Finite Group Databasebeta

← #157452

Subgroups — #157452

Order 512.

3208 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#391C211yesmaximal, characteristic
2C2×#1446C212yesmaximal
3C2×#1445C211yesmaximal, characteristic
4C2×#1444C211yesmaximal, characteristic
5C2×#1441C211yesmaximal, characteristic
6C2×#1436C212yesmaximal
7#7557C212yesmaximal
8#7557C211yesmaximal, characteristic
9#7556C211yesmaximal, characteristic
10#7556C212yesmaximal
11#7556C211yesmaximal, characteristic
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C4⋊C4C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×#391—24no—
18C2×#391—24no—
19C2×#391—24no—
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2211yescharacteristic
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38#1446—28no—
39#1445—24no—
40#1444—24no—
41#1441—24no—
42#1436—28no—
43C23×Q8—22no—
44C23×Q8—22no—
45C23×Q8—22no—
46C23×Q8—24no—
47C23×Q8—22no—
48C23×Q8—22no—
49C23×Q8—22no—
50C23×Q8—24no—
51C23×Q8—42no—
52C23×Q8—42no—
53C23×Q8Q814yes—
54C24×C4C2311yescharacteristic
55C24×C4C2312yes—
56C24×C4C2312yes—
57C24×C4C2312yes—
58C24×C4C2311yescharacteristic
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2312yes—
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C22×C4⋊C4—24no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—22no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—42no—
78C22×C4⋊C4—42no—
79C22×C4⋊C4—42no—
80C22×C4⋊C4—42no—
81C22×C4⋊C4D414yes—
82C22×C42—22no—
83C22×C42—22no—
84C22×C42—22no—
85C22×C42—24no—
86C22×C42—42no—
87#391—232no—
88C2×#95—24no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
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—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—22no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—22no—
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—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95—42no—
132C2×#95—42no—
133C2×#95—42no—
134C2×#95—42no—
135C2×#95D418yes—
136C2×#95D414yes—
137C2×#95D414yes—
138C2×#95Q818yescomplemented
139C25C2411yescharacteristic
140C22×Q8—28no—
141C22×Q8—28no—
142C22×Q8—28no—
143C22×Q8—28no—
144C22×Q8—28no—
145C22×Q8—28no—
146C22×Q8—28no—
147C22×Q8—216no—
148C22×Q8—48no—
149C22×Q8—48no—
150C22×Q8—48no—
151C22×Q8—48no—
152C22×Q8—48no—
153C22×Q8—48no—
154C22×Q8—48no—
155C22×Q8—48no—
156C22×Q8—48no—
157C22×Q8—44no—
158C22×Q8—44no—
159C22×Q8—48no—
160C22×Q8—48no—
161C22×Q8—44no—
162C22×Q8—44no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
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—21no—
219C23×C4—21no—
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×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4C2×D412yes—
268C23×C4C2×D414yes—
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4C2×D412yes—
272C23×C4C2×D414yes—
273C23×C4C2×D412yes—
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D412yes—
277C23×C4C2×D412yes—
278C23×C4C2×D414yes—
279C23×C4C2×Q814yes—
280C23×C4C2×Q812yes—
281C23×C4C2×Q812yes—
282C23×C4C2×Q814yes—
283C23×C4C2×Q814yes—
284C23×C4C2×Q812yes—
285C23×C4#4114yes—
286C23×C4#4112yes—
287C23×C4#4112yes—
288C23×C4#4114yes—
289C23×C4#4114yes—
290C23×C4#4114yes—
291C23×C4#4112yes—
292C2×C4⋊C4—216no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—48no—
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—44no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—48no—
