Finite Group Databasebeta

← C2×#30534 #7501032

Subgroups — C2×#30534 #7501032

Order 512.

2926 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×#488C211yesmaximal, characteristic, complemented
2C22×#451C211yesmaximal, characteristic, complemented
3C2×#2489C211yesmaximal, characteristic, complemented
4C2×#2436C211yesmaximal, characteristic
5#30534C2116yesmaximal, direct product factor
6C2×#2056C211yesmaximal, characteristic, complemented
7C2×#2033C211yesmaximal, characteristic
8C2×#2026C211yesmaximal, characteristic, complemented
9C2×#2015C211yesmaximal, characteristic, complemented
10C2×#2015C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic
12C2×#1983C211yesmaximal, characteristic, complemented
13C2×#1969C211yesmaximal, characteristic, complemented
14C2×#1928C211yesmaximal, characteristic, complemented
15C2×#1923C211yesmaximal, characteristic, complemented
16C2×#1787C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C2×#488—28no—
27C2×#488C2218yescomplemented
28C2×#451—28no—
29C2×#451C2218yescomplemented
30C22×#107C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×C4×C8C2211yescharacteristic
45#2489—24no—
46#2489C2218yescomplemented
47#2436—24no—
48#2436C2218yes—
49C2×#400—21no—
50C2×#397—21no—
51C2×#393—21no—
52C2×#393—21no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#388—21no—
58C2×#386—21no—
59C2×#386—21no—
60C2×#382—21no—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64#2056C2218yescomplemented
65#2033C2218yes—
66#2026C2218yescomplemented
67#2015C2218yescomplemented
68#2015C2218yescomplemented
69#2000C2218yes—
70#1983C2218yescomplemented
71#1969C2218yescomplemented
72#1928C2218yescomplemented
73#1923C2218yescomplemented
74#1787C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8—21no—
80C23×Q8—22no—
81C23×Q8—24no—
82C23×Q8—24no—
83C23×Q8—42no—
84C23×Q8—42no—
85C23×Q8—42no—
86C23×Q8—42no—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×Q8C2314yes—
91C23×D4—21no—
92C23×D4C2311yescharacteristic
93C24×C4—21no—
94C24×C4C2311yescharacteristic
95C22×Q16—24no—
96C22×Q16—24no—
97C22×Q16—24no—
98C22×Q16—42no—
99C22×Q16—42no—
100C22×Q16—42no—
101C22×Q16C2314yes—
102C22×Q16C2314yes—
103C22×SD16—42no—
104C22×SD16—42no—
105C22×SD16—42no—
106C22×SD16C2314yes—
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C2×#125—24no—
112C2×#125—22no—
113C2×#125—42no—
114C2×#125C2314yes—
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—22no—
118C2×#124—22no—
119C2×#124—42no—
120C2×#124—42no—
121C2×#124C2314yes—
122C2×#124C2314yes—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8C2314yes—
127C2×#121—22no—
128C2×#121—42no—
129C2×#121—42no—
130C2×#121C2314yes—
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×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×C42—21no—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#488—232no—
151#451—232no—
152C2×#107—42no—
153C2×#107C2314yes—
154C2×C4⋊C8—42no—
155C2×C4⋊C8C2314yes—
156C2×#103—24no—
157C2×#103—24no—
158C2×#103—42no—
159C2×#103—42no—
160C2×#103—42no—
161C2×#103—42no—
162C2×#103D418yescomplemented
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—42no—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8—24no—
177C2×C22⋊C8—42no—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180C2×C4×C8—24no—
181C2×C4×C8C2314yes—
182#400—28no—
183#397—28no—
184#393—28no—
185#393—28no—
186#391—22no—
187#391—22no—
188#391—22no—
189#391—22no—
190#391C2314yes—
191#391C2314yes—
192#391C2314yes—
193#391C2314yes—
194#388—28no—
195#386—28no—
196#386—28no—
197#382—28no—
198#380—22no—
199#380C2314yes—
200C4×C4⋊C4—22no—
201C4×C4⋊C4C2314yes—
202C4×C22⋊C4D414yes—
203C4×C22⋊C4C2314yes—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95D411yescharacteristic
215C2×#95D411yescharacteristic
216#340C2314yes—
217#340C2314yes—
218#336C2314yes—
219#336C2314yes—
220C25—21no—
221C25C2×D411yescharacteristic
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—28no—
229C22×Q8—28no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—44no—
245C22×Q8—44no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8—48no—
251C22×Q8—48no—
252C22×Q8—44no—
253C22×Q8—48no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8—416no—
258C22×Q8C2×D414yes—
259C22×Q8#4114yes—
260C22×Q8C2412yes—
261C22×Q8C2412yes—
262C22×Q8C2412yes—
263C22×D4—24no—
264C22×D4—22no—
265C22×D4—21no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4C2412yes—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C2×Q16—28no—
301C2×Q16—28no—
302C2×Q16—28no—
303C2×Q16—44no—
304C2×Q16—44no—
305C2×Q16—44no—
306C2×Q16—416no—
307C2×Q16—416no—
308C2×SD16—44no—
309C2×SD16—44no—
310C2×SD16—44no—
311C2×SD16—416no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8C2×D414yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328#125—28no—
329#125—44no—
330#125—48no—
331#124—28no—
332#124—28no—
333#124—44no—
334#124—44no—
335#124—48no—
336#124—48no—
337C22⋊Q8—28no—
