Finite Group Databasebeta

← #521327

Subgroups — #521327

Order 512.

5134 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2308C211yesmaximal, characteristic
2C22×#386C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic, complemented
4#14681C211yesmaximal, characteristic, complemented
5#14375C214yesmaximal, complemented
6#14373C214yesmaximal, complemented
7#14338C211yesmaximal, characteristic, complemented
8#14335C211yesmaximal, characteristic
9#14064C214yesmaximal, complemented
10#13984C214yesmaximal, complemented
11#13877C212yesmaximal, complemented
12#13874C212yesmaximal, complemented
13#13874C212yesmaximal, complemented
14C22⋊C42C212yesmaximal, complemented
15#13775C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×#117C2212yescomplemented
19C23×C22⋊C4C2212yes—
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2308—28no—
24C2×#386C4116yescomplemented
25C2×#386C2214yes—
26C2×#386C2214yes—
27C2×#386C2212yes—
28C2×#386C2212yes—
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#385C2214yescomplemented
32#2280—28no—
33C2×#381C2212yes—
34C2×#381C2212yes—
35C2×#381C2212yescomplemented
36C2×#381C2212yescomplemented
37C2×#381C2212yescomplemented
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2212yescomplemented
41C2×#379C2211yescharacteristic
42C2×#379C2211yescharacteristic
43C2×#379C2212yes—
44C2×#379C2211yescharacteristic
45C2×#379C2211yescharacteristic
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yescomplemented
49C2×C4×C22⋊C4C2214yescomplemented
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52#1443C2214yescomplemented
53#1443C2214yescomplemented
54#1442C2214yescomplemented
55#1442C2214yescomplemented
56#1439C2214yescomplemented
57#1439C2214yescomplemented
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1438C2214yes—
61#1438C2214yes—
62#1437C2214yescomplemented
63#1437C2214yescomplemented
64#1437C2214yescomplemented
65#1437C2214yescomplemented
66#1436C2214yescomplemented
67#1436C2214yescomplemented
68#1434C2214yescomplemented
69#1434C2214yescomplemented
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2214yescomplemented
75C22⋊#95C2212yescomplemented
76C22⋊#95C2214yescomplemented
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—24no—
88C24×C4—24no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4C2×C418yescomplemented
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2314yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C2×#117—28no—
103C2×#117—44no—
104C2×#117—44no—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C22⋊C4—28no—
108C22×C22⋊C4—28no—
109C22×C22⋊C4—44no—
110C22×C22⋊C4—44no—
111C22×C22⋊C4—44no—
112C22×C22⋊C4—44no—
113C22×C22⋊C4C2×C418yes—
114C22×C22⋊C4C2×C418yes—
115C22×C22⋊C4C2×C418yescomplemented
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C42C2314yes—
138C22×C42C2314yes—
139#386—216no—
140#386—216no—
141#386C2×C4116yescomplemented
142#386C2×C4116yescomplemented
143#386C2×C4116yescomplemented
144#386C2×C4116yescomplemented
145#385—48no—
146#381—28no—
147#381—28no—
148#381—44no—
149#381—44no—
150#381—44no—
151#380—28no—
152#380—28no—
153#380—44no—
154#379—24no—
155#379—24no—
156#379—28no—
157#379—24no—
158#379D418yes—
159C4×C22⋊C4—28no—
160C4×C22⋊C4—28no—
161C4×C22⋊C4—48no—
162C4×C22⋊C4—44no—
163C2×#95C2×C418yescomplemented
164C2×#95C2×C418yescomplemented
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×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C25—24no—
186C25—24no—
187C25—22no—
188C25—22no—
189C25—24no—
190C25—42no—
191C25—42no—
192C25—42no—
193C25—42no—
194C25—42no—
195C25—42no—
196C25—42no—
197C25—42no—
198C25C22×C414yes—
199C25C22×C414yes—
200C25C2×D414yes—
201C25#4118yes—
202C25#4114yes—
203C25C2411yescharacteristic
204C25C2411yescharacteristic
205C25C2412yes—
