Finite Group Databasebeta

← #364449

Subgroups — #364449

Order 512.

2784 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#451C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic
3C22×#391C211yesmaximal, characteristic
4C2×#1878C212yesmaximal, complemented
5C2×#1872C211yesmaximal, characteristic
6C2×#1787C211yesmaximal, characteristic
7#11067C212yesmaximal, complemented
8#11024C212yesmaximal, complemented
9#10932C212yesmaximal, complemented
10#10730C211yesmaximal, characteristic
11#10712C211yesmaximal, characteristic
12C24×Q8C2211yescharacteristic
13C23×Q16C2212yes—
14C22×C22⋊Q8C2211yescharacteristic
15C22×C4×Q8C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C2×#451—24no—
19C2×#451—24no—
20C2×#451C418yescomplemented
21C22×#103C2212yes—
22C22×#103C2212yes—
23C22×#103C2212yes—
24C22×#103C2212yes—
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C4×C22⋊Q8—24no—
28C4×C22⋊Q8—24no—
29C2×#391—21no—
30C2×#391—21no—
31C2×#391—28no—
32C2×#391C2211yescharacteristic
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#389C2211yescharacteristic
36C2×#387—21no—
37C2×#385—21no—
38C2×#380C2211yescharacteristic
39C2×C4×C4⋊C4—21no—
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4—21no—
42C22×#95—21no—
43C22×#95—21no—
44#1878—28no—
45#1872—24no—
46#1787—24no—
47C2×#340C2212yes—
48C2×#340C2212yes—
49C2×#340C2212yes—
50C2×#336C2212yes—
51C2×#336C2212yes—
52C23×Q8—24no—
53C23×Q8—24no—
54C23×Q8—21no—
55C23×Q8—22no—
56C23×Q8—22no—
57C23×Q8—22no—
58C23×Q8—22no—
59C23×Q8—22no—
60C23×Q8—42no—
61C23×Q8—42no—
62C23×Q8C2×C414yes—
63C23×Q8C2311yescharacteristic
64C23×Q8C2312yes—
65C24×C4—21no—
66C24×C4—21no—
67C24×C4D411yescharacteristic
68C24×C4D411yescharacteristic
69C24×C4C2311yescharacteristic
70C22×Q16—24no—
71C22×Q16—24no—
72C22×Q16—24no—
73C22×Q16—24no—
74C22×Q16—42no—
75C22×Q16—42no—
76C22×Q16C2×C418yescomplemented
77C23×C8C2312yes—
78C23×C8C2312yes—
79C2×C22⋊Q8—22no—
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8C2×C414yes—
83C2×C22⋊Q8D414yes—
84C2×C22⋊Q8D414yes—
85C2×C4×Q8—22no—
86C2×C4×Q8—22no—
87C2×C4×Q8—24no—
88C2×C4×Q8—42no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—22no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2311yescharacteristic
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—21no—
106C22×C42—21no—
107C22×C42—24no—
108C22×C42—42no—
109C22×C42D411yescharacteristic
110C22×C42D411yescharacteristic
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113#451—232no—
114C2×#103—24no—
115C2×#103—24no—
116C2×#103—24no—
117C2×#103—24no—
118C2×#103—24no—
119C2×#103—24no—
120C2×#103—24no—
121C2×#103—24no—
122C2×#103—42no—
123C2×#103—42no—
124C2×#103—42no—
125C2×#103C2×C418yescomplemented
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8C2×C414yes—
132#391—28no—
133#391—28no—
134#391—24no—
135#391—22no—
136#391—24no—
137#391—22no—
138#391—24no—
139#391D418yes—
140#389—22no—
141#389—22no—
142#387—28no—
143#385—28no—
144#380—22no—
145#380D414yes—
146C4×C4⋊C4—28no—
147C4×C4⋊C4—22no—
148C4×C4⋊C4—22no—
149C4×C22⋊C4—28no—
150C2×#95—28no—
151C2×#95—28no—
152C2×#95—22no—
153C2×#95—22no—
154C2×#95—22no—
155C2×#95—22no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161#340—24no—
162#340—24no—
163#340—42no—
164#336—24no—
165#336—42no—
166C25C2×D411yescharacteristic
167C22×Q8—24no—
168C22×Q8—216no—
169C22×Q8—24no—
170C22×Q8—216no—
171C22×Q8—24no—
172C22×Q8—21no—
173C22×Q8—22no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—22no—
177C22×Q8—22no—
178C22×Q8—28no—
179C22×Q8—28no—
180C22×Q8—22no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—22no—
184C22×Q8—22no—
185C22×Q8—22no—
186C22×Q8—22no—
187C22×Q8—22no—
188C22×Q8—22no—
189C22×Q8—22no—
190C22×Q8—22no—
191C22×Q8—22no—
192C22×Q8—48no—
193C22×Q8—48no—
194C22×Q8—48no—
195C22×Q8—48no—
196C22×Q8—48no—
197C22×Q8—48no—
198C22×Q8—48no—
199C22×Q8—48no—
200C22×Q8—48no—
201C22×Q8—42no—
202C22×Q8—42no—
203C22×Q8—48no—
204C22×Q8—42no—
205C22×Q8—42no—
206C22×Q8—44no—
