Finite Group Databasebeta

← #156302

Subgroups — #156302

Order 512.

3162 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1439C211yesmaximal, characteristic
2C2×#1439C211yesmaximal, characteristic
3C2×#1437C211yesmaximal, characteristic
4C2×C4⋊#95C211yesmaximal, characteristic, complemented
5C2×#1434C211yesmaximal, characteristic, complemented
6#7557C211yesmaximal, characteristic, complemented
7#7557C211yesmaximal, characteristic, complemented
8#7556C212yesmaximal, complemented
9#7556C212yesmaximal, complemented
10#7555C212yesmaximal
11#7555C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2212yes—
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2212yes—
19C23×C42C2211yescharacteristic
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35#1439—24no—
36#1439C418yescomplemented
37#1437—24no—
38C4⋊#95—24no—
39#1434—24no—
40C26C2311yescharacteristic
41C24×C4C2312yes—
42C24×C4C2311yescharacteristic
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—42no—
58C22×C4⋊C4—42no—
59C22×C4⋊C4—42no—
60C22×C4⋊C4C2×C414yes—
61C22×C22⋊C4—22no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4—22no—
65C22×C22⋊C4—22no—
66C22×C22⋊C4—22no—
67C22×C22⋊C4—22no—
68C22×C22⋊C4—22no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—22no—
71C22×C22⋊C4—22no—
72C22×C22⋊C4—24no—
73C22×C22⋊C4—24no—
74C22×C22⋊C4—24no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—42no—
77C22×C22⋊C4—42no—
78C22×C22⋊C4—42no—
79C22×C22⋊C4—42no—
80C22×C22⋊C4—42no—
81C22×C22⋊C4—42no—
82C22×C22⋊C4—42no—
83C22×C22⋊C4—42no—
84C22×C22⋊C4—42no—
85C22×C22⋊C4—42no—
86C22×C22⋊C4—42no—
87C22×C22⋊C4—42no—
88C22×C22⋊C4—42no—
89C22×C22⋊C4C2×C414yes—
90C22×C22⋊C4C2×C418yes—
91C22×C22⋊C4Q814yes—
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—24no—
95C22×C42—42no—
96C22×C42D414yes—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—22no—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—22no—
114C2×#95—22no—
115C2×#95—42no—
116C2×#95—42no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—42no—
123C2×#95—42no—
124C2×#95—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95—42no—
132C2×#95—42no—
133C2×#95—42no—
134C2×#95—42no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95C2×C414yes—
138C2×#95C2×C418yes—
139C2×#95D414yes—
140C25—21no—
141C25—21no—
142C25—21no—
143C25—21no—
144C25—21no—
145C25—21no—
146C25—21no—
147C25—21no—
148C25—22no—
149C25—22no—
150C25—21no—
151C25—21no—
152C25—22no—
153C25—22no—
154C25—22no—
155C25—22no—
156C25—22no—
157C25—21no—
158C25—22no—
159C25—21no—
160C25C22×C412yes—
161C25C2×Q812yes—
162C25#4112yes—
163C25C2411yescharacteristic
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
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—22no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
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—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—21no—
216C23×C4—22no—
217C23×C4—21no—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
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—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
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—21no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—21no—
271C23×C4C22×C414yes—
272C23×C4C22×C412yes—
273C23×C4C22×C414yes—
274C23×C4C22×C412yes—
275C23×C4C2×D414yes—
276C23×C4C2×D412yes—
277C23×C4C2×D412yes—
278C23×C4C2×D412yes—
279C23×C4C2×D412yes—
280C23×C4C2×Q812yes—
281C23×C4C2×Q812yes—
282C23×C4#4114yes—
283C23×C4#4112yes—
284C23×C4#4112yes—
285C23×C4#4114yes—
286C23×C4#4112yes—
287C23×C4#4112yes—
288C23×C4#4112yes—
289C23×C4#4112yes—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—48no—
294C2×C4⋊C4—48no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—48no—
299C2×C4⋊C4—44no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—48no—
306C2×C22⋊C4—48no—
307C2×C22⋊C4—48no—
308C2×C22⋊C4—48no—
309C2×C22⋊C4—48no—
310C2×C22⋊C4—48no—
311C2×C22⋊C4—48no—
312C2×C22⋊C4—48no—
