Finite Group Databasebeta

← #154575

Subgroups — #154575

Order 512.

3162 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C4⋊C4C211yesmaximal, characteristic
2C2×#1445C212yesmaximal
3C2×#1444C211yesmaximal, characteristic
4C2×#1436C211yesmaximal, characteristic
5C2×#1436C212yesmaximal
6C2×#1436C212yesmaximal
7#7557C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C211yesmaximal, characteristic
10#7556C212yesmaximal
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C42C2211yescharacteristic
17C23×C42C2212yes—
18C2×C4×C4⋊C4—24no—
19C2×C4×C4⋊C4—28no—
20C22×#95C2211yescharacteristic
21C22×#95C2211yescharacteristic
22C22×#95C2211yescharacteristic
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2212yes—
37#1445—28no—
38#1444C418yescomplemented
39#1436—24no—
40#1436—28no—
41#1436—28no—
42C24×C4C2311yescharacteristic
43C24×C4C2312yes—
44C24×C4C2311yescharacteristic
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2312yes—
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2312yes—
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—24no—
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—42no—
70C22×C4⋊C4—42no—
71C22×C4⋊C4C2×C414yes—
72C22×C4⋊C4C2×C418yes—
73C22×C4⋊C4Q814yes—
74C22×C4⋊C4Q814yes—
75C22×C42—24no—
76C22×C42—22no—
77C22×C42—22no—
78C22×C42—24no—
79C22×C42—24no—
80C22×C42—24no—
81C22×C42—24no—
82C22×C42—24no—
83C22×C42—24no—
84C22×C42—42no—
85C22×C42—42no—
86C22×C42D414yes—
87C4×C4⋊C4—232no—
88C2×#95—24no—
89C2×#95—22no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—22no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—22no—
96C2×#95—24no—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—24no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—22no—
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—24no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—22no—
125C2×#95—22no—
126C2×#95—22no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95—42no—
132C2×#95C2×C414yes—
133C2×#95C2×C414yes—
134C2×#95C2×C418yes—
135C2×#95D418yes—
136C2×#95D418yes—
137C25C2411yescharacteristic
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—22no—
148C23×C4—21no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
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—21no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
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—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—21no—
204C23×C4—22no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—21no—
227C23×C4—22no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—21no—
245C23×C4C22×C412yes—
246C23×C4C22×C414yes—
247C23×C4C22×C414yes—
248C23×C4C22×C412yes—
249C23×C4C22×C412yes—
250C23×C4C2×D414yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4C2×D412yes—
254C23×C4C2×D414yes—
255C23×C4C2×D414yes—
256C23×C4C2×D412yes—
257C23×C4C2×D414yes—
258C23×C4C2×D412yes—
259C23×C4C2×Q812yes—
260C23×C4C2×Q812yes—
261C23×C4C2×Q814yes—
262C23×C4C2×Q812yes—
263C23×C4C2×Q812yes—
264C23×C4#4112yes—
265C23×C4#4114yes—
266C23×C4#4114yes—
267C23×C4#4112yes—
268C23×C4#4114yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
271C23×C4#4112yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4114yes—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—216no—
278C2×C4⋊C4—216no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—216no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—216no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—216no—
286C2×C4⋊C4—216no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—216no—
289C2×C4⋊C4—48no—
290C2×C4⋊C4—48no—
291C2×C4⋊C4—48no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—48no—
294C2×C4⋊C4—48no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C42—216no—
298C2×C42—216no—
299C2×C42—28no—
300C2×C42—28no—
301C2×C42—28no—
302C2×C42—216no—
303C2×C42—48no—
304C2×C42—48no—
305C2×C42—48no—
306C2×C42—48no—
307C2×C42—48no—
308C2×C42—48no—
309#95—28no—
310#95—216no—
311#95—216no—
312#95—28no—
313#95—216no—
314#95—28no—
315#95—216no—
316#95—216no—
317#95—48no—
318#95—48no—
319#95—48no—
320#95—48no—
321#95—48no—
322#95—44no—
323#95—44no—
324#95—44no—
325#95—44no—
326C24C23×C411yescharacteristic
327C24C22×D411yescharacteristic
328C24C22×D412yes—
329C24C22×D412yes—
330C24C22×Q811yescharacteristic
331C24C22×Q811yescharacteristic
332C24C2×#4111yescharacteristic
333C24C2×#4111yescharacteristic
334C24C2×#4111yescharacteristic
335C24C2×#4112yes—
