Finite Group Databasebeta

← #158192

Subgroups — #158192

Order 512.

2916 conjugacy classes of subgroups.

The subgroup lattice has 1027 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C2×#1445C212yesmaximal
3C2×#1444C212yesmaximal
4C2×#1444C211yesmaximal, characteristic
5C2×#1442C212yesmaximal
6C2×#1436C211yesmaximal, characteristic
7C2×#1434C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C211yesmaximal, characteristic
10#7557C211yesmaximal, characteristic
11#7556C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2212yes—
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C2×#389—24no—
19C2×#389—28no—
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2211yescharacteristic
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37#1445—28no—
38#1444—28no—
39#1444—24no—
40#1442—28no—
41#1436—24no—
42#1434—24no—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2312yes—
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C22×C4⋊C4—24no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—42no—
77C22×C4⋊C4—42no—
78C22×C4⋊C4—42no—
79C22×C4⋊C4—42no—
80C22×C4⋊C4—42no—
81C22×C4⋊C4—42no—
82C22×C4⋊C4Q814yes—
83C22×C42—22no—
84C22×C42—24no—
85C22×C42—22no—
86C22×C42—42no—
87C22×C42D414yes—
88#389—232no—
89C2×#95—24no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—22no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—22no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—24no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—22no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—22no—
127C2×#95—22no—
128C2×#95—22no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95—42no—
132C2×#95—42no—
133C2×#95—42no—
134C2×#95D414yes—
135C2×#95D418yes—
136C2×#95D418yes—
137C2×#95Q814yes—
138C25C2411yescharacteristic
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—21no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—21no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
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—21no—
184C23×C4—21no—
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—21no—
198C23×C4—22no—
199C23×C4—21no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—21no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—21no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—21no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—21no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—21no—
250C23×C4—22no—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D412yes—
254C23×C4C2×D414yes—
255C23×C4C2×D414yes—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×Q812yes—
263C23×C4C2×Q814yes—
264C23×C4C2×Q812yes—
265C23×C4C2×Q812yes—
266C23×C4C2×Q812yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4#4114yes—
270C23×C4#4114yes—
271C23×C4#4112yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C23×C4#4112yes—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—216no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—216no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—216no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—216no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—48no—
287C2×C4⋊C4—48no—
288C2×C4⋊C4—48no—
289C2×C4⋊C4—48no—
290C2×C4⋊C4—48no—
291C2×C4⋊C4—48no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—48no—
294C2×C4⋊C4—48no—
295C2×C4⋊C4—48no—
296C2×C4⋊C4—48no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—48no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—48no—
305C2×C42—28no—
306C2×C42—28no—
307C2×C42—44no—
308C2×C42—48no—
309C2×C42—48no—
310#95—216no—
311#95—28no—
312#95—216no—
313#95—216no—
314#95—216no—
315#95—28no—
316#95—28no—
317#95—48no—
318#95—48no—
319#95—48no—
320#95—48no—
321#95—48no—
322#95—44no—
323#95—48no—
324#95—44no—
325#95—44no—
326#95—44no—
327C24C22×D411yescharacteristic
328C24C22×D412yes—
329C24C22×D411yescharacteristic
330C24C22×D412yes—
331C24C22×Q811yescharacteristic
332C24C22×Q811yescharacteristic
333C24C2×#4112yes—
334C24C2×#4111yescharacteristic
335C24C2×#4111yescharacteristic
336C24C2×#4111yescharacteristic
337C24C2×#4112yes—