313C2×C22⋊C4—48no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—48no—
318C2×C22⋊C4—48no—
319C2×C22⋊C4—48no—
320C2×C22⋊C4—48no—
321C2×C22⋊C4—48no—
322C2×C22⋊C4—48no—
323C2×C22⋊C4—48no—
324C2×C22⋊C4—48no—
325C2×C22⋊C4—48no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C42—28no—
332C2×C42—28no—
333C2×C42—44no—
334C2×C42—48no—
335C2×C42—48no—
336#95—28no—
337#95—28no—
338#95—48no—
339#95—48no—
340#95—48no—
341#95—48no—
342#95—48no—
343#95—44no—
344#95—44no—
345#95—48no—
346#95—48no—
347#95—48no—
348#95—48no—
349#95—48no—
350#95—44no—
351C24—22no—
352C24—22no—
353C24—22no—
354C24—24no—
355C24—22no—
356C24—22no—
357C24—24no—
358C24—24no—
359C24—24no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—24no—
366C24—24no—
367C24—24no—
368C24—24no—
369C24—22no—
370C24—22no—
371C24—24no—
372C24—24no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—24no—
380C24—24no—
381C24—41no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24—41no—
387C24—42no—
388C24—41no—
389C24—42no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—41no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—41no—
423C24—42no—
424C24—41no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—41no—
429C24—41no—
430C24—41no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—41no—
438C24—41no—
439C24—41no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24C4×Q814yes—
450C24C23×C411yescharacteristic
451C24C22×D411yescharacteristic
452C24C22×D411yescharacteristic
453C24C22×Q811yescharacteristic
454C24C2×#4111yescharacteristic
455C24C2×#4111yescharacteristic
456C24C2×#4111yescharacteristic
457C24C2×#4111yescharacteristic
458C24C2×#4111yescharacteristic
459C24C2×#4111yescharacteristic
460C24C2×#4112yes—
461C24C2×#4112yes—
462C24C2×#4111yescharacteristic
463C24H(5,𝔽2)12yes—
464C24H(5,𝔽2)12yes—
465C24H(5,𝔽2)12yes—
466C24H(5,𝔽2)12yes—
467C24H(5,𝔽2)11yescharacteristic
468C24H(5,𝔽2)11yescharacteristic
469C24H(5,𝔽2)12yes—
470C24H(5,𝔽2)11yescharacteristic
471C242−1+412yes—
472C242−1+411yescharacteristic
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
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—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—41no—
577C22×C4—42no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—42no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—41no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—41no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
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—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
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—42no—
684C22×C4—42no—
685C22×C4—41no—
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—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—41no—
703C22×C4—41no—
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#11714yes—
743C22×C4C4×D414yes—
744C22×C4C4×D414yes—
745C22×C4#12114yes—
746C22×C4C22⋊Q814yes—
747C22×C4#12314yes—
748C22×C4#12314yes—
749C22×C4#12414yes—
750C22×C4#12614yes—
751C4⋊C4—416no—
752C4⋊C4—416no—
753C22⋊C4—416no—
754C22⋊C4—416no—
755C22⋊C4—432no—
756C22⋊C4—432no—
757C22⋊C4—416no—
758C42—416no—
759C23—28no—
760C23—24no—
761C23—24no—
762C23—28no—
763C23—24no—
764C23—42no—
765C23—42no—
766C23—44no—
767C23—42no—
768C23—42no—
769C23—44no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—42no—
777C23—42no—
778C23—44no—
779C23—42no—
780C23—44no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—44no—
785C23—42no—
786C23—44no—
787C23—42no—
788C23—44no—
789C23—44no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—42no—
799C23—44no—
800C23—42no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—42no—
805C23—42no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—42no—
817C23—42no—
818C23—81no—
819C23—81no—
820C23—82no—
821C23—82no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23—81no—
826C23—81no—
827C23—82no—
828C23—81no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—82no—
