Finite Group Databasebeta

← #360974

Subgroups — #360974

Order 512.

2134 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×D4C211yesmaximal, characteristic
2C2×#1923C212yesmaximal, complemented
3C2×#1817C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
5#11042C212yesmaximal, complemented
6#10964C212yesmaximal
7#10874C212yesmaximal, complemented
8#10832C211yesmaximal, characteristic, complemented
9#10795C211yesmaximal, characteristic, complemented
10#10712C211yesmaximal, characteristic, complemented
11#10712C211yesmaximal, characteristic, complemented
12C22×C4×D4C411yescharacteristic
13C22×C4×D4C411yescharacteristic
14C22×C4×D4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C22×C4⋊C8C2212yes—
18C22×C22⋊C8C2212yes—
19C22×C22⋊C8C2212yes—
20C22×C22⋊C8C2212yes—
21C22×C22⋊C8C2212yes—
22C22×C4×C8C2212yes—
23C42×D4—28no—
24C2×C4×C4⋊C4C411yescharacteristic
25C2×C4×C4⋊C4C411yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×C4×C22⋊C4C411yescharacteristic
28C2×C4×C22⋊C4C411yescharacteristic
29C2×C4×C22⋊C4C411yescharacteristic
30C2×C4×C22⋊C4C411yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C43C2211yescharacteristic
34#1923—28no—
35#1817—24no—
36C4×C22⋊C8—24no—
37C2×#336C2212yes—
38C2×#336C2212yes—
39C2×#336C2212yes—
40C2×#336C2211yescharacteristic
41C2×#336C2212yes—
42C2×#336C2212yes—
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2212yes—
46C2×#336C2211yescharacteristic
47C23×D4C2×C411yescharacteristic
48C24×C4C2×C411yescharacteristic
49C24×C4C2×C411yescharacteristic
50C24×C4C2×C411yescharacteristic
51C24×C4C2×C411yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C23×C8C2312yes—
55C23×C8C2312yes—
56C23×C8C2312yes—
57C23×C8C2312yes—
58C2×C4×D4—24no—
59C2×C4×D4—24no—
60C2×C4×D4—24no—
61C2×C4×D4—24no—
62C2×C4×D4—24no—
63C2×C4×D4—24no—
64C2×C4×D4—24no—
65C2×C4×D4—22no—
66C2×C4×D4—22no—
67C2×C4×D4C818yescomplemented
68C22×C4⋊C4C2×C411yescharacteristic
69C22×C4⋊C4C2×C411yescharacteristic
70C22×C4⋊C4C2×C411yescharacteristic
71C22×C22⋊C4C2×C411yescharacteristic
72C22×C22⋊C4C2×C411yescharacteristic
73C22×C22⋊C4C2×C411yescharacteristic
74C22×C22⋊C4C2×C411yescharacteristic
75C22×C22⋊C4C2×C411yescharacteristic
76C22×C22⋊C4C2×C411yescharacteristic
77C22×C42—24no—
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—24no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—42no—
84C22×C42—42no—
85C22×C42C2×C411yescharacteristic
86C22×C42C2×C411yescharacteristic
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42C2×C411yescharacteristic
92C22×C42C2×C411yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×C4⋊C8—24no—
99C2×C4⋊C8—24no—
100C2×C4⋊C8—42no—
101C2×C22⋊C8—24no—
102C2×C22⋊C8—24no—
103C2×C22⋊C8—24no—
104C2×C22⋊C8—24no—
105C2×C22⋊C8—24no—
106C2×C22⋊C8—24no—
107C2×C22⋊C8—24no—
108C2×C22⋊C8—24no—
109C2×C22⋊C8—42no—
110C2×C22⋊C8—42no—
111C2×C22⋊C8—42no—
112C2×C22⋊C8—42no—
113C2×C4×C8—24no—
114C2×C4×C8—24no—
115C2×C4×C8—42no—
116C4×C4⋊C4—24no—
117C4×C4⋊C4—24no—
118C4×C4⋊C4—24no—
119C4×C22⋊C4—24no—
120C4×C22⋊C4—24no—
121C4×C22⋊C4—24no—
122C4×C22⋊C4—24no—
123C4×C22⋊C4—24no—
124C4×C22⋊C4D418yes—
125C2×#95C2×C411yescharacteristic
126C2×#95C2×C411yescharacteristic
127C2×#95C2×C411yescharacteristic
128C2×#95C2×C411yescharacteristic
129C2×#95C2×C411yescharacteristic
130C2×#95C2×C411yescharacteristic
131C43—24no—
132#336—24no—
133#336—22no—
134#336—24no—
135#336—24no—
136#336—22no—
137#336—24no—
138#336—24no—
139#336—22no—
140#336—42no—
141#336D414yescomplemented
142C25C22×C411yescharacteristic
143C25C22×C411yescharacteristic
144C22×D4—22no—
145C22×D4—22no—
146C22×D4—22no—
147C22×D4—22no—
148C22×D4—22no—
149C22×D4—22no—
150C22×D4C2×C814yes—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—22no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—41no—
187C23×C4—41no—
188C23×C4—41no—
