Finite Group Databasebeta

← #158292

Subgroups — #158292

Order 512.

3036 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic
3C2×#1444C211yesmaximal, characteristic
4C2×#1444C212yesmaximal
5C2×#1442C211yesmaximal, characteristic
6#7557C212yesmaximal
7#7557C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7557C212yesmaximal
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2211yescharacteristic
16C23×C4⋊C4C2212yes—
17C23×C4⋊C4C2212yes—
18C23×C42C2211yescharacteristic
19C2×#389—24no—
20C2×#389—28no—
21C2×#387—24no—
22C2×#387—24no—
23C2×#387—24no—
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2212yes—
39C22×#95C2212yes—
40#1444—24no—
41#1444—28no—
42#1442—24no—
43C24×C4C2312yes—
44C24×C4C2311yescharacteristic
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2312yes—
53C24×C4C2311yescharacteristic
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—24no—
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—22no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—42no—
78C22×C4⋊C4—42no—
79C22×C4⋊C4—42no—
80C22×C4⋊C4—42no—
81C22×C4⋊C4—42no—
82C22×C4⋊C4—42no—
83C22×C4⋊C4—42no—
84C22×C4⋊C4—42no—
85C22×C4⋊C4—42no—
86C22×C4⋊C4—42no—
87C22×C4⋊C4D418yes—
88C22×C4⋊C4Q814yes—
89C22×C4⋊C4Q814yes—
90C22×C42—22no—
91C22×C42—22no—
92C22×C42—24no—
93C22×C42—42no—
94C22×C42D414yes—
95#389—232no—
96#387—232no—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
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×#95—42no—
140C2×#95—42no—
141C2×#95D414yes—
142C2×#95D414yes—
143C2×#95Q814yes—
144C2×#95Q814yes—
145C25C2411yescharacteristic
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—21no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—22no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—22no—
170C23×C4—21no—
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—21no—
186C23×C4—21no—
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—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—21no—
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—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
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×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4C2×D412yes—
256C23×C4C2×D414yes—
257C23×C4C2×D412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D414yes—
260C23×C4C2×D412yes—
261C23×C4C2×D414yes—
262C23×C4C2×D412yes—
263C23×C4C2×D412yes—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2×Q814yes—
268C23×C4C2×Q812yes—
269C23×C4C2×Q812yes—
270C23×C4C2×Q812yes—
271C23×C4C2×Q814yes—
272C23×C4C2×Q814yes—
273C23×C4C2×Q812yes—
274C23×C4C2×Q812yes—
275C23×C4C2×Q812yes—
276C23×C4#4112yes—
277C23×C4#4112yes—
278C23×C4#4112yes—
279C23×C4#4114yes—
280C23×C4#4114yes—
281C23×C4#4114yes—
282C23×C4#4112yes—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—216no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—216no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—216no—
298C2×C4⋊C4—48no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—48no—
302C2×C4⋊C4—48no—
303C2×C4⋊C4—48no—
304C2×C4⋊C4—48no—
305C2×C4⋊C4—48no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—48no—
310C2×C4⋊C4—48no—
311C2×C4⋊C4—48no—
312C2×C4⋊C4—48no—
313C2×C4⋊C4—48no—
314C2×C4⋊C4—48no—
315C2×C4⋊C4—48no—
316C2×C4⋊C4—48no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C42—28no—
320C2×C42—28no—
321C2×C42—44no—
322C2×C42—48no—
323C2×C42—48no—
324#95—216no—
325#95—28no—
326#95—28no—
327#95—216no—
328#95—28no—
329#95—28no—
330#95—28no—
331#95—28no—
332#95—48no—
333#95—48no—
334#95—48no—
335#95—48no—
336#95—48no—
337#95—48no—
338#95—48no—
339#95—48no—
340C24C22×D411yescharacteristic
341C24C22×D411yescharacteristic
342C24C22×D411yescharacteristic
343C24C22×D412yes—
344C24C22×Q811yescharacteristic
345C24C22×Q811yescharacteristic
346C24C22×Q811yescharacteristic
347C24C22×Q811yescharacteristic
