Finite Group Databasebeta

← #357437

Subgroups — #357437

Order 512.

4562 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#536C211yesmaximal, characteristic
2C22×#419C211yesmaximal, characteristic, complemented
3C23×#103C211yesmaximal, characteristic, complemented
4C22×#408C211yesmaximal, characteristic
5C2×#2311C211yesmaximal, characteristic
6C2×#1736C211yesmaximal, characteristic, complemented
7C2×#1735C211yesmaximal, characteristic, complemented
8#10970C218yesmaximal, complemented
9C23×#41C2211yescharacteristic
10C24×Q8C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C24×C8C2211yescharacteristic
13C2×#536—24no—
14C2×#536—24no—
15C2×#536—24no—
16C2×#536—24no—
17C2×#536—24no—
18C2×#536C418yescomplemented
19C22×C4⋊Q8—21no—
20C22×#124—21no—
21C22×#123—22no—
22C22×C22⋊Q8C2214yes—
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C2×#419—24no—
27C2×#419—24no—
28C2×#419—24no—
29C22×#103—24no—
30C22×#103—24no—
31C22×#103—24no—
32C22×#103C2214yes—
33C22×#103C2214yes—
34C2×#408—24no—
35C2×#408—24no—
36C2×#408—24no—
37C22×C22⋊C8C2214yes—
38#2311—24no—
39#2311—24no—
40C2×#391—21no—
41C2×#390—21no—
42C2×#386—22no—
43C2×#380C2214yes—
44#1736—24no—
45#1735—24no—
46C2×#340C2214yes—
47C2×#340C2214yes—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41—22no—
56C22×#41—22no—
57C22×#41—22no—
58C22×#41—22no—
59C22×#41—22no—
60C22×#41C2×C414yes—
61C22×#41D414yes—
62C23×Q8—21no—
63C23×Q8—22no—
64C23×Q8—22no—
65C23×Q8—22no—
66C23×Q8—22no—
67C23×Q8—22no—
68C23×Q8—22no—
69C23×Q8—22no—
70C23×Q8—22no—
71C23×Q8—22no—
72C23×Q8—22no—
73C23×Q8—22no—
74C23×Q8C2×C414yes—
75C23×Q8D414yes—
76C23×Q8D414yes—
77C23×Q8D411yescharacteristic
78C23×Q8C2312yes—
79C23×D4D412yes—
80C23×D4D411yescharacteristic
81C24×C4—21no—
82C24×C4—21no—
83C24×C4C2312yes—
84C24×C4C2311yescharacteristic
85C22×M16—22no—
86C22×M16—22no—
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16D414yes—
92C23×C8—22no—
93C23×C8—22no—
94C23×C8—22no—
95C23×C8—22no—
96C23×C8—22no—
97C23×C8—22no—
98C23×C8D414yes—
99C23×C8C2312yes—
100C23×C8C2312yes—
101#536—232no—
102#536—232no—
103#536—232no—
104#536—232no—
105C2×C4⋊Q8—28no—
106C2×C4⋊Q8—28no—
107C2×C4⋊Q8—28no—
108C2×#124—28no—
109C2×#124—28no—
110C2×#124—28no—
111C2×#123—216no—
112C2×#123—216no—
113C2×#123—216no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8C2×C4116yescomplemented
120C2×#117—22no—
121C2×#117—22no—
122C2×#117—22no—
123C2×#117—22no—
124C2×#117—22no—
125C2×#117—22no—
126C2×#117—22no—
127C2×#117—22no—
128C2×#117C2×C414yes—
129C2×#117D414yes—
130C2×#117D414yes—
131C2×#117D414yes—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—22no—
134C22×C4⋊C4—22no—
135C22×C4⋊C4—22no—
136C22×C4⋊C4—22no—
137C22×C4⋊C4—22no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4D414yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—24no—
147C22×C42—21no—
148C22×C42—21no—
149#419—232no—
150C2×#103—232no—
151C2×#103—28no—
152C2×#103—28no—
153C2×#103—28no—
154C2×#103—28no—
155C2×#103—28no—
156C2×#103—28no—
157#408—232no—
158C2×C22⋊C8—28no—
159C2×C22⋊C8—28no—
160C2×C22⋊C8—28no—
161#391—28no—
162#390—28no—
163#386—216no—
164#380—28no—
165#380—28no—
166C2×#95—24no—
167#340—28no—
168#340—28no—
169C25C2×D412yes—
170C25C2×D411yescharacteristic
171C2×#41—28no—
172C2×#41—28no—
