Finite Group Databasebeta

← #357762

Subgroups — #357762

Order 512.

2990 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#410C211yesmaximal, characteristic
2C2×#2317C211yesmaximal, characteristic, complemented
3#34044C211yesmaximal, characteristic
4C2×#2311C211yesmaximal, characteristic
5C2×#1740C211yesmaximal, characteristic, complemented
6C2×#1740C211yesmaximal, characteristic, complemented
7#13795C211yesmaximal, characteristic, complemented
8#11087C218yesmaximal, complemented
9C23×#41C2211yescharacteristic
10C22×#117C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C2×#410—24no—
17C2×#410—24no—
18C2×#410C418yescomplemented
19C22×#99C2214yes—
20#2317—24no—
21#2317—24no—
22#2311—24no—
23#2311—24no—
24#2311—22no—
25#2311—21no—
26#2311—21no—
27#2310—21no—
28#2309—21no—
29#2308C2214yes—
30#2297—22no—
31#2297—22no—
32C2×#391—21no—
33C2×#390—21no—
34C2×#389—22no—
35C2×#386C2214yes—
36C2×#385C2214yes—
37C2×#384—21no—
38C2×#382—21no—
39#2280—22no—
40C2×#380—22no—
41#1740—24no—
42#1740—24no—
43C2×#342C2214yes—
44C2×#342C2214yes—
45C4⋊#95—22no—
46C4⋊#95—22no—
47C22⋊#95C2214yes—
48C22×#41—21no—
49C22×#41—22no—
50C22×#41—21no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—21no—
55C22×#41—21no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41—22no—
61C22×#41—22no—
62C22×#41C2×C414yes—
63C22×#41Q814yes—
64C23×Q8D411yescharacteristic
65C23×D4D411yescharacteristic
66C23×D4C2312yes—
67C24×C4D412yes—
68C24×C4C2312yes—
69C24×C4C2311yescharacteristic
70C2×#117—22no—
71C2×#117—22no—
72C2×#117—22no—
73C2×#117—21no—
74C2×#117—21no—
75C2×#117—21no—
76C2×#117—21no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—21no—
83C2×#117—21no—
84C2×#117—21no—
85C2×#117—21no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—22no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117C2×C414yes—
100C2×#117C2×C414yes—
101C2×#117D414yes—
102C2×#117D414yes—
103C2×#117D414yes—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—22no—
106C22×C4⋊C4—22no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—22no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4D414yes—
118C22×C4⋊C4D412yes—
119C22×C4⋊C4D411yescharacteristic
120C22×C4⋊C4D411yescharacteristic
121C22×C22⋊C4—24no—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C42—21no—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42D412yes—
131C22×C42D412yes—
132#410—232no—
133C2×#99—28no—
134C2×#99—28no—
135C2×#99C2×C4116yes—
136#391—24no—
137#391—22no—
138#391—22no—
139#391—28no—
140#390—24no—
141#390—22no—
142#390—22no—
143#390—28no—
144#389—216no—
145#386—24no—
146#386—24no—
147#386—28no—
148#386—28no—
149#386—28no—
150#385—28no—
151#385—28no—
152#384—28no—
153#382—28no—
154#381—24no—
155#380—216no—
156#380—24no—
157#380—24no—
158#379—24no—
159C4×C22⋊C4—28no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—28no—
163#342—28no—
164#342—28no—
165C25C2×D412yes—
166C25C2411yescharacteristic
167C2×#41—28no—
168C2×#41—28no—
169C2×#41—24no—
170C2×#41—24no—
171C2×#41—28no—
172C2×#41—24no—
173C2×#41—24no—
174C2×#41—28no—
175C2×#41—28no—
176C2×#41—28no—
177C2×#41—24no—
178C2×#41—28no—
179C2×#41—24no—
180C2×#41—24no—
181C2×#41—28no—
182C2×#41—24no—
183C2×#41—42no—
184C2×#41—42no—
185C2×#41—42no—
186C2×#41—42no—
187C2×#41—42no—
188C2×#41—42no—
189C2×#41—42no—
190C2×#41—42no—
191C2×#41—44no—
192C2×#41—42no—
193C2×#41—42no—
194C2×#41—44no—
195C2×#41—42no—
196C2×#41—42no—
197C2×#41—44no—
198C2×#41—44no—
199C2×#41—42no—
200C2×#41—44no—
201C2×#41—42no—
202C2×#41—44no—
203C2×#41—44no—
204C2×#41—44no—
205C2×#41—42no—
206C2×#41—42no—
207C22×Q8—22no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8C4⋊C414yescomplemented
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4C4⋊C414yescomplemented
235C22×D4C22×C414yes—
236C22×D4C2×Q814yes—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—84no—
254C23×C4C4⋊C418yescomplemented
255C23×C4C22×C412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D412yes—
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D412yes—
