Finite Group Databasebeta

← #521413

Subgroups — #521413

Order 512.

5054 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2312C211yesmaximal, characteristic, complemented
2C2×#2308C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4#14680C211yesmaximal, characteristic, complemented
5#14427C214yesmaximal, complemented
6#14391C214yesmaximal, complemented
7#14341C211yesmaximal, characteristic, complemented
8#14335C211yesmaximal, characteristic
9#14068C214yesmaximal, complemented
10#13988C214yesmaximal, complemented
11#13877C212yesmaximal, complemented
12#13874C212yesmaximal, complemented
13#13874C212yesmaximal, complemented
14C22⋊C42C212yesmaximal, complemented
15C4×#379C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C23×C22⋊C4C2212yes—
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22#2312—28no—
23#2308—28no—
24C2×#388C2214yescomplemented
25C2×#388C2214yescomplemented
26C2×#386C4116yescomplemented
27C2×#386C2214yes—
28C2×#386C2214yes—
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#386C2212yes—
33C2×#385C2214yescomplemented
34C2×#381C2212yes—
35C2×#381C2212yes—
36C2×#380C2212yes—
37C2×#380C2212yes—
38C2×#380C2212yescomplemented
39C2×#380C2212yescomplemented
40C2×#379C2211yescharacteristic
41C2×#379C2211yescharacteristic
42C2×#379C2212yes—
43C2×#379C2211yescharacteristic
44C2×#379C2211yescharacteristic
45C2×C4×C22⋊C4C2212yes—
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yescomplemented
48C2×C4×C22⋊C4C2214yescomplemented
49C2×C4×C22⋊C4C2212yescomplemented
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52#1443C2214yescomplemented
53#1443C2214yescomplemented
54#1442C2214yescomplemented
55#1442C2214yescomplemented
56#1440C2214yescomplemented
57#1440C2214yescomplemented
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1438C2214yes—
61#1438C2214yes—
62#1437C2214yescomplemented
63#1437C2214yescomplemented
64#1436C2214yescomplemented
65#1436C2214yescomplemented
66#1434C2214yescomplemented
67#1434C2214yescomplemented
68C22⋊#95C2212yes—
69C22⋊#95C2212yes—
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2214yescomplemented
73C22⋊#95C2212yescomplemented
74C22⋊#95C2214yescomplemented
75C22⋊#95C2212yescomplemented
76C22⋊#95C2212yescomplemented
77C22⋊#95C2212yescomplemented
78C26C2311yescharacteristic
79C26C2311yescharacteristic
80C23×D4—24no—
81C23×D4—28no—
82C23×D4—24no—
83C23×D4—44no—
84C23×D4C2×C418yes—
85C23×D4C2312yes—
86C23×D4C2312yes—
87C24×C4—44no—
88C24×C4—44no—
89C24×C4—44no—
90C24×C4C2×C418yescomplemented
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2314yes—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2314yes—
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—28no—
106C22×C22⋊C4—28no—
107C22×C22⋊C4—44no—
108C22×C22⋊C4—44no—
109C22×C22⋊C4—44no—
110C22×C22⋊C4C2×C418yes—
111C22×C22⋊C4C2×C418yes—
112C22×C22⋊C4C2×C418yescomplemented
113C22×C22⋊C4C2312yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2314yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C42C2314yes—
135C22×C42C2314yes—
136#388—216no—
137#388—216no—
138#386—216no—
139#386—216no—
140#386C2×C4116yescomplemented
141#386C2×C4116yescomplemented
142#386C2×C4116yescomplemented
143#386C2×C4116yescomplemented
144#385—48no—
145#381—28no—
146#381—44no—
147#380—28no—
148#380—44no—
149#380—44no—
150#380—44no—
151#379—24no—
152#379—24no—
153#379—24no—
154#379—28no—
155#379D418yes—
156C4×C22⋊C4—28no—
157C4×C22⋊C4—44no—
158C4×C22⋊C4—48no—
159C4×C22⋊C4—44no—
160C4×C22⋊C4—44no—
161C2×#95C2×C418yescomplemented
162C2×#95C2×C418yescomplemented
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C25—24no—
184C25—24no—
185C25—22no—
186C25—22no—
187C25—24no—
188C25—42no—
189C25—42no—
190C25—42no—
191C25—42no—
192C25—42no—
193C25—42no—
194C25—42no—
195C25—42no—
196C25C22×C414yes—
197C25C22×C414yes—
198C25C2×D414yes—
199C25#4118yes—
200C25#4114yes—
