Finite Group Databasebeta

← #355845

Subgroups — #355845

Order 512.

1672 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1954C211yesmaximal, characteristic
2C2×#1870C211yesmaximal, characteristic
3C2×#1753C211yesmaximal, characteristic, complemented
4C2×#1749C211yesmaximal, characteristic, complemented
5C4×#386C211yesmaximal, characteristic
6#10922C211yesmaximal, characteristic, complemented
7#10922C211yesmaximal, characteristic, complemented
8#10922C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10877C211yesmaximal, characteristic, complemented
11#10876C211yesmaximal, characteristic, complemented
12#10797C211yesmaximal, characteristic, complemented
13#10715C211yesmaximal, characteristic, complemented
14#10712C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
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
31C22×C4×C8C2211yescharacteristic
32C2×#386C412yes—
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36#1954C418yescomplemented
37#1870C418yescomplemented
38#1753—24no—
39#1749—24no—
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
54#1437C412yes—
55#1436C412yes—
56C22⋊#95C412yes—
57C4×#95C2211yescharacteristic
58C4×#95C2211yescharacteristic
59C23×D4C2×C411yescharacteristic
60C24×C4C2×C412yes—
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C22×M16—22no—
64C22×M16—22no—
65C22×M16—41no—
66C22×M16—41no—
67C22×M16—41no—
68C22×M16—41no—
69C22×M16C2×C414yescomplemented
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C4×D4—41no—
79C2×C4×D4—41no—
80C2×C4×D4—41no—
81C2×C4×D4—41no—
82C2×C4×D4C2×C414yes—
83C2×C4×D4C2×C414yes—
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C22⋊C4C2×C412yes—
86C22×C22⋊C4C2×C412yes—
87C22×C22⋊C4C2×C412yes—
88C22×C22⋊C4C2×C411yescharacteristic
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—41no—
93C22×C42—41no—
94C22×C42—41no—
95C22×C42—41no—
96C22×C42C2×C412yes—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C2×C4⋊C8—41no—
103C2×C4⋊C8—41no—
104C2×C4⋊C8C2×C414yescomplemented
105C2×C22⋊C8—22no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—22no—
111C2×C22⋊C8—41no—
112C2×C22⋊C8—41no—
113C2×C22⋊C8—41no—
114C2×C22⋊C8—41no—
115C2×C22⋊C8—41no—
116C2×C22⋊C8—41no—
117C2×C22⋊C8—41no—
118C2×C22⋊C8—41no—
119C2×C22⋊C8C2×C414yes—
120C2×C22⋊C8C2×C414yes—
121C2×C22⋊C8C2×C414yes—
122C2×C22⋊C8C2×C414yes—
123C2×C22⋊C8C2×C414yescomplemented
124C2×C22⋊C8C2×C414yescomplemented
125C2×C22⋊C8C2×C414yescomplemented
126C2×#97—22no—
127C2×#97—22no—
128C2×#97—41no—
129C2×#97—41no—
130C2×#97—41no—
131C2×#97—41no—
132C2×#97—41no—
133C2×#97—41no—
134C2×#97D414yescomplemented
135C2×C4×C8—22no—
136C2×C4×C8—41no—
137C2×C4×C8—41no—
138C2×C4×C8—41no—
139C2×C4×C8—41no—
140C2×C4×C8C2×C414yescomplemented
141#386—28no—
142C4×C22⋊C4—22no—
143C4×C22⋊C4—22no—
144C4×C22⋊C4—41no—
145C4×C22⋊C4—41no—
146C4×C22⋊C4—41no—
147C4×C22⋊C4—41no—
148C2×#95C2×C412yes—
149C2×#95C2×C412yes—
150C2×#95C2×C412yes—
151C2×#95C2×C412yes—
152C2×#95C2×C412yes—
153C2×#95C2×C412yes—
154C2×#95C2×C412yes—
155#336—22no—
156#336—22no—
157#336—22no—
158#336—22no—
159#336—22no—
160#336—22no—
161#336—41no—
162#336—41no—
163#336—41no—
164#336—41no—
165#336—41no—
166#336—41no—
167#336C2×C414yescomplemented
168#336C2×C414yescomplemented
169C25C22×C411yescharacteristic
170C25C22×C411yescharacteristic
171C22×D4—24no—
172C22×D4—24no—
173C22×D4—41no—
174C22×D4—41no—
175C22×D4C4214yes—
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×C4—21no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4C22×C412yes—
