Finite Group Databasebeta

← C2×#30997 #7503090

Subgroups — C2×#30997 #7503090

Order 512.

2910 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#462C211yesmaximal, characteristic, complemented
2C22×#452C211yesmaximal, characteristic
3C2×#2432C211yesmaximal, characteristic
4C2×#2421C211yesmaximal, characteristic, complemented
5#30997C2116yesmaximal, direct product factor
6C2×#2074C211yesmaximal, characteristic, complemented
7C2×#2067C211yesmaximal, characteristic, complemented
8C2×#2043C211yesmaximal, characteristic, complemented
9C2×#2036C211yesmaximal, characteristic, complemented
10C2×#2015C211yesmaximal, characteristic, complemented
11C2×#2001C211yesmaximal, characteristic, complemented
12C2×#1969C211yesmaximal, characteristic, complemented
13C2×#1958C211yesmaximal, characteristic, complemented
14C2×#1923C211yesmaximal, characteristic, complemented
15C2×#1880C211yesmaximal, characteristic, complemented
16C2×#1788C211yesmaximal, characteristic
17C23×#41C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C2×#462—28no—
27C2×#462C2218yescomplemented
28C2×#452—28no—
29C2×#452C2218yes—
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#2432—24no—
46#2432C2218yes—
47#2421—24no—
48#2421C2218yescomplemented
49C2×#400—21no—
50C2×#397—21no—
51C2×#394—21no—
52C2×#394—21no—
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#388—21no—
58C2×#387—21no—
59C2×#385—21no—
60C2×#385—21no—
61C2×#382C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64#2074C2218yescomplemented
65#2067C2218yescomplemented
66#2043C2218yescomplemented
67#2036C2218yescomplemented
68#2015C2218yescomplemented
69#2001C2218yescomplemented
70#1969C2218yescomplemented
71#1958C2218yescomplemented
72#1923C2218yescomplemented
73#1880C2218yescomplemented
74#1788C2218yes—
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C22×#41—22no—
80C22×#41—24no—
81C22×#41—24no—
82C22×#41—42no—
83C22×#41—42no—
84C22×#41—42no—
85C22×#41—42no—
86C22×#41C2314yes—
87C23×Q8C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4—21no—
91C23×D4C2311yescharacteristic
92C24×C4—21no—
93C24×C4C2311yescharacteristic
94C22×Q16—24no—
95C22×Q16—42no—
96C22×Q16—42no—
97C22×Q16—42no—
98C22×Q16—42no—
99C22×Q16D418yes—
100C22×Q16C2314yes—
101C22×Q16C2314yes—
102C22×SD16—24no—
103C22×SD16—24no—
104C22×SD16—42no—
105C22×SD16C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—22no—
112C2×C4⋊Q8—42no—
113C2×C4⋊Q8C2314yes—
114C2×#124—24no—
115C2×#124—22no—
116C2×#124—42no—
117C2×#124C2314yes—
118C2×C22⋊Q8—22no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8C2314yes—
125C2×C22⋊Q8C2314yes—
126C2×C4×Q8—22no—
127C2×C4×Q8—24no—
128C2×C4×Q8—42no—
129C2×C4×Q8C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
147C22×C22⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42—21no—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#462—232no—
153#452—232no—
154C2×#107—42no—
155C2×#107C2314yes—
156C2×C4⋊C8—24no—
157C2×C4⋊C8C2314yes—
158C2×#103—24no—
159C2×#103—24no—
160C2×#103—24no—
161C2×#103—42no—
162C2×#103—42no—
163C2×#103—42no—
164C2×#103—42no—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#102—24no—
173C2×#102—42no—
174C2×#102—42no—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×C22⋊C8—24no—
179C2×C22⋊C8—42no—
180C2×C22⋊C8C2314yes—
181C2×C22⋊C8C2314yes—
182C2×C4×C8—42no—
183C2×C4×C8C2314yes—
184#400—28no—
185#397—28no—
186#394—28no—
187#394—28no—
188#391—22no—
189#391—22no—
190#391C2314yes—
191#391C2314yes—
192#390—22no—
193#390C2314yes—
194#389—22no—
195#389C2314yes—
196#388—28no—
197#387—28no—
198#385—28no—
199#385—28no—
200#382—22no—
201#382C2314yes—
202#380—22no—
203#380C2314yes—
204C4×C22⋊C4D414yes—
205C4×C22⋊C4C2314yes—
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
222C2×#41—28no—
223C2×#41—28no—
224C2×#41—44no—
225C2×#41—44no—
226C2×#41—44no—
227C2×#41—44no—
228C2×#41—48no—
229C2×#41—48no—
230C2×#41—48no—
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8C2×D414yes—
255C22×Q8C2×D414yes—
256C22×Q8C2412yes—
257C22×Q8C2412yes—
258C22×Q8C2412yes—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—21no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4#4114yes—
270C22×D4C2412yes—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—24no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4C2×D412yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C2×Q16—28no—
297C2×Q16—416no—
298C2×Q16—44no—
299C2×Q16—44no—
300C2×Q16—44no—
301C2×Q16—44no—
302C2×Q16—416no—
303C2×Q16C2×D4116yes—
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—44no—
307C2×SD16—416no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8C2×D414yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C4⋊Q8—28no—
325C4⋊Q8—44no—
326C4⋊Q8—48no—
327#124—28no—
328#124—44no—
329#124—48no—
330C22⋊Q8—28no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334C22⋊Q8—48no—
335C22⋊Q8—48no—
336C4×Q8—28no—
337C4×Q8—44no—
338C4×Q8—48no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—21no—
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⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
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—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4C2×D414yes—
