Finite Group Databasebeta

← #154254

Subgroups — #154254

Order 512.

5910 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#385C211yesmaximal, characteristic
2C22×#380C211yesmaximal, characteristic
3C23×#95C211yesmaximal, characteristic
4C2×#1441C212yesmaximal, complemented
5C2×C22⋊#95C211yesmaximal, characteristic
6C2×C22⋊#95C211yesmaximal, characteristic
7C2×C22⋊#95C211yesmaximal, characteristic
8C2×C22⋊#95C211yesmaximal, characteristic
9#7557C212yesmaximal, complemented
10#7557C212yesmaximal, complemented
11#7556C212yesmaximal, complemented
12C25×C4C2211yescharacteristic
13C25×C4C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2212yes—
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C2×#385—24no—
22C2×#385—24no—
23C2×#385—24no—
24C2×#380—24no—
25C2×#380—24no—
26C2×#380C418yescomplemented
27C22×#95—28no—
28C22×#95—24no—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2212yes—
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2212yes—
40C22×#95C2211yescharacteristic
41C22×#95C2212yes—
42C22×#95C2211yescharacteristic
43#1441—28no—
44C22⋊#95—24no—
45C22⋊#95—24no—
46C22⋊#95—24no—
47C22⋊#95—24no—
48C26C2311yescharacteristic
49C24×C4—22no—
50C24×C4—22no—
51C24×C4—22no—
52C24×C4—22no—
53C24×C4—22no—
54C24×C4—22no—
55C24×C4—22no—
56C24×C4—22no—
57C24×C4—24no—
58C24×C4—24no—
59C24×C4—24no—
60C24×C4—24no—
61C24×C4—24no—
62C24×C4—24no—
63C24×C4—22no—
64C24×C4—22no—
65C24×C4—22no—
66C24×C4—22no—
67C24×C4—22no—
68C24×C4—22no—
69C24×C4—22no—
70C24×C4—22no—
71C24×C4—42no—
72C24×C4—42no—
73C24×C4—42no—
74C24×C4—42no—
75C24×C4—42no—
76C24×C4—42no—
77C24×C4C2×C414yes—
78C24×C4D414yes—
79C24×C4D414yes—
80C24×C4Q814yes—
81C24×C4Q814yes—
82C24×C4C2312yes—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4—42no—
104C22×C4⋊C4—42no—
105C22×C4⋊C4C2×C418yescomplemented
106C22×C22⋊C4—22no—
107C22×C22⋊C4—22no—
108C22×C22⋊C4—22no—
109C22×C22⋊C4—22no—
110C22×C22⋊C4—22no—
111C22×C22⋊C4—22no—
112C22×C22⋊C4—22no—
113C22×C22⋊C4—22no—
114C22×C22⋊C4—22no—
115C22×C22⋊C4—22no—
116C22×C22⋊C4—22no—
117C22×C22⋊C4—22no—
118C22×C22⋊C4—22no—
119C22×C22⋊C4—22no—
120C22×C22⋊C4—22no—
121C22×C22⋊C4—22no—
122C22×C22⋊C4—22no—
123C22×C22⋊C4—22no—
124C22×C22⋊C4—22no—
125C22×C22⋊C4—22no—
126C22×C22⋊C4—22no—
127C22×C22⋊C4—22no—
128C22×C22⋊C4C2×C414yes—
129C22×C22⋊C4C2×C414yes—
130C22×C22⋊C4D414yes—
131C22×C22⋊C4D414yes—
132C22×C22⋊C4D414yes—
133C22×C22⋊C4Q814yes—
134#385—232no—
135#380—232no—
136C2×#95—232no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—22no—
152C2×#95—22no—
153C2×#95—24no—
154C2×#95—22no—
155C2×#95—24no—
156C2×#95—22no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—42no—
166C2×#95—42no—
167C2×#95—42no—
168C2×#95—42no—
169C2×#95—42no—
170C2×#95—42no—
171C2×#95—42no—
172C2×#95—42no—
173C2×#95C2×C418yescomplemented
174C2×#95D418yes—
175C25—22no—
176C25—22no—
177C25—22no—
178C25—22no—
179C25—22no—
180C25—22no—
181C25—22no—
182C25—22no—
183C25C22×C412yes—
184C25C2×D412yes—
185C25C2×D412yes—
186C25C2×D412yes—
187C25C2×D412yes—
188C25C2×D412yes—
189C25C2×Q812yes—
190C25C2×Q812yes—
191C25C2×Q812yes—
192C25#4112yes—
193C25#4112yes—
194C25#4112yes—
195C25#4112yes—
196C25#4112yes—
197C25#4112yes—
198C25C2411yescharacteristic
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—216no—
206C23×C4—216no—
207C23×C4—28no—
