Finite Group Databasebeta

← C2×#11387 #358797

Subgroups — C2×#11387 #358797

Order 512.

2974 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#533C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1740C211yesmaximal, characteristic
4C2×#1733C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7C22×H(3,ℤ/4)C211yesmaximal, characteristic
8#11387C218yesmaximal, direct product factor
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C2×#533—24no—
12C2×#533—22no—
13C2×#533—24no—
14C2×#533—22no—
15C2×#533—24no—
16C2×#533—22no—
17C2×#533C418yescomplemented
18C2×#533C2214yes—
19C22×C4⋊Q8—21no—
20C22×#125—21no—
21C22×C22⋊Q8—22no—
22C22×C4×Q8—22no—
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C2×#344—24no—
29C2×#344C2214yes—
30#1740—22no—
31#1740C2214yes—
32C2×#342—22no—
33#1733—22no—
34#1733C2214yes—
35C2×#339—21no—
36C2×#339—21no—
37C2×#339—24no—
38C2×#339—22no—
39C2×#339—22no—
40C2×#339C2214yes—
41C2×#339C2214yes—
42C2×H(3,ℤ/4)—24no—
43C2×H(3,ℤ/4)C2214yes—
44C23×Q8—22no—
45C24×C4—21no—
46C24×C4C2311yescharacteristic
47C22×M16—22no—
48C22×M16—22no—
49C22×M16—21no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—22no—
54C22×M16—21no—
55C22×M16—21no—
56C22×M16—22no—
57C22×M16—21no—
58C22×M16—21no—
59C22×M16—22no—
60C22×M16—22no—
61C22×M16—21no—
62C22×M16—21no—
63C22×M16Q814yescomplemented
64C22×M16Q814yescomplemented
65C22×M16C2312yes—
66C22×M16C2312yes—
67C23×C8—21no—
68C23×C8—21no—
69#533—216no—
70#533—216no—
71#533—216no—
72#533—216no—
73#533—216no—
74#533—28no—
75#533—28no—
76#533—216no—
77#533—28no—
78#533C2×C4116yescomplemented
79C2×C4⋊Q8—28no—
80C2×C4⋊Q8—24no—
81C2×C4⋊Q8—28no—
82C2×C4⋊Q8—24no—
83C2×#125—28no—
84C2×#125—24no—
85C2×#125—28no—
86C2×#125—24no—
87C2×C22⋊Q8—216no—
88C2×C22⋊Q8—28no—
89C2×C22⋊Q8—216no—
90C2×C22⋊Q8—28no—
91C2×C4×Q8—216no—
92C2×C4×Q8—28no—
93C2×C4×Q8—216no—
94C2×C4×Q8—28no—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—21no—
99C2×#117—21no—
100C2×#117—22no—
101C2×#117—21no—
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—21no—
105C2×#117—22no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—22no—
109C2×#117—22no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117C2×C414yes—
120C2×#117C2×C414yes—
121C2×#117D414yes—
122C2×#117D412yes—
123C2×#117D414yes—
124C2×#117D412yes—
125C2×#117Q814yescomplemented
126C2×#117Q812yescomplemented
127C2×#117C2312yes—
128C2×#117C2312yes—
129C2×#117C2312yes—
130C2×#117C2312yes—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—22no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4Q812yescomplemented
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4D412yes—
141C22×C42—21no—
142C22×C42—22no—
143C22×C42—21no—
144C22×C42—21no—
145C22×C42—22no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—21no—
149C22×C42C2×C414yes—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D414yes—
153C22×C42D412yes—
154C22×C42D412yes—
155C22×C42C2312yes—
156#344—28no—
