Finite Group Databasebeta

← #154334

Subgroups — #154334

Order 512.

2986 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#382C211yesmaximal, characteristic
2C2×#1444C211yesmaximal, characteristic
3C2×#1442C211yesmaximal, characteristic
4C2×#1436C212yesmaximal
5C2×#1434C211yesmaximal, characteristic
6C2×C4×#95C211yesmaximal, characteristic
7#7557C211yesmaximal, characteristic
8#7557C212yesmaximal
9#7557C211yesmaximal, characteristic
10#7556C212yesmaximal
11#7554C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C2×#382—24no—
19C2×#382—28no—
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2212yes—
37#1444—24no—
38#1442—24no—
39#1436—28no—
40#1434C418yescomplemented
41C4×#95—24no—
42C24×C4C2312yes—
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—24no—
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—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4—42no—
69C22×C4⋊C4—42no—
70C22×C42—24no—
71C22×C42—24no—
72C22×C42—22no—
73C22×C42—22no—
74C22×C42—22no—
75C22×C42—22no—
76C22×C42—22no—
77C22×C42—22no—
78C22×C42—24no—
79C22×C42—24no—
80C22×C42—42no—
81C22×C42—42no—
82C22×C42C2×C414yes—
83C22×C42D414yes—
84C22×C42Q814yes—
85#382—232no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—22no—
108C2×#95—24no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—24no—
113C2×#95—24no—
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×#95C2×C418yes—
131C2×#95C2×C414yes—
132C2×#95C2×C418yes—
133C2×#95C2×C414yes—
134C2×#95D418yes—
135C2×#95D414yes—
136C2×#95Q814yes—
137C25C2411yescharacteristic
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
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—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
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—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×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4C22×C414yes—
243C23×C4C22×C412yes—
244C23×C4C22×C414yes—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C2×D414yes—
248C23×C4C2×D414yes—
249C23×C4C2×D412yes—
250C23×C4C2×D412yes—
251C23×C4C2×D412yes—
252C23×C4C2×D412yes—
253C23×C4C2×D412yes—
254C23×C4C2×D414yes—
255C23×C4C2×D412yes—
256C23×C4C2×Q812yes—
257C23×C4C2×Q812yes—
258C23×C4C2×Q812yes—
259C23×C4C2×Q812yes—
260C23×C4C2×Q812yes—
261C23×C4C2×Q812yes—
262C23×C4#4114yes—
263C23×C4#4114yes—
264C23×C4#4112yes—
265C23×C4#4112yes—
266C23×C4#4112yes—
267C23×C4#4112yes—
268C23×C4#4112yes—
269C23×C4#4112yes—
270C23×C4#4112yes—
271C23×C4#4112yes—
272C23×C4#4114yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C2×C4⋊C4—216no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—48no—
279C2×C4⋊C4—48no—
280C2×C4⋊C4—48no—
281C2×C4⋊C4—48no—
282C2×C4⋊C4—48no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—48no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—48no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—48no—
292C2×C42—216no—
293C2×C42—28no—
294C2×C42—216no—
295C2×C42—28no—
296C2×C42—28no—
297C2×C42—28no—
298C2×C42—48no—
299C2×C42—48no—
300C2×C42—48no—
301C2×C42—48no—
302C2×C42—44no—
303C2×C42—44no—
304C2×C42—44no—
305C2×C42—44no—
306C2×C42C4⋊C4116yescomplemented
307#95—28no—
308#95—28no—
309#95—216no—
310#95—216no—
311#95—216no—
312#95—28no—
313#95—216no—
314#95—28no—
315#95—216no—
316#95—28no—
317#95—28no—
318#95—48no—
319#95—48no—
320#95—48no—
321#95—48no—
322#95—48no—
323#95—48no—
324C24C23×C411yescharacteristic
325C24C22×D411yescharacteristic
326C24C22×D412yes—
327C24C22×D411yescharacteristic
328C24C22×Q811yescharacteristic
329C24C22×Q811yescharacteristic
330C24C2×#4112yes—
331C24C2×#4112yes—
332C24C2×#4112yes—
333C24C2×#4111yescharacteristic
334C24C2×#4111yescharacteristic
335C24C2×#4111yescharacteristic
336C24C2×#4111yescharacteristic
337C24C2×#4111yescharacteristic
