Finite Group Databasebeta

← #154603

Subgroups — #154603

Order 512.

3570 conjugacy classes of subgroups.

The subgroup lattice has 1253 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1439C211yesmaximal, characteristic
2C2×#1439C211yesmaximal, characteristic
3C2×#1437C212yesmaximal
4C2×#1437C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic, complemented
6C2×#1434C212yesmaximal, complemented
7C2×C4×#95C211yesmaximal, characteristic, complemented
8#7557C211yesmaximal, characteristic, complemented
9#7557C211yesmaximal, characteristic, complemented
10#7556C212yesmaximal, complemented
11#7555C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2212yes—
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2212yes—
19C23×C42C2212yes—
20C23×C42C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2211yescharacteristic
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35#1439—24no—
36#1439C418yescomplemented
37#1437—28no—
38#1437—24no—
39C4⋊#95—24no—
40#1434—28no—
41C4×#95—24no—
42C26C2311yescharacteristic
43C24×C4C2312yes—
44C24×C4C2311yescharacteristic
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2312yes—
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—42no—
60C22×C4⋊C4—42no—
61C22×C4⋊C4—42no—
62C22×C4⋊C4C2×C414yes—
63C22×C22⋊C4—24no—
64C22×C22⋊C4—22no—
65C22×C22⋊C4—24no—
66C22×C22⋊C4—22no—
67C22×C22⋊C4—24no—
68C22×C22⋊C4—22no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—24no—
71C22×C22⋊C4—22no—
72C22×C22⋊C4—24no—
73C22×C22⋊C4—22no—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—22no—
76C22×C22⋊C4—24no—
77C22×C22⋊C4—22no—
78C22×C22⋊C4—22no—
79C22×C22⋊C4—24no—
80C22×C22⋊C4—22no—
81C22×C22⋊C4—24no—
82C22×C22⋊C4—24no—
83C22×C22⋊C4—24no—
84C22×C22⋊C4—42no—
85C22×C22⋊C4—42no—
86C22×C22⋊C4—42no—
87C22×C22⋊C4—42no—
88C22×C22⋊C4—42no—
89C22×C22⋊C4—42no—
90C22×C22⋊C4—42no—
91C22×C22⋊C4C2×C414yes—
92C22×C22⋊C4C2×C418yes—
93C22×C22⋊C4Q814yes—
94C22×C42—24no—
95C22×C42—22no—
96C22×C42—24no—
97C22×C42—22no—
98C22×C42—24no—
99C22×C42—24no—
100C22×C42—24no—
101C22×C42—42no—
102C22×C42—42no—
103C22×C42—42no—
104C22×C42D418yes—
105C22×C42D414yes—
106C2×#95—24no—
107C2×#95—22no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—22no—
115C2×#95—24no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—22no—
127C2×#95—22no—
128C2×#95—22no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—22no—
134C2×#95—22no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95C2×C418yes—
144C2×#95C2×C414yes—
145C2×#95D414yes—
146C25—21no—
147C25—22no—
148C25—21no—
149C25—21no—
150C25—21no—
151C25—21no—
152C25—22no—
153C25—21no—
154C25—22no—
155C25—21no—
156C25—22no—
157C25—21no—
158C25—22no—
159C25—22no—
160C25—21no—
161C25—21no—
162C25—22no—
163C25—22no—
164C25—21no—
165C25—21no—
166C25C22×C412yes—
167C25C2×Q812yes—
168C25#4112yes—
169C25C2411yescharacteristic
170C23×C4—21no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—21no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—22no—
217C23×C4—21no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—21no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—22no—
270C23×C4—21no—
271C23×C4C22×C414yes—
272C23×C4C22×C412yes—
273C23×C4C22×C414yes—
274C23×C4C22×C412yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D412yes—
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2×D412yes—
282C23×C4C2×D414yes—
283C23×C4C2×Q812yes—
284C23×C4C2×Q812yes—
285C23×C4#4114yes—
286C23×C4#4112yes—
287C23×C4#4114yes—
288C23×C4#4114yes—
289C23×C4#4114yes—
290C23×C4#4112yes—
291C23×C4#4112yes—
292C23×C4#4112yes—
293C23×C4#4112yes—
294C23×C4#4114yes—
295C23×C4#4112yes—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—48no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—48no—
305C2×C4⋊C4—44no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—216no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—216no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—216no—
314C2×C22⋊C4—48no—
315C2×C22⋊C4—48no—
316C2×C22⋊C4—48no—
317C2×C22⋊C4—48no—
318C2×C22⋊C4—48no—
319C2×C22⋊C4—48no—
320C2×C22⋊C4—48no—
