Finite Group Databasebeta

← #357503

Subgroups — #357503

Order 512.

4522 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#536C211yesmaximal, characteristic
2C22×#417C211yesmaximal, characteristic
3C22×#419C211yesmaximal, characteristic, complemented
4C22×#416C211yesmaximal, characteristic
5C23×#103C211yesmaximal, characteristic, complemented
6C2×#1729C211yesmaximal, characteristic, complemented
7#13795C211yesmaximal, characteristic, complemented
8#11010C214yesmaximal, complemented
9#11009C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C24×Q8C2211yescharacteristic
12C23×M16C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C2×#536—24no—
15C2×#536—24no—
16C2×#536—24no—
17C2×#536—24no—
18C2×#536—24no—
19C2×#536C418yescomplemented
20C22×C4⋊Q8C2212yes—
21C22×#124C2212yes—
22C22×#123—22no—
23C22×C22⋊Q8—22no—
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#417—24no—
28C2×#417—24no—
29C2×#417—24no—
30C2×#419—24no—
31C2×#419—24no—
32C2×#419—24no—
33C2×#416—24no—
34C2×#416—24no—
35C2×#416—24no—
36C22×#103—24no—
37C22×#103—24no—
38C22×#103—24no—
39C22×#103C2214yes—
40C22×#103C2214yes—
41C22×#103C2212yes—
42C22×#103C2212yes—
43C22×#102C2212yes—
44C22×#102C2212yes—
45#1729—24no—
46C2×#336C2214yes—
47C4⋊#95—22no—
48C4⋊#95C2214yes—
49C22⋊#95—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×#41—22no—
61C22×#41C2×C414yes—
62C22×#41D414yes—
63C22×#41D414yes—
64C23×Q8—21no—
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×Q8—22no—
75C23×Q8—22no—
76C23×Q8C2×C414yes—
77C23×Q8D414yes—
78C23×Q8D414yes—
79C23×Q8C2312yes—
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4—21no—
85C24×C4—21no—
86C24×C4C2311yescharacteristic
87C22×M16—22no—
88C22×M16—22no—
89C22×M16—22no—
90C22×M16—22no—
91C22×M16—22no—
92C22×M16—22no—
93C22×M16D414yes—
94C23×C8—22no—
95C23×C8—22no—
96C23×C8—22no—
97C23×C8—22no—
98C23×C8—22no—
99C23×C8—22no—
100C23×C8D414yes—
101C23×C8C2312yes—
102C23×C8C2312yes—
103#536—232no—
104#536—232no—
105#536—232no—
106#536—232no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8C2×C418yescomplemented
113C2×#124—24no—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—24no—
118C2×#124C2×C418yescomplemented
119C2×#123—216no—
120C2×#123—216no—
121C2×#123—216no—
122C2×C22⋊Q8—216no—
123C2×C22⋊Q8—216no—
124C2×C22⋊Q8—216no—
125C2×#117—22no—
126C2×#117—22no—
127C2×#117—22no—
128C2×#117—22no—
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—22no—
133C2×#117—22no—
134C2×#117C2×C414yes—
135C2×#117D414yes—
136C2×#117D414yes—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—22no—
139C22×C4⋊C4—22no—
140C22×C4⋊C4—22no—
141C22×C4⋊C4—22no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—22no—
144C22×C4⋊C4D414yes—
145C22×C4⋊C4D412yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C22⋊C4—24no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4D412yes—
151C22×C42—21no—
152C22×C42C2312yes—
153#419—232no—
154#417—232no—
155#416—232no—
156C2×#103—232no—
157C2×#103—28no—
158C2×#103—24no—
159C2×#103—28no—
160C2×#103—24no—
161C2×#103—28no—
162C2×#103—24no—
163C2×#103—28no—
164C2×#103—24no—
165C2×#103—28no—
166C2×#103—24no—
167C2×#103—28no—
168C2×#103—24no—
169C2×#102—24no—
170C2×#102—24no—
171C2×#102—24no—
172C2×#102—24no—
173C2×#102—24no—
174C2×#102—24no—
175C2×#95—28no—
176#336—28no—
177C25—21no—
178C25C2×D411yescharacteristic
179C2×#41—28no—
180C2×#41—28no—
181C2×#41—28no—
182C2×#41—28no—
183C2×#41—28no—
184C2×#41—28no—
