Finite Group Databasebeta

← #355413

Subgroups — #355413

Order 512.

1894 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2290C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic
3C2×#1869C211yesmaximal, characteristic
4C2×#1750C211yesmaximal, characteristic, complemented
5C2×#1729C211yesmaximal, characteristic, complemented
6#10922C211yesmaximal, characteristic, complemented
7#10921C211yesmaximal, characteristic, complemented
8#10875C211yesmaximal, characteristic, complemented
9#10874C211yesmaximal, characteristic, complemented
10#10796C211yesmaximal, characteristic, complemented
11#10796C211yesmaximal, characteristic, complemented
12#10715C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic, complemented
14#10712C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29#2290—24no—
30#2290—24no—
31C2×#388C412yes—
32C2×#387C412yes—
33C2×#386C412yes—
34C2×#385C412yes—
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38C2×#376C2211yescharacteristic
39#1870C418yescomplemented
40#1869C418yescomplemented
41#1750—24no—
42#1729—24no—
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C23×D4C2×C411yescharacteristic
62C24×C4C2×C412yes—
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—41no—
68C22×M16—41no—
69C22×M16—41no—
70C22×M16—41no—
71C22×M16C2×C414yescomplemented
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—41no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8—41no—
78C23×C8C2×C414yescomplemented
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4C2×C414yes—
92C2×C4×D4C2×C414yes—
93C2×#117—41no—
94C2×#117—41no—
95C2×#117—41no—
96C2×#117—41no—
97C2×#117D414yes—
98C2×#117D414yes—
99C22×C4⋊C4C2×C412yes—
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C4⋊C4C2×C412yes—
102C22×C22⋊C4C2×C412yes—
103C22×C22⋊C4C2×C412yes—
104C22×C22⋊C4C2×C411yescharacteristic
105C22×C22⋊C4C2×C411yescharacteristic
106C22×C22⋊C4C2×C412yes—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42—41no—
110C22×C42—41no—
111C22×C42—41no—
112C22×C42—41no—
113C22×C42C2×C412yes—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—41no—
124C2×C22⋊C8—41no—
125C2×C22⋊C8—41no—
126C2×C22⋊C8—41no—
127C2×C22⋊C8—41no—
128C2×C22⋊C8—41no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8C2×C414yes—
132C2×C22⋊C8C2×C414yes—
133C2×C22⋊C8C2×C414yes—
134C2×C22⋊C8C2×C414yes—
135C2×C22⋊C8C2×C414yescomplemented
136C2×C22⋊C8C2×C414yescomplemented
137C2×#97—22no—
138C2×#97—41no—
139C2×#97—41no—
140C2×C4×C8—22no—
141C2×C4×C8—41no—
142C2×C4×C8—41no—
143#388—28no—
144#387—28no—
145#386—28no—
146#385—28no—
147C4×C4⋊C4—22no—
148C4×C4⋊C4—22no—
149C4×C22⋊C4—22no—
150C4×C22⋊C4—22no—
151C4×C22⋊C4—22no—
152C4×C22⋊C4—22no—
153#376—22no—
154#376—22no—
155C2×#95C2×C412yes—
156C2×#95C2×C412yes—
157C2×#95C2×C412yes—
158C2×#95C2×C412yes—
159C2×#95C2×C412yes—
160#336—22no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—22no—
165#336—22no—
166#336—41no—
167#336—41no—
168#336—41no—
169#336—41no—
170#336—41no—
171#336—41no—
172#336—41no—
173#336—41no—
174#336C2×C414yescomplemented
175#336C2×C414yescomplemented
176#336C2×C414yescomplemented
177#336C2×C414yescomplemented
178C25C22×C411yescharacteristic
179C25C22×C411yescharacteristic
180C22×D4—22no—
181C22×D4—22no—
182C22×D4—24no—
183C22×D4—42no—
184C22×D4C4214yes—
