Finite Group Databasebeta

← C2×#14363 #520661

Subgroups — C2×#14363 #520661

Order 512.

9022 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#121C211yesmaximal, characteristic
2C22×#390C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5C22×#381C211yesmaximal, characteristic, complemented
6#14363C2116yesmaximal, direct product factor
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1440C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1438C211yesmaximal, characteristic, complemented
11C2×#1438C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic, complemented
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C24×D4C2211yescharacteristic
20C25×C4C2211yescharacteristic
21C25×C4C2211yescharacteristic
22C22×#121—28no—
23C22×#121—28no—
24C22×#121C4116yescomplemented
25C22×#121C2218yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C22⋊C4C2211yescharacteristic
41C23×C42C2211yescharacteristic
42C2×#390—28no—
43C2×#390C2218yescomplemented
44C2×#386—28no—
45C2×#386—28no—
46C2×#386C2218yescomplemented
47C2×#386C2218yescomplemented
48C2×#381—28no—
49C2×#381C2218yescomplemented
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1441C2218yescomplemented
65#1440C2218yescomplemented
66#1439C2218yescomplemented
67#1438C2218yescomplemented
68#1438C2218yescomplemented
69#1438C2218yescomplemented
70#1437C2218yescomplemented
71#1436C2218yescomplemented
72C22⋊#95C2218yescomplemented
73C22⋊#95C2218yescomplemented
74C26C2311yescharacteristic
75C26C2311yescharacteristic
76C26C2311yescharacteristic
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—24no—
83C23×D4—42no—
84C23×D4—42no—
85C23×D4—42no—
86C23×D4—42no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4—42no—
91C23×D4—42no—
92C23×D4—42no—
93C23×D4C2×C418yes—
94C23×D4C2×C418yes—
95C23×D4C2×C418yescomplemented
96C23×D4D418yes—
97C23×D4D418yes—
98C23×D4C2314yes—
99C23×D4C2314yes—
100C23×D4C2314yes—
101C24×C4—24no—
102C24×C4—24no—
103C24×C4—24no—
104C24×C4—24no—
105C24×C4—24no—
106C24×C4—24no—
107C24×C4—24no—
108C24×C4—42no—
109C24×C4—42no—
110C24×C4—42no—
111C24×C4—42no—
112C24×C4—42no—
113C24×C4—42no—
114C24×C4C2×C418yescomplemented
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C24×C4C2311yescharacteristic
125C24×C4C2314yes—
126C24×C4C2311yescharacteristic
127C24×C4C2311yescharacteristic
128C24×C4C2314yes—
129C2×#121—2128no—
130C2×#121—232no—
131C2×#121—232no—
132C2×#121C2×C4164yescomplemented
133C22×C4⋊C4—24no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—24no—
136C22×C4⋊C4—42no—
137C22×C4⋊C4—42no—
138C22×C4⋊C4C2×C418yescomplemented
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2314yes—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—24no—
148C22×C22⋊C4—24no—
149C22×C22⋊C4—24no—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—24no—
158C22×C22⋊C4—24no—
159C22×C22⋊C4—24no—
160C22×C22⋊C4—24no—
161C22×C22⋊C4—24no—
