Finite Group Databasebeta

← #154236

Subgroups — #154236

Order 512.

4586 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#380C211yesmaximal, characteristic
2C22×C4×C22⋊C4C211yesmaximal, characteristic
3C2×#1444C211yesmaximal, characteristic, complemented
4C2×#1442C211yesmaximal, characteristic, complemented
5C2×#1439C212yesmaximal
6C2×#1436C212yesmaximal, complemented
7C2×C22⋊#95C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic, complemented
9#7557C211yesmaximal, characteristic, complemented
10#7555C212yesmaximal
11#7554C212yesmaximal, complemented
12C25×C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C22⋊C4C2211yescharacteristic
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2212yes—
19C23×C22⋊C4C2212yes—
20C23×C42C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#380—28no—
23C2×#380—24no—
24C2×C4×C22⋊C4—24no—
25C2×C4×C22⋊C4—24no—
26C2×C4×C22⋊C4—24no—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2212yes—
39C22×#95C2212yes—
40#1444—24no—
41#1442—24no—
42#1439—28no—
43#1436—28no—
44C22⋊#95C418yescomplemented
45C26C2311yescharacteristic
46C24×C4—22no—
47C24×C4—22no—
48C24×C4—24no—
49C24×C4—22no—
50C24×C4—22no—
51C24×C4—24no—
52C24×C4—42no—
53C24×C4—42no—
54C24×C4C2×C414yes—
55C24×C4D414yes—
56C24×C4Q814yes—
57C24×C4C2312yes—
58C24×C4C2312yes—
59C24×C4C2312yes—
60C24×C4C2312yes—
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—24no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—42no—
81C22×C4⋊C4—42no—
82C22×C4⋊C4—42no—
83C22×C4⋊C4—42no—
84C22×C22⋊C4—22no—
85C22×C22⋊C4—22no—
86C22×C22⋊C4—22no—
87C22×C22⋊C4—22no—
88C22×C22⋊C4—22no—
89C22×C22⋊C4—22no—
90C22×C22⋊C4—22no—
91C22×C22⋊C4—22no—
92C22×C22⋊C4—22no—
93C22×C22⋊C4—22no—
94C22×C22⋊C4—22no—
95C22×C22⋊C4—22no—
96C22×C22⋊C4—24no—
97C22×C22⋊C4—24no—
98C22×C22⋊C4—24no—
99C22×C22⋊C4—24no—
100C22×C22⋊C4—24no—
101C22×C22⋊C4—24no—
102C22×C22⋊C4—24no—
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—42no—
106C22×C22⋊C4—42no—
107C22×C22⋊C4—42no—
108C22×C22⋊C4—42no—
109C22×C22⋊C4C2×C418yes—
110C22×C22⋊C4D414yes—
111C22×C22⋊C4Q814yes—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—22no—
115C22×C42—22no—
116C22×C42—22no—
117C22×C42—22no—
118C22×C42—24no—
119C22×C42—24no—
120C22×C42—42no—
121C22×C42—42no—
122#380—232no—
123C4×C22⋊C4—232no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—22no—
127C2×#95—22no—
128C2×#95—22no—
129C2×#95—22no—
130C2×#95—22no—
131C2×#95—22no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—22no—
137C2×#95—24no—
138C2×#95—22no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—42no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95—42no—
155C2×#95—42no—
156C2×#95—42no—
157C2×#95C2×C414yes—
158C2×#95C2×C418yes—
159C2×#95C2×C414yes—
160C2×#95D418yes—
161C2×#95D414yes—
162C2×#95D414yes—
163C25—21no—
164C25—21no—
165C25—22no—
166C25—22no—
167C25—22no—
168C25—21no—
169C25—21no—
170C25—21no—
171C25—21no—
172C25—21no—
173C25—21no—
174C25—22no—
175C25—22no—
176C25—22no—
177C25—22no—
178C25—22no—
179C25C22×C412yes—
180C25C2×D412yes—
181C25C2×D412yes—
182C25C2×Q812yes—
183C25C2×Q812yes—
184C25#4112yes—
185C25#4112yes—
186C25C2411yescharacteristic
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—22no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—28no—
