Finite Group Databasebeta

← C2×#11066 #357724

Subgroups — C2×#11066 #357724

Order 512.

4182 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#102C211yesmaximal, characteristic
2C23×#102C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic, complemented
5C22×#340C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic, complemented
7C22×#336C211yesmaximal, characteristic, complemented
8#11066C218yesmaximal, direct product factor
9C24×D4C2211yescharacteristic
10C24×C8C2211yescharacteristic
11C24×C8C2211yescharacteristic
12C23×C4⋊C4—21no—
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C22⋊C4—21no—
17C23×C22⋊C4—21no—
18C23×C42C2211yescharacteristic
19C22×#102—24no—
20C22×#102—24no—
21C22×#102—24no—
22C22×#102—24no—
23C22×#102—24no—
24C22×#102C418yescomplemented
25C22×#102C2214yes—
26C22×#102C2214yes—
27C2×#390—22no—
28C2×#390—24no—
29C2×#390—24no—
30C2×#390C2214yes—
31C2×#389—22no—
32C2×#389—24no—
33C2×#389—24no—
34C2×#389C2214yescomplemented
35C22×#95—21no—
36C2×#340—24no—
37C2×#340—24no—
38C2×#340C2214yescomplemented
39C2×#340C2214yescomplemented
40C2×#336—24no—
41C2×#336C2214yescomplemented
42C26—21no—
43C23×D4—22no—
44C23×D4—22no—
45C23×D4—22no—
46C23×D4—22no—
47C23×D4—21no—
48C23×D4—22no—
49C23×D4—22no—
50C23×D4—22no—
51C23×D4—22no—
52C23×D4—22no—
53C23×D4—22no—
54C23×D4—22no—
55C23×D4C2×C414yes—
56C23×D4D414yes—
57C23×D4Q814yes—
58C23×D4C2312yes—
59C24×C4—21no—
60C24×C4—21no—
61C24×C4—21no—
62C24×C4D411yescharacteristic
63C24×C4D411yescharacteristic
64C24×C4C2311yescharacteristic
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8C2×C414yes—
78C23×C8D414yes—
79C23×C8C2312yes—
80C23×C8C2312yes—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—22no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—22no—
92C22×C4⋊C4—22no—
93C22×C4⋊C4—28no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—22no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—22no—
99C22×C4⋊C4—44no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4C2×C414yes—
102C22×C4⋊C4D414yes—
103C22×C4⋊C4D414yes—
104C22×C4⋊C4D414yes—
105C22×C4⋊C4D414yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C22⋊C4—28no—
110C22×C22⋊C4—28no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—44no—
114C22×C22⋊C4—44no—
115C22×C22⋊C4—44no—
116C22×C22⋊C4—44no—
117C22×C42—22no—
118C22×C42—22no—
119C22×C42—22no—
120C22×C42—22no—
121C22×C42—22no—
122C22×C42—22no—
123C22×C42D412yes—
124C22×C42C2312yes—
125C2×#102—232no—
126C2×#102—28no—
127C2×#102—28no—
128C2×#102—232no—
129C2×#102—28no—
130C2×#102—28no—
131C2×#102—28no—
132C2×#102C2×C4116yescomplemented
133#390—216no—
134#390—28no—
135#390—28no—
136#389—216no—
137#389—28no—
138#389—28no—
139C2×#95—28no—
140C2×#95—24no—
141#340—28no—
142#340—28no—
143#336—28no—
144C25—24no—
145C25—24no—
146C25—24no—
147C25—22no—
148C25—42no—
149C25—42no—
150C25—42no—
151C25—42no—
152C25—42no—
153C25—42no—
154C25—42no—
155C25—42no—
156C25—42no—
157C25—42no—
158C25—42no—
159C25—42no—
160C25C2×D411yescharacteristic
161C22×D4—28no—
