Finite Group Databasebeta

← #556134

Subgroups — #556134

Order 512.

3670 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2311C211yesmaximal, characteristic
2C2×#2311C211yesmaximal, characteristic
3C2×#2297C211yesmaximal, characteristic
4#14697C212yesmaximal, complemented
5#14513C212yesmaximal, complemented
6#14501C212yesmaximal, complemented
7#14467C212yesmaximal, complemented
8#14438C214yesmaximal, complemented
9#14407C214yesmaximal, complemented
10#14401C212yesmaximal, complemented
11#14264C212yesmaximal, complemented
12#14130C212yesmaximal, complemented
13#14129C212yesmaximal, complemented
14#13951C212yesmaximal, complemented
15#13907C212yesmaximal, complemented
16C23×#41C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#2311—28no—
24#2311C4116yescomplemented
25#2297—28no—
26C2×#391C2211yescharacteristic
27C2×#391C2212yes—
28C2×#391C2211yescharacteristic
29C2×#391C2212yes—
30C2×#390C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2211yescharacteristic
33C2×#390C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#385C2214yes—
45C2×#385C2214yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2214yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53#1444C2214yes—
54#1444C2214yes—
55#1442C2214yes—
56#1442C2214yes—
57#1441C2214yes—
58#1441C2214yes—
59#1439C2214yes—
60#1439C2214yes—
61#1439C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yes—
65#1436C2214yes—
66#1436C2214yes—
67#1436C2214yes—
68#1436C2214yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2214yes—
74#1434C2214yes—
75C22⋊#95C2214yes—
76C22⋊#95C2214yes—
77C22⋊#95C2214yes—
78C22×#41—42no—
79C22×#41—42no—
80C22×#41—42no—
81C22×#41—42no—
82C22×#41C2×C418yes—
83C22×#41D418yes—
84C22×#41Q818yes—
85C23×Q8C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2312yes—
94C24×C4C2312yes—
95C2×#117—24no—
96C2×#117—24no—
97C2×#117—42no—
98C2×#117—42no—
99C2×#117—42no—
100C2×#117—42no—
101C2×#117—42no—
102C2×#117—42no—
103C2×#117C2×C418yescomplemented
104C22×C4⋊C4—24no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4C2×C418yescomplemented
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C42—24no—
134C22×C42—42no—
135C22×C42—42no—
136C22×C42C2312yes—
137C22×C42C2312yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2312yes—
141C22×C42C2312yes—
142#391—28no—
143#391—24no—
144#391—24no—
145#391C2×C4116yescomplemented
146#390—28no—
147#390—24no—
148#390—24no—
149#390C2×C4116yes—
150#389—44no—
151#389—44no—
152#389—44no—
153#389—44no—
154#386—28no—
155#386—28no—
156#386—28no—
157#386—28no—
158#386C2×C4116yescomplemented
159#386C2×C4116yescomplemented
160#385—48no—
161#385—48no—
162#380—28no—
163#380—28no—
164#380—48no—
165#380C2×C4116yescomplemented
166#380C2×C4116yescomplemented
167C4×C22⋊C4—28no—
168C4×C22⋊C4—28no—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C25C2411yescharacteristic
190C25C2411yescharacteristic
191C25C2411yescharacteristic
192C2×#41—416no—
193C2×#41—416no—
194C2×#41—416no—
195C2×#41—416no—
196C2×#41—416no—
197C2×#41—416no—
198C2×#41C4⋊C4164yescomplemented
199C22×Q8—41no—
200C22×Q8—41no—
201C22×Q8—41no—
202C22×Q8—41no—
203C22×Q8C22×C414yes—
204C22×Q8C2×D414yes—
205C22×Q8C2×Q814yes—
206C22×D4—41no—
207C22×D4—41no—
208C22×D4—41no—
209C22×D4—41no—
210C22×D4—41no—
211C22×D4—41no—
212C22×D4—41no—
213C22×D4—41no—
214C22×D4—41no—
215C22×D4—41no—
216C22×D4—41no—
217C22×D4—41no—
218C22×D4C22×C414yes—
219C22×D4C22×C414yes—
220C22×D4C22×C414yes—
221C22×D4C2×D414yes—
222C22×D4C2×D414yes—
223C22×D4C2×D414yes—
224C22×D4C2×Q814yes—
225C22×D4C2×Q814yes—
226C22×D4C2×Q814yes—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
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—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4C22×C414yes—
256C23×C4C22×C414yes—
257C23×C4C22×C414yes—
258C23×C4C22×C418yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4C2×Q814yes—
263C23×C4C2×Q814yes—
264C23×C4C2×Q814yes—
265C23×C4C2412yes—
266C23×C4C2414yes—
267C23×C4C2412yes—
268C23×C4C2414yes—
269C23×C4C2414yes—
270C23×C4C2414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277#117—416no—
278#117—416no—
279#117—416no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—416no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—416no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4C22×C418yes—
316C2×C4⋊C4C22×C418yes—
317C2×C4⋊C4C22×C418yes—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
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—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4C22×C418yes—
349C2×C22⋊C4C22×C4116yes—
350C2×C22⋊C4C22×C4116yes—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—42no—
