Finite Group Databasebeta

← #154572

Subgroups — #154572

Order 512.

3118 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C4⋊C4C211yesmaximal, characteristic
2C2×#1444C211yesmaximal, characteristic
3C2×#1441C211yesmaximal, characteristic
4C2×#1441C211yesmaximal, characteristic
5C2×#1436C211yesmaximal, characteristic
6C2×#1436C212yesmaximal
7#7557C211yesmaximal, characteristic
8#7557C212yesmaximal
9#7556C212yesmaximal
10#7554C211yesmaximal, characteristic
11#7554C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C42C2211yescharacteristic
17C23×C42C2212yes—
18C2×C4×C4⋊C4—28no—
19C2×C4×C4⋊C4—24no—
20C22×#95C2211yescharacteristic
21C22×#95C2212yes—
22C22×#95C2211yescharacteristic
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2212yes—
37#1444—24no—
38#1441—24no—
39#1441C418yescomplemented
40#1436—24no—
41#1436—28no—
42C24×C4C2311yescharacteristic
43C24×C4C2312yes—
44C24×C4C2311yescharacteristic
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2312yes—
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—24no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4C2×C414yes—
75C22×C4⋊C4C2×C414yes—
76C22×C4⋊C4D414yes—
77C22×C42—24no—
78C22×C42—24no—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—24no—
82C22×C42—24no—
83C22×C42—42no—
84C22×C42—42no—
85C22×C42—42no—
86C22×C42—42no—
87C22×C42D414yes—
88C22×C42D418yes—
89C4×C4⋊C4—232no—
90C2×#95—22no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—24no—
105C2×#95—22no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—22no—
113C2×#95—24no—
114C2×#95—22no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—22no—
122C2×#95—24no—
123C2×#95—22no—
124C2×#95—22no—
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×#95C2×C418yes—
135C2×#95C2×C414yes—
136C2×#95C2×C418yes—
137C2×#95Q818yes—
138C2×#95Q814yes—
139C25C2411yescharacteristic
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—22no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—22no—
147C23×C4—21no—
148C23×C4—22no—
149C23×C4—21no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—21no—
164C23×C4—21no—
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—21no—
174C23×C4—22no—
175C23×C4—21no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—21no—
193C23×C4—21no—
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—21no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—22no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—22no—
237C23×C4—21no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4—21no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—21no—
250C23×C4—22no—
251C23×C4C22×C412yes—
252C23×C4C22×C414yes—
253C23×C4C22×C412yes—
254C23×C4C22×C414yes—
255C23×C4C22×C412yes—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D414yes—
264C23×C4C2×Q814yes—
265C23×C4C2×Q812yes—
266C23×C4C2×Q814yes—
267C23×C4C2×Q812yes—
268C23×C4C2×Q814yes—
269C23×C4C2×Q812yes—
270C23×C4#4112yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4112yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4#4112yes—
277C23×C4#4112yes—
278C23×C4#4112yes—
279C23×C4#4112yes—
280C23×C4#4112yes—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—216no—
284C2×C4⋊C4—216no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—216no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—216no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—216no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—48no—
296C2×C4⋊C4—48no—
297C2×C4⋊C4—48no—
298C2×C4⋊C4—48no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C42—216no—
306C2×C42—216no—
307C2×C42—28no—
308C2×C42—28no—
309C2×C42—28no—
310C2×C42—216no—
311C2×C42—48no—
312C2×C42—48no—
313C2×C42—48no—
314C2×C42—48no—
315C2×C42—48no—
316C2×C42—48no—
317#95—28no—
318#95—216no—
319#95—28no—
320#95—216no—
321#95—216no—
322#95—28no—
323#95—48no—
324#95—48no—
325#95—48no—
326#95—48no—
327#95—48no—
328#95—48no—
329#95—44no—
330#95—48no—
331#95—44no—
332#95—44no—
333#95—44no—
334C24C23×C411yescharacteristic
335C24C22×D411yescharacteristic
336C24C22×D412yes—
337C24C22×D411yescharacteristic
338C24C22×Q811yescharacteristic
339C24C22×Q812yes—
340C24C2×#4111yescharacteristic
341C24C2×#4111yescharacteristic
342C24C2×#4111yescharacteristic
343C24C2×#4111yescharacteristic
344C24C2×#4112yes—
345C24C2×#4112yes—
