Finite Group Databasebeta

← #154113

Subgroups — #154113

Order 512.

2854 conjugacy classes of subgroups.

The subgroup lattice has 1009 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C4⋊C4C211yesmaximal, characteristic
2C2×#1443C212yesmaximal
3C2×#1434C211yesmaximal, characteristic
4C2×#1434C211yesmaximal, characteristic
5#7557C212yesmaximal
6#7557C212yesmaximal
7#7556C212yesmaximal
8#7554C211yesmaximal, characteristic
9#7554C211yesmaximal, characteristic
10#7554C211yesmaximal, characteristic
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×C4×C4⋊C4—28no—
18C2×C4×C4⋊C4C418yescomplemented
19C22×#95C2211yescharacteristic
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37#1443—28no—
38#1434—24no—
39#1434—24no—
40C24×C4C2312yes—
41C24×C4C2312yes—
42C24×C4C2312yes—
43C24×C4C2312yes—
44C24×C4C2311yescharacteristic
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C22×C4⋊C4—24no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4C2×C414yes—
60C22×C4⋊C4C2×C414yes—
61C22×C42—24no—
62C22×C42—22no—
63C22×C42—22no—
64C22×C42—24no—
65C22×C42—22no—
66C22×C42—22no—
67C22×C42—24no—
68C22×C42—24no—
69C22×C42—22no—
70C22×C42—22no—
71C22×C42—42no—
72C22×C42—42no—
73C22×C42C2×C414yes—
74C22×C42C2×C414yes—
75C22×C42C2×C414yes—
76C4×C4⋊C4—232no—
77C2×#95—24no—
78C2×#95—22no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—22no—
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—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—22no—
113C2×#95—22no—
114C2×#95—42no—
115C2×#95—42no—
116C2×#95—42no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—42no—
123C2×#95—42no—
124C2×#95C2×C414yes—
125C2×#95C2×C414yes—
126C2×#95D414yes—
127C2×#95D418yes—
128C2×#95Q814yes—
129C25C2411yescharacteristic
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—22no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
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—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
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×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4C22×C412yes—
241C23×C4C22×C412yes—
242C23×C4C22×C412yes—
243C23×C4C22×C412yes—
244C23×C4C22×C412yes—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C2×D414yes—
248C23×C4C2×D414yes—
249C23×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4C2×D412yes—
252C23×C4C2×Q814yes—
253C23×C4C2×Q812yes—
254C23×C4#4114yes—
255C23×C4#4114yes—
256C23×C4#4114yes—
257C23×C4#4112yes—
258C23×C4#4112yes—
259C23×C4#4112yes—
260C23×C4#4112yes—
261C23×C4#4114yes—
262C23×C4#4112yes—
263C23×C4#4112yes—
264C23×C4#4114yes—
265C23×C4#4112yes—
266C23×C4#4112yes—
267C2×C4⋊C4—216no—
268C2×C4⋊C4—216no—
269C2×C4⋊C4—216no—
270C2×C4⋊C4—216no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C42—216no—
278C2×C42—216no—
279C2×C42—28no—
280C2×C42—28no—
281C2×C42—28no—
282C2×C42—28no—
283C2×C42—28no—
284C2×C42—28no—
285C2×C42—28no—
286C2×C42—44no—
287C2×C42—44no—
288C2×C42—48no—
289C2×C42—48no—
290C2×C42—48no—
291C2×C42—48no—
292#95—216no—
293#95—28no—
294#95—28no—
295#95—28no—
296#95—48no—
297#95—48no—
298#95—48no—
299#95—48no—
300#95—48no—
301#95—48no—
302#95—48no—
303#95—48no—
304#95—48no—
305#95—44no—
306#95—48no—
307#95—48no—
308#95—44no—
309#95C22⋊C4116yes—
310C24C23×C411yescharacteristic
311C24C22×D412yes—
312C24C22×D411yescharacteristic
313C24C22×Q811yescharacteristic
314C24C2×#4111yescharacteristic
315C24C2×#4111yescharacteristic
316C24C2×#4112yes—
317C24C2×#4112yes—
318C24C2×#4112yes—
319C24C2×#4111yescharacteristic
320C24C2×#4111yescharacteristic
321C24C2×#4111yescharacteristic
322C24C2×#4111yescharacteristic
323C24C2×#4111yescharacteristic
324C24C2×#4111yescharacteristic
325C24C2×#4112yes—
326C24C2×#4112yes—
327C24H(5,𝔽2)12yes—
328C24H(5,𝔽2)11yescharacteristic
329C24H(5,𝔽2)11yescharacteristic
330C242−1+412yes—
331C242−1+411yescharacteristic
332C242−1+411yescharacteristic
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