321C2×C22⋊C4—48no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—48no—
324C2×C22⋊C4—48no—
325C2×C22⋊C4—48no—
326C2×C22⋊C4—48no—
327C2×C22⋊C4—48no—
328C2×C22⋊C4—48no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—48no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C42—216no—
338C2×C42—28no—
339C2×C42—28no—
340C2×C42—216no—
341C2×C42—44no—
342C2×C42—48no—
343C2×C42—48no—
344C2×C42—48no—
345C2×C42—48no—
346C2×C42—48no—
347C2×C42—48no—
348C2×C42—48no—
349#95—216no—
350#95—216no—
351#95—28no—
352#95—216no—
353#95—28no—
354#95—48no—
355#95—48no—
356#95—48no—
357#95—48no—
358#95—48no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95—48no—
363C24—22no—
364C24—22no—
365C24—24no—
366C24—22no—
367C24—24no—
368C24—22no—
369C24—24no—
370C24—22no—
371C24—24no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—22no—
376C24—24no—
377C24—22no—
378C24—24no—
379C24—22no—
380C24—24no—
381C24—22no—
382C24—22no—
383C24—24no—
384C24—24no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—24no—
393C24—42no—
394C24—41no—
395C24—42no—
396C24—41no—
397C24—41no—
398C24—41no—
399C24—42no—
400C24—42no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—41no—
412C24—41no—
413C24—42no—
414C24—42no—
415C24—41no—
416C24—42no—
417C24—42no—
418C24—41no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—41no—
423C24—41no—
424C24—41no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—41no—
430C24—42no—
431C24—41no—
432C24—42no—
433C24—42no—
434C24—41no—
435C24—42no—
436C24—41no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—41no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—41no—
456C24—41no—
457C24—42no—
458C24—41no—
459C24—42no—
460C24—42no—
461C24C4×Q814yes—
462C24C23×C411yescharacteristic
463C24C22×D411yescharacteristic
464C24C22×D411yescharacteristic
465C24C22×D412yes—
466C24C22×Q811yescharacteristic
467C24C2×#4111yescharacteristic
468C24C2×#4111yescharacteristic
469C24C2×#4111yescharacteristic
470C24C2×#4112yes—
471C24C2×#4111yescharacteristic
472C24C2×#4111yescharacteristic
473C24C2×#4112yes—
474C24C2×#4112yes—
475C24C2×#4111yescharacteristic
476C24C2×#4112yes—
477C24C2×#4111yescharacteristic
478C24C2×#4112yes—
479C24H(5,𝔽2)12yes—
480C24H(5,𝔽2)11yescharacteristic
481C24H(5,𝔽2)12yes—
482C24H(5,𝔽2)11yescharacteristic
483C24H(5,𝔽2)11yescharacteristic
484C242−1+411yescharacteristic
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—41no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—41no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—41no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—41no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—41no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—41no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—41no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—41no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—41no—
731C22×C4—41no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4#11714yes—
749C22×C4C4×D418yes—
750C22×C4C4×D414yes—
751C22×C4C4×D414yes—
752C22×C4#12118yes—
753C22×C4#12114yes—
754C22×C4C22⋊Q814yes—
755C22×C4C22⋊Q818yes—
756C22×C4#12314yes—
757C22×C4#12318yes—
758C22×C4#12314yes—
759C22×C4#12414yes—
760C22×C4#12414yes—
761C22×C4#12614yes—
762C22×C4#12714yes—
763C4⋊C4—416no—
764C4⋊C4—416no—
765C22⋊C4—416no—
766C22⋊C4—432no—
767C22⋊C4—432no—
768C22⋊C4—416no—
769C22⋊C4—416no—
770C42—416no—
771C42—432no—
772C23—24no—
773C23—24no—
774C23—28no—
775C23—28no—
776C23—24no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—42no—
791C23—44no—
792C23—44no—
793C23—42no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—42no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—42no—
802C23—42no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—42no—
808C23—44no—
809C23—42no—
810C23—44no—
811C23—42no—
812C23—42no—
813C23—44no—
814C23—42no—
815C23—44no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—44no—
820C23—44no—
821C23—42no—
822C23—42no—
823C23—44no—
824C23—44no—
825C23—42no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—42no—