207C22×Q8—44no—
208C22×Q8C22×C412yes—
209C22×Q8C22×C414yes—
210C22×Q8C2×D412yes—
211C22×Q8C2×D412yes—
212C22×Q8C2×D414yes—
213C22×Q8#4114yes—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—22no—
237C23×C4—41no—
238C23×C4—41no—
239C23×C4—41no—
240C23×C4—41no—
241C23×C4—42no—
242C23×C4—42no—
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×C4Q1614yescomplemented
252C23×C4C22×C412yes—
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D412yes—
260C23×C4C2×D411yescharacteristic
261C23×C4#4112yes—
262C23×C4#4112yes—
263C23×C4C2411yescharacteristic
264C2×Q16—216no—
265C2×Q16—216no—
266C2×Q16—48no—
267C2×Q16—48no—
268C2×Q16—48no—
269C2×Q16—48no—
270C2×Q16—48no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8C22×C414yes—
285C22⋊Q8—28no—
286C22⋊Q8—28no—
287C22⋊Q8—28no—
288C22⋊Q8C22⋊C4116yes—
289C4×Q8—48no—
290C4×Q8—48no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—48no—
312C2×C4⋊C4—48no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4C22×C412yes—
320C2×C4⋊C4C2×D414yes—
321C2×C4⋊C4C2×D412yes—
322C2×C4⋊C4C2×D412yes—
323C2×C4⋊C4C2×D412yes—
324C2×C4⋊C4C2×D412yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—22no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—48no—
345C2×C42—48no—
346C2×C42—41no—
347C2×C42—41no—
348C2×C42—42no—
349C2×C42—42no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42C2×D414yes—
353#103—216no—
354#103—48no—
355#103—48no—
356#103—48no—
357C22⋊C8—28no—
358C22⋊C8—44no—
359#95—28no—
360#95—28no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—28no—
366#95—28no—
367#95—24no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24C4×D412yes—
377C24#12012yes—
378C24#12112yes—
379C24C2×Q1612yes—
380C24#13512yes—
381C24#13712yes—
382C24#13712yes—
383C24C22×D411yescharacteristic
384C2×Q8—216no—
385C2×Q8—22no—
386C2×Q8—24no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—24no—
390C2×Q8—24no—
391C2×Q8—24no—
392C2×Q8—24no—
393C2×Q8—24no—
394C2×Q8—24no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—24no—
403C2×Q8—24no—
404C2×Q8—24no—
405C2×Q8—24no—
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—24no—
409C2×Q8—432no—
410C2×Q8—432no—
411C2×Q8—48no—
412C2×Q8—48no—
413C2×Q8—48no—
414C2×Q8—48no—
415C2×Q8—48no—
416C2×Q8—432no—
417C2×Q8—432no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—48no—
437C2×Q8C2×C22⋊C414yes—
438C2×Q8C4×D418yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—28no—
460C22×C4—216no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—41no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—48no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—42no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—42no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—42no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—84no—
544C22×C4—84no—
545C22×C4—84no—
546C22×C4—84no—
547C22×C4C2×C22⋊C414yes—
548C22×C4C4×D414yes—
549C22×C4C4×D412yes—
550C22×C4#12012yes—
551C22×C4#12012yes—
552C22×C4#12012yes—
553C22×C4#12114yes—
554C22×C4#12112yes—
555C22×C4#12314yes—
556C22×C4C2×Q1612yes—
557C22×C4C2×Q1612yes—
558C22×C4#13712yes—
559C22×C4#13712yes—
560C22×C4C23×C411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D412yes—
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4112yes—
567C22×C4C2×#4111yescharacteristic
568C22×C4H(5,𝔽2)12yes—
569C22×C4H(5,𝔽2)12yes—
570Q16—432no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—42no—
575C2×C8—42no—
576C2×C8—42no—
577C2×C8—42no—
578C2×C8—42no—
579C2×C8—42no—
580C2×C8—42no—
581C2×C8—42no—
582C2×C8—42no—
583C2×C8—42no—
584C2×C8—42no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—216no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4C2×C22⋊C414yes—
601C22⋊C4—216no—
602C22⋊C4—48no—
603C42—24no—
604C42—24no—
605C42—44no—
606C42—44no—
607C42—48no—
608C42—48no—
609C42—42no—
610C42—42no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
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—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23#38614yes—
