Finite Group Databasebeta

← #153893

Subgroups — #153893

Order 512.

3422 conjugacy classes of subgroups.

The subgroup lattice has 1036 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×#1442C211yesmaximal, characteristic
4C2×#1436C212yesmaximal
5C2×#1436C212yesmaximal
6C2×#1434C211yesmaximal, characteristic
7C2×C4×#95C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C211yesmaximal, characteristic
10#7554C212yesmaximal
11#7554C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C42C2211yescharacteristic
16C23×C42C2212yes—
17C23×C42C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C2×C4×C4⋊C4—24no—
20C2×C4×C4⋊C4—28no—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2211yescharacteristic
28C22×#95C2211yescharacteristic
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37#1444C418yescomplemented
38#1442C418yescomplemented
39#1436—28no—
40#1436—28no—
41#1434C418yescomplemented
42C4×#95—24no—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2312yes—
46C24×C4C2311yescharacteristic
47C24×C4C2312yes—
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C22×C4⋊C4—24no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4C2×C414yes—
69C22×C4⋊C4C2×C414yes—
70C22×C4⋊C4C2×C418yes—
71C22×C42—24no—
72C22×C42—24no—
73C22×C42—22no—
74C22×C42—22no—
75C22×C42—24no—
76C22×C42—24no—
77C22×C42—24no—
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—22no—
82C22×C42—24no—
83C22×C42—24no—
84C22×C42—24no—
85C22×C42—24no—
86C22×C42—42no—
87C22×C42—42no—
88C22×C42—42no—
89C22×C42—42no—
90C22×C42C2×C414yes—
91C22×C42D414yes—
92C22×C42Q814yes—
93C4×C4⋊C4—232no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—22no—
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—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—42no—
123C2×#95—42no—
124C2×#95—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95C2×C414yes—
129C2×#95C2×C418yes—
130C2×#95C2×C418yes—
131C2×#95C2×C418yes—
132C2×#95C2×C418yes—
133C2×#95C2×C414yes—
134C2×#95C2×C414yes—
135C2×#95C2×C418yes—
136C2×#95C2×C414yes—
137C2×#95C2×C414yes—
138C2×#95C2×C414yes—
139C2×#95D414yes—
140C2×#95D418yes—
141C2×#95Q814yes—
142C25C2411yescharacteristic
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4—21no—
152C23×C4—21no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
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—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
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×C4C22×C414yes—
240C23×C4C22×C414yes—
241C23×C4C22×C414yes—
242C23×C4C22×C414yes—
243C23×C4C22×C412yes—
244C23×C4C22×C414yes—
245C23×C4C22×C414yes—
246C23×C4C22×C412yes—
247C23×C4C22×C412yes—
248C23×C4C22×C412yes—
249C23×C4C22×C412yes—
250C23×C4C22×C412yes—
251C23×C4C22×C412yes—
252C23×C4C22×C412yes—
253C23×C4C22×C412yes—
254C23×C4C2×D412yes—
255C23×C4C2×D414yes—
256C23×C4C2×D414yes—
257C23×C4C2×D412yes—
258C23×C4C2×D412yes—
259C23×C4C2×D412yes—
260C23×C4C2×D412yes—
261C23×C4C2×D414yes—
262C23×C4C2×D412yes—
263C23×C4C2×Q812yes—
264C23×C4C2×Q812yes—
265C23×C4C2×Q812yes—
266C23×C4C2×Q812yes—
267C23×C4C2×Q812yes—
268C23×C4C2×Q812yes—
269C23×C4#4114yes—
270C23×C4#4112yes—
271C23×C4#4114yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C23×C4#4112yes—
276C23×C4#4112yes—
277C23×C4#4114yes—
278C23×C4#4112yes—
279C23×C4#4112yes—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—216no—
283C2×C4⋊C4—216no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—216no—
287C2×C4⋊C4—216no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—216no—
291C2×C4⋊C4—216no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—48no—
294C2×C4⋊C4—48no—
295C2×C4⋊C4—48no—
296C2×C4⋊C4—48no—
297C2×C42—216no—
298C2×C42—28no—
299C2×C42—216no—
300C2×C42—28no—
301C2×C42—216no—
302C2×C42—28no—
303C2×C42—28no—
304C2×C42—48no—
305C2×C42—48no—
306C2×C42—48no—
307C2×C42—48no—
308C2×C42—48no—
309C2×C42—48no—
310C2×C42—48no—
311C2×C42—48no—
312C2×C42—44no—
313C2×C42—44no—
314C2×C42—48no—
315C2×C42—44no—
316C2×C42—48no—
317C2×C42—44no—
318C2×C42C4⋊C4116yescomplemented
319#95—28no—
320#95—216no—
321#95—216no—
322#95—28no—
323#95—28no—
324#95—216no—
325#95—216no—
326#95—216no—
327#95—28no—
328#95—28no—
329#95—48no—
330#95—48no—
331#95—48no—
332#95—48no—
333#95—48no—