242C23×C4—28no—
243C23×C4—216no—
244C23×C4—28no—
245C23×C4—28no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—216no—
249C23×C4—28no—
250C23×C4—28no—
251C23×C4—22no—
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—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—22no—
280C23×C4—22no—
281C23×C4—22no—
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—48no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—48no—
297C23×C4—48no—
298C23×C4—48no—
299C23×C4—48no—
300C23×C4—48no—
301C23×C4—48no—
302C23×C4—48no—
303C23×C4—48no—
304C23×C4—48no—
305C23×C4C4⋊C4116yescomplemented
306C23×C4C22×C414yes—
307C23×C4C22×C414yes—
308C23×C4C22×C412yes—
309C23×C4C22×C412yes—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2×D412yes—
313C23×C4C2×D412yes—
314C23×C4C2×D412yes—
315C23×C4C2×D412yes—
316C23×C4C2×D412yes—
317C23×C4C2×D412yes—
318C23×C4C2×D412yes—
319C23×C4C2×D412yes—
320C23×C4C2×D412yes—
321C23×C4C2×D412yes—
322C23×C4C2×D414yes—
323C23×C4C2×Q812yes—
324C23×C4C2×Q812yes—
325C23×C4C2×Q812yes—
326C23×C4C2×Q812yes—
327C23×C4#4114yes—
328C23×C4#4114yes—
329C23×C4#4112yes—
330C23×C4#4112yes—
331C23×C4#4112yes—
332C23×C4#4112yes—
333C23×C4#4112yes—
334C23×C4#4112yes—
335C23×C4#4114yes—
336C2×C4⋊C4—216no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—48no—
340C2×C4⋊C4—48no—
341C2×C4⋊C4—48no—
342C2×C4⋊C4—48no—
343C2×C4⋊C4—48no—
344C2×C4⋊C4—48no—
345C2×C4⋊C4—48no—
346C2×C4⋊C4—48no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—48no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—48no—
352C2×C4⋊C4—44no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—216no—
368C2×C22⋊C4—216no—
369C2×C22⋊C4—216no—
370C2×C22⋊C4—48no—
371C2×C22⋊C4—48no—
372C2×C22⋊C4—48no—
373C2×C22⋊C4—48no—
374C2×C22⋊C4—48no—
375C2×C22⋊C4—48no—
376C2×C22⋊C4—48no—
377C2×C22⋊C4—48no—
378C2×C22⋊C4—48no—
379C2×C22⋊C4—48no—
380C2×C22⋊C4—48no—
381C2×C42—28no—
382C2×C42—28no—
383C2×C42—48no—
384C2×C42—48no—
385C2×C42—48no—
386C2×C42—48no—
387C2×C42—44no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42—44no—
391#95—216no—
392#95—28no—
393#95—216no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—216no—
398#95—48no—
399#95—48no—
400#95—48no—
401#95—48no—
402#95—48no—
403#95—48no—
404C24—24no—
405C24—24no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—24no—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—24no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—42no—
483C24—42no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24—42no—
489C24—42no—
490C24—42no—
491C24—42no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24C2×C4⋊C414yes—
497C24C4×D414yes—
498C24C4×Q814yes—
499C24#12114yes—
500C24C22⋊Q814yes—
501C24#12514yes—
502C24C4⋊Q814yes—
503C24C23×C411yescharacteristic
504C24C22×D411yescharacteristic
505C24C22×D411yescharacteristic
506C24C22×D411yescharacteristic
507C24C22×D412yes—
508C24C22×D411yescharacteristic
509C24C22×Q811yescharacteristic
510C24C22×Q811yescharacteristic
511C24C2×#4112yes—
512C24C2×#4112yes—
513C24C2×#4112yes—
514C24C2×#4111yescharacteristic
515C24C2×#4111yescharacteristic
516C24C2×#4111yescharacteristic
517C24C2×#4111yescharacteristic
518C24C2×#4111yescharacteristic
519C24C2×#4111yescharacteristic
520C24C2×#4111yescharacteristic