346C24C2×#4111yescharacteristic
347C24C2×#4112yes—
348C24C2×#4111yescharacteristic
349C24C2×#4112yes—
350C24C2×#4111yescharacteristic
351C24H(5,𝔽2)11yescharacteristic
352C24H(5,𝔽2)11yescharacteristic
353C24H(5,𝔽2)12yes—
354C24H(5,𝔽2)11yescharacteristic
355C242−1+411yescharacteristic
356C242−1+412yes—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
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—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
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—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—42no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
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—41no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—41no—
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—42no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—41no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—41no—
557C22×C4—42no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—42no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—42no—
575C22×C4—41no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—41no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—41no—
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—41no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—42no—
620C22×C4—41no—
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—41no—
632C22×C4—42no—
633C22×C4—41no—
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—41no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4#11714yes—
654C22×C4C4×D418yes—
655C22×C4C4×D414yes—
656C22×C4C4×D414yes—
657C22×C4C4×Q814yes—
658C22×C4C4×Q818yes—
659C22×C4#12014yes—
660C22×C4#12118yes—
661C22×C4#12114yes—
662C22×C4C22⋊Q818yes—
663C22×C4C22⋊Q814yes—
664C22×C4#12314yes—
665C22×C4#12314yes—
666C22×C4#12414yes—
667C22×C4#12614yes—
668C22×C4C4⋊Q818yes—
669C22×C4C4⋊Q814yes—
670C4⋊C4—232no—
671C4⋊C4—232no—
672C4⋊C4—432no—
673C4⋊C4—416no—
674C42—232no—
675C42—432no—
676C23C2×#11711yescharacteristic
677C23C2×C4×D412yes—
678C23C2×C4×D411yescharacteristic
679C23C2×C4×D411yescharacteristic
680C23C2×C4×Q811yescharacteristic
681C23C2×C4×Q812yes—
682C23C4×#4111yescharacteristic
683C23C4×#4112yes—
684C23#51811yescharacteristic
685C23#52011yescharacteristic
686C23#52012yes—
687C23C2×#12011yescharacteristic
688C23C2×#12112yes—
689C23C2×#12111yescharacteristic
690C23C2×C22⋊Q812yes—
691C23C2×C22⋊Q811yescharacteristic
692C23C2×#12311yescharacteristic
693C23C2×#12311yescharacteristic
694C23#52512yes—
695C23#52512yes—
696C23#52512yes—
697C23#52511yescharacteristic
698C23#52512yes—
699C23#52511yescharacteristic
700C23#52511yescharacteristic
701C23#52512yes—
702C23C2×#12411yescharacteristic
703C23C2×#12611yescharacteristic
704C23#52912yes—
705C23#52912yes—
706C23#52912yes—
707C23#52912yes—
708C23#52912yes—
709C23#52911yescharacteristic
710C23C2×C4⋊Q812yes—
711C23C2×C4⋊Q811yescharacteristic
712C23#53212yes—
713C23#53211yescharacteristic
714C23#53212yes—
715C23#53312yes—
716C23#53312yes—
717C23#53312yes—
718C23#53312yes—
719C23#53311yescharacteristic
720C23#53412yes—
721C23#53412yes—
722C23#53511yescharacteristic
723C23#53511yescharacteristic
724C23#53612yes—
725C23#53611yescharacteristic
726C23#53711yescharacteristic
727C23#53712yes—
728C23#53812yes—
729C23#53912yes—
730C23#53912yes—
731C23#53912yes—
732C23#54011yescharacteristic
733C23#54211yescharacteristic
734C23#54212yes—
735C23#54611yescharacteristic
736C23#54612yes—
737C23#54611yescharacteristic
738C23D4×Q812yes—
739C23D4×Q811yescharacteristic
740C23#55011yescharacteristic
741C23#55112yes—
742C23#55112yes—
743C23#55112yes—
744C23#55212yes—
745C23#55211yescharacteristic
746C23#55212yes—
747C23#55212yes—
748C23#55212yes—
749C23#55311yescharacteristic
750C23#55311yescharacteristic
751C23#55312yes—
752C23#55312yes—
753C23#55312yes—
754C23#55311yescharacteristic
755C23#55311yescharacteristic
756C23#55311yescharacteristic
757C23#55412yes—
758C23#55412yes—
759C23#55412yes—
760C23#55412yes—
761C23#55412yes—
762C23#55411yescharacteristic
763C23#55411yescharacteristic
764C23#55412yes—
765C23#55411yescharacteristic
766C23#55511yescharacteristic
767C23#55612yes—
768C23#55611yescharacteristic
769C23#55611yescharacteristic
770C23#55612yes—
771C23#55712yes—
772C23#55712yes—
