Finite Group Databasebeta

← #515289

Subgroups — #515289

Order 512.

7698 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C22×#520C211yesmaximal, characteristic, complemented
3C2×#2311C211yesmaximal, characteristic, complemented
4C2×#2280C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic, complemented
6#13970C214yesmaximal, complemented
7#13969C214yesmaximal, complemented
8#13968C214yesmaximal, complemented
9#13967C214yesmaximal, complemented
10#13872C214yesmaximal, complemented
11#13871C214yesmaximal, complemented
12#13795C211yesmaximal, characteristic, complemented
13#13795C211yesmaximal, characteristic, complemented
14C23×#41C2211yescharacteristic
15C25×C4C2211yescharacteristic
16C2×#525—28no—
17C2×#525—28no—
18C2×#525C4116yescomplemented
19C22×#123C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×#121C2212yes—
22C22×#120C2212yes—
23C2×#520—28no—
24C2×#520—28no—
25C2×#520—28no—
26C22×C4×Q8C2212yescomplemented
27C22×C4×D4C2214yes—
28C22×C4×D4C2214yes—
29C22×C4×D4C2212yescomplemented
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2212yescomplemented
34C23×C4⋊C4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C4⋊C4C2212yescomplemented
37C23×C22⋊C4C2212yes—
38#2311—28no—
39C2×#391C2212yescomplemented
40C2×#390C2212yescomplemented
41C2×#386C2214yes—
42C2×#386C2218yes—
43#2280—28no—
44C2×#381C2212yes—
45C2×#380—28no—
46C2×#380C2212yes—
47C2×#380C2214yes—
48C2×#380C2212yes—
49C2×#380C2214yes—
50C2×#380C2214yescomplemented
51C2×#379C2212yes—
52C2×C4×C22⋊C4C2214yes—
53C22×#95C2212yes—
54#1441C2218yescomplemented
55#1440C2218yescomplemented
56#1439C2218yes—
57#1438C2218yes—
58#1437C2218yes—
59#1436C2218yescomplemented
60C4⋊#95C2212yescomplemented
61C4⋊#95C2214yescomplemented
62C4⋊#95C2212yescomplemented
63C4⋊#95C2214yescomplemented
64C4⋊#95C2214yescomplemented
65C22⋊#95C2214yes—
66C22⋊#95C2214yes—
67C22⋊#95C2218yescomplemented
68C26C2311yescharacteristic
69C22×#41—24no—
70C22×#41—24no—
71C22×#41—24no—
72C22×#41—24no—
73C22×#41C2×C418yes—
74C22×#41D418yes—
75C22×#41D418yes—
76C23×Q8C2311yescharacteristic
77C23×D4C2314yes—
78C23×D4C2312yes—
79C23×D4C2311yescharacteristic
80C24×C4—24no—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4C2×C418yescomplemented
87C24×C4C2312yes—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2314yes—
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95#525—2128no—
96C2×#123—28no—
97C2×#123—28no—
98C2×#123C2×C4116yescomplemented
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8C2×C4116yescomplemented
102C2×#121—28no—
103C2×#121—28no—
104C2×#121C2×C4116yescomplemented
105C2×#120—28no—
106C2×#120—28no—
107C2×#120C2×C4116yescomplemented
108#520—2128no—
109C2×C4×Q8—28no—
110C2×C4×Q8—28no—
111C2×C4×Q8—28no—
112C2×C4×D4—216no—
113C2×C4×D4—28no—
114C2×C4×D4—216no—
115C2×C4×D4—216no—
116C2×C4×D4—216no—
117C2×C4×D4—28no—
118C2×C4×D4—216no—
119C2×C4×D4—28no—
120C2×C4×D4C2×C4132yescomplemented
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117—28no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117—28no—
130C2×#117—28no—
131C2×#117C2×C418yescomplemented
132C2×#117D418yescomplemented
133C22×C4⋊C4—24no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—28no—
136C22×C4⋊C4—28no—
137C22×C4⋊C4—28no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4D418yescomplemented
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4—28no—
153C22×C22⋊C4—48no—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2318yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2318yes—
