Finite Group Databasebeta

← C2×#13968 #514247

Subgroups — C2×#13968 #514247

Order 512.

10234 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic
2C23×C4×D4C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#381C211yesmaximal, characteristic, complemented
5C23×#95C211yesmaximal, characteristic, complemented
6#13968C2116yesmaximal, direct product factor
7C2×#1441C212yesmaximal, complemented
8C2×#1440C212yesmaximal, complemented
9C2×#1436C212yesmaximal, complemented
10C2×C22⋊#95C212yesmaximal, complemented
11C2×C22⋊#95C211yesmaximal, characteristic, complemented
12C2×C22⋊#95C211yesmaximal, characteristic, complemented
13C24×D4C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C25×C4C2211yescharacteristic
16C25×C4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×#123—28no—
19C22×#123—28no—
20C22×#123C4116yescomplemented
21C22×#123C2218yes—
22C22×C4×D4—28no—
23C22×C4×D4—28no—
24C22×C4×D4—28no—
25C22×C4×D4C2218yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2212yes—
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2212yes—
31C23×C22⋊C4C2212yes—
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C2×#386—28no—
36C2×#386C2218yes—
37C2×#381—28no—
38C2×#381C2218yescomplemented
39C22×#95—28no—
40C22×#95C2212yes—
41C22×#95C2212yes—
42C22×#95C2212yes—
43C22×#95C2212yes—
44C22×#95C2212yes—
45C22×#95C2212yes—
46C22×#95C2212yes—
47C22×#95C2212yes—
48C22×#95C2212yes—
49C22×#95C2218yescomplemented
50#1441C22116yescomplemented
51#1440C22116yescomplemented
52#1436C22116yescomplemented
53C22⋊#95C2218yescomplemented
54C22⋊#95C22116yescomplemented
55C22⋊#95C2218yescomplemented
56C26C2311yescharacteristic
57C26C2311yescharacteristic
58C23×D4—24no—
59C23×D4—24no—
60C23×D4—24no—
61C23×D4—24no—
62C23×D4C2×C418yes—
63C23×D4D418yes—
64C23×D4D418yes—
65C23×D4C2314yes—
66C24×C4—24no—
67C24×C4—24no—
68C24×C4—24no—
69C24×C4—24no—
70C24×C4—24no—
71C24×C4—24no—
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—28no—
79C24×C4—28no—
80C24×C4—24no—
81C24×C4—24no—
82C24×C4—28no—
83C24×C4—44no—
84C24×C4—44no—
85C24×C4—44no—
86C24×C4C2×C418yescomplemented
87C24×C4D418yes—
88C24×C4C2312yes—
89C24×C4C2312yes—
90C24×C4C2312yes—
91C24×C4C2314yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2314yes—
97C24×C4C2314yes—
98C24×C4C2314yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×#123—2128no—
102C2×#123—232no—
103C2×#123—232no—
104C2×#123C2×C4164yescomplemented
105C2×C4×D4—2128no—
106C2×C4×D4—232no—
107C2×C4×D4—232no—
108C2×C4×D4—232no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—28no—
113C22×C4⋊C4—28no—
114C22×C4⋊C4C2×C4116yescomplemented
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2318yes—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—28no—
123C22×C22⋊C4—28no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—28no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—28no—
131C22×C22⋊C4—44no—
132C22×C22⋊C4C2×C418yescomplemented
133C22×C22⋊C4C2×C4116yescomplemented
134C22×C22⋊C4D418yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2318yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2318yes—
140C22×C22⋊C4C2314yes—
141C22×C42—24no—
142C22×C42—24no—
143C22×C42—24no—
144C22×C42C2314yes—
145#386—232no—
146#381—232no—
147C2×#95—28no—
148C2×#95—28no—
149C2×#95—232no—
150C2×#95—28no—
151C2×#95—28no—
152C2×#95—28no—
153C2×#95—28no—
154C2×#95—28no—
155C2×#95—44no—
156C2×#95—44no—
157C2×#95C2318yes—
158C2×#95C2318yes—
159C2×#95C2318yes—
160C2×#95C2318yes—
161C2×#95C2318yes—
162C2×#95C2318yes—
163C2×#95C2318yes—
164C2×#95C2318yes—
165C2×#95C2318yes—
166C25—24no—