162C22×C22⋊C4—42no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4—42no—
166C22×C22⋊C4—42no—
167C22×C22⋊C4—42no—
168C22×C22⋊C4—42no—
169C22×C22⋊C4—42no—
170C22×C22⋊C4—42no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4—42no—
173C22×C22⋊C4—42no—
174C22×C22⋊C4—42no—
175C22×C22⋊C4—42no—
176C22×C22⋊C4—42no—
177C22×C22⋊C4—42no—
178C22×C22⋊C4C2×C418yes—
179C22×C22⋊C4C2×C418yescomplemented
180C22×C22⋊C4C2314yes—
181C22×C22⋊C4C2314yes—
182C22×C22⋊C4C2314yes—
183C22×C22⋊C4C2314yes—
184C22×C22⋊C4C2314yes—
185C22×C22⋊C4C2314yes—
186C22×C22⋊C4C2314yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2314yes—
193C22×C42—24no—
194C22×C42—42no—
195C22×C42—42no—
196C22×C42C2314yes—
197#390—232no—
198#386—232no—
199#386—232no—
200#381—232no—
201C2×#95—24no—
202C2×#95—24no—
203C2×#95—24no—
204C2×#95—24no—
205C2×#95—24no—
206C2×#95—24no—
207C2×#95—24no—
208C2×#95—42no—
209C2×#95—42no—
210C2×#95—42no—
211C2×#95—42no—
212C2×#95—42no—
213C2×#95—42no—
214C2×#95D418yescomplemented
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—22no—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—22no—
245C25—22no—
246C25—22no—
247C25—22no—
248C25—22no—
249C25—22no—
250C25—22no—
251C25—22no—
252C25—22no—
253C25—22no—
254C25—22no—
255C25—22no—
256C25—22no—
257C25—22no—
258C25—22no—
259C25—22no—
260C25—22no—
261C25—22no—
262C25—22no—
263C25—22no—
264C25—22no—
265C25—22no—
266C25—22no—
267C25C22×C414yes—
268C25C22×C414yes—
269C25C22×C414yes—
270C25C2×D414yes—
271C25C2×D414yes—
272C25C2×D414yes—
273C25C2×D414yes—
274C25C2412yes—
275C25C2412yes—
276C25C2412yes—
277C25C2411yescharacteristic
278C22×D4—232no—
279C22×D4—232no—
280C22×D4—28no—
281C22×D4—28no—
282C22×D4—28no—
283C22×D4—28no—
284C22×D4—232no—
285C22×D4—28no—
286C22×D4—28no—
287C22×D4—416no—
288C22×D4—416no—
289C22×D4—416no—
290C22×D4—416no—
291C22×D4—416no—
292C22×D4—416no—
293C22×D4—416no—
294C22×D4—416no—
295C22×D4—416no—
296C22×D4—44no—
297C22×D4—44no—
298C22×D4—44no—
299C22×D4—44no—
300C22×D4—44no—
301C22×D4—44no—
302C22×D4—44no—
303C22×D4—44no—
304C22×D4—44no—
305C22×D4—44no—
306C22×D4—416no—
307C22×D4—416no—
308C22×D4—416no—
309C22×D4—416no—
310C22×D4—416no—
311C22×D4—416no—
312C22×D4—416no—
313C22×D4—416no—
314C22×D4C22⋊C4164yescomplemented
315C22×D4C22×C4116yes—
316C22×D4C22×C4116yes—
317C22×D4C22×C4116yescomplemented
318C22×D4C2×D4116yes—
319C22×D4C2×D4116yes—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—232no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—28no—
339C23×C4—28no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—232no—
368C23×C4—28no—
369C23×C4—28no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—28no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—28no—
400C23×C4—28no—
401C23×C4—416no—
402C23×C4—44no—
403C23×C4—44no—
404C23×C4—44no—
405C23×C4—44no—
406C23×C4—44no—
407C23×C4—44no—
408C23×C4—416no—
409C23×C4—416no—
410C23×C4—416no—
