Finite Group Databasebeta

← #392957

Subgroups — #392957

Order 512.

2266 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#405C211yesmaximal, characteristic, complemented
2C2×#2392C211yesmaximal, characteristic
3C2×#1955C211yesmaximal, characteristic, complemented
4C2×#1954C211yesmaximal, characteristic, complemented
5C2×#1870C212yesmaximal, complemented
6C2×#1869C212yesmaximal, complemented
7C2×#1798C211yesmaximal, characteristic, complemented
8#10922C212yesmaximal, complemented
9#10921C212yesmaximal, complemented
10#10835C211yesmaximal, characteristic, complemented
11#10834C211yesmaximal, characteristic, complemented
12C23×M16C2211yescharacteristic
13C24×C8C2211yescharacteristic
14C22×C4×D4C2212yes—
15C22×C4×D4C2211yescharacteristic
16C22×#117C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C22⋊C8C2212yes—
20C22×C22⋊C8C2212yes—
21C22×C22⋊C8C2212yes—
22C22×C22⋊C8C2212yes—
23C22×C22⋊C8C2212yes—
24C2×#405—24no—
25C2×#405—24no—
26C2×#405—24no—
27C22×#97C2211yescharacteristic
28C22×#97C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2392—24no—
32#2392—24no—
33C2×#398C411yescharacteristic
34C2×#397C411yescharacteristic
35C2×#396C412yes—
36C2×#394C411yescharacteristic
37C2×#394C412yes—
38C2×#392C411yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2212yes—
41#1955—24no—
42#1954—24no—
43#1870—28no—
44#1869—28no—
45#1798—24no—
46C2×#336C2212yes—
47C2×#336C2212yes—
48C2×#336C2212yes—
49C2×#336C2212yes—
50C2×#336C2212yes—
51C23×D4C2×C412yes—
52C23×D4C2×C411yescharacteristic
53C24×C4C2312yes—
54C24×C4C2311yescharacteristic
55C22×M16—22no—
56C22×M16—22no—
57C22×M16—22no—
58C22×M16—22no—
59C22×M16—22no—
60C22×M16—22no—
61C22×M16D414yescomplemented
62C23×C8—22no—
63C23×C8—22no—
64C23×C8—22no—
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—22no—
68C23×C8D414yescomplemented
69C23×C8C2312yes—
70C23×C8C2312yes—
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×C4×D4—24no—
76C2×C4×D4—24no—
77C2×C4×D4—24no—
78C2×C4×D4—24no—
79C2×C4×D4—24no—
80C2×C4×D4—24no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—22no—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117D414yes—
92C2×#117D414yes—
93C22×C4⋊C4C2×C412yes—
94C22×C4⋊C4C2×C411yescharacteristic
95C22×C4⋊C4C2×C412yes—
96C22×C4⋊C4C2×C411yescharacteristic
97C22×C4⋊C4C2×C411yescharacteristic
98C22×C22⋊C4C2×C412yes—
99C22×C22⋊C4C2×C412yes—
100C22×C22⋊C4C2×C412yes—
101C22×C22⋊C4C2×C412yes—
102C22×C22⋊C4C2×C412yes—
103C22×C22⋊C4C2×C411yescharacteristic
104C22×C22⋊C4C2×C411yescharacteristic
105C22×C42C2312yes—
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C22⋊C8—24no—
115C2×C22⋊C8—24no—
116C2×C22⋊C8—24no—
117C2×C22⋊C8—24no—
118C2×C22⋊C8—24no—
119C2×C22⋊C8—24no—
120C2×C22⋊C8—24no—
121C2×C22⋊C8—24no—
122C2×C22⋊C8—24no—
123C2×C22⋊C8—24no—
124C2×C22⋊C8—24no—
125C2×C22⋊C8—24no—
126C2×C22⋊C8—24no—
127C2×C22⋊C8—24no—
128C2×C22⋊C8—24no—
129#405—232no—
130C2×#97—22no—
131C2×#97—22no—
132C2×#97—22no—
133C2×#97—22no—
134C2×#97—22no—
135C2×#97D414yescomplemented
136C2×C4×C8—22no—
137C2×C4×C8—22no—
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—22no—
141C2×C4×C8D414yescomplemented
142#398—24no—
143#397—24no—
144#396—28no—
145#394—24no—
146#394—28no—
147#392—24no—
148C4×C4⋊C4—22no—
149C4×C4⋊C4—22no—
150C4×C22⋊C4—24no—
151C4×C22⋊C4—24no—
152C2×#95C2×C411yescharacteristic
153C2×#95C2×C411yescharacteristic
154C2×#95C2×C412yes—
155C2×#95C2×C412yes—
156#336—24no—
157#336—24no—
158#336—24no—
159#336—24no—
160#336—24no—
161C25C22×C412yes—
162C25C22×C411yescharacteristic
163C22×D4—24no—
164C22×D4—24no—
165C22×D4—24no—
166C22×D4—24no—