185C2×#41—28no—
186C2×#41—28no—
187C2×#41—28no—
188C2×#41—28no—
189C2×#41—28no—
190C2×#41—28no—
191C2×#41—28no—
192C2×#41—28no—
193C2×#41—28no—
194C2×#41—44no—
195C2×#41—44no—
196C2×#41—44no—
197C2×#41—44no—
198C2×#41—44no—
199C2×#41—44no—
200C2×#41—44no—
201C2×#41—44no—
202C2×#41—44no—
203C2×#41—44no—
204C2×#41—44no—
205C2×#41—44no—
206C2×#41C22⋊C4116yes—
207C22×Q8—24no—
208C22×Q8—28no—
209C22×Q8—24no—
210C22×Q8—24no—
211C22×Q8—28no—
212C22×Q8—28no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—28no—
220C22×Q8—28no—
221C22×Q8—28no—
222C22×Q8—28no—
223C22×Q8—28no—
224C22×Q8—28no—
225C22×Q8—28no—
226C22×Q8—28no—
227C22×Q8—28no—
228C22×Q8—28no—
229C22×Q8—28no—
230C22×Q8—28no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—44no—
252C22×Q8—44no—
253C22×Q8—44no—
254C22×Q8—44no—
255C22×Q8—44no—
256C22×Q8—44no—
257C22×Q8—44no—
258C22×Q8—44no—
259C22×Q8—42no—
260C22×Q8—44no—
261C22×Q8—42no—
262C22×Q8—44no—
263C22×Q8C22⋊C4116yes—
264C22×Q8C22×C414yes—
265C22×Q8C22×C412yes—
266C22×Q8C2×D414yes—
267C22×Q8C2×D414yes—
268C22×Q8C2×D412yes—
269C22×Q8C2×D412yes—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—24no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—42no—
285C22×D4—42no—
286C22×D4—42no—
287C22×D4—42no—
288C22×D4C22×C412yes—
289C22×D4C2×D412yes—
290C22×D4C2×D412yes—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—22no—
295C23×C4—21no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—24no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—84no—
313C23×C4C22×C412yes—
314C23×C4C2×D414yes—
315C23×C4C2×D412yes—
316C23×C4C2×D412yes—
317C23×C4C2×D412yes—
318C23×C4C2×D412yes—
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D412yes—
321C23×C4C2×D412yes—
322C23×C4C2×D412yes—
323C23×C4C2×D412yes—
324C23×C4C2×D412yes—
325C23×C4#4112yes—
326C23×C4#4112yes—
327C23×C4#4112yes—
328C23×C4#4112yes—
329C23×C4C2411yescharacteristic
330C2×M16—28no—
331C2×M16—28no—
332C2×M16—28no—
333C2×M16—44no—
334C2×M16—44no—
335C2×M16—44no—
336C2×M16—44no—
337C22×C8—28no—
338C22×C8—28no—
339C22×C8—28no—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—44no—
353C22×C8—44no—
354C22×C8—44no—
355C22×C8—44no—
356C22×C8C2×D414yes—
357C22×C8C2×D414yes—
358C4⋊Q8—216no—
359C4⋊Q8—216no—
360C4⋊Q8—216no—
361C4⋊Q8—216no—
362#124—216no—
363#124—216no—
364#124—216no—
365#124—216no—
366#123—2128no—
367C22⋊Q8—2128no—
368#117—28no—
369#117—28no—
370#117—28no—
371#117—28no—
372#117—28no—
373#117—28no—
374#117—44no—
375#117—44no—
376C2×C4⋊C4—216no—
377C2×C4⋊C4—216no—
378C2×C4⋊C4—216no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4C22⋊C418yes—
399C2×C4⋊C4C2×D414yes—
400C2×C4⋊C4C2×D414yes—
401C2×C22⋊C4—216no—
402C2×C22⋊C4—216no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—216no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C22⋊C418yes—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—24no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42C22×C414yes—
418C2×C42C2×D414yes—
419#103—232no—
420#103—216no—
421#103—216no—
422#103—232no—
423#102—216no—
424#102—216no—
425#95—88no—
426C24—24no—
427C24—24no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—44no—
436C24—44no—
437C24C2×C22⋊C412yes—
438C24#12012yes—
439C24#12012yes—
440C24#12112yes—
441C24#12112yes—
442C24#12412yes—
443C24#12712yes—
444C24C22×D411yescharacteristic
445#41—232no—
446#41—232no—
447#41—416no—
448#41—416no—
449#41—416no—
450#41—416no—
451#41—416no—
452#41—416no—