834C23—82no—
835C23—81no—
836C23—81no—
837C23—82no—
838C23—82no—
839C23—82no—
840C23—82no—
841C23—82no—
842C23—82no—
843C23—82no—
844C23—82no—
845C23—82no—
846C23—82no—
847C23—81no—
848C23—82no—
849C23—82no—
850C23—82no—
851C23—82no—
852C23—82no—
853C23—82no—
854C23—82no—
855C23—82no—
856C23—81no—
857C23—81no—
858C23C2×#11711yescharacteristic
859C23C2×C4×D411yescharacteristic
860C23C2×C4×D411yescharacteristic
861C23C2×C4×Q811yescharacteristic
862C23C4×#4112yes—
863C23C4×#4111yescharacteristic
864C23#51812yes—
865C23#51812yes—
866C23#51811yescharacteristic
867C23#52012yes—
868C23#52011yescharacteristic
869C23C2×#12111yescharacteristic
870C23C2×C22⋊Q811yescharacteristic
871C23C2×#12311yescharacteristic
872C23C2×#12311yescharacteristic
873C23#52511yescharacteristic
874C23#52511yescharacteristic
875C23C2×#12411yescharacteristic
876C23C2×#12611yescharacteristic
877C23#52912yes—
878C23#52911yescharacteristic
879C23#53311yescharacteristic
880C23#53411yescharacteristic
881C23#53511yescharacteristic
882C23#53511yescharacteristic
883C23#53511yescharacteristic
884C23#53511yescharacteristic
885C23#53512yes—
886C23#53511yescharacteristic
887C23#53611yescharacteristic
888C23#53711yescharacteristic
889C23#53712yes—
890C23#53812yes—
891C23#53812yes—
892C23#53812yes—
893C23#53812yes—
894C23#53812yes—
895C23#53812yes—
896C23#53912yes—
897C23#53912yes—
898C23#53912yes—
899C23#54011yescharacteristic
900C23#54012yes—
901C23#54012yes—
902C23#54012yes—
903C23#54012yes—
904C23#54012yes—
905C23#54112yes—
906C23#54211yescharacteristic
907C23#54212yes—
908C23#54212yes—
909C23#54212yes—
910C23#54212yes—
911C23#54212yes—
912C23#54212yes—
913C23#54212yes—
914C23#54212yes—
915C23#54312yes—
916C23#54412yes—
917C23#54611yescharacteristic
918C23#54611yescharacteristic
919C23#54612yes—
920C23#54612yes—
921C23D4×Q811yescharacteristic
922C23#55011yescharacteristic
923C23#55112yes—
924C23#55112yes—
925C23#55112yes—
926C23#55112yes—
927C23#55112yes—
928C23#55211yescharacteristic
929C23#55211yescharacteristic
930C23#55211yescharacteristic
931C23#55311yescharacteristic
932C23#55311yescharacteristic
933C23#55312yes—
934C23#55312yes—
935C23#55312yes—
936C23#55311yescharacteristic
937C23#55312yes—
938C23#55312yes—
939C23#55312yes—
940C23#55411yescharacteristic
941C23#55411yescharacteristic
942C23#55412yes—
943C23#55411yescharacteristic
944C23#55412yes—
945C23#55511yescharacteristic
946C23#55511yescharacteristic
947C23#55511yescharacteristic
948C23#55912yes—
949C23#56012yes—
950C23#56012yes—
951C23#56012yes—
952C23#56012yes—
953C23#56012yes—
954C23H(3,𝔽4)12yes—
955C23#56212yes—
956C23#56212yes—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—28no—
960C2×C4—28no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—44no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—44no—
992C2×C4—44no—
993C2×C4—44no—
994C2×C4—44no—
995C2×C4—44no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—44no—
1006C2×C4—42no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—42no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—44no—
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—42no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—44no—
1031C2×C4—42no—
1032C2×C4—82no—
1033C2×C4—82no—
1034C2×C4—82no—
1035C2×C4—81no—
1036C2×C4—82no—
1037C2×C4—82no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—81no—
1042C2×C4—82no—
1043C2×C4—81no—
1044C2×C4—81no—
1045C2×C4—81no—
1046C2×C4—82no—
1047C2×C4—82no—
1048C2×C4—81no—
1049C2×C4—81no—
1050C2×C4—81no—
1051C2×C4—81no—
1052C2×C4—81no—
1053C2×C4—82no—
1054C2×C4—82no—
1055C2×C4—82no—
1056C2×C4—82no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—82no—
1060C2×C4—82no—
1061C2×C4—82no—
1062C2×C4—82no—
1063C2×C4—82no—
1064C2×C4—82no—
1065C2×C4—82no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—82no—
1069C2×C4—81no—
1070C2×C4—82no—
1071C2×C4—82no—
1072C2×C4—82no—
1073C2×C4—82no—
1074C2×C4—82no—
1075C2×C4—82no—