173C2×#41—28no—
174C2×#41—28no—
175C2×#41—28no—
176C2×#41—28no—
177C2×#41—28no—
178C2×#41—28no—
179C2×#41—28no—
180C2×#41—28no—
181C2×#41—28no—
182C2×#41—28no—
183C2×#41—44no—
184C2×#41—44no—
185C2×#41—44no—
186C2×#41—44no—
187C2×#41—44no—
188C2×#41—44no—
189C2×#41—44no—
190C2×#41—44no—
191C2×#41—44no—
192C2×#41—44no—
193C2×#41—44no—
194C2×#41—44no—
195C2×#41—44no—
196C2×#41—44no—
197C2×#41—44no—
198C2×#41—44no—
199C22×Q8—24no—
200C22×Q8—28no—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—28no—
206C22×Q8—28no—
207C22×Q8—22no—
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—28no—
215C22×Q8—28no—
216C22×Q8—28no—
217C22×Q8—28no—
218C22×Q8—28no—
219C22×Q8—28no—
220C22×Q8—28no—
221C22×Q8—28no—
222C22×Q8—28no—
223C22×Q8—28no—
224C22×Q8—28no—
225C22×Q8—28no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—42no—
235C22×Q8—44no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×Q8—44no—
239C22×Q8—44no—
240C22×Q8—44no—
241C22×Q8—44no—
242C22×Q8—44no—
243C22×Q8—44no—
244C22×Q8—42no—
245C22×Q8—44no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8C22⋊C414yes—
251C22×Q8C22⋊C4116yescomplemented
252C22×Q8C22×C414yes—
253C22×Q8C2×D414yes—
254C22×Q8C2×D414yes—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4C22⋊C418yes—
268C22×D4C22⋊C414yes—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—84no—
296C23×C4C22×C414yes—
297C23×C4C22×C412yes—
298C23×C4C2×D412yes—
299C23×C4C2×D414yes—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D412yes—
302C23×C4C2×D412yes—
303C23×C4C2×D412yes—
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D412yes—
307C23×C4C2×D412yes—
308C23×C4C2×D412yes—
309C23×C4C2×D412yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4#4112yes—
313C23×C4#4112yes—
314C23×C4C2411yescharacteristic
315C2×M16—28no—
316C2×M16—28no—
317C2×M16—28no—
318C2×M16—44no—
319C2×M16—44no—
320C2×M16—44no—
321C2×M16—44no—
322C22×C8—28no—
323C22×C8—28no—
324C22×C8—28no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—44no—
338C22×C8—44no—
339C22×C8—44no—
340C22×C8—44no—
341C22×C8C2×D414yes—
342C22×C8C2×D414yes—
343C4⋊Q8—264no—
344#124—264no—
345#123—2128no—
346C22⋊Q8—232no—
347C22⋊Q8—232no—
348C22⋊Q8—232no—
349C22⋊Q8—232no—
350#117—28no—
351#117—28no—
352#117—28no—
353#117—28no—
354#117—28no—
355#117—44no—
356#117—44no—
357#117C22⋊C4116yescomplemented
358C2×C4⋊C4—216no—
359C2×C4⋊C4—216no—
360C2×C4⋊C4—216no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4C22×C414yes—
382C2×C4⋊C4C2×D414yes—
383C2×C4⋊C4C2×D414yes—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2×D414yes—
386C2×C22⋊C4—216no—
387C2×C22⋊C4—216no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—216no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—216no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—88no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—42no—
403#103—232no—
404#103—232no—
405C22⋊C8—232no—
406#95—216no—
407C24—24no—
408C24—24no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—28no—
416C24—28no—
417C24C2×C22⋊C414yes—
418C24C2×C22⋊C412yes—
419C24#12012yes—
420C24#12012yes—
421C24#12012yes—
422C24#12112yes—
423C24#12112yes—
424C24#12312yes—
425C24C22×D411yescharacteristic
426#41—416no—
427#41—416no—
428#41—416no—
429#41—416no—
430#41—416no—
431#41—416no—