162C22×D4—28no—
163C22×D4—28no—
164C22×D4—28no—
165C22×D4—28no—
166C22×D4—24no—
167C22×D4—28no—
168C22×D4—24no—
169C22×D4—28no—
170C22×D4—28no—
171C22×D4—28no—
172C22×D4—28no—
173C22×D4—28no—
174C22×D4—28no—
175C22×D4—28no—
176C22×D4—24no—
177C22×D4—28no—
178C22×D4—28no—
179C22×D4—22no—
180C22×D4—22no—
181C22×D4—22no—
182C22×D4—22no—
183C22×D4—22no—
184C22×D4—22no—
185C22×D4—22no—
186C22×D4—22no—
187C22×D4—22no—
188C22×D4—22no—
189C22×D4—22no—
190C22×D4—42no—
191C22×D4—44no—
192C22×D4—44no—
193C22×D4—44no—
194C22×D4—44no—
195C22×D4—42no—
196C22×D4—42no—
197C22×D4—44no—
198C22×D4—44no—
199C22×D4—44no—
200C22×D4—44no—
201C22×D4—44no—
202C22×D4—42no—
203C22×D4—44no—
204C22×D4—44no—
205C22×D4—44no—
206C22×D4C4⋊C4116yescomplemented
207C22×D4C22×C414yes—
208C22×D4C2×D414yes—
209C22×D4C2×Q814yes—
210C23×C4—24no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—24no—
215C23×C4—22no—
216C23×C4—24no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4D814yes—
247C23×C4SD1614yes—
248C23×C4C22×C412yes—
249C23×C4C2×D412yes—
250C23×C4C2×D412yes—
251C23×C4C2×D412yes—
252C23×C4C2×D412yes—
253C23×C4C2×D412yes—
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D412yes—
258C23×C4C2×Q812yes—
259C23×C4#4112yes—
260C23×C4#4112yes—
261C23×C4#4112yes—
262C23×C4#4112yes—
263C23×C4#4112yes—
264C23×C4#4112yes—
265C23×C4C2411yescharacteristic
266C22×C8—28no—
267C22×C8—28no—
268C22×C8—28no—
269C22×C8—28no—
270C22×C8—28no—
271C22×C8—28no—
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×C8—44no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8—44no—
289C22×C8—44no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8C22×C414yes—
293C22×C8C2×D414yes—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—216no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—48no—
321C2×C4⋊C4—432no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—48no—
331C2×C4⋊C4C22⋊C4116yescomplemented
332C2×C4⋊C4C22×C414yes—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4C2×D414yes—
337C2×C22⋊C4—216no—
338C2×C22⋊C4—216no—
339C2×C22⋊C4—48no—
340C2×C22⋊C4—48no—
341C2×C22⋊C4—432no—
342C2×C22⋊C4—432no—
343C2×C22⋊C4—48no—
344C2×C22⋊C4—48no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—44no—
355C2×C42—44no—
356C2×C42—44no—
357C2×C42—44no—
358#102—232no—
359#102—232no—
360#95—216no—
361C24—24no—
362C24—24no—
363C24—24no—
364C24—216no—
365C24—42no—
366C24—42no—
367C24—42no—
368C24—42no—
369C24—42no—
370C24—42no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24—42no—
377C24—48no—
378C24—48no—
379C24—48no—
380C24—48no—
381C24—48no—
382C24—48no—
383C24—48no—
384C24—48no—
385C24—48no—
386C24—48no—
387C24—48no—
388C24—48no—
389C24—48no—
390C24—48no—
391C24—48no—
392C24—48no—
393C24—48no—
394C24—48no—
395C24—84no—
396C24—84no—
397C24—84no—
398C24—84no—
399C24—84no—
400C24—84no—
401C24—84no—
402C24—84no—
403C24—84no—
404C24—84no—
405C24—84no—
406C24—84no—
407C24—84no—
408C24—84no—
409C24—84no—
410C24—84no—
411C24C4×D412yes—
412C24#12012yes—
413C24#12012yes—