208C23×C4—28no—
209C23×C4—28no—
210C23×C4—28no—
211C23×C4—28no—
212C23×C4—28no—
213C23×C4—28no—
214C23×C4—28no—
215C23×C4—28no—
216C23×C4—28no—
217C23×C4—28no—
218C23×C4—28no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—21no—
225C23×C4—21no—
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—21no—
238C23×C4—21no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—216no—
264C23×C4—28no—
265C23×C4—216no—
266C23×C4—216no—
267C23×C4—216no—
268C23×C4—28no—
269C23×C4—28no—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—28no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—48no—
328C23×C4—44no—
329C23×C4—44no—
330C23×C4—48no—
331C23×C4—48no—
332C23×C4—48no—
333C23×C4—48no—
334C23×C4—48no—
335C23×C4—48no—
336C23×C4—48no—
337C23×C4—48no—
338C23×C4—48no—
339C23×C4—48no—
340C23×C4—48no—
341C23×C4—48no—
342C23×C4—48no—
343C23×C4—48no—
344C23×C4—48no—
345C23×C4—48no—
346C23×C4—48no—
347C23×C4—48no—
348C23×C4—48no—
349C23×C4—48no—
350C23×C4—48no—
351C23×C4—48no—
352C23×C4—48no—
353C23×C4—48no—
354C23×C4—48no—
355C23×C4—48no—
356C23×C4—48no—
357C23×C4—44no—
358C23×C4—44no—
359C23×C4—44no—
360C23×C4—44no—
361C23×C4—48no—
362C23×C4—48no—
363C23×C4—44no—
364C23×C4—44no—
365C23×C4—44no—
366C23×C4—44no—
367C23×C4—44no—
368C23×C4—44no—
369C23×C4—44no—
370C23×C4—44no—
371C23×C4C4⋊C4116yescomplemented
372C23×C4C22×C414yes—
373C23×C4C22×C414yes—
374C23×C4C22×C412yes—
375C23×C4C22×C412yes—
376C23×C4C2×D412yes—
377C23×C4C2×D412yes—
378C23×C4C2×D414yes—
379C23×C4C2×D414yes—
380C23×C4C2×D412yes—
381C23×C4C2×D414yes—
382C23×C4C2×D414yes—
383C23×C4C2×D414yes—
384C23×C4C2×D412yes—
385C23×C4C2×D414yes—
386C23×C4C2×Q812yes—
387C23×C4C2×Q812yes—
388C23×C4C2×Q812yes—
389C23×C4C2×Q814yes—
390C23×C4C2×Q812yes—
391C23×C4#4114yes—
392C23×C4#4114yes—
393C23×C4#4114yes—
394C2×C4⋊C4—216no—
395C2×C4⋊C4—216no—
396C2×C4⋊C4—216no—
397C2×C4⋊C4—48no—
398C2×C4⋊C4—48no—
399C2×C4⋊C4—48no—
400C2×C4⋊C4—48no—
401C2×C4⋊C4—48no—
402C2×C4⋊C4—48no—
403C2×C4⋊C4—48no—
404C2×C4⋊C4—48no—
405C2×C4⋊C4—48no—
406C2×C4⋊C4—48no—
407C2×C4⋊C4—48no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4C22⋊C4116yes—
436#95—216no—
437#95—216no—
438#95—216no—
439#95—216no—
440#95—48no—
441#95—48no—
442#95—48no—
443#95—48no—
444#95—44no—
445#95—44no—
446#95—48no—
447#95—44no—
448#95—48no—
449#95—44no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—24no—
465C24—24no—
466C24—24no—
467C24—24no—
468C24—22no—
469C24—22no—
470C24—24no—
471C24—22no—
472C24—22no—
473C24—24no—
474C24—24no—
475C24—24no—
476C24—24no—
477C24—24no—
478C24—24no—
479C24—24no—
480C24—24no—
481C24—24no—
482C24—24no—
483C24—24no—
484C24—24no—
485C24—24no—
486C24—24no—
487C24—24no—
488C24—24no—
489C24—24no—
490C24—24no—
491C24—24no—
492C24—24no—
493C24—24no—
494C24—24no—
495C24—24no—
496C24—24no—
497C24—24no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—24no—
502C24—24no—
503C24—24no—
504C24—24no—
505C24—24no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—24no—
511C24—24no—
512C24—24no—
513C24—24no—
514C24C2×C22⋊C414yes—
515C24C2×C4⋊C414yes—
516C24#11714yes—
517C24C4×D414yes—
518C24C4×D414yes—
519C24C4×Q814yes—
520C24C4×Q814yes—
521C24#12014yes—
522C24#12114yes—
523C24#12114yes—
524C24#12114yes—
525C24#12114yes—
526C24#12114yes—
527C24#12114yes—
528C24C22⋊Q814yes—
529C24C22⋊Q814yