Finite Group Databasebeta

← C2×#30596 #7501249

Subgroups — C2×#30596 #7501249

Order 512.

2822 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#465C211yesmaximal, characteristic, complemented
2C22×#460C211yesmaximal, characteristic, complemented
3C2×#2421C211yesmaximal, characteristic, complemented
4C2×#2428C211yesmaximal, characteristic
5#30596C2116yesmaximal, direct product factor
6C2×#2092C211yesmaximal, characteristic, complemented
7C2×#2088C211yesmaximal, characteristic, complemented
8C2×#2055C211yesmaximal, characteristic, complemented
9C2×#2041C211yesmaximal, characteristic, complemented
10C2×#2033C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1893C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1863C211yesmaximal, characteristic, complemented
15C2×#1850C211yesmaximal, characteristic, complemented
16C2×#1804C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C24×C8C2211yescharacteristic
20C22×#127C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121—21no—
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C2×#465—28no—
28C2×#465C2218yescomplemented
29C2×#460—28no—
30C2×#460C2218yescomplemented
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×C4⋊C8C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2428—24no—
45#2428C2218yes—
46#2421—24no—
47#2421C2218yescomplemented
48C2×#400—21no—
49C2×#397—21no—
50C2×#394—21no—
51C2×#392—21no—
52C2×#391C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388—21no—
57C2×#387—21no—
58C2×#386—21no—
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2092C2218yescomplemented
63#2088C2218yescomplemented
64#2055C2218yescomplemented
65#2041C2218yescomplemented
66#2033C2218yescomplemented
67#2000C2218yescomplemented
68#1893C2218yescomplemented
69#1877C2218yescomplemented
70#1863C2218yescomplemented
71#1850C2218yescomplemented
72#1804C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—42no—
90C22×SD16—42no—
91C22×SD16—42no—
92C22×SD16—42no—
93C22×SD16D418yescomplemented
94C22×SD16C2314yes—
95C22×SD16C2314yes—
96C23×C8—24no—
97C23×C8—42no—
98C23×C8—42no—
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102C23×C8C2311yescharacteristic
103C23×C8C2314yes—
104C2×#127—24no—
105C2×#127—22no—
106C2×#127—42no—
107C2×#127C2314yes—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—42no—
111C2×C22⋊Q8C2314yes—
112C2×#121—22no—
113C2×#121—22no—
114C2×#121—28no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—48no—
118C2×#121—42no—
119C2×#121—42no—
120C2×#121C2314yes—
121C2×#121C2314yes—
122C2×C4×Q8—22no—
123C2×C4×Q8—24no—
124C2×C4×Q8—42no—
125C2×C4×Q8C2314yes—
126C2×C4×D4—24no—
127C2×C4×D4—22no—
128C2×C4×D4—42no—
129C2×C4×D4C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
146C22×C22⋊C4D411yescharacteristic
147C22×C22⋊C4D411yescharacteristic
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#465—232no—
152#460—232no—
153C2×#107—42no—
154C2×#107C2314yes—
155C2×#106—24no—
156C2×#106C2314yes—
157C2×C4⋊C8—24no—
158C2×C4⋊C8—42no—
159C2×C4⋊C8C2314yes—
160C2×C4⋊C8C2314yes—
161C2×#103—24no—
162C2×#103—24no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—24no—
168C2×#102—42no—
169C2×#102—42no—
170C2×#102—42no—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8—42no—
178C2×C22⋊C8C2314yes—
179#400—28no—
180#397—28no—
181#394—28no—
182#392—28no—
183#391—22no—
184#391C2314yes—
185#390—22no—
186#390C2314yes—
187#389—22no—
188#389—22no—
189#389C2314yes—
190#389C2314yes—
191#388—28no—
192#387—28no—
193#386—28no—
194#382—22no—
195#382C2314yes—
196#380—22no—
197#380C2314yes—
198C4×C22⋊C4D414yes—
199C4×C22⋊C4C2314yes—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25—21no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2×D414yes—
225C22×Q8C2412yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—82no—
252C22×D4—82no—
253C22×D4—82no—
254C22×D4—82no—
255C22×D4C2×D414yes—
256C22×D4C2412yes—
257C22×D4C2412yes—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—82no—
274C23×C4C2×D412yes—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—28no—
283C2×SD16—416no—
284C2×SD16—44no—
285C2×SD16—44no—
286C2×SD16—44no—
287C2×SD16—44no—
288C2×SD16—416no—
289C2×SD16C2×D4116yescomplemented
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×C8—22no—
301C22×C8—28no—
302C22×C8—44no—
303C22×C8—44no—
304C22×C8—416no—
305C22×C8C2×D414yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C22×C8C2412yes—
309C22×C8C2412yes—
310#127—28no—
311#127—44no—
312#127—48no—
313C22⋊Q8—28no—
314C22⋊Q8—44no—
315C22⋊Q8—48no—
316#121—28no—
317#121—28no—
318#121—432no—
319#121—44no—
320#121—44no—
321#121—48no—
322#121—48no—
323C4×Q8—28no—
324C4×Q8—44no—
325C4×Q8—48no—
326C4×D4—28no—
327C4×D4—44no—
328C4×D4—48no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4#4114yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
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—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—82no—
373C2×C22⋊C4C2×D414yes—
374C2×C22⋊C4C2×D414yes—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—24no—
380C2×C42—44no—
381C2×C42C2×D412yes—
382C2×C42C2×D412yes—
383C2×C42C2412yes—
384C2×C42C2412yes—
385#107—44no—
386#106—28no—
387C4⋊C8—28no—
388C4⋊C8—44no—
389#103—28no—
390#103—28no—
391#102—28no—
392#102—28no—
393#102—28no—
394#102—44no—
395#102—44no—
396#102—44no—
