Finite Group Databasebeta

← C2×#11067 #357725

Subgroups — C2×#11067 #357725

Order 512.

3342 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#103C211yesmaximal, characteristic
2C23×#103C211yesmaximal, characteristic
3C22×#391C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic
5C22×#340C211yesmaximal, characteristic
6C22×#340C211yesmaximal, characteristic
7C22×#336C211yesmaximal, characteristic
8#11067C218yesmaximal, direct product factor
9C24×Q8C2211yescharacteristic
10C24×C8C2211yescharacteristic
11C24×C8C2211yescharacteristic
12C23×C4⋊C4—21no—
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C22×#103—24no—
18C22×#103—24no—
19C22×#103—24no—
20C22×#103—24no—
21C22×#103—24no—
22C22×#103C418yescomplemented
23C22×#103C2214yes—
24C22×#103C2214yes—
25C2×#391—22no—
26C2×#391—24no—
27C2×#391—24no—
28C2×#391C2214yes—
29C2×#389—22no—
30C2×#389—24no—
31C2×#389—24no—
32C2×#389C2214yes—
33C22×#95—21no—
34C22×#95—21no—
35C22×#95—21no—
36C2×#340—24no—
37C2×#340—24no—
38C2×#340C2214yes—
39C2×#340C2214yes—
40C2×#336—24no—
41C2×#336C2214yes—
42C23×Q8—22no—
43C23×Q8—21no—
44C23×Q8—22no—
45C23×Q8—22no—
46C23×Q8—22no—
47C23×Q8—22no—
48C23×Q8—22no—
49C23×Q8—22no—
50C23×Q8—22no—
51C23×Q8—22no—
52C23×Q8—22no—
53C23×Q8—22no—
54C23×Q8C2×C414yes—
55C23×Q8D414yes—
56C23×Q8Q814yes—
57C23×Q8C2312yes—
58C24×C4—21no—
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×C42—22no—
110C22×C42—22no—
111C22×C42—22no—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—22no—
115C22×C42D412yes—
116C22×C42C2312yes—
117C2×#103—232no—
118C2×#103—28no—
119C2×#103—28no—
120C2×#103—232no—
121C2×#103—28no—
122C2×#103—28no—
123C2×#103—28no—
124C2×#103C2×C4116yescomplemented
125#391—216no—
126#391—28no—
127#391—28no—
128#389—216no—
129#389—28no—
130#389—28no—
131C2×#95—28no—
132C2×#95—28no—
133C2×#95—28no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137#340—28no—
138#340—28no—
139#336—28no—
140C25C2×D411yescharacteristic
141C22×Q8—24no—
142C22×Q8—28no—
143C22×Q8—24no—
144C22×Q8—24no—
145C22×Q8—28no—
146C22×Q8—28no—
147C22×Q8—22no—
148C22×Q8—22no—
149C22×Q8—22no—
150C22×Q8—28no—
151C22×Q8—28no—
152C22×Q8—28no—
153C22×Q8—28no—
154C22×Q8—28no—
155C22×Q8—28no—
156C22×Q8—28no—
157C22×Q8—28no—
158C22×Q8—28no—
159C22×Q8—28no—
160C22×Q8—28no—
161C22×Q8—28no—
162C22×Q8—22no—
163C22×Q8—22no—
164C22×Q8—22no—
165C22×Q8—22no—
166C22×Q8—22no—
167C22×Q8—22no—
168C22×Q8—22no—
169C22×Q8—22no—
170C22×Q8—42no—
171C22×Q8—42no—
172C22×Q8—42no—
173C22×Q8—44no—
174C22×Q8—44no—
175C22×Q8—44no—
176C22×Q8—44no—
177C22×Q8—44no—
178C22×Q8—44no—
179C22×Q8—44no—
180C22×Q8—42no—
181C22×Q8—44no—
182C22×Q8—44no—
183C22×Q8—44no—
184C22×Q8—44no—
185C22×Q8—44no—
186C22×Q8C4⋊C4116yescomplemented
187C22×Q8C22×C414yes—
188C22×Q8C2×D414yes—
189C22×Q8C2×Q814yes—
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—22no—
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—24no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—24no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4—42no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—42no—
222C23×C4—42no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4—42no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4SD1614yes—
235C23×C4Q1614yes—
236C23×C4C22×C412yes—
237C23×C4C2×D412yes—