411C23×C4—416no—
412C23×C4—416no—
413C23×C4—416no—
414C23×C4—416no—
415C23×C4—416no—
416C23×C4—416no—
417C23×C4—416no—
418C23×C4—416no—
419C23×C4C22×C414yes—
420C23×C4C22×C414yes—
421C23×C4C22×C414yes—
422C23×C4C22×C414yes—
423C23×C4C22×C4116yescomplemented
424C23×C4C2×D414yes—
425C23×C4C2×D414yes—
426C23×C4C2×D414yes—
427C23×C4C2×D414yes—
428C23×C4C2×D414yes—
429C23×C4#4114yes—
430C23×C4#4114yes—
431C23×C4#4114yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2412yes—
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444#121—2256no—
445C2×C4⋊C4—232no—
446C2×C4⋊C4—28no—
447C2×C4⋊C4—28no—
448C2×C4⋊C4—28no—
449C2×C4⋊C4—44no—
450C2×C4⋊C4—44no—
451C2×C4⋊C4—416no—
452C2×C4⋊C4C22×C4116yescomplemented
453C2×C22⋊C4—232no—
454C2×C22⋊C4—28no—
455C2×C22⋊C4—28no—
456C2×C22⋊C4—232no—
457C2×C22⋊C4—28no—
458C2×C22⋊C4—28no—
459C2×C22⋊C4—28no—
460C2×C22⋊C4—28no—
461C2×C22⋊C4—28no—
462C2×C22⋊C4—28no—
463C2×C22⋊C4—28no—
464C2×C22⋊C4—28no—
465C2×C22⋊C4—28no—
466C2×C22⋊C4—28no—
467C2×C22⋊C4—28no—
468C2×C22⋊C4—28no—
469C2×C22⋊C4—28no—
470C2×C22⋊C4—28no—
471C2×C22⋊C4—28no—
472C2×C22⋊C4—28no—
473C2×C22⋊C4—28no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—28no—
476C2×C22⋊C4—44no—
477C2×C22⋊C4—44no—
478C2×C22⋊C4—44no—
479C2×C22⋊C4—44no—
480C2×C22⋊C4—44no—
481C2×C22⋊C4—44no—
482C2×C22⋊C4—44no—
483C2×C22⋊C4—44no—
484C2×C22⋊C4—44no—
485C2×C22⋊C4—44no—
486C2×C22⋊C4—44no—
487C2×C22⋊C4—44no—
488C2×C22⋊C4—44no—
489C2×C22⋊C4—44no—
490C2×C22⋊C4—44no—
491C2×C22⋊C4—44no—
492C2×C22⋊C4—416no—
493C2×C22⋊C4—416no—
494C2×C22⋊C4—416no—
495C2×C22⋊C4—416no—
496C2×C22⋊C4—416no—
497C2×C22⋊C4—416no—
498C2×C22⋊C4—416no—
499C2×C22⋊C4—416no—
500C2×C22⋊C4—416no—
501C2×C22⋊C4—416no—
502C2×C22⋊C4—416no—
503C2×C22⋊C4C22×C4116yes—
504C2×C22⋊C4C22×C4116yescomplemented
505C2×C42—28no—
506C2×C42—44no—
507C2×C42—44no—
508C2×C42—416no—
509#95—28no—
510#95—28no—
511#95—28no—
512#95—28no—
513#95—28no—
514#95—28no—
515#95—28no—
516#95—44no—
517#95—44no—
518#95—44no—
519#95—44no—
520#95—44no—
521#95—44no—
522#95C2×D4116yescomplemented
523C24—28no—
524C24—28no—
525C24—28no—
526C24—28no—
527C24—28no—
528C24—28no—
529C24—28no—
530C24—28no—
531C24—28no—
532C24—28no—
533C24—28no—
534C24—28no—
535C24—28no—
536C24—28no—
537C24—28no—
538C24—28no—
539C24—28no—
540C24—28no—
541C24—28no—
542C24—28no—
543C24—28no—
544C24—28no—
545C24—28no—
546C24—28no—
547C24—28no—
548C24—28no—
549C24—28no—
550C24—28no—
551C24—28no—
552C24—28no—
553C24—28no—
554C24—28no—
555C24—28no—
556C24—28no—
557C24—28no—
558C24—28no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—28no—
584C24—28no—
585C24—28no—
586C24—28no—
587C24—28no—
588C24—28no—
589C24—28no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—44no—
605C24—44no—
606C24—44no—
607C24—44no—
608C24—44no—
609C24—44no—
610C24—44no—
611C24—44no—
612C24—44no—
613C24—44no—
614C24—44no—
615C24—44no—
616C24—44no—
617C24—44no—
618C24—44no—
619C24—44no—