309C2×C42—28no—
310C2×C42—48no—
311C2×C42—48no—
312C2×C42—44no—
313C2×C42—44no—
314#95—28no—
315#95—28no—
316#95—28no—
317#95—28no—
318#95—28no—
319#95—216no—
320#95—216no—
321#95—48no—
322#95—48no—
323#95—48no—
324#95—48no—
325#95—48no—
326#95—48no—
327#95—48no—
328#95—44no—
329#95—44no—
330#95—48no—
331#95—48no—
332C24C22×D411yescharacteristic
333C24C22×D411yescharacteristic
334C24C22×D411yescharacteristic
335C24C22×D412yes—
336C24C22×Q811yescharacteristic
337C24C22×Q812yes—
338C24C2×#4111yescharacteristic
339C24C2×#4112yes—
340C24C2×#4111yescharacteristic
341C24C2×#4111yescharacteristic
342C24C2×#4112yes—
343C24C2×#4112yes—
344C24C2×#4112yes—
345C24H(5,𝔽2)12yes—
346C24H(5,𝔽2)12yes—
347C24H(5,𝔽2)12yes—
348C242−1+412yes—
349C242−1+412yes—
350C242−1+412yes—
351C2×Q8—232no—
352C2×Q8—432no—
353C2×Q8—432no—
354C2×Q8—416no—
355C2×Q8—416no—
356C2×Q8—432no—
357C2×Q8—432no—
358C2×Q8—416no—
359C2×Q8—416no—
360C2×Q8—416no—
361C2×Q8—416no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
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—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
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—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—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
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—41no—
546C22×C4—41no—
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—41no—
561C22×C4—42no—
562C22×C4—41no—
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×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#12014yes—
645C22×C4C22⋊Q818yes—
646C22×C4C22⋊Q814yes—
647C22×C4C22⋊Q814yes—
648C22×C4C22⋊Q814yes—
649C22×C4C22⋊Q818yes—
650C22×C4#12318yes—
651C22×C4#12314yes—
652C22×C4#12414yes—
653C22×C4#12714yes—
654C22×C4C4⋊Q814yes—
655C4⋊C4—416no—
656C4⋊C4—416no—
657C4⋊C4—432no—
658C42—416no—
659C23C2×#12011yescharacteristic
660C23C2×C22⋊Q811yescharacteristic
661C23C2×C22⋊Q811yescharacteristic
662C23C2×C22⋊Q812yes—
663C23C2×C22⋊Q812yes—
664C23C2×C22⋊Q811yescharacteristic
665C23C2×#12312yes—
666C23C2×#12311yescharacteristic
667C23#52512yes—
668C23#52511yescharacteristic
669C23#52511yescharacteristic
670C23#52511yescharacteristic
671C23#52511yescharacteristic
672C23#52511yescharacteristic
673C23C2×#12411yescharacteristic
674C23#52912yes—
675C23#52912yes—
676C23#52912yes—
677C23C2×#12711yescharacteristic
678C23C2×C4⋊Q811yescharacteristic
679C23#53312yes—
680C23#53312yes—
681C23#53312yes—
682C23#53411yescharacteristic
683C23#53511yescharacteristic
684C23#53511yescharacteristic
685C23#53611yescharacteristic
686C23#53612yes—
687C23#53611yescharacteristic
688C23#53611yescharacteristic
689C23#53712yes—
690C23#53812yes—
691C23#53812yes—
692C23#53812yes—
693C23#53912yes—
694C23#53912yes—
695C23#54112yes—
696C23#54112yes—
697C23#54112yes—
698C23#54212yes—
699C23#54212yes—
700C23#54212yes—
701C23#54212yes—
702C23#54212yes—
703C23#54312yes—
704C23#54412yes—
705C23#54412yes—
706C23D4212yes—
707C23D4212yes—
708C23#54612yes—
709C23#54612yes—
710C23#54612yes—
711C23#54612yes—
712C23#54612yes—
713C23#54612yes—
714C23#54612yes—
715C23#54712yes—
716C23#54712yes—
717C23#54712yes—
718C23#54812yes—
719C23#54812yes—
720C23#54812yes—
721C23D4×Q812yes—
722C23D4×Q812yes—
723C23D4×Q812yes—
724C23#55112yes—
725C23#55112yes—
726C23#55112yes—
727C23#55412yes—
728C23#55412yes—