338C22⋊Q8—44no—
339C22⋊Q8—48no—
340#121—44no—
341#121—44no—
342#121—48no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—44no—
389C2×C42C2×D412yes—
390C2×C42C2×D412yes—
391C2×C42C2412yes—
392C2×C42C2412yes—
393#107—44no—
394C4⋊C8—44no—
395#103—28no—
396#103—28no—
397#103—44no—
398#103—44no—
399#103—44no—
400#103—44no—
401#103C2×D4116yescomplemented
402#102—28no—
403#102—28no—
404#102—44no—
405C22⋊C8—28no—
406C22⋊C8—44no—
407C4×C8—28no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95C2×D414yes—
419#95C2×D414yes—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24#13514yes—
435C24C22×D412yes—
436C24C22×D411yescharacteristic
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—48no—
462C2×Q8—416no—
463C2×Q8—416no—
464C2×Q8—416no—
465C2×Q8—464no—
466C2×Q8—416no—
467C2×Q8—432no—
468C2×Q8—44no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—44no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8C22×D414yes—
484C2×Q8C2×#4114yes—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—44no—
499C2×D4—42no—
500C2×D4—44no—
501C2×D4—816no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—432no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D412yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4C2511yescharacteristic
575Q16—416no—
576Q16—416no—
577SD16—416no—
578C2×C8—28no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—44no—
591C2×C8—44no—
592C2×C8—44no—
593C2×C8C22×D414yes—
594C4⋊C4—24no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4C22×D414yes—
609C22⋊C4—28no—
610C22⋊C4—44no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C42—24no—
619C42—24no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—48no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23#53512yes—
653C23D4212yes—
654C23#54612yes—
655C23C2×#13514yes—
656C23C2×#13512yes—
657C23#57512yes—
658C23#57812yes—
659C23#57812yes—
660C23C23×D411yescharacteristic
661Q8—24no—
662Q8—24no—
663Q8—24no—
664Q8—24no—
665Q8—432no—
666Q8—48no—
667Q8—48no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676Q8—84no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—816no—
682D4—84no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—432no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—48no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—48no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—48no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—84no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4#53512yes—
738C2×C4#53514yes—
739C2×C4#53814yes—
740C2×C4D4212yes—
741C2×C4#54612yes—
742C2×C4#54614yes—
743C2×C4H(3,𝔽4)14yes—
744C2×C4C23×D411yescharacteristic
745C2×C4C22×#4111yescharacteristic
746C2×C4C2×H(5,𝔽2)11yescharacteristic
747C2×C4C2×H(5,𝔽2)11yescharacteristic
748C2×C4C2×H(5,𝔽2)11yescharacteristic
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C8—24no—
751C8—42no—
752C8—42no—
753C8—42no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—416no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—168no—
770C22#267014yes—
771C22#321114yes—
772C22#322314yes—
773C22#326914yes—
774C22#328514yes—
775C22#330014yes—
776C22#332714yes—
777C22C2×#53511yescharacteristic
778C22C2×D4211yescharacteristic
779C22C2×#54611yescharacteristic
780C22C22×#13511yescharacteristic
781C22C2×#57511yescharacteristic
782C22C2×#57811yescharacteristic
783C22C2×#57811yescharacteristic
784C4—42no—
785C4—44no—
786C4—42no—
787C4—42no—
788C4—44no—
789C4—44no—
790C4—42no—
791C4—42no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4#267014yes—
797C4C2×#53511yescharacteristic
798C4C2×#53811yescharacteristic
799C4C2×#54611yescharacteristic
800C4C2×H(3,𝔽4)11yescharacteristic
801C2—44no—
802C2—162no—
803C2#3053418yesdirect product factor
804C2C2×#267011yescharacteristic
805C2C2×#321111yescharacteristic
806C2C2×#322311yescharacteristic
807C2C2×#326911yescharacteristic
808C2C2×#328511yescharacteristic
809C2C2×#330011yescharacteristic
810C2C2×#332711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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×#488C2semidirect
2. C22×#451C2semidirect
3. C2×#2489C2semidirect
5. #30534C2direct (N × H)
6. C2×#2056C2semidirect
8. C2×#2026C2semidirect
9. C2×#2015C2semidirect
10. C2×#2015C2semidirect
12. C2×#1983C2semidirect
13. C2×#1969C2semidirect
14. C2×#1928C2semidirect
15. C2×#1923C2semidirect
16. C2×#1787C2semidirect
27. C2×#488C22semidirect
29. C2×#451C22semidirect
46. #2489C22semidirect
64. #2056C22semidirect
66. #2026C22semidirect
67. #2015C22semidirect
68. #2015C22semidirect
70. #1983C22semidirect
71. #1969C22semidirect
72. #1928C22semidirect
73. #1923C22semidirect
74. #1787C22semidirect
162. C2×#103D4semidirect
401. #103C2×D4semidirect
803. C2#30534direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4882
C22×#4512
C2×#24892
C2×#24362
#305342
C2×#20562
C2×#20332
C2×#20262
C2×#20152
C2×#20002
C2×#19832
C2×#19692
C2×#19282
C2×#19232
C2×#17872