Finite Group Databasebeta

← #531691

Subgroups — #531691

Order 512.

5096 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2352C212yesmaximal, complemented
2C2×C4×#120C211yesmaximal, characteristic
3C22×#380C212yesmaximal, complemented
4#14410C212yesmaximal, complemented
5#14409C212yesmaximal, complemented
6#14134C212yesmaximal
7#13999C214yesmaximal, complemented
8#13980C214yesmaximal, complemented
9#13905C211yesmaximal, characteristic, complemented
10#13881C212yesmaximal, complemented
11#13875C212yesmaximal, complemented
12#13872C212yesmaximal, complemented
13#13871C211yesmaximal, characteristic, complemented
14C22⋊C4×C4⋊C4C212yesmaximal, complemented
15C22⋊C42C212yesmaximal, complemented
16C25×C4C2211yescharacteristic
17C22×#120C2211yescharacteristic
18C22×C4×D4C2212yes—
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic, complemented
21C23×C4⋊C4C2212yes—
22C23×C4⋊C4C2212yes—
23C23×C22⋊C4C2214yes—
24#2352—216no—
25C4×#120C4116yescomplemented
26C2×#388C2214yescomplemented
27C2×#387C2214yescomplemented
28C2×#386C2214yes—
29C2×#386C2214yes—
30C2×#386C2211yescharacteristic
31C2×#386C2212yes—
32C2×#385C2211yescharacteristic
33C2×#385C2212yes—
34C2×#382C2212yescomplemented
35C2×#382C2211yescharacteristic, complemented
36C2×#380—216no—
37C2×#380C2212yes—
38C2×#380C2212yes—
39C2×#380C2212yes—
40C2×#380C2214yes—
41C2×#380C2214yes—
42C2×#380C2212yes—
43C2×#380C2212yescomplemented
44C2×#380C2211yescharacteristic, complemented
45C2×#379C2211yescharacteristic
46C2×C4×C4⋊C4C2212yescomplemented
47C2×C4×C4⋊C4C2211yescharacteristic, complemented
48C2×C4×C22⋊C4C2214yes—
49C2×C4×C22⋊C4C2214yes—
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C22×#95C2214yes—
53#1445C2212yescomplemented
54#1443C2214yescomplemented
55#1442C2214yescomplemented
56#1442C2214yescomplemented
57#1441C2214yescomplemented
58#1440C2214yes—
59#1440C2212yescomplemented
60#1439C2214yescomplemented
61#1438C2212yes—
62#1438C2212yes—
63#1437C2212yes—
64#1437C2214yes—
65#1437C2212yes—
66#1437C2212yescomplemented
67#1436C2212yescomplemented
68#1436C2214yescomplemented
69#1436C2214yescomplemented
70C4⋊#95C2212yescomplemented
71C4⋊#95C2212yescomplemented
72C4⋊#95C2212yescomplemented
73#1434C2214yescomplemented
74C22⋊#95C2214yes—
75C22⋊#95C2214yes—
76C22⋊#95C2214yes—
77C22⋊#95C2214yes—
78C26C2311yescharacteristic
79C23×D4C2312yes—
80C23×D4C2311yescharacteristic
81C24×C4—28no—
82C24×C4—28no—
83C24×C4—42no—
84C24×C4—42no—
85C24×C4C2×C418yes—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2314yes—
89C24×C4C2314yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C2×#120—28no—
94C2×#120C2×C418yes—
95C2×C4×D4—28no—
96C2×C4×D4—28no—
97C2×C4×D4—42no—
98C2×C4×D4—42no—
99C2×C4×D4C2×C4116yescomplemented
100C2×C4×D4C2×C418yescomplemented
101C2×#117—28no—
102C2×#117—42no—
103C22×C4⋊C4—28no—
104C22×C4⋊C4—28no—
105C22×C4⋊C4—28no—
106C22×C4⋊C4—28no—
107C22×C4⋊C4—44no—
108C22×C4⋊C4—44no—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C22⋊C4—216no—
118C22×C22⋊C4—216no—
119C22×C22⋊C4—48no—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C42C2312yes—
136C22×C42C2312yes—
137C22×C42C2311yescharacteristic
138C22×C42C2314yes—
139C22×C42C2312yes—
140#388—216no—
141#387—216no—
142#386—216no—
143#386—48no—
144#386C2×C418yescomplemented
145#386C2×C4116yescomplemented
146#385C2×C4116yescomplemented
147#385C2×C418yescomplemented
148#382—28no—
149#382—42no—
150#380—28no—
151#380—28no—
152#380—28no—
153#380—28no—
154#380—216no—
155#380—216no—
156#380—42no—
157#380D4116yescomplemented
158#379C2×C418yes—
159C4×C4⋊C4—28no—
160C4×C4⋊C4—42no—
161C4×C22⋊C4—216no—
162C4×C22⋊C4—48no—
163C4×C22⋊C4C2×C4116yescomplemented
164C4×C22⋊C4C2×C418yescomplemented
165C2×#95—216no—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C25—24no—
188C25—24no—
189C25—24no—
190C25—24no—
191C25—41no—
192C25—41no—
193C25—42no—
194C25C22×C414yes—
195C25#4118yes—
196C25C2411yescharacteristic
197C25C2411yescharacteristic
198C25C2412yes—
199C22×D4—24no—
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—41no—
207C22×D4—41no—
208C22×D4—42no—
209C22×D4C22×C418yes—