206C25C2411yescharacteristic
207C22×D4—232no—
208C22×D4—232no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—416no—
218C22×D4—42no—
219C22×D4—42no—
220C22×D4—42no—
221C22×D4—42no—
222C22×D4—432no—
223C22×D4—432no—
224C22×D4C22×C418yes—
225C22×D4C22×C418yes—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—232no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—28no—
252C23×C4—28no—
253C23×C4—416no—
254C23×C4—416no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—44no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—44no—
266C23×C4—42no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—432no—
271C23×C4—432no—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C22×C414yes—
275C23×C4C22×C414yes—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C22×C414yes—
280C23×C4C22×C414yes—
281C23×C4C2414yes—
282C23×C4C2414yes—
283C23×C4C2414yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2414yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292#117—432no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—416no—
323C2×C22⋊C4—416no—
324C2×C22⋊C4—432no—
325C2×C22⋊C4—416no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4C22×C418yes—
354C2×C22⋊C4C22×C418yes—
355C2×C22⋊C4C22×C418yes—
356C2×C22⋊C4C22×C418yes—
357C2×C22⋊C4C22×C418yes—
358C2×C22⋊C4C22×C418yes—
359C2×C22⋊C4C2×D418yes—
360C2×C22⋊C4C2×D418yes—
361C2×C22⋊C4C2×D418yes—
362C2×C42—28no—
363C2×C42—28no—
364C2×C42—44no—
365C2×C42—44no—
366C2×C42—44no—
367C2×C42—44no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95C22×C418yes—
385#95C22×C418yes—
386#95C22×C418yes—
387#95C22×C418yes—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—28no—
393C24—28no—
394C24—216no—
395C24—216no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—24no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—24no—
416C24—28no—
417C24—28no—
418C24—216no—
419C24—216no—
420C24—44no—
421C24—44no—
422C24—48no—
423C24—48no—
424C24—44no—
425C24—44no—
426C24—48no—
427C24—48no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—44no—
432C24—416no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24—416no—
438C24—84no—
439C24—84no—
440C24—84no—
441C24—84no—
442C24—88no—
443C24—88no—
444C24#117116yescomplemented
445C24C4×D4116yes—
446C24C23×C414yes—
447C24C23×C412yes—
448C24C23×C412yes—
449C24C23×C412yes—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C2×#4114yes—
454C24C2×#4114yes—
455C24C2×#4112yes—
456C24C2×#4112yes—
457C24C2×#4114yes—
458C24C2×#4112yes—
459C24H(5,𝔽2)14yes—
460C24C2511yescharacteristic
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—216no—
464C2×D4—216no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—4128no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C22×C4—216no—
477C22×C4—216no—
478C22×C4—28no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—4128no—
569C22×C4—416no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—416no—
575C22×C4—88no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4—88no—
581C22×C4—88no—
582C22×C4C23×C414yes—
583C22×C4C23×C414yes—
584C22×C4C23×C414yes—
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C412yes—
589C22×C4C22×D418yes—
590C22×C4H(5,𝔽2)14yes—
591C22×C4H(5,𝔽2)14yes—
592C4⋊C4—416no—
593C4⋊C4—88no—
594C22⋊C4—216no—
595C22⋊C4—216no—
596C22⋊C4—216no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—416no—
604C22⋊C4—416no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—84no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C22⋊C4—84no—
614C22⋊C4—88no—
615C42—416no—
616C42—88no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—28no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—232no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—28no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—28no—
