Finite Group Databasebeta

← #155939

Subgroups — #155939

Order 512.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#391C211yesmaximal, characteristic
2C2×#1446C211yesmaximal, characteristic
3C2×#1446C211yesmaximal, characteristic
4C2×#1444C211yesmaximal, characteristic
5C2×#1442C212yesmaximal
6C2×#1434C211yesmaximal, characteristic
7#7557C211yesmaximal, characteristic
8#7557C212yesmaximal
9#7556C212yesmaximal
10#7556C212yesmaximal
11#7554C211yesmaximal, characteristic
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C42C2211yescharacteristic
16C2×#391—24no—
17C2×#391—28no—
18C22×#95C2211yescharacteristic
19C22×#95C2211yescharacteristic
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2212yes—
37#1446—24no—
38#1446C418yescomplemented
39#1444—24no—
40#1442—28no—
41#1434—24no—
42C23×Q8—24no—
43C23×Q8—22no—
44C23×Q8—22no—
45C23×Q8—24no—
46C23×Q8—22no—
47C23×Q8—22no—
48C23×Q8—22no—
49C23×Q8—22no—
50C23×Q8—42no—
51C23×Q8—42no—
52C23×Q8C2×C414yes—
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2312yes—
56C24×C4C2311yescharacteristic
57C24×C4C2311yescharacteristic
58C24×C4C2312yes—
59C24×C4C2312yes—
60C24×C4C2312yes—
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C22×C4⋊C4—24no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—42no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—42no—
76C22×C42—24no—
77C22×C42—22no—
78C22×C42—22no—
79C22×C42—42no—
80C22×C42D414yes—
81#391—232no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—24no—
85C2×#95—22no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—22no—
92C2×#95—24no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—22no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—42no—
113C2×#95—42no—
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×#95—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95C2×C414yes—
129C2×#95C2×C418yes—
130C2×#95C2×C414yes—
131C2×#95C2×C418yes—
132C2×#95D418yes—
133C2×#95D414yes—
134C2×#95Q818yescomplemented
135C25C2411yescharacteristic
136C22×Q8—28no—
137C22×Q8—216no—
138C22×Q8—28no—
139C22×Q8—28no—
140C22×Q8—216no—
141C22×Q8—28no—
142C22×Q8—28no—
143C22×Q8—48no—
144C22×Q8—48no—
145C22×Q8—48no—
146C22×Q8—48no—
147C22×Q8—48no—
148C22×Q8—48no—
149C22×Q8—48no—
150C22×Q8—48no—
151C22×Q8—48no—
152C22×Q8—44no—
153C22×Q8—44no—
154C22×Q8—48no—
155C22×Q8—44no—
156C22×Q8—44no—
157C22×Q8—44no—
158C22×Q8—44no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
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—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—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—22no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—22no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—21no—
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—21no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—21no—
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—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—21no—
261C23×C4—22no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4C22×C412yes—
274C23×C4C22×C412yes—
275C23×C4C22×C414yes—
276C23×C4C22×C414yes—
277C23×C4C22×C412yes—
278C23×C4C2×D414yes—
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2×D414yes—
282C23×C4C2×D412yes—
283C23×C4C2×D414yes—
284C23×C4C2×D412yes—
285C23×C4C2×D412yes—
286C23×C4C2×D412yes—
287C23×C4C2×Q814yes—
288C23×C4C2×Q814yes—
289C23×C4C2×Q814yes—
290C23×C4#4114yes—
291C23×C4#4114yes—
292C23×C4#4112yes—
293C23×C4#4112yes—
294C23×C4#4112yes—
295C23×C4#4112yes—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—48no—
298C2×C4⋊C4—48no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—48no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—48no—
304C2×C4⋊C4—48no—
305C2×C4⋊C4—48no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4—44no—
308C2×C42—28no—
309C2×C42—28no—
310C2×C42—44no—
311C2×C42—48no—
312C2×C42—48no—
313#95—216no—
314#95—28no—
315#95—216no—
316#95—28no—
317#95—216no—
318#95—28no—
319#95—48no—
320#95—48no—
321#95—48no—
322#95—48no—
323#95—48no—
324#95—48no—
325#95—44no—
326#95—44no—
327#95—44no—
328#95—48no—
329#95—48no—
330#95—44no—
331#95—44no—
332C24C23×C411yescharacteristic
333C24C22×D411yescharacteristic
334C24C22×D412yes—
