Finite Group Databasebeta

← #355827

Subgroups — #355827

Order 512.

1556 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1870C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1752C211yesmaximal, characteristic, complemented
4C2×#1753C211yesmaximal, characteristic, complemented
5#13847C211yesmaximal, characteristic
6#10922C211yesmaximal, characteristic, complemented
7#10921C211yesmaximal, characteristic, complemented
8#10921C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10875C211yesmaximal, characteristic, complemented
11#10874C211yesmaximal, characteristic, complemented
12#10796C211yesmaximal, characteristic, complemented
13#10715C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10694C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×#376C2211yescharacteristic
35#1870C418yescomplemented
36#1869C418yescomplemented
37#1753—24no—
38#1752—24no—
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1445C412yes—
56#1439C412yes—
57#1439C412yes—
58#1438C412yes—
59C23×D4C2×C411yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C22×M16—22no—
63C22×M16—22no—
64C22×M16—41no—
65C22×M16—41no—
66C22×M16—41no—
67C22×M16—41no—
68C22×M16C2×C414yes—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—41no—
72C23×C8—41no—
73C23×C8—41no—
74C23×C8—41no—
75C23×C8C2×C414yes—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4C2×C414yes—
89C2×C4×D4C2×C414yes—
90C22×C4⋊C4C2×C412yes—
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C412yes—
93C22×C22⋊C4C2×C412yes—
94C22×C22⋊C4C2×C412yes—
95C22×C22⋊C4C2×C412yes—
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C2×C22⋊C8—22no—
104C2×C22⋊C8—22no—
105C2×C22⋊C8—22no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—41no—
108C2×C22⋊C8—41no—
109C2×C22⋊C8—41no—
110C2×C22⋊C8—41no—
111C2×C22⋊C8—41no—
112C2×C22⋊C8—41no—
113C2×C22⋊C8—41no—
114C2×C22⋊C8—41no—
115C2×C22⋊C8C2×C414yes—
116C2×C22⋊C8C2×C414yes—
117C2×C22⋊C8C2×C414yes—
118C2×C22⋊C8C2×C414yes—
119C2×C22⋊C8C2×C414yes—
120C2×C22⋊C8C2×C414yes—
121C2×#97—22no—
122C2×#97—41no—
123C2×#97—41no—
124C2×#97—41no—
125C2×#97—41no—
126C2×#97D414yescomplemented
127C2×C4×C8—22no—
128C2×C4×C8—22no—
129C2×C4×C8—41no—
130C2×C4×C8—41no—
131C2×C4×C8—41no—
132C2×C4×C8—41no—
133C4×C4⋊C4—41no—
134C4×C4⋊C4—41no—
135C4×C22⋊C4—22no—
136C4×C22⋊C4—22no—
137C4×C22⋊C4—22no—
138C4×C22⋊C4—22no—
139C4×C22⋊C4—41no—
140C4×C22⋊C4—41no—
141C4×C22⋊C4—41no—
142C4×C22⋊C4—41no—
143#376—41no—
144#376—41no—
145C2×#95C2×C412yes—
146C2×#95C2×C412yes—
147C2×#95C2×C412yes—
148C2×#95C2×C412yes—
149C2×#95C2×C412yes—
150C2×#95C2×C412yes—
151C2×#95C2×C412yes—
152#336—22no—
153#336—22no—
154#336—22no—
155#336—22no—
156#336—22no—
157#336—22no—
158#336—41no—
159#336—41no—
160#336—41no—
161#336—41no—
162#336—41no—
163#336—41no—
164#336C2×C414yes—
165#336C2×C414yes—
166#336C2×C414yes—
167#336C2×C414yes—
168C25C22×C411yescharacteristic
169C25C22×C411yescharacteristic
170C22×D4—24no—
171C22×D4—41no—
172C22×D4—41no—
173C22×D4—42no—
174C22×D4C4214yes—
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—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4C22×C412yes—
200C23×C4C22×C412yes—
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C412yes—
206C23×C4C22×C412yes—
207C23×C4C22×C412yes—
208C23×C4C22×C412yes—
209C23×C4C22×C412yes—
210C23×C4C22×C412yes—
211C23×C4C2411yescharacteristic
212C2×M16—28no—
213C2×M16—44no—
214C2×M16—44no—
215C2×M16—44no—
216C2×M16—44no—
217C2×M16—44no—
218C2×M16—44no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
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—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—28no—
264C22×C8—44no—
265C22×C8—44no—
266C22×C8—44no—
267C22×C8—44no—
268C22×C8—44no—
269C22×C8—44no—
270C22×C8C22×C412yes—
271C22×C8C22×C412yes—
272C22×C8C22×C412yes—
273C22×C8C22×C412yes—
274C22×C8C22×C412yes—
275C22×C8C22×C412yes—
276C22×C8C22×C412yes—
277C22×C8C22×C412yes—
278C22×C8C2×D412yes—
279C22×C8C2×D412yes—
280C22×C8#4112yes—
281C22×C8#4112yes—
282C4×D4—44no—
283C4×D4—44no—
284C4×D4—44no—
285C4×D4—44no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4C4214yes—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—41no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4C4214yes—
309C2×C22⋊C4C4214yes—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42C22×C412yes—
337C2×C42C22×C412yes—
338C2×C42C2×D412yes—
339C2×C42#4112yes—
340C22⋊C8—28no—
341C22⋊C8—28no—
342C22⋊C8—44no—
343C22⋊C8—44no—
344C22⋊C8—44no—
345C22⋊C8—44no—
346#97—44no—
347#97—44no—
348C4×C8—44no—
349C4×C8—44no—
350#95—24no—
351#95—24no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24C2×C4212yes—
377C24C2×C4212yes—
378C24#13114yes—
379C24C23×C411yescharacteristic
380C2×D4—28no—