397C22⋊C8—44no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95C2×D414yes—
406#95C2×D414yes—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24AGL(1,ℤ/8)14yes—
430C24C22×D412yes—
431C24C22×D411yescharacteristic
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—42no—
443C2×Q8—44no—
444C2×Q8C22×D414yes—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—28no—
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—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—44no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—48no—
478C2×D4—84no—
479C2×D4—84no—
480C2×D4—816no—
481C2×D4—84no—
482C2×D4—84no—
483C2×D4—816no—
484C2×D4—816no—
485C2×D4—816no—
486C2×D4C22×D414yes—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
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—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—84no—
541C22×C4—816no—
542C22×C4#13514yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C2×#4112yes—
551C22×C4H(5,𝔽2)12yes—
552C22×C4H(5,𝔽2)12yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C42−1+412yes—
555C22×C4C2511yescharacteristic
556SD16—416no—
557SD16—416no—
558C2×C8—28no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—416no—
571C2×C8—44no—
572C2×C8—44no—
573C2×C8—44no—
574C2×C8C22×D414yes—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—48no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—48no—
593C4⋊C4C2×#4114yes—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—84no—
603C42—24no—
604C42—24no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—48no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—28no—
614C23—28no—
615C23—28no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—44no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—48no—
625C23—42no—
626C23—42no—
627C23—48no—
628C23—48no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—84no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23#53712yes—
652C23D4212yes—
653C23#54612yes—
654C23C2×#13512yes—
655C23C2×AGL(1,ℤ/8)14yes—
656C23C2×AGL(1,ℤ/8)12yes—
657C23#57712yes—
658C23#57712yes—
659C23C23×D411yescharacteristic
660Q8—24no—
661Q8—24no—
662Q8—48no—
663Q8—42no—
664Q8—42no—
665D4—24no—
666D4—24no—
667D4—48no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—816no—
675D4—816no—
676D4—816no—
677D4—816no—
678D4—84no—
679C2×C4—22no—
680C2×C4—28no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
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—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—48no—
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—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—816no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4#53414yes—
729C2×C4#53712yes—
730C2×C4#54014yes—
731C2×C4D4212yes—
732C2×C4#54612yes—
733C2×C4#54714yes—
734C2×C4#56214yes—
735C2×C4C2×#13514yes—
736C2×C4C23×D411yescharacteristic
737C2×C4C22×#4111yescharacteristic
738C2×C4C2×H(5,𝔽2)11yescharacteristic
739C2×C4C2×H(5,𝔽2)11yescharacteristic
740C2×C4C2×H(5,𝔽2)11yescharacteristic
741C2×C4C2×2−1+411yescharacteristic
742C8—24no—
743C8—42no—
744C8—42no—
745C8—42no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—416no—
752C22—42no—
753C22—42no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—816no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—168no—
770C22#267114yes—
771C22#324714yes—
772C22#326014yes—
773C22#326514yes—
774C22#328214yes—
775C22#330414yes—
776C22#331014yes—
777C22C2×#53711yescharacteristic
778C22C2×D4211yescharacteristic
779C22C2×#54611yescharacteristic
780C22C22×#13511yescharacteristic
781C22C22×AGL(1,ℤ/8)11yescharacteristic
782C22C2×#57711yescharacteristic
783C22C2×#57711yescharacteristic
784C4—24no—
785C4—42no—
786C4—42no—
787C4—44no—
788C4—42no—
789C4—42no—
790C4—44no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4#267114yes—
796C4C2×#53411yescharacteristic
797C4C2×#54011yescharacteristic
798C4C2×#54711yescharacteristic
799C4C2×#56211yescharacteristic
800C2—44no—
801C2—84no—
802C2—162no—
803C2#3059618yesdirect product factor
804C2C2×#267111yescharacteristic
805C2C2×#324711yescharacteristic
806C2C2×#326011yescharacteristic
807C2C2×#326511yescharacteristic
808C2C2×#328211yescharacteristic
809C2C2×#330411yescharacteristic
810C2C2×#331011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ 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×#460C2semidirect
3. C2×#2421C2semidirect
5. #30596C2direct (N × H)
6. C2×#2092C2semidirect
7. C2×#2088C2semidirect
8. C2×#2055C2semidirect
9. C2×#2041C2semidirect
10. C2×#2033C2semidirect
11. C2×#2000C2semidirect
12. C2×#1893C2semidirect
13. C2×#1877C2semidirect
14. C2×#1863C2semidirect
15. C2×#1850C2semidirect
16. C2×#1804C2semidirect
28. C2×#465C22semidirect
30. C2×#460C22semidirect
47. #2421C22semidirect
62. #2092C22semidirect
63. #2088C22semidirect
64. #2055C22semidirect
65. #2041C22semidirect
66. #2033C22semidirect
67. #2000C22semidirect
68. #1893C22semidirect
69. #1877C22semidirect
70. #1863C22semidirect
71. #1850C22semidirect
72. #1804C22semidirect
93. C22×SD16D4semidirect
289. C2×SD16C2×D4semidirect
803. C2#30596direct (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×#4602
C2×#24212
C2×#24282
#305962
C2×#20922
C2×#20882
C2×#20552
C2×#20412
C2×#20332
C2×#20002
C2×#18932
C2×#18772
C2×#18632
C2×#18502
C2×#18042