164C22×C42C2312yes—
165C22×C42C2314yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168#391—28no—
169#390—28no—
170#386—216no—
171#386—416no—
172#381—28no—
173#380—216no—
174#380—216no—
175#380—216no—
176#380—28no—
177#380—28no—
178#379—28no—
179C4×C22⋊C4—216no—
180C2×#95—28no—
181C2×#95C2314yes—
182C2×#95C2318yes—
183C2×#95C2314yes—
184C2×#95C2318yes—
185C2×#95C2318yes—
186C2×#95C2318yes—
187C2×#95C2318yes—
188C2×#95C2318yes—
189C25—22no—
190C25—22no—
191C25—24no—
192C25—24no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—42no—
198C25—42no—
199C25C22×C414yes—
200C25C2412yes—
201C25C2412yes—
202C25C2411yescharacteristic
203C2×#41—232no—
204C2×#41—232no—
205C2×#41—232no—
206C2×#41—232no—
207C2×#41—232no—
208C2×#41—232no—
209C2×#41C22⋊C4164yescomplemented
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8C22×C414yes—
215C22×Q8C2×D414yes—
216C22×Q8C2×D414yes—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—44no—
230C22×D4—44no—
231C22×D4C22×C4116yes—
232C22×D4C22×C418yes—
233C22×D4C22×C414yes—
234C22×D4C2×D418yes—
235C22×D4C2×D418yes—
236C22×D4C2×D414yes—
237C22×D4C2×D414yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—28no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—232no—
252C23×C4—232no—
253C23×C4—232no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—28no—
267C23×C4—28no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—48no—
276C23×C4—48no—
277C23×C4—416no—
278C23×C4—416no—
279C23×C4—416no—
280C23×C4—416no—
281C23×C4C22×C418yes—
282C23×C4C22×C418yes—
283C23×C4C22×C414yes—
284C23×C4C22×C418yes—
285C23×C4C22×C414yes—
286C23×C4C2×D418yes—
287C23×C4C2×D418yes—
288C23×C4C2×D418yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4#4114yes—
294C23×C4#4114yes—
295C23×C4C2414yes—
296C23×C4C2414yes—
297C23×C4C2414yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2414yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305#123—264no—
306C22⋊Q8—264no—
307#121—264no—
308#120—264no—
309C4×Q8—264no—
310C4×D4—2128no—
311C4×D4—264no—
312C4×D4—2128no—
313#117—264no—
314#117—232no—
315#117—232no—
316#117—416no—
317C2×C4⋊C4—264no—
318C2×C4⋊C4—232no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4C22×C418yes—
345C2×C4⋊C4C22×C4116yes—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D418yes—
348C2×C4⋊C4C2×D418yes—
349C2×C4⋊C4C2×D414yes—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—216no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—216no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—216no—
371C2×C22⋊C4—48no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—432no—
375C2×C22⋊C4—48no—
376C2×C22⋊C4—48no—
377C2×C22⋊C4C22×C418yes—
378C2×C22⋊C4C22×C4116yes—
379C2×C22⋊C4C22×C4116yes—
380C2×C22⋊C4C2×D418yes—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—28no—
384C2×C42—28no—
385C2×C42—28no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42C22×C418yes—
392C2×C42C2×D418yes—
393#95—216no—
394#95—28no—
395#95—28no—
396#95—216no—
397#95—48no—
398#95—48no—
399#95—48no—
400#95—48no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—28no—
406C24—28no—
407C24—216no—
408C24—28no—
409C24—216no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—24no—
428C24—22no—
429C24—22no—
430C24—28no—
431C24—28no—
432C24—48no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—44no—
442C24—44no—
443C24—48no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24C23×C414yes—