729C23#55412yes—
730C23#55512yes—
731C23#55612yes—
732C23#55612yes—
733C23#55612yes—
734C23#55612yes—
735C23#55612yes—
736C23#55712yes—
737C23#55712yes—
738C23#55712yes—
739C23#55712yes—
740C23Q8212yes—
741C23#55912yes—
742C23#56212yes—
743C23#56212yes—
744C23#56312yes—
745C23#56312yes—
746Q8—464no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
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—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
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—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
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—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
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—82no—
874C2×C4—82no—
875C2×C4#39918yes—
876C22C2×#39911yescharacteristic
877C22#239811yescharacteristic
878C22#239911yescharacteristic
879C22#240411yescharacteristic
880C22#240511yescharacteristic
881C22#240611yescharacteristic
882C22#241812yes—
883C22#241812yes—
884C22#243311yescharacteristic
885C22#243411yescharacteristic
886C22#243611yescharacteristic
887C22#243712yes—
888C22#243712yes—
889C22#243912yes—
890C22#244012yes—
891C22#244612yes—
892C22#244612yes—
893C22#244712yes—
894C22#244712yes—
895C22#244912yes—
896C22#245012yes—
897C22#245112yes—
898C22#245112yes—
899C22#245112yes—
900C22#245312yes—
901C22#245312yes—
902C22#245312yes—
903C22#245912yes—
904C22#246312yes—
905C22#246512yes—
906C22#246512yes—
907C22#246512yes—
908C22#246912yes—
909C22#246912yes—
910C22#247212yes—
911C22#247412yes—
912C22#247412yes—
913C22#248211yescharacteristic
914C22#249212yes—
915C22#252312yes—
916C22#253911yescharacteristic
917C22#254012yes—
918C22#254212yes—
919C22#255012yes—
920C22#256711yescharacteristic
921C22#256811yescharacteristic
922C22#257412yes—
923C22#258111yescharacteristic
924C22#258111yescharacteristic
925C22#258112yes—
926C22#258212yes—
927C22#258812yes—
928C22#258912yes—
929C22#260512yes—
930C22#262512yes—
931C22#262611yescharacteristic
932C22#263211yescharacteristic
933C22#263411yescharacteristic
934C22#265312yes—
935C22#266612yes—
936C22#267612yes—
937C22#267712yes—
938C22#268012yes—
939C22#268112yes—
940C22#268612yes—
941C22#269612yes—
942C22#270012yes—
943C22#270012yes—
944C22#270412yes—
945C22#271012yes—
946C22#271312yes—
947C22#271512yes—
948C22#271612yes—
949C22#271612yes—
950C22#272012yes—
951C22#272912yes—
952C22#275512yes—
953C22#275912yes—
954C22#278912yes—
955C22#279812yes—
956C22#279912yes—
957C22#280612yes—
958C22#280612yes—
959C22#280912yes—
960C22#283112yes—
961C22#284811yescharacteristic
962C22#285512yes—
963C4—28no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—44no—
969C4—48no—
970C4—84no—
971C4—84no—
972C4—82no—
973C4—84no—
974C2#1473411yescharacteristic
975C2#1479712yes—
976C2#1480012yes—
977C2#1488111yescharacteristic
978C2#1488411yescharacteristic
979C2#1519312yes—
980C2#1533212yes—
981C2#1533312yes—
982C2#1543011yescharacteristic
983C2#1545311yescharacteristic
984C2#1578311yescharacteristic
985C2#1582512yes—
986C2#1596312yes—
987C2#1596512yes—
988C2#1603211yescharacteristic
989C2#1606812yes—
990C2#1627812yes—
991C2#1627912yes—
992C2#1663112yes—
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
138. C2×#95Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#3912
C2×#14462
C2×#14452
C2×#14442
C2×#14412
C2×#14362
#75572
#75562