271C23×C4C2×Q812yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C23×C4#4112yes—
276C23×C4#4112yes—
277C23×C4#4112yes—
278#117—28no—
279#117—28no—
280#117—28no—
281#117—28no—
282#117—28no—
283#117—28no—
284#117—28no—
285#117—42no—
286#117—42no—
287#117—44no—
288#117—42no—
289#117—42no—
290#117—42no—
291#117—42no—
292#117—42no—
293#117—42no—
294#117—42no—
295#117—42no—
296#117—44no—
297#117—42no—
298#117—42no—
299#117—44no—
300#117—42no—
301#117—42no—
302#117—44no—
303#117—42no—
304#117—42no—
305#117C22⋊C4116yescomplemented
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—216no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—88no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—216no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—88no—
374C2×C22⋊C4C22×C414yes—
375C2×C22⋊C4C22×C414yes—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396#99—232no—
397#95—216no—
398#95—216no—
399#95—28no—
400#95—28no—
401#95—88no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—42no—
409C24—42no—
410C24—44no—
411C24—44no—
412C24C2×C4⋊C414yes—
413C24C23×C411yescharacteristic
414C24C22×D411yescharacteristic
415C24C22×D411yescharacteristic
416C24C22×D411yescharacteristic
417C24C22×D411yescharacteristic
418C24C22×D411yescharacteristic
419C24C22×D411yescharacteristic
420C24C22×D411yescharacteristic
421C24C22×Q811yescharacteristic
422C24C2×#4111yescharacteristic
423C24C2×#4111yescharacteristic
424C24C2×#4111yescharacteristic
425C24C2×#4111yescharacteristic
426C24C2×#4111yescharacteristic
427C24C2×#4111yescharacteristic
428#41—48no—
429#41—48no—
430#41—48no—
431#41—48no—
432#41—48no—
433#41—48no—
434#41—48no—
435#41—48no—
436#41—48no—
437#41—48no—
438#41—48no—
439#41—48no—
440#41—48no—
441#41—48no—
442#41—48no—
443#41—48no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—42no—
449C2×Q8—42no—
450C2×Q8—44no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—44no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—24no—
469C2×D4—24no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—44no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—216no—
502C22×C4—28no—
503C22×C4—216no—
504C22×C4—28no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—48no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—84no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4—84no—
550C22×C4C2×C22⋊C414yes—
551C22×C4C2×C4⋊C414yes—
552C22×C4C2×C4⋊C412yes—
553C22×C4C2×C4⋊C412yes—
554C22×C4#11714yes—
555C22×C4C4×D412yes—
556C22×C4C4×D412yes—
557C22×C4C4×D414yes—
558C22×C4C4×D412yes—
559C22×C4C4×D412yes—
560C22×C4C4×D414yes—
561C22×C4#12012yes—
562C22×C4#12012yes—
563C22×C4#12011yescharacteristic
564C22×C4#12011yescharacteristic
565C22×C4#12011yescharacteristic
566C22×C4#12011yescharacteristic
567C22×C4#12012yes—
568C22×C4#12012yes—
569C22×C4#12112yes—
570C22×C4#12112yes—
571C22×C4#12112yes—
572C22×C4#12112yes—
573C22×C4#12112yes—
574C22×C4#12112yes—
575C22×C4#12114yes—
576C22×C4#12112yes—
577C22×C4#12112yes—
578C22×C4#12112yes—
579C22×C4#12112yes—
580C22×C4#12112yes—
581C22×C4#12112yes—
582C22×C4#12114yes—
583C22×C4C22⋊Q814yes—
584C22×C4C22⋊Q814yes—
585C22×C4C22⋊Q812yes—
586C22×C4C22⋊Q812yes—
587C22×C4C22⋊Q814yes—
588C22×C4C22⋊Q812yes—
589C22×C4C22⋊Q812yes—
590C22×C4C22⋊Q814yes—
591C22×C4#12312yes—
592C22×C4#12312yes—
593C22×C4#12312yes—
594C22×C4#12312yes—
595C22×C4#12314yes—
596C22×C4#12312yes—
597C22×C4#12312yes—
598C22×C4#12314yes—
599C22×C4#12412yes—
600C22×C4#12412yes—
601C22×C4#12414yes—
602C22×C4#12414yes—
603C22×C4#12614yes—
604C22×C4#12614yes—
605C22×C4#12712yes—
606C22×C4#12712yes—
607C4⋊C4—216no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—816no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—88no—
641C22⋊C4—88no—
642C22⋊C4—816no—
643C22⋊C4C2×C22⋊C418yes—
644C42—216no—
645C42—48no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—48no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—48no—
677C23—44no—
678C23—44no—
679C23—48no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—44no—
685C23—44no—
686C23—84no—
687C23—82no—