620C24—44no—
621C24—44no—
622C24—44no—
623C24—44no—
624C24—44no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24—44no—
634C24—44no—
635C24—44no—
636C24—44no—
637C24—44no—
638C24—44no—
639C24—44no—
640C24—44no—
641C24—44no—
642C24—44no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24C2×C22⋊C4116yes—
665C24C2×C22⋊C4116yes—
666C24C23×C414yes—
667C24C23×C414yes—
668C24C23×C414yes—
669C24C23×C412yes—
670C24C22×D414yes—
671C24C22×D414yes—
672C24C22×D414yes—
673C24C22×D414yes—
674C24C22×D412yes—
675C24C22×D412yes—
676C24C22×D412yes—
677C24C2×#4112yes—
678C24C2×#4112yes—
679C24C2×#4112yes—
680C24H(5,𝔽2)12yes—
681C24H(5,𝔽2)12yes—
682C24H(5,𝔽2)12yes—
683C24H(5,𝔽2)12yes—
684C24H(5,𝔽2)12yes—
685C24H(5,𝔽2)12yes—
686C24H(5,𝔽2)12yes—
687C242−1+412yes—
688C24C2511yescharacteristic
689C2×D4—232no—
690C2×D4—232no—
691C2×D4—232no—
692C2×D4—4128no—
693C2×D4—416no—
694C2×D4—416no—
695C2×D4—416no—
696C2×D4—416no—
697C2×D4—416no—
698C2×D4—416no—
699C2×D4—416no—
700C2×D4—416no—
701C2×D4—416no—
702C2×D4—4128no—
703C2×D4—416no—
704C2×D4—416no—
705C2×D4—416no—
706C2×D4—416no—
707C2×D4—4128no—
708C2×D4—416no—
709C2×D4—416no—
710C2×D4—416no—
711C2×D4—416no—
712C2×D4C2×C22⋊C4164yescomplemented
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—232no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—232no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—416no—
818C22×C4—416no—
819C22×C4—4128no—
820C22×C4—416no—
821C22×C4—416no—
822C22×C4—416no—
823C22×C4—416no—
824C22×C4—416no—
825C22×C4—416no—
826C22×C4—416no—
827C22×C4—416no—
828C22×C4—416no—
829C22×C4—4128no—
830C22×C4—416no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4C2×C22⋊C4116yes—
884C22×C4C4×D4116yes—
885C22×C4C23×C414yes—
886C22×C4C23×C414yes—
887C22×C4C23×C414yes—
888C22×C4C23×C414yes—
889C22×C4C22×D414yes—
890C22×C4C22×D414yes—
891C22×C4C22×D414yes—
892C22×C4C22×D414yes—
893C22×C4C22×D414yes—
894C22×C4C2×#4114yes—
895C22×C4C2×#4114yes—
896C22×C4C2×#4114yes—
897C4⋊C4—232no—
898C4⋊C4—416no—
899C22⋊C4—232no—
900C22⋊C4—232no—
901C22⋊C4—416no—
902C22⋊C4—416no—
903C22⋊C4—416no—
904C22⋊C4—416no—
905C22⋊C4—416no—
906C22⋊C4—416no—
907C22⋊C4—416no—
908C22⋊C4—416no—
909C22⋊C4—416no—
910C22⋊C4—416no—
911C22⋊C4—416no—
912C42—416no—
913C23—232no—
914C23—232no—
915C23—232no—
916C23—232no—
917C23—232no—
918C23—232no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—416no—
963C23—416no—
964C23—416no—
965C23—416no—
966C23—416no—
967C23—416no—
968C23—416no—
969C23—416no—
970C23—416no—
971C23—416no—
972C23—416no—
973C23—416no—
974C23—416no—
975C23—416no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—416no—
981C23—416no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—416no—
993C23—416no—
994C23—42no—
995C23—42no—
996C23—416no—
997C23—416no—
998C23—42no—
999C23—42no—
1000C23—416no—
1001C23—416no—
1002C23—42no—
1003C23—42no—
1004C23—416no—