338C24C2×#4111yescharacteristic
339C24C2×#4111yescharacteristic
340C24C2×#4111yescharacteristic
341C24C2×#4111yescharacteristic
342C24H(5,𝔽2)12yes—
343C24H(5,𝔽2)11yescharacteristic
344C24H(5,𝔽2)11yescharacteristic
345C242−1+411yescharacteristic
346C242−1+411yescharacteristic
347C242−1+412yes—
348C242−1+412yes—
349C242−1+412yes—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
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—22no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
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—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—41no—
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—41no—
477C22×C4—42no—
478C22×C4—41no—
479C22×C4—42no—
480C22×C4—41no—
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—41no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—41no—
511C22×C4—42no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—41no—
516C22×C4—42no—
517C22×C4—41no—
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—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
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—41no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—41no—
561C22×C4—42no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—41no—
577C22×C4—42no—
578C22×C4—42no—
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—41no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
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—41no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—41no—
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—41no—
629C22×C4—42no—
630C22×C4—41no—
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#12014yes—
640C22×C4#12118yes—
641C22×C4#12114yes—
642C22×C4C22⋊Q818yes—
643C22×C4C22⋊Q814yes—
644C22×C4C22⋊Q814yes—
645C22×C4#12314yes—
646C22×C4#12514yes—
647C22×C4#12514yes—
648C22×C4#12514yes—
649C22×C4#12714yes—
650C22×C4C4⋊Q814yes—
651C4⋊C4—232no—
652C4⋊C4—416no—
653C4⋊C4—432no—
654C4⋊C4—432no—
655C4⋊C4—416no—
656C42—416no—
657C23C2×#12011yescharacteristic
658C23C2×#12111yescharacteristic
659C23C2×#12112yes—
660C23C2×C22⋊Q811yescharacteristic
661C23C2×C22⋊Q811yescharacteristic
662C23C2×C22⋊Q812yes—
663C23C2×#12311yescharacteristic
664C23#52511yescharacteristic
665C23#52511yescharacteristic
666C23#52511yescharacteristic
667C23#52512yes—
668C23#52512yes—
669C23#52512yes—
670C23#52512yes—
671C23C2×#12511yescharacteristic
672C23C2×#12511yescharacteristic
673C23C2×#12511yescharacteristic
674C23#52911yescharacteristic
675C23#52911yescharacteristic
676C23C2×#12711yescharacteristic
677C23C2×C4⋊Q811yescharacteristic
678C23#53211yescharacteristic
679C23#53212yes—
680C23#53212yes—
681C23#53311yescharacteristic
682C23#53411yescharacteristic
683C23#53511yescharacteristic
684C23#53611yescharacteristic
685C23#53611yescharacteristic
686C23#53611yescharacteristic
687C23#53612yes—
688C23#53611yescharacteristic
689C23#53612yes—
690C23#53612yes—
691C23#53612yes—
692C23#53612yes—
693C23#53812yes—
694C23#53912yes—
695C23#53912yes—
696C23#53912yes—
697C23#53912yes—
698C23#54012yes—
699C23#54112yes—
700C23#54112yes—
701C23#54112yes—
702C23#54211yescharacteristic
703C23#54211yescharacteristic
704C23#54212yes—
705C23#54411yescharacteristic
706C23#54411yescharacteristic
707C23#54412yes—
708C23D4212yes—
709C23D4212yes—
710C23D4212yes—
711C23#54612yes—
712C23#54611yescharacteristic
713C23#54612yes—
714C23#54612yes—
715C23#54712yes—
716C23#54712yes—
717C23#54711yescharacteristic
718C23#54712yes—
719C23#54712yes—
720C23#54712yes—
721C23#54812yes—
722C23#54811yescharacteristic
723C23D4×Q812yes—
724C23D4×Q812yes—
725C23D4×Q812yes—
726C23#55011yescharacteristic
727C23#55212yes—
728C23#55212yes—
729C23#55212yes—
730C23#55212yes—
731C23#55211yescharacteristic
732C23#55212yes—
733C23#55212yes—
734C23#55212yes—
735C23#55311yescharacteristic
736C23#55312yes—
737C23#55412yes—
738C23#55411yescharacteristic
739C23#55411yescharacteristic
740C23#55511yescharacteristic
741C23#55611yescharacteristic
742C23#55611yescharacteristic
743C23#55611yescharacteristic
744C23#55612yes—
745C23#55612yes—