167C22×D4—24no—
168C22×D4—22no—
169C22×D4—22no—
170C22×D4—22no—
171C22×D4—24no—
172C22×D4—42no—
173C22×D4—42no—
174C22×D4—42no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4C22×C412yes—
198C23×C4C22×C412yes—
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C412yes—
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C2×D412yes—
206C23×C4C2×D412yes—
207C23×C4C2×D412yes—
208C23×C4C2×D412yes—
209C23×C4#4112yes—
210C23×C4#4112yes—
211C23×C4C2411yescharacteristic
212C2×M16—28no—
213C2×M16—28no—
214C2×M16—28no—
215C2×M16—28no—
216C2×M16—28no—
217C2×M16—28no—
218C2×M16—28no—
219C22×C8—28no—
220C22×C8—28no—
221C22×C8—28no—
222C22×C8—28no—
223C22×C8—28no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—28no—
241C22×C8—28no—
242C22×C8—22no—
243C22×C8—22no—
244C22×C8—22no—
245C22×C8—22no—
246C22×C8—22no—
247C22×C8—22no—
248C22×C8—22no—
249C22×C8—22no—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8—22no—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8C2×D412yes—
259C22×C8C2×D412yes—
260C22×C8C2×D412yes—
261C22×C8C2×D412yes—
262C22×C8C2×D412yes—
263C22×C8C2×D412yes—
264C22×C8#4112yes—
265C22×C8#4112yes—
266C22×C8#4112yes—
267C22×C8#4112yes—
268C4×D4—48no—
269C4×D4—48no—
270C4×D4—48no—
271C4×D4—48no—
272C4×D4—44no—
273C4×D4—44no—
274C4×D4—44no—
275C4×D4—44no—
276#117—28no—
277#117—28no—
278#117—28no—
279#117—28no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4C22⋊C414yes—
294C2×C4⋊C4C22⋊C414yes—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4C22⋊C414yes—
315C2×C22⋊C4C22⋊C414yes—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—22no—
326C2×C42C2×D412yes—
327C2×C42C2×D412yes—
328C2×C42C2×D412yes—
329C2×C42C2×D412yes—
330C2×C42C2×D412yes—
331C2×C42C2×D412yes—
332C2×C42#4112yes—
333C2×C42#4112yes—
334C4⋊C8—44no—
335C4⋊C8—44no—
336C22⋊C8—48no—
337C22⋊C8—48no—
338C22⋊C8—48no—
339C22⋊C8—48no—
340C22⋊C8—48no—
341#97—28no—
342#97—28no—
343C4×C8—28no—
344C4×C8—28no—
345#95—24no—
346#95—24no—
347#95—22no—
348#95—22no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—22no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24C2×C22⋊C412yes—
372C24C4×D412yes—
373C24C4×D412yes—
374C24#13114yes—
375C24C23×C411yescharacteristic
376C2×D4—28no—
377C2×D4—216no—
378C2×D4—48no—
379C2×D4—48no—
380C2×D4—48no—
381C2×D4—48no—
382C2×D4—44no—
383C2×D4—48no—
384C2×D4—48no—
385C2×D4—48no—
386C2×D4—48no—
387C2×D4—44no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
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—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4C2×C22⋊C412yes—
477C22×C4C2×C22⋊C412yes—
478C22×C4C2×C22⋊C412yes—
479C22×C4C2×C22⋊C412yes—
480C22×C4C2×C22⋊C412yes—
481C22×C4C4×D412yes—
482C22×C4C4×D412yes—
483C22×C4C4×D412yes—
484C22×C4C4×D412yes—
485C22×C4C4×D412yes—
486C22×C4C4×D412yes—
487C22×C4#12114yes—
488C22×C4#12114yes—
489C22×C4#12414yes—
490C22×C4#12714yes—
491C22×C4#13114yes—
492C22×C4C22×D411yescharacteristic
493C22×C4C22×D411yescharacteristic
494C22×C4C22×D411yescharacteristic
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506M16—232no—
507C2×C8—232no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—42no—
533C2×C8—42no—
534C2×C8—42no—
535C2×C8—42no—
536C2×C8—42no—
537C2×C8—42no—
538C2×C8—42no—
539C2×C8—42no—
540C2×C8—42no—
541C2×C8—42no—
542C2×C8—42no—
543C2×C8—42no—
544C2×C8—42no—
545C2×C8—42no—
546C2×C8#12114yes—
547C2×C8#12114yes—
548C2×C8#12114yes—
549C2×C8#12114yes—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—48no—
553C4⋊C4—44no—
554C4⋊C4—48no—
555C22⋊C4—28no—
556C22⋊C4—28no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C42—22no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—42no—