167C25—24no—
168C25—24no—
169C25—24no—
170C25—22no—
171C25—22no—
172C25—24no—
173C25—24no—
174C25—22no—
175C25—22no—
176C25—24no—
177C25—24no—
178C25C22×C414yes—
179C25C22×C414yes—
180C25C2×D414yes—
181C25C2×D414yes—
182C25C2×D414yes—
183C25C2×D414yes—
184C25C2×D414yes—
185C25C2×D414yes—
186C25#4114yes—
187C25#4114yes—
188C25C2412yes—
189C25C2412yes—
190C25C2411yescharacteristic
191C22×D4—232no—
192C22×D4—232no—
193C22×D4—232no—
194C22×D4—232no—
195C22×D4—232no—
196C22×D4—232no—
197C22×D4—28no—
198C22×D4—28no—
199C22×D4—28no—
200C22×D4—28no—
201C22×D4C22⋊C4164yes—
202C22×D4C22×C4116yes—
203C22×D4C2×D4116yes—
204C22×D4C2×D4116yes—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—24no—
212C23×C4—232no—
213C23×C4—232no—
214C23×C4—232no—
215C23×C4—232no—
216C23×C4—232no—
217C23×C4—232no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—28no—
230C23×C4—28no—
231C23×C4—28no—
232C23×C4—28no—
233C23×C4—28no—
234C23×C4—28no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—28no—
238C23×C4—24no—
239C23×C4—28no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—28no—
243C23×C4—28no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—232no—
259C23×C4—28no—
260C23×C4—28no—
261C23×C4—216no—
262C23×C4—216no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—28no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—28no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—216no—
273C23×C4—416no—
274C23×C4—48no—
275C23×C4—48no—
276C23×C4—48no—
277C23×C4—432no—
278C23×C4—432no—
279C23×C4—432no—
280C23×C4—432no—
281C23×C4—432no—
282C23×C4—432no—
283C23×C4—416no—
284C23×C4—416no—
285C23×C4—416no—
286C23×C4—416no—
287C23×C4—416no—
288C23×C4—416no—
289C23×C4—416no—
290C23×C4—416no—
291C23×C4C22×C418yes—
292C23×C4C22×C418yes—
293C23×C4C22×C414yes—
294C23×C4C22×C4116yescomplemented
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D4116yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4#4118yes—
303C23×C4#4118yes—
304C23×C4C2414yes—
305C23×C4C2414yes—
306C23×C4C2414yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2414yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313#123—2256no—
314C4×D4—2256no—
315C2×C4⋊C4—232no—
316C2×C4⋊C4—264no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—216no—
321C2×C4⋊C4—216no—
322C2×C4⋊C4C22×C4132yescomplemented
323C2×C22⋊C4—232no—
324C2×C22⋊C4—232no—
325C2×C22⋊C4—264no—
326C2×C22⋊C4—232no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—216no—
333C2×C22⋊C4—216no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—216no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—216no—
341C2×C22⋊C4—48no—
342C2×C22⋊C4—432no—
343C2×C22⋊C4—416no—
344C2×C22⋊C4C22×C4116yescomplemented
345C2×C22⋊C4C22×C4132yescomplemented
346C2×C22⋊C4C2×D4116yes—
347C2×C42—232no—
348C2×C42—28no—
349C2×C42—28no—
350C2×C42—28no—
351#95—216no—
352#95—216no—
353#95—216no—
354#95—216no—
355#95—216no—
356#95—216no—
357#95—216no—
358#95—48no—
359#95—48no—
360C24—216no—
361C24—216no—
362C24—28no—
363C24—28no—
364C24—216no—
365C24—28no—
366C24—28no—
367C24—216no—
368C24—216no—
369C24—216no—
370C24—216no—
371C24—216no—
372C24—216no—
373C24—216no—
374C24—216no—
375C24—216no—
376C24—24no—
377C24—24no—
378C24—24no—
379C24—24no—
380C24—28no—
381C24—28no—
382C24—216no—
383C24—216no—
384C24—28no—
385C24—28no—
386C24—28no—
387C24—28no—
388C24—216no—
389C24—216no—
390C24—216no—
391C24—216no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—44no—
401C24—44no—
402C24—48no—
403C24—44no—
404C24—44no—
405C24—48no—
406C24—48no—
407C24—48no—
408C24—48no—
409C24—48no—
