Finite Group Databasebeta

← #155663

Subgroups — #155663

Order 512.

2786 conjugacy classes of subgroups.

The subgroup lattice has 953 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C2×#1445C212yesmaximal
3C2×#1441C212yesmaximal
4C2×#1441C212yesmaximal
5#7557C212yesmaximal
6#7557C212yesmaximal
7#7556C212yesmaximal
8#7554C211yesmaximal, characteristic
9#7554C211yesmaximal, characteristic
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2212yes—
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#389—28no—
16C2×#389C418yescomplemented
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33#1445—28no—
34#1441—28no—
35#1441—28no—
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2312yes—
39C24×C4C2312yes—
40C24×C4C2312yes—
41C24×C4C2312yes—
42C24×C4C2311yescharacteristic
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—41no—
55C22×C4⋊C4—42no—
56C22×C4⋊C4—41no—
57C22×C4⋊C4—42no—
58C22×C4⋊C4—42no—
59C22×C4⋊C4—42no—
60C22×C4⋊C4—42no—
61C22×C4⋊C4—42no—
62C22×C4⋊C4—42no—
63C22×C4⋊C4C2×C418yes—
64C22×C4⋊C4C2×C414yes—
65C22×C4⋊C4C2×C414yes—
66C22×C4⋊C4D414yes—
67C22×C4⋊C4D418yes—
68C22×C4⋊C4Q814yes—
69C22×C42—24no—
70C22×C42—41no—
71C22×C42—41no—
72C22×C42—42no—
73C22×C42C2×C414yes—
74#389—232no—
75C2×#95—24no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—24no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
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—22no—
99C2×#95—22no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—41no—
103C2×#95—41no—
104C2×#95—41no—
105C2×#95—41no—
106C2×#95—42no—
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×#95—42no—
116C2×#95—41no—
117C2×#95—41no—
118C2×#95—41no—
119C2×#95—41no—
120C2×#95C2×C418yes—
121C2×#95D414yes—
122C2×#95Q814yes—
123C25C2411yescharacteristic
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—21no—
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—21no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—21no—
167C23×C4—21no—
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—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×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×C4C22×C414yes—
227C23×C4C22×C414yes—
228C23×C4C22×C412yes—
229C23×C4C22×C412yes—
230C23×C4C22×C412yes—
231C23×C4C2×D414yes—
232C23×C4C2×D414yes—
233C23×C4C2×D414yes—
234C23×C4C2×D414yes—
235C23×C4C2×D412yes—
236C23×C4C2×D414yes—
237C23×C4C2×D412yes—
238C23×C4C2×Q814yes—
239C23×C4C2×Q814yes—
240C23×C4C2×Q812yes—
241C23×C4C2×Q812yes—
242C23×C4#4114yes—
243C23×C4#4114yes—
244C23×C4#4112yes—
245C23×C4#4112yes—
246C23×C4#4114yes—
247C2×C4⋊C4—28no—
248C2×C4⋊C4—28no—
249C2×C4⋊C4—216no—
250C2×C4⋊C4—216no—
251C2×C4⋊C4—216no—
252C2×C4⋊C4—216no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4—44no—
255C2×C4⋊C4—48no—
256C2×C4⋊C4—48no—
257C2×C4⋊C4—48no—
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⋊C4C22⋊C4116yes—
270C2×C4⋊C4C4⋊C4116yescomplemented
271C2×C42—28no—
272C2×C42—44no—
273C2×C42—44no—
274C2×C42—48no—
275C2×C42—48no—
276#95—216no—
277#95—44no—
278#95—44no—
279#95—48no—
280#95—48no—
281#95—48no—
282#95—48no—
283#95—48no—
284#95—48no—
285#95—48no—
286#95—48no—
287#95—48no—
288#95—44no—
289#95—44no—
290#95—48no—
291#95—48no—
292C24C23×C411yescharacteristic
293C24C22×D412yes—
294C24C22×D411yescharacteristic
295C24C22×D411yescharacteristic
296C24C22×Q811yescharacteristic
297C24C22×Q811yescharacteristic
298C24C2×#4112yes—
299C24C2×#4111yescharacteristic
300C24C2×#4111yescharacteristic
301C24C2×#4112yes—
