Finite Group Databasebeta

← C2×#14737 #607669

Subgroups — C2×#14737 #607669

Order 512.

7402 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#397C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#386C211yesmaximal, characteristic
5C22×#385C211yesmaximal, characteristic, complemented
6C23×#95C211yesmaximal, characteristic, complemented
7#14737C2116yesmaximal, direct product factor
8C2×#1445C211yesmaximal, characteristic, complemented
9C2×#1443C211yesmaximal, characteristic, complemented
10C2×#1443C211yesmaximal, characteristic, complemented
11C2×#1442C211yesmaximal, characteristic, complemented
12C2×#1440C211yesmaximal, characteristic, complemented
13C2×#1440C211yesmaximal, characteristic, complemented
14C2×#1439C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C25×C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C2×#397—28no—
33C2×#397C2218yescomplemented
34C2×#386—28no—
35C2×#386—28no—
36C2×#386—28no—
37C2×#386C2218yes—
38C2×#386C2218yes—
39C2×#386C2218yes—
40C2×#385—28no—
41C2×#385C2218yescomplemented
42C22×#95—28no—
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
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×#95C2218yescomplemented
64#1445C2218yescomplemented
65#1443C2218yescomplemented
66#1443C2218yescomplemented
67#1442C2218yescomplemented
68#1440C2218yescomplemented
69#1440C2218yescomplemented
70#1439C2218yescomplemented
71C22⋊#95C2218yescomplemented
72C22⋊#95C2218yescomplemented
73C26C2311yescharacteristic
74C26C2311yescharacteristic
75C23×D4—24no—
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4D418yes—
82C23×D4C2314yes—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—24no—
96C24×C4—24no—
97C24×C4—24no—
98C24×C4—42no—
99C24×C4—42no—
100C24×C4—42no—
101C24×C4—42no—
102C24×C4—42no—
103C24×C4—42no—
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C24×C4C2314yes—
118C24×C4C2314yes—
119C24×C4C2314yes—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4—42no—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
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—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
151C22×C22⋊C4—42no—
152C22×C22⋊C4—42no—
153C22×C22⋊C4—42no—
154C22×C22⋊C4D418yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164#397—232no—
165#386—232no—
166#386—232no—
167#386—232no—
168#385—232no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—24no—
173C2×#95—24no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—232no—
185C2×#95—42no—
186C2×#95—42no—
187C2×#95—42no—
188C2×#95—42no—
189C2×#95D418yescomplemented
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25C2×D414yes—
233C25C2×D414yes—
234C25C2×D414yes—
235C25#4114yes—
236C25#4114yes—
237C25#4114yes—
238C25#4114yes—
239C25#4114yes—
240C25C2412yes—
241C25C2412yes—
242C25C2411yescharacteristic
243C22×D4—232no—
244C22×D4—232no—
245C22×D4—232no—
246C22×D4—28no—
247C22×D4—28no—
248C22×D4—28no—
249C22×D4—28no—
250C22×D4—28no—
251C22×D4—28no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4—416no—
255C22×D4—416no—
256C22×D4C2×D4116yes—
257C23×C4—232no—
258C23×C4—232no—
259C23×C4—232no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—28no—
280C23×C4—28no—
281C23×C4—28no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—28no—
318C23×C4—28no—
319C23×C4—28no—
