Finite Group Databasebeta

← #156808

Subgroups — #156808

Order 512.

3148 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C211yesmaximal, characteristic
2C22×#389C211yesmaximal, characteristic
3C22×#387C211yesmaximal, characteristic
4C2×#1445C211yesmaximal, characteristic
5C2×#1444C212yesmaximal
6C2×#1441C211yesmaximal, characteristic
7C2×#1434C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7557C212yesmaximal
11#7556C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2212yes—
17C23×C4⋊C4C2212yes—
18C23×C42C2211yescharacteristic
19C2×#398—24no—
20C2×#398—24no—
21C2×#398—24no—
22C2×#389—24no—
23C2×#389—24no—
24C2×#389—24no—
25C2×#387—24no—
26C2×#387—24no—
27C2×#387—24no—
28C22×#95C2211yescharacteristic
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2212yes—
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2212yes—
43C22×#95C2212yes—
44#1445—24no—
45#1444—28no—
46#1441—24no—
47#1434—24no—
48C24×C4C2312yes—
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C24×C4C2312yes—
57C24×C4C2312yes—
58C24×C4C2311yescharacteristic
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—24no—
82C22×C4⋊C4—24no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—24no—
88C22×C4⋊C4—24no—
89C22×C4⋊C4—24no—
90C22×C4⋊C4—24no—
91C22×C4⋊C4—42no—
92C22×C4⋊C4—42no—
93C22×C4⋊C4—42no—
94C22×C4⋊C4—42no—
95C22×C4⋊C4D414yes—
96C22×C4⋊C4D414yes—
97C22×C4⋊C4D414yes—
98C22×C4⋊C4D414yes—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42D414yes—
106#398—232no—
107#389—232no—
108#387—232no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—22no—
113C2×#95—22no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—22no—
125C2×#95—22no—
126C2×#95—22no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—22no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—22no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—22no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—42no—
150C2×#95—42no—
151C2×#95—42no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95D414yes—
155C2×#95D414yes—
156C2×#95Q818yes—
157C25C2411yescharacteristic
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
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—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—21no—
222C23×C4—21no—
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—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—22no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—21no—
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—21no—
262C23×C4—21no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—21no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4C2×D414yes—
276C23×C4C2×D412yes—
277C23×C4C2×D412yes—
278C23×C4C2×D412yes—
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D412yes—
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2×Q814yes—
294C23×C4C2×Q814yes—
295C23×C4C2×Q814yes—
296C23×C4#4112yes—
297C23×C4#4112yes—
298C23×C4#4112yes—
299C23×C4#4114yes—
300C23×C4#4114yes—
301C23×C4#4114yes—
302C23×C4#4112yes—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—216no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—216no—
315C2×C4⋊C4—216no—
316C2×C4⋊C4—216no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—48no—
324C2×C4⋊C4—48no—
325C2×C4⋊C4—48no—
326C2×C4⋊C4—48no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4—48no—
329C2×C4⋊C4—48no—
330C2×C4⋊C4—48no—
331C2×C4⋊C4—48no—
332C2×C4⋊C4—48no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—48no—
336C2×C4⋊C4—48no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C42—28no—
344C2×C42—28no—
345C2×C42—28no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42—44no—
349C2×C42—44no—
350#95—216no—
351#95—28no—
352#95—28no—
353#95—28no—
354#95—216no—
355#95—216no—
356#95—28no—
357#95—28no—
358#95—216no—
359#95—48no—
360#95—48no—
361#95—48no—
362#95—48no—
363#95—48no—
364#95—48no—
365#95—44no—
366C24C22×D411yescharacteristic
367C24C22×D411yescharacteristic
368C24C22×D411yescharacteristic
369C24C22×D411yescharacteristic
370C24C22×D411yescharacteristic
371C24C22×D411yescharacteristic