348C24C2×#4111yescharacteristic
349C24C2×#4111yescharacteristic
350C24C2×#4111yescharacteristic
351C24C2×#4112yes—
352C24C2×#4111yescharacteristic
353C24C2×#4112yes—
354C24C2×#4112yes—
355C24H(5,𝔽2)11yescharacteristic
356C24H(5,𝔽2)11yescharacteristic
357C24H(5,𝔽2)12yes—
358C24H(5,𝔽2)12yes—
359C24H(5,𝔽2)11yescharacteristic
360C242−1+412yes—
361C242−1+412yes—
362C242−1+411yescharacteristic
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
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—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
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—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
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—41no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
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—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
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—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
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—42no—
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#12014yes—
652C22×C4#12014yes—
653C22×C4C22⋊Q818yes—
654C22×C4C22⋊Q814yes—
655C22×C4C22⋊Q814yes—
656C22×C4C22⋊Q814yes—
657C22×C4C22⋊Q814yes—
658C22×C4C22⋊Q814yes—
659C22×C4C22⋊Q814yes—
660C22×C4#12518yes—
661C22×C4C4⋊Q814yes—
662C22×C4C4⋊Q814yes—
663C22×C4C4⋊Q814yes—
664C4⋊C4—232no—
665C4⋊C4—232no—
666C4⋊C4—416no—
667C4⋊C4—432no—
668C4⋊C4—416no—
669C4⋊C4—432no—
670C42—416no—
671C23C2×#12011yescharacteristic
672C23C2×#12011yescharacteristic
673C23C2×C22⋊Q811yescharacteristic
674C23C2×C22⋊Q812yes—
675C23C2×C22⋊Q811yescharacteristic
676C23C2×C22⋊Q811yescharacteristic
677C23C2×C22⋊Q811yescharacteristic
678C23C2×C22⋊Q811yescharacteristic
679C23C2×C22⋊Q811yescharacteristic
680C23#52512yes—
681C23#52511yescharacteristic
682C23#52511yescharacteristic
683C23#52511yescharacteristic
684C23#52511yescharacteristic
685C23#52512yes—
686C23C2×#12512yes—
687C23#52912yes—
688C23C2×C4⋊Q811yescharacteristic
689C23C2×C4⋊Q811yescharacteristic
690C23C2×C4⋊Q811yescharacteristic
691C23#53211yescharacteristic
692C23#53212yes—
693C23#53211yescharacteristic
694C23#53312yes—
695C23#53312yes—
696C23#53411yescharacteristic
697C23#53412yes—
698C23#53412yes—
699C23#53511yescharacteristic
700C23#53511yescharacteristic
701C23#53511yescharacteristic
702C23#53511yescharacteristic
703C23#53611yescharacteristic
704C23#53611yescharacteristic
705C23#53711yescharacteristic
706C23#53711yescharacteristic
707C23#53711yescharacteristic
708C23#53812yes—
709C23#53912yes—
710C23#53912yes—
711C23#53912yes—
712C23#54012yes—
713C23#54112yes—
714C23#54112yes—
715C23#54212yes—
716C23#54212yes—
717C23#54212yes—
718C23#54412yes—
719C23#54412yes—
720C23#54412yes—
721C23#54412yes—
722C23D4212yes—
723C23D4212yes—
724C23#54612yes—
725C23#54612yes—
726C23#54712yes—
727C23#54712yes—
728C23#54712yes—
729C23#54712yes—
730C23#54812yes—
731C23#54812yes—
732C23D4×Q812yes—
733C23D4×Q812yes—
734C23D4×Q812yes—
735C23#55012yes—
736C23#55112yes—
737C23#55112yes—
738C23#55112yes—
739C23#55212yes—
740C23#55212yes—
741C23#55212yes—
742C23#55312yes—
743C23#55312yes—
744C23#55312yes—
745C23#55411yescharacteristic
746C23#55412yes—
747C23#55412yes—
748C23#55411yescharacteristic
749C23#55411yescharacteristic
750C23#55411yescharacteristic
751C23#55411yescharacteristic
752C23#55411yescharacteristic
753C23#55412yes—
754C23#55412yes—
755C23#55712yes—
756C23#55711yescharacteristic
757C23#55711yescharacteristic
758C23#55711yescharacteristic
759C23#55711yescharacteristic
760C23Q8211yescharacteristic
761C23Q8211yescharacteristic
762C23Q8211yescharacteristic
763C23#55911yescharacteristic
764C23#55911yescharacteristic
765C23#55911yescharacteristic
766C23#56012yes—
767C23#56212yes—
768C23#56312yes—