334#95C42116yescomplemented
335C24C23×C411yescharacteristic
336C24C23×C411yescharacteristic
337C24C23×C411yescharacteristic
338C24C22×D411yescharacteristic
339C24C22×D412yes—
340C24C22×D411yescharacteristic
341C24C22×Q811yescharacteristic
342C24C22×Q811yescharacteristic
343C24C2×#4111yescharacteristic
344C24C2×#4111yescharacteristic
345C24C2×#4112yes—
346C24C2×#4111yescharacteristic
347C24C2×#4112yes—
348C24C2×#4112yes—
349C24C2×#4111yescharacteristic
350C24C2×#4111yescharacteristic
351C24C2×#4111yescharacteristic
352C24C2×#4111yescharacteristic
353C24C2×#4111yescharacteristic
354C24H(5,𝔽2)12yes—
355C24H(5,𝔽2)12yes—
356C242−1+412yes—
357C242−1+412yes—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—24no—
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—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—24no—
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—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
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—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
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—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—41no—
528C22×C4—41no—
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—41no—
538C22×C4—41no—
539C22×C4—42no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—42no—
546C22×C4—41no—
547C22×C4—41no—
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×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×C4C2×C4218yes—
634C22×C4C2×C4214yes—
635C22×C4C2×C4⋊C414yes—
636C22×C4C2×C4⋊C414yes—
637C22×C4C2×C4⋊C414yes—
638C22×C4#11714yes—
639C22×C4C4×D414yes—
640C22×C4C4×D418yes—
641C22×C4C4×D414yes—
642C22×C4C4×D418yes—
643C22×C4C4×D414yes—
644C22×C4C4×D414yes—
645C22×C4C4×D418yes—
646C22×C4C4×D414yes—
647C22×C4C4×Q814yes—
648C22×C4C4×Q814yes—
649C22×C4C4×Q814yes—
650C22×C4C4×Q814yes—
651C22×C4C4×Q814yes—
652C22×C4#12014yes—
653C22×C4#12114yes—
654C22×C4C22⋊Q818yes—
655C22×C4C22⋊Q814yes—
656C22×C4#12314yes—
657C22×C4#12514yes—
658C22×C4C4⋊Q814yes—
659C4⋊C4—232no—
660C4⋊C4—232no—
661C4⋊C4—432no—
662C42—232no—
663C42—416no—
664C42—432no—
665C42—416no—
666C23C22×C4211yescharacteristic
667C23C22×C4⋊C411yescharacteristic
668C23C2×#11711yescharacteristic
669C23C2×C4×D411yescharacteristic
670C23C2×C4×D411yescharacteristic
671C23C2×C4×D411yescharacteristic
672C23C2×C4×D411yescharacteristic
673C23C2×C4×D412yes—
674C23C2×C4×D412yes—
675C23C2×C4×D412yes—
676C23C2×C4×D411yescharacteristic
677C23C2×C4×Q811yescharacteristic
678C23C2×C4×Q811yescharacteristic
679C23C2×C4×Q811yescharacteristic
680C23C2×C4×Q811yescharacteristic
681C23C2×C4×Q811yescharacteristic
682C23C4×#4111yescharacteristic
683C23C4×#4111yescharacteristic
684C23C4×#4111yescharacteristic
685C23C4×#4111yescharacteristic
686C23C4×#4111yescharacteristic
687C23C4×#4111yescharacteristic
688C23C4×#4112yes—
689C23C4×#4112yes—
690C23C4×#4112yes—
691C23#51812yes—
692C23#51912yes—
693C23#52012yes—
694C23#52012yes—
695C23#52012yes—
696C23#52012yes—
697C23C2×#12011yescharacteristic
698C23C2×#12111yescharacteristic
699C23C2×C22⋊Q811yescharacteristic
700C23C2×C22⋊Q812yes—
701C23C2×#12311yescharacteristic
702C23#52511yescharacteristic
703C23#52511yescharacteristic
704C23#52511yescharacteristic
705C23#52511yescharacteristic
706C23#52512yes—
707C23#52512yes—
708C23C2×#12511yescharacteristic
709C23#52911yescharacteristic
710C23#52911yescharacteristic
711C23#52911yescharacteristic
712C23#52911yescharacteristic
713C23#52912yes—
714C23#52912yes—
715C23C2×C4⋊Q811yescharacteristic
716C23#53211yescharacteristic
717C23#53211yescharacteristic
718C23#53311yescharacteristic
719C23#53311yescharacteristic
720C23#53311yescharacteristic
721C23#53311yescharacteristic
722C23#53312yes—
723C23#53511yescharacteristic
724C23#53511yescharacteristic
725C23#53611yescharacteristic
726C23#53611yescharacteristic
727C23#54012yes—
728C23#54112yes—
729C23#54212yes—
730C23#54212yes—
731C23#54412yes—
732C23#54412yes—
733C23D4212yes—
734C23#54612yes—
735C23#54612yes—
736C23#54612yes—
737C23#54612yes—
738C23#54712yes—
739C23#54712yes—
740C23#54712yes—
741C23#54812yes—
742C23#54812yes—
743C23D4×Q812yes—
744C23#55112yes—
745C23#55112yes—
746C23#55112yes—
747C23#55112yes—