372C24C22×D411yescharacteristic
373C24C22×Q812yes—
374C24C2×#4111yescharacteristic
375C24C2×#4111yescharacteristic
376C24C2×#4111yescharacteristic
377C24C2×#4111yescharacteristic
378C24C2×#4112yes—
379C24C2×#4112yes—
380C24C2×#4112yes—
381C24H(5,𝔽2)11yescharacteristic
382C24H(5,𝔽2)11yescharacteristic
383C24H(5,𝔽2)11yescharacteristic
384C242−1+412yes—
385C242−1+412yes—
386C242−1+412yes—
387C242−1+412yes—
388C242−1+411yescharacteristic
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
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—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—41no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—42no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—42no—
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—42no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—42no—
624C22×C4—41no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—42no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—41no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—41no—
649C22×C4—41no—
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—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#12014yes—
702C22×C4#12014yes—
703C22×C4#12014yes—
704C22×C4#12114yes—
705C22×C4#12114yes—
706C22×C4#12114yes—
707C22×C4#12114yes—
708C22×C4#12114yes—
709C22×C4#12114yes—
710C22×C4C22⋊Q818yes—
711C22×C4#12318yes—
712C22×C4#12714yes—
713C22×C4C4⋊Q814yes—
714C4⋊C4—232no—
715C4⋊C4—232no—
716C4⋊C4—432no—
717C4⋊C4—432no—
718C4⋊C4—416no—
719C4⋊C4—416no—
720C42—416no—
721C23C2×#12011yescharacteristic
722C23C2×#12011yescharacteristic
723C23C2×#12011yescharacteristic
724C23C2×#12111yescharacteristic
725C23C2×#12111yescharacteristic
726C23C2×#12111yescharacteristic
727C23C2×#12111yescharacteristic
728C23C2×#12111yescharacteristic
729C23C2×#12111yescharacteristic
730C23C2×C22⋊Q812yes—
731C23C2×#12312yes—
732C23#52511yescharacteristic
733C23#52511yescharacteristic
734C23#52511yescharacteristic
735C23#52511yescharacteristic
736C23#52511yescharacteristic
737C23#52512yes—
738C23#52512yes—
739C23#52912yes—
740C23C2×#12711yescharacteristic
741C23C2×C4⋊Q811yescharacteristic
742C23#53211yescharacteristic
743C23#53312yes—
744C23#53312yes—
745C23#53312yes—
746C23#53511yescharacteristic
747C23#53511yescharacteristic
748C23#53511yescharacteristic
749C23#53611yescharacteristic
750C23#53611yescharacteristic
751C23#53611yescharacteristic
752C23#53611yescharacteristic
753C23#53612yes—
754C23#53612yes—
755C23#53612yes—
756C23#53612yes—
757C23#53711yescharacteristic
758C23#53711yescharacteristic
759C23#53711yescharacteristic
760C23#53912yes—
761C23#53912yes—
762C23#53912yes—
763C23#54112yes—
764C23#54112yes—
765C23#54112yes—
766C23#54112yes—
767C23#54112yes—
768C23#54112yes—
769C23#54212yes—
770C23#54412yes—
771C23#54412yes—
772C23D4211yescharacteristic
773C23D4211yescharacteristic
774C23D4211yescharacteristic
775C23#54611yescharacteristic
776C23#54611yescharacteristic
777C23#54611yescharacteristic
778C23#54611yescharacteristic
779C23#54712yes—
780C23#54712yes—
781C23#54712yes—
782C23#54712yes—
783C23#54712yes—
784C23#54712yes—
785C23#54711yescharacteristic
786C23#54712yes—
787C23#54711yescharacteristic
788C23#54712yes—
789C23#54811yescharacteristic
790C23#54811yescharacteristic
791C23#54812yes—
792C23#54812yes—
793C23#54812yes—
794C23D4×Q812yes—
795C23D4×Q812yes—
796C23D4×Q812yes—
797C23D4×Q812yes—
798C23D4×Q812yes—
799C23#55011yescharacteristic
800C23#55011yescharacteristic
801C23#55112yes—
802C23#55212yes—
803C23#55212yes—
804C23#55212yes—
805C23#55212yes—
806C23#55212yes—
807C23#55212yes—
808C23#55311yescharacteristic
809C23#55312yes—
810C23#55311yescharacteristic
811C23#55412yes—
812C23#55511yescharacteristic
813C23#55612yes—
814C23#55712yes—
815C23#55712yes—
816C23#56312yes—
817C23#56312yes—
818C23#56312yes—
819C23#56412yes—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—28no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—44no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—44no—
896C2×C4—44no—