521C24C2×#4111yescharacteristic
522C24H(5,𝔽2)12yes—
523C24H(5,𝔽2)12yes—
524C24H(5,𝔽2)12yes—
525C242−1+412yes—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—232no—
627C22×C4—232no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—416no—
650C22×C4—432no—
651C22×C4—432no—
652C22×C4—416no—
653C22×C4—416no—
654C22×C4—416no—
655C22×C4—432no—
656C22×C4—432no—
657C22×C4—416no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—42no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—42no—
670C22×C4—41no—
671C22×C4—42no—
672C22×C4—41no—
673C22×C4—42no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
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—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
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—42no—
731C22×C4—42no—
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—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4C2×C4⋊C414yes—
799C22×C4C2×C4⋊C414yes—
800C22×C4#11718yes—
801C22×C4C4×D414yes—
802C22×C4C4×D414yes—
803C22×C4C4×D418yes—
804C22×C4#12014yes—
805C22×C4#12014yes—
806C22×C4#12114yes—
807C22×C4#12114yes—
808C22×C4C22⋊Q814yes—
809C22×C4C22⋊Q814yes—
810C22×C4C22⋊Q814yes—
811C22×C4C22⋊Q814yes—
812C22×C4C22⋊Q818yes—
813C22×C4#12314yes—
814C22×C4#12314yes—
815C4⋊C4—416no—
816C4⋊C4—416no—
817C4⋊C4—432no—
818C22⋊C4—232no—
819C22⋊C4—232no—
820C22⋊C4—432no—
821C22⋊C4—432no—
822C42—416no—
823C42—416no—
824C23—24no—
825C23—24no—
826C23—28no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—28no—
834C23—24no—
835C23—24no—
836C23—28no—
837C23—24no—
838C23—24no—
839C23—28no—
840C23—28no—
841C23—24no—
842C23—24no—
843C23—28no—
844C23—28no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—28no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—44no—
877C23—44no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—44no—
882C23—44no—
883C23—44no—
884C23—44no—
885C23—44no—
886C23—44no—
887C23—42no—
888C23—42no—
889C23—44no—
890C23—44no—
891C23—44no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23—44no—
896C23—44no—
897C23—44no—
898C23—44no—
899C23—44no—
900C23—44no—
901C23—44no—
902C23—44no—
903C23—44no—
904C23—44no—
905C23—44no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—44no—
921C23—44no—
922C23#38918yes—
923C23C22×C4⋊C411yescharacteristic
924C23C2×#11712yes—
925C23C2×C4×D411yescharacteristic
926C23C2×C4×D411yescharacteristic
927C23C2×C4×D411yescharacteristic
928C23C2×C4×D412yes—
929C23C2×C4×Q811yescharacteristic
930C23C4×#4111yescharacteristic
931C23C4×#4111yescharacteristic
932C23#51812yes—
933C23#52012yes—
934C23C2×#12011yescharacteristic
935C23C2×#12011yescharacteristic
936C23C2×#12111yescharacteristic
937C23C2×#12111yescharacteristic
938C23C2×#12111yescharacteristic
939C23C2×C22⋊Q811yescharacteristic
940C23C2×C22⋊Q811yescharacteristic
941C23C2×C22⋊Q811yescharacteristic
942C23C2×C22⋊Q811yescharacteristic
943C23C2×C22⋊Q811yescharacteristic
944C23C2×C22⋊Q812yes—
945C23C2×#12311yescharacteristic
946C23C2×#12311yescharacteristic
947C23#52511yescharacteristic
948C23#52511yescharacteristic
949C23#52511yescharacteristic
950C23#52511yescharacteristic
951C23#52511yescharacteristic
952C23#52511yescharacteristic
953C23#52512yes—
954C23#52512yes—
955C23C2×#12511yescharacteristic
956C23#52911yescharacteristic