338C24C2×#4111yescharacteristic
339C24C2×#4111yescharacteristic
340C24C2×#4111yescharacteristic
341C24C2×#4111yescharacteristic
342C24C2×#4111yescharacteristic
343C24H(5,𝔽2)12yes—
344C24H(5,𝔽2)12yes—
345C242−1+412yes—
346C242−1+412yes—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
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—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
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—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
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—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—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—42no—
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—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
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—42no—
546C22×C4—42no—
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—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×C4C2×C4⋊C414yes—
631C22×C4C2×C4⋊C414yes—
632C22×C4C2×C4⋊C414yes—
633C22×C4#11718yes—
634C22×C4C4×D418yes—
635C22×C4C4×D414yes—
636C22×C4C4×Q814yes—
637C22×C4#12014yes—
638C22×C4#12114yes—
639C22×C4C22⋊Q818yes—
640C22×C4C22⋊Q814yes—
641C22×C4#12314yes—
642C22×C4#12414yes—
643C22×C4#12414yes—
644C22×C4#12514yes—
645C22×C4#12514yes—
646C22×C4#12514yes—
647C22×C4C4⋊Q814yes—
648C4⋊C4—416no—
649C4⋊C4—416no—
650C4⋊C4—432no—
651C42—232no—
652C42—416no—
653C42—416no—
654C23C22×C4⋊C411yescharacteristic
655C23C2×#11712yes—
656C23C2×C4×D411yescharacteristic
657C23C2×C4×D412yes—
658C23C2×C4×Q811yescharacteristic
659C23C4×#4111yescharacteristic
660C23C4×#4111yescharacteristic
661C23C4×#4111yescharacteristic
662C23C4×#4111yescharacteristic
663C23#52012yes—
664C23#52012yes—
665C23C2×#12011yescharacteristic
666C23C2×#12111yescharacteristic
667C23C2×C22⋊Q811yescharacteristic
668C23C2×C22⋊Q812yes—
669C23C2×#12311yescharacteristic
670C23#52511yescharacteristic
671C23#52511yescharacteristic
672C23#52511yescharacteristic
673C23#52511yescharacteristic
674C23#52512yes—
675C23#52512yes—
676C23C2×#12411yescharacteristic
677C23C2×#12411yescharacteristic
678C23C2×#12511yescharacteristic
679C23C2×#12511yescharacteristic
680C23C2×#12511yescharacteristic
681C23#52911yescharacteristic
682C23#52911yescharacteristic
683C23#52911yescharacteristic
684C23#52911yescharacteristic
685C23#52912yes—
686C23#52912yes—
687C23#52911yescharacteristic
688C23#52911yescharacteristic
689C23#52911yescharacteristic
690C23#52911yescharacteristic
691C23#52912yes—
692C23#52912yes—
693C23C2×C4⋊Q811yescharacteristic
694C23#53211yescharacteristic
695C23#53211yescharacteristic
696C23#53211yescharacteristic
697C23#53211yescharacteristic
698C23#53212yes—
699C23#53212yes—
700C23#53311yescharacteristic
701C23#53311yescharacteristic
702C23#53312yes—
703C23#53311yescharacteristic
704C23#53311yescharacteristic
705C23#53311yescharacteristic
706C23#53311yescharacteristic
707C23#53511yescharacteristic
708C23#53511yescharacteristic
709C23#53611yescharacteristic
710C23#53611yescharacteristic
711C23#53812yes—
712C23#53812yes—
713C23#53912yes—
714C23#53912yes—
715C23#54112yes—
716C23#54112yes—
717C23#54212yes—
718C23#54212yes—
719C23#54412yes—
720C23#54412yes—
721C23D4212yes—
722C23#54612yes—
723C23#54612yes—
724C23#54612yes—
725C23#54612yes—
726C23#54712yes—
727C23#54712yes—
728C23#54712yes—
729C23#54812yes—
730C23#54812yes—
731C23D4×Q812yes—
732C23#55112yes—
733C23#55112yes—
734C23#55112yes—
735C23#55112yes—
736C23#55212yes—
737C23#55212yes—
738C23#55212yes—
739C23#55212yes—
740C23#55212yes—
741C23#55212yes—
742C23#55212yes—
743C23#55212yes—
744C23#55312yes—
745C23#55312yes—
746C23#55412yes—
747C23#55412yes—
748C23#55512yes—
749C23#55512yes—
750C23#55612yes—
751C23#55712yes—