210C22×D4C22×C414yes—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—264no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—28no—
231C23×C4—28no—
232C23×C4—28no—
233C23×C4—28no—
234C23×C4—28no—
235C23×C4—28no—
236C23×C4—28no—
237C23×C4—28no—
238C23×C4—416no—
239C23×C4—41no—
240C23×C4—41no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—416no—
244C23×C4—432no—
245C23×C4—416no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4—44no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4C22×C414yes—
253C23×C4C22×C414yes—
254C23×C4C22×C418yes—
255C23×C4C22×C414yes—
256C23×C4C22×C418yes—
257C23×C4C2×D418yes—
258C23×C4#4118yes—
259C23×C4C2414yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2414yes—
268C23×C4C2414yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271#120—232no—
272C4×D4—264no—
273C4×D4—416no—
274#117—416no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—432no—
292C2×C4⋊C4—432no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4C22×C418yes—
298C2×C4⋊C4C22×C414yes—
299C2×C4⋊C4C2×D418yes—
300C2×C4⋊C4C2×D418yes—
301C2×C22⋊C4—24no—
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—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—464no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4C22×C418yes—
335C2×C22⋊C4C22×C418yes—
336C2×C22⋊C4C22×C414yes—
337C2×C22⋊C4C22×C418yes—
338C2×C22⋊C4C22×C418yes—
339C2×C22⋊C4C22×C414yes—
340C2×C22⋊C4C22×C414yes—
341C2×C22⋊C4C22×C414yes—
342C2×C22⋊C4C2×D4116yes—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—28no—
348C2×C42—28no—
349C2×C42—42no—
350C2×C42—44no—
351C2×C42—44no—
352C2×C42—42no—
353C2×C42—44no—
354C2×C42C22×C418yes—
355C2×C42C22×C414yes—
356#95—28no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95—44no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—44no—
372#95—44no—
373#95C22×C418yes—
374#95C22×C418yes—
375#95C22×C418yes—
376#95C2×D4116yes—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—216no—
386C24—216no—
387C24—216no—
388C24—216no—
389C24—216no—
390C24—216no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—21no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—44no—
407C24—44no—
408C24—48no—
409C24—48no—
410C24—44no—
411C24—48no—
412C24—44no—
413C24—48no—
414C24—48no—
415C24—48no—
416C24—48no—
417C24—48no—
418C24—44no—
419C24—44no—
420C24#117116yescomplemented
421C24C23×C412yes—
422C24C23×C412yes—
423C24C23×C414yes—
424C24C22×D414yes—
425C24C2×#4114yes—
426C24C2×#4114yes—
427C24C2×#4114yes—
428C24C2×#4114yes—
429C24H(5,𝔽2)14yes—
430C242−1+414yes—
431C24C2511yescharacteristic
432C2×D4—28no—
433C2×D4—216no—
434C2×D4—216no—
435C2×D4—216no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—48no—
443C2×D4—48no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—216no—
449C22×C4—216no—
450C22×C4—216no—
451C22×C4—216no—
452C22×C4—216no—
453C22×C4—216no—
454C22×C4—216no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—216no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—28no—
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—44no—
516C22×C4—48no—
517C22×C4—44no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—4128no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—416no—
526C22×C4—416no—
527C22×C4—416no—
528C22×C4—416no—
529C22×C4—416no—
530C22×C4—416no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—416no—
538C22×C4—416no—
539C22×C4—88no—
540C22×C4—88no—
541C22×C4—88no—
542C22×C4—88no—
543C22×C4—88no—
544C22×C4—88no—
545C22×C4C4×D4132yes—
546C22×C4C23×C414yes—
547C22×C4C23×C412yes—
548C22×C4C23×C414yes—
549C22×C4C23×C412yes—
550C22×C4C23×C412yes—
551C22×C4C23×C412yes—
552C22×C4C23×C414yes—
553C22×C4C23×C412yes—
554C22×C4C22×D418yes—
555C22×C4C22×D418yes—
556C22×C4C22×D414yes—
557C22×C4C22×D414yes—
558C22×C4C2×#4114yes—
559C22×C4C2×#4114yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4H(5,𝔽2)12yes—
562C4⋊C4—216no—
563C4⋊C4—216no—
564C4⋊C4—216no—
565C4⋊C4—44no—
566C4⋊C4—416no—
567C4⋊C4—416no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C22⋊C4—28no—
571C22⋊C4—216no—
572C22⋊C4—216no—
573C22⋊C4—216no—
574C22⋊C4—232no—