320C23×C4—28no—
321C23×C4—28no—
322C23×C4—28no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—28no—
332C23×C4—28no—
333C23×C4—28no—
334C23×C4—28no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—28no—
345C23×C4—28no—
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—44no—
358C23×C4—44no—
359C23×C4—44no—
360C23×C4—44no—
361C23×C4—44no—
362C23×C4—44no—
363C23×C4—416no—
364C23×C4—416no—
365C23×C4—416no—
366C23×C4—416no—
367C23×C4—416no—
368C23×C4—416no—
369C23×C4—416no—
370C23×C4—416no—
371C23×C4—416no—
372C23×C4—416no—
373C23×C4—416no—
374C23×C4—416no—
375C23×C4—416no—
376C23×C4—416no—
377C23×C4—416no—
378C23×C4—416no—
379C23×C4—416no—
380C23×C4—416no—
381C23×C4C2×D414yes—
382C23×C4C2×D414yes—
383C23×C4C2×D414yes—
384C23×C4C2×D414yes—
385C23×C4C2×D414yes—
386C23×C4C2×D414yes—
387C23×C4#4114yes—
388C23×C4#4114yes—
389C23×C4#4114yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2412yes—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—44no—
409C2×C4⋊C4—416no—
410C2×C4⋊C4—416no—
411C2×C22⋊C4—232no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—416no—
439C2×C22⋊C4—416no—
440C2×C22⋊C4—416no—
441C2×C22⋊C4—416no—
442C2×C22⋊C4—416no—
443C2×C22⋊C4—416no—
444C2×C22⋊C4—416no—
445C2×C22⋊C4—416no—
446C2×C22⋊C4C2×D4116yes—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—28no—
455#95—28no—
456#95—28no—
457#95—28no—
458#95—28no—
459#95—28no—
460#95—28no—
461#95—28no—
462#95—44no—
463#95—44no—
464#95—44no—
465#95—44no—
466#95C2×D4116yescomplemented
467C24—28no—
468C24—28no—
469C24—28no—
470C24—28no—
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—28no—
485C24—28no—
486C24—28no—
487C24—28no—
488C24—28no—
489C24—28no—
490C24—28no—
491C24—28no—
492C24—28no—
493C24—28no—
494C24—28no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—28no—
504C24—28no—
505C24—28no—
506C24—28no—
507C24—28no—
508C24—28no—
509C24—28no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24—44no—
542C24—44no—
543C24—44no—
544C24—44no—
545C24—44no—
546C24—44no—
547C24—44no—
548C24—44no—
549C24—44no—
550C24—44no—
551C24—44no—
552C24#121116yes—
553C24#123116yes—
554C24#123116yes—
555C24#123116yes—
556C24#124116yes—
557C24#126116yes—
558C24#126116yes—
559C24C22×D414yes—
560C24C22×D414yes—
561C24C22×D414yes—
562C24C22×D412yes—
563C24C22×D412yes—
564C24C22×D412yes—
565C24C2×#4114yes—
566C24C2×#4114yes—
567C24C2×#4114yes—
568C24C2×#4114yes—
569C24C2×#4114yes—
570C24C2×#4112yes—
571C24C2×#4112yes—
572C24C2×#4112yes—
573C24C2×#4112yes—
574C24C2×#4112yes—
575C24C2×#4112yes—
576C24C2×#4112yes—
577C24C2×#4112yes—
578C24H(5,𝔽2)12yes—
579C24H(5,𝔽2)12yes—
580C24H(5,𝔽2)12yes—
581C242−1+412yes—
582C24C2511yescharacteristic
583C2×D4—232no—
584C2×D4—232no—
585C2×D4—232no—
586C2×D4—416no—
587C2×D4—416no—
588C2×D4—416no—
589C2×D4—416no—
590C2×D4—4128no—
591C22×C4—232no—
592C22×C4—232no—
593C22×C4—232no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—416no—
704C22×C4—416no—
705C22×C4—416no—
706C22×C4—416no—
707C22×C4—416no—
708C22×C4—416no—
709C22×C4—416no—
710C22×C4—416no—
711C22×C4—416no—
712C22×C4—416no—
713C22×C4—416no—
714C22×C4—416no—
715C22×C4—4128no—
716C22×C4—4128no—
717C22×C4—416no—
718C22×C4—416no—
719C22×C4—416no—
720C22×C4—4128no—
