Finite Group Databasebeta

← #156389

Subgroups — #156389

Order 512.

3182 conjugacy classes of subgroups.

The subgroup lattice has 1241 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1442C211yesmaximal, characteristic, complemented
2C2×#1440C212yesmaximal
3C2×#1439C211yesmaximal, characteristic
4C2×#1439C211yesmaximal, characteristic
5C2×#1437C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic, complemented
7#7557C211yesmaximal, characteristic, complemented
8#7556C212yesmaximal, complemented
9#7556C212yesmaximal, complemented
10#7555C212yesmaximal
11#7554C211yesmaximal, characteristic, complemented
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2212yes—
17C23×C22⋊C4C2212yes—
18C23×C22⋊C4C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2211yescharacteristic
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35#1442—24no—
36#1440—28no—
37#1439—24no—
38#1439C418yescomplemented
39#1437—24no—
40C4⋊#95—24no—
41C26C2311yescharacteristic
42C24×C4C2312yes—
43C24×C4C2311yescharacteristic
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2311yescharacteristic
47C24×C4C2312yes—
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—42no—
57C22×C4⋊C4—42no—
58C22×C4⋊C4—42no—
59C22×C4⋊C4—42no—
60C22×C4⋊C4C2×C414yes—
61C22×C4⋊C4D414yes—
62C22×C22⋊C4—24no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4—24no—
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—22no—
73C22×C22⋊C4—22no—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—24no—
77C22×C22⋊C4—24no—
78C22×C22⋊C4—24no—
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⋊C4—42no—
90C22×C22⋊C4C2×C414yes—
91C22×C22⋊C4C2×C418yes—
92C22×C22⋊C4D414yes—
93C22×C42—22no—
94C22×C42—22no—
95C22×C42—42no—
96C22×C42—42no—
97C22×C42D414yes—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—22no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—22no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—22no—
120C2×#95—24no—
121C2×#95—22no—
122C2×#95—22no—
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×#95—42no—
138C2×#95—42no—
139C2×#95C2×C414yes—
140C2×#95C2×C418yes—
141C25—21no—
142C25—21no—
143C25—21no—
144C25—21no—
145C25—21no—
146C25—21no—
147C25—21no—
148C25—21no—
149C25—22no—
150C25—22no—
151C25—22no—
152C25—22no—
153C25—22no—
154C25—22no—
155C25—21no—
156C25—22no—
157C25—21no—
158C25—21no—
159C25—21no—
160C25—22no—
161C25C22×C412yes—
162C25C2×D412yes—
163C25#4112yes—
164C25C2411yescharacteristic
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—22no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—22no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—22no—
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—22no—
204C23×C4—21no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—21no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—21no—
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—21no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—22no—
272C23×C4C22×C414yes—
273C23×C4C22×C412yes—
274C23×C4C22×C414yes—
275C23×C4C22×C412yes—
276C23×C4C2×D414yes—
277C23×C4C2×D412yes—
278C23×C4C2×D412yes—
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4#4112yes—
284C23×C4#4114yes—
285C23×C4#4112yes—
286C23×C4#4114yes—
287C23×C4#4112yes—
288C23×C4#4112yes—
289C23×C4#4112yes—
290C23×C4#4112yes—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—48no—
294C2×C4⋊C4—48no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—216no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—28no—
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—48no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
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—48no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C42—28no—
333C2×C42—44no—
334C2×C42—44no—
335C2×C42—48no—
336C2×C42—48no—
337#95—28no—
338#95—48no—
339#95—48no—
340#95—48no—
341#95—48no—
342#95—48no—
343#95—44no—