238C23×C4C2×D412yes—
239C23×C4C2×D412yes—
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D412yes—
246C23×C4C2×Q812yes—
247C23×C4#4112yes—
248C23×C4#4112yes—
249C23×C4#4112yes—
250C23×C4#4112yes—
251C23×C4#4112yes—
252C23×C4#4112yes—
253C23×C4C2411yescharacteristic
254C22×C8—28no—
255C22×C8—28no—
256C22×C8—28no—
257C22×C8—28no—
258C22×C8—28no—
259C22×C8—28no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—44no—
273C22×C8—44no—
274C22×C8—44no—
275C22×C8—44no—
276C22×C8—44no—
277C22×C8—44no—
278C22×C8—44no—
279C22×C8—44no—
280C22×C8C22×C414yes—
281C22×C8C2×D414yes—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
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—216no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—48no—
309C2×C4⋊C4—432no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—48no—
319C2×C4⋊C4C22⋊C4116yes—
320C2×C4⋊C4C22×C414yes—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D414yes—
325C2×C42—24no—
326C2×C42—24no—
327C2×C42—24no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—44no—
335C2×C42—44no—
336C2×C42—44no—
337C2×C42—44no—
338#103—232no—
339#103—232no—
340#95—216no—
341#95—216no—
342#95—216no—
343C24C4×D412yes—
344C24#12012yes—
345C24#12012yes—
346C24#12112yes—
347C24#12112yes—
348C24C22⋊Q812yes—
349C24#12412yes—
350C24C2×SD1612yes—
351C24C2×Q1612yes—
352C24#13512yes—
353C24#13512yes—
354C24AGL(1,ℤ/8)12yes—
355C24#13712yes—
356C24#13712yes—
357C24#13712yes—
358C24C22×D411yescharacteristic
359C2×Q8—24no—
360C2×Q8—24no—
361C2×Q8—24no—
362C2×Q8—216no—
363C2×Q8—24no—
364C2×Q8—24no—
365C2×Q8—24no—
366C2×Q8—24no—
367C2×Q8—24no—
368C2×Q8—24no—
369C2×Q8—24no—
370C2×Q8—24no—
371C2×Q8—24no—
372C2×Q8—24no—
373C2×Q8—24no—
374C2×Q8—24no—
375C2×Q8—232no—
376C2×Q8—232no—
377C2×Q8—42no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×Q8—42no—
387C2×Q8—42no—
388C2×Q8—42no—
389C2×Q8—48no—
390C2×Q8—416no—
391C2×Q8—48no—
392C2×Q8—416no—
393C2×Q8—48no—
394C2×Q8—48no—
395C2×Q8—48no—
396C2×Q8—416no—
397C2×Q8—48no—
398C2×Q8—416no—
399C2×Q8—416no—
400C2×Q8—416no—
401C2×Q8C2×C4⋊C418yescomplemented
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—216no—
421C22×C4—216no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—28no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—48no—
443C22×C4—48no—
444C22×C4—48no—
445C22×C4—48no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—44no—
449C22×C4—48no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—48no—
454C22×C4—48no—
455C22×C4—48no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—48no—
471C22×C4—48no—
472C22×C4—48no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—48no—
476C22×C4—84no—
477C22×C4—84no—
478C22×C4—84no—
479C22×C4—84no—
480C22×C4—84no—
481C22×C4—84no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4C2×C22⋊C414yes—
485C22×C4C2×C4⋊C414yes—
486C22×C4#11714yes—
487C22×C4C4×D414yes—
488C22×C4C4×D414yes—
489C22×C4C4×D414yes—
490C22×C4C4×D412yes—
491C22×C4#12014yes—
492C22×C4#12012yes—
493C22×C4#12012yes—
494C22×C4#12114yes—
495C22×C4#12114yes—
496C22×C4#12114yes—
497C22×C4#12114yes—
498C22×C4#12114yes—
499C22×C4#12114yes—
500C22×C4#12112yes—
501C22×C4#12112yes—
502C22×C4C22⋊Q814yes—
503C22×C4C22⋊Q814yes—
504C22×C4C22⋊Q814yes—
505C22×C4C22⋊Q814yes—
506C22×C4C22⋊Q814yes—
507C22×C4C22⋊Q812yes—
