Finite Group Databasebeta

← #154649

Subgroups — #154649

Order 512.

3790 conjugacy classes of subgroups.

The subgroup lattice has 1101 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic
2C22×#391C211yesmaximal, characteristic
3C2×#1446C211yesmaximal, characteristic
4C2×#1444C211yesmaximal, characteristic
5C2×#1441C211yesmaximal, characteristic
6C2×#1436C211yesmaximal, characteristic
7C2×C4⋊#95C212yesmaximal
8C2×C4×#95C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7557C212yesmaximal
11#7554C212yesmaximal
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2212yes—
17C23×C42C2211yescharacteristic
18C23×C42C2212yes—
19C2×#395—24no—
20C2×#395—24no—
21C2×#395C418yescomplemented
22C2×#391—24no—
23C2×#391—28no—
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40#1446—24no—
41#1444—24no—
42#1441—24no—
43#1436—24no—
44C4⋊#95—28no—
45C4×#95—24no—
46C23×Q8—24no—
47C23×Q8—22no—
48C23×Q8—22no—
49C23×Q8—22no—
50C23×Q8—22no—
51C23×Q8—24no—
52C23×Q8—22no—
53C23×Q8—22no—
54C23×Q8—42no—
55C23×Q8—42no—
56C23×Q8C2×C414yes—
57C24×C4C2311yescharacteristic
58C24×C4C2312yes—
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2312yes—
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C24×C4C2312yes—
65C24×C4C2311yescharacteristic
66C24×C4C2312yes—
67C24×C4C2311yescharacteristic
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—24no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—24no—
79C22×C4⋊C4—24no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—24no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—24no—
87C22×C4⋊C4—42no—
88C22×C4⋊C4—42no—
89C22×C4⋊C4—42no—
90C22×C4⋊C4—42no—
91C22×C4⋊C4—42no—
92C22×C4⋊C4C2×C414yes—
93C22×C4⋊C4C2×C418yes—
94C22×C42—22no—
95C22×C42—24no—
96C22×C42—24no—
97C22×C42—24no—
98C22×C42—22no—
99C22×C42—24no—
100C22×C42—24no—
101C22×C42—42no—
102C22×C42—42no—
103C22×C42—42no—
104C22×C42D414yes—
105C22×C42Q818yescomplemented
106#395—232no—
107#391—232no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—22no—
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—22no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—24no—
123C2×#95—22no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—22no—
128C2×#95—22no—
129C2×#95—22no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—22no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—22no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95C2×C418yes—
147C2×#95C2×C414yes—
148C2×#95D418yes—
149C2×#95D414yes—
150C2×#95D414yes—
151C2×#95D414yes—
152C2×#95Q814yescomplemented
153C2×#95Q818yescomplemented
154C25C2411yescharacteristic
155C22×Q8—28no—
156C22×Q8—216no—
157C22×Q8—28no—
158C22×Q8—28no—
159C22×Q8—216no—
160C22×Q8—28no—
161C22×Q8—28no—
162C22×Q8—48no—
163C22×Q8—48no—
164C22×Q8—48no—
165C22×Q8—48no—
166C22×Q8—48no—
167C22×Q8—48no—
168C22×Q8—48no—
169C22×Q8—48no—
170C22×Q8—48no—
171C22×Q8—44no—
172C22×Q8—44no—
173C22×Q8—48no—
174C22×Q8—44no—
175C22×Q8—44no—
176C22×Q8—44no—
177C22×Q8—44no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
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—21no—
194C23×C4—22no—
195C23×C4—21no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—21no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—21no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—21no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—22no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—22no—
247C23×C4—21no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—21no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4C22×C412yes—
286C23×C4C22×C414yes—
287C23×C4C22×C412yes—
288C23×C4C22×C412yes—
289C23×C4C22×C414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D414yes—