449C24C23×C414yes—
450C24C23×C412yes—
451C24C22×D414yes—
452C24C22×D414yes—
453C24C22×D412yes—
454C24C22×D412yes—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C2×#4112yes—
458C24C2×#4112yes—
459C24H(5,𝔽2)14yes—
460C242−1+414yes—
461C24C2511yescharacteristic
462#41—2256no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8C2×C22⋊C4116yescomplemented
470C2×D4—216no—
471C2×D4—216no—
472C2×D4—216no—
473C2×D4—216no—
474C2×D4—216no—
475C2×D4—216no—
476C2×D4—232no—
477C2×D4—232no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—416no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4C2×C22⋊C4132yes—
490C2×D4C2×C22⋊C4116yescomplemented
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—216no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—28no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—28no—
527C22×C4—24no—
528C22×C4—232no—
529C22×C4—216no—
530C22×C4—216no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—216no—
534C22×C4—216no—
535C22×C4—216no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—28no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—28no—
547C22×C4—24no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
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—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—88no—
567C22×C4—88no—
568C22×C4—816no—
569C22×C4—88no—
570C22×C4—88no—
571C22×C4—816no—
572C22×C4—88no—
573C22×C4—88no—
574C22×C4C2×C22⋊C4116yes—
575C22×C4C2×C22⋊C4132yescomplemented
576C22×C4C4×D4116yes—
577C22×C4C4×D4116yes—
578C22×C4#120116yes—
579C22×C4#121116yes—
580C22×C4#121116yes—
581C22×C4#123116yes—
582C22×C4C23×C418yes—
583C22×C4C23×C414yes—
584C22×C4C23×C414yes—
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C22×D414yes—
588C22×C4C22×D418yes—
589C22×C4C22×D414yes—
590C22×C4C22×D414yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C4⋊C4—232no—
605C4⋊C4—216no—
606C4⋊C4—232no—
607C4⋊C4—28no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—28no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C22⋊C4—232no—
615C22⋊C4—216no—
616C22⋊C4—232no—
617C22⋊C4—216no—
618C22⋊C4—232no—
619C22⋊C4—416no—
620C22⋊C4—416no—
621C22⋊C4—432no—
622C22⋊C4—48no—
623C22⋊C4—816no—
624C42—232no—
625C42—216no—
626C42—216no—
627C42—48no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—232no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—28no—
651C23—24no—
652C23—24no—
653C23—28no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—28no—
663C23—28no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—28no—
670C23—28no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—432no—
676C23—432no—
677C23—416no—
678C23—416no—
679C23—416no—
680C23—416no—
681C23—432no—
682C23—432no—
683C23—416no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—44no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—44no—
709C23—42no—
710C23—416no—
711C23C22×C22⋊C418yes—
712C23C22×C22⋊C414yes—
713C23C2×C4×D414yes—
714C23C2×C4×D414yes—
715C23#52018yescomplemented
716C23C2×#12014yes—
717C23C2×#12114yes—
718C23C2×#12114yes—
719C23C2×#12314yes—
720C23C24×C411yescharacteristic
721C23C23×D411yescharacteristic
722C23C23×D411yescharacteristic
723C23C23×D411yescharacteristic
724C23C23×D411yescharacteristic
725C23C22×#4111yescharacteristic
726C23C22×#4111yescharacteristic
727C23C2×H(5,𝔽2)12yes—
728C23C2×2−1+412yes—
729C23#58512yes—
730C23#58512yes—
731Q8—232no—
732D4—264no—
733D4—232no—