302C24C2×#4112yes—
303C24H(5,𝔽2)11yescharacteristic
304C24H(5,𝔽2)11yescharacteristic
305C24H(5,𝔽2)12yes—
306C24H(5,𝔽2)12yes—
307C24H(5,𝔽2)11yescharacteristic
308C24H(5,𝔽2)11yescharacteristic
309C242−1+412yes—
310C242−1+411yescharacteristic
311C242−1+411yescharacteristic
312C242−1+412yes—
313C242−1+411yescharacteristic
314C242−1+411yescharacteristic
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
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—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—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
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—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×C4—42no—
574C22×C4—42no—
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—42no—
584C22×C4—42no—
585C22×C4C2×C22⋊C418yes—
586C22×C4C2×C22⋊C414yes—
587C22×C4C2×C4⋊C418yes—
588C22×C4C2×C4⋊C414yes—
589C22×C4#11714yes—
590C22×C4C4×D414yes—
591C22×C4C4×Q814yes—
592C22×C4#12118yes—
593C22×C4C22⋊Q818yes—
594C4⋊C4—232no—
595C4⋊C4—416no—
596C4⋊C4—432no—
597C4⋊C4—432no—
598C42—416no—
599C23C22×C22⋊C411yescharacteristic
600C23C22×C4⋊C411yescharacteristic
601C23C2×#11711yescharacteristic
602C23C2×C4×D411yescharacteristic
603C23C2×C4×Q811yescharacteristic
604C23C4×#4111yescharacteristic
605C23C4×#4111yescharacteristic
606C23#51811yescharacteristic
607C23#51811yescharacteristic
608C23#51811yescharacteristic
609C23#51911yescharacteristic
610C23#51911yescharacteristic
611C23#51911yescharacteristic
612C23#52011yescharacteristic
613C23#52011yescharacteristic
614C23C2×#12112yes—
615C23C2×C22⋊Q812yes—
616C23#52912yes—
617C23#52912yes—
618C23#53212yes—
619C23#53312yes—
620C23#53412yes—
621C23#53412yes—
622C23#53411yescharacteristic
623C23#53612yes—
624C23#53612yes—
625C23#53612yes—
626C23#53712yes—
627C23#53711yescharacteristic
628C23#53711yescharacteristic
629C23#53711yescharacteristic
630C23#53811yescharacteristic
631C23#53811yescharacteristic
632C23#53812yes—
633C23#53912yes—
634C23#53912yes—
635C23#53912yes—
636C23#53912yes—
637C23#53911yescharacteristic
638C23#53911yescharacteristic
639C23#53912yes—
640C23#53912yes—
641C23#53912yes—
642C23#54012yes—
643C23#54012yes—
644C23#54112yes—
645C23#54112yes—
646C23#54112yes—
647C23#54112yes—
648C23#54212yes—
649C23#54212yes—
650C23#54212yes—
651C23#54212yes—
652C23#54311yescharacteristic
653C23#54412yes—
654C23#54411yescharacteristic
655C23#54411yescharacteristic
656C23#54411yescharacteristic
657C23#54412yes—
658C23D4212yes—
659C23D4211yescharacteristic
660C23#54612yes—
661C23#54612yes—
662C23#54612yes—
663C23#54612yes—
664C23#54712yes—
665C23#54711yescharacteristic
666C23#54711yescharacteristic
667C23#54812yes—
668C23#54812yes—
669C23#54812yes—
670C23D4×Q812yes—
671C23D4×Q811yescharacteristic
672C23D4×Q811yescharacteristic
673C23D4×Q811yescharacteristic
674C23#55012yes—
675C23#55011yescharacteristic
676C23#55112yes—
677C23#55212yes—
678C23#55212yes—
679C23#55312yes—
680C23#55412yes—
681C23#55411yescharacteristic
682C23#55412yes—
683C23#55611yescharacteristic
684C23#55711yescharacteristic
685C23#55711yescharacteristic
686C23#55712yes—
687C23Q8211yescharacteristic
688C23#56012yes—
689C23#56212yes—
690C23#56212yes—
691C23#56211yescharacteristic
692C23#56311yescharacteristic
693C23#56312yes—
694C23#56312yes—
695C23#56311yescharacteristic
696C23#56312yes—
697C23#56411yescharacteristic
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
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—44no—
744C2×C4—44no—