189C23×C4—41no—
190C23×C4—41no—
191C23×C4—41no—
192C23×C4—41no—
193C23×C4—41no—
194C23×C4C2×C814yes—
195C23×C4C2×C814yes—
196C23×C4M1614yes—
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C411yescharacteristic
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C411yescharacteristic
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C411yescharacteristic
209C23×C4C2×D414yes—
210C23×C4#4114yes—
211C23×C4C2411yescharacteristic
212C22×C8—22no—
213C22×C8—22no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8—22no—
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—22no—
228C22×C8—22no—
229C22×C8—22no—
230C22×C8—22no—
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8—22no—
238C22×C8C2×D414yes—
239C22×C8#4114yes—
240C4×D4—232no—
241C4×D4—216no—
242C4×D4—216no—
243C4×D4—232no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4C2×C814yes—
252C2×C4⋊C4M1614yes—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4C22⋊C414yes—
267C2×C22⋊C4C22⋊C414yes—
268C2×C22⋊C4C2×C814yes—
269C2×C22⋊C4C2×C814yes—
270C2×C22⋊C4M1614yes—
271C2×C42—22no—
272C2×C42—22no—
273C2×C42—22no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42—21no—
279C2×C42—22no—
280C2×C42—22no—
281C2×C42—21no—
282C2×C42—22no—
283C2×C42—21no—
284C2×C42—22no—
285C2×C42—21no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42—22no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—21no—
299C2×C42—22no—
300C2×C42—21no—
301C2×C42—22no—
302C2×C42—48no—
303C2×C42—48no—
304C2×C42—48no—
305C2×C42—48no—
306C2×C42—41no—
307C2×C42—41no—
308C2×C42—41no—
309C2×C42—41no—
310C2×C42—41no—
311C2×C42—41no—
312C2×C42C2×C814yes—
313C2×C42C2×D414yes—
314C2×C42C2×D414yes—
315C2×C42C2×D412yes—
316C2×C42#4112yes—
317C2×C42#4112yes—
318C2×C42#4112yes—
319C4⋊C8—48no—
320C22⋊C8—216no—
321C22⋊C8—48no—
322C22⋊C8—48no—
323C22⋊C8—48no—
324C4×C8—48no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—22no—
329#95C22⋊C414yes—
330#95C22⋊C414yes—
331C24—21no—
332C24—21no—
333C24—21no—
334C24—21no—
335C24—21no—
336C24—21no—
337C24—21no—
338C24—21no—
339C24—21no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24C2×C22⋊C412yes—
356C24#11712yes—
357C24C22×C812yes—
358C24C22×C812yes—
359C24C2×M1612yes—
360C24C2×M1612yes—
361C24C23×C411yescharacteristic
362C2×D4—28no—
363C2×D4—28no—
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—28no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—28no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—28no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
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×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—44no—
489C22×C4C2×C22⋊C412yes—
490C22×C4C2×C22⋊C412yes—
491C22×C4C2×C22⋊C412yes—
492C22×C4C2×C22⋊C412yes—
493C22×C4C2×C22⋊C412yes—
494C22×C4#11712yes—
495C22×C4#11712yes—
496C22×C4#11712yes—
497C22×C4C4×D412yes—
498C22×C4C4×D412yes—
499C22×C4C22×C812yes—
500C22×C4C22×C812yes—
501C22×C4C22×C812yes—
502C22×C4C22×C812yes—
503C22×C4C22×C812yes—
504C22×C4C2×M1612yes—
505C22×C4C2×M1612yes—
506C22×C4C2×M1612yes—
507C22×C4C2×M1612yes—
508C22×C4C2×M1612yes—
509C22×C4C2×M1612yes—
510C22×C4C2×M1612yes—
511C22×C4#13112yes—
512C22×C4#13112yes—
513C22×C4C22×D411yescharacteristic
514C22×C4C22×D412yes—
515C22×C4C2×#4112yes—
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4112yes—
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)12yes—
522C22×C42−1+411yescharacteristic
523C2×C8—24no—
524C2×C8—24no—
525C2×C8—24no—
526C2×C8—24no—
527C2×C8—24no—
528C2×C8—24no—
529C2×C8—42no—
530C2×C8—42no—
531C2×C8—42no—
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—42no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8—42no—
550C2×C8—42no—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C22⋊C4—28no—
555C22⋊C4—28no—
556C22⋊C4—28no—
557C22⋊C4—28no—
558C22⋊C4—28no—