830C23—42no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—82no—
835C23—81no—
836C23—82no—
837C23—82no—
838C23—81no—
839C23—81no—
840C23—82no—
841C23—81no—
842C23—82no—
843C23—81no—
844C23—81no—
845C23—81no—
846C23—82no—
847C23—82no—
848C23—81no—
849C23—81no—
850C23—82no—
851C23—81no—
852C23—82no—
853C23—82no—
854C23—82no—
855C23—82no—
856C23—81no—
857C23—82no—
858C23—82no—
859C23—82no—
860C23—81no—
861C23—81no—
862C23—82no—
863C23—82no—
864C23—82no—
865C23—82no—
866C23—82no—
867C23—82no—
868C23—82no—
869C23—82no—
870C23—82no—
871C23C2×#11711yescharacteristic
872C23C2×C4×D411yescharacteristic
873C23C2×C4×D412yes—
874C23C2×C4×D411yescharacteristic
875C23C2×C4×Q811yescharacteristic
876C23C4×#4111yescharacteristic
877C23C4×#4112yes—
878C23C4×#4112yes—
879C23#51811yescharacteristic
880C23#51812yes—
881C23#52011yescharacteristic
882C23C2×#12111yescharacteristic
883C23C2×#12112yes—
884C23C2×C22⋊Q811yescharacteristic
885C23C2×C22⋊Q812yes—
886C23C2×#12311yescharacteristic
887C23C2×#12312yes—
888C23C2×#12311yescharacteristic
889C23#52511yescharacteristic
890C23#52511yescharacteristic
891C23#52512yes—
892C23#52512yes—
893C23#52512yes—
894C23C2×#12411yescharacteristic
895C23C2×#12411yescharacteristic
896C23C2×#12611yescharacteristic
897C23#52911yescharacteristic
898C23#52912yes—
899C23#52912yes—
900C23#52912yes—
901C23#52912yes—
902C23#52912yes—
903C23#52912yes—
904C23#52912yes—
905C23#52912yes—
906C23C2×#12711yescharacteristic
907C23#53211yescharacteristic
908C23#53212yes—
909C23#53212yes—
910C23#53211yescharacteristic
911C23#53212yes—
912C23#53212yes—
913C23#53311yescharacteristic
914C23#53312yes—
915C23#53411yescharacteristic
916C23#53412yes—
917C23#53511yescharacteristic
918C23#53511yescharacteristic
919C23#53512yes—
920C23#53512yes—
921C23#53711yescharacteristic
922C23#53712yes—
923C23#53812yes—
924C23#53812yes—
925C23#53812yes—
926C23#54011yescharacteristic
927C23#54012yes—
928C23#54211yescharacteristic
929C23#54212yes—
930C23#54611yescharacteristic
931C23#54611yescharacteristic
932C23#54612yes—
933C23#54612yes—
934C23D4×Q811yescharacteristic
935C23#55011yescharacteristic
936C23#55112yes—
937C23#55112yes—
938C23#55112yes—
939C23#55112yes—
940C23#55112yes—
941C23#55112yes—
942C23#55112yes—
943C23#55112yes—
944C23#55211yescharacteristic
945C23#55211yescharacteristic
946C23#55211yescharacteristic
947C23#55212yes—
948C23#55311yescharacteristic
949C23#55311yescharacteristic
950C23#55312yes—
951C23#55312yes—
952C23#55312yes—
953C23#55312yes—
954C23#55311yescharacteristic
955C23#55312yes—
956C23#55312yes—
957C23#55312yes—
958C23#55412yes—
959C23#55411yescharacteristic
960C23#55411yescharacteristic
961C23#55412yes—
962C23#55411yescharacteristic
963C23#55512yes—
964C23#55511yescharacteristic
965C23#55511yescharacteristic
966C23#55512yes—
967C23#55511yescharacteristic
968C23#55612yes—
969C23#55912yes—
970C2×C4—24no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—28no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—28no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—44no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—42no—
1010C2×C4—44no—
1011C2×C4—42no—
1012C2×C4—44no—
1013C2×C4—42no—
1014C2×C4—44no—
1015C2×C4—42no—
1016C2×C4—44no—
1017C2×C4—44no—
1018C2×C4—44no—
1019C2×C4—44no—
1020C2×C4—44no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—44no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—44no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—44no—
1050C2×C4—42no—
1051C2×C4—44no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—42no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—42no—
1060C2×C4—81no—
1061C2×C4—81no—
1062C2×C4—81no—
1063C2×C4—82no—
1064C2×C4—82no—
1065C2×C4—81no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—81no—
1069C2×C4—81no—
1070C2×C4—81no—
1071C2×C4—82no—
1072C2×C4—82no—
1073C2×C4—81no—
1074C2×C4—82no—
1075C2×C4—82no—
1076C2×C4—81no—
1077C2×C4—82no—
1078C2×C4—82no—
1079C2×C4—81no—
1080C2×C4—82no—
1081C2×C4—82no—
1082C2×C4—82no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4—82no—