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—22no—
351C22×C4—24no—
352C22×C4—24no—
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—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
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—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—22no—
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—22no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
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—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—41no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
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—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—41no—
502C22×C4—41no—
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×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
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—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×C4C2×C22⋊C414yes—
618C22×C4C2×C22⋊C414yes—
619C22×C4C2×C22⋊C414yes—
620C22×C4#11714yes—
621C22×C4#11714yes—
622C22×C4#11714yes—
623C22×C4#11714yes—
624C22×C4#11714yes—
625C22×C4#11714yes—
626C22×C4C4×D414yes—
627C22×C4C4×Q814yes—
628C22×C4C22⋊Q814yes—
629C22×C4#12314yes—
630C22×C4#12514yes—
631C22×C4#12618yes—
632C22×C4#12618yes—
633C22×C4#12614yes—
634C4⋊C4—232no—
635C4⋊C4—232no—
636C42—232no—
637C42—416no—
638C42—416no—
639C23C22×C22⋊C411yescharacteristic
640C23C2×#11711yescharacteristic
641C23C2×#11711yescharacteristic
642C23C2×#11711yescharacteristic
643C23C2×#11711yescharacteristic
644C23C2×#11711yescharacteristic
645C23C2×#11711yescharacteristic
646C23C2×C4×D411yescharacteristic
647C23C2×C4×Q811yescharacteristic
648C23C4×#4111yescharacteristic
649C23C4×#4111yescharacteristic
650C23#51811yescharacteristic
651C23#51911yescharacteristic
652C23#52011yescharacteristic
653C23#52011yescharacteristic
654C23C2×C22⋊Q811yescharacteristic
655C23C2×#12311yescharacteristic
656C23#52512yes—
657C23#52512yes—
658C23#52512yes—
659C23#52512yes—
660C23#52512yes—
661C23#52512yes—
662C23#52512yes—
663C23C2×#12511yescharacteristic
664C23C2×#12612yes—
665C23C2×#12612yes—
666C23C2×#12611yescharacteristic
667C23#52911yescharacteristic
668C23#52912yes—
669C23#52911yescharacteristic
670C23#52912yes—
671C23#52912yes—
672C23#52912yes—
673C23#52911yescharacteristic
674C23#52912yes—
675C23#52911yescharacteristic
676C23#52912yes—
677C23#52912yes—
678C23#52912yes—
679C23#52912yes—
680C23#52912yes—
681C23#53212yes—
682C23#53312yes—
683C23#53312yes—
684C23#53812yes—
685C23#53912yes—
686C23#53912yes—
687C23#53912yes—
688C23#54011yescharacteristic
689C23#54012yes—
690C23#54111yescharacteristic
691C23#54112yes—
692C23#54112yes—
693C23#54211yescharacteristic
694C23#54211yescharacteristic
695C23#54212yes—
696C23#54212yes—
697C23#54212yes—
698C23D4212yes—
699C23#54612yes—
700C23#54612yes—
701C23#54612yes—
702C23#54611yescharacteristic
703C23#54712yes—
704C23#54712yes—
705C23#54712yes—
706C23#54711yescharacteristic
707C23#54812yes—
708C23#54811yescharacteristic
709C23D4×Q812yes—
710C23#55011yescharacteristic
711C23#55112yes—
712C23#55212yes—
713C23#55212yes—
714C23#55212yes—
715C23#55212yes—
716C23#55211yescharacteristic
717C23#55312yes—
718C23#55312yes—
719C23#55312yes—
720C23#55312yes—
721C23#55311yescharacteristic
722C23#55411yescharacteristic
723C23#55412yes—
724C23#55411yescharacteristic
725C23#55512yes—
726C23#55511yescharacteristic
727C23#55612yes—
728C23#55612yes—
729C23#55611yescharacteristic
730C23#55612yes—
731C23#55611yescharacteristic
732C23#55611yescharacteristic
733C23#55711yescharacteristic
734C23#55711yescharacteristic
735C23#55912yes—
736C23#55911yescharacteristic
737C23#55911yescharacteristic
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
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—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