432#41—416no—
433#41—416no—
434C2×Q8—24no—
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—216no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—24no—
442C2×Q8—24no—
443C2×Q8—24no—
444C2×Q8—24no—
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—24no—
450C2×Q8—24no—
451C2×Q8—24no—
452C2×Q8—24no—
453C2×Q8—232no—
454C2×Q8—232no—
455C2×Q8—42no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—416no—
470C2×Q8—416no—
471C2×Q8—48no—
472C2×Q8—48no—
473C2×Q8—416no—
474C2×Q8—416no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—416no—
480C2×Q8—416no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8C2×C22⋊C418yes—
484C2×D4—216no—
485C2×D4—216no—
486C2×D4—216no—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—216no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—42no—
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—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—44no—
558C22×C4—48no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—88no—
562C22×C4—88no—
563C22×C4—88no—
564C22×C4C2×C22⋊C414yes—
565C22×C4C2×C22⋊C414yes—
566C22×C4C2×C22⋊C414yes—
567C22×C4C2×C22⋊C412yes—
568C22×C4C4×D414yes—
569C22×C4C4×D414yes—
570C22×C4C4×D414yes—
571C22×C4C4×D414yes—
572C22×C4#12014yes—
573C22×C4#12014yes—
574C22×C4#12014yes—
575C22×C4#12014yes—
576C22×C4#12014yes—
577C22×C4#12012yes—
578C22×C4#12012yes—
579C22×C4#12012yes—
580C22×C4#12114yes—
581C22×C4#12114yes—
582C22×C4#12114yes—
583C22×C4#12114yes—
584C22×C4#12114yes—
585C22×C4#12114yes—
586C22×C4#12114yes—
587C22×C4#12114yes—
588C22×C4#12114yes—
589C22×C4#12114yes—
590C22×C4#12112yes—
591C22×C4#12112yes—
592C22×C4#12314yes—
593C22×C4#12314yes—
594C22×C4#12314yes—
595C22×C4#12312yes—
596C22×C4#12414yes—
597C22×C4#12414yes—
598C22×C4#12714yes—
599C22×C4#12714yes—
600C22×C4C23×C411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C2×#4111yescharacteristic
611C22×C4C2×#4111yescharacteristic
612C22×C4C2×#4111yescharacteristic
613C22×C4C2×#4111yescharacteristic
614M16—416no—
615C2×C8—24no—
616C2×C8—24no—
617C2×C8—24no—
618C2×C8—24no—
619C2×C8—24no—
620C2×C8—24no—
621C2×C8—42no—
622C2×C8—42no—
623C2×C8—42no—
624C2×C8—42no—
625C2×C8—42no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8—42no—
629C2×C8—416no—
630C4⋊C4—264no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4—48no—
643C4⋊C4C2×C22⋊C418yes—
644C22⋊C4—264no—
645C22⋊C4—216no—
646C22⋊C4—48no—
647C22⋊C4—816no—
648C42—216no—
649C42—48no—
650C23—28no—
651C23—28no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—28no—
657C23—24no—
658C23—24no—
659C23—28no—
660C23—216no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—48no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—48no—
674C23—44no—
675C23—44no—
676C23—48no—
677C23#37914yes—
678C23#38614yes—
679C23#38614yes—
680C23#39214yes—
681C23#39214yes—
682C23#39414yes—
683C23#39414yes—
684C23C22×C22⋊C411yescharacteristic
685C23C2×#12011yescharacteristic
686C23C2×#12011yescharacteristic
687C23C2×#12011yescharacteristic
688C23C2×#12111yescharacteristic
689C23C2×#12111yescharacteristic
690C23C2×#12311yescharacteristic
691C23#57714yes—
692C23#57814yes—
693Q8—28no—
694Q8—28no—
695Q8—44no—
696Q8—44no—
697Q8—44no—
698Q8—44no—
699Q8—432no—
700Q8—416no—
701Q8—44no—
702Q8—44no—
703D4—432no—
