Finite Group Databasebeta

← #155227

Subgroups — #155227

Order 512.

2914 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#387C211yesmaximal, characteristic
2C2×#1445C211yesmaximal, characteristic
3C2×#1444C211yesmaximal, characteristic
4C2×#1442C212yesmaximal
5C2×#1442C211yesmaximal, characteristic
6C2×#1436C212yesmaximal
7C2×C4⋊#95C211yesmaximal, characteristic
8#7557C212yesmaximal
9#7556C212yesmaximal
10#7554C211yesmaximal, characteristic
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C4⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C2×#387—24no—
19C2×#387—24no—
20C2×#387—24no—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38#1445C418yescomplemented
39#1444—24no—
40#1442—28no—
41#1442—24no—
42#1436—28no—
43C4⋊#95—24no—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C24×C4C2312yes—
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2312yes—
54C24×C4C2311yescharacteristic
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—42no—
76C22×C4⋊C4C2×C414yes—
77C22×C4⋊C4D414yes—
78C22×C4⋊C4Q814yes—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—24no—
84C22×C42—24no—
85C22×C42—22no—
86C22×C42—22no—
87C22×C42—42no—
88C22×C42—42no—
89#387—232no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—22no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
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—42no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95—42no—
132C2×#95—42no—
133C2×#95—42no—
134C2×#95C2×C414yes—
135C2×#95C2×C418yes—
136C2×#95C2×C418yes—
137C2×#95C2×C414yes—
138C2×#95D418yes—
139C2×#95D414yes—
140C2×#95D414yes—
141C25C2411yescharacteristic
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—21no—
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—22no—
167C23×C4—22no—
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—21no—
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—21no—
211C23×C4—21no—
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×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4C22×C414yes—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C22×C414yes—
248C23×C4C22×C412yes—
249C23×C4C2×D412yes—
250C23×C4C2×D412yes—
251C23×C4C2×D412yes—
252C23×C4C2×D412yes—
253C23×C4C2×D414yes—
254C23×C4C2×D414yes—
255C23×C4C2×D412yes—
256C23×C4C2×D412yes—
257C23×C4C2×D414yes—
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×Q812yes—
262C23×C4C2×Q812yes—
263C23×C4C2×Q812yes—
264C23×C4#4114yes—
265C23×C4#4114yes—
266C23×C4#4114yes—
267C23×C4#4114yes—
268C23×C4#4114yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
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×C4⋊C4—28no—
278C2×C4⋊C4—216no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—48no—
281C2×C4⋊C4—48no—
282C2×C4⋊C4—48no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—48no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—48no—
287C2×C4⋊C4—48no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—48no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4C4⋊C4116yescomplemented
295C2×C42—28no—
296C2×C42—28no—
297C2×C42—48no—
298C2×C42—48no—
299C2×C42—48no—
300C2×C42—48no—
301C2×C42—44no—
302C2×C42—44no—
303C2×C42—44no—
304C2×C42—44no—
305#95—28no—
306#95—28no—
307#95—28no—
308#95—216no—
309#95—216no—
310#95—28no—
311#95—28no—
312#95—28no—
313#95—216no—
314#95—48no—
315#95—48no—
316#95—48no—
317#95—48no—
318#95—48no—
319#95—48no—
320#95—48no—
321#95—48no—
322C24C23×C411yescharacteristic
323C24C22×D411yescharacteristic
324C24C22×D411yescharacteristic
325C24C22×D411yescharacteristic
326C24C22×D412yes—
327C24C22×Q811yescharacteristic
328C24C2×#4111yescharacteristic
329C24C2×#4111yescharacteristic
330C24C2×#4112yes—
331C24C2×#4112yes—
332C24C2×#4112yes—
333C24C2×#4112yes—
334C24C2×#4112yes—
335C24H(5,𝔽2)12yes—
336C24H(5,𝔽2)12yes—
337C242−1+412yes—
338C242−1+412yes—
339C242−1+412yes—
340C242−1+412yes—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
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—24no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
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—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—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
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—42no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
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—41no—
537C22×C4—41no—
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—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—41no—
551C22×C4—42no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—41no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—41no—
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×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4C2×C4⋊C414yes—
622C22×C4C2×C4⋊C414yes—
623C22×C4C2×C4⋊C414yes—
624C22×C4C4×D418yes—
625C22×C4C4×D414yes—
626C22×C4C4×D414yes—
627C22×C4#12014yes—
628C22×C4C22⋊Q814yes—
629C22×C4C22⋊Q814yes—
630C22×C4#12318yes—
631C22×C4#12314yes—
632C22×C4#12414yes—
633C22×C4#12714yes—
634C4⋊C4—232no—
635C4⋊C4—416no—
636C4⋊C4—416no—
637C4⋊C4—432no—