748C23#55212yes—
749C23#55212yes—
750C23#55212yes—
751C23#55212yes—
752C23#55212yes—
753C23#55212yes—
754C23#55312yes—
755C23#55312yes—
756C23#55312yes—
757C23#55312yes—
758C23#55412yes—
759C23#55412yes—
760C23#55612yes—
761C23#55612yes—
762C23#55612yes—
763C23#55712yes—
764C23#55912yes—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
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—42no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—42no—
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—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—42no—
877C2×C4—44no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4C4×C4⋊C418yes—
900C2×C4#38518yes—
901C2×C4#38918yes—
902C22C2×C4×C4⋊C411yescharacteristic
903C22C42×D412yes—
904C22C42×D411yescharacteristic
905C22C42×Q811yescharacteristic
906C22#227412yes—
907C22C2×#38511yescharacteristic
908C22#229012yes—
909C22C2×#38911yescharacteristic
910C22#229311yescharacteristic
911C22#229511yescharacteristic
912C22#229611yescharacteristic
913C22#229611yescharacteristic
914C22C4×#12011yescharacteristic
915C22C4×#12011yescharacteristic
916C22C4×#12111yescharacteristic
917C22C4×#12111yescharacteristic
918C22C4×#12311yescharacteristic
919C22C4×#12311yescharacteristic
920C22C4×C22⋊Q811yescharacteristic
921C22C4×C22⋊Q811yescharacteristic
922C22C4×C22⋊Q812yes—
923C22C4×C22⋊Q812yes—
924C22C4×#12511yescharacteristic
925C22C4×#12511yescharacteristic
926C22C4×C4⋊Q811yescharacteristic
927C22C4×C4⋊Q811yescharacteristic
928C22#231412yes—
929C22#231711yescharacteristic
930C22#231711yescharacteristic
931C22#232611yescharacteristic
932C22#232611yescharacteristic
933C22#232711yescharacteristic
934C22#232811yescharacteristic
935C22#233012yes—
936C22#233112yes—
937C22#235812yes—
938C22#235912yes—
939C22#235912yes—
940C22#235912yes—
941C22#235912yes—
942C22#236012yes—
943C22#236012yes—
944C22#236112yes—
945C22#236112yes—
946C22#236212yes—
947C22#236212yes—
948C22#236412yes—
949C22#236512yes—
950C22#236712yes—
951C22#236712yes—
952C22#236812yes—
953C22#237012yes—
954C22#237012yes—
955C22#237112yes—
956C22#237312yes—
957C22#237312yes—
958C22#237312yes—
959C22#237312yes—
960C22#237412yes—
961C22#240411yescharacteristic
962C22#240611yescharacteristic
963C22#240811yescharacteristic
964C22#240911yescharacteristic
965C22#243812yes—
966C22#243812yes—
967C22#244012yes—
968C22#244212yes—
969C22#245712yes—
970C22#245812yes—
971C22#246112yes—
972C22#246212yes—
973C22#246412yes—
974C22#246512yes—
975C22#246812yes—
976C22#246912yes—
977C22#248211yescharacteristic
978C22#248411yescharacteristic
979C22#248611yescharacteristic
980C22#248711yescharacteristic
981C22#251512yes—
982C22#251612yes—
983C22#251912yes—
984C22#252012yes—
985C22#252112yes—
986C22#252212yes—
987C22#252412yes—
988C22#252512yes—
989C22#253511yescharacteristic
990C22#253611yescharacteristic
991C22#255012yes—
992C22#257012yes—
993C22#258011yescharacteristic
994C22#258111yescharacteristic
995C22#259811yescharacteristic
996C22#259811yescharacteristic
997C22#259911yescharacteristic
998C22#259911yescharacteristic
999C22#260512yes—
1000C22#260612yes—
1001C4—28no—
1002C4—28no—
1003C4—28no—
1004C4—44no—
1005C4—44no—
1006C4—48no—
1007C4—48no—
1008C4—44no—
1009C4—44no—
1010C4—48no—
1011C4—84no—
1012C2C4×#38511yescharacteristic
1013C2C4×#38911yescharacteristic
1014C2#1377911yescharacteristic
1015C2#1382312yes—
1016C2#1382512yes—
1017C2#1412811yescharacteristic
1018C2#1413011yescharacteristic
1019C2#1414412yes—
1020C2#1414612yes—
1021C2#1415011yescharacteristic
1022C2#1416411yescharacteristic
1023C2#1417211yescharacteristic
1024C2#1417411yescharacteristic
1025C2#1417511yescharacteristic
1026C2#1417611yescharacteristic
1027C2#1421112yes—
1028C2#1421212yes—
1029C2#1421412yes—
1030C2#1421612yes—
1031C2#1422311yescharacteristic
1032C2#1422511yescharacteristic
1033C2#1423911yescharacteristic
1034C2#1424011yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC23C22×C42
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
37. #1444C4semidirect
38. #1442C4semidirect
41. #1434C4semidirect
318. C2×C42C4⋊C4semidirect
334. #95C42semidirect

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×#14422
C2×#14362
C2×#14342
C2×C4×#952
#75572
#75542