Finite Group Databasebeta

← #158435

Subgroups — #158435

Order 512.

3068 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#384C211yesmaximal, characteristic
2C2×#1441C212yesmaximal
3C2×#1441C212yesmaximal
4C2×#1441C212yesmaximal
5C2×#1441C211yesmaximal, characteristic
6C2×#1436C212yesmaximal
7#7557C212yesmaximal
8#7557C212yesmaximal
9#7557C211yesmaximal, characteristic
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×#384—24no—
18C2×#384—28no—
19C22×#95C2211yescharacteristic
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33#1441—28no—
34#1441—28no—
35#1441—28no—
36#1441—24no—
37#1436—28no—
38C24×C4C2311yescharacteristic
39C24×C4C2312yes—
40C24×C4C2312yes—
41C24×C4C2312yes—
42C24×C4C2312yes—
43C24×C4C2311yescharacteristic
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2311yescharacteristic
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—42no—
70C22×C4⋊C4—41no—
71C22×C4⋊C4—41no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—41no—
76C22×C4⋊C4—41no—
77C22×C4⋊C4—42no—
78C22×C4⋊C4—41no—
79C22×C4⋊C4—41no—
80C22×C4⋊C4D418yes—
81C22×C4⋊C4D414yes—
82C22×C4⋊C4Q818yes—
83C22×C42—24no—
84C22×C42—22no—
85C22×C42—24no—
86C22×C42—22no—
87C22×C42D414yes—
88#384—232no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—22no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—42no—
116C2×#95—41no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—42no—
123C2×#95—42no—
124C2×#95—41no—
125C2×#95—42no—
126C2×#95D418yes—
127C2×#95Q818yes—
128C25C2411yescharacteristic
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
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—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—21no—
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—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4C2×D414yes—
227C23×C4C2×D412yes—
228C23×C4C2×D414yes—
229C23×C4C2×D412yes—
230C23×C4C2×D414yes—
231C23×C4C2×D414yes—
232C23×C4C2×D414yes—
233C23×C4C2×D414yes—
234C23×C4C2×D414yes—
235C23×C4C2×D412yes—
236C23×C4C2×D412yes—
237C23×C4C2×Q814yes—
238C23×C4C2×Q814yes—
239C23×C4C2×Q814yes—
240C23×C4C2×Q814yes—
241C23×C4C2×Q814yes—
242C23×C4C2×Q814yes—
243C23×C4#4114yes—
244C23×C4#4114yes—
245C23×C4#4114yes—
246C23×C4#4112yes—
247C23×C4#4114yes—
248C2×C4⋊C4—28no—
249C2×C4⋊C4—216no—
250C2×C4⋊C4—28no—
251C2×C4⋊C4—216no—
252C2×C4⋊C4—216no—
253C2×C4⋊C4—216no—
254C2×C4⋊C4—216no—
255C2×C4⋊C4—216no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—44no—
258C2×C4⋊C4—48no—
259C2×C4⋊C4—48no—
260C2×C4⋊C4—48no—
261C2×C4⋊C4—48no—
262C2×C4⋊C4—48no—
263C2×C4⋊C4—48no—
264C2×C4⋊C4—48no—
265C2×C4⋊C4—48no—
266C2×C4⋊C4—48no—
267C2×C4⋊C4—48no—
268C2×C4⋊C4—48no—
269C2×C4⋊C4—48no—
270C2×C4⋊C4—48no—
271C2×C4⋊C4—48no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4—48no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4—48no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4—48no—
279C2×C4⋊C4—48no—
280C2×C4⋊C4—48no—
281C2×C4⋊C4—48no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—48no—
284C2×C42—28no—
285C2×C42—216no—
286C2×C42—28no—
287C2×C42—216no—
288C2×C42—28no—
289#95—216no—
290#95—216no—
291#95—44no—
292#95—48no—
293#95—48no—
294#95—48no—
295#95—48no—
296#95—48no—
297#95—48no—
298#95—44no—
299#95—44no—
300#95—48no—
301#95—48no—
302#95—48no—
303C24C22×D412yes—