344#95—48no—
345#95—48no—
346#95—48no—
347#95—48no—
348#95—48no—
349#95—44no—
350#95—44no—
351#95—44no—
352C24—22no—
353C24—22no—
354C24—22no—
355C24—24no—
356C24—22no—
357C24—24no—
358C24—24no—
359C24—22no—
360C24—24no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—24no—
367C24—24no—
368C24—24no—
369C24—24no—
370C24—22no—
371C24—24no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—22no—
376C24—22no—
377C24—24no—
378C24—22no—
379C24—22no—
380C24—24no—
381C24—22no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24—41no—
387C24—42no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—42no—
392C24—41no—
393C24—41no—
394C24—41no—
395C24—41no—
396C24—41no—
397C24—41no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—41no—
417C24—41no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—41no—
424C24—41no—
425C24—42no—
426C24—42no—
427C24—41no—
428C24—41no—
429C24—42no—
430C24—41no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—41no—
436C24—41no—
437C24—42no—
438C24—42no—
439C24—41no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24C4×D414yes—
451C24C23×C411yescharacteristic
452C24C22×D411yescharacteristic
453C24C22×D411yescharacteristic
454C24C22×D411yescharacteristic
455C24C2×#4111yescharacteristic
456C24C2×#4111yescharacteristic
457C24C2×#4111yescharacteristic
458C24C2×#4111yescharacteristic
459C24C2×#4111yescharacteristic
460C24C2×#4111yescharacteristic
461C24C2×#4111yescharacteristic
462C24C2×#4112yes—
463C24C2×#4112yes—
464C24H(5,𝔽2)12yes—
465C24H(5,𝔽2)12yes—
466C24H(5,𝔽2)12yes—
467C24H(5,𝔽2)12yes—
468C24H(5,𝔽2)12yes—
469C24H(5,𝔽2)11yescharacteristic
470C242−1+411yescharacteristic
471C242−1+411yescharacteristic
472C242−1+412yes—
473C242−1+411yescharacteristic
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
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—24no—
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—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
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—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
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—42no—
569C22×C4—41no—
570C22×C4—42no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—41no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—41no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—42no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—41no—
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—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—41no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—41no—
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—41no—
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—41no—
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#11714yes—
744C22×C4C4×D414yes—
745C22×C4C4×D414yes—
746C22×C4#12114yes—
747C22×C4#12114yes—
748C22×C4#12314yes—
749C22×C4#12414yes—
750C22×C4#12414yes—
751C22×C4#12614yes—
752C4⋊C4—416no—
753C4⋊C4—416no—
754C22⋊C4—416no—
755C22⋊C4—416no—
756C22⋊C4—432no—
757C22⋊C4—432no—
758C22⋊C4—416no—
759C42—416no—
760C23—28no—
761C23—24no—
762C23—28no—
763C23—24no—
764C23—24no—
765C23—42no—
766C23—44no—
767C23—44no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—44no—
772C23—42no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—42no—
777C23—42no—
778C23—44no—
779C23—42no—
780C23—42no—
781C23—44no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—44no—
786C23—44no—
787C23—42no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—44no—
805C23—42no—
806C23—44no—
807C23—42no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—44no—
818C23—42no—
819C23—81no—
820C23—81no—
821C23—81no—
822C23—82no—
823C23—82no—
824C23—81no—
825C23—81no—
826C23—81no—
827C23—81no—
828C23—82no—
829C23—81no—
830C23—81no—
831C23—82no—
832C23—82no—
833C23—82no—
834C23—81no—
835C23—81no—
836C23—82no—
837C23—82no—
838C23—82no—
839C23—82no—