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—24no—
456C2×Q8—24no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—216no—
460C2×Q8—24no—
461C2×Q8—24no—
462C2×Q8—24no—
463C2×Q8—24no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—24no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—24no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—232no—
485C2×Q8—232no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—41no—
489C2×Q8—41no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8—42no—
507C2×Q8—41no—
508C2×Q8—42no—
509C2×Q8—41no—
510C2×Q8—416no—
511C2×Q8—416no—
512C2×Q8—48no—
513C2×Q8—48no—
514C2×Q8—48no—
515C2×Q8—48no—
516C2×Q8—416no—
517C2×Q8—416no—
518C2×Q8—48no—
519C2×Q8—48no—
520C2×Q8—416no—
521C2×Q8—416no—
522C2×Q8C2×C22⋊C418yes—
523C2×Q8C2×C22⋊C414yes—
524C2×D4—216no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4C2×C22⋊C414yes—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—216no—
570C22×C4—216no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—41no—
578C22×C4—42no—
579C22×C4—41no—
580C22×C4—42no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—88no—
602C22×C4—88no—
603C22×C4—88no—
604C22×C4C2×C22⋊C418yes—
605C22×C4C2×C22⋊C414yes—
606C22×C4C2×C22⋊C414yes—
607C22×C4C2×C22⋊C412yes—
608C22×C4C4×D414yes—
609C22×C4C4×D414yes—
610C22×C4C4×D414yes—
611C22×C4C4×D414yes—
612C22×C4#12014yes—
613C22×C4#12014yes—
614C22×C4#12014yes—
615C22×C4#12014yes—
616C22×C4#12014yes—
617C22×C4#12014yes—
618C22×C4#12012yes—
619C22×C4#12012yes—
620C22×C4#12114yes—
621C22×C4#12114yes—
622C22×C4#12114yes—
623C22×C4#12114yes—
624C22×C4#12114yes—
625C22×C4#12114yes—
626C22×C4#12114yes—
627C22×C4#12114yes—
628C22×C4#12114yes—
629C22×C4#12114yes—
630C22×C4#12112yes—
631C22×C4#12112yes—
632C22×C4#12314yes—
633C22×C4#12314yes—
634C22×C4#12314yes—
635C22×C4#12314yes—
636C22×C4#12414yes—
637C22×C4#12412yes—
638C22×C4#12714yes—
639C22×C4#12712yes—
640C22×C4C23×C411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C22×D411yescharacteristic
650C22×C4C2×#4111yescharacteristic
651C22×C4C2×#4111yescharacteristic
652C22×C4C2×#4111yescharacteristic
653C22×C4C2×#4111yescharacteristic
654M16—416no—
655C2×C8—24no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—24no—
660C2×C8—24no—
661C2×C8—42no—
662C2×C8—42no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8—42no—
666C2×C8—42no—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—416no—
670C4⋊C4—264no—
671C4⋊C4—216no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—48no—
681C22⋊C4—264no—
682C22⋊C4—216no—
683C22⋊C4—48no—
684C42—24no—
685C42—24no—
686C42—24no—
687C42—24no—
688C42—48no—
689C23—28no—
690C23—28no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—28no—
696C23—24no—
697C23—24no—
698C23—28no—
699C23—24no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—48no—
705C23—44no—
706C23—44no—
707C23—48no—
708C23—42no—
709C23—42no—
710C23—84no—
711C23—82no—
712C23—82no—
713C23—82no—
714C23—82no—
715C23—84no—
716C23#37914yes—
717C23#39014yes—
718C23#39014yes—
719C23#39214yes—
720C23#39214yes—
721C23#39414yes—
722C23#39414yes—
723C23C22×C22⋊C411yescharacteristic
724C23C2×#12011yescharacteristic
725C23C2×#12011yescharacteristic
726C23C2×#12111yescharacteristic
727C23C2×#12111yescharacteristic
728C23C2×#12411yescharacteristic
729C23C2×#12711yescharacteristic
730C23#57714yes—
731C23#57814yes—
732Q8—28no—
733Q8—28no—
734Q8—24no—
735Q8—24no—
736Q8—44no—
737Q8—44no—
738Q8—42no—
739Q8—42no—
740Q8—44no—
741Q8—44no—
742Q8—42no—
743Q8—42no—
744Q8—432no—
745Q8—44no—
746Q8—44no—
747Q8—42no—
748Q8—42no—
749D4—24no—
750D4—24no—
751D4—432no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—42no—
757D4—42no—
758C2×C4—216no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—432no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—432no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—816no—
784C2×C4—82no—
785C2×C4—84no—
786C2×C4—82no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4#37914yes—
790C2×C4#38618yes—
791C2×C4#38618yes—
792C2×C4#38618yes—
793C2×C4#38618yes—
794C2×C4#39014yes—
795C2×C4#39014yes—
796C2×C4#39218yes—
797C2×C4#39218yes—
798C2×C4#39214yes—
799C2×C4#39214yes—
800C2×C4#39418yes—
801C2×C4#39418yes—
802C2×C4#39414yes—
803C2×C4#39414yes—
804C2×C4C22×C22⋊C411yescharacteristic
805C2×C4C22×C22⋊C411yescharacteristic
806C2×C4C2×C4×D411yescharacteristic
807C2×C4C2×C4×D411yescharacteristic
808C2×C4C2×C4×D411yescharacteristic
809C2×C4C2×C4×D411yescharacteristic
810C2×C4C2×#12011yescharacteristic
811C2×C4C2×#12011yescharacteristic
812C2×C4C2×#12011yescharacteristic
813C2×C4C2×#12011yescharacteristic
814C2×C4C2×#12011yescharacteristic
815C2×C4C2×#12011yescharacteristic
816C2×C4C2×#12111yescharacteristic
817C2×C4C2×#12111yescharacteristic
818C2×C4C2×#12111yescharacteristic
819C2×C4C2×#12111yescharacteristic
820C2×C4C2×#12111yescharacteristic
821C2×C4C2×#12111yescharacteristic
822C2×C4C2×#12111yescharacteristic
823C2×C4C2×#12111yescharacteristic
824C2×C4C2×#12111yescharacteristic
825C2×C4C2×#12111yescharacteristic
826C2×C4C2×#12311yescharacteristic
827C2×C4C2×#12311yescharacteristic
828C2×C4C2×#12311yescharacteristic
829C2×C4C2×#12311yescharacteristic
830C2×C4C2×#12411yescharacteristic
831C2×C4C2×#12711yescharacteristic
832C8—44no—
833C8—44no—
834C22—28no—
835C22—28no—
836C22—24no—
837C22—24no—
838C22—28no—
839C22—28no—
840C22—28no—
841C22—28no—
842C22—44no—
843C22—48no—
844C22—84no—
845C22—82no—
846C22—82no—
847C22—84no—
848C22—84no—
849C22—84no—
850C22—84no—
851C22#143818yes—
852C22C2×#37911yescharacteristic
853C22C2×#39011yescharacteristic
854C22C2×#39011yescharacteristic
855C22C2×#39211yescharacteristic
856C22C2×#39211yescharacteristic
857C22C2×#39411yescharacteristic
858C22C2×#39411yescharacteristic
859C22#289814yes—
860C22#301012yes—
861C22#301112yes—
862C22#301314yes—
863C22#304212yes—
864C22#304412yes—
865C22#304614yes—
866C22#313714yes—
867C22#315412yes—
868C22#315612yes—
869C4—44no—
870C4—48no—
871C4—48no—
872C4—84no—
873C4—84no—
874C4#143818yes—
875C4C2×#38611yescharacteristic
876C4C2×#38611yescharacteristic
877C4C2×#38611yescharacteristic
878C4C2×#38611yescharacteristic
879C4C2×#39211yescharacteristic
880C4C2×#39211yescharacteristic
881C4C2×#39411yescharacteristic
882C4C2×#39411yescharacteristic
883C2—28no—
884C2—84no—
885C2C2×#143811yescharacteristic
886C2#2060312yes—
887C2#2120512yes—
888C2#2126212yes—
889C2#2342411yescharacteristic
890C2#2342511yescharacteristic
891C2#2342712yes—
892C2#2351012yes—
893C2#2351212yes—
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#419C2semidirect
5. C23×#103C2semidirect
6. C2×#1729C2semidirect
7. #13795C2semidirect
8. #11010C2semidirect
9. #11009C2semidirect
19. C2×#536C4semidirect
112. C2×C4⋊Q8C2×C4semidirect
118. C2×#124C2×C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5362
C22×#4172
C22×#4192
C22×#4162
C23×#1032
C2×#17292
#137952
#110102
#110092