Finite Group Databasebeta

← #154559

Subgroups — #154559

Order 512.

2802 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1445C211yesmaximal, characteristic
2C2×#1445C211yesmaximal, characteristic
3C2×#1436C212yesmaximal
4C2×#1436C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×C4×#95C211yesmaximal, characteristic
7#7557C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7556C212yesmaximal
10#7556C212yesmaximal
11#7554C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2212yes—
16C23×C42C2211yescharacteristic
17C22×#95C2211yescharacteristic
18C22×#95C2211yescharacteristic
19C22×#95C2212yes—
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2211yescharacteristic
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35#1445—24no—
36#1445C418yescomplemented
37#1436—24no—
38#1436—28no—
39C4⋊#95—24no—
40C4×#95—24no—
41C24×C4C2312yes—
42C24×C4C2311yescharacteristic
43C24×C4C2311yescharacteristic
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C24×C4C2312yes—
48C24×C4C2311yescharacteristic
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4C2×C414yes—
68C22×C4⋊C4D414yes—
69C22×C42—24no—
70C22×C42—22no—
71C22×C42—24no—
72C22×C42—24no—
73C22×C42—22no—
74C22×C42—24no—
75C22×C42—24no—
76C22×C42—24no—
77C22×C42—42no—
78C22×C42—42no—
79C22×C42—42no—
80C22×C42D414yes—
81C2×#95—22no—
82C2×#95—24no—
83C2×#95—22no—
84C2×#95—24no—
85C2×#95—22no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—24no—
91C2×#95—22no—
92C2×#95—24no—
93C2×#95—22no—
94C2×#95—24no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—24no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—22no—
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—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×#95C2×C418yes—
128C2×#95C2×C414yes—
129C2×#95C2×C414yes—
130C2×#95C2×C418yes—
131C2×#95D414yes—
132C2×#95Q818yes—
133C25C2411yescharacteristic
134C23×C4—21no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—21no—
142C23×C4—22no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—21no—
148C23×C4—22no—
149C23×C4—21no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—21no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—21no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—21no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—22no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—21no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—21no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—21no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—21no—
238C23×C4—22no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4C22×C414yes—
244C23×C4C22×C412yes—
245C23×C4C22×C412yes—
246C23×C4C22×C414yes—
247C23×C4C22×C412yes—
248C23×C4C2×D412yes—
249C23×C4C2×D412yes—
250C23×C4C2×D414yes—
251C23×C4C2×D412yes—
252C23×C4C2×D412yes—
253C23×C4C2×D412yes—
254C23×C4C2×D412yes—
255C23×C4C2×D412yes—
256C23×C4C2×Q814yes—
257C23×C4C2×Q814yes—
258C23×C4C2×Q814yes—
259C23×C4#4114yes—
260C23×C4#4112yes—
261C23×C4#4112yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4#4112yes—
265C23×C4#4112yes—
266C23×C4#4112yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4#4114yes—
270C23×C4#4114yes—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—216no—
277C2×C4⋊C4—48no—
278C2×C4⋊C4—48no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—48no—
288C2×C42—216no—
289C2×C42—28no—
290C2×C42—28no—
291C2×C42—44no—
292C2×C42—48no—
293C2×C42—48no—
294C2×C42—48no—
295C2×C42—48no—
296C2×C42—48no—
297C2×C42—48no—
298C2×C42—48no—
299C2×C42—48no—
300#95—28no—
301#95—216no—
302#95—28no—
303#95—216no—
304#95—28no—
305#95—216no—
306#95—28no—
307#95—48no—
308#95—48no—
309#95—48no—
310#95—48no—
311#95—48no—
312#95—44no—
313#95—48no—
314#95—48no—
315#95—44no—
316#95—48no—
317#95—44no—
318C24C23×C411yescharacteristic
319C24C22×D411yescharacteristic
320C24C22×D411yescharacteristic
321C24C22×D411yescharacteristic
322C24C22×Q812yes—