667C23—28no—
668C23—232no—
669C23—416no—
670C23—416no—
671C23—416no—
672C23—416no—
673C23—416no—
674C23—416no—
675C23—416no—
676C23—464no—
677C23—416no—
678C23—464no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—88no—
696C23—88no—
697C23—832no—
698C23—832no—
699C23—88no—
700C23—88no—
701C23C2×#11718yes—
702C23C2×#11714yes—
703C23C2×C4×D414yes—
704C23C2×C4×D414yes—
705C23C2×C4×D414yes—
706C23#51814yes—
707C23#54618yes—
708C23#55118yes—
709C23C24×C411yescharacteristic
710C23C23×D411yescharacteristic
711C23C22×#4112yes—
712C23C22×#4111yescharacteristic
713C23C2×H(5,𝔽2)12yes—
714C23C2×H(5,𝔽2)12yes—
715C23C2×H(5,𝔽2)12yes—
716C23#58512yes—
717C23#58512yes—
718D4—432no—
719D4—432no—
720C2×C4—232no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—416no—
748C2×C4—416no—
749C2×C4—416no—
750C2×C4—416no—
751C2×C4—416no—
752C2×C4—416no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
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—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—88no—
791C2×C4—88no—
792C2×C4—832no—
793C2×C4#51814yes—
794C2×C4#51814yes—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—216no—
799C22—24no—
800C22—216no—
801C22—24no—
802C22—24no—
803C22—28no—
804C22—28no—
805C22—24no—
806C22—24no—
807C22—28no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—464no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—48no—
822C22—48no—
823C22—48no—
824C22—48no—
825C22—42no—
826C22—42no—
827C22—48no—
828C22—48no—
829C22—48no—
830C22—48no—
831C22—44no—
832C22—44no—
833C22—832no—
834C22#234218yes—
835C22C22×#11711yescharacteristic
836C22C22×C4×D411yescharacteristic
837C22C2×#51811yescharacteristic
838C22C2×#51811yescharacteristic
839C22C2×#51811yescharacteristic
840C22#342811yescharacteristic
841C22#342811yescharacteristic
842C22#345914yes—
843C22C2×#54612yes—
844C22C2×#55112yes—
845C22#348412yes—
846C22#348512yes—
847C22#349012yes—
848C22#349112yes—
849C22#350514yes—
850C22#354214yes—
851C22#354214yes—
852C4—24no—
853C4—24no—
854C4—44no—
855C4—44no—
856C4—44no—
857C4—48no—
858C4—42no—
859C4—42no—
860C4—84no—
861C4—84no—
862C4—84no—
863C2—28no—
864C2—44no—
865C2—44no—
866C2—48no—
867C2#3405711yescharacteristic
868C2C2×#234211yescharacteristic
869C2#3418511yescharacteristic
870C2#3419811yescharacteristic
871C2#3419911yescharacteristic
872C2#3436311yescharacteristic
873C2#3436311yescharacteristic
874C2#3777614yes—
875C2#3796414yes—
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
3. C2×#2280C2semidirect
4. #14681C2semidirect
5. #14375C2semidirect
6. #14373C2semidirect
7. #14338C2semidirect
9. #14064C2semidirect
10. #13984C2semidirect
11. #13877C2semidirect
12. #13874C2semidirect
13. #13874C2semidirect
14. C22⋊C42C2semidirect
15. #13775C2semidirect
18. C22×#117C22semidirect
24. C2×#386C4semidirect
31. C2×#385C22semidirect
35. C2×#381C22semidirect
36. C2×#381C22semidirect
37. C2×#381C22semidirect
40. C2×#380C22semidirect
48. C2×C4×C22⋊C4C22semidirect
49. C2×C4×C22⋊C4C22semidirect
52. #1443C22semidirect
53. #1443C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1439C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
62. #1437C22semidirect
63. #1437C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1436C22semidirect
67. #1436C22semidirect
68. #1434C22semidirect
69. #1434C22semidirect
74. C22⋊#95C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
91. C24×C4C2×C4semidirect
115. C22×C22⋊C4C2×C4semidirect
141. #386C2×C4semidirect
142. #386C2×C4semidirect
143. #386C2×C4semidirect
144. #386C2×C4semidirect
163. C2×#95C2×C4semidirect
164. C2×#95C2×C4semidirect
444. C24#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23082
C22×#3862
C2×#22802
#146812
#143752
#143732
#143382
#143352
#140642
#139842
#138772
#138742
C22⋊C422
#137752