559C22⋊C4C22⋊C8116yescomplemented
560C42—28no—
561C42—24no—
562C42—24no—
563C42—24no—
564C42—24no—
565C42—24no—
566C42—24no—
567C42—24no—
568C42—24no—
569C42—28no—
570C42—44no—
571C42—44no—
572C42—44no—
573C42—44no—
574C42—44no—
575C42—44no—
576C42—42no—
577C42—42no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23C2×C22⋊C814yes—
647C23#43114yes—
648C23C22×C22⋊C411yescharacteristic
649C23C2×#11711yescharacteristic
650C23C2×#11711yescharacteristic
651C23C2×C4×D411yescharacteristic
652C23C4×#4111yescharacteristic
653C23#51811yescharacteristic
654C23#52011yescharacteristic
655C23C23×C811yescharacteristic
656C23C22×M1611yescharacteristic
657C23C22×M1611yescharacteristic
658C23C22×M1611yescharacteristic
659C23C2×#13111yescharacteristic
660C23C2×#13111yescharacteristic
661C23#56811yescharacteristic
662C23#56811yescharacteristic
663D4—232no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—416no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4C2×C22⋊C814yes—
755C2×C4C2×C22⋊C814yes—
756C2×C4#40714yes—
757C2×C4#43114yes—
758C2×C4C8×D414yes—
759C2×C4#43514yes—
760C2×C4#52512yes—
761C2×C4#52512yes—
762C2×C4#52512yes—
763C2×C4#52912yes—
764C2×C4#53812yes—
765C2×C4#53912yes—
766C2×C4D4212yes—
767C2×C4#54612yes—
768C2×C4#54612yes—
769C2×C4#54711yescharacteristic
770C2×C4#54712yes—
771C2×C4#55011yescharacteristic
772C2×C4#55312yes—
773C2×C4#55511yescharacteristic
774C2×C4#55611yescharacteristic
775C2×C4#55912yes—
776C8—44no—
777C8—44no—
778C8—82no—
779C8—82no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22#228011yescharacteristic
811C22#229011yescharacteristic
812C22#231811yescharacteristic
813C22D4×C22⋊C411yescharacteristic
814C22#233911yescharacteristic
815C22#235411yescharacteristic
816C22#235711yescharacteristic
817C22C22×C22⋊C811yescharacteristic
818C22C2×#40711yescharacteristic
819C22#288011yescharacteristic
820C22#288011yescharacteristic
821C22C2×#43111yescharacteristic
822C22C2×#43111yescharacteristic
823C22#292011yescharacteristic
824C22#292011yescharacteristic
825C22#292211yescharacteristic
826C22#292311yescharacteristic
827C22#292511yescharacteristic
828C22#292511yescharacteristic
829C22C2×C8×D411yescharacteristic
830C22C2×#43511yescharacteristic
831C22D4×M1611yescharacteristic
832C22D4×M1611yescharacteristic
833C22C8×#4111yescharacteristic
834C22#296511yescharacteristic
835C22#297011yescharacteristic
836C22#297111yescharacteristic
837C22#297211yescharacteristic
838C22#297311yescharacteristic
839C22#297411yescharacteristic
840C22#297411yescharacteristic
841C22#298811yescharacteristic
842C22#298911yescharacteristic
843C22#299011yescharacteristic
844C22#299111yescharacteristic
845C4—24no—
846C4—24no—
847C4—24no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4#245512yes—
858C4#245612yes—
859C4#245912yes—
860C4#246612yes—
861C2—44no—
862C2—44no—
863C2#1388611yescharacteristic
864C2#2071411yescharacteristic
865C2#2072011yescharacteristic
866C2#2110111yescharacteristic
867C2#2110811yescharacteristic
868C2#2199611yescharacteristic
869C2#2199811yescharacteristic
870C2D4×C22⋊C811yescharacteristic
871C2#2239911yescharacteristic
872C2#2246911yescharacteristic
873C2#2247311yescharacteristic
874C2#2279511yescharacteristic
875C2#2279711yescharacteristic
876C2#2283511yescharacteristic
877C2#2283711yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
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
2. C2×#1923C2semidirect
3. C2×#1817C2semidirect
4. C2×C4×C22⋊C8C2semidirect
5. #11042C2semidirect
7. #10874C2semidirect
8. #10832C2semidirect
9. #10795C2semidirect
10. #10712C2semidirect
11. #10712C2semidirect
67. C2×C4×D4C8semidirect
141. #336D4semidirect
559. C22⋊C4C22⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D42
C2×#19232
C2×#18172
C2×C4×C22⋊C82
#110422
#109642
#108742
#108322
#107952
#107122