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×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4C22×C412yes—
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C22×C412yes—
217C23×C4C22×C412yes—
218C23×C4C22×C412yes—
219C23×C4C22×C412yes—
220C23×C4C22×C412yes—
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C412yes—
223C23×C4C22×C412yes—
224C23×C4C2×D412yes—
225C23×C4C2×D412yes—
226C23×C4#4112yes—
227C23×C4#4112yes—
228C23×C4C2411yescharacteristic
229C2×M16—28no—
230C2×M16—44no—
231C2×M16—44no—
232C2×M16—44no—
233C2×M16—44no—
234C2×M16—44no—
235C2×M16—44no—
236C22×C8—28no—
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—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8—44no—
289C22×C8—44no—
290C22×C8—44no—
291C22×C8C22×C412yes—
292C22×C8C22×C412yes—
293C22×C8C22×C412yes—
294C22×C8C22×C412yes—
295C22×C8C22×C412yes—
296C22×C8C22×C412yes—
297C22×C8C22×C412yes—
298C22×C8C22×C412yes—
299C4×D4—28no—
300C4×D4—28no—
301C4×D4—28no—
302C4×D4—28no—
303#117—44no—
304#117—44no—
305#117—44no—
306#117—44no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4C4214yes—
315C2×C4⋊C4C22⋊C418yes—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4C4214yes—
329C2×C22⋊C4C4214yes—
330C2×C22⋊C4C22⋊C418yes—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—24no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—44no—
357C2×C42—44no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42—42no—
361C2×C42—42no—
362C2×C42C22×C412yes—
363C2×C42C22×C412yes—
364C2×C42C2×D412yes—
365C2×C42C2×D412yes—
366C2×C42C2×D412yes—
367C2×C42C2×D412yes—
368C22⋊C8—28no—
369C22⋊C8—28no—
370C22⋊C8—44no—
371C22⋊C8—44no—
372C22⋊C8—44no—
373C22⋊C8—44no—
374#97—44no—
375C4×C8—44no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24C2×C4212yes—
399C24C2×C4212yes—
400C24C2×C22⋊C412yes—
401C24#11712yes—
402C24#13114yes—
403C24C23×C411yescharacteristic
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—44no—
407C2×D4—48no—
408C2×D4—48no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
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—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4C2×C4212yes—
512C22×C4C2×C4212yes—
513C22×C4C2×C4212yes—
514C22×C4C2×C4212yes—
515C22×C4C2×C22⋊C414yes—
516C22×C4C2×C22⋊C414yes—
517C22×C4C2×C22⋊C412yes—
518C22×C4#11712yes—
519C22×C4C4×D414yes—
520C22×C4C4×D414yes—
521C22×C4C4×D414yes—
522C22×C4C4×D414yes—
523C22×C4#13114yes—
524C22×C4C23×C411yescharacteristic
525C22×C4C23×C411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C4H(5,𝔽2)11yescharacteristic
532C22×C4H(5,𝔽2)11yescharacteristic
533C22×C4H(5,𝔽2)11yescharacteristic
534C22×C4H(5,𝔽2)11yescharacteristic
535C22×C4H(5,𝔽2)11yescharacteristic
536C22×C42−1+411yescharacteristic
537C22×C42−1+411yescharacteristic
538M16—416no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—416no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C4⋊C4—28no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C22⋊C4—28no—
600C22⋊C4—28no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—48no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—41no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23C4×C22⋊C414yes—
670C23#40514yes—
671C23C22×C4211yescharacteristic
672C23C22×C22⋊C411yescharacteristic
673C23C2×#11711yescharacteristic
674C23#51811yescharacteristic
675C23#51811yescharacteristic