323C24C2×#4111yescharacteristic
324C24C2×#4111yescharacteristic
325C24C2×#4111yescharacteristic
326C24C2×#4111yescharacteristic
327C24C2×#4111yescharacteristic
328C24C2×#4112yes—
329C24C2×#4111yescharacteristic
330C24C2×#4112yes—
331C24C2×#4112yes—
332C24C2×#4112yes—
333C24C2×#4112yes—
334C24C2×#4111yescharacteristic
335C24H(5,𝔽2)11yescharacteristic
336C24H(5,𝔽2)11yescharacteristic
337C24H(5,𝔽2)12yes—
338C24H(5,𝔽2)11yescharacteristic
339C242−1+412yes—
340C242−1+411yescharacteristic
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—41no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—41no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—41no—
512C22×C4—42no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—41no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—41no—
549C22×C4—42no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—42no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—41no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—41no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—41no—
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—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—41no—
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#11714yes—
627C22×C4C4×D414yes—
628C22×C4C4×D414yes—
629C22×C4C4×D414yes—
630C22×C4C4×Q818yes—
631C22×C4#12114yes—
632C22×C4#12114yes—
633C22×C4C22⋊Q818yes—
634C22×C4#12314yes—
635C22×C4#12314yes—
636C22×C4#12318yes—
637C22×C4#12414yes—
638C22×C4#12414yes—
639C22×C4#12614yes—
640C22×C4#12618yes—
641C22×C4C4⋊Q814yes—
642C4⋊C4—416no—
643C4⋊C4—416no—
644C4⋊C4—416no—
645C42—416no—
646C42—432no—
647C23C2×#11711yescharacteristic
648C23C2×C4×D411yescharacteristic
649C23C2×C4×D411yescharacteristic
650C23C2×C4×D411yescharacteristic
651C23C2×C4×Q812yes—
652C23C4×#4111yescharacteristic
653C23C4×#4112yes—
654C23C4×#4112yes—
655C23#51811yescharacteristic
656C23#52012yes—
657C23#52011yescharacteristic
658C23C2×#12111yescharacteristic
659C23C2×#12111yescharacteristic
660C23C2×C22⋊Q812yes—
661C23C2×#12311yescharacteristic
662C23C2×#12311yescharacteristic
663C23C2×#12312yes—
664C23#52511yescharacteristic
665C23#52511yescharacteristic
666C23#52512yes—
667C23#52512yes—
668C23C2×#12411yescharacteristic
669C23C2×#12411yescharacteristic
670C23C2×#12612yes—
671C23C2×#12611yescharacteristic
672C23#52912yes—
673C23#52912yes—
674C23#52912yes—
675C23#52912yes—
676C23#52912yes—
677C23#52911yescharacteristic
678C23#52912yes—
679C23#52912yes—
680C23#52912yes—
681C23#52912yes—
682C23#52912yes—
683C23C2×C4⋊Q811yescharacteristic
684C23#53211yescharacteristic
685C23#53211yescharacteristic
686C23#53211yescharacteristic
687C23#53312yes—
688C23#53312yes—
689C23#53312yes—
690C23#53312yes—
691C23#53411yescharacteristic
692C23#53511yescharacteristic
693C23#53611yescharacteristic
694C23#53711yescharacteristic
695C23#53812yes—
696C23#53812yes—
697C23#53912yes—
698C23#53912yes—
699C23#53912yes—
700C23#54011yescharacteristic
701C23#54012yes—
702C23#54112yes—
703C23#54211yescharacteristic
704C23#54212yes—
705C23#54212yes—
706C23D4211yescharacteristic
707C23#54612yes—
708C23#54612yes—
709C23#54611yescharacteristic
710C23#54711yescharacteristic
711C23#54712yes—
712C23#54811yescharacteristic
713C23D4×Q812yes—
714C23#55011yescharacteristic
715C23#55011yescharacteristic
716C23#55011yescharacteristic
717C23#55112yes—
718C23#55112yes—
719C23#55112yes—
720C23#55112yes—
721C23#55112yes—
722C23#55212yes—
723C23#55212yes—
724C23#55212yes—
725C23#55212yes—
726C23#55212yes—
727C23#55212yes—
728C23#55311yescharacteristic
729C23#55312yes—
730C23#55312yes—
731C23#55311yescharacteristic
732C23#55412yes—
733C23#55412yes—
734C23#55412yes—
735C23#55412yes—
736C23#55412yes—
737C23#55511yescharacteristic
738C23#55611yescharacteristic
739C23#55611yescharacteristic
740C23#55712yes—
741C23#55712yes—
742C23#55911yescharacteristic
743C23#55911yescharacteristic