296C23×C4C2×D412yes—
297C23×C4C2×D414yes—
298C23×C4C2×D412yes—
299C23×C4C2×D412yes—
300C23×C4C2×D412yes—
301C23×C4C2×D414yes—
302C23×C4C2×Q812yes—
303C23×C4C2×Q812yes—
304C23×C4C2×Q814yes—
305C23×C4C2×Q814yes—
306C23×C4C2×Q814yes—
307C23×C4C2×Q814yes—
308C23×C4C2×Q814yes—
309C23×C4C2×Q812yes—
310C23×C4C2×Q814yes—
311C23×C4#4112yes—
312C23×C4#4114yes—
313C23×C4#4112yes—
314C23×C4#4112yes—
315C23×C4#4112yes—
316C23×C4#4114yes—
317C23×C4#4114yes—
318C23×C4#4112yes—
319C2×C4⋊C4—216no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—216no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—216no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—48no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4—48no—
329C2×C4⋊C4—48no—
330C2×C4⋊C4—48no—
331C2×C4⋊C4—48no—
332C2×C4⋊C4—48no—
333C2×C4⋊C4—48no—
334C2×C4⋊C4—48no—
335C2×C4⋊C4—48no—
336C2×C4⋊C4—48no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—48no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—48no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C42—28no—
346C2×C42—28no—
347C2×C42—216no—
348C2×C42—216no—
349C2×C42—44no—
350C2×C42—48no—
351C2×C42—48no—
352C2×C42—48no—
353C2×C42—48no—
354C2×C42—48no—
355C2×C42—48no—
356C2×C42—48no—
357#95—28no—
358#95—216no—
359#95—216no—
360#95—216no—
361#95—28no—
362#95—216no—
363#95—28no—
364#95—48no—
365#95—48no—
366#95—48no—
367#95—48no—
368#95—44no—
369#95—44no—
370#95—48no—
371#95—44no—
372#95C22⋊C4116yes—
373C24C23×C411yescharacteristic
374C24C22×D411yescharacteristic
375C24C22×D411yescharacteristic
376C24C22×D411yescharacteristic
377C24C22×D412yes—
378C24C22×D411yescharacteristic
379C24C22×Q812yes—
380C24C22×Q812yes—
381C24C22×Q811yescharacteristic
382C24C2×#4111yescharacteristic
383C24C2×#4111yescharacteristic
384C24C2×#4112yes—
385C24C2×#4112yes—
386C24C2×#4112yes—
387C24C2×#4111yescharacteristic
388C24C2×#4111yescharacteristic
389C24C2×#4111yescharacteristic
390C24H(5,𝔽2)12yes—
391C24H(5,𝔽2)12yes—
392C24H(5,𝔽2)11yescharacteristic
393C242−1+411yescharacteristic
394C242−1+411yescharacteristic
395C242−1+411yescharacteristic
396C2×Q8—232no—
397C2×Q8—432no—
398C2×Q8—432no—
399C2×Q8—416no—
400C2×Q8—416no—
401C2×Q8—416no—
402C2×Q8—432no—
403C2×Q8—416no—
404C2×Q8—432no—
405C2×Q8—416no—
406C2×Q8—416no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
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—22no—
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—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—41no—
581C22×C4—41no—
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—41no—
594C22×C4—41no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—42no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—42no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—41no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—42no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—42no—
637C22×C4—41no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—41no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—42no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—42no—
653C22×C4—41no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—41no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—41no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×C22⋊C414yes—
698C22×C4C2×C22⋊C418yes—
699C22×C4C4×D418yes—
700C22×C4C4×D414yes—
701C22×C4C4×D414yes—
702C22×C4C4×Q814yes—
703C22×C4C4×Q818yes—
704C22×C4C4×Q818yes—
705C22×C4#12014yes—
706C22×C4#12114yes—
707C22×C4#12114yes—
708C22×C4C22⋊Q818yes—
709C22×C4C22⋊Q818yes—
710C22×C4C22⋊Q814yes—
711C22×C4C22⋊Q818yes—
712C22×C4#12414yes—
713C22×C4#12418yes—