1005C23—416no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—416no—
1019C23—416no—
1020C23—416no—
1021C23—416no—
1022C23—416no—
1023C23—416no—
1024C23—416no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—88no—
1054C23—88no—
1055C23—88no—
1056C23—88no—
1057C23—88no—
1058C23—88no—
1059C23—88no—
1060C23—88no—
1061C23C22×C22⋊C418yes—
1062C23C22×C22⋊C418yes—
1063C23C22×C22⋊C414yes—
1064C23C2×C4×D414yes—
1065C23C4×#4114yes—
1066C23#51814yes—
1067C23#51814yes—
1068C23#51814yes—
1069C23#52014yes—
1070C23#53414yes—
1071C23#53414yes—
1072C23#53414yes—
1073C23#53414yes—
1074C23#53514yes—
1075C23#53714yes—
1076C23#53814yes—
1077C23#53814yes—
1078C23#54014yes—
1079C23#54014yes—
1080C23#54014yes—
1081C23#54214yes—
1082C23D4214yes—
1083C23D4214yes—
1084C23#54614yes—
1085C23#54614yes—
1086C23#54614yes—
1087C23#54614yes—
1088C23#54614yes—
1089C23#54714yes—
1090C23#54714yes—
1091C23#55014yes—
1092C23#55314yes—
1093C23#55514yes—
1094C23#56014yes—
1095C23#56014yes—
1096C23#56214yes—
1097C23#56214yes—
1098C23C24×C411yescharacteristic
1099C23C23×D411yescharacteristic
1100C23C23×D411yescharacteristic
1101C23C23×D411yescharacteristic
1102C23C22×#4111yescharacteristic
1103C23C22×#4111yescharacteristic
1104C23C22×#4111yescharacteristic
1105C23C2×H(5,𝔽2)11yescharacteristic
1106C23C2×H(5,𝔽2)11yescharacteristic
1107C23C2×H(5,𝔽2)11yescharacteristic
1108C23C2×H(5,𝔽2)11yescharacteristic
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×H(5,𝔽2)11yescharacteristic
1112C23C2×2−1+411yescharacteristic
1113D4—464no—
1114D4—464no—
1115D4—464no—
1116C2×C4—232no—
1117C2×C4—232no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—464no—
1149C2×C4—464no—
1150C2×C4—416no—
1151C2×C4—416no—
1152C2×C4—416no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—416no—
1162C2×C4—416no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—416no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—88no—
1209C2×C4—88no—
1210C2×C4—88no—
1211C2×C4—88no—
1212C2×C4C22×C22⋊C418yes—
1213C2×C4C2×C4×D418yes—
1214C22—28no—
1215C22—28no—
1216C22—28no—
1217C22—28no—
1218C22—28no—
1219C22—28no—
1220C22—44no—
1221C22—44no—
1222C22—464no—
1223C22—464no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—832no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22#230818yes—
1263C22#232418yes—
1264C22#233318yes—
1265C22D4×C22⋊C418yes—
1266C22#233918yes—
1267C22#236318yes—
1268C22#237718yes—
1269C22#267118yes—
1270C22#267318yes—
1271C22#267818yes—
1272C22#268218yes—
1273C22#268618yes—
1274C22#268818yes—
1275C22#269918yes—
1276C22#270118yes—
1277C22C23×C22⋊C411yescharacteristic
1278C22C22×C4×D411yescharacteristic
1279C22C2×C4×#4111yescharacteristic
1280C22C2×#51811yescharacteristic
1281C22C2×#51811yescharacteristic
1282C22C2×#51811yescharacteristic
1283C22C2×#52011yescharacteristic
1284C22C2×#53411yescharacteristic
1285C22C2×#53411yescharacteristic
1286C22C2×#53411yescharacteristic