201C25C2411yescharacteristic
202C25C2411yescharacteristic
203C25C2412yes—
204C25C2411yescharacteristic
205C22×D4—232no—
206C22×D4—232no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—416no—
216C22×D4—42no—
217C22×D4—42no—
218C22×D4—42no—
219C22×D4—42no—
220C22×D4—432no—
221C22×D4—432no—
222C22×D4C22×C418yes—
223C22×D4C22×C418yes—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—28no—
241C23×C4—28no—
242C23×C4—416no—
243C23×C4—416no—
244C23×C4—416no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—44no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—464no—
265C23×C4C22×C414yes—
266C23×C4C22×C414yes—
267C23×C4C22×C414yes—
268C23×C4C22×C414yes—
269C23×C4C22×C414yes—
270C23×C4C22×C414yes—
271C23×C4C22×C414yes—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C2414yes—
275C23×C4C2414yes—
276C23×C4C2414yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2414yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C22⋊C4—232no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—416no—
320C2×C22⋊C4—416no—
321C2×C22⋊C4—432no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4C22×C418yes—
346C2×C22⋊C4C22×C418yes—
347C2×C22⋊C4C22×C418yes—
348C2×C22⋊C4C22×C418yes—
349C2×C22⋊C4C22×C418yes—
350C2×C22⋊C4C22×C418yes—
351C2×C22⋊C4C2×D418yes—
352C2×C22⋊C4C2×D418yes—
353C2×C22⋊C4C2×D418yes—
354C2×C42—28no—
355C2×C42—28no—
356C2×C42—44no—
357C2×C42—44no—
358C2×C42—44no—
359C2×C42—44no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—28no—
364#95—28no—
365#95—28no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95C22×C418yes—
377#95C22×C418yes—
378#95C22×C418yes—
379#95C22×C418yes—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—28no—
385C24—28no—
386C24—216no—
387C24—216no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—24no—
393C24—24no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—24no—
408C24—28no—
409C24—28no—
410C24—216no—
411C24—216no—
412C24—44no—
413C24—44no—
414C24—44no—
415C24—44no—
416C24—48no—
417C24—48no—
418C24—48no—
419C24—48no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—44no—
424C24—416no—
425C24—416no—
426C24—416no—
427C24—416no—
428C24—416no—
429C24—416no—
430C24—84no—
431C24—84no—
432C24—84no—
433C24—84no—
434C24—88no—
435C24—88no—
436C24#117116yes—
437C24C4×D4116yes—
438C24C23×C414yes—
439C24C23×C412yes—
440C24C23×C412yes—
441C24C23×C412yes—
442C24C22×D412yes—
443C24C22×D412yes—
444C24C22×D412yes—
445C24C2×#4114yes—
446C24C2×#4114yes—
447C24C2×#4112yes—
448C24C2×#4112yes—
449C24C2×#4114yes—
450C24C2×#4112yes—
451C24H(5,𝔽2)14yes—
452C24C2511yescharacteristic
453C2×D4—216no—
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—4128no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
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—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—416no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—416no—
548C22×C4—416no—
549C22×C4—416no—
550C22×C4—416no—
551C22×C4—416no—
552C22×C4—4128no—
553C22×C4—416no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—416no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4—84no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—84no—
563C22×C4—88no—
564C22×C4—88no—
565C22×C4—88no—
566C22×C4C23×C414yes—
567C22×C4C23×C414yes—
568C22×C4C23×C414yes—
569C22×C4C23×C412yes—
570C22×C4C23×C412yes—
571C22×C4C23×C412yes—
572C22×C4C23×C412yes—
573C22×C4C22×D418yes—
574C22×C4H(5,𝔽2)14yes—
575C22×C4H(5,𝔽2)14yes—
576C4⋊C4—88no—
577C4⋊C4—88no—
578C22⋊C4—216no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—216no—
582C22⋊C4—216no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—416no—
588C22⋊C4—416no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—84no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C22⋊C4—84no—
598C22⋊C4—88no—
599C42—88no—
600C42—88no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—28no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—28no—