769C23#56312yes—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—24no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
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—42no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—81no—
879C2×C4—82no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—82no—
883C2×C4—81no—
884C2×C4—82no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—82no—
888C2×C4—82no—
889C2×C4—82no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—81no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—82no—
900C2×C4—82no—
901C2×C4—82no—
902C2×C4—82no—
903C2×C4—82no—
904C2×C4—82no—
905C2×C4—81no—
906C2×C4#39518yes—
907C22C2×#39511yescharacteristic
908C22#238811yescharacteristic
909C22#239611yescharacteristic
910C22#240311yescharacteristic
911C22#240611yescharacteristic
912C22#240911yescharacteristic
913C22#243011yescharacteristic
914C22#243111yescharacteristic
915C22#243211yescharacteristic
916C22#243411yescharacteristic
917C22#243812yes—
918C22#244012yes—
919C22#244012yes—
920C22#244112yes—
921C22#244112yes—
922C22#244212yes—
923C22#244912yes—
924C22#244912yes—
925C22#244912yes—
926C22#245112yes—
927C22#245212yes—
928C22#245312yes—
929C22#245812yes—
930C22#246112yes—
931C22#246212yes—
932C22#246212yes—
933C22#246312yes—
934C22#247012yes—
935C22#247312yes—
936C22#247912yes—
937C22#250512yes—
938C22#250612yes—
939C22#250712yes—
940C22#252212yes—
941C22#255012yes—
942C22#255212yes—
943C22#255612yes—
944C22#256411yescharacteristic
945C22#256412yes—
946C22#256511yescharacteristic
947C22#256611yescharacteristic
948C22#256711yescharacteristic
949C22#256711yescharacteristic
950C22#256711yescharacteristic
951C22#257912yes—
952C22#258011yescharacteristic
953C22#258011yescharacteristic
954C22#258011yescharacteristic
955C22#258211yescharacteristic
956C22#258211yescharacteristic
957C22#258211yescharacteristic
958C22#258311yescharacteristic
959C22#258411yescharacteristic
960C22#258411yescharacteristic
961C22#258411yescharacteristic
962C22#258612yes—
963C22#259811yescharacteristic
964C22#260012yes—
965C22#260212yes—
966C22#260311yescharacteristic
967C22#261111yescharacteristic
968C22#261311yescharacteristic
969C22#261511yescharacteristic
970C22#262711yescharacteristic
971C22#262811yescharacteristic
972C22#263711yescharacteristic
973C22#263811yescharacteristic
974C22#266011yescharacteristic
975C22#266111yescharacteristic
976C22#266411yescharacteristic
977C22#267112yes—
978C22#267312yes—
979C22#267812yes—
980C22#268212yes—
981C22#271812yes—
982C22#272212yes—
983C22#272312yes—
984C22#272512yes—
985C22#272912yes—
986C22#272912yes—
987C22#273412yes—
988C22#273412yes—
989C22#274212yes—
990C22#275512yes—
991C22#275512yes—
992C22#277112yes—
993C22#277312yes—
994C22#277412yes—
995C22#279012yes—
996C22#279112yes—
997C22#279212yes—
998C22#279612yes—
999C22#280212yes—
1000C22#280212yes—
1001C22#281311yescharacteristic
1002C22#282111yescharacteristic
1003C22#284811yescharacteristic
1004C22#284811yescharacteristic
1005C22#285911yescharacteristic
1006C4—28no—
1007C4—44no—
1008C4—48no—
1009C4—48no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—84no—
1014C4—82no—
1015C4—84no—
1016C4—82no—
1017C2#1472011yescharacteristic
1018C2#1472311yescharacteristic
1019C2#1487811yescharacteristic
1020C2#1489311yescharacteristic
1021C2#1492911yescharacteristic
1022C2#1506811yescharacteristic
1023C2#1520211yescharacteristic
1024C2#1520311yescharacteristic
1025C2#1522811yescharacteristic
1026C2#1536612yes—
1027C2#1536712yes—
1028C2#1543812yes—
1029C2#1546012yes—
1030C2#1562612yes—
1031C2#1562712yes—
1032C2#1597512yes—
1033C2#1597612yes—
1034C2#1625011yescharacteristic
1035C2#1660311yescharacteristic
1036C2#1667311yescharacteristic
1037C2#1690011yescharacteristic
1038C2#1699111yescharacteristic
1039C2#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
C22×#3872
C2×#14442
C2×#14422
#75572
#75542