361C2×C42—42no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42—41no—
365C2×C42—41no—
366C2×C42—41no—
367C2×C42—41no—
368C2×C42—416no—
369C2×C42C22×C418yes—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95C22×C4116yes—
389#95C22×C4116yes—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24C23×C412yes—
415C24C23×C412yes—
416C24C23×C412yes—
417C24C22×D412yes—
418C24C22×D412yes—
419C24C22×D412yes—
420C24C22×Q812yes—
421C24C22×Q812yes—
422C24C22×Q812yes—
423C24C2511yescharacteristic
424#41—4128no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8C2×C4⋊C4116yes—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4C2×C4⋊C4116yes—
451C2×D4C2×C4⋊C4116yes—
452C2×D4C2×C4⋊C4116yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—416no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—88no—
546C22×C4—88no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4—88no—
550C22×C4—84no—
551C22×C4—84no—
552C22×C4C2×C4⋊C4116yes—
553C22×C4C2×C4⋊C4116yes—
554C22×C4C2×C4⋊C4116yes—
555C22×C4C23×C418yes—
556C22×C4C23×C418yes—
557C22×C4C23×C412yes—
558C22×C4C23×C412yes—
559C22×C4C23×C412yes—
560C22×C4C23×C412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×Q812yes—
566C22×C4C22×Q812yes—
567C22×C4C22×Q812yes—
568C22×C4C22×Q812yes—
569C22×C4H(5,𝔽2)14yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C42−1+414yes—
575C4⋊C4—216no—
576C4⋊C4—216no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—88no—
584C4⋊C4—88no—
585C4⋊C4—88no—
586C4⋊C4—88no—
587C22⋊C4—416no—
588C22⋊C4—416no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—88no—
597C22⋊C4—88no—
598C42—48no—
599C42—44no—
600C42—44no—
601C42—48no—
602C42—48no—
603C42—48no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23C22×C4⋊C414yes—
671C23C22×C4⋊C414yes—
672C23C22×C4⋊C414yes—
673C23C24×C411yescharacteristic
674C23C23×D411yescharacteristic
675C23C23×Q811yescharacteristic
676C23C2×H(5,𝔽2)11yescharacteristic
677C23C2×H(5,𝔽2)11yescharacteristic
678C23C2×H(5,𝔽2)11yescharacteristic
679C23C2×H(5,𝔽2)11yescharacteristic
680C23C2×H(5,𝔽2)12yes—
681C23C2×2−1+412yes—
682C23#58512yes—
683C23#58512yes—
684Q8—416no—
685D4—416no—
686D4—416no—
687D4—416no—
688C2×C4—22no—
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—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—232no—
707C2×C4—232no—
708C2×C4—232no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—432no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—816no—
767C2×C4—816no—
768C2×C4C22×C4⋊C414yes—
769C2×C4C22×C4⋊C414yes—
770C2×C4C22×C4⋊C414yes—
771C2×C4C22×C4⋊C414yes—
772C2×C4#51814yes—
773C2×C4#51814yes—
774C2×C4#53414yes—
775C2×C4#53414yes—
776C2×C4#54314yes—
777C2×C4#54314yes—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—28no—
782C22—28no—
783C22—28no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22C23×C4⋊C411yescharacteristic
812C22C2×#51811yescharacteristic
813C22C2×#51811yescharacteristic
814C22C4×H(5,𝔽2)12yes—
815C22C4×2−1+412yes—
816C22C2×#53411yescharacteristic
817C22C2×#53411yescharacteristic
818C22C2×#54311yescharacteristic
819C22C2×#54311yescharacteristic
820C22#348812yes—
821C22#348912yes—
822C22#350312yes—
823C22#350412yes—
824C22#353612yes—
825C22#353912yes—
826C22#354112yes—
827C22#354212yes—
828C22#354612yes—
829C22#354712yes—
830C22#354911yescharacteristic
831C22#355011yescharacteristic
832C22#355111yescharacteristic
833C22#355111yescharacteristic
834C4—24no—
835C4—24no—
836C4—24no—
837C4—48no—
838C4—48no—
839C4—44no—
840C4—44no—
841C4—82no—
842C4—84no—
843C4—82no—
844C4—84no—
845C4#231518yes—
846C2—44no—
847C2—44no—
848C2—44no—
849C2C2×#231511yescharacteristic
850C2#3425012yes—
851C2#3441012yes—
852C2#3441311yescharacteristic
853C2#3441511yescharacteristic
854C2#3726812yes—
855C2#3727311yescharacteristic
856C2#3730611yescharacteristic
857C2#3731012yes—
858C2#3737611yescharacteristic
859C2#3742511yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #14697C2semidirect
5. #14513C2semidirect
6. #14501C2semidirect
7. #14467C2semidirect
8. #14438C2semidirect
9. #14407C2semidirect
10. #14401C2semidirect
11. #14264C2semidirect
12. #14130C2semidirect
13. #14129C2semidirect
14. #13951C2semidirect
15. #13907C2semidirect
24. #2311C4semidirect
103. C2×#117C2×C4semidirect
109. C22×C4⋊C4C2×C4semidirect
145. #391C2×C4semidirect
158. #386C2×C4semidirect
159. #386C2×C4semidirect
165. #380C2×C4semidirect
166. #380C2×C4semidirect
198. C2×#41C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23112
C2×#22972
#146972
#145132
#145012
#144672
#144382
#144072
#144012
#142642
#141302
#141292
#139512
#139072