714C22×C4#12714yes—
715C22×C4C4⋊Q814yes—
716C22×C4C4⋊Q818yes—
717C22×C4C4⋊Q818yes—
718C22×C4C4⋊Q814yes—
719C22×C4C4⋊Q818yes—
720C4⋊C4—432no—
721C4⋊C4—416no—
722C4⋊C4—432no—
723C4⋊C4—416no—
724C42—416no—
725C42—432no—
726C23C22×C22⋊C411yescharacteristic
727C23C2×C4×D411yescharacteristic
728C23C2×C4×D411yescharacteristic
729C23C2×C4×D412yes—
730C23C2×C4×Q812yes—
731C23C2×C4×Q811yescharacteristic
732C23C2×C4×Q812yes—
733C23C4×#4111yescharacteristic
734C23#51812yes—
735C23#51911yescharacteristic
736C23#52011yescharacteristic
737C23C2×#12011yescharacteristic
738C23C2×#12111yescharacteristic
739C23C2×#12111yescharacteristic
740C23C2×C22⋊Q811yescharacteristic
741C23C2×C22⋊Q812yes—
742C23C2×C22⋊Q812yes—
743C23C2×C22⋊Q812yes—
744C23#52511yescharacteristic
745C23#52511yescharacteristic
746C23#52512yes—
747C23#52512yes—
748C23C2×#12412yes—
749C23C2×#12411yescharacteristic
750C23#52911yescharacteristic
751C23#52912yes—
752C23C2×#12711yescharacteristic
753C23C2×C4⋊Q811yescharacteristic
754C23C2×C4⋊Q811yescharacteristic
755C23C2×C4⋊Q812yes—
756C23C2×C4⋊Q812yes—
757C23C2×C4⋊Q812yes—
758C23#53211yescharacteristic
759C23#53211yescharacteristic
760C23#53212yes—
761C23#53212yes—
762C23#53312yes—
763C23#53312yes—
764C23#53312yes—
765C23#53312yes—
766C23#53312yes—
767C23#53312yes—
768C23#53311yescharacteristic
769C23#53312yes—
770C23#53411yescharacteristic
771C23#53511yescharacteristic
772C23#53611yescharacteristic
773C23#53711yescharacteristic
774C23#53812yes—
775C23#53812yes—
776C23#53912yes—
777C23#54111yescharacteristic
778C23#54211yescharacteristic
779C23#54212yes—
780C23#54212yes—
781C23#54312yes—
782C23#54412yes—
783C23#54412yes—
784C23#54412yes—
785C23D4212yes—
786C23D4212yes—
787C23D4212yes—
788C23#54612yes—
789C23#54612yes—
790C23#54611yescharacteristic
791C23#54611yescharacteristic
792C23#54612yes—
793C23#54612yes—
794C23#54611yescharacteristic
795C23#54612yes—
796C23#54711yescharacteristic
797C23#54711yescharacteristic
798C23#54711yescharacteristic
799C23#54712yes—
800C23#54811yescharacteristic
801C23#54811yescharacteristic
802C23#54811yescharacteristic
803C23D4×Q811yescharacteristic
804C23D4×Q811yescharacteristic
805C23D4×Q811yescharacteristic
806C23D4×Q812yes—
807C23D4×Q812yes—
808C23#55112yes—
809C23#55112yes—
810C23#55112yes—
811C23#55212yes—
812C23#55211yescharacteristic
813C23#55211yescharacteristic
814C23#55412yes—
815C23#55412yes—
816C23#55412yes—
817C23#55412yes—
818C23#55412yes—
819C23#55411yescharacteristic
820C23#55512yes—
821C23#55612yes—
822C23#55611yescharacteristic
823C23#55712yes—
824C23Q8212yes—
825Q8—464no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—28no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—28no—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—28no—
853C2×C4—28no—
854C2×C4—28no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—24no—
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—42no—
882C2×C4—44no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—42no—
893C2×C4—44no—
894C2×C4—42no—
895C2×C4—44no—
896C2×C4—44no—
897C2×C4—44no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—44no—
919C2×C4—42no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—44no—
937C2×C4—44no—
938C2×C4—82no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—82no—
943C2×C4—82no—
944C2×C4—81no—
945C2×C4—81no—
946C2×C4—81no—
947C2×C4—81no—
948C2×C4—82no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—81no—
952C2×C4—82no—
953C2×C4—82no—
954C2×C4—82no—
955C2×C4—82no—
956C2×C4—82no—
957C2×C4—82no—
958C2×C4—82no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4—82no—
964C2×C4#39018yes—
965C2×C4#391116yescomplemented