773C23#55712yes—
774C23#55912yes—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—28no—
783C2×C4—28no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—28no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—42no—
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—44no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—42no—
870C2×C4—44no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—42no—
879C2×C4—44no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—44no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—42no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—82no—
900C2×C4—82no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—82no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—81no—
907C2×C4—82no—
908C2×C4—82no—
909C2×C4—82no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—82no—
913C2×C4—82no—
914C2×C4#38818yes—
915C2×C4#39518yes—
916C22C2×#38811yescharacteristic
917C22#229012yes—
918C22C4×#12011yescharacteristic
919C22C4×#12112yes—
920C22C4×#12311yescharacteristic
921C22C4×C22⋊Q812yes—
922C22C4×C22⋊Q811yescharacteristic
923C22C4×C4⋊Q812yes—
924C22C4×C4⋊Q811yescharacteristic
925C22#232212yes—
926C22#232411yescharacteristic
927C22#232512yes—
928C22#232611yescharacteristic
929C22#234511yescharacteristic
930C22#234711yescharacteristic
931C22#235512yes—
932C22#236012yes—
933C22#236011yescharacteristic
934C22#236311yescharacteristic
935C22#236812yes—
936C22#237012yes—
937C22#237012yes—
938C22#237312yes—
939C22C2×#39511yescharacteristic
940C22#238811yescharacteristic
941C22#239612yes—
942C22#239611yescharacteristic
943C22#239911yescharacteristic
944C22#239912yes—
945C22#248411yescharacteristic
946C22#248511yescharacteristic
947C22#248711yescharacteristic
948C22#248711yescharacteristic
949C22#249011yescharacteristic
950C22#249211yescharacteristic
951C22#249212yes—
952C22#249411yescharacteristic
953C22#249711yescharacteristic
954C22#249811yescharacteristic
955C22#249911yescharacteristic
956C22#250211yescharacteristic
957C22#250211yescharacteristic
958C22#251112yes—
959C22#252012yes—
960C22#252012yes—
961C22#252212yes—
962C22#252512yes—
963C22#253412yes—
964C22#253511yescharacteristic
965C22#253812yes—
966C22#253811yescharacteristic
967C22#254312yes—
968C22#254411yescharacteristic
969C22#254611yescharacteristic
970C22#254612yes—
971C22#255412yes—
972C22#255612yes—
973C22#255612yes—
974C22#255612yes—
975C22#257312yes—
976C22#257412yes—
977C22#257912yes—
978C22#257912yes—
979C22#258111yescharacteristic
980C22#258112yes—
981C22#258312yes—
982C22#258312yes—
983C22#258412yes—
984C22#258411yescharacteristic
985C22#258512yes—
986C22#258512yes—
987C22#258712yes—
988C22#258812yes—
989C22#258812yes—
990C22#258912yes—
991C22#259012yes—
992C22#259012yes—
993C22#259412yes—
994C22#259612yes—
995C22#259811yescharacteristic
996C22#259912yes—
997C22#260012yes—
998C22#260112yes—
999C22#260212yes—
1000C22#260311yescharacteristic
1001C22#260912yes—
1002C22#261112yes—
1003C22#261311yescharacteristic
1004C22#261611yescharacteristic
1005C22#263012yes—
1006C22#263311yescharacteristic
1007C22#263611yescharacteristic
1008C22#263812yes—
1009C22#284711yescharacteristic
1010C22#284911yescharacteristic
1011C22#285012yes—
1012C22#285212yes—
1013C22#285311yescharacteristic
1014C22#285411yescharacteristic
1015C4—28no—
1016C4—28no—
1017C4—44no—
1018C4—48no—
1019C4—48no—
1020C4—44no—
1021C4—48no—
1022C4—82no—
1023C4—82no—
1024C4—84no—
1025C4—82no—
1026C2C4×#39511yescharacteristic
1027C2#1399311yescharacteristic
1028C2#1400011yescharacteristic
1029C2#1406912yes—
1030C2#1408312yes—
1031C2#1422212yes—
1032C2#1422612yes—
1033C2#1423911yescharacteristic
1034C2#1424411yescharacteristic
1035C2#1430011yescharacteristic
1036C2#1469611yescharacteristic
1037C2#1509211yescharacteristic
1038C2#1509312yes—
1039C2#1509612yes—
1040C2#1509712yes—
1041C2#1509912yes—
1042C2#1510111yescharacteristic
1043C2#1510211yescharacteristic
1044C2#1510311yescharacteristic
1045C2#1510611yescharacteristic
1046C2#1511411yescharacteristic
1047C2#1515811yescharacteristic
1048C2#1515911yescharacteristic
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
39. #1441C4semidirect

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×#14442
C2×#14412
C2×#14362
#75572
#75562
#75542