384C2×C22⋊C4C2×D414yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—44no—
391C2×C42C2×D412yes—
392C2×C42C2×D412yes—
393C2×C42C2412yes—
394C2×C42C2412yes—
395#107—44no—
396C4⋊C8—28no—
397#103—28no—
398#103—28no—
399#103—28no—
400#103—44no—
401#103—44no—
402#103—44no—
403#103—44no—
404#102—28no—
405#102—44no—
406#102—44no—
407C22⋊C8—28no—
408C22⋊C8—44no—
409C4×C8—44no—
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—24no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24C22×D412yes—
436C24C22×D411yescharacteristic
437#41—416no—
438#41—416no—
439#41—416no—
440#41—464no—
441#41—416no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—28no—
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—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8C22×D414yes—
480C2×Q8C22×D414yes—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—432no—
493C2×D4—44no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4C2×#4114yes—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
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—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—432no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4#13514yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D411yescharacteristic
565C22×C4C2×#4112yes—
566C22×C4H(5,𝔽2)12yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4C2511yescharacteristic
571Q16—416no—
572Q16—416no—
573SD16—416no—
574C2×C8—28no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—44no—
587C2×C8—44no—
588C2×C8—44no—
589C2×C8C22×D414yes—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—48no—
608C22⋊C4—28no—
609C22⋊C4—44no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C42—24no—
618C42—24no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—48no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—48no—
633C23—44no—
634C23—42no—
635C23—42no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—48no—
642C23—44no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23#53512yes—
653C23D4212yes—
654C23#54612yes—
655C23C2×#13512yes—
656C23#57512yes—
657C23#57812yes—
658C23#57812yes—
659C23C23×D411yescharacteristic
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—24no—
664Q8—48no—
665Q8—48no—
666Q8—42no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—84no—
675D4—24no—
676D4—24no—
677D4—432no—
678D4—42no—
679D4—48no—
680D4—42no—
681C2×C4—22no—
682C2×C4—28no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
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—22no—
697C2×C4—22no—
698C2×C4—432no—
699C2×C4—44no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—48no—
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—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4#53414yes—
735C2×C4#53512yes—
736C2×C4#53814yes—
737C2×C4D4212yes—
738C2×C4#54612yes—
739C2×C4#54614yes—
740C2×C4#56014yes—
741C2×C4C2×#13514yes—
742C2×C4C23×D411yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4C2×H(5,𝔽2)11yescharacteristic
746C2×C4C2×H(5,𝔽2)11yescharacteristic
747C2×C4C2×H(5,𝔽2)11yescharacteristic
748C8—24no—
749C8—42no—
750C8—42no—
751C8—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—44no—
760C22—42no—
761C22—44no—
762C22—88no—
763C22—816no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#267814yes—
769C22#321214yes—
770C22#322314yes—
771C22#327714yes—
772C22#328514yes—
773C22#330214yes—
774C22#331514yes—
775C22C2×#53511yescharacteristic
776C22C2×D4211yescharacteristic
777C22C2×#54611yescharacteristic
778C22C22×#13511yescharacteristic
779C22C2×#57511yescharacteristic
780C22C2×#57811yescharacteristic
781C22C2×#57811yescharacteristic
782C4—24no—
783C4—42no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—42no—
788C4—42no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4#267814yes—
795C4C2×#53411yescharacteristic
796C4C2×#53811yescharacteristic
797C4C2×#54611yescharacteristic
798C4C2×#56011yescharacteristic
799C2—82no—
800C2—84no—
801C2#3099718yesdirect product factor
802C2C2×#267811yescharacteristic
803C2C2×#321211yescharacteristic
804C2C2×#322311yescharacteristic
805C2C2×#327711yescharacteristic
806C2C2×#328511yescharacteristic
807C2C2×#330211yescharacteristic
808C2C2×#331511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
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×#462C2semidirect
4. C2×#2421C2semidirect
5. #30997C2direct (N × H)
6. C2×#2074C2semidirect
7. C2×#2067C2semidirect
8. C2×#2043C2semidirect
9. C2×#2036C2semidirect
10. C2×#2015C2semidirect
11. C2×#2001C2semidirect
12. C2×#1969C2semidirect
13. C2×#1958C2semidirect
14. C2×#1923C2semidirect
15. C2×#1880C2semidirect
27. C2×#462C22semidirect
48. #2421C22semidirect
64. #2074C22semidirect
65. #2067C22semidirect
66. #2043C22semidirect
67. #2036C22semidirect
68. #2015C22semidirect
69. #2001C22semidirect
70. #1969C22semidirect
71. #1958C22semidirect
72. #1923C22semidirect
73. #1880C22semidirect
801. C2#30997direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4622
C22×#4522
C2×#24322
C2×#24212
#309972
C2×#20742
C2×#20672
C2×#20432
C2×#20362
C2×#20152
C2×#20012
C2×#19692
C2×#19582
C2×#19232
C2×#18802
C2×#17882