1076C2×C4—82no—
1077C2×C4—82no—
1078C2×C4—82no—
1079C2×C4—82no—
1080C2×C4—82no—
1081C2×C4—81no—
1082C2×C4#38818yes—
1083C22—48no—
1084C22—44no—
1085C22—44no—
1086C22—48no—
1087C22—44no—
1088C22—82no—
1089C22—82no—
1090C22—82no—
1091C22—82no—
1092C22—82no—
1093C22—84no—
1094C22—84no—
1095C22—84no—
1096C22—84no—
1097C22—82no—
1098C22—82no—
1099C22—82no—
1100C22—84no—
1101C22—82no—
1102C22—82no—
1103C22—82no—
1104C22—82no—
1105C22—84no—
1106C22C2×#38811yescharacteristic
1107C22C4×#12311yescharacteristic
1108C22C4×C22⋊Q811yescharacteristic
1109C22#231912yes—
1110C22#232111yescharacteristic
1111C22#232411yescharacteristic
1112C22#232412yes—
1113C22#232611yescharacteristic
1114C22#232811yescharacteristic
1115C22#232912yes—
1116C22#233412yes—
1117C22#233512yes—
1118C22#233712yes—
1119C22#234511yescharacteristic
1120C22#234611yescharacteristic
1121C22#235312yes—
1122C22#236011yescharacteristic
1123C22#236311yescharacteristic
1124C22#236412yes—
1125C22#236812yes—
1126C22#237412yes—
1127C22#237512yes—
1128C22#237712yes—
1129C22#241111yescharacteristic
1130C22#241211yescharacteristic
1131C22#241411yescharacteristic
1132C22#241711yescharacteristic
1133C22#242011yescharacteristic
1134C22#242311yescharacteristic
1135C22#244412yes—
1136C22#248211yescharacteristic
1137C22#248711yescharacteristic
1138C22#249511yescharacteristic
1139C22#249711yescharacteristic
1140C22#250411yescharacteristic
1141C22#251012yes—
1142C22#251612yes—
1143C22#252212yes—
1144C22#256211yescharacteristic
1145C22#256311yescharacteristic
1146C22#258011yescharacteristic
1147C22#259111yescharacteristic
1148C22#259811yescharacteristic
1149C22#261911yescharacteristic
1150C22#262011yescharacteristic
1151C22#262311yescharacteristic
1152C22#262411yescharacteristic
1153C22#262412yes—
1154C22#262611yescharacteristic
1155C22#262811yescharacteristic
1156C22#263111yescharacteristic
1157C22#263111yescharacteristic
1158C22#263711yescharacteristic
1159C22#263811yescharacteristic
1160C22#264011yescharacteristic
1161C22#264111yescharacteristic
1162C22#264412yes—
1163C22#265012yes—
1164C22#265112yes—
1165C22#265312yes—
1166C22#266512yes—
1167C22#268512yes—
1168C22#269212yes—
1169C22#269312yes—
1170C22#270312yes—
1171C22#270412yes—
1172C22#270512yes—
1173C22#271212yes—
1174C22#271412yes—
1175C22#273712yes—
1176C22#273912yes—
1177C22#274112yes—
1178C22#274612yes—
1179C22#274812yes—
1180C22#274912yes—
1181C22#275312yes—
1182C22#275312yes—
1183C22#275412yes—
1184C22#275612yes—
1185C22#275712yes—
1186C22#276112yes—
1187C22#276112yes—
1188C22#276312yes—
1189C22#277212yes—
1190C22#278012yes—
1191C22#278012yes—
1192C22#279012yes—
1193C22#279012yes—
1194C22#279512yes—
1195C22#279512yes—
1196C22#280112yes—
1197C22#280312yes—
1198C22#280312yes—
1199C22#281311yescharacteristic
1200C22#281511yescharacteristic
1201C22#281811yescharacteristic
1202C22#281911yescharacteristic
1203C22#282812yes—
1204C22#282912yes—
1205C4—28no—
1206C4—44no—
1207C4—44no—
1208C4—84no—
1209C4—84no—
1210C4—82no—
1211C4—84no—
1212C4—82no—
1213C4—82no—
1214C4—84no—
1215C2—84no—
1216C2#1397311yescharacteristic
1217C2#1402011yescharacteristic
1218C2#1424011yescharacteristic
1219C2#1426011yescharacteristic
1220C2#1430611yescharacteristic
1221C2#1431911yescharacteristic
1222C2#1445612yes—
1223C2#1451212yes—
1224C2#1454712yes—
1225C2#1456612yes—
1226C2#1462311yescharacteristic
1227C2#1639511yescharacteristic
1228C2#1639811yescharacteristic
1229C2#1644112yes—
1230C2#1644212yes—
1231C2#1656611yescharacteristic
1232C2#1666211yescharacteristic
1233C2#1669111yescharacteristic
1234C2#1672312yes—
1235C2#1672512yes—
1236C2#1700711yescharacteristic
1237C2#1700911yescharacteristic
1238C2#1706611yescharacteristic
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
4. C2×C4⋊#95C2semidirect
5. C2×#1434C2semidirect
6. #7557C2semidirect
7. #7557C2semidirect
8. #7556C2semidirect
9. #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
#75572
#75562
#75552