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—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—82no—
842C2×C4—82no—
843C2×C4—82no—
844C2×C4—82no—
845C2×C4—82no—
846C2×C4—82no—
847C2×C4—82no—
848C2×C4—82no—
849C2×C4—82no—
850C2×C4—82no—
851C2×C4—82no—
852C2×C4—82no—
853C2×C4—82no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—82no—
857C2×C4—82no—
858C2×C4—82no—
859C2×C4—82no—
860C2×C4—82no—
861C2×C4—82no—
862C2×C4—82no—
863C2×C4—82no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4—82no—
867C2×C4—82no—
868C2×C4—82no—
869C2×C4—82no—
870C2×C4—82no—
871C2×C4—82no—
872C2×C4—82no—
873C2×C4#38318yes—
874C2×C4#38718yes—
875C22#228011yescharacteristic
876C22#228011yescharacteristic
877C22#228011yescharacteristic
878C22C2×#38311yescharacteristic
879C22#228311yescharacteristic
880C22#228311yescharacteristic
881C22#228311yescharacteristic
882C22C2×#38711yescharacteristic
883C22#229011yescharacteristic
884C22#229311yescharacteristic
885C22#229511yescharacteristic
886C22#229511yescharacteristic
887C22#229811yescharacteristic
888C22#231311yescharacteristic
889C22#231411yescharacteristic
890C22#231811yescharacteristic
891C22#231911yescharacteristic
892C22#232011yescharacteristic
893C22#232011yescharacteristic
894C22D4×C22⋊C411yescharacteristic
895C22#233911yescharacteristic
896C22#233911yescharacteristic
897C22Q8×C22⋊C411yescharacteristic
898C22#234411yescharacteristic
899C22#234511yescharacteristic
900C22#234611yescharacteristic
901C22#234711yescharacteristic
902C22#235211yescharacteristic
903C22#235311yescharacteristic
904C22#235411yescharacteristic
905C22#235511yescharacteristic
906C22#235511yescharacteristic
907C22#235611yescharacteristic
908C22#235611yescharacteristic
909C22#235711yescharacteristic
910C22#239512yes—
911C22#239612yes—
912C22#240112yes—
913C22#240212yes—
914C22#244312yes—
915C22#244711yescharacteristic
916C22#244811yescharacteristic
917C22#244912yes—
918C22#245311yescharacteristic
919C22#245411yescharacteristic
920C22#245512yes—
921C22#245612yes—
922C22#245712yes—
923C22#245812yes—
924C22#245812yes—
925C22#245912yes—
926C22#246112yes—
927C22#246212yes—
928C22#246212yes—
929C22#246412yes—
930C22#246512yes—
931C22#246512yes—
932C22#246612yes—
933C22#246812yes—
934C22#246912yes—
935C22#246912yes—
936C22#247012yes—
937C22#247312yes—
938C22#247412yes—
939C22#247412yes—
940C22#247512yes—
941C22#247612yes—
942C22#247812yes—
943C22#248112yes—
944C22#249412yes—
945C22#249512yes—
946C22#249612yes—
947C22#249712yes—
948C22#250811yescharacteristic
949C22#250911yescharacteristic
950C22#251112yes—
951C22#251212yes—
952C22#251311yescharacteristic
953C22#251312yes—
954C22#251412yes—
955C22#251411yescharacteristic
956C22#252812yes—
957C22#252912yes—
958C22#257512yes—
959C22#257712yes—
960C22#258712yes—
961C22#258812yes—
962C22#259412yes—
963C22#259412yes—
964C22#259512yes—
965C22#259612yes—
966C22#265012yes—
967C22#265112yes—
968C22#265412yes—
969C22#265512yes—
970C22#285212yes—
971C22#285212yes—
972C22#285212yes—
973C22#285212yes—
974C4—28no—
975C4—28no—
976C4—44no—
977C4—44no—
978C4—44no—
979C4—44no—
980C4—44no—
981C4—84no—
982C4—84no—
983C4—84no—
984C4—84no—
985C2#1384611yescharacteristic
986C2#1388211yescharacteristic
987C2#1388511yescharacteristic
988C2#1388611yescharacteristic
989C2#1389711yescharacteristic
990C2#1391211yescharacteristic
991C2#1392111yescharacteristic
992C2#1392711yescharacteristic
993C2#1392711yescharacteristic
994C2#1393211yescharacteristic
995C2#1393611yescharacteristic
996C2#1394311yescharacteristic
997C2#1395011yescharacteristic
998C2#1435211yescharacteristic
999C2#1468311yescharacteristic
1000C2#1478212yes—
1001C2#1478312yes—
1002C2#1479112yes—
1003C2#1479212yes—
1004C2#1484812yes—
1005C2#1484912yes—
1006C2#1485612yes—
1007C2#1485712yes—
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
18. C2×C4×C4⋊C4C4semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C4⋊C42
C2×#14432
C2×#14342
#75572
#75562
#75542