966C2×C4#39518yescomplemented
967C22C2×#39011yescharacteristic
968C22C2×#39112yes—
969C22C4×#12011yescharacteristic
970C22C4×C22⋊Q812yes—
971C22C4×C22⋊Q811yescharacteristic
972C22C4×C4⋊Q811yescharacteristic
973C22C4×C4⋊Q812yes—
974C22C4×C4⋊Q811yescharacteristic
975C22C4×C4⋊Q812yes—
976C22#232111yescharacteristic
977C22#232311yescharacteristic
978C22#232912yes—
979C22#233112yes—
980C22D4×C22⋊C412yes—
981C22#233911yescharacteristic
982C22Q8×C22⋊C411yescharacteristic
983C22#235812yes—
984C22#236012yes—
985C22#236011yescharacteristic
986C22#236211yescharacteristic
987C22#236512yes—
988C22#236812yes—
989C22#236912yes—
990C22C2×#39511yescharacteristic
991C22#238811yescharacteristic
992C22#239611yescharacteristic
993C22#239612yes—
994C22#239911yescharacteristic
995C22#239912yes—
996C22#241011yescharacteristic
997C22#241111yescharacteristic
998C22#241511yescharacteristic
999C22#241711yescharacteristic
1000C22#242412yes—
1001C22#242711yescharacteristic
1002C22#242911yescharacteristic
1003C22#243011yescharacteristic
1004C22#243311yescharacteristic
1005C22#243411yescharacteristic
1006C22#243712yes—
1007C22#243812yes—
1008C22#243812yes—
1009C22#243912yes—
1010C22#244012yes—
1011C22#244012yes—
1012C22#244012yes—
1013C22#244912yes—
1014C22#245012yes—
1015C22#245112yes—
1016C22#245212yes—
1017C22#246112yes—
1018C22#246212yes—
1019C22#246512yes—
1020C22#246512yes—
1021C22#247212yes—
1022C22#247212yes—
1023C22#248812yes—
1024C22#248911yescharacteristic
1025C22#249112yes—
1026C22#249211yescharacteristic
1027C22#249212yes—
1028C22#252012yes—
1029C22#252112yes—
1030C22#253911yescharacteristic
1031C22#254011yescharacteristic
1032C22#254211yescharacteristic
1033C22#254912yes—
1034C22#254912yes—
1035C22#254912yes—
1036C22#255012yes—
1037C22#255012yes—
1038C22#255112yes—
1039C22#255112yes—
1040C22#255512yes—
1041C22#255612yes—
1042C22#255612yes—
1043C22#256411yescharacteristic
1044C22#256711yescharacteristic
1045C22#257412yes—
1046C22#258311yescharacteristic
1047C22#258411yescharacteristic
1048C22#258612yes—
1049C22#258612yes—
1050C22#260411yescharacteristic
1051C22#260512yes—
1052C22#261011yescharacteristic
1053C22#261212yes—
1054C22#265911yescharacteristic
1055C22#266011yescharacteristic
1056C22#266211yescharacteristic
1057C22#266311yescharacteristic
1058C22#266512yes—
1059C22#266612yes—
1060C22#285711yescharacteristic
1061C22#285711yescharacteristic
1062C22#285712yes—
1063C22#285811yescharacteristic
1064C22#286212yes—
1065C22#286811yescharacteristic
1066C4—28no—
1067C4—28no—
1068C4—216no—
1069C4—48no—
1070C4—44no—
1071C4—44no—
1072C4—48no—
1073C4—82no—
1074C4—84no—
1075C4—82no—
1076C4—82no—
1077C2C4×#39511yescharacteristic
1078C2#1399511yescharacteristic
1079C2#1399711yescharacteristic
1080C2#1405212yes—
1081C2#1405312yes—
1082C2#1418611yescharacteristic
1083C2#1421412yes—
1084C2#1423612yes—
1085C2#1424111yescharacteristic
1086C2#1432711yescharacteristic
1087C2#1471411yescharacteristic
1088C2#1475811yescharacteristic
1089C2#1476311yescharacteristic
1090C2#1477012yes—
1091C2#1481612yes—
1092C2#1487211yescharacteristic
1093C2#1490111yescharacteristic
1094C2#1492811yescharacteristic
1095C2#1493712yes—
1096C2#1501112yes—
1097C2#1506511yescharacteristic
1098C2#1514311yescharacteristic
1099C2#1517311yescharacteristic
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
21. C2×#395C4semidirect
105. C22×C42Q8semidirect
152. C2×#95Q8semidirect
153. C2×#95Q8semidirect
965. C2×C4#391semidirect
966. C2×C4#395semidirect

Maximal subgroups

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

subgroupindex
C22×#3952
C22×#3912
C2×#14462
C2×#14442
C2×#14412
C2×#14362
C2×C4⋊#952
C2×C4×#952
#75572
#75542