414C24#12112yes—
415C24#12112yes—
416C24C22⋊Q812yes—
417C24#12412yes—
418C24C2×D812yes—
419C24C2×SD1612yes—
420C24#13512yes—
421C24#13512yes—
422C24AGL(1,ℤ/8)12yes—
423C24AGL(1,ℤ/8)12yes—
424C24AGL(1,ℤ/8)12yes—
425C24#13712yes—
426C24C22×D411yescharacteristic
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—232no—
443C2×D4—232no—
444C2×D4—216no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—416no—
460C2×D4—416no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—416no—
464C2×D4—48no—
465C2×D4—416no—
466C2×D4—48no—
467C2×D4—416no—
468C2×D4—416no—
469C2×D4C2×C4⋊C418yescomplemented
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—216no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—48no—
507C22×C4—44no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4C2×C22⋊C414yes—
539C22×C4C2×C4⋊C414yes—
540C22×C4#11714yes—
541C22×C4C4×D414yes—
542C22×C4C4×D414yes—
543C22×C4C4×D414yes—
544C22×C4C4×D412yes—
545C22×C4#12014yes—
546C22×C4#12012yes—
547C22×C4#12012yes—
548C22×C4#12114yes—
549C22×C4#12114yes—
550C22×C4#12114yes—
551C22×C4#12114yes—
552C22×C4#12114yes—
553C22×C4#12114yes—
554C22×C4#12112yes—
555C22×C4#12112yes—
556C22×C4C22⋊Q814yes—
557C22×C4C22⋊Q814yes—
558C22×C4C22⋊Q814yes—
559C22×C4C22⋊Q814yes—
560C22×C4C22⋊Q814yes—
561C22×C4C22⋊Q812yes—
562C22×C4#12314yes—
563C22×C4#12314yes—
564C22×C4#12314yes—
565C22×C4#12314yes—
566C22×C4#12314yes—
567C22×C4#12414yes—
568C22×C4#12414yes—
569C22×C4#12412yes—
570C22×C4#12614yes—
571C22×C4#12614yes—
572C22×C4#12714yes—
573C22×C4C2×D814yes—
574C22×C4C2×SD1614yes—
575C22×C4C23×C411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×Q811yescharacteristic
583C22×C4C2×#4111yescharacteristic
584C22×C4C2×#4111yescharacteristic
585C22×C4C2×#4111yescharacteristic
586C22×C4C2×#4111yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C2×C8—24no—
590C2×C8—24no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—42no—
596C2×C8—42no—
597C2×C8—42no—
598C2×C8—42no—
599C2×C8—42no—
600C2×C8—42no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—416no—
604C2×C8—416no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—216no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—432no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4C2×C22⋊C418yescomplemented
621C22⋊C4—432no—
622C22⋊C4—432no—
623C42—42no—
624C42—42no—
625C42—42no—
626C42—42no—
627C42—48no—
628C23—28no—
629C23—44no—
630C23—44no—
631C23—432no—
632C23—432no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—432no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—816no—
651C23—816no—
652C23—82no—
653C23—82no—
654C23—82no—
655C23—82no—
656C23—816no—
657C23—816no—
658C23—816no—
659C23—816no—
660C23—82no—
661C23—82no—
662C23—82no—
663C23—82no—
664C23—816no—
665C23—816no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23—816no—
671C23—82no—
672C23—82no—
673C23—816no—
674C23—82no—
675C23—82no—
676C23—816no—
677C23—816no—
678C23#38514yes—
679C23#38614yes—
680C23#38814yes—
681C23#39214yes—
682C23#39314yes—