957C23#52912yes—
958C23#52911yescharacteristic
959C23#52912yes—
960C23#52911yescharacteristic
961C23#52911yescharacteristic
962C23#52912yes—
963C23#52912yes—
964C23C2×C4⋊Q811yescharacteristic
965C23#53212yes—
966C23#53211yescharacteristic
967C23#53211yescharacteristic
968C23#53211yescharacteristic
969C23#53211yescharacteristic
970C23#53212yes—
971C23#53312yes—
972C23#53311yescharacteristic
973C23#53311yescharacteristic
974C23#53311yescharacteristic
975C23#53311yescharacteristic
976C23#53411yescharacteristic
977C23#53411yescharacteristic
978C23#53511yescharacteristic
979C23#53611yescharacteristic
980C23#53812yes—
981C23#53812yes—
982C23#53912yes—
983C23#53912yes—
984C23#54012yes—
985C23#54012yes—
986C23#54212yes—
987C23#54212yes—
988C23#54312yes—
989C23#54412yes—
990C23D4212yes—
991C23D4212yes—
992C23D4212yes—
993C23#54612yes—
994C23#54612yes—
995C23#54612yes—
996C23#54612yes—
997C23#54612yes—
998C23#54612yes—
999C23#54612yes—
1000C23#54612yes—
1001C23#54712yes—
1002C23#54712yes—
1003C23#54812yes—
1004C23#54812yes—
1005C23D4×Q812yes—
1006C23#55012yes—
1007C23#55112yes—
1008C23#55112yes—
1009C23#55112yes—
1010C23#55112yes—
1011C23#55212yes—
1012C23#55212yes—
1013C23#55312yes—
1014C23#55312yes—
1015C23#55312yes—
1016C23#55312yes—
1017C23#55412yes—
1018C23#55412yes—
1019C23#55412yes—
1020C23#55512yes—
1021C23#55612yes—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—28no—
1025C2×C4—28no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—28no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—28no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—28no—
1047C2×C4—28no—
1048C2×C4—28no—
1049C2×C4—28no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—28no—
1053C2×C4—464no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—42no—
1070C2×C4—42no—
1071C2×C4—42no—
1072C2×C4—42no—
1073C2×C4—42no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—42no—
1079C2×C4—42no—
1080C2×C4—42no—
1081C2×C4—42no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—44no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—44no—
1121C2×C4—44no—
1122C2×C4—44no—
1123C2×C4—82no—
1124C2×C4—82no—
1125C2×C4—82no—
1126C2×C4—82no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—82no—
1130C2×C4—82no—
1131C2×C4—82no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4—82no—
1135C2×C4—82no—
1136C2×C4—82no—
1137C2×C4—82no—
1138C2×C4—82no—
1139C2×C4—82no—
1140C2×C4—82no—
1141C2×C4—82no—
1142C2×C4—82no—
1143C2×C4—82no—
1144C2×C4—82no—
1145C2×C4—82no—
1146C2×C4—82no—
1147C2×C4#38518yes—
1148C2×C4#38518yes—
1149C22—28no—
1150C22—28no—
1151C22—28no—
1152C22—44no—
1153C22—44no—
1154C22—44no—
1155C22—44no—
1156C22—44no—
1157C22—44no—
1158C22—44no—
1159C22—48no—
1160C22—48no—
1161C22—48no—
1162C22—48no—
1163C22—48no—
1164C22—48no—
1165C22—48no—
1166C22—48no—
1167C22—44no—
1168C22—44no—
1169C22—44no—
1170C22—44no—
1171C22—44no—
1172C22#228511yescharacteristic
1173C22C2×#38511yescharacteristic
1174C22C2×#38511yescharacteristic
1175C22#229012yes—
1176C22C2×#38911yescharacteristic
1177C22#229312yes—
1178C22#229611yescharacteristic
1179C22C4×#12111yescharacteristic
1180C22C4×#12111yescharacteristic
1181C22C4×C22⋊Q811yescharacteristic
1182C22C4×C22⋊Q811yescharacteristic
1183C22#231511yescharacteristic