336C24C2×#4112yes—
337C24C2×#4111yescharacteristic
338C24C2×#4111yescharacteristic
339C24C2×#4112yes—
340C24C2×#4111yescharacteristic
341C24C2×#4112yes—
342C24C2×#4111yescharacteristic
343C24H(5,𝔽2)11yescharacteristic
344C24H(5,𝔽2)11yescharacteristic
345C24H(5,𝔽2)11yescharacteristic
346C242−1+412yes—
347C242−1+412yes—
348C242−1+411yescharacteristic
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—24no—
363C22×C4—24no—
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—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—22no—
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—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
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—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
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—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—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
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—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—41no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—41no—
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—41no—
502C22×C4—42no—
503C22×C4—41no—
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—41no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—42no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—41no—
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—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—41no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
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—41no—
623C22×C4—41no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4#11714yes—
634C22×C4C4×D418yes—
635C22×C4C4×D418yes—
636C22×C4C4×D414yes—
637C22×C4C4×Q814yes—
638C22×C4C4×Q814yes—
639C22×C4#12014yes—
640C22×C4C22⋊Q818yes—
641C22×C4C22⋊Q814yes—
642C22×C4C22⋊Q814yes—
643C22×C4C22⋊Q818yes—
644C22×C4#12314yes—
645C22×C4#12318yes—
646C22×C4#12314yes—
647C22×C4#12514yes—
648C22×C4#12614yes—
649C22×C4#12714yes—
650C4⋊C4—232no—
651C4⋊C4—232no—
652C4⋊C4—432no—
653C4⋊C4—416no—
654C42—232no—
655C42—432no—
656C23C2×#11711yescharacteristic
657C23C2×C4×D411yescharacteristic
658C23C2×C4×D412yes—
659C23C2×C4×D412yes—
660C23C2×C4×Q811yescharacteristic
661C23C2×C4×Q811yescharacteristic
662C23C4×#4112yes—
663C23C4×#4111yescharacteristic
664C23#51811yescharacteristic
665C23#51912yes—
666C23#52011yescharacteristic
667C23C2×#12011yescharacteristic
668C23C2×C22⋊Q811yescharacteristic
669C23C2×C22⋊Q811yescharacteristic
670C23C2×C22⋊Q812yes—
671C23C2×C22⋊Q812yes—
672C23C2×#12311yescharacteristic
673C23C2×#12311yescharacteristic
674C23C2×#12312yes—
675C23#52511yescharacteristic
676C23#52511yescharacteristic
677C23#52512yes—
678C23#52511yescharacteristic
679C23#52512yes—
680C23#52512yes—
681C23#52512yes—
682C23#52512yes—
683C23#52512yes—
684C23C2×#12511yescharacteristic
685C23C2×#12611yescharacteristic
686C23#52912yes—
687C23#52912yes—
688C23#52912yes—
689C23#52912yes—
690C23#52912yes—
691C23#52912yes—
692C23#52912yes—
693C23#52911yescharacteristic
694C23C2×#12711yescharacteristic
695C23#53211yescharacteristic
696C23#53212yes—
697C23#53312yes—
698C23#53312yes—
699C23#53311yescharacteristic
700C23#53511yescharacteristic
701C23#53611yescharacteristic
702C23#53611yescharacteristic
703C23#53711yescharacteristic
704C23#53912yes—
705C23#53912yes—
706C23#53912yes—
707C23#53912yes—
708C23#54011yescharacteristic
709C23#54112yes—
710C23#54112yes—
711C23#54112yes—
712C23#54211yescharacteristic
713C23#54212yes—
714C23#54212yes—
715C23D4212yes—
716C23D4212yes—
717C23#54612yes—
718C23#54612yes—
719C23#54712yes—
720C23#54712yes—
721C23#54712yes—
722C23#54712yes—
723C23#54712yes—
724C23#54712yes—
725C23#54812yes—
726C23#54812yes—
727C23D4×Q812yes—
728C23D4×Q812yes—
729C23#55112yes—
730C23#55212yes—
731C23#55212yes—
732C23#55212yes—
733C23#55211yescharacteristic
734C23#55311yescharacteristic
735C23#55312yes—
736C23#55311yescharacteristic
737C23#55311yescharacteristic
738C23#55411yescharacteristic
739C23#55411yescharacteristic
740C23#55411yescharacteristic
741C23#55411yescharacteristic
742C23#55511yescharacteristic
743C23#55612yes—
744C23#55612yes—
745C23#55612yes—
746C23#55611yescharacteristic
747C23#55712yes—
748C23#55712yes—
749C23#55711yescharacteristic
750C23#55711yescharacteristic
751C23Q8211yescharacteristic
752C23#55911yescharacteristic
753C23#55911yescharacteristic
754C23#55911yescharacteristic