840C23—82no—
841C23—82no—
842C23—81no—
843C23—82no—
844C23—81no—
845C23—82no—
846C23—82no—
847C23—82no—
848C23—82no—
849C23—82no—
850C23—82no—
851C23—82no—
852C23—82no—
853C23—82no—
854C23—81no—
855C23—82no—
856C23—81no—
857C23—82no—
858C23—81no—
859C23C2×#11711yescharacteristic
860C23C2×C4×D411yescharacteristic
861C23C2×C4×D411yescharacteristic
862C23C2×C4×D411yescharacteristic
863C23C4×#4112yes—
864C23C4×#4111yescharacteristic
865C23#51812yes—
866C23#51812yes—
867C23#51911yescharacteristic
868C23#52012yes—
869C23#52011yescharacteristic
870C23C2×#12111yescharacteristic
871C23C2×#12111yescharacteristic
872C23C2×#12311yescharacteristic
873C23#52511yescharacteristic
874C23C2×#12411yescharacteristic
875C23C2×#12411yescharacteristic
876C23C2×#12611yescharacteristic
877C23#52911yescharacteristic
878C23#52912yes—
879C23#53211yescharacteristic
880C23#53211yescharacteristic
881C23#53411yescharacteristic
882C23#53411yescharacteristic
883C23#53412yes—
884C23#53412yes—
885C23#53511yescharacteristic
886C23#53511yescharacteristic
887C23#53511yescharacteristic
888C23#53512yes—
889C23#53611yescharacteristic
890C23#53611yescharacteristic
891C23#53711yescharacteristic
892C23#53712yes—
893C23#53812yes—
894C23#53812yes—
895C23#53812yes—
896C23#53812yes—
897C23#53812yes—
898C23#53812yes—
899C23#53812yes—
900C23#53812yes—
901C23#53812yes—
902C23#53812yes—
903C23#53912yes—
904C23#53912yes—
905C23#53912yes—
906C23#53912yes—
907C23#53912yes—
908C23#53912yes—
909C23#54012yes—
910C23#54012yes—
911C23#54012yes—
912C23#54111yescharacteristic
913C23#54211yescharacteristic
914C23#54212yes—
915C23#54212yes—
916C23#54212yes—
917C23#54212yes—
918C23D4211yescharacteristic
919C23#54612yes—
920C23#54612yes—
921C23#54711yescharacteristic
922C23#54711yescharacteristic
923C23#54712yes—
924C23#54711yescharacteristic
925C23#54711yescharacteristic
926C23#54811yescharacteristic
927C23#54811yescharacteristic
928C23#55012yes—
929C23#55112yes—
930C23#55112yes—
931C23#55212yes—
932C23#55211yescharacteristic
933C23#55211yescharacteristic
934C23#55211yescharacteristic
935C23#55211yescharacteristic
936C23#55212yes—
937C23#55211yescharacteristic
938C23#55312yes—
939C23#55312yes—
940C23#55312yes—
941C23#55311yescharacteristic
942C23#55312yes—
943C23#55511yescharacteristic
944C23#55511yescharacteristic
945C23#55512yes—
946C23#55612yes—
947C23#55611yescharacteristic
948C23#55912yes—
949C23#55912yes—
950C23#56012yes—
951C23#56212yes—
952C23#56212yes—
953C23#56212yes—
954C23#56212yes—
955C23#56312yes—
956C23#56312yes—
957C23#56312yes—
958C2×C4—28no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—28no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—44no—
980C2×C4—44no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—42no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—44no—
988C2×C4—44no—
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—44no—
998C2×C4—44no—
999C2×C4—44no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—42no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—42no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—44no—
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—42no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—44no—
1031C2×C4—44no—
1032C2×C4—42no—
1033C2×C4—81no—
1034C2×C4—81no—
1035C2×C4—82no—
1036C2×C4—82no—
1037C2×C4—81no—
1038C2×C4—81no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4—81no—
1044C2×C4—82no—
1045C2×C4—81no—
1046C2×C4—82no—
1047C2×C4—82no—
1048C2×C4—82no—
1049C2×C4—82no—
1050C2×C4—82no—
1051C2×C4—82no—
1052C2×C4—82no—
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—81no—
1069C2×C4—82no—
1070C2×C4—81no—
1071C2×C4—82no—
1072C2×C4—82no—
1073C2×C4—82no—
1074C2×C4—82no—
1075C2×C4—81no—
1076C2×C4—82no—
1077C2×C4—82no—
1078C2×C4—81no—
1079C2×C4—81no—
1080C2×C4—81no—
1081C2×C4—82no—
1082C2×C4—82no—
1083C2×C4#38818yes—
1084C22—48no—
1085C22—44no—