208C23×C4C22×C411yescharacteristic
209C23×C4C22×C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C412yes—
212C23×C4C22×C412yes—
213C23×C4C22×C412yes—
214C23×C4C22×C412yes—
215C23×C4C22×C412yes—
216C23×C4C22×C412yes—
217C23×C4C22×C412yes—
218C23×C4C22×C411yescharacteristic
219C23×C4C2411yescharacteristic
220C2×M16—28no—
221C2×M16—44no—
222C2×M16—44no—
223C2×M16—44no—
224C2×M16—44no—
225C2×M16—44no—
226C2×M16—44no—
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—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8C22×C412yes—
272C22×C8C22×C412yes—
273C22×C8C22×C412yes—
274C22×C8C22×C412yes—
275C22×C8C22×C412yes—
276C22×C8C22×C412yes—
277C22×C8C22×C412yes—
278C22×C8C22×C412yes—
279C22×C8C2×D412yes—
280C22×C8C2×D412yes—
281C22×C8#4112yes—
282C22×C8#4112yes—
283C4×D4—44no—
284C4×D4—44no—
285C4×D4—44no—
286C4×D4—44no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4C4214yes—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—41no—
298C2×C22⋊C4—41no—
299C2×C22⋊C4—41no—
300C2×C22⋊C4—41no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4C4214yes—
304C2×C22⋊C4C4214yes—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—24no—
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—44no—
333C2×C42—44no—
334C2×C42—44no—
335C2×C42—44no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42C22×C412yes—
339C2×C42C22×C412yes—
340C2×C42C2×D412yes—
341C2×C42#4112yes—
342C4⋊C8—44no—
343C22⋊C8—28no—
344C22⋊C8—28no—
345C22⋊C8—28no—
346C22⋊C8—44no—
347C22⋊C8—44no—
348C22⋊C8—44no—
349C22⋊C8—44no—
350#97—44no—
351#97—44no—
352#97—44no—
353C4×C8—44no—
354C4×C8—44no—
355#95—24no—
356#95—24no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95M1618yescomplemented
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24C2×C4212yes—
382C24C2×C4212yes—
383C24#13114yes—
384C24C23×C411yescharacteristic
385C2×D4—28no—
386C2×D4—28no—
387C2×D4—44no—
388C2×D4—48no—
389C2×D4—48no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
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—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—48no—
459C22×C4—48no—
460C22×C4—48no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—48no—
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×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4C2×C4212yes—
498C22×C4C2×C4212yes—
499C22×C4C2×C4212yes—
500C22×C4C2×C4212yes—
501C22×C4C4×D414yes—
502C22×C4C2×M1614yes—
503C22×C4C2×M1614yes—
504C22×C4C2×M1614yes—
505C22×C4C23×C411yescharacteristic
506C22×C4C23×C411yescharacteristic
507C22×C4C22×D411yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4H(5,𝔽2)11yescharacteristic
512C22×C4H(5,𝔽2)11yescharacteristic
513C22×C4H(5,𝔽2)11yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C4H(5,𝔽2)11yescharacteristic
516C22×C4H(5,𝔽2)11yescharacteristic
517C22×C4H(5,𝔽2)11yescharacteristic
518C22×C42−1+411yescharacteristic
519M16—416no—
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—22no—
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—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×C8—41no—
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×C8C4×D414yes—
575C2×C8C4×D414yes—
576C4⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—48no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23#40514yes—
649C23C22×C4211yescharacteristic
650C23C2×C4×D411yescharacteristic
651C23C4×#4111yescharacteristic
652C23#51811yescharacteristic
653C23#51811yescharacteristic
654C23#51811yescharacteristic
655C23#52011yescharacteristic
656C23C22×M1612yes—
657C23C2×#13112yes—
