximal, characteristic, complemented
16C2×#1735C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×M16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C2×#465—28no—
28C2×#465C2218yescomplemented
29C2×#435—28no—
30C2×#435C2218yescomplemented
31C22×#106C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40C22×C22⋊C8C2211yescharacteristic
41C22×#97C2211yescharacteristic
42#2415—24no—
43#2415C2218yescomplemented
44#2414—24no—
45#2414C2218yes—
46C2×#397—21no—
47C2×#394—21no—
48C2×#394—21no—
49C2×#392—21no—
50C2×#391C2211yescharacteristic
51C2×#390—21no—
52C2×#390C2211yescharacteristic
53C2×#389—21no—
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388—21no—
57C2×#388—21no—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60#2088C2218yescomplemented
61#2077C2218yescomplemented
62#2055C2218yescomplemented
63#2000C2218yescomplemented
64#1936C2218yescomplemented
65#1935C2218yescomplemented
66#1895C2218yescomplemented
67#1894C2218yescomplemented
68#1875C2218yescomplemented
69#1873C2218yescomplemented
70#1735C2218yescomplemented
71C2×#340C2211yescharacteristic
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4D411yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C22×SD16—24no—
87C22×SD16—42no—
88C22×SD16—42no—
89C22×SD16C2314yes—
90C22×M16—24no—
91C22×M16—42no—
92C22×M16—42no—
93C22×M16C2314yes—
94C23×C8—42no—
95C23×C8—42no—
96C23×C8D418yescomplemented
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2314yes—
102C2×C22⋊Q8—22no—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×C22⋊Q8C2314yes—
109C2×C22⋊Q8C2314yes—
110C2×#121—22no—
111C2×#121—22no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—42no—
116C2×#121C2314yes—
117C2×#121C2314yes—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4D414yes—
121C2×C4×D4C2314yes—
122C2×#117—22no—
123C2×#117—22no—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—42no—
127C2×#117—42no—
128C2×#117C2314yes—
129C2×#117C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4D411yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4D411yescharacteristic
152C22×C22⋊C4D411yescharacteristic
153C22×C42—21no—
154C22×C42—21no—
155C22×C42C2311yescharacteristic
156#465—232no—
157#435—232no—
158C2×#106—24no—
159C2×#106C2314yes—
160C2×C4⋊C8—24no—
161C2×C4⋊C8C2314yes—
162C2×#103—24no—
163C2×#103—24no—
164C2×#103—42no—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102—24no—
169C2×#102—24no—
170C2×#102—42no—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8—24no—
175C2×C22⋊C8—24no—
176C2×C22⋊C8C2314yes—
177C2×C22⋊C8C2314yes—
178C2×#97—24no—
179C2×#97C2314yes—
180#397—28no—
181#394—28no—
182#394—28no—
183#392—28no—
184#391—22no—
185#391C2314yes—
186#390—28no—
187#390—22no—
188#390C2314yes—
189#389—28no—
190#389—22no—
191#389—22no—
192#389C2314yes—
193#389C2314yes—
194#388—28no—
195#388—28no—
196#380—22no—
197#380—22no—
198#380C2314yes—
199#380C2314yes—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206#340C2314yes—
207#340C2314yes—
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#340C2314yes—
214C25—21no—
215C25C2×D411yescharacteristic
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2412yes—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—21no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—82no—
241C22×D4—82no—
242C22×D4—82no—
243C22×D4C2×D414yes—
244C22×D4C2412yes—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D414yes—
269C23×C4#4114yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C2×SD16—28no—
274C2×SD16—44no—
275C2×SD16—44no—
276C2×SD16—416no—
277C2×M16—28no—
278C2×M16—44no—
279C2×M16—44no—
280C2×M16—416no—
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—22no—
290C22×C8—22no—
291C22×C8—416no—
292C22×C8—44no—
293C22×C8—44no—
294C22×C8C2×D414yes—
295C22×C8C2×D414yes—
296C22×C8C2×D4116yescomplemented
297C22×C8C2412yes—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22⋊Q8—28no—
302C22⋊Q8—28no—
303C22⋊Q8—28no—
304C22⋊Q8—44no—
305C22⋊Q8—48no—
306C22⋊Q8—48no—
307#121—28no—
308#121—28no—
309#121—28no—
310#121—44no—
311#121—48no—
312#121—48no—
313C4×D4—216no—
314C4×D4—28no—
315C4×D4—28no—
316#117—28no—
317#117—28no—
318#117—44no—
319#117—44no—
320#117—48no—
321#117—48no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—82no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4#4114yes—
349C2×C4⋊C4#4114yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—82no—
377C2×C22⋊C4—82no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—44no—
385C2×C42—44no—
386C2×C42C2×D412yes—
387C2×C42C2412yes—
388#106—28no—
389C4⋊C8—28no—
390#103—28no—
391#103—28no—
392#103—44no—
393#102—28no—
394#102—28no—
395#102—44no—
396C22⋊C8—28no—
397C22⋊C8—28no—
398#97—28no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24#12114yes—
427C24C22×D412yes—