746C23#55711yescharacteristic
747C23#55712yes—
748C23#55712yes—
749C23#55711yescharacteristic
750C23#55911yescharacteristic
751C23#55911yescharacteristic
752C23#56312yes—
753C23#56312yes—
754C23#56312yes—
755C23#56312yes—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
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—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—44no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—82no—
861C2×C4—81no—
862C2×C4—82no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—82no—
869C2×C4—81no—
870C2×C4—81no—
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—81no—
881C2×C4—81no—
882C2×C4—82no—
883C2×C4—82no—
884C2×C4—82no—
885C2×C4—82no—
886C2×C4—82no—
887C2×C4—82no—
888C2×C4—82no—
889C2×C4—82no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4#39818yes—
893C22#238811yescharacteristic
894C22C2×#39811yescharacteristic
895C22#239711yescharacteristic
896C22#240611yescharacteristic
897C22#240911yescharacteristic
898C22#241011yescharacteristic
899C22#241312yes—
900C22#241311yescharacteristic
901C22#241411yescharacteristic
902C22#241512yes—
903C22#241511yescharacteristic
904C22#242412yes—
905C22#242812yes—
906C22#243311yescharacteristic
907C22#244012yes—
908C22#244212yes—
909C22#244312yes—
910C22#244711yescharacteristic
911C22#244811yescharacteristic
912C22#244912yes—
913C22#244912yes—
914C22#245512yes—
915C22#245512yes—
916C22#246212yes—
917C22#246412yes—
918C22#246512yes—
919C22#246612yes—
920C22#247012yes—
921C22#247312yes—
922C22#247312yes—
923C22#247512yes—
924C22#248612yes—
925C22#250612yes—
926C22#250612yes—
927C22#250612yes—
928C22#250811yescharacteristic
929C22#250911yescharacteristic
930C22#251912yes—
931C22#253911yescharacteristic
932C22#254211yescharacteristic
933C22#254211yescharacteristic
934C22#254612yes—
935C22#255011yescharacteristic
936C22#255211yescharacteristic
937C22#255512yes—
938C22#256512yes—
939C22#256511yescharacteristic
940C22#256511yescharacteristic
941C22#257011yescharacteristic
942C22#257111yescharacteristic
943C22#257911yescharacteristic
944C22#258011yescharacteristic
945C22#258112yes—
946C22#258111yescharacteristic
947C22#259911yescharacteristic
948C22#259912yes—
949C22#260412yes—
950C22#260411yescharacteristic
951C22#260412yes—
952C22#261112yes—
953C22#261111yescharacteristic
954C22#261411yescharacteristic
955C22#262111yescharacteristic
956C22#262711yescharacteristic
957C22#262811yescharacteristic
958C22#263311yescharacteristic
959C22#263411yescharacteristic
960C22#263811yescharacteristic
961C22#265811yescharacteristic
962C22#266111yescharacteristic
963C22#267412yes—
964C22#267412yes—
965C22#267412yes—
966C22#267712yes—
967C22#267712yes—
968C22#268012yes—
969C22#268912yes—
970C22#268912yes—
971C22#268912yes—
972C22#268912yes—
973C22#269812yes—
974C22#271312yes—
975C22#271312yes—
976C22#272112yes—
977C22#276512yes—
978C22#276912yes—
979C22#277112yes—
980C22#277312yes—
981C22#277412yes—
982C22#277612yes—
983C22#277712yes—
984C22#279112yes—
985C22#279112yes—
986C22#280512yes—
987C22#281711yescharacteristic
988C22#282111yescharacteristic
989C22#284811yescharacteristic
990C22#285111yescharacteristic
991C22#285611yescharacteristic
992C4—28no—
993C4—48no—
994C4—44no—
995C4—44no—
996C4—44no—
997C4—48no—
998C4—82no—
999C4—82no—
1000C4—84no—
1001C4—82no—
1002C4—84no—
1003C2#1472811yescharacteristic
1004C2#1476211yescharacteristic
1005C2#1480711yescharacteristic
1006C2#1491011yescharacteristic
1007C2#1496911yescharacteristic
1008C2#1507111yescharacteristic
1009C2#1515111yescharacteristic
1010C2#1521411yescharacteristic
1011C2#1522111yescharacteristic
1012C2#1535112yes—
1013C2#1536012yes—
1014C2#1536412yes—
1015C2#1539812yes—
1016C2#1540112yes—
1017C2#1552112yes—
1018C2#1562912yes—
1019C2#1568512yes—
1020C2#1626211yescharacteristic
1021C2#1651111yescharacteristic
1022C2#1667711yescharacteristic
1023C2#1681311yescharacteristic
1024C2#1697911yescharacteristic
1025C2#1704211yescharacteristic
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×#3892
C2×#14452
C2×#14442
C2×#14422
C2×#14362
C2×#14342
#75572
#75562