704D4—416no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—48no—
719C2×C4—432no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—48no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—48no—
737C2×C4—44no—
738C2×C4—816no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#37914yes—
744C2×C4#38614yes—
745C2×C4#38614yes—
746C2×C4#38618yes—
747C2×C4#38618yes—
748C2×C4#39018yes—
749C2×C4#39018yes—
750C2×C4#39218yes—
751C2×C4#39218yes—
752C2×C4#39214yes—
753C2×C4#39214yes—
754C2×C4#39418yes—
755C2×C4#39418yes—
756C2×C4#39414yes—
757C2×C4#39414yes—
758C2×C4C22×C22⋊C411yescharacteristic
759C2×C4C22×C22⋊C411yescharacteristic
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C2×C4×D411yescharacteristic
762C2×C4C2×C4×D411yescharacteristic
763C2×C4C2×C4×D411yescharacteristic
764C2×C4C2×#12011yescharacteristic
765C2×C4C2×#12011yescharacteristic
766C2×C4C2×#12011yescharacteristic
767C2×C4C2×#12011yescharacteristic
768C2×C4C2×#12011yescharacteristic
769C2×C4C2×#12111yescharacteristic
770C2×C4C2×#12111yescharacteristic
771C2×C4C2×#12111yescharacteristic
772C2×C4C2×#12111yescharacteristic
773C2×C4C2×#12111yescharacteristic
774C2×C4C2×#12111yescharacteristic
775C2×C4C2×#12111yescharacteristic
776C2×C4C2×#12111yescharacteristic
777C2×C4C2×#12111yescharacteristic
778C2×C4C2×#12111yescharacteristic
779C2×C4C2×#12311yescharacteristic
780C2×C4C2×#12311yescharacteristic
781C2×C4C2×#12311yescharacteristic
782C2×C4C2×#12411yescharacteristic
783C2×C4C2×#12411yescharacteristic
784C2×C4C2×#12711yescharacteristic
785C2×C4C2×#12711yescharacteristic
786C8—44no—
787C8—44no—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—28no—
792C22—28no—
793C22—28no—
794C22—28no—
795C22—28no—
796C22—44no—
797C22—48no—
798C22—48no—
799C22—48no—
800C22—82no—
801C22—82no—
802C22—84no—
803C22—84no—
804C22—84no—
805C22#143818yes—
806C22C2×#37911yescharacteristic
807C22C2×#38611yescharacteristic
808C22C2×#38611yescharacteristic
809C22C2×#39211yescharacteristic
810C22C2×#39211yescharacteristic
811C22C2×#39411yescharacteristic
812C22C2×#39411yescharacteristic
813C22#289814yes—
814C22#300912yes—
815C22#301012yes—
816C22#301112yes—
817C22#301112yes—
818C22#301314yes—
819C22#305712yes—
820C22#305912yes—
821C22#306314yes—
822C22#309714yes—
823C4—44no—
824C4—48no—
825C4—48no—
826C4—84no—
827C4—84no—
828C4#143818yes—
829C4C2×#38611yescharacteristic
830C4C2×#38611yescharacteristic
831C4C2×#39011yescharacteristic
832C4C2×#39011yescharacteristic
833C4C2×#39211yescharacteristic
834C4C2×#39211yescharacteristic
835C4C2×#39411yescharacteristic
836C4C2×#39411yescharacteristic
837C2—28no—
838C2—84no—
839C2C2×#143811yescharacteristic
840C2#2060312yes—
841C2#2091312yes—
842C2#2097412yes—
843C2#2338811yescharacteristic
844C2#2338911yescharacteristic
845C2#2339412yes—
846C2#2348412yes—
847C2#2348712yes—
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×#41 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#419C2semidirect
3. C23×#103C2semidirect
6. C2×#1736C2semidirect
7. C2×#1735C2semidirect
8. #10970C2semidirect
18. C2×#536C4semidirect
119. C2×C22⋊Q8C2×C4semidirect
251. C22×Q8C22⋊C4semidirect
357. #117C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5362
C22×#4192
C23×#1032
C22×#4082
C2×#23112
C2×#17362
C2×#17352
#109702