410C24C2×C22⋊C4116yes—
411C24C2×C22⋊C4116yes—
412C24C4×D4116yes—
413C24C4×D4116yes—
414C24#120116yes—
415C24#121116yes—
416C24#121116yes—
417C24#123116yes—
418C24C23×C414yes—
419C24C23×C414yes—
420C24C23×C412yes—
421C24C22×D414yes—
422C24C22×D414yes—
423C24C22×D414yes—
424C24C22×D414yes—
425C24C22×D414yes—
426C24C22×D414yes—
427C24C22×D412yes—
428C24C22×D412yes—
429C24C22×D412yes—
430C24C22×D412yes—
431C24C2×#4114yes—
432C24C2×#4114yes—
433C24C2×#4112yes—
434C24C2×#4112yes—
435C24C2×#4114yes—
436C24C2×#4114yes—
437C24H(5,𝔽2)14yes—
438C242−1+414yes—
439C24C2511yescharacteristic
440C2×D4—232no—
441C2×D4—232no—
442C2×D4—232no—
443C2×D4—232no—
444C2×D4—232no—
445C2×D4—232no—
446C2×D4—2256no—
447C2×D4C2×C22⋊C4164yes—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—216no—
457C22×C4—216no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—232no—
466C22×C4—232no—
467C22×C4—216no—
468C22×C4—216no—
469C22×C4—232no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—232no—
473C22×C4—232no—
474C22×C4—216no—
475C22×C4—216no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—232no—
480C22×C4—28no—
481C22×C4—216no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—216no—
485C22×C4—216no—
486C22×C4—216no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—232no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—416no—
526C22×C4—432no—
527C22×C4—4128no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—432no—
532C22×C4—432no—
533C22×C4—4128no—
534C22×C4—416no—
535C22×C4—416no—
536C22×C4—4128no—
537C22×C4—416no—
538C22×C4—48no—
539C22×C4—416no—
540C22×C4—48no—
541C22×C4—416no—
542C22×C4—416no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—44no—
546C22×C4—416no—
547C22×C4—48no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—48no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—4128no—
563C22×C4—416no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4C2×C22⋊C4116yes—
572C22×C4#123116yescomplemented
573C22×C4C23×C418yes—
574C22×C4C23×C418yes—
575C22×C4C23×C414yes—
576C22×C4C22×D414yes—
577C22×C4C22×D414yes—
578C22×C4C22×D414yes—
579C22×C4C22×D414yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4C2×#4118yes—
583C22×C4C2×#4118yes—
584C4⋊C4—232no—
585C4⋊C4—264no—
586C22⋊C4—232no—
587C22⋊C4—232no—
588C22⋊C4—264no—
589C22⋊C4—232no—
590C22⋊C4—432no—
591C22⋊C4—416no—
592C42—232no—
593C23—232no—
594C23—264no—
595C23—264no—
596C23—28no—
597C23—28no—
598C23—232no—
599C23—232no—
600C23—24no—
601C23—24no—
602C23—28no—
603C23—264no—
604C23—24no—
605C23—24no—
606C23—264no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—28no—
611C23—28no—
612C23—28no—
613C23—28no—
614C23—28no—
615C23—28no—
616C23—232no—
617C23—232no—
618C23—232no—
619C23—264no—
620C23—24no—
621C23—24no—
622C23—28no—
623C23—28no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—28no—
632C23—232no—
633C23—416no—
634C23—432no—
635C23—416no—
636C23—416no—
637C23—42no—
638C23—42no—
639C23—44no—
640C23—432no—
641C23—42no—
642C23—42no—
643C23—432no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—416no—
650C23—416no—
651C23—416no—
652C23#386164yes—
653C23C22×C22⋊C418yes—
654C23C22×C22⋊C418yes—
655C23C22×C22⋊C414yes—
656C23C2×C4×D418yes—
657C23C2×C4×D418yes—
658C23C2×C4×D414yes—
659C23C2×C4×D414yes—
660C23C4×#4118yes—
661C23#52018yes—
662C23C2×#12018yes—
663C23C2×#12014yes—
664C23C2×#12118yes—
665C23C2×#12118yes—
666C23C2×#12114yes—
667C23C2×#12114yes—
668C23C2×#12318yes—
669C23C2×#12314yes—
670C23C2×#12314yes—
671C23#52514yes—
672C23#52918yes—
673C23#53414yes—
674C23#53614yes—
675C23#53918yes—
676C23#54618yes—