1287C22C2×#53411yescharacteristic
1288C22C2×#53511yescharacteristic
1289C22C2×#53711yescharacteristic
1290C22C2×#53811yescharacteristic
1291C22C2×#53811yescharacteristic
1292C22C2×#54011yescharacteristic
1293C22C2×#54011yescharacteristic
1294C22C2×#54011yescharacteristic
1295C22C2×#54211yescharacteristic
1296C22C2×D4211yescharacteristic
1297C22C2×D4211yescharacteristic
1298C22C2×#54611yescharacteristic
1299C22C2×#54611yescharacteristic
1300C22C2×#54611yescharacteristic
1301C22C2×#54611yescharacteristic
1302C22C2×#54611yescharacteristic
1303C22C2×#54711yescharacteristic
1304C22C2×#54711yescharacteristic
1305C22C2×#55011yescharacteristic
1306C22C2×#55311yescharacteristic
1307C22C2×#55511yescharacteristic
1308C22C2×#56011yescharacteristic
1309C22C2×#56011yescharacteristic
1310C22C2×#56211yescharacteristic
1311C22C2×#56211yescharacteristic
1312C4—28no—
1313C4—28no—
1314C4—44no—
1315C4—44no—
1316C4—44no—
1317C4—44no—
1318C4—44no—
1319C4—44no—
1320C4—82no—
1321C4—82no—
1322C4—82no—
1323C4—82no—
1324C2—48no—
1325C2—48no—
1326C2—84no—
1327C2#14363116yesdirect product factor
1328C2C2×#230811yescharacteristic
1329C2C2×#232411yescharacteristic
1330C2C2×#233311yescharacteristic
1331C2C2×D4×C22⋊C411yescharacteristic
1332C2C2×#233911yescharacteristic
1333C2C2×#236311yescharacteristic
1334C2C2×#237711yescharacteristic
1335C2C2×#267111yescharacteristic
1336C2C2×#267311yescharacteristic
1337C2C2×#267811yescharacteristic
1338C2C2×#268211yescharacteristic
1339C2C2×#268611yescharacteristic
1340C2C2×#268811yescharacteristic
1341C2C2×#269911yescharacteristic
1342C2C2×#270111yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC23×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#390C2semidirect
3. C22×#386C2semidirect
4. C22×#386C2semidirect
5. C22×#381C2semidirect
6. #14363C2direct (N × H)
7. C2×#1441C2semidirect
8. C2×#1440C2semidirect
9. C2×#1439C2semidirect
10. C2×#1438C2semidirect
11. C2×#1438C2semidirect
12. C2×#1438C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
24. C22×#121C4semidirect
43. C2×#390C22semidirect
46. C2×#386C22semidirect
47. C2×#386C22semidirect
49. C2×#381C22semidirect
64. #1441C22semidirect
65. #1440C22semidirect
66. #1439C22semidirect
67. #1438C22semidirect
68. #1438C22semidirect
69. #1438C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. C22⋊#95C22semidirect
73. C22⋊#95C22semidirect
95. C23×D4C2×C4semidirect
114. C24×C4C2×C4semidirect
132. C2×#121C2×C4semidirect
138. C22×C4⋊C4C2×C4semidirect
179. C22×C22⋊C4C2×C4semidirect
214. C2×#95D4semidirect
314. C22×D4C22⋊C4semidirect
317. C22×D4C22×C4semidirect
423. C23×C4C22×C4semidirect
452. C2×C4⋊C4C22×C4semidirect
504. C2×C22⋊C4C22×C4semidirect
522. #95C2×D4semidirect
712. C2×D4C2×C22⋊C4semidirect
1327. C2#14363direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1212
C22×#3902
C22×#3862
C22×#3812
#143632
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C22⋊#952