Finite Group Databasebeta

← #154351

Subgroups — #154351

Order 512.

2878 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1441C212yesmaximal
2C2×#1436C212yesmaximal
3C2×C4⋊#95C211yesmaximal, characteristic
4C2×#1434C211yesmaximal, characteristic
5C2×C4×#95C211yesmaximal, characteristic
6#7557C212yesmaximal
7#7557C212yesmaximal
8#7556C212yesmaximal
9#7554C212yesmaximal
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2212yes—
12C23×C42C2212yes—
13C23×C42C2211yescharacteristic
14C22×#95C2212yes—
15C22×#95C2212yes—
16C22×#95C2212yes—
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31#1441—28no—
32#1436—28no—
33C4⋊#95C418yescomplemented
34#1434—24no—
35C4×#95—24no—
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2312yes—
39C24×C4C2311yescharacteristic
40C24×C4C2312yes—
41C24×C4C2312yes—
42C24×C4C2312yes—
43C24×C4C2311yescharacteristic
44C24×C4C2311yescharacteristic
45C22×C4⋊C4—24no—
46C22×C4⋊C4—24no—
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—42no—
55C22×C4⋊C4—42no—
56C22×C4⋊C4—42no—
57C22×C4⋊C4—42no—
58C22×C4⋊C4C2×C418yes—
59C22×C42—24no—
60C22×C42—24no—
61C22×C42—24no—
62C22×C42—24no—
63C22×C42—24no—
64C22×C42—42no—
65C22×C42—42no—
66C22×C42—42no—
67C22×C42—42no—
68C22×C42C2×C414yes—
69C22×C42D414yes—
70C22×C42Q814yes—
71C2×#95—24no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—24no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—24no—
88C2×#95—24no—
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—41no—
104C2×#95—41no—
105C2×#95—41no—
106C2×#95—41no—
107C2×#95—42no—
108C2×#95—42no—
109C2×#95—42no—
110C2×#95—42no—
111C2×#95—42no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95C2×C418yes—
116C2×#95C2×C414yes—
117C2×#95C2×C414yes—
118C2×#95D414yes—
119C2×#95D414yes—
120C2×#95Q814yes—
121C2×#95Q814yes—
122C25C2411yescharacteristic
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
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—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
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—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
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—22no—
199C23×C4—22no—
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×C4C22×C414yes—
218C23×C4C22×C412yes—
219C23×C4C22×C414yes—
220C23×C4C22×C412yes—
221C23×C4C22×C412yes—
222C23×C4C2×D414yes—
223C23×C4C2×D412yes—
224C23×C4C2×D414yes—
225C23×C4C2×D412yes—
226C23×C4C2×D412yes—
227C23×C4C2×D412yes—
228C23×C4C2×D412yes—
229C23×C4C2×Q814yes—
230C23×C4C2×Q812yes—
231C23×C4C2×Q814yes—
232C23×C4C2×Q812yes—
233C23×C4C2×Q812yes—
234C23×C4C2×Q812yes—
235C23×C4C2×Q812yes—
236C23×C4#4114yes—
237C23×C4#4114yes—
238C23×C4#4114yes—
239C23×C4#4114yes—
240C23×C4#4114yes—
241C23×C4#4114yes—
242C23×C4#4112yes—
243C23×C4#4112yes—
244C23×C4#4112yes—
245C23×C4#4112yes—
246C2×C4⋊C4—216no—
247C2×C4⋊C4—216no—
248C2×C4⋊C4—216no—
249C2×C4⋊C4—48no—
250C2×C4⋊C4—48no—
251C2×C4⋊C4—48no—
252C2×C4⋊C4—48no—
253C2×C4⋊C4—48no—
254C2×C4⋊C4—48no—
255C2×C4⋊C4—48no—
256C2×C4⋊C4—48no—
257C2×C4⋊C4—48no—
258C2×C4⋊C4—48no—
259C2×C4⋊C4—48no—
260C2×C42—216no—
261C2×C42—48no—
262C2×C42—48no—
263C2×C42—44no—
264C2×C42—44no—
265C2×C42—48no—
266C2×C42—48no—
267C2×C42—48no—
268C2×C42—48no—
269C2×C42—48no—
270C2×C42—48no—
271C2×C42C4⋊C4116yescomplemented
272#95—216no—
273#95—216no—
274#95—216no—
275#95—28no—
276#95—28no—
277#95—28no—
278#95—28no—
279#95—44no—
280#95—44no—
281#95—48no—
282#95—48no—
283#95—48no—
284#95—48no—
285#95—48no—
286#95—48no—
287#95—48no—
288#95—48no—
289C24C23×C411yescharacteristic
290C24C22×D411yescharacteristic
291C24C22×D411yescharacteristic
292C24C22×D411yescharacteristic
293C24C22×Q811yescharacteristic
294C24C22×Q811yescharacteristic
295C24C22×Q811yescharacteristic
296C24C2×#4112yes—
297C24C2×#4112yes—
298C24C2×#4111yescharacteristic
299C24C2×#4111yescharacteristic
300C24C2×#4111yescharacteristic
301C24C2×#4111yescharacteristic