304C24C22×D411yescharacteristic
305C24C22×D411yescharacteristic
306C24C22×D412yes—
307C24C22×Q812yes—
308C24C22×Q812yes—
309C24C2×#4112yes—
310C24C2×#4112yes—
311C24C2×#4112yes—
312C24C2×#4111yescharacteristic
313C24C2×#4112yes—
314C24H(5,𝔽2)11yescharacteristic
315C24H(5,𝔽2)12yes—
316C24H(5,𝔽2)11yescharacteristic
317C24H(5,𝔽2)12yes—
318C242−1+411yescharacteristic
319C242−1+412yes—
320C242−1+411yescharacteristic
321C242−1+412yes—
322C22×C4—22no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
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—24no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
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—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—41no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
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—42no—
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—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
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—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—41no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
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—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
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—42no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—41no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4#12014yes—
584C22×C4#12118yes—
585C22×C4#12118yes—
586C22×C4#12118yes—
587C22×C4#12114yes—
588C22×C4C22⋊Q818yes—
589C22×C4C22⋊Q818yes—
590C22×C4C22⋊Q818yes—
591C22×C4C22⋊Q818yes—
592C22×C4#12314yes—
593C22×C4#12518yes—
594C22×C4#12618yes—
595C22×C4C4⋊Q818yes—
596C22×C4C4⋊Q814yes—
597C4⋊C4—416no—
598C4⋊C4—432no—
599C4⋊C4—416no—
600C4⋊C4—432no—
601C4⋊C4—416no—
602C4⋊C4—432no—
603C42—232no—
604C23C2×#12011yescharacteristic
605C23C2×#12112yes—
606C23C2×#12111yescharacteristic
607C23C2×#12112yes—
608C23C2×#12112yes—
609C23C2×C22⋊Q812yes—
610C23C2×C22⋊Q812yes—
611C23C2×C22⋊Q812yes—
612C23C2×C22⋊Q812yes—
613C23C2×#12311yescharacteristic
614C23#52512yes—
615C23#52511yescharacteristic
616C23C2×#12512yes—
617C23C2×#12612yes—
618C23C2×C4⋊Q812yes—
619C23C2×C4⋊Q811yescharacteristic
620C23#53212yes—
621C23#53312yes—
622C23#53312yes—
623C23#53412yes—
624C23#53411yescharacteristic
625C23#53512yes—
626C23#53612yes—
627C23#53612yes—
628C23#53611yescharacteristic
629C23#53711yescharacteristic
630C23#53712yes—
631C23#53712yes—
632C23#53711yescharacteristic
633C23#53911yescharacteristic
634C23#53912yes—
635C23#53912yes—
636C23#53911yescharacteristic
637C23#54012yes—
638C23#54012yes—
639C23#54112yes—
640C23#54112yes—
641C23#54212yes—
642C23#54212yes—
643C23#54412yes—
644C23#54412yes—
645C23#54412yes—
646C23#54412yes—
647C23D4212yes—
648C23D4212yes—
649C23D4211yescharacteristic
650C23#54612yes—
651C23#54612yes—
652C23#54612yes—
653C23#54612yes—
654C23#54712yes—
655C23#54712yes—
656C23#54712yes—
657C23#54812yes—
658C23#54812yes—
659C23D4×Q812yes—
660C23D4×Q812yes—
661C23D4×Q812yes—
662C23D4×Q812yes—
663C23D4×Q812yes—
664C23#55012yes—
665C23#55212yes—
666C23#55212yes—
667C23#55212yes—
668C23#55212yes—
669C23#55312yes—
670C23#55312yes—
671C23#55412yes—
672C23#55412yes—
673C23#55412yes—
674C23#55412yes—
675C23#55412yes—
676C23#55511yescharacteristic