157#342—28no—
158#339—24no—
159#339—24no—
160#339—28no—
161#339—28no—
162H(3,ℤ/4)—28no—
163C25C2×D411yescharacteristic
164C22×Q8—28no—
165C22×Q8—216no—
166C22×Q8—416no—
167C23×C4—21no—
168C23×C4—24no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—24no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—48no—
177C23×C4—41no—
178C23×C4C22×C412yes—
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D412yes—
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D412yes—
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D412yes—
187C23×C4C2×Q812yes—
188C23×C4C2×Q812yes—
189C23×C4C2×Q811yescharacteristic
190C23×C4C2×Q812yes—
191C23×C4C2×Q811yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4#4111yescharacteristic
194C23×C4#4111yescharacteristic
195C23×C4#4111yescharacteristic
196C23×C4#4111yescharacteristic
197C23×C4#4112yes—
198C23×C4#4111yescharacteristic
199C23×C4C2411yescharacteristic
200C2×M16—24no—
201C2×M16—24no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—24no—
205C2×M16—24no—
206C2×M16—24no—
207C2×M16—24no—
208C2×M16—24no—
209C2×M16—24no—
210C2×M16—24no—
211C2×M16—24no—
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—42no—
221C2×M16—42no—
222C2×M16—42no—
223C2×M16—42no—
224C2×M16—41no—
225C2×M16—41no—
226C2×M16—41no—
227C2×M16—42no—
228C2×M16—41no—
229C2×M16—42no—
230C2×M16—42no—
231C2×M16—42no—
232C2×M16—42no—
233C2×M16—42no—
234C2×M16C2×Q814yescomplemented
235C2×M16C2×Q814yescomplemented
236C22×C8—24no—
237C22×C8—24no—
238C22×C8—22no—
239C22×C8—22no—
240C22×C8—41no—
241C22×C8—41no—
242C22×C8—42no—
243C22×C8—41no—
244C22×C8—42no—
245C22×C8—41no—
246C4⋊Q8—216no—
247C4⋊Q8—232no—
248C4⋊Q8—216no—
249#125—216no—
250#125—232no—
251#125—216no—
252C22⋊Q8—232no—
253C22⋊Q8—264no—
254C22⋊Q8—232no—
255C4×Q8—232no—
256C4×Q8—264no—
257C4×Q8—232no—
258#117—24no—
259#117—24no—
260#117—24no—
261#117—24no—
262#117—24no—
263#117—24no—
264#117—24no—
265#117—24no—
266#117—24no—
267#117—24no—
268#117—22no—
269#117—22no—
270#117—22no—
271#117—22no—
272#117—24no—
273#117—22no—
274#117—24no—
275#117—22no—
276#117—24no—
277#117—22no—
278#117—22no—
279#117—22no—
280#117—22no—
281#117—22no—
282#117—22no—
283#117—22no—
284#117—22no—
285#117—22no—
286#117—41no—
287#117—41no—
288#117—42no—
289#117—41no—
290#117—41no—
291#117—41no—
292#117—41no—
293#117—42no—
294#117—41no—
295#117—41no—
296#117—42no—
297#117C22⋊C418yes—
298#117C22⋊C418yes—
299#117C22×C414yes—
300#117C22×C414yes—
301#117C2×D414yes—
302#117C2×D414yes—
303#117C2×Q814yescomplemented
304C2×C4⋊C4—216no—
305C2×C4⋊C4—232no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—216no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4C2×Q814yescomplemented
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4C22⋊C418yes—
343C2×C22⋊C4C2×D414yes—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—22no—
352C2×C42—24no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—21no—
356C2×C42—22no—
