Finite Group Databasebeta

← #356592

Subgroups — #356592

Order 512.

1982 conjugacy classes of subgroups.

The subgroup lattice has 871 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×#1752C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic, complemented
6C2×#1749C211yesmaximal, characteristic, complemented
7C2×#1729C211yesmaximal, characteristic, complemented
8#10922C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10875C211yesmaximal, characteristic, complemented
11#10875C211yesmaximal, characteristic, complemented
12#10796C211yesmaximal, characteristic, complemented
13#10713C211yesmaximal, characteristic, complemented
14#10712C211yesmaximal, characteristic, complemented
15#10694C211yesmaximal, 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×#97C2211yescharacteristic
29C22×#97C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2290—24no—
32#2290—24no—
33C2×#388C412yes—
34C2×#387C412yes—
35C2×#386C412yes—
36C2×#385C412yes—
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×#376C2211yescharacteristic
41#1870C418yescomplemented
42#1869C418yescomplemented
43#1753—24no—
44#1752—24no—
45#1749—24no—
46#1729—24no—
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
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C23×D4C2×C411yescharacteristic
64C24×C4C2×C412yes—
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—41no—
72C22×M16—41no—
73C22×M16C2×C414yescomplemented
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8—22no—
78C23×C8—41no—
79C23×C8—41no—
80C23×C8C2×C414yescomplemented
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C2×C4×D4—22no—
90C2×C4×D4—22no—
91C2×C4×D4—22no—
92C2×C4×D4—22no—
93C2×C4×D4C2×C414yes—
94C2×C4×D4C2×C414yes—
95C2×#117—22no—
96C2×#117—22no—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—41no—
100C2×#117—41no—
101C22×C4⋊C4C2×C412yes—
102C22×C4⋊C4C2×C411yescharacteristic
103C22×C4⋊C4C2×C412yes—
104C22×C22⋊C4C2×C412yes—
105C22×C22⋊C4C2×C412yes—
106C22×C22⋊C4C2×C411yescharacteristic
107C22×C22⋊C4C2×C411yescharacteristic
108C22×C22⋊C4C2×C412yes—
109C22×C42—22no—
110C22×C42—22no—
111C22×C42—22no—
112C22×C42—22no—
113C22×C42—41no—
114C22×C42—41no—
115C22×C42C2×C412yes—
116C22×C42C2311yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C2×C22⋊C8—22no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—41no—
130C2×C22⋊C8—41no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8—41no—
133C2×C22⋊C8C2×C414yes—
134C2×C22⋊C8C2×C414yes—
135C2×C22⋊C8C2×C414yes—
136C2×C22⋊C8C2×C414yes—
137C2×C22⋊C8C2×C414yescomplemented
138C2×C22⋊C8C2×C414yescomplemented
139C2×#97—22no—
140C2×#97—22no—
141C2×#97—22no—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—41no—
146C2×#97—41no—
147C2×#97—41no—
148C2×C4×C8—22no—
149C2×C4×C8—22no—
150C2×C4×C8—41no—
151#388—28no—
152#387—28no—
153#386—28no—
154#385—28no—
155C4×C4⋊C4—22no—
156C4×C4⋊C4—22no—
157C4×C22⋊C4—22no—
158C4×C22⋊C4—22no—
159C4×C22⋊C4D414yes—
160C4×C22⋊C4D414yes—
161#376—22no—
162#376—22no—
163C2×#95C2×C412yes—
164C2×#95C2×C412yes—
165C2×#95C2×C412yes—
166C2×#95C2×C412yes—
167C2×#95C2×C412yes—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—41no—
178#336—41no—
179#336C2×C414yescomplemented
180#336C2×C414yescomplemented
181#336C2×C414yescomplemented
182#336C2×C414yescomplemented
183#336D414yescomplemented
184C25C22×C411yescharacteristic
185C25C22×C411yescharacteristic
186C22×D4—22no—
187C22×D4—22no—
188C22×D4—24no—
189C22×D4—42no—
190C22×D4C4214yes—
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—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4C22×C412yes—
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C412yes—