567C42—42no—
568C42—42no—
569C42—42no—
570C42#12014yes—
571C42#12114yes—
572C42#12114yes—
573C42#12314yes—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23#39014yes—
632C23C22×C22⋊C411yescharacteristic
633C23C2×C4×D411yescharacteristic
634C23C2×C4×D411yescharacteristic
635C23C2×C4×D411yescharacteristic
636C23C2×C4×D411yescharacteristic
637C23C4×#4111yescharacteristic
638C23C4×#4111yescharacteristic
639C23C2×#13112yes—
640C23C2×#13112yes—
641C23#56812yes—
642C23#56812yes—
643D4—416no—
644D4—432no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#38614yes—
707C2×C4#38614yes—
708C2×C4#39014yes—
709C2×C4C2×#12011yescharacteristic
710C2×C4C2×#12111yescharacteristic
711C2×C4C2×#12111yescharacteristic
712C2×C4C2×#12111yescharacteristic
713C2×C4C2×#12111yescharacteristic
714C2×C4C2×#12111yescharacteristic
715C2×C4C2×#12111yescharacteristic
716C2×C4C2×#12111yescharacteristic
717C2×C4C2×#12111yescharacteristic
718C2×C4C2×#12311yescharacteristic
719C2×C4#52511yescharacteristic
720C2×C4#52511yescharacteristic
721C2×C4#52511yescharacteristic
722C2×C4#52511yescharacteristic
723C2×C4#52511yescharacteristic
724C2×C4#52511yescharacteristic
725C2×C4C2×#12411yescharacteristic
726C2×C4#52911yescharacteristic
727C2×C4#52911yescharacteristic
728C2×C4#52911yescharacteristic
729C2×C4#52911yescharacteristic
730C2×C4C2×#12711yescharacteristic
731C2×C4#53211yescharacteristic
732C2×C4#53211yescharacteristic
733C2×C4#53211yescharacteristic
734C2×C4#53211yescharacteristic
735C2×C4#53211yescharacteristic
736C2×C4#53211yescharacteristic
737C8—24no—
738C8—24no—
739C8—24no—
740C8—24no—
741C8—82no—
742C8—82no—
743C22—24no—
744C22—28no—
745C22—44no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22C2×#38611yescharacteristic
770C22C2×#39011yescharacteristic
771C22#229711yescharacteristic
772C22C4×#12111yescharacteristic
773C22C4×#12111yescharacteristic
774C22C4×#12111yescharacteristic
775C22C4×#12111yescharacteristic
776C22#288012yes—
777C22#288012yes—
778C22#292911yescharacteristic
779C22#292912yes—
780C22#293011yescharacteristic
781C22#293012yes—
782C22#293111yescharacteristic
783C22#293211yescharacteristic
784C22#293312yes—
785C22#293312yes—
786C22#293312yes—
787C22#293512yes—
788C22#296612yes—
789C22#296712yes—
790C22#296812yes—
791C22#296912yes—
792C4—24no—
793C4—24no—
794C4—24no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—82no—
799C4—82no—
800C4#284711yescharacteristic
801C4#284711yescharacteristic
802C4#285011yescharacteristic
803C4#285011yescharacteristic
804C4#285411yescharacteristic
805C4#285411yescharacteristic
806C4#285611yescharacteristic
807C4#285611yescharacteristic
808C2—44no—
809C2—84no—
810C2#1469811yescharacteristic
811C2#2089911yescharacteristic
812C2#2090011yescharacteristic
813C2#2119112yes—
814C2#2138112yes—
815C2#2149111yescharacteristic
816C2#2149211yescharacteristic
817C2#2149311yescharacteristic
818C2#2149411yescharacteristic
819C2#2149512yes—
820C2#2149612yes—
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC2×#392C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#405C2semidirect
3. C2×#1955C2semidirect
4. C2×#1954C2semidirect
5. C2×#1870C2semidirect
6. C2×#1869C2semidirect
7. C2×#1798C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10835C2semidirect
11. #10834C2semidirect
61. C22×M16D4semidirect
68. C23×C8D4semidirect
135. C2×#97D4semidirect
141. C2×C4×C8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#4052
C2×#23922
C2×#19552
C2×#19542
C2×#18702
C2×#18692
C2×#17982
#109222
#109212
#108352
#108342