357C2×C42—21no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—42no—
370C2×C42—41no—
371C2×C42—41no—
372C2×C42—41no—
373C2×C42—41no—
374C2×C42—41no—
375C2×C42C22⋊C418yes—
376C2×C42C22⋊C414yes—
377C2×C42C22⋊C414yes—
378C2×C42C22⋊C418yes—
379C2×C42C22×C414yes—
380C2×C42C2×D414yes—
381C2×C42C2×D412yes—
382C2×C42C2×D412yes—
383C2×C42C2×D414yes—
384C24—44no—
385C24C2×C22⋊C412yes—
386C24#12011yescharacteristic
387C24#12011yescharacteristic
388C24#12012yes—
389C24C22⋊Q811yescharacteristic
390C24C22⋊Q811yescharacteristic
391C24C22⋊Q812yes—
392C24#12411yescharacteristic
393C24#12411yescharacteristic
394C24C4⋊Q812yes—
395C24C22×D411yescharacteristic
396C2×Q8—232no—
397C2×Q8—464no—
398C2×Q8—432no—
399C22×C4—28no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—28no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—24no—
412C22×C4—416no—
413C22×C4—416no—
414C22×C4—48no—
415C22×C4—48no—
416C22×C4—44no—
417C22×C4—48no—
418C22×C4—48no—
419C22×C4—42no—
420C22×C4—44no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—84no—
424C22×C4—84no—
425C22×C4C2×C22⋊C412yes—
426C22×C4C2×C22⋊C412yes—
427C22×C4C2×C22⋊C412yes—
428C22×C4C2×C22⋊C412yes—
429C22×C4C2×C22⋊C412yes—
430C22×C4C4×Q812yes—
431C22×C4C4×Q812yes—
432C22×C4C4×Q812yes—
433C22×C4C4×Q812yes—
434C22×C4C4×Q812yes—
435C22×C4C4×Q812yes—
436C22×C4C4×Q812yes—
437C22×C4C4×Q812yes—
438C22×C4#12012yes—
439C22×C4#12012yes—
440C22×C4#12012yes—
441C22×C4#12012yes—
442C22×C4#12011yescharacteristic
443C22×C4#12011yescharacteristic
444C22×C4#12012yes—
445C22×C4C22⋊Q812yes—
446C22×C4C22⋊Q812yes—
447C22×C4C22⋊Q812yes—
448C22×C4C22⋊Q812yes—
449C22×C4C22⋊Q812yes—
450C22×C4C22⋊Q812yes—
451C22×C4C22⋊Q812yes—
452C22×C4C22⋊Q812yes—
453C22×C4C22⋊Q812yes—
454C22×C4C22⋊Q812yes—
455C22×C4C22⋊Q811yescharacteristic
456C22×C4C22⋊Q811yescharacteristic
457C22×C4C22⋊Q811yescharacteristic
458C22×C4C22⋊Q811yescharacteristic
459C22×C4C22⋊Q812yes—
460C22×C4C22⋊Q811yescharacteristic
461C22×C4C22⋊Q811yescharacteristic
462C22×C4C22⋊Q812yes—
463C22×C4C22⋊Q811yescharacteristic
464C22×C4C22⋊Q811yescharacteristic
465C22×C4C22⋊Q812yes—
466C22×C4C22⋊Q812yes—
467C22×C4C22⋊Q812yes—
468C22×C4C22⋊Q812yes—
469C22×C4C22⋊Q811yescharacteristic
470C22×C4C22⋊Q811yescharacteristic
471C22×C4C22⋊Q812yes—
472C22×C4#12411yescharacteristic
473C22×C4#12411yescharacteristic
474C22×C4#12412yes—
475C22×C4#12411yescharacteristic
476C22×C4#12412yes—
477C22×C4#12411yescharacteristic
478C22×C4#12411yescharacteristic
479C22×C4#12411yescharacteristic
480C22×C4#12412yes—
481C22×C4#12411yescharacteristic
482C22×C4#12412yes—
483C22×C4#12412yes—
484C22×C4#12412yes—
485C22×C4#12411yescharacteristic
486C22×C4#12411yescharacteristic
487C22×C4#12411yescharacteristic
488C22×C4C4⋊Q812yes—
489C22×C4C4⋊Q812yes—
490C22×C4C4⋊Q812yes—
491C22×C4C4⋊Q812yes—
492C22×C4C4⋊Q812yes—
493C22×C4C4⋊Q812yes—
494C22×C4C4⋊Q812yes—
495C22×C4C4⋊Q812yes—
496C22×C4C4⋊Q812yes—
497C22×C4C4⋊Q812yes—
498C22×C4C4⋊Q812yes—