658C23#56812yes—
659C23#56812yes—
660D4—416no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—432no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
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×C4—42no—
720C2×C4—42no—
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×C4C4×M1614yes—
730C2×C4C2×C4×D411yescharacteristic
731C2×C4C2×C4×D411yescharacteristic
732C2×C4C4×#4111yescharacteristic
733C2×C4C4×#4111yescharacteristic
734C2×C4#51811yescharacteristic
735C2×C4#51811yescharacteristic
736C2×C4#51811yescharacteristic
737C2×C4#51811yescharacteristic
738C2×C4#51811yescharacteristic
739C2×C4#51811yescharacteristic
740C2×C4#52011yescharacteristic
741C2×C4#52011yescharacteristic
742C2×C4#53411yescharacteristic
743C2×C4#53511yescharacteristic
744C2×C4#53511yescharacteristic
745C2×C4#53711yescharacteristic
746C2×C4#53811yescharacteristic
747C2×C4#53811yescharacteristic
748C2×C4#53811yescharacteristic
749C2×C4#53811yescharacteristic
750C2×C4#53811yescharacteristic
751C2×C4#53911yescharacteristic
752C2×C4#54011yescharacteristic
753C2×C4#54011yescharacteristic
754C2×C4#54011yescharacteristic
755C2×C4#54011yescharacteristic
756C2×C4#54211yescharacteristic
757C2×C4#54211yescharacteristic
758C8—24no—
759C8—24no—
760C8—42no—
761C8—42no—
762C8—42no—
763C8—42no—
764C8—42no—
765C8—42no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—44no—
771C22—42no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22C42×D411yescharacteristic
789C22#227311yescharacteristic
790C22#227511yescharacteristic
791C22#232111yescharacteristic
792C22#232411yescharacteristic
793C22#233311yescharacteristic
794C22#233511yescharacteristic
795C22C2×C4×M1611yescharacteristic
796C22C2×#40511yescharacteristic
797C22#287511yescharacteristic
798C22#287511yescharacteristic
799C22#293312yes—
800C22D4×M1612yes—
801C22#296812yes—
802C22#297112yes—
803C22#297412yes—
804C22#297412yes—
805C22#297512yes—
806C22#297612yes—
807C22#297812yes—
808C22#298012yes—
809C22#298912yes—
810C22#299212yes—
811C4—24no—
812C4—44no—
813C4—44no—
814C4—42no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—82no—
819C4#232111yescharacteristic
820C4#232411yescharacteristic
821C4#232511yescharacteristic
822C4#232811yescharacteristic
823C4#233311yescharacteristic
824C4#233311yescharacteristic
825C4#233511yescharacteristic
826C4#233711yescharacteristic
827C2—44no—
828C2—82no—
829C2#1379111yescharacteristic
830C2#2049311yescharacteristic
831C2#2049411yescharacteristic
832C2#2052511yescharacteristic
833C2#2053211yescharacteristic
834C2#2056011yescharacteristic
835C2#2056811yescharacteristic
836C2#2203812yes—
837C2#2214112yes—
838C2#2233112yes—
839C2#2235912yes—
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×#1753C2semidirect
4. C2×#1749C2semidirect
6. #10922C2semidirect
7. #10922C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10877C2semidirect
11. #10876C2semidirect
12. #10797C2semidirect
13. #10715C2semidirect
14. #10712C2semidirect
15. #10696C2semidirect
36. #1954C4semidirect
37. #1870C4semidirect
69. C22×M16C2×C4semidirect
104. C2×C4⋊C8C2×C4semidirect
123. C2×C22⋊C8C2×C4semidirect
124. C2×C22⋊C8C2×C4semidirect
125. C2×C22⋊C8C2×C4semidirect
134. C2×#97D4semidirect
140. C2×C4×C8C2×C4semidirect
167. #336C2×C4semidirect
168. #336C2×C4semidirect
361. #95M16semidirect

Maximal subgroups

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

subgroupindex
C2×#19542
C2×#18702
C2×#17532
C2×#17492
C4×#3862
#109222
#109212
#108772
#108762
#107972
#107152
#107122
#106962