677C23#54618yes—
678C23#54618yes—
679C23#54718yes—
680C23#54718yes—
681C23#54718yes—
682C23#55118yes—
683C23#55218yes—
684C23C24×C411yescharacteristic
685C23C23×D411yescharacteristic
686C23C23×D411yescharacteristic
687C23C23×D411yescharacteristic
688C23C23×D411yescharacteristic
689C23C22×#4111yescharacteristic
690C23C22×#4111yescharacteristic
691C23C22×#4112yes—
692C23C22×#4112yes—
693C23C2×H(5,𝔽2)12yes—
694C23C2×2−1+412yes—
695D4—2128no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—232no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—232no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—464no—
725C2×C4—464no—
726C2×C4—464no—
727C2×C4—432no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—416no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—432no—
752C2×C4—464no—
753C2×C4—432no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—816no—
762C2×C4C22×C22⋊C418yes—
763C2×C4C2×#12318yescomplemented
764C22—28no—
765C22—28no—
766C22—216no—
767C22—216no—
768C22—28no—
769C22—216no—
770C22—216no—
771C22—2128no—
772C22—28no—
773C22—28no—
774C22—28no—
775C22—216no—
776C22—28no—
777C22—44no—
778C22—44no—
779C22—48no—
780C22—44no—
781C22—48no—
782C22—48no—
783C22—464no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22C2×#386116yes—
788C22C2×#38618yes—
789C22C4×#12318yes—
790C22#232218yes—
791C22#2339116yes—
792C22#2359116yes—
793C22#240518yes—
794C22#240618yes—
795C22#2419116yes—
796C22#2425116yes—
797C22#248618yes—
798C22#253418yes—
799C22C23×C22⋊C411yescharacteristic
800C22C22×C4×D411yescharacteristic
801C22C22×C4×D411yescharacteristic
802C22C2×C4×#4112yes—
803C22C2×#52012yes—
804C22C22×#12011yescharacteristic
805C22C22×#12111yescharacteristic
806C22C22×#12111yescharacteristic
807C22C22×#12311yescharacteristic
808C22C22×#12311yescharacteristic
809C22C2×#52511yescharacteristic
810C22C2×#52912yes—
811C22C2×#53411yescharacteristic
812C22C2×#53611yescharacteristic
813C22C2×#53912yes—
814C22C2×#54612yes—
815C22C2×#54612yes—
816C22C2×#54612yes—
817C22C2×#54712yes—
818C22C2×#54712yes—
819C22C2×#54712yes—
820C22C2×#55112yes—
821C22C2×#55212yes—
822C4—28no—
823C4—28no—
824C4—48no—
825C4—48no—
826C4—44no—
827C4—44no—
828C4—44no—
829C4—48no—
830C4—84no—
831C2—216no—
832C2—48no—
833C2#13968116yesdirect product factor
834C2C22×#38611yescharacteristic
835C2C2×C4×#12311yescharacteristic
836C2C2×#232211yescharacteristic
837C2C2×#233912yes—
838C2C2×#235912yes—
839C2C2×#240511yescharacteristic
840C2C2×#241912yes—
841C2C2×#242512yes—
842C2C2×#240611yescharacteristic
843C2C2×#248611yescharacteristic
844C2C2×#253411yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#381C2semidirect
5. C23×#95C2semidirect
6. #13968C2direct (N × H)
7. C2×#1441C2semidirect
8. C2×#1440C2semidirect
9. C2×#1436C2semidirect
10. C2×C22⋊#95C2semidirect
11. C2×C22⋊#95C2semidirect
12. C2×C22⋊#95C2semidirect
20. C22×#123C4semidirect
38. C2×#381C22semidirect
49. C22×#95C22semidirect
50. #1441C22semidirect
51. #1440C22semidirect
52. #1436C22semidirect
53. C22⋊#95C22semidirect
54. C22⋊#95C22semidirect
55. C22⋊#95C22semidirect
86. C24×C4C2×C4semidirect
104. C2×#123C2×C4semidirect
114. C22×C4⋊C4C2×C4semidirect
132. C22×C22⋊C4C2×C4semidirect
133. C22×C22⋊C4C2×C4semidirect
294. C23×C4C22×C4semidirect
322. C2×C4⋊C4C22×C4semidirect
344. C2×C22⋊C4C22×C4semidirect
345. C2×C22⋊C4C22×C4semidirect
572. C22×C4#123semidirect
763. C2×C4C2×#123semidirect
833. C2#13968direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1232
C23×C4×D42
C22×#3862
C22×#3812
C23×#952
#139682
C2×#14412
C2×#14402
C2×#14362
C2×C22⋊#952