575C22⋊C4—216no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—416no—
581C22⋊C4—416no—
582C22⋊C4—416no—
583C22⋊C4—88no—
584C22⋊C4—84no—
585C42—216no—
586C42—28no—
587C42—48no—
588C42—88no—
589C42—84no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—264no—
619C23—24no—
620C23—22no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—416no—
635C23—416no—
636C23—416no—
637C23—432no—
638C23—432no—
639C23—432no—
640C23—432no—
641C23—432no—
642C23—41no—
643C23—42no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23C2×#11714yes—
669C23C2×#11718yes—
670C23C2×C4×D418yes—
671C23#52018yes—
672C23#54618yes—
673C23#54818yes—
674C23#55218yes—
675C23#55318yes—
676C23C24×C411yescharacteristic
677C23C23×D412yes—
678C23C22×#4112yes—
679C23C22×#4112yes—
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)12yes—
683C23C2×2−1+412yes—
684C23#58512yes—
685D4—416no—
686D4—432no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—264no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—416no—
716C2×C4—432no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—41no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—416no—
745C2×C4—416no—
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—832no—
761C2×C4—832no—
762C2×C4C2×C4×D418yes—
763C2×C4C2×C4×D418yes—
764C2×C4#51814yes—
765C2×C4D4214yes—
766C2×C4#54618yes—
767C2×C4#55114yes—
768C22—28no—
769C22—28no—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—28no—
774C22—28no—
775C22—28no—
776C22—28no—
777C22—28no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—28no—
783C22—24no—
784C22—464no—
785C22—42no—
786C22—44no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22#2352116yescomplemented
802C22C22×#11711yescharacteristic
803C22C22×C4×D412yes—
804C22C2×#51811yescharacteristic
805C22C2×#52012yes—
806C22#342811yescharacteristic
807C22C2×D4211yescharacteristic
808C22C2×#54612yes—
809C22C2×#54612yes—
810C22C2×#54812yes—
811C22C2×#55111yescharacteristic
812C22C2×#55212yes—
813C22C2×#55312yes—
814C22#348812yes—
815C22#348912yes—
816C22#349412yes—
817C22#349512yes—
818C22#350512yes—
819C22#350512yes—
820C22#353612yes—
821C22#353711yescharacteristic
822C22#353811yescharacteristic
823C4—28no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4—42no—
828C4—48no—
829C4—48no—
830C4—42no—
831C4—44no—
832C4—84no—
833C4—84no—
834C4#235818yes—
835C2—216no—
836C2—44no—
837C2—82no—
838C2C2×#235212yes—
839C2C2×#235811yescharacteristic
840C2#3418511yescharacteristic
841C2#3420212yes—
842C2#3436011yescharacteristic
843C2#5899612yes—
844C2#5901312yes—
845C2#5901412yes—
846C2#5919712yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#120C22
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×#2352C2semidirect
3. C22×#380C2semidirect
4. #14410C2semidirect
5. #14409C2semidirect
7. #13999C2semidirect
8. #13980C2semidirect
9. #13905C2semidirect
10. #13881C2semidirect
11. #13875C2semidirect
12. #13872C2semidirect
13. #13871C2semidirect
14. C22⋊C4×C4⋊C4C2semidirect
15. C22⋊C42C2semidirect
20. C22×#117C22semidirect
25. C4×#120C4semidirect
26. C2×#388C22semidirect
27. C2×#387C22semidirect
34. C2×#382C22semidirect
35. C2×#382C22semidirect
43. C2×#380C22semidirect
44. C2×#380C22semidirect
46. C2×C4×C4⋊C4C22semidirect
47. C2×C4×C4⋊C4C22semidirect
53. #1445C22semidirect
54. #1443C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1441C22semidirect
59. #1440C22semidirect
60. #1439C22semidirect
66. #1437C22semidirect
67. #1436C22semidirect
68. #1436C22semidirect
69. #1436C22semidirect
70. C4⋊#95C22semidirect
71. C4⋊#95C22semidirect
72. C4⋊#95C22semidirect
73. #1434C22semidirect
99. C2×C4×D4C2×C4semidirect
100. C2×C4×D4C2×C4semidirect
144. #386C2×C4semidirect
145. #386C2×C4semidirect
146. #385C2×C4semidirect
147. #385C2×C4semidirect
157. #380D4semidirect
163. C4×C22⋊C4C2×C4semidirect
164. C4×C22⋊C4C2×C4semidirect
420. C24#117semidirect
801. C22#2352semidirect

Maximal subgroups

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

subgroupindex
C2×#23522
C2×C4×#1202
C22×#3802
#144102
#144092
#141342
#139992
#139802
#139052
#138812
#138752
#138722
#138712
C22⋊C4×C4⋊C42
C22⋊C422