223C23×C4C22×C412yes—
224C23×C4C22×C412yes—
225C23×C4C22×C412yes—
226C23×C4C22×C412yes—
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C412yes—
229C23×C4C22×C412yes—
230C23×C4C2×D412yes—
231C23×C4C2×D412yes—
232C23×C4#4112yes—
233C23×C4#4112yes—
234C23×C4C2411yescharacteristic
235C2×M16—28no—
236C2×M16—28no—
237C2×M16—44no—
238C2×M16—44no—
239C2×M16—44no—
240C2×M16—44no—
241C2×M16—44no—
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—28no—
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—21no—
286C22×C8—21no—
287C22×C8—28no—
288C22×C8—44no—
289C22×C8—44no—
290C22×C8—44no—
291C22×C8—44no—
292C22×C8—44no—
293C22×C8C22×C412yes—
294C22×C8C22×C412yes—
295C22×C8C22×C412yes—
296C22×C8C22×C412yes—
297C22×C8C22×C412yes—
298C22×C8C22×C412yes—
299C22×C8C22×C412yes—
300C22×C8C22×C412yes—
301C22×C8C2×D412yes—
302C22×C8C2×D412yes—
303C22×C8#4112yes—
304C22×C8#4112yes—
305C4×D4—28no—
306C4×D4—28no—
307C4×D4—28no—
308C4×D4—28no—
309#117—44no—
310#117—44no—
311#117—44no—
312#117—44no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4C4214yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4C4214yes—
335C2×C22⋊C4C4214yes—
336C2×C22⋊C4C22⋊C418yes—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
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—24no—
354C2×C42—24no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—44no—
362C2×C42—44no—
363C2×C42—44no—
364C2×C42—44no—
365C2×C42—42no—
366C2×C42C22×C412yes—
367C2×C42C22×C412yes—
368C2×C42C2×D412yes—
369C2×C42C2×D412yes—
370C2×C42C2×D412yes—
371C2×C42C2×D412yes—
372C2×C42C2×D412yes—
373C2×C42#4112yes—
374C22⋊C8—28no—
375C22⋊C8—28no—
376C22⋊C8—28no—
377C22⋊C8—28no—
378C22⋊C8—44no—
379C22⋊C8—44no—
380#97—44no—
381#97—44no—
382#97—44no—
383C4×C8—44no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95C22⋊C418yes—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24C2×C4212yes—
407C24C2×C4212yes—
408C24C2×C22⋊C412yes—
409C24#11712yes—
410C24#13114yes—
411C24C23×C411yescharacteristic
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—44no—
415C2×D4—48no—
416C2×D4—48no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
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—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
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—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
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×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4C2×C4212yes—
520C22×C4C2×C4212yes—
521C22×C4C2×C4212yes—
522C22×C4C2×C4212yes—
523C22×C4C2×C22⋊C414yes—
524C22×C4C2×C22⋊C414yes—
525C22×C4C2×C22⋊C412yes—
526C22×C4#11712yes—
527C22×C4C4×D414yes—
528C22×C4C4×D414yes—
529C22×C4C4×D414yes—
530C22×C4C4×D414yes—
531C22×C4C4×D414yes—
532C22×C4C23×C411yescharacteristic
533C22×C4C23×C411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541C22×C4C2×#4111yescharacteristic
542C22×C4H(5,𝔽2)11yescharacteristic
543C22×C4H(5,𝔽2)11yescharacteristic
544C22×C4H(5,𝔽2)11yescharacteristic
545C22×C42−1+411yescharacteristic
546M16—416no—
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—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—416no—
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—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8C4×D414yes—
603C2×C8C4×D414yes—
604C4⋊C4—28no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C22⋊C4—28no—
608C22⋊C4—28no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—48no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C4×C22⋊C414yes—
678C23#40514yes—
679C23C22×C4211yescharacteristic
680C23C22×C22⋊C411yescharacteristic