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—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—82no—
809C2×C4—82no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4#38018yes—
821C22C2×#38011yescharacteristic
822C22#229311yescharacteristic
823C22#229511yescharacteristic
824C22#230811yescharacteristic
825C22#231011yescharacteristic
826C22#231311yescharacteristic
827C22#231311yescharacteristic
828C22#231611yescharacteristic
829C22#231611yescharacteristic
830C22#231911yescharacteristic
831C22#232011yescharacteristic
832C22#232511yescharacteristic
833C22#232711yescharacteristic
834C22#232911yescharacteristic
835C22#233111yescharacteristic
836C22#233211yescharacteristic
837C22#233311yescharacteristic
838C22#233611yescharacteristic
839C22#233611yescharacteristic
840C22D4×C22⋊C411yescharacteristic
841C22#233911yescharacteristic
842C22Q8×C22⋊C411yescharacteristic
843C22#234111yescharacteristic
844C22D4×C4⋊C411yescharacteristic
845C22#234911yescharacteristic
846C22Q8×C4⋊C411yescharacteristic
847C22#235111yescharacteristic
848C22#236411yescharacteristic
849C22#236511yescharacteristic
850C22#236811yescharacteristic
851C22#237111yescharacteristic
852C22#237711yescharacteristic
853C22#237811yescharacteristic
854C22#238111yescharacteristic
855C22#238211yescharacteristic
856C22#242612yes—
857C22#242712yes—
858C22#242812yes—
859C22#242912yes—
860C22#245112yes—
861C22#245212yes—
862C22#245312yes—
863C22#245412yes—
864C22#255312yes—
865C22#255612yes—
866C22#257312yes—
867C22#258512yes—
868C22#261812yes—
869C22#261812yes—
870C22#262712yes—
871C22#262712yes—
872C22#264912yes—
873C22#265212yes—
874C22#265412yes—
875C22#265512yes—
876C22#266312yes—
877C22#266412yes—
878C22#266612yes—
879C22#266712yes—
880C22#266812yes—
881C22#267112yes—
882C22#267412yes—
883C22#267712yes—
884C22#268112yes—
885C22#268211yescharacteristic
886C22#268311yescharacteristic
887C22#268812yes—
888C22#269012yes—
889C22#269412yes—
890C22#270212yes—
891C22#270412yes—
892C22#270512yes—
893C22#270712yes—
894C22#270812yes—
895C22#271312yes—
896C22#271312yes—
897C22#271612yes—
898C22#271912yes—
899C22#272112yes—
900C22#272512yes—
901C22#272611yescharacteristic
902C22#272611yescharacteristic
903C22#272711yescharacteristic
904C22#272812yes—
905C22#272912yes—
906C22#273012yes—
907C22#273212yes—
908C22#273411yescharacteristic
909C22#275512yes—
910C22#277412yes—
911C22#279112yes—
912C22#279212yes—
913C22#280212yes—
914C22#280511yescharacteristic
915C22#280611yescharacteristic
916C22#283612yes—
917C22#283712yes—
918C22#283812yes—
919C22#283912yes—
920C4—28no—
921C4—48no—
922C4—44no—
923C4—48no—
924C4—44no—
925C4—84no—
926C4—84no—
927C4—84no—
928C4—84no—
929C2#1392011yescharacteristic
930C2#1393511yescharacteristic
931C2#1415611yescharacteristic
932C2#1428011yescharacteristic
933C2#1428611yescharacteristic
934C2#1433911yescharacteristic
935C2#1441711yescharacteristic
936C2#1442011yescharacteristic
937C2#1443911yescharacteristic
938C2#1444111yescharacteristic
939C2#1444911yescharacteristic
940C2#1446511yescharacteristic
941C2#1447411yescharacteristic
942C2#1448711yescharacteristic
943C2#1467011yescharacteristic
944C2#1654912yes—
945C2#1655012yes—
946C2#1655312yes—
947C2#1655412yes—
948C2#1659412yes—
949C2#1659512yes—
950C2#1659712yes—
951C2#1659812yes—
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
16. C2×#389C4semidirect
270. C2×C4⋊C4C4⋊C4semidirect

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×#14412
#75572
#75562
#75542