1184C22#231711yescharacteristic
1185C22#233512yes—
1186C22#233512yes—
1187C22#234212yes—
1188C22#234512yes—
1189C22#235212yes—
1190C22#235412yes—
1191C22#235812yes—
1192C22#235812yes—
1193C22#236012yes—
1194C22#236112yes—
1195C22#238811yescharacteristic
1196C22#238811yescharacteristic
1197C22#239511yescharacteristic
1198C22#239511yescharacteristic
1199C22#239612yes—
1200C22#239612yes—
1201C22#240311yescharacteristic
1202C22#240511yescharacteristic
1203C22#240511yescharacteristic
1204C22#240811yescharacteristic
1205C22#240911yescharacteristic
1206C22#242412yes—
1207C22#242512yes—
1208C22#242712yes—
1209C22#242812yes—
1210C22#243111yescharacteristic
1211C22#243211yescharacteristic
1212C22#243712yes—
1213C22#243712yes—
1214C22#243912yes—
1215C22#244012yes—
1216C22#244112yes—
1217C22#244212yes—
1218C22#244912yes—
1219C22#245012yes—
1220C22#245212yes—
1221C22#245412yes—
1222C22#245612yes—
1223C22#245712yes—
1224C22#246012yes—
1225C22#246112yes—
1226C22#246312yes—
1227C22#246412yes—
1228C22#246412yes—
1229C22#246512yes—
1230C22#246712yes—
1231C22#246812yes—
1232C22#247612yes—
1233C22#247712yes—
1234C22#248311yescharacteristic
1235C22#248611yescharacteristic
1236C22#248711yescharacteristic
1237C22#249911yescharacteristic
1238C22#250011yescharacteristic
1239C22#252112yes—
1240C22#252212yes—
1241C22#253012yes—
1242C22#253112yes—
1243C22#254311yescharacteristic
1244C22#254311yescharacteristic
1245C22#254912yes—
1246C22#255312yes—
1247C22#255512yes—
1248C22#255612yes—
1249C22#255912yes—
1250C22#256012yes—
1251C22#256411yescharacteristic
1252C22#256411yescharacteristic
1253C22#256912yes—
1254C22#257412yes—
1255C22#257712yes—
1256C22#257812yes—
1257C22#263511yescharacteristic
1258C22#263511yescharacteristic
1259C22#263811yescharacteristic
1260C22#263811yescharacteristic
1261C22#266512yes—
1262C22#266712yes—
1263C22#284711yescharacteristic
1264C22#284811yescharacteristic
1265C22#285111yescharacteristic
1266C22#285111yescharacteristic
1267C22#285411yescharacteristic
1268C22#285511yescharacteristic
1269C22#285711yescharacteristic
1270C22#285711yescharacteristic
1271C4—28no—
1272C4—28no—
1273C4—44no—
1274C4—44no—
1275C4—48no—
1276C4—44no—
1277C4—44no—
1278C4—84no—
1279C4—84no—
1280C4—84no—
1281C2—48no—
1282C2#1384411yescharacteristic
1283C2#1387911yescharacteristic
1284C2#1390811yescharacteristic
1285C2#1398712yes—
1286C2#1398812yes—
1287C2#1401112yes—
1288C2#1401212yes—
1289C2#1412711yescharacteristic
1290C2#1413011yescharacteristic
1291C2#1429511yescharacteristic
1292C2#1469711yescharacteristic
1293C2#1472211yescharacteristic
1294C2#1472311yescharacteristic
1295C2#1477012yes—
1296C2#1477112yes—
1297C2#1477412yes—
1298C2#1477512yes—
1299C2#1482411yescharacteristic
1300C2#1482511yescharacteristic
1301C2#1499611yescharacteristic
1302C2#1500111yescharacteristic
1303C2#1506111yescharacteristic
1304C2#1506311yescharacteristic
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
3. C2×#1444C2semidirect
4. C2×#1442C2semidirect
6. C2×#1436C2semidirect
8. #7557C2semidirect
9. #7557C2semidirect
11. #7554C2semidirect
44. C22⋊#95C4semidirect
305. C23×C4C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3802
C22×C4×C22⋊C42
C2×#14442
C2×#14422
C2×#14392
C2×#14362
C2×C22⋊#952
#75572
#75552
#75542