508C22×C4#12314yes—
509C22×C4#12314yes—
510C22×C4#12314yes—
511C22×C4#12314yes—
512C22×C4#12314yes—
513C22×C4#12414yes—
514C22×C4#12414yes—
515C22×C4#12412yes—
516C22×C4#12614yes—
517C22×C4#12614yes—
518C22×C4#12714yes—
519C22×C4C2×SD1614yes—
520C22×C4C2×Q1614yes—
521C22×C4C23×C411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×Q811yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C2×C8—24no—
536C2×C8—24no—
537C2×C8—24no—
538C2×C8—24no—
539C2×C8—24no—
540C2×C8—24no—
541C2×C8—42no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—42no—
545C2×C8—42no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8—416no—
550C2×C8—416no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—216no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—432no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4C2×C22⋊C418yes—
567C42—42no—
568C42—42no—
569C42—42no—
570C42—42no—
571C42—48no—
572C23#38514yes—
573C23#38614yes—
574C23#38814yes—
575C23#39214yes—
576C23#39314yes—
577C23#39414yes—
578C23#39614yes—
579C23C4×SD1614yes—
580C23C4×Q1614yes—
581C23#44014yes—
582C23#44114yes—
583C23#44814yes—
584C23#44914yes—
585C23#45014yes—
586C23#45114yes—
587C23#45114yes—
588C23#45214yes—
589C23#45214yes—
590C23#45214yes—
591C23#46114yes—
592C23#46214yes—
593C23#46314yes—
594C23#46414yes—
595C23#46514yes—
596C23#46714yes—
597C23#46814yes—
598C23#47014yes—
599C23#47514yes—
600C23#47714yes—
601C23#47914yes—
602C23#47914yes—
603C23#48714yes—
604C23#48814yes—
605C23#48914yes—
606C23#49114yes—
607C23C2×C4×D411yescharacteristic
608C23C2×#12011yescharacteristic
609C23C2×#12011yescharacteristic
610C23C2×#12111yescharacteristic
611C23C2×#12111yescharacteristic
612C23C2×C22⋊Q811yescharacteristic
613C23C2×#12411yescharacteristic
614C23C22×SD1611yescharacteristic
615C23C22×Q1611yescharacteristic
616C23C2×#13511yescharacteristic
617C23C2×#13511yescharacteristic
618C23C2×AGL(1,ℤ/8)11yescharacteristic
619C23C2×#13711yescharacteristic
620C23C2×#13711yescharacteristic
621C23C2×#13711yescharacteristic
622Q8—28no—
623Q8—28no—
624Q8—44no—
625Q8—44no—
626Q8—44no—
627Q8—44no—
628Q8—432no—
629Q8—44no—
630Q8—44no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—432no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—432no—
649C2×C4—44no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—44no—
655C2×C4—416no—
656C2×C4—416no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—816no—
674C2×C4—82no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—816no—
679C2×C4#38018yes—
680C2×C4#38514yes—
681C2×C4#38518yes—
682C2×C4#38614yes—
683C2×C4#38814yes—
684C2×C4#38818yes—
685C2×C4#39018yes—
686C2×C4#39214yes—
687C2×C4#39314yes—
688C2×C4#39418yes—
689C2×C4#39414yes—
690C2×C4#39618yes—
691C2×C4#39614yes—
692C2×C4#39718yes—
693C2×C4#39918yes—
694C2×C4C22×C22⋊C411yescharacteristic
695C2×C4C22×C4⋊C411yescharacteristic
696C2×C4C2×#11711yescharacteristic
697C2×C4C2×C4×D411yescharacteristic
698C2×C4C2×C4×D411yescharacteristic
699C2×C4C2×C4×D411yescharacteristic
700C2×C4C2×#12011yescharacteristic
701C2×C4C2×#12111yescharacteristic
702C2×C4C2×#12111yescharacteristic
703C2×C4C2×#12111yescharacteristic
704C2×C4C2×#12111yescharacteristic
705C2×C4C2×#12111yescharacteristic
706C2×C4C2×#12111yescharacteristic
707C2×C4C2×C22⋊Q811yescharacteristic