683C23#39414yes—
684C23#39614yes—
685C23C4×D814yes—
686C23C4×SD1614yes—
687C23#44014yes—
688C23#44214yes—
689C23#44714yes—
690C23#44714yes—
691C23#44814yes—
692C23#44914yes—
693C23#44914yes—
694C23#44914yes—
695C23#45014yes—
696C23#45214yes—
697C23#45914yes—
698C23#46014yes—
699C23#46314yes—
700C23#46414yes—
701C23#46514yes—
702C23#46614yes—
703C23#46814yes—
704C23#46914yes—
705C23#47414yes—
706C23#47614yes—
707C23#47814yes—
708C23#47814yes—
709C23#48614yes—
710C23#48814yes—
711C23#48914yes—
712C23#49014yes—
713C23C2×C4×D411yescharacteristic
714C23C2×#12011yescharacteristic
715C23C2×#12011yescharacteristic
716C23C2×#12111yescharacteristic
717C23C2×#12111yescharacteristic
718C23C2×C22⋊Q811yescharacteristic
719C23C2×#12411yescharacteristic
720C23C22×D811yescharacteristic
721C23C22×SD1611yescharacteristic
722C23C2×#13511yescharacteristic
723C23C2×#13511yescharacteristic
724C23C2×AGL(1,ℤ/8)11yescharacteristic
725C23C2×AGL(1,ℤ/8)11yescharacteristic
726C23C2×AGL(1,ℤ/8)11yescharacteristic
727C23C2×#13711yescharacteristic
728D4—28no—
729D4—28no—
730D4—44no—
731D4—44no—
732D4—44no—
733D4—44no—
734D4—432no—
735D4—44no—
736D4—44no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—432no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—416no—
756C2×C4—416no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—82no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—82no—
771C2×C4—816no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4—82no—
775C2×C4—82no—
776C2×C4—816no—
777C2×C4#38018yes—
778C2×C4#38514yes—
779C2×C4#38518yes—
780C2×C4#38614yes—
781C2×C4#38814yes—
782C2×C4#38818yes—
783C2×C4#39018yes—
784C2×C4#39214yes—
785C2×C4#39314yes—
786C2×C4#39418yes—
787C2×C4#39414yes—
788C2×C4#39618yes—
789C2×C4#39614yes—
790C2×C4#39718yes—
791C2×C4#39918yes—
792C2×C4C22×C22⋊C411yescharacteristic
793C2×C4C22×C4⋊C411yescharacteristic
794C2×C4C2×#11711yescharacteristic
795C2×C4C2×C4×D411yescharacteristic
796C2×C4C2×C4×D411yescharacteristic
797C2×C4C2×C4×D411yescharacteristic
798C2×C4C2×#12011yescharacteristic
799C2×C4C2×#12111yescharacteristic
800C2×C4C2×#12111yescharacteristic
801C2×C4C2×#12111yescharacteristic
802C2×C4C2×#12111yescharacteristic
803C2×C4C2×#12111yescharacteristic
804C2×C4C2×#12111yescharacteristic
805C2×C4C2×C22⋊Q811yescharacteristic
806C2×C4C2×C22⋊Q811yescharacteristic
807C2×C4C2×C22⋊Q811yescharacteristic
808C2×C4C2×C22⋊Q811yescharacteristic
809C2×C4C2×C22⋊Q811yescharacteristic
810C2×C4C2×#12311yescharacteristic
811C2×C4C2×#12311yescharacteristic
812C2×C4C2×#12311yescharacteristic
813C2×C4C2×#12311yescharacteristic
814C2×C4C2×#12311yescharacteristic
815C2×C4C2×#12411yescharacteristic
816C2×C4C2×#12411yescharacteristic
817C2×C4C2×#12611yescharacteristic
818C2×C4C2×#12611yescharacteristic
819C2×C4C2×#12711yescharacteristic
820C8—44no—
821C8—44no—
822C22—48no—
823C22—48no—
824C22—48no—
825C22—84no—
826C22—84no—
827C22—864no—
828C22—84no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—84no—
833C22—84no—
834C22—84no—
835C22—84no—