335C24C22×D411yescharacteristic
336C24C22×Q812yes—
337C24C2×#4111yescharacteristic
338C24C2×#4111yescharacteristic
339C24C2×#4111yescharacteristic
340C24C2×#4111yescharacteristic
341C24C2×#4112yes—
342C24C2×#4112yes—
343C24H(5,𝔽2)12yes—
344C24H(5,𝔽2)12yes—
345C24H(5,𝔽2)11yescharacteristic
346C24H(5,𝔽2)12yes—
347C24H(5,𝔽2)11yescharacteristic
348C242−1+411yescharacteristic
349C242−1+411yescharacteristic
350C242−1+411yescharacteristic
351C242−1+411yescharacteristic
352C242−1+411yescharacteristic
353C242−1+412yes—
354C242−1+411yescharacteristic
355C2×Q8—232no—
356C2×Q8—432no—
357C2×Q8—432no—
358C2×Q8—416no—
359C2×Q8—416no—
360C2×Q8—416no—
361C2×Q8—432no—
362C2×Q8—432no—
363C2×Q8—416no—
364C2×Q8—416no—
365C2×Q8—416no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
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—22no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
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—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
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—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—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
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—41no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—41no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—42no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—42no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—41no—
572C22×C4—41no—
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—41no—
583C22×C4—41no—
584C22×C4—42no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—41no—
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—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4#11714yes—
657C22×C4C4×D418yes—
658C22×C4C4×D414yes—
659C22×C4C4×D414yes—
660C22×C4C4×Q818yes—
661C22×C4#12014yes—
662C22×C4#12114yes—
663C22×C4#12314yes—
664C22×C4#12414yes—
665C22×C4#12614yes—
666C22×C4C4⋊Q814yes—
667C4⋊C4—416no—
668C4⋊C4—432no—
669C42—416no—
670C23C2×#11711yescharacteristic
671C23C2×C4×D411yescharacteristic
672C23C2×C4×D412yes—
673C23C2×C4×D411yescharacteristic
674C23C2×C4×Q812yes—
675C23#51812yes—
676C23#51911yescharacteristic
677C23#51911yescharacteristic
678C23#52011yescharacteristic
679C23#52011yescharacteristic
680C23#52012yes—
681C23C2×#12011yescharacteristic
682C23C2×#12111yescharacteristic
683C23C2×#12311yescharacteristic
684C23#52511yescharacteristic
685C23#52512yes—
686C23C2×#12411yescharacteristic
687C23C2×#12611yescharacteristic
688C23C2×C4⋊Q811yescharacteristic
689C23#53211yescharacteristic
690C23#53312yes—
691C23#53411yescharacteristic
692C23#53511yescharacteristic
693C23#53511yescharacteristic
694C23#53512yes—
695C23#53511yescharacteristic
696C23#53611yescharacteristic
697C23#53611yescharacteristic
698C23#53611yescharacteristic
699C23#53612yes—
700C23#53612yes—
701C23#53611yescharacteristic
702C23#53611yescharacteristic
703C23#53611yescharacteristic
704C23#53711yescharacteristic
705C23#53711yescharacteristic
706C23#53712yes—
707C23#53812yes—
708C23#53812yes—
709C23#53912yes—
710C23#54111yescharacteristic
711C23#54111yescharacteristic
712C23#54111yescharacteristic
713C23#54111yescharacteristic
714C23#54111yescharacteristic
715C23#54111yescharacteristic
716C23#54112yes—
717C23#54111yescharacteristic
718C23#54111yescharacteristic
719C23#54212yes—
720C23#54211yescharacteristic
721C23#54211yescharacteristic
722C23#54211yescharacteristic
723C23#54211yescharacteristic
724C23#54211yescharacteristic
725C23#54211yescharacteristic
726C23#54212yes—
727C23#54211yescharacteristic
728C23#54211yescharacteristic
729C23#54212yes—
730C23#54212yes—
731C23#54212yes—
732C23#54212yes—
733C23#54312yes—
734C23#54412yes—
735C23#54412yes—
736C23#54412yes—
737C23D4212yes—
738C23#54612yes—
739C23#54612yes—
740C23#54612yes—
741C23#54612yes—
742C23#54612yes—
743C23#54612yes—
744C23#54712yes—
745C23D4×Q812yes—
746C23D4×Q812yes—
747C23D4×Q812yes—
748C23#55112yes—
749C23#55112yes—
750C23#55112yes—
751C23#55212yes—
752C23#55212yes—
753C23#55412yes—
754C23#55412yes—
755C23#55412yes—
756C23#55612yes—
757C23#55612yes—
758C23#55712yes—
759C23#55712yes—
760C23#55912yes—
761C23H(3,𝔽4)12yes—
762C23#56212yes—
763C23#56212yes—