688C23—82no—
689C23—84no—
690C23C22×C22⋊C411yescharacteristic
691C23C22×C4⋊C411yescharacteristic
692C23C2×#11711yescharacteristic
693C23C2×C4×D411yescharacteristic
694C23C2×C4×D411yescharacteristic
695C23C2×C4×D411yescharacteristic
696C23C2×C4×D411yescharacteristic
697C23C2×#12011yescharacteristic
698C23C2×#12011yescharacteristic
699C23C2×#12011yescharacteristic
700C23C2×#12111yescharacteristic
701C23C2×#12111yescharacteristic
702C23C2×#12111yescharacteristic
703C23C2×#12111yescharacteristic
704C23C2×#12111yescharacteristic
705C23C2×#12111yescharacteristic
706C23C2×#12111yescharacteristic
707C23C2×#12111yescharacteristic
708C23C2×C22⋊Q811yescharacteristic
709C23C2×C22⋊Q811yescharacteristic
710C23C2×C22⋊Q811yescharacteristic
711C23C2×C22⋊Q811yescharacteristic
712C23C2×C22⋊Q811yescharacteristic
713C23C2×C22⋊Q811yescharacteristic
714C23C2×#12311yescharacteristic
715C23C2×#12311yescharacteristic
716C23C2×#12311yescharacteristic
717C23C2×#12311yescharacteristic
718C23C2×#12311yescharacteristic
719C23C2×#12411yescharacteristic
720C23C2×#12411yescharacteristic
721C23C2×#12411yescharacteristic
722C23C2×#12611yescharacteristic
723C23C2×#12611yescharacteristic
724C23C2×#12711yescharacteristic
725Q8—48no—
726Q8—48no—
727D4—44no—
728D4—44no—
729D4—44no—
730D4—44no—
731D4—44no—
732D4—44no—
733D4—44no—
734D4—44no—
735D4—48no—
736D4—48no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—28no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—416no—
750C2×C4—416no—
751C2×C4—44no—
752C2×C4—48no—
753C2×C4—44no—
754C2×C4—48no—
755C2×C4—44no—
756C2×C4—48no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—48no—
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—82no—
771C2×C4—82no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—84no—
782C2×C4#38014yes—
783C2×C4#38014yes—
784C2×C4#38514yes—
785C2×C4#38512yes—
786C2×C4#38512yes—
787C2×C4#38514yes—
788C2×C4#38512yes—
789C2×C4#38512yes—
790C2×C4#38614yes—
791C2×C4#38614yes—
792C2×C4#38814yes—
793C2×C4#38814yes—
794C2×C4#38814yes—
795C2×C4#38814yes—
796C2×C4#39014yes—
797C2×C4#39014yes—
798C2×C4#39212yes—
799C2×C4#39212yes—
800C2×C4#39212yes—
801C2×C4#39212yes—
802C2×C4#39314yes—
803C2×C4#39314yes—
804C2×C4#39412yes—
805C2×C4#39414yes—
806C2×C4#39412yes—
807C2×C4#39414yes—
808C2×C4#39412yes—
809C2×C4#39412yes—
810C2×C4#39614yes—
811C2×C4#39614yes—
812C2×C4#39614yes—
813C2×C4#39614yes—
814C2×C4#39714yes—
815C2×C4#39714yes—
816C2×C4#39914yes—
817C2×C4#39914yes—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—48no—
859C22—44no—
860C22—48no—
861C22—84no—
862C22—84no—
863C22—84no—
864C22—82no—
865C22—82no—
866C22—84no—
867C22C2×#38011yescharacteristic
868C22C2×#38511yescharacteristic
869C22C2×#38511yescharacteristic
870C22C2×#38611yescharacteristic
871C22C2×#38811yescharacteristic
872C22C2×#38811yescharacteristic
873C22C2×#39011yescharacteristic
874C22C2×#39211yescharacteristic
875C22C2×#39311yescharacteristic
876C22C2×#39411yescharacteristic
877C22C2×#39411yescharacteristic
878C22C2×#39611yescharacteristic
879C22C2×#39611yescharacteristic
880C22C2×#39711yescharacteristic
881C22C2×#39911yescharacteristic
882C22#302712yes—
883C22#302812yes—
884C4—48no—
885C4—44no—
886C4—84no—
887C4—84no—
888C4—84no—
889C4—82no—
890C4—82no—
891C4—84no—
892C4#143914yes—
893C4#143914yes—
894C4#143914yes—
895C4#143914yes—
896C2—21no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—84no—
909C2C2×#143911yescharacteristic
910C2#2089012yes—
911C2#2344511yescharacteristic
912C2#2344611yescharacteristic
913C2#2351612yes—
subgroupG/H
center, socleC23C2×#120
commutatorC24C23×C4
Frattini, cosocleC25C24
prime radicalC23×#41C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2317C2semidirect
5. C2×#1740C2semidirect
6. C2×#1740C2semidirect
7. #13795C2semidirect
8. #11087C2semidirect
18. C2×#410C4semidirect
214. C22×Q8C4⋊C4semidirect
234. C22×D4C4⋊C4semidirect
254. C23×C4C4⋊C4semidirect
305. #117C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4102
C2×#23172
#340442
C2×#23112
C2×#17402
#137952
#110872