381C2×D4—44no—
382C2×D4—44no—
383C2×D4—48no—
384C2×D4—48no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
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—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
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—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C2×C4212yes—
488C22×C4C2×C4212yes—
489C22×C4C2×C4212yes—
490C22×C4C2×C4212yes—
491C22×C4C4×D414yes—
492C22×C4#13114yes—
493C22×C4C23×C411yescharacteristic
494C22×C4C23×C411yescharacteristic
495C22×C4C22×D411yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C4H(5,𝔽2)11yescharacteristic
501C22×C4H(5,𝔽2)11yescharacteristic
502C22×C4H(5,𝔽2)11yescharacteristic
503C22×C4H(5,𝔽2)11yescharacteristic
504C22×C4H(5,𝔽2)11yescharacteristic
505C22×C4H(5,𝔽2)11yescharacteristic
506C22×C42−1+411yescharacteristic
507M16—416no—
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—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—416no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8C4×D414yes—
564C2×C8C4×D414yes—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—41no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23#40514yes—
639C23C22×C4211yescharacteristic
640C23C2×C4×D411yescharacteristic
641C23C4×#4111yescharacteristic
642C23#51811yescharacteristic
643C23#51811yescharacteristic
644C23#51811yescharacteristic
645C23#52011yescharacteristic
646C23C2×#13112yes—
647C23C2×#13112yes—
648C23#56812yes—
649C23#56812yes—
650D4—416no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
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—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4C2×C4×D411yescharacteristic
720C2×C4C2×C4×D411yescharacteristic
721C2×C4C4×#4111yescharacteristic
722C2×C4C4×#4111yescharacteristic
723C2×C4#51811yescharacteristic
724C2×C4#51811yescharacteristic
725C2×C4#51811yescharacteristic
726C2×C4#51811yescharacteristic
727C2×C4#51811yescharacteristic
728C2×C4#51811yescharacteristic
729C2×C4#52011yescharacteristic
730C2×C4#52011yescharacteristic
731C2×C4#53411yescharacteristic
732C2×C4#53511yescharacteristic
733C2×C4#53511yescharacteristic
734C2×C4#53711yescharacteristic
735C2×C4#53811yescharacteristic
736C2×C4#53811yescharacteristic
737C2×C4#53811yescharacteristic
738C2×C4#53811yescharacteristic
739C2×C4#53811yescharacteristic
740C2×C4#53911yescharacteristic
741C2×C4#54011yescharacteristic
742C2×C4#54011yescharacteristic
743C2×C4#54011yescharacteristic
744C2×C4#54011yescharacteristic
745C2×C4#54211yescharacteristic
746C2×C4#54211yescharacteristic
747C8—24no—
748C8—24no—
749C8—42no—
750C8—42no—
751C8—42no—
752C8—42no—
753C8—42no—
754C8—42no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—42no—
762C22—44no—
763C22—44no—
764C22—42no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22C42×D411yescharacteristic
778C22#227311yescharacteristic
779C22#227511yescharacteristic
780C22#232511yescharacteristic
781C22#232811yescharacteristic
782C22#233311yescharacteristic
783C22#233711yescharacteristic
784C22C2×#40511yescharacteristic
785C22#287311yescharacteristic
786C22C4×#13111yescharacteristic
787C22#287511yescharacteristic
788C22#293312yes—
789C22#293312yes—
790C22#296812yes—
791C22#296912yes—
792C22#297612yes—
793C22#297612yes—
794C22#297612yes—
795C22#297712yes—
796C22#297812yes—
797C22#298112yes—
798C22#299412yes—
799C22#299512yes—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—42no—
804C4—42no—
805C4—44no—
806C4—82no—
807C4—82no—
808C4#232111yescharacteristic
809C4#232111yescharacteristic
810C4#232411yescharacteristic
811C4#232411yescharacteristic
812C4#233311yescharacteristic
813C4#233311yescharacteristic
814C4#233511yescharacteristic
815C4#233511yescharacteristic
816C2—44no—
817C2—82no—
818C2#1379111yescharacteristic
819C2#2049011yescharacteristic
820C2#2049311yescharacteristic
821C2#2052711yescharacteristic
822C2#2053111yescharacteristic
823C2#2055711yescharacteristic
824C2#2056411yescharacteristic
825C2#2217512yes—
826C2#2226712yes—
827C2#2233612yes—
828C2#2239212yes—
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C22×C42
socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1752C2semidirect
4. C2×#1753C2semidirect
6. #10922C2semidirect
7. #10921C2semidirect
8. #10921C2semidirect
9. #10921C2semidirect
10. #10875C2semidirect
11. #10874C2semidirect
12. #10796C2semidirect
13. #10715C2semidirect
14. #10714C2semidirect
15. #10694C2semidirect
35. #1870C4semidirect
36. #1869C4semidirect
126. C2×#97D4semidirect

Maximal subgroups

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

subgroupindex
C2×#18702
C2×#18692
C2×#17522
C2×#17532
#138472
#109222
#109212
#108752
#108742
#107962
#107152
#107142
#106942