302C24C2×#4112yes—
303C24C2×#4112yes—
304C24C2×#4112yes—
305C24C2×#4112yes—
306C24H(5,𝔽2)12yes—
307C24H(5,𝔽2)12yes—
308C24H(5,𝔽2)11yescharacteristic
309C24H(5,𝔽2)11yescharacteristic
310C242−1+411yescharacteristic
311C242−1+411yescharacteristic
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—22no—
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—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
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—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—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—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
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—42no—
453C22×C4—42no—
454C22×C4—42no—
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—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—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—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4C2×C4⋊C414yes—
574C22×C4C2×C4⋊C414yes—
575C22×C4C2×C4⋊C414yes—
576C22×C4#11718yes—
577C22×C4C4×D414yes—
578C22×C4C4×D414yes—
579C22×C4C4×Q814yes—
580C22×C4C4×Q814yes—
581C22×C4#12114yes—
582C22×C4#12114yes—
583C22×C4C22⋊Q814yes—
584C22×C4C22⋊Q814yes—
585C22×C4#12418yes—
586C22×C4#12518yes—
587C22×C4#12514yes—
588C22×C4#12514yes—
589C22×C4C4⋊Q814yes—
590C22×C4C4⋊Q814yes—
591C4⋊C4—432no—
592C4⋊C4—432no—
593C42—416no—
594C42—432no—
595C23C22×C4⋊C411yescharacteristic
596C23C2×#11712yes—
597C23C2×C4×D411yescharacteristic
598C23C2×C4×D411yescharacteristic
599C23C2×C4×Q811yescharacteristic
600C23C2×C4×Q811yescharacteristic
601C23C4×#4112yes—
602C23C4×#4112yes—
603C23#51812yes—
604C23#51811yescharacteristic
605C23#51911yescharacteristic
606C23C2×#12111yescharacteristic
607C23C2×#12111yescharacteristic
608C23C2×C22⋊Q811yescharacteristic
609C23C2×C22⋊Q811yescharacteristic
610C23#52512yes—
611C23#52512yes—
612C23#52512yes—
613C23#52512yes—
614C23C2×#12412yes—
615C23C2×#12512yes—
616C23C2×#12511yescharacteristic
617C23C2×#12511yescharacteristic
618C23#52912yes—
619C23#52912yes—
620C23#52912yes—
621C23#52912yes—
622C23#52912yes—
623C23#52912yes—
624C23#52912yes—
625C23#52912yes—
626C23C2×C4⋊Q811yescharacteristic
627C23C2×C4⋊Q811yescharacteristic
628C23#53212yes—
629C23#53212yes—
630C23#53312yes—
631C23#53311yescharacteristic
632C23#53311yescharacteristic
633C23#53311yescharacteristic
634C23#53311yescharacteristic
635C23#53312yes—
636C23#53312yes—
637C23#53311yescharacteristic
638C23#53311yescharacteristic
639C23#53412yes—
640C23#53711yescharacteristic
641C23#53711yescharacteristic
642C23#53812yes—
643C23#53812yes—
644C23#53912yes—
645C23#53912yes—
646C23#54012yes—
647C23#54012yes—
648C23#54212yes—
649C23#54212yes—
650C23#54311yescharacteristic
651C23#54311yescharacteristic
652C23#54411yescharacteristic
653C23#54411yescharacteristic
654C23D4211yescharacteristic
655C23#54612yes—
656C23#54612yes—
657C23#54612yes—
658C23#54612yes—
659C23#54711yescharacteristic
660C23#54711yescharacteristic
661C23D4×Q811yescharacteristic
662C23D4×Q811yescharacteristic
663C23#55011yescharacteristic
664C23#55011yescharacteristic
665C23#55112yes—
666C23#55112yes—
667C23#55112yes—
668C23#55112yes—
669C23#55112yes—
670C23#55112yes—
671C23#55212yes—
672C23#55212yes—
673C23#55312yes—
674C23#55312yes—
675C23#55312yes—
676C23#55312yes—
677C23#55312yes—
678C23#55312yes—
679C23#55412yes—
680C23#55412yes—
681C23#55412yes—
682C23#55412yes—
683C23#55411yescharacteristic
684C23#55411yescharacteristic
685C23#55511yescharacteristic
686C23#55611yescharacteristic
687C23#55611yescharacteristic
688C23#55612yes—
689C23#55612yes—
690C23#55711yescharacteristic
691C23#55711yescharacteristic
692C23Q8211yescharacteristic
693C23#55911yescharacteristic
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
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—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—24no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