836C22—84no—
837C22—84no—
838C22#143918yes—
839C22#186218yes—
840C22#186418yes—
841C22#187918yes—
842C22#188018yes—
843C22#193418yes—
844C22#193618yes—
845C22#199918yes—
846C22#200018yes—
847C22#202318yes—
848C22#202518yes—
849C22#204118yes—
850C22#204218yes—
851C22#206518yes—
852C22#206718yes—
853C22C2×#38511yescharacteristic
854C22C2×#38611yescharacteristic
855C22C2×#38811yescharacteristic
856C22C2×#39211yescharacteristic
857C22C2×#39311yescharacteristic
858C22C2×#39411yescharacteristic
859C22C2×#39611yescharacteristic
860C22C2×C4×D811yescharacteristic
861C22C2×C4×SD1611yescharacteristic
862C22C2×#44011yescharacteristic
863C22C2×#44211yescharacteristic
864C22C2×#44711yescharacteristic
865C22C2×#44711yescharacteristic
866C22C2×#45011yescharacteristic
867C22C2×#44811yescharacteristic
868C22C2×#44911yescharacteristic
869C22C2×#44911yescharacteristic
870C22C2×#44911yescharacteristic
871C22C2×#45211yescharacteristic
872C22C2×#45911yescharacteristic
873C22C2×#46311yescharacteristic
874C22C2×#46011yescharacteristic
875C22C2×#46411yescharacteristic
876C22C2×#46511yescharacteristic
877C22C2×#46611yescharacteristic
878C22C2×#46811yescharacteristic
879C22C2×#46911yescharacteristic
880C22C2×#47411yescharacteristic
881C22C2×#47611yescharacteristic
882C22C2×#47811yescharacteristic
883C22C2×#47811yescharacteristic
884C22C2×#48611yescharacteristic
885C22C2×#48811yescharacteristic
886C22C2×#48911yescharacteristic
887C22C2×#49011yescharacteristic
888C4—44no—
889C4—44no—
890C4—48no—
891C4—84no—
892C4—84no—
893C4#143918yes—
894C4C2×#38011yescharacteristic
895C4C2×#38511yescharacteristic
896C4C2×#38811yescharacteristic
897C4C2×#39011yescharacteristic
898C4C2×#39411yescharacteristic
899C4C2×#39611yescharacteristic
900C4C2×#39711yescharacteristic
901C4C2×#39911yescharacteristic
902C2—88no—
903C2#11066116yesdirect product factor
904C2C2×#143911yescharacteristic
905C2C2×#186211yescharacteristic
906C2C2×#186411yescharacteristic
907C2C2×#187911yescharacteristic
908C2C2×#188011yescharacteristic
909C2C2×#193411yescharacteristic
910C2C2×#193611yescharacteristic
911C2C2×#199911yescharacteristic
912C2C2×#200011yescharacteristic
913C2C2×#202311yescharacteristic
914C2C2×#202511yescharacteristic
915C2C2×#204111yescharacteristic
916C2C2×#204211yescharacteristic
917C2C2×#206511yescharacteristic
918C2C2×#206711yescharacteristic
subgroupG/H
center, socleC25C2×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC24×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#389C2semidirect
5. C22×#340C2semidirect
6. C22×#340C2semidirect
7. C22×#336C2semidirect
8. #11066C2direct (N × H)
24. C22×#102C4semidirect
34. C2×#389C22semidirect
38. C2×#340C22semidirect
39. C2×#340C22semidirect
41. C2×#336C22semidirect
132. C2×#102C2×C4semidirect
206. C22×D4C4⋊C4semidirect
331. C2×C4⋊C4C22⋊C4semidirect
469. C2×D4C2×C4⋊C4semidirect
620. C4⋊C4C2×C22⋊C4semidirect
903. C2#11066direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1022
C22×#3902
C22×#3892
C22×#3402
C22×#3362
#110662