677C23#55612yes—
678C23#55712yes—
679C23#55712yes—
680C23#55712yes—
681C23Q8211yescharacteristic
682C23Q8212yes—
683C23#55912yes—
684C23#55911yescharacteristic
685C23#56011yescharacteristic
686C23#56011yescharacteristic
687C23#56312yes—
688C23#56312yes—
689C23#56311yescharacteristic
690C23#56311yescharacteristic
691C2×C4—28no—
692C2×C4—24no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4—82no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4—82no—
790C2×C4—82no—
791C2×C4—82no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4—82no—
800C2×C4—82no—
801C2×C4—82no—
802C2×C4—82no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—82no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4#396116yes—
809C2×C4#39818yes—
810C22C2×#39612yes—
811C22C2×#39811yescharacteristic
812C22#240511yescharacteristic
813C22#240912yes—
814C22#241012yes—
815C22#241312yes—
816C22#241612yes—
817C22#241612yes—
818C22#241712yes—
819C22#241712yes—
820C22#241712yes—
821C22#241712yes—
822C22#242812yes—
823C22#242912yes—
824C22#243411yescharacteristic
825C22#243912yes—
826C22#244012yes—
827C22#244012yes—
828C22#244112yes—
829C22#244512yes—
830C22#244612yes—
831C22#244912yes—
832C22#244912yes—
833C22#245112yes—
834C22#245112yes—
835C22#247312yes—
836C22#247312yes—
837C22#248112yes—
838C22#248112yes—
839C22#248411yescharacteristic
840C22#249612yes—
841C22#249712yes—
842C22#250612yes—
843C22#250712yes—
844C22#251112yes—
845C22#251112yes—
846C22#253711yescharacteristic
847C22#253812yes—
848C22#254412yes—
849C22#254612yes—
850C22#255012yes—
851C22#255112yes—
852C22#255212yes—
853C22#256512yes—
854C22#256712yes—
855C22#257012yes—
856C22#257912yes—
857C22#258212yes—
858C22#258211yescharacteristic
859C22#258311yescharacteristic
860C22#261811yescharacteristic
861C22#261812yes—
862C22#262012yes—
863C22#262912yes—
864C22#262912yes—
865C22#266911yescharacteristic
866C22#267312yes—
867C22#267412yes—
868C22#267712yes—
869C22#268011yescharacteristic
870C22#270911yescharacteristic
871C22#270912yes—
872C22#271312yes—
873C22#271312yes—
874C22#271312yes—
875C22#271612yes—
876C22#271812yes—
877C22#272012yes—
878C22#272112yes—
879C22#272912yes—
880C22#273111yescharacteristic
881C22#273411yescharacteristic
882C22#273412yes—
883C22#279012yes—
884C22#279112yes—
885C22#279112yes—
886C22#279112yes—
887C22#279212yes—
888C22#279211yescharacteristic
889C22#279312yes—
890C22#279412yes—
891C22#279411yescharacteristic
892C22#279511yescharacteristic
893C22#282311yescharacteristic
894C22#282311yescharacteristic
895C22#284711yescharacteristic
896C22#285712yes—
897C4—216no—
898C4—28no—
899C4—48no—
900C4—44no—
901C4—84no—
902C4—84no—
903C4—84no—
904C4—82no—
905C4—84no—
906C2#1472912yes—
907C2#1482111yescharacteristic
908C2#1513112yes—
909C2#1513312yes—
910C2#1518412yes—
911C2#1531311yescharacteristic
912C2#1531812yes—
913C2#1543412yes—
914C2#1543812yes—
915C2#1562511yescharacteristic
916C2#1562912yes—
917C2#1578912yes—
918C2#1579811yescharacteristic
919C2#1609311yescharacteristic
920C2#1609512yes—
921C2#1651411yescharacteristic
922C2#1651512yes—
923C2#1656312yes—
924C2#1656311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Maximal subgroups

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

subgroupindex
C22×#3842
C2×#14412
C2×#14362
#75572