681C23C2×#11711yescharacteristic
682C23C2×C4×D411yescharacteristic
683C23C4×#4111yescharacteristic
684C23#51811yescharacteristic
685C23#52011yescharacteristic
686C23C2×#13112yes—
687C23#56812yes—
688C23#56812yes—
689C23#56812yes—
690D4—416no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—432no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
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×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4C4×C22⋊C414yes—
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C2×C4×D411yescharacteristic
762C2×C4C2×C4×D411yescharacteristic
763C2×C4C2×C4×D411yescharacteristic
764C2×C4C2×C4×D411yescharacteristic
765C2×C4C2×C4×D411yescharacteristic
766C2×C4C4×#4111yescharacteristic
767C2×C4C4×#4111yescharacteristic
768C2×C4#51811yescharacteristic
769C2×C4#51811yescharacteristic
770C2×C4#52011yescharacteristic
771C2×C4#52011yescharacteristic
772C2×C4D4211yescharacteristic
773C2×C4D4211yescharacteristic
774C2×C4#54611yescharacteristic
775C2×C4#54611yescharacteristic
776C2×C4#54611yescharacteristic
777C2×C4#54611yescharacteristic
778C2×C4#54611yescharacteristic
779C2×C4#54711yescharacteristic
780C2×C4#54711yescharacteristic
781C2×C4#54811yescharacteristic
782C2×C4#55111yescharacteristic
783C2×C4#55111yescharacteristic
784C2×C4#55211yescharacteristic
785C2×C4#55311yescharacteristic
786C2×C4#55311yescharacteristic
787C2×C4#55311yescharacteristic
788C8—24no—
789C8—24no—
790C8—42no—
791C8—42no—
792C8—42no—
793C8—42no—
794C8—42no—
795C8—42no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—42no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—42no—
818C22C2×C4×C22⋊C411yescharacteristic
819C22C42×D411yescharacteristic
820C22#227511yescharacteristic
821C22D4×C22⋊C411yescharacteristic
822C22#233911yescharacteristic
823C22#235211yescharacteristic
824C22#235311yescharacteristic
825C22C2×#40511yescharacteristic
826C22#287311yescharacteristic
827C22#287511yescharacteristic
828C22#287511yescharacteristic
829C22#287912yes—
830C22#288012yes—
831C22#292312yes—
832C22#292412yes—
833C22#293012yes—
834C22#293312yes—
835C22#296712yes—
836C22#296812yes—
837C22#297612yes—
838C22#297812yes—
839C22#299212yes—
840C22#299512yes—
841C4—24no—
842C4—44no—
843C4—44no—
844C4—42no—
845C4—42no—
846C4—44no—
847C4—42no—
848C4—82no—
849C4#235811yescharacteristic
850C4#235811yescharacteristic
851C4#235911yescharacteristic
852C4#235911yescharacteristic
853C4#236111yescharacteristic
854C4#236111yescharacteristic
855C4#236411yescharacteristic
856C4#236411yescharacteristic
857C2—44no—
858C2—44no—
859C2#1381311yescharacteristic
860C2#2037511yescharacteristic
861C2#2037911yescharacteristic
862C2#2048711yescharacteristic
863C2#2049311yescharacteristic
864C2#2056011yescharacteristic
865C2#2056411yescharacteristic
866C2#2240012yes—
867C2#2247512yes—
868C2#2275312yes—
869C2#2279412yes—
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×#1752C2semidirect
5. C2×#1753C2semidirect
6. C2×#1749C2semidirect
7. C2×#1729C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10875C2semidirect
11. #10875C2semidirect
12. #10796C2semidirect
13. #10713C2semidirect
14. #10712C2semidirect
15. #10694C2semidirect
41. #1870C4semidirect
42. #1869C4semidirect
73. C22×M16C2×C4semidirect
80. C23×C8C2×C4semidirect
137. C2×C22⋊C8C2×C4semidirect
138. C2×C22⋊C8C2×C4semidirect
179. #336C2×C4semidirect
180. #336C2×C4semidirect
181. #336C2×C4semidirect
182. #336C2×C4semidirect
183. #336D4semidirect

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×#17522
C2×#17532
C2×#17492
C2×#17292
#109222
#109212
#108752
#107962
#107132
#107122
#106942