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×D411yescharacteristic
504C22×C4C22×D411yescharacteristic
505C22×C4C22×Q811yescharacteristic
506C22×C4C22×Q811yescharacteristic
507C22×C4C22×Q811yescharacteristic
508C22×C4C22×Q811yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513M16—24no—
514M16—24no—
515M16—24no—
516M16—24no—
517M16—42no—
518M16—42no—
519M16—42no—
520M16—42no—
521M16—44no—
522M16—44no—
523M16—44no—
524M16—44no—
525C2×C8—24no—
526C2×C8—24no—
527C2×C8—42no—
528C2×C8—42no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—44no—
532C2×C8—44no—
533C2×C8—44no—
534C2×C8—44no—
535C4⋊C4—264no—
536C4⋊C4—232no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—44no—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—28no—
554C22⋊C4—28no—
555C22⋊C4—24no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—44no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4C2×C22⋊C418yes—
563C42—24no—
564C42—24no—
565C42—24no—
566C42—22no—
567C42—22no—
568C42—24no—
569C42—24no—
570C42—28no—
571C42—24no—
572C42—24no—
573C42—28no—
574C42—28no—
575C42—24no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42—44no—
580C42—42no—
581C42—42no—
582C42C2×C22⋊C414yes—
583C42C2×C22⋊C414yes—
584C42C2×C22⋊C418yes—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—44no—
589C23—44no—
590C23—42no—
591C23—42no—
592C23—44no—
593C23—42no—
594C23—42no—
595C23—44no—
596C23#37912yes—
597C23#37912yes—
598C23#39112yes—
599C23#39112yes—
600C23#39112yes—
601C23#39112yes—
602C23#39311yescharacteristic
603C23#39311yescharacteristic
604C23#39312yes—
605C23#39311yescharacteristic
606C23#39312yes—
607C23#39311yescharacteristic
608C23#39512yes—
609C23#39512yes—
610C23#39512yes—
611C23#39512yes—
612C23C22×C22⋊C411yescharacteristic
613C23C2×#12011yescharacteristic
614C23C2×#12011yescharacteristic
615C23C2×C22⋊Q811yescharacteristic
616C23C2×C22⋊Q811yescharacteristic
617C23C2×#12411yescharacteristic
618C23C2×C4⋊Q811yescharacteristic
619Q8—464no—
620C2×C4—216no—
621C2×C4—28no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—48no—
627C2×C4—48no—
628C2×C4—416no—
629C2×C4—48no—
630C2×C4—44no—
631C2×C4—416no—
632C2×C4—416no—
633C2×C4—48no—
634C2×C4—48no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—88no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4#37912yes—
643C2×C4#37912yes—
644C2×C4#39112yes—
645C2×C4#39112yes—
646C2×C4#39112yes—
647C2×C4#39112yes—
648C2×C4#39112yes—
649C2×C4#39112yes—
650C2×C4#39112yes—
651C2×C4#39112yes—
652C2×C4#39112yes—
653C2×C4#39112yes—
654C2×C4#39112yes—
655C2×C4#39112yes—
656C2×C4#39112yes—
657C2×C4#39112yes—
658C2×C4#39112yes—
659C2×C4#39112yes—
660C2×C4#39112yes—
661C2×C4#39112yes—
662C2×C4#39112yes—
663C2×C4#39112yes—
664C2×C4#39312yes—
665C2×C4#39312yes—
666C2×C4#39312yes—
667C2×C4#39312yes—
668C2×C4#39312yes—
669C2×C4#39312yes—
670C2×C4#39312yes—
671C2×C4#39312yes—
672C2×C4#39312yes—
673C2×C4#39311yescharacteristic
674C2×C4#39311yescharacteristic