721C22×C4—416no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—416no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—416no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4C22×D414yes—
789C22×C4C22×D414yes—
790C22×C4C22×D414yes—
791C22×C4C22×D414yes—
792C22×C4C22×D414yes—
793C22×C4C22×D414yes—
794C22×C4C2×#4114yes—
795C22×C4C2×#4114yes—
796C22×C4C2×#4114yes—
797C4⋊C4—416no—
798C4⋊C4—416no—
799C22⋊C4—232no—
800C22⋊C4—416no—
801C22⋊C4—416no—
802C22⋊C4—416no—
803C22⋊C4—416no—
804C22⋊C4—416no—
805C22⋊C4—416no—
806C22⋊C4—416no—
807C22⋊C4—416no—
808C23—232no—
809C23—232no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—232no—
817C23—232no—
818C23—232no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—232no—
837C23—232no—
838C23—232no—
839C23—232no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—232no—
847C23—232no—
848C23—232no—
849C23—232no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—416no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—416no—
869C23—416no—
870C23—416no—
871C23—416no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—416no—
885C23—416no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—88no—
893C23—88no—
894C23—88no—
895C23—88no—
896C23—88no—
897C23—88no—
898C23—88no—
899C23—88no—
900C23#397164yescomplemented
901C23C2×#12118yes—
902C23C2×#12114yes—
903C23C2×#12318yes—
904C23C2×#12318yes—
905C23C2×#12318yes—
906C23C2×#12314yes—
907C23C2×#12314yes—
908C23C2×#12314yes—
909C23#52514yes—
910C23#52514yes—
911C23#52514yes—
912C23C2×#12418yes—
913C23C2×#12414yes—
914C23C2×#12618yes—
915C23C2×#12618yes—
916C23C2×#12614yes—
917C23C2×#12614yes—
918C23#52914yes—
919C23#52914yes—
920C23#52914yes—
921C23#53814yes—
922C23#53814yes—
923C23#53814yes—
924C23#53914yes—
925C23#53914yes—
926C23#53914yes—
927C23D4214yes—
928C23D4214yes—
929C23#54614yes—
930C23#54614yes—
931C23#54614yes—
932C23#54614yes—
933C23#54614yes—
934C23#54714yes—
935C23#54714yes—
936C23#54814yes—
937C23#55114yes—
938C23#55114yes—
939C23#55214yes—
940C23#55314yes—
941C23#55314yes—
942C23#55314yes—
943C23C23×D411yescharacteristic
944C23C23×D411yescharacteristic
945C23C23×D411yescharacteristic
946C23C22×#4111yescharacteristic
947C23C22×#4111yescharacteristic
948C23C22×#4111yescharacteristic
949C23C22×#4111yescharacteristic
950C23C22×#4111yescharacteristic
951C23C22×#4111yescharacteristic
952C23C22×#4111yescharacteristic
953C23C22×#4111yescharacteristic
954C23C2×H(5,𝔽2)11yescharacteristic
955C23C2×H(5,𝔽2)11yescharacteristic
956C23C2×H(5,𝔽2)11yescharacteristic
957C23C2×2−1+411yescharacteristic
958D4—464no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—464no—
987C2×C4—464no—
988C2×C4—464no—
989C2×C4—416no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—416no—
1003C2×C4—416no—
1004C2×C4—416no—
1005C2×C4—416no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—416no—
1026C2×C4—416no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—416no—
1033C2×C4—416no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—88no—
1063C2×C4—88no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C22—28no—
1067C22—28no—
1068C22—28no—
1069C22—28no—
1070C22—28no—
1071C22—28no—
1072C22—28no—
1073C22—28no—
1074C22—28no—
1075C22—28no—
1076C22—28no—
1077C22—28no—
1078C22—2128no—
1079C22—28no—
1080C22—28no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—82no—
1089C22—82no—