752C23#55912yes—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—28no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—42no—
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—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—44no—
863C2×C4—44no—
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—82no—
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—82no—
886C2×C4—82no—
887C2×C4—82no—
888C2×C4#38518yes—
889C2×C4#38918yes—
890C22#228511yescharacteristic
891C22C2×#38511yescharacteristic
892C22#229012yes—
893C22C2×#38911yescharacteristic
894C22#229312yes—
895C22#229611yescharacteristic
896C22#229611yescharacteristic
897C22C4×#12411yescharacteristic
898C22C4×#12411yescharacteristic
899C22C4×#12511yescharacteristic
900C22C4×#12511yescharacteristic
901C22#231711yescharacteristic
902C22#231711yescharacteristic
903C22#233412yes—
904C22#233412yes—
905C22#234312yes—
906C22#234612yes—
907C22#235212yes—
908C22#235512yes—
909C22#235912yes—
910C22#235912yes—
911C22#236012yes—
912C22#236112yes—
913C22#238811yescharacteristic
914C22#238811yescharacteristic
915C22#239511yescharacteristic
916C22#239511yescharacteristic
917C22#239612yes—
918C22#239612yes—
919C22#240411yescharacteristic
920C22#240611yescharacteristic
921C22#240811yescharacteristic
922C22#240911yescharacteristic
923C22#243812yes—
924C22#243812yes—
925C22#244012yes—
926C22#244212yes—
927C22#245912yes—
928C22#246012yes—
929C22#246112yes—
930C22#246212yes—
931C22#247212yes—
932C22#247312yes—
933C22#247412yes—
934C22#247512yes—
935C22#248211yescharacteristic
936C22#248411yescharacteristic
937C22#248611yescharacteristic
938C22#248711yescharacteristic
939C22#248812yes—
940C22#248912yes—
941C22#249112yes—
942C22#250512yes—
943C22#250612yes—
944C22#250812yes—
945C22#251512yes—
946C22#251712yes—
947C22#251812yes—
948C22#251912yes—
949C22#251912yes—
950C22#252012yes—
951C22#252112yes—
952C22#252412yes—
953C22#252812yes—
954C22#252912yes—
955C22#254411yescharacteristic
956C22#254511yescharacteristic
957C22#255012yes—
958C22#255312yes—
959C22#255512yes—
960C22#255612yes—
961C22#255712yes—
962C22#255812yes—
963C22#256511yescharacteristic
964C22#256611yescharacteristic
965C22#257012yes—
966C22#257412yes—
967C22#257512yes—
968C22#257612yes—
969C22#261011yescharacteristic
970C22#261011yescharacteristic
971C22#261111yescharacteristic
972C22#261111yescharacteristic
973C22#261212yes—
974C22#261212yes—
975C22#263111yescharacteristic
976C22#263211yescharacteristic
977C22#263311yescharacteristic
978C22#263411yescharacteristic
979C22#266612yes—
980C22#266612yes—
981C22#285011yescharacteristic
982C22#285011yescharacteristic
983C22#285111yescharacteristic
984C22#285111yescharacteristic
985C22#285911yescharacteristic
986C22#286211yescharacteristic
987C22#286411yescharacteristic
988C22#286411yescharacteristic
989C4—28no—
990C4—28no—
991C4—44no—
992C4—44no—
993C4—44no—
994C4—48no—
995C4—44no—
996C4—44no—
997C4—84no—
998C4—84no—
999C4—84no—
1000C2#1384411yescharacteristic
1001C2#1390911yescharacteristic
1002C2#1396311yescharacteristic
1003C2#1398512yes—
1004C2#1398612yes—
1005C2#1400912yes—
1006C2#1401012yes—
1007C2#1412811yescharacteristic
1008C2#1413011yescharacteristic
1009C2#1429811yescharacteristic
1010C2#1470711yescharacteristic
1011C2#1491511yescharacteristic
1012C2#1491611yescharacteristic
1013C2#1493712yes—
1014C2#1493812yes—
1015C2#1494112yes—
1016C2#1494212yes—
1017C2#1501611yescharacteristic
1018C2#1501711yescharacteristic
1019C2#1507011yescharacteristic
1020C2#1507111yescharacteristic
1021C2#1508511yescharacteristic
1022C2#1508611yescharacteristic
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
40. #1434C4semidirect
306. C2×C42C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3822
C2×#14442
C2×#14422
C2×#14362
C2×#14342
C2×C4×#952
#75572
#75562
#75542