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—28no—
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—24no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—28no—
789C2×C4—42no—
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—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
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—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—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—44no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—42no—
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—42no—
861C2×C4—42no—
862C2×C4—44no—
863C2×C4—42no—
864C2×C4—81no—
865C2×C4—82no—
866C2×C4—82no—
867C2×C4—82no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—81no—
871C2×C4—81no—
872C2×C4—82no—
873C2×C4—81no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—82no—
877C2×C4—82no—
878C2×C4—82no—
879C2×C4—82no—
880C2×C4—82no—
881C2×C4—82no—
882C2×C4—82no—
883C2×C4—82no—
884C2×C4—82no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—82no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4#38718yes—
891C2×C4#39918yes—
892C22C2×#38711yescharacteristic
893C22#229012yes—
894C22C4×#12011yescharacteristic
895C22C4×#12311yescharacteristic
896C22C4×#12312yes—
897C22C4×C22⋊Q811yescharacteristic
898C22C4×C22⋊Q812yes—
899C22C4×C22⋊Q812yes—
900C22C4×#12711yescharacteristic
901C22#232411yescharacteristic
902C22#232711yescharacteristic
903C22#233212yes—
904C22#233612yes—
905C22#234412yes—
906C22#235511yescharacteristic
907C22#235711yescharacteristic
908C22#235812yes—
909C22#236112yes—
910C22#236212yes—
911C22#236512yes—
912C22#236512yes—
913C22#236911yescharacteristic
914C22#237011yescharacteristic
915C22C2×#39911yescharacteristic
916C22#239511yescharacteristic
917C22#239512yes—
918C22#239611yescharacteristic
919C22#239612yes—
920C22#239711yescharacteristic
921C22#240611yescharacteristic
922C22#240911yescharacteristic
923C22#243011yescharacteristic
924C22#243311yescharacteristic
925C22#244312yes—
926C22#244312yes—
927C22#244612yes—
928C22#244712yes—
929C22#244912yes—
930C22#244912yes—
931C22#244912yes—
932C22#244912yes—
933C22#245112yes—
934C22#245112yes—
935C22#245312yes—
936C22#245312yes—
937C22#245512yes—
938C22#245512yes—
939C22#245812yes—
940C22#246112yes—
941C22#246212yes—
942C22#246212yes—
943C22#246412yes—
944C22#246812yes—
945C22#246912yes—
946C22#246912yes—
947C22#247012yes—
948C22#247412yes—
949C22#247412yes—
950C22#247512yes—
951C22#247812yes—
952C22#247812yes—
953C22#248511yescharacteristic
954C22#248711yescharacteristic
955C22#249612yes—
956C22#249911yescharacteristic
957C22#250111yescharacteristic
958C22#250612yes—
959C22#250711yescharacteristic
960C22#250911yescharacteristic
961C22#251111yescharacteristic
962C22#251311yescharacteristic
963C22#254011yescharacteristic
964C22#254211yescharacteristic
965C22#256511yescharacteristic
966C22#257312yes—
967C22#257512yes—
968C22#258011yescharacteristic
969C22#258111yescharacteristic
970C22#258211yescharacteristic
971C22#258512yes—
972C22#258812yes—
973C22#258812yes—
974C22#259012yes—
975C22#259412yes—
976C22#259612yes—
977C22#259911yescharacteristic
978C22#260311yescharacteristic
979C22#262311yescharacteristic
980C22#262511yescharacteristic
981C22#263311yescharacteristic
982C22#263711yescharacteristic
983C22#265412yes—
984C22#265512yes—
985C22#284811yescharacteristic
986C22#284911yescharacteristic
987C22#285112yes—
988C22#285212yes—
989C22#285311yescharacteristic
990C22#285511yescharacteristic
991C4—28no—
992C4—28no—
993C4—44no—
994C4—44no—
995C4—48no—
996C4—48no—
997C4—48no—
998C4—82no—
999C4—82no—
1000C4—84no—
1001C4—82no—
1002C2C4×#39911yescharacteristic
1003C2#1398312yes—
1004C2#1403512yes—
1005C2#1404111yescharacteristic
1006C2#1404911yescharacteristic
1007C2#1417411yescharacteristic
1008C2#1418911yescharacteristic
1009C2#1419112yes—
1010C2#1421912yes—
1011C2#1430811yescharacteristic
1012C2#1469511yescharacteristic
1013C2#1477711yescharacteristic
1014C2#1478112yes—
1015C2#1478212yes—
1016C2#1479012yes—
1017C2#1479112yes—
1018C2#1480711yescharacteristic
1019C2#1487811yescharacteristic
1020C2#1489211yescharacteristic
1021C2#1507911yescharacteristic
1022C2#1510211yescharacteristic
1023C2#1519311yescharacteristic
1024C2#1521211yescharacteristic
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. #1444C4semidirect

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×#14452
C2×#14442
C2×#14362
#75572
#75562
#75542