1086C22—44no—
1087C22—48no—
1088C22—44no—
1089C22—82no—
1090C22—84no—
1091C22—84no—
1092C22—82no—
1093C22—82no—
1094C22—84no—
1095C22—82no—
1096C22—82no—
1097C22—82no—
1098C22—82no—
1099C22—82no—
1100C22—82no—
1101C22—84no—
1102C22—84no—
1103C22—82no—
1104C22—82no—
1105C22—82no—
1106C22—84no—
1107C22C2×#38811yescharacteristic
1108C22C4×#12111yescharacteristic
1109C22C4×#12411yescharacteristic
1110C22#231812yes—
1111C22#232112yes—
1112C22#232111yescharacteristic
1113C22#232211yescharacteristic
1114C22#232311yescharacteristic
1115C22#232512yes—
1116C22#232811yescharacteristic
1117C22#233212yes—
1118C22#233312yes—
1119C22#233712yes—
1120C22#234411yescharacteristic
1121C22#234611yescharacteristic
1122C22#235712yes—
1123C22#235912yes—
1124C22#236111yescharacteristic
1125C22#236211yescharacteristic
1126C22#236312yes—
1127C22#237312yes—
1128C22#237612yes—
1129C22#237812yes—
1130C22#248511yescharacteristic
1131C22#248611yescharacteristic
1132C22#248911yescharacteristic
1133C22#249012yes—
1134C22#249111yescharacteristic
1135C22#249511yescharacteristic
1136C22#249611yescharacteristic
1137C22#250011yescharacteristic
1138C22#250411yescharacteristic
1139C22#251312yes—
1140C22#253611yescharacteristic
1141C22#253711yescharacteristic
1142C22#254311yescharacteristic
1143C22#254411yescharacteristic
1144C22#254711yescharacteristic
1145C22#254811yescharacteristic
1146C22#255312yes—
1147C22#256111yescharacteristic
1148C22#257312yes—
1149C22#261111yescharacteristic
1150C22#261711yescharacteristic
1151C22#261711yescharacteristic
1152C22#261811yescharacteristic
1153C22#261911yescharacteristic
1154C22#262211yescharacteristic
1155C22#262311yescharacteristic
1156C22#263111yescharacteristic
1157C22#263511yescharacteristic
1158C22#263912yes—
1159C22#263911yescharacteristic
1160C22#264011yescharacteristic
1161C22#264312yes—
1162C22#264812yes—
1163C22#265012yes—
1164C22#265312yes—
1165C22#266112yes—
1166C22#266211yescharacteristic
1167C22#266311yescharacteristic
1168C22#267812yes—
1169C22#268212yes—
1170C22#268612yes—
1171C22#270112yes—
1172C22#270212yes—
1173C22#270712yes—
1174C22#270812yes—
1175C22#271012yes—
1176C22#271812yes—
1177C22#271812yes—
1178C22#272412yes—
1179C22#272712yes—
1180C22#273012yes—
1181C22#273012yes—
1182C22#275012yes—
1183C22#275112yes—
1184C22#275112yes—
1185C22#275612yes—
1186C22#276512yes—
1187C22#277112yes—
1188C22#277312yes—
1189C22#277512yes—
1190C22#277812yes—
1191C22#277912yes—
1192C22#278112yes—
1193C22#278112yes—
1194C22#278112yes—
1195C22#278612yes—
1196C22#279312yes—
1197C22#279312yes—
1198C22#280312yes—
1199C22#280812yes—
1200C22#281311yescharacteristic
1201C22#281611yescharacteristic
1202C22#282011yescharacteristic
1203C22#282111yescharacteristic
1204C22#283612yes—
1205C22#283712yes—
1206C4—28no—
1207C4—44no—
1208C4—44no—
1209C4—82no—
1210C4—82no—
1211C4—84no—
1212C4—84no—
1213C4—84no—
1214C4—84no—
1215C4—82no—
1216C2—84no—
1217C2#1399411yescharacteristic
1218C2#1400211yescharacteristic
1219C2#1422911yescharacteristic
1220C2#1425911yescharacteristic
1221C2#1431111yescharacteristic
1222C2#1432311yescharacteristic
1223C2#1438412yes—
1224C2#1450012yes—
1225C2#1452712yes—
1226C2#1458812yes—
1227C2#1462811yescharacteristic
1228C2#1681611yescharacteristic
1229C2#1681911yescharacteristic
1230C2#1685812yes—
1231C2#1686112yes—
1232C2#1688411yescharacteristic
1233C2#1688711yescharacteristic
1234C2#1693412yes—
1235C2#1694012yes—
1236C2#1703911yescharacteristic
1237C2#1704611yescharacteristic
1238C2#1706011yescharacteristic
1239C2#1706911yescharacteristic
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
1. C2×#1442C2semidirect
6. C2×C4⋊#95C2semidirect
7. #7557C2semidirect
8. #7556C2semidirect
9. #7556C2semidirect
11. #7554C2semidirect
38. #1439C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14422
C2×#14402
C2×#14392
C2×#14372
C2×C4⋊#952
#75572
#75562
#75552
#75542