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—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
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—44no—
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—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
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—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
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—82no—
809C2×C4—82no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4#38918yes—
816C2×C4#38918yes—
817C22#228511yescharacteristic
818C22#229012yes—
819C22C2×#38911yescharacteristic
820C22C2×#38911yescharacteristic
821C22#229512yes—
822C22#229611yescharacteristic
823C22#229611yescharacteristic
824C22C4×#12412yes—
825C22C4×#12512yes—
826C22#231511yescharacteristic
827C22#231611yescharacteristic
828C22#233212yes—
829C22#233312yes—
830C22#234212yes—
831C22#234512yes—
832C22#235312yes—
833C22#235612yes—
834C22#236412yes—
835C22#236511yescharacteristic
836C22#236511yescharacteristic
837C22#236611yescharacteristic
838C22#236812yes—
839C22#236911yescharacteristic
840C22#239212yes—
841C22#239612yes—
842C22#239911yescharacteristic
843C22#239911yescharacteristic
844C22#240211yescharacteristic
845C22#240211yescharacteristic
846C22#246412yes—
847C22#246512yes—
848C22#246612yes—
849C22#246712yes—
850C22#247012yes—
851C22#247112yes—
852C22#247212yes—
853C22#247312yes—
854C22#248812yes—
855C22#249012yes—
856C22#249212yes—
857C22#250512yes—
858C22#250712yes—
859C22#250912yes—
860C22#251612yes—
861C22#251812yes—
862C22#252012yes—
863C22#252112yes—
864C22#252212yes—
865C22#252212yes—
866C22#252312yes—
867C22#252512yes—
868C22#252612yes—
869C22#252712yes—
870C22#253412yes—
871C22#253711yescharacteristic
872C22#253811yescharacteristic
873C22#253811yescharacteristic
874C22#254312yes—
875C22#254911yescharacteristic
876C22#254911yescharacteristic
877C22#254911yescharacteristic
878C22#254911yescharacteristic
879C22#255111yescharacteristic
880C22#255211yescharacteristic
881C22#255211yescharacteristic
882C22#255412yes—
883C22#255612yes—
884C22#256412yes—
885C22#256911yescharacteristic
886C22#256911yescharacteristic
887C22#256911yescharacteristic
888C22#256911yescharacteristic
889C22#257111yescharacteristic
890C22#257912yes—
891C22#258211yescharacteristic
892C22#258512yes—
893C22#258612yes—
894C22#258712yes—
895C22#258812yes—
896C22#259412yes—
897C22#259512yes—
898C22#260112yes—
899C22#260112yes—
900C22#260511yescharacteristic
901C22#260511yescharacteristic
902C22#260611yescharacteristic
903C22#260611yescharacteristic
904C22#263012yes—
905C22#263012yes—
906C22#266511yescharacteristic
907C22#266511yescharacteristic
908C22#266711yescharacteristic
909C22#266711yescharacteristic
910C22#285012yes—
911C22#285112yes—
912C22#285911yescharacteristic
913C22#286211yescharacteristic
914C22#286411yescharacteristic
915C22#286411yescharacteristic
916C4—28no—
917C4—28no—
918C4—48no—
919C4—48no—
920C4—48no—
921C4—44no—
922C4—84no—
923C4—84no—
924C4—84no—
925C2#1384811yescharacteristic
926C2#1390811yescharacteristic
927C2#1396411yescharacteristic
928C2#1403312yes—
929C2#1403412yes—
930C2#1405712yes—
931C2#1405812yes—
932C2#1414911yescharacteristic
933C2#1415111yescharacteristic
934C2#1429711yescharacteristic
935C2#1470711yescharacteristic
936C2#1496812yes—
937C2#1497311yescharacteristic
938C2#1497812yes—
939C2#1498111yescharacteristic
940C2#1500811yescharacteristic
941C2#1501111yescharacteristic
942C2#1504811yescharacteristic
943C2#1505211yescharacteristic
944C2#1506611yescharacteristic
945C2#1506711yescharacteristic
946C2#1509312yes—
947C2#1509412yes—
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
33. C4⋊#95C4semidirect
271. C2×C42C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14412
C2×#14362
C2×C4⋊#952
C2×#14342
C2×C4×#952
#75572
#75562
#75542