734D4—464no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—264no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—416no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—48no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—816no—
787C2×C4—832no—
788C2×C4—816no—
789C2×C4#386164yescomplemented
790C2×C4C22×C22⋊C418yes—
791C2×C4C22×C22⋊C414yes—
792C2×C4C22×C22⋊C414yes—
793C2×C4C2×C4×D414yes—
794C2×C4C2×C4×D414yes—
795C2×C4C2×C4×D414yes—
796C2×C4C2×C4×D414yes—
797C2×C4C2×#12014yes—
798C2×C4C2×#12014yes—
799C2×C4C2×#12114yes—
800C2×C4C2×#12114yes—
801C2×C4C2×#12114yes—
802C2×C4C2×#12114yes—
803C2×C4C2×#12314yes—
804C2×C4C2×#12314yes—
805C22—24no—
806C22—24no—
807C22—28no—
808C22—24no—
809C22—24no—
810C22—28no—
811C22—24no—
812C22—28no—
813C22—28no—
814C22—24no—
815C22—28no—
816C22—216no—
817C22—28no—
818C22—28no—
819C22—28no—
820C22—464no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—48no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—48no—
834C22—44no—
835C22—44no—
836C22—48no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22C2×#38618yes—
843C22C23×C22⋊C411yescharacteristic
844C22C22×C4×D411yescharacteristic
845C22C22×C4×D411yescharacteristic
846C22C2×#52012yes—
847C22#342812yes—
848C22C22×#12011yescharacteristic
849C22C22×#12111yescharacteristic
850C22C22×#12111yescharacteristic
851C22C22×#12311yescharacteristic
852C22#348411yescharacteristic
853C22#348511yescharacteristic
854C22#348611yescharacteristic
855C22#348711yescharacteristic
856C22#348812yes—
857C22#348812yes—
858C22#348812yes—
859C22#348912yes—
860C22#348912yes—
861C22#348912yes—
862C22#349212yes—
863C22#349312yes—
864C22#349412yes—
865C22#349512yes—
866C4—28no—
867C4—44no—
868C4—48no—
869C4—48no—
870C4—44no—
871C4—44no—
872C4—84no—
873C4—84no—
874C4C2×#38618yes—
875C4C2×#38618yes—
876C2—28no—
877C2—48no—
878C2—48no—
879C2C22×#38611yescharacteristic
880C2#3417512yes—
881C2#3420011yescharacteristic
882C2#3420111yescharacteristic
883C2#3420212yes—
884C2#3551211yescharacteristic
885C2#3551612yes—
886C2#3551812yes—
887C2#3556311yescharacteristic
888C2#3563311yescharacteristic
889C2#3565911yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#525C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#520C2semidirect
3. C2×#2311C2semidirect
4. C2×#2280C2semidirect
5. C22×#380C2semidirect
6. #13970C2semidirect
7. #13969C2semidirect
8. #13968C2semidirect
9. #13967C2semidirect
10. #13872C2semidirect
11. #13871C2semidirect
12. #13795C2semidirect
13. #13795C2semidirect
18. C2×#525C4semidirect
26. C22×C4×Q8C22semidirect
29. C22×C4×D4C22semidirect
33. C22×#117C22semidirect
36. C23×C4⋊C4C22semidirect
39. C2×#391C22semidirect
40. C2×#390C22semidirect
50. C2×#380C22semidirect
54. #1441C22semidirect
55. #1440C22semidirect
59. #1436C22semidirect
60. C4⋊#95C22semidirect
61. C4⋊#95C22semidirect
62. C4⋊#95C22semidirect
63. C4⋊#95C22semidirect
64. C4⋊#95C22semidirect
67. C22⋊#95C22semidirect
86. C24×C4C2×C4semidirect
98. C2×#123C2×C4semidirect
101. C2×C22⋊Q8C2×C4semidirect
104. C2×#121C2×C4semidirect
107. C2×#120C2×C4semidirect
120. C2×C4×D4C2×C4semidirect
131. C2×#117C2×C4semidirect
132. C2×#117D4semidirect
141. C22×C4⋊C4D4semidirect
209. C2×#41C22⋊C4semidirect
469. C2×Q8C2×C22⋊C4semidirect
490. C2×D4C2×C22⋊C4semidirect
575. C22×C4C2×C22⋊C4semidirect
715. C23#520semidirect
789. C2×C4#386semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C22×#5202
C2×#23112
C2×#22802
C22×#3802
#139702
#139692
#139682
#139672
#138722
#138712
#137952