638C42—416no—
639C42—416no—
640C23C22×C4⋊C411yescharacteristic
641C23C2×C4×D412yes—
642C23C2×C4×D411yescharacteristic
643C23C2×C4×D411yescharacteristic
644C23C4×#4112yes—
645C23C4×#4112yes—
646C23#51912yes—
647C23#52012yes—
648C23#52012yes—
649C23C2×#12011yescharacteristic
650C23C2×C22⋊Q811yescharacteristic
651C23C2×C22⋊Q811yescharacteristic
652C23C2×#12312yes—
653C23C2×#12311yescharacteristic
654C23#52512yes—
655C23#52511yescharacteristic
656C23#52511yescharacteristic
657C23C2×#12411yescharacteristic
658C23#52912yes—
659C23#52912yes—
660C23#52912yes—
661C23C2×#12711yescharacteristic
662C23#53211yescharacteristic
663C23#53211yescharacteristic
664C23#53212yes—
665C23#53312yes—
666C23#53511yescharacteristic
667C23#53511yescharacteristic
668C23#53611yescharacteristic
669C23#53611yescharacteristic
670C23#53611yescharacteristic
671C23#53612yes—
672C23#53611yescharacteristic
673C23#53712yes—
674C23#53812yes—
675C23#53912yes—
676C23#53912yes—
677C23#53912yes—
678C23#54112yes—
679C23#54112yes—
680C23#54112yes—
681C23#54112yes—
682C23#54112yes—
683C23#54212yes—
684C23#54212yes—
685C23#54212yes—
686C23#54412yes—
687C23D4212yes—
688C23D4212yes—
689C23#54612yes—
690C23#54612yes—
691C23#54612yes—
692C23#54712yes—
693C23#54712yes—
694C23#54712yes—
695C23#54712yes—
696C23#54712yes—
697C23#54712yes—
698C23#54712yes—
699C23#54812yes—
700C23#54812yes—
701C23#54812yes—
702C23#54812yes—
703C23#54812yes—
704C23D4×Q812yes—
705C23#55112yes—
706C23#55112yes—
707C23#55112yes—
708C23#55112yes—
709C23#55212yes—
710C23#55212yes—
711C23#55212yes—
712C23#55212yes—
713C23#55212yes—
714C23#55212yes—
715C23#55312yes—
716C23#55312yes—
717C23#55412yes—
718C23#55612yes—
719C23#55612yes—
720C23#55612yes—
721C23#55712yes—
722C23#55712yes—
723C23#56212yes—
724C23#56312yes—
725C23#56312yes—
726C23#56412yes—
727C2×C4—24no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—28no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
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—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
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—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
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—82no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—82no—
835C2×C4—82no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—82no—
839C2×C4—82no—
840C2×C4—82no—
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#38518yes—
856C22C2×#38511yescharacteristic
857C22#229611yescharacteristic
858C22C4×#12312yes—
859C22C4×#12411yescharacteristic
860C22C4×#12711yescharacteristic
861C22#231711yescharacteristic
862C22#232312yes—
863C22#232611yescharacteristic
864C22#232711yescharacteristic
865C22#233412yes—
866C22#233612yes—
867C22D4×C4⋊C412yes—
868C22#235112yes—
869C22#235912yes—
870C22#235912yes—
871C22#235912yes—
872C22#236112yes—
873C22#236212yes—
874C22#236212yes—
875C22#237312yes—
876C22#238212yes—
877C22#240411yescharacteristic
878C22#240611yescharacteristic
879C22#241912yes—
880C22#242112yes—
881C22#242212yes—
882C22#242212yes—
883C22#243211yescharacteristic
884C22#243211yescharacteristic
885C22#243311yescharacteristic
886C22#243611yescharacteristic
887C22#243812yes—
888C22#243812yes—
889C22#244312yes—
890C22#244612yes—
891C22#245212yes—
892C22#245312yes—
893C22#246212yes—
894C22#246312yes—
895C22#246912yes—
896C22#247212yes—
897C22#247512yes—
898C22#247812yes—
899C22#248211yescharacteristic
900C22#248411yescharacteristic
901C22#248912yes—
902C22#249812yes—
903C22#250112yes—
904C22#251912yes—
905C22#251912yes—
906C22#252112yes—
907C22#252112yes—
908C22#253012yes—
909C22#254012yes—
910C22#254211yescharacteristic
911C22#256012yes—
912C22#256511yescharacteristic
913C22#256611yescharacteristic
914C22#256811yescharacteristic
915C22#257812yes—
916C22#258512yes—
917C22#258812yes—
918C22#260412yes—
919C22#267412yes—
920C22#267612yes—
921C22#268012yes—
922C22#268112yes—
923C22#268912yes—
924C22#269612yes—
925C22#271312yes—
926C22#271612yes—
927C22#271812yes—
928C22#271912yes—
929C22#271912yes—
930C22#271912yes—
931C22#271912yes—
932C22#272212yes—
933C22#272312yes—
934C22#272612yes—
935C22#273912yes—
936C22#274512yes—
937C22#274712yes—
938C22#275512yes—
939C22#275812yes—
940C22#276712yes—
941C22#277412yes—
942C22#277612yes—
943C4—28no—
944C4—44no—
945C4—48no—
946C4—44no—
947C4—48no—
948C4—44no—
949C4—44no—
950C4—82no—
951C4—82no—
952C4—84no—
953C4—84no—
954C2#1397711yescharacteristic
955C2#1397811yescharacteristic
956C2#1411712yes—
957C2#1412811yescharacteristic
958C2#1418312yes—
959C2#1423112yes—
960C2#1440412yes—
961C2#1455712yes—
962C2#1458212yes—
963C2#1538411yescharacteristic
964C2#1538612yes—
965C2#1545311yescharacteristic
966C2#1545412yes—
967C2#1563812yes—
968C2#1564612yes—
969C2#1580412yes—
970C2#1588111yescharacteristic
971C2#1589212yes—
972C2#1591011yescharacteristic
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
38. #1445C4semidirect
294. 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×#3872
C2×#14452
C2×#14442
C2×#14422
C2×#14362
C2×C4⋊#952
#75572
#75562
#75542