428C24C22×D412yes—
429C24C22×D411yescharacteristic
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×D4—28no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—416no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—42no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—84no—
464C2×D4—84no—
465C2×D4—84no—
466C2×D4—816no—
467C2×D4—816no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
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—24no—
494C22×C4—24no—
495C22×C4—24no—
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—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
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—42no—
529C22×C4—42no—
530C22×C4#12114yes—
531C22×C4#12118yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D414yes—
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D412yes—
539C22×C4C2×#4114yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4C2511yescharacteristic
546SD16—416no—
547M16—416no—
548C2×C8—28no—
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—22no—
559C2×C8—22no—
560C2×C8—416no—
561C2×C8—44no—
562C2×C8—44no—
563C2×C8C22×D414yes—
564C2×C8C22×D414yes—
565C4⋊C4—28no—
566C4⋊C4—24no—
567C4⋊C4—24no—
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—22no—
577C4⋊C4—22no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—48no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—84no—
586C4⋊C4C2×#4114yes—
587C4⋊C4C2×#4114yes—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—84no—
599C22⋊C4—84no—
600C42—24no—
601C42—22no—
602C42—22no—
603C42—48no—
604C42—48no—
605C23—22no—
606C23—22no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23C2×#12114yes—
647C23C2×#12112yes—
648C23#54612yes—
649C23#54612yes—
650C23#57512yes—
651C23#57512yes—
652C23#57712yes—
653C23#57712yes—
654C23C23×D411yescharacteristic
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—84no—
660D4—416no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—816no—
666D4—816no—
667D4—84no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—216no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—48no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—48no—
691C2×C4—44no—
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—48no—
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—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4C2×#12114yes—
722C2×C4C2×#12112yes—
723C2×C4#53214yes—
724C2×C4#53414yes—
725C2×C4#54612yes—
726C2×C4#54612yes—
727C2×C4#55314yes—
728C2×C4#55314yes—
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—24no—
737C8—42no—
738C8—42no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—416no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—88no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—168no—
763C22#254314yes—
764C22#305414yes—
765C22#305714yes—
766C22#330714yes—
767C22#331114yes—
768C22#331714yes—
769C22#332114yes—
770C22C22×#12111yescharacteristic
771C22C2×#54611yescharacteristic
772C22C2×#54611yescharacteristic
773C22C2×#57511yescharacteristic
774C22C2×#57511yescharacteristic
775C22C2×#57711yescharacteristic
776C22C2×#57711yescharacteristic
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—44no—
782C4—44no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#254314yes—
789C4C2×#53211yescharacteristic
790C4C2×#53411yescharacteristic
791C4C2×#55311yescharacteristic
792C4C2×#55311yescharacteristic
793C2—44no—
794C2—82no—
795C2—162no—
796C2#2856618yesdirect product factor
797C2C2×#254311yescharacteristic
798C2C2×#305411yescharacteristic
799C2C2×#305711yescharacteristic
800C2C2×#330711yescharacteristic
801C2C2×#331111yescharacteristic
802C2C2×#331711yescharacteristic
803C2C2×#332111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2414C2
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
1. C22×#465C2semidirect
2. C22×#435C2semidirect
3. C2×#2415C2semidirect
5. #28566C2direct (N × H)
6. C2×#2088C2semidirect
7. C2×#2077C2semidirect
8. C2×#2055C2semidirect
9. C2×#2000C2semidirect
10. C2×#1936C2semidirect
11. C2×#1935C2semidirect
12. C2×#1895C2semidirect
13. C2×#1894C2semidirect
14. C2×#1875C2semidirect
15. C2×#1873C2semidirect
16. C2×#1735C2semidirect
28. C2×#465C22semidirect
30. C2×#435C22semidirect
43. #2415C22semidirect
60. #2088C22semidirect
61. #2077C22semidirect
62. #2055C22semidirect
63. #2000C22semidirect
64. #1936C22semidirect
65. #1935C22semidirect
66. #1895C22semidirect
67. #1894C22semidirect
68. #1875C22semidirect
69. #1873C22semidirect
70. #1735C22semidirect
96. C23×C8D4semidirect
296. C22×C8C2×D4semidirect
796. C2#28566direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4652
C22×#4352
C2×#24152
C2×#24142
#285662
C2×#20882
C2×#20772
C2×#20552
C2×#20002
C2×#19362
C2×#19352
C2×#18952
C2×#18942
C2×#18752
C2×#18732
C2×#17352