1086C2×C4—82no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4—82no—
1092C2×C4—81no—
1093C2×C4—81no—
1094C2×C4#38818yes—
1095C2×C4#39918yes—
1096C22—44no—
1097C22—48no—
1098C22—44no—
1099C22—44no—
1100C22—48no—
1101C22—84no—
1102C22—82no—
1103C22—82no—
1104C22—82no—
1105C22—84no—
1106C22—82no—
1107C22—82no—
1108C22—82no—
1109C22—84no—
1110C22—82no—
1111C22—82no—
1112C22—82no—
1113C22—84no—
1114C22—82no—
1115C22—82no—
1116C22—84no—
1117C22—84no—
1118C22—82no—
1119C22C2×#38811yescharacteristic
1120C22#229312yes—
1121C22C4×#12112yes—
1122C22C4×#12312yes—
1123C22C4×#12311yescharacteristic
1124C22C4×C22⋊Q812yes—
1125C22C4×C22⋊Q811yescharacteristic
1126C22C4×#12411yescharacteristic
1127C22C4×#12711yescharacteristic
1128C22#232112yes—
1129C22#232111yescharacteristic
1130C22#232412yes—
1131C22#232411yescharacteristic
1132C22#234511yescharacteristic
1133C22#234611yescharacteristic
1134C22#235312yes—
1135C22#236011yescharacteristic
1136C22#236311yescharacteristic
1137C22#236412yes—
1138C22#236812yes—
1139C22#237212yes—
1140C22#237312yes—
1141C22#237412yes—
1142C22C2×#39911yescharacteristic
1143C22#239512yes—
1144C22#239511yescharacteristic
1145C22#239612yes—
1146C22#239611yescharacteristic
1147C22#239711yescharacteristic
1148C22#241111yescharacteristic
1149C22#241112yes—
1150C22#241212yes—
1151C22#241211yescharacteristic
1152C22#241412yes—
1153C22#241411yescharacteristic
1154C22#241712yes—
1155C22#241711yescharacteristic
1156C22#242011yescharacteristic
1157C22#242311yescharacteristic
1158C22#244412yes—
1159C22#245712yes—
1160C22#245912yes—
1161C22#246512yes—
1162C22#246712yes—
1163C22#249511yescharacteristic
1164C22#249711yescharacteristic
1165C22#249811yescharacteristic
1166C22#249812yes—
1167C22#250012yes—
1168C22#250012yes—
1169C22#250411yescharacteristic
1170C22#250411yescharacteristic
1171C22#251012yes—
1172C22#251512yes—
1173C22#251612yes—
1174C22#251812yes—
1175C22#251812yes—
1176C22#252212yes—
1177C22#252512yes—
1178C22#252612yes—
1179C22#252912yes—
1180C22#253112yes—
1181C22#253212yes—
1182C22#256111yescharacteristic
1183C22#256211yescharacteristic
1184C22#256311yescharacteristic
1185C22#256311yescharacteristic
1186C22#256411yescharacteristic
1187C22#256412yes—
1188C22#256612yes—
1189C22#256612yes—
1190C22#257212yes—
1191C22#257412yes—
1192C22#257612yes—
1193C22#257812yes—
1194C22#258712yes—
1195C22#258912yes—
1196C22#259111yescharacteristic
1197C22#259211yescharacteristic
1198C22#260112yes—
1199C22#260112yes—
1200C22#260212yes—
1201C22#260212yes—
1202C22#260311yescharacteristic
1203C22#260312yes—
1204C22#261011yescharacteristic
1205C22#261012yes—
1206C22#265611yescharacteristic
1207C22#265711yescharacteristic
1208C22#266111yescharacteristic
1209C22#266112yes—
1210C22#266212yes—
1211C22#266211yescharacteristic
1212C22#285011yescharacteristic
1213C22#285412yes—
1214C22#285611yescharacteristic
1215C22#285811yescharacteristic
1216C22#286012yes—
1217C22#286111yescharacteristic
1218C4—28no—
1219C4—28no—
1220C4—48no—
1221C4—48no—
1222C4—44no—
1223C4—84no—
1224C4—82no—
1225C4—82no—
1226C4—82no—
1227C4—84no—
1228C2—84no—
1229C2C4×#39911yescharacteristic
1230C2#1397311yescharacteristic
1231C2#1402011yescharacteristic
1232C2#1407412yes—
1233C2#1407512yes—
1234C2#1419812yes—
1235C2#1419912yes—
1236C2#1424311yescharacteristic
1237C2#1424911yescharacteristic
1238C2#1432111yescharacteristic
1239C2#1470011yescharacteristic
1240C2#1483611yescharacteristic
1241C2#1483812yes—
1242C2#1484211yescharacteristic
1243C2#1486412yes—
1244C2#1486611yescharacteristic
1245C2#1490011yescharacteristic
1246C2#1502312yes—
1247C2#1502511yescharacteristic
1248C2#1504711yescharacteristic
1249C2#1505912yes—
1250C2#1524411yescharacteristic
1251C2#1525011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC24C23×C4
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊#95C2semidirect
6. C2×#1434C2semidirect
7. C2×C4×#95C2semidirect
8. #7557C2semidirect
9. #7557C2semidirect
10. #7556C2semidirect
36. #1439C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14392
C2×#14372
C2×C4⋊#952
C2×#14342
C2×C4×#952
#75572
#75562
#75552