708C2×C4C2×C22⋊Q811yescharacteristic
709C2×C4C2×C22⋊Q811yescharacteristic
710C2×C4C2×C22⋊Q811yescharacteristic
711C2×C4C2×C22⋊Q811yescharacteristic
712C2×C4C2×#12311yescharacteristic
713C2×C4C2×#12311yescharacteristic
714C2×C4C2×#12311yescharacteristic
715C2×C4C2×#12311yescharacteristic
716C2×C4C2×#12311yescharacteristic
717C2×C4C2×#12411yescharacteristic
718C2×C4C2×#12411yescharacteristic
719C2×C4C2×#12611yescharacteristic
720C2×C4C2×#12611yescharacteristic
721C2×C4C2×#12711yescharacteristic
722C8—44no—
723C8—44no—
724C22#143918yes—
725C22#186318yes—
726C22#186518yes—
727C22#187718yes—
728C22#187818yes—
729C22#193318yes—
730C22#193518yes—
731C22#200018yes—
732C22#200118yes—
733C22#202418yes—
734C22#202618yes—
735C22#204218yes—
736C22#204318yes—
737C22#206618yes—
738C22#206818yes—
739C22C2×#38511yescharacteristic
740C22C2×#38611yescharacteristic
741C22C2×#38811yescharacteristic
742C22C2×#39211yescharacteristic
743C22C2×#39311yescharacteristic
744C22C2×#39411yescharacteristic
745C22C2×#39611yescharacteristic
746C22C2×C4×SD1611yescharacteristic
747C22C2×C4×Q1611yescharacteristic
748C22C2×#44011yescharacteristic
749C22C2×#44111yescharacteristic
750C22C2×#45011yescharacteristic
751C22C2×#44811yescharacteristic
752C22C2×#45111yescharacteristic
753C22C2×#45111yescharacteristic
754C22C2×#44911yescharacteristic
755C22C2×#45211yescharacteristic
756C22C2×#45211yescharacteristic
757C22C2×#45211yescharacteristic
758C22C2×#46111yescharacteristic
759C22C2×#46311yescharacteristic
760C22C2×#46211yescharacteristic
761C22C2×#46411yescharacteristic
762C22C2×#46511yescharacteristic
763C22C2×#46711yescharacteristic
764C22C2×#46811yescharacteristic
765C22C2×#47011yescharacteristic
766C22C2×#47511yescharacteristic
767C22C2×#47711yescharacteristic
768C22C2×#47911yescharacteristic
769C22C2×#47911yescharacteristic
770C22C2×#48711yescharacteristic
771C22C2×#48811yescharacteristic
772C22C2×#48911yescharacteristic
773C22C2×#49111yescharacteristic
774C4—48no—
775C4—44no—
776C4—44no—
777C4—48no—
778C4—84no—
779C4—84no—
780C4#143918yes—
781C4C2×#38011yescharacteristic
782C4C2×#38511yescharacteristic
783C4C2×#38811yescharacteristic
784C4C2×#39011yescharacteristic
785C4C2×#39411yescharacteristic
786C4C2×#39611yescharacteristic
787C4C2×#39711yescharacteristic
788C4C2×#39911yescharacteristic
789C2#11067116yesdirect product factor
790C2C2×#143911yescharacteristic
791C2C2×#186311yescharacteristic
792C2C2×#186511yescharacteristic
793C2C2×#187711yescharacteristic
794C2C2×#187811yescharacteristic
795C2C2×#193311yescharacteristic
796C2C2×#193511yescharacteristic
797C2C2×#200011yescharacteristic
798C2C2×#200111yescharacteristic
799C2C2×#202411yescharacteristic
800C2C2×#202611yescharacteristic
801C2C2×#204211yescharacteristic
802C2C2×#204311yescharacteristic
803C2C2×#206611yescharacteristic
804C2C2×#206811yescharacteristic
subgroupG/H
center, socle, prime radicalC25C2×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
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
8. #11067C2direct (N × H)
22. C22×#103C4semidirect
124. C2×#103C2×C4semidirect
186. C22×Q8C4⋊C4semidirect
401. C2×Q8C2×C4⋊C4semidirect
789. C2#11067direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1032
C22×#3912
C22×#3892
C22×#3402
C22×#3362
#110672