897C2×C4—44no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—44no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—44no—
912C2×C4—42no—
913C2×C4—44no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—42no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—81no—
937C2×C4—82no—
938C2×C4—81no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—82no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—82no—
945C2×C4—81no—
946C2×C4—81no—
947C2×C4—82no—
948C2×C4—82no—
949C2×C4—82no—
950C2×C4—82no—
951C2×C4—82no—
952C2×C4—82no—
953C2×C4—82no—
954C2×C4—82no—
955C2×C4—82no—
956C2×C4—82no—
957C2×C4—82no—
958C2×C4—82no—
959C2×C4—82no—
960C2×C4—82no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4—82no—
964C2×C4#39218yes—
965C22C2×#39211yescharacteristic
966C22#239211yescharacteristic
967C22#239911yescharacteristic
968C22#240611yescharacteristic
969C22#240611yescharacteristic
970C22#240612yes—
971C22#240711yescharacteristic
972C22#240711yescharacteristic
973C22#240811yescharacteristic
974C22#240811yescharacteristic
975C22#240912yes—
976C22#241311yescharacteristic
977C22#241311yescharacteristic
978C22#241312yes—
979C22#241312yes—
980C22#241411yescharacteristic
981C22#241411yescharacteristic
982C22#241512yes—
983C22#241611yescharacteristic
984C22#241611yescharacteristic
985C22#241912yes—
986C22#242312yes—
987C22#242912yes—
988C22#242912yes—
989C22#242912yes—
990C22#242912yes—
991C22#243211yescharacteristic
992C22#243211yescharacteristic
993C22#243411yescharacteristic
994C22#243411yescharacteristic
995C22#243812yes—
996C22#244112yes—
997C22#244312yes—
998C22#244612yes—
999C22#244912yes—
1000C22#245312yes—
1001C22#246012yes—
1002C22#246212yes—
1003C22#246212yes—
1004C22#246212yes—
1005C22#246212yes—
1006C22#246312yes—
1007C22#246512yes—
1008C22#247512yes—
1009C22#247812yes—
1010C22#248612yes—
1011C22#250112yes—
1012C22#253511yescharacteristic
1013C22#253611yescharacteristic
1014C22#253711yescharacteristic
1015C22#254011yescharacteristic
1016C22#254111yescharacteristic
1017C22#254212yes—
1018C22#254611yescharacteristic
1019C22#258411yescharacteristic
1020C22#258512yes—
1021C22#259911yescharacteristic
1022C22#260311yescharacteristic
1023C22#260612yes—
1024C22#261111yescharacteristic
1025C22#261212yes—
1026C22#261411yescharacteristic
1027C22#261511yescharacteristic
1028C22#262111yescharacteristic
1029C22#262111yescharacteristic
1030C22#263311yescharacteristic
1031C22#263411yescharacteristic
1032C22#263711yescharacteristic
1033C22#266011yescharacteristic
1034C22#266411yescharacteristic
1035C22#267412yes—
1036C22#267712yes—
1037C22#267712yes—
1038C22#268912yes—
1039C22#269012yes—
1040C22#271312yes—
1041C22#271312yes—
1042C22#271812yes—
1043C22#271912yes—
1044C22#271912yes—
1045C22#271912yes—
1046C22#271912yes—
1047C22#272012yes—
1048C22#272012yes—
1049C22#272112yes—
1050C22#272112yes—
1051C22#272212yes—
1052C22#272312yes—
1053C22#272512yes—
1054C22#272612yes—
1055C22#272612yes—
1056C22#276612yes—
1057C22#276912yes—
1058C22#277612yes—
1059C22#282111yescharacteristic
1060C22#282211yescharacteristic
1061C22#284711yescharacteristic
1062C22#284911yescharacteristic
1063C22#285711yescharacteristic
1064C4—28no—
1065C4—44no—
1066C4—44no—
1067C4—44no—
1068C4—44no—
1069C4—48no—
1070C4—48no—
1071C4—84no—
1072C4—82no—
1073C4—84no—
1074C4—82no—
1075C2#1480111yescharacteristic
1076C2#1481811yescharacteristic
1077C2#1487911yescharacteristic
1078C2#1488011yescharacteristic
1079C2#1490311yescharacteristic
1080C2#1490711yescharacteristic
1081C2#1506911yescharacteristic
1082C2#1512311yescharacteristic
1083C2#1517811yescharacteristic
1084C2#1534712yes—
1085C2#1535412yes—
1086C2#1576512yes—
1087C2#1577812yes—
1088C2#1580412yes—
1089C2#1581212yes—
1090C2#1587412yes—
1091C2#1610412yes—
1092C2#1650711yescharacteristic
1093C2#1651711yescharacteristic
1094C2#1660711yescharacteristic
1095C2#1667311yescharacteristic
1096C2#1667711yescharacteristic
1097C2#1668311yescharacteristic
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×#3982
C22×#3892
C22×#3872
C2×#14452
C2×#14442
C2×#14412
C2×#14342
#75572
#75562