611C23—28no—
612C23—28no—
613C23—232no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—28no—
633C23—28no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—28no—
649C23—28no—
650C23—24no—
651C23—24no—
652C23—232no—
653C23—416no—
654C23—416no—
655C23—416no—
656C23—416no—
657C23—416no—
658C23—464no—
659C23—416no—
660C23—416no—
661C23—464no—
662C23—416no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—832no—
680C23—88no—
681C23—88no—
682C23—832no—
683C23—88no—
684C23—88no—
685C23C2×#11718yes—
686C23C2×#11714yes—
687C23C2×C4×D414yes—
688C23C2×C4×D414yes—
689C23C2×C4×D414yes—
690C23#51814yes—
691C23#54618yes—
692C23#55118yes—
693C23C24×C411yescharacteristic
694C23C23×D411yescharacteristic
695C23C22×#4112yes—
696C23C22×#4111yescharacteristic
697C23C2×H(5,𝔽2)12yes—
698C23C2×H(5,𝔽2)12yes—
699C23C2×H(5,𝔽2)12yes—
700C23#58512yes—
701C23#58512yes—
702D4—432no—
703D4—432no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—416no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
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—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—88no—
771C2×C4—88no—
772C2×C4—832no—
773C2×C4#51814yes—
774C2×C4#51814yes—
775C22—216no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—216no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—28no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—464no—
793C22—48no—
794C22—48no—
795C22—48no—
796C22—48no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—48no—
806C22—48no—
807C22—48no—
808C22—48no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—44no—
813C22—832no—
814C22#234218yes—
815C22C22×#11711yescharacteristic
816C22C22×C4×D411yescharacteristic
817C22C2×#51811yescharacteristic
818C22C2×#51811yescharacteristic
819C22C2×#51811yescharacteristic
820C22#342811yescharacteristic
821C22#342811yescharacteristic
822C22#345914yes—
823C22C2×#54612yes—
824C22C2×#55112yes—
825C22#349612yes—
826C22#349612yes—
827C22#350514yes—
828C22#350512yes—
829C22#350512yes—
830C22#353214yes—
831C22#353314yes—
832C4—24no—
833C4—24no—
834C4—48no—
835C4—42no—
836C4—42no—
837C4—44no—
838C4—44no—
839C4—44no—
840C4—84no—
841C4—84no—
842C4—84no—
843C2—28no—
844C2—44no—
845C2—44no—
846C2—48no—
847C2#3405711yescharacteristic
848C2C2×#234211yescharacteristic
849C2#3418511yescharacteristic
850C2#3420511yescharacteristic
851C2#3420511yescharacteristic
852C2#3435611yescharacteristic
853C2#3435711yescharacteristic
854C2#3942814yes—
855C2#3955614yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2312C2semidirect
4. #14680C2semidirect
5. #14427C2semidirect
6. #14391C2semidirect
7. #14341C2semidirect
9. #14068C2semidirect
10. #13988C2semidirect
11. #13877C2semidirect
12. #13874C2semidirect
13. #13874C2semidirect
14. C22⋊C42C2semidirect
15. C4×#379C2semidirect
24. C2×#388C22semidirect
25. C2×#388C22semidirect
26. C2×#386C4semidirect
33. C2×#385C22semidirect
38. C2×#380C22semidirect
39. C2×#380C22semidirect
47. C2×C4×C22⋊C4C22semidirect
48. C2×C4×C22⋊C4C22semidirect
49. C2×C4×C22⋊C4C22semidirect
52. #1443C22semidirect
53. #1443C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1440C22semidirect
57. #1440C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
62. #1437C22semidirect
63. #1437C22semidirect
64. #1436C22semidirect
65. #1436C22semidirect
66. #1434C22semidirect
67. #1434C22semidirect
72. C22⋊#95C22semidirect
73. C22⋊#95C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
90. C24×C4C2×C4semidirect
112. C22×C22⋊C4C2×C4semidirect
140. #386C2×C4semidirect
141. #386C2×C4semidirect
142. #386C2×C4semidirect
143. #386C2×C4semidirect
161. C2×#95C2×C4semidirect
162. C2×#95C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23122
C2×#23082
C22×#3862
#146802
#144272
#143912
#143412
#143352
#140682
#139882
#138772
#138742
C22⋊C422
C4×#3792