676C23#52011yescharacteristic
677C23#52011yescharacteristic
678C23C2×#13112yes—
679C23C2×#13112yes—
680C23#56812yes—
681C23#56812yes—
682D4—416no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—432no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4C4×C22⋊C414yes—
752C2×C4C2×C4×D411yescharacteristic
753C2×C4C2×C4×D411yescharacteristic
754C2×C4C2×C4×D411yescharacteristic
755C2×C4C2×C4×D411yescharacteristic
756C2×C4#51811yescharacteristic
757C2×C4#51811yescharacteristic
758C2×C4#51811yescharacteristic
759C2×C4#51811yescharacteristic
760C2×C4#52011yescharacteristic
761C2×C4#52011yescharacteristic
762C2×C4#52011yescharacteristic
763C2×C4#52011yescharacteristic
764C2×C4#53411yescharacteristic
765C2×C4#53411yescharacteristic
766C2×C4#53411yescharacteristic
767C2×C4#53411yescharacteristic
768C2×C4#53511yescharacteristic
769C2×C4#53611yescharacteristic
770C2×C4#53711yescharacteristic
771C2×C4#53711yescharacteristic
772C2×C4#53811yescharacteristic
773C2×C4#53811yescharacteristic
774C2×C4#53811yescharacteristic
775C2×C4#53811yescharacteristic
776C2×C4#53911yescharacteristic
777C2×C4#53911yescharacteristic
778C2×C4#53911yescharacteristic
779C2×C4#53911yescharacteristic
780C8—42no—
781C8—42no—
782C8—42no—
783C8—42no—
784C8—42no—
785C8—42no—
786C8—42no—
787C8—42no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22C2×C4×C22⋊C411yescharacteristic
811C22#227511yescharacteristic
812C22#227511yescharacteristic
813C22#230811yescharacteristic
814C22#231111yescharacteristic
815C22#231811yescharacteristic
816C22#231811yescharacteristic
817C22C2×#40511yescharacteristic
818C22#287311yescharacteristic
819C22C4×#13111yescharacteristic
820C22#287511yescharacteristic
821C22#288012yes—
822C22#288012yes—
823C22#292412yes—
824C22#292512yes—
825C22#297612yes—
826C22#297612yes—
827C22#297712yes—
828C22#297812yes—
829C22#299212yes—
830C22#299312yes—
831C22#299412yes—
832C22#299512yes—
833C4—24no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—44no—
838C4—44no—
839C4—44no—
840C4—82no—
841C4#232111yescharacteristic
842C4#232111yescharacteristic
843C4#232211yescharacteristic
844C4#232211yescharacteristic
845C4#232511yescharacteristic
846C4#232511yescharacteristic
847C4#232511yescharacteristic
848C4#232511yescharacteristic
849C2—44no—
850C2—44no—
851C2#1378411yescharacteristic
852C2#2037811yescharacteristic
853C2#2037911yescharacteristic
854C2#2055711yescharacteristic
855C2#2056011yescharacteristic
856C2#2056111yescharacteristic
857C2#2056411yescharacteristic
858C2#2174412yes—
859C2#2185512yes—
860C2#2200412yes—
861C2#2200612yes—
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
4. C2×#1750C2semidirect
5. C2×#1729C2semidirect
6. #10922C2semidirect
7. #10921C2semidirect
8. #10875C2semidirect
9. #10874C2semidirect
10. #10796C2semidirect
11. #10796C2semidirect
12. #10715C2semidirect
13. #10714C2semidirect
14. #10712C2semidirect
15. #10712C2semidirect
39. #1870C4semidirect
40. #1869C4semidirect
71. C22×M16C2×C4semidirect
78. C23×C8C2×C4semidirect
135. C2×C22⋊C8C2×C4semidirect
136. C2×C22⋊C8C2×C4semidirect
174. #336C2×C4semidirect
175. #336C2×C4semidirect
176. #336C2×C4semidirect
177. #336C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#22902
C2×#18702
C2×#18692
C2×#17502
C2×#17292
#109222
#109212
#108752
#108742
#107962
#107152
#107142
#107122