764C23#56212yes—
765C23#56212yes—
766C23#56312yes—
767C23#56312yes—
768C23#56312yes—
769Q8—464no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—28no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—44no—
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—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—42no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—82no—
871C2×C4—81no—
872C2×C4—82no—
873C2×C4—82no—
874C2×C4—82no—
875C2×C4—81no—
876C2×C4—81no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—82no—
880C2×C4—81no—
881C2×C4—82no—
882C2×C4—81no—
883C2×C4—82no—
884C2×C4—82no—
885C2×C4—81no—
886C2×C4—82no—
887C2×C4—82no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—81no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—82no—
900C2×C4—82no—
901C2×C4—82no—
902C2×C4—82no—
903C2×C4—82no—
904C2×C4—82no—
905C2×C4—81no—
906C2×C4#38818yes—
907C22C2×#38811yescharacteristic
908C22C4×#12011yescharacteristic
909C22C4×C4⋊Q811yescharacteristic
910C22#232011yescharacteristic
911C22#232011yescharacteristic
912C22#232111yescharacteristic
913C22#232311yescharacteristic
914C22#232312yes—
915C22#232311yescharacteristic
916C22#232611yescharacteristic
917C22#232612yes—
918C22#232611yescharacteristic
919C22#232711yescharacteristic
920C22#232912yes—
921C22#233112yes—
922C22#234212yes—
923C22#235512yes—
924C22#235812yes—
925C22#236012yes—
926C22#236012yes—
927C22#236512yes—
928C22#237812yes—
929C22#237912yes—
930C22#240511yescharacteristic
931C22#240811yescharacteristic
932C22#243011yescharacteristic
933C22#243411yescharacteristic
934C22#246212yes—
935C22#246512yes—
936C22#247212yes—
937C22#248012yes—
938C22#248211yescharacteristic
939C22#249212yes—
940C22#249911yescharacteristic
941C22#250211yescharacteristic
942C22#251112yes—
943C22#253411yescharacteristic
944C22#254411yescharacteristic
945C22#254611yescharacteristic
946C22#258411yescharacteristic
947C22#260411yescharacteristic
948C22#261411yescharacteristic
949C22#261511yescharacteristic
950C22#262011yescharacteristic
951C22#262111yescharacteristic
952C22#262511yescharacteristic
953C22#262511yescharacteristic
954C22#263212yes—
955C22#263211yescharacteristic
956C22#263712yes—
957C22#263711yescharacteristic
958C22#264011yescharacteristic
959C22#264211yescharacteristic
960C22#264511yescharacteristic
961C22#264511yescharacteristic
962C22#265911yescharacteristic
963C22#266011yescharacteristic
964C22#266211yescharacteristic
965C22#266311yescharacteristic
966C22#266512yes—
967C22#266612yes—
968C22#267012yes—
969C22#267212yes—
970C22#267712yes—
971C22#267712yes—
972C22#268712yes—
973C22#268712yes—
974C22#268912yes—
975C22#269212yes—
976C22#269212yes—
977C22#269212yes—
978C22#269812yes—
979C22#270012yes—
980C22#270012yes—
981C22#270412yes—
982C22#270412yes—
983C22#271012yes—
984C22#271212yes—
985C22#271312yes—
986C22#271312yes—
987C22#271312yes—
988C22#275412yes—
989C22#275512yes—
990C22#275512yes—
991C22#275512yes—
992C22#275812yes—
993C22#275912yes—
994C22#276212yes—
995C22#276312yes—
996C22#276312yes—
997C22#276412yes—
998C22#279812yes—
999C22#279912yes—
1000C22#281411yescharacteristic
1001C22#281611yescharacteristic
1002C22#281911yescharacteristic
1003C22#282111yescharacteristic
1004C22#283112yes—
1005C22#283212yes—
1006C4—28no—
1007C4—48no—
1008C4—44no—
1009C4—44no—
1010C4—48no—
1011C4—82no—
1012C4—84no—
1013C4—82no—
1014C4—82no—
1015C4—82no—
1016C4—84no—
1017C2#1399111yescharacteristic
1018C2#1400011yescharacteristic
1019C2#1418611yescharacteristic
1020C2#1426111yescharacteristic
1021C2#1430111yescharacteristic
1022C2#1432711yescharacteristic
1023C2#1437812yes—
1024C2#1443012yes—
1025C2#1452412yes—
1026C2#1457512yes—
1027C2#1462511yescharacteristic
1028C2#1636411yescharacteristic
1029C2#1636511yescharacteristic
1030C2#1637512yes—
1031C2#1637712yes—
1032C2#1638812yes—
1033C2#1638912yes—
1034C2#1650411yescharacteristic
1035C2#1650711yescharacteristic
1036C2#1669411yescharacteristic
1037C2#1669611yescharacteristic
1038C2#1680311yescharacteristic
1039C2#1680611yescharacteristic
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. #1446C4semidirect
134. 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×#14442
C2×#14422
C2×#14342
#75572
#75562
#75542