640C23C4×Q1614yes—
641C23#44114yes—
642C23#45114yes—
643C23#45214yes—
644C23#46214yes—
645C23#46414yes—
646C23C2×C4×D411yescharacteristic
647C23C2×#12011yescharacteristic
648C23C2×#12011yescharacteristic
649C23C2×#12111yescharacteristic
650C23#52511yescharacteristic
651C23#53411yescharacteristic
652C23#53511yescharacteristic
653C23C22×Q1611yescharacteristic
654C23C2×#13511yescharacteristic
655C23C2×#13711yescharacteristic
656C23C2×#13711yescharacteristic
657C23C2×#13711yescharacteristic
658C23C2×#13711yescharacteristic
659C23#57511yescharacteristic
660C23#57511yescharacteristic
661Q8—28no—
662Q8—28no—
663Q8—28no—
664Q8—432no—
665Q8—44no—
666Q8—44no—
667Q8—44no—
668Q8—44no—
669Q8—44no—
670Q8—44no—
671Q8—44no—
672Q8—44no—
673Q8—44no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—28no—
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—24no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—416no—
704C2×C4—432no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—816no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—82no—
751C2×C4—82no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#38614yes—
758C2×C4#45114yescomplemented
759C2×C4C22×C22⋊C411yescharacteristic
760C2×C4C2×C4×D412yes—
761C2×C4C2×C4×D411yescharacteristic
762C2×C4#51812yes—
763C2×C4C2×#12111yescharacteristic
764C2×C4C2×#12311yescharacteristic
765C2×C4#52512yes—
766C2×C4#53812yes—
767C2×C4D4212yes—
768C2×C4D4212yes—
769C2×C4D4212yes—
770C2×C4#54612yes—
771C2×C4#54612yes—
772C2×C4#54612yes—
773C2×C4#54612yes—
774C2×C4#55112yes—
775C8—44no—
776C8—82no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22#187818yescomplemented
792C22C2×#38611yescharacteristic
793C22C4×#12011yescharacteristic
794C22#232111yescharacteristic
795C22#240311yescharacteristic
796C22#240411yescharacteristic
797C22#240811yescharacteristic
798C22#253411yescharacteristic
799C22C2×C4×Q1611yescharacteristic
800C22C2×#44111yescharacteristic
801C22C4×#13711yescharacteristic
802C22C4×#13711yescharacteristic
803C22C2×#45111yescharacteristic
804C22C2×#45111yescharacteristic
805C22C2×#45211yescharacteristic
806C22#300211yescharacteristic
807C22#300411yescharacteristic
808C22#300711yescharacteristic
809C22#300711yescharacteristic
810C22#300711yescharacteristic
811C22C2×#46211yescharacteristic
812C22C2×#46411yescharacteristic
813C22#303911yescharacteristic
814C22#304011yescharacteristic
815C22#310411yescharacteristic
816C22#310811yescharacteristic
817C22#311311yescharacteristic
818C22#311711yescharacteristic
819C22#318911yescharacteristic
820C22#319011yescharacteristic
821C22#319511yescharacteristic
822C22#319611yescharacteristic
823C22#320911yescharacteristic
824C22#321111yescharacteristic
825C22#321511yescharacteristic
826C22#321811yescharacteristic
827C4—24no—
828C4—24no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—48no—
833C4—44no—
834C4—44no—
835C4—82no—
836C4—82no—
837C4—84no—
838C4D4×C22⋊C412yes—
839C4#235812yes—
840C4#241812yes—
841C4#242412yes—
842C2—28no—
843C2#1396711yescharacteristic
844C2C2×#187811yescharacteristic
845C2#2092711yescharacteristic
846C2C4×#45111yescharacteristic
847C2#2145511yescharacteristic
848C2#2204411yescharacteristic
849C2#2205011yescharacteristic
850C2#2392111yescharacteristic
851C2#2392211yescharacteristic
852C2#2393411yescharacteristic
853C2#2393711yescharacteristic
854C2#2421211yescharacteristic
855C2#2421711yescharacteristic
856C2#2812111yescharacteristic
857C2#2812411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1878C2semidirect
7. #11067C2semidirect
8. #11024C2semidirect
9. #10932C2semidirect
20. C2×#451C4semidirect
76. C22×Q16C2×C4semidirect
125. C2×#103C2×C4semidirect
251. C23×C4Q16semidirect
758. C2×C4#451semidirect
791. C22#1878semidirect

Maximal subgroups

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

subgroupindex
C22×#4512
C2×C4×C22⋊Q82
C22×#3912
C2×#18782
C2×#18722
C2×#17872
#110672
#110242
#109322
#107302
#107122