1090C22—82no—
1091C22—82no—
1092C22—82no—
1093C22—82no—
1094C22—832no—
1095C22—82no—
1096C22—82no—
1097C22C2×#39718yes—
1098C22C2×#397116yescomplemented
1099C22#241818yes—
1100C22#241918yes—
1101C22#242418yes—
1102C22#242518yes—
1103C22#244318yes—
1104C22#244318yes—
1105C22#244418yes—
1106C22#244418yes—
1107C22#247218yes—
1108C22#248118yes—
1109C22#248818yes—
1110C22#251018yes—
1111C22#264318yes—
1112C22#285218yes—
1113C22C22×#12111yescharacteristic
1114C22C22×#12311yescharacteristic
1115C22C22×#12311yescharacteristic
1116C22C22×#12311yescharacteristic
1117C22C2×#52511yescharacteristic
1118C22C2×#52511yescharacteristic
1119C22C2×#52511yescharacteristic
1120C22C22×#12411yescharacteristic
1121C22C22×#12611yescharacteristic
1122C22C22×#12611yescharacteristic
1123C22C2×#52911yescharacteristic
1124C22C2×#52911yescharacteristic
1125C22C2×#52911yescharacteristic
1126C22C2×#53811yescharacteristic
1127C22C2×#53811yescharacteristic
1128C22C2×#53811yescharacteristic
1129C22C2×#53911yescharacteristic
1130C22C2×#53911yescharacteristic
1131C22C2×#53911yescharacteristic
1132C22C2×D4211yescharacteristic
1133C22C2×D4211yescharacteristic
1134C22C2×#54611yescharacteristic
1135C22C2×#54611yescharacteristic
1136C22C2×#54611yescharacteristic
1137C22C2×#54611yescharacteristic
1138C22C2×#54611yescharacteristic
1139C22C2×#54711yescharacteristic
1140C22C2×#54711yescharacteristic
1141C22C2×#54811yescharacteristic
1142C22C2×#55111yescharacteristic
1143C22C2×#55111yescharacteristic
1144C22C2×#55211yescharacteristic
1145C22C2×#55311yescharacteristic
1146C22C2×#55311yescharacteristic
1147C22C2×#55311yescharacteristic
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—44no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—44no—
1157C4—82no—
1158C4—82no—
1159C4—82no—
1160C4—82no—
1161C2—216no—
1162C2—84no—
1163C2#14737116yesdirect product factor
1164C2C22×#39711yescharacteristic
1165C2C2×#264311yescharacteristic
1166C2C2×#241811yescharacteristic
1167C2C2×#244311yescharacteristic
1168C2C2×#244311yescharacteristic
1169C2C2×#242411yescharacteristic
1170C2C2×#247211yescharacteristic
1171C2C2×#248111yescharacteristic
1172C2C2×#241911yescharacteristic
1173C2C2×#242511yescharacteristic
1174C2C2×#244411yescharacteristic
1175C2C2×#244411yescharacteristic
1176C2C2×#248811yescharacteristic
1177C2C2×#251011yescharacteristic
1178C2C2×#285211yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#397C2semidirect
5. C22×#385C2semidirect
6. C23×#95C2semidirect
7. #14737C2direct (N × H)
8. C2×#1445C2semidirect
9. C2×#1443C2semidirect
10. C2×#1443C2semidirect
11. C2×#1442C2semidirect
12. C2×#1440C2semidirect
13. C2×#1440C2semidirect
14. C2×#1439C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
33. C2×#397C22semidirect
41. C2×#385C22semidirect
63. C22×#95C22semidirect
64. #1445C22semidirect
65. #1443C22semidirect
66. #1443C22semidirect
67. #1442C22semidirect
68. #1440C22semidirect
69. #1440C22semidirect
70. #1439C22semidirect
71. C22⋊#95C22semidirect
72. C22⋊#95C22semidirect
189. C2×#95D4semidirect
466. #95C2×D4semidirect
900. C23#397semidirect
1098. C22C2×#397semidirect
1163. C2#14737direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3972
C22×#3862
C22×#3852
C23×#952
#147372
C2×#14452
C2×#14432
C2×#14422
C2×#14402
C2×#14392
C2×C22⋊#952