744C23#55911yescharacteristic
745C23#55911yescharacteristic
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—82no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—82no—
851C2×C4—81no—
852C2×C4—82no—
853C2×C4—81no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4—81no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4—82no—
867C2×C4—82no—
868C2×C4—82no—
869C2×C4—82no—
870C2×C4—82no—
871C2×C4—82no—
872C2×C4—81no—
873C2×C4—82no—
874C2×C4—82no—
875C2×C4—82no—
876C2×C4—82no—
877C2×C4—82no—
878C2×C4—82no—
879C2×C4—82no—
880C2×C4—82no—
881C2×C4#38818yes—
882C2×C4#39718yes—
883C22C2×#38811yescharacteristic
884C22#229512yes—
885C22C4×#12111yescharacteristic
886C22C4×#12312yes—
887C22C4×#12311yescharacteristic
888C22C4×C22⋊Q812yes—
889C22C4×#12411yescharacteristic
890C22C4×#12612yes—
891C22C4×C4⋊Q811yescharacteristic
892C22#232211yescharacteristic
893C22#232411yescharacteristic
894C22#233412yes—
895C22#233512yes—
896C22#234312yes—
897C22#235411yescharacteristic
898C22#235711yescharacteristic
899C22#235912yes—
900C22#236012yes—
901C22#236611yescharacteristic
902C22#236711yescharacteristic
903C22#236812yes—
904C22#237012yes—
905C22#237012yes—
906C22C2×#39711yescharacteristic
907C22#239211yescharacteristic
908C22#239512yes—
909C22#239511yescharacteristic
910C22#239811yescharacteristic
911C22#240112yes—
912C22#241211yescharacteristic
913C22#241311yescharacteristic
914C22#241411yescharacteristic
915C22#241611yescharacteristic
916C22#241812yes—
917C22#241912yes—
918C22#241912yes—
919C22#242312yes—
920C22#242312yes—
921C22#244511yescharacteristic
922C22#244811yescharacteristic
923C22#244912yes—
924C22#245012yes—
925C22#245312yes—
926C22#245412yes—
927C22#246212yes—
928C22#246712yes—
929C22#247012yes—
930C22#247112yes—
931C22#247912yes—
932C22#248112yes—
933C22#249312yes—
934C22#249811yescharacteristic
935C22#250211yescharacteristic
936C22#250311yescharacteristic
937C22#251012yes—
938C22#251112yes—
939C22#251112yes—
940C22#251211yescharacteristic
941C22#251311yescharacteristic
942C22#251612yes—
943C22#251712yes—
944C22#252012yes—
945C22#252212yes—
946C22#252212yes—
947C22#252412yes—
948C22#252812yes—
949C22#252912yes—
950C22#253012yes—
951C22#254311yescharacteristic
952C22#254611yescharacteristic
953C22#254811yescharacteristic
954C22#255612yes—
955C22#256111yescharacteristic
956C22#257412yes—
957C22#257512yes—
958C22#258311yescharacteristic
959C22#258411yescharacteristic
960C22#258512yes—
961C22#258512yes—
962C22#258812yes—
963C22#258812yes—
964C22#258912yes—
965C22#258912yes—
966C22#259211yescharacteristic
967C22#259512yes—
968C22#260311yescharacteristic
969C22#261111yescharacteristic
970C22#263911yescharacteristic
971C22#264011yescharacteristic
972C22#264912yes—
973C22#265412yes—
974C22#266111yescharacteristic
975C22#266411yescharacteristic
976C22#285011yescharacteristic
977C22#285512yes—
978C22#285711yescharacteristic
979C22#286111yescharacteristic
980C22#286211yescharacteristic
981C22#286312yes—
982C4—28no—
983C4—28no—
984C4—44no—
985C4—48no—
986C4—48no—
987C4—44no—
988C4—82no—
989C4—84no—
990C4—82no—
991C4—84no—
992C4—82no—
993C2C4×#39711yescharacteristic
994C2#1397211yescharacteristic
995C2#1402211yescharacteristic
996C2#1405612yes—
997C2#1406112yes—
998C2#1417812yes—
999C2#1422112yes—
1000C2#1422611yescharacteristic
1001C2#1424411yescharacteristic
1002C2#1432411yescharacteristic
1003C2#1470311yescharacteristic
1004C2#1473511yescharacteristic
1005C2#1474212yes—
1006C2#1481811yescharacteristic
1007C2#1484011yescharacteristic
1008C2#1485212yes—
1009C2#1489411yescharacteristic
1010C2#1497512yes—
1011C2#1498211yescharacteristic
1012C2#1502411yescharacteristic
1013C2#1503712yes—
1014C2#1518511yescharacteristic
1015C2#1520911yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
36. #1445C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14452
C2×#14362
C2×C4⋊#952
C2×C4×#952
#75572
#75562
#75542