675C2×C4#39312yes—
676C2×C4#39311yescharacteristic
677C2×C4#39311yescharacteristic
678C2×C4#39512yes—
679C2×C4#39512yes—
680C2×C4#39512yes—
681C2×C4#39512yes—
682C2×C4#39512yes—
683C2×C4#39512yes—
684C2×C4#39512yes—
685C2×C4#39512yes—
686C2×C4#39512yes—
687C2×C4#39512yes—
688C2×C4#39512yes—
689C2×C4#39512yes—
690C2×C4C22×C22⋊C411yescharacteristic
691C2×C4C22×C22⋊C411yescharacteristic
692C2×C4C2×C4×Q811yescharacteristic
693C2×C4C2×C4×Q811yescharacteristic
694C2×C4C2×C4×Q811yescharacteristic
695C2×C4C2×C4×Q811yescharacteristic
696C2×C4C2×#12011yescharacteristic
697C2×C4C2×#12011yescharacteristic
698C2×C4C2×C22⋊Q811yescharacteristic
699C2×C4C2×C22⋊Q811yescharacteristic
700C2×C4C2×C22⋊Q811yescharacteristic
701C2×C4C2×C22⋊Q811yescharacteristic
702C2×C4C2×C22⋊Q811yescharacteristic
703C2×C4C2×C22⋊Q811yescharacteristic
704C2×C4C2×C22⋊Q811yescharacteristic
705C2×C4C2×C22⋊Q811yescharacteristic
706C2×C4C2×C22⋊Q811yescharacteristic
707C2×C4C2×C22⋊Q811yescharacteristic
708C2×C4C2×#12411yescharacteristic
709C2×C4C2×#12411yescharacteristic
710C2×C4C2×#12411yescharacteristic
711C2×C4C2×#12411yescharacteristic
712C2×C4C2×#12411yescharacteristic
713C2×C4C2×C4⋊Q811yescharacteristic
714C2×C4C2×C4⋊Q811yescharacteristic
715C2×C4C2×C4⋊Q811yescharacteristic
716C2×C4C2×C4⋊Q811yescharacteristic
717C2×C4C2×C4⋊Q811yescharacteristic
718C8—44no—
719C8—44no—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22#144612yes—
743C22#144612yes—
744C22#144612yes—
745C22#144612yes—
746C22#203114yes—
747C22C2×#37911yescharacteristic
748C22C2×#39111yescharacteristic
749C22C2×#39111yescharacteristic
750C22C2×#39311yescharacteristic
751C22C2×#39311yescharacteristic
752C22C2×#39511yescharacteristic
753C22C2×#39511yescharacteristic
754C4—28no—
755C4—44no—
756C4—48no—
757C4—48no—
758C4—84no—
759C4—84no—
760C4#144612yes—
761C4#144612yes—
762C4#144612yes—
763C4#144612yes—
764C4C2×#39111yescharacteristic
765C4C2×#39111yescharacteristic
766C4C2×#39111yescharacteristic
767C4C2×#39111yescharacteristic
768C4C2×#39311yescharacteristic
769C4C2×#39311yescharacteristic
770C4C2×#39511yescharacteristic
771C4C2×#39511yescharacteristic
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—22no—
777C2—22no—
778C2—22no—
779C2—21no—
780C2—21no—
781C2#1138714yesdirect product factor
782C2C2×#144611yescharacteristic
783C2C2×#203112yes—
subgroupG/H
centerC22×C4#124
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23#393
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11387C2direct (N × H)
17. C2×#533C4semidirect
63. C22×M16Q8semidirect
64. C22×M16Q8semidirect
78. #533C2×C4semidirect
125. C2×#117Q8semidirect
126. C2×#117Q8semidirect
136. C22×C4⋊C4Q8semidirect
234. C2×M16C2×Q8semidirect
235. C2×M16C2×Q8semidirect
303. #117C2×Q8semidirect
325. C2×C4⋊C4C2×Q8semidirect
781. C2#11387direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5332
C22×#3442
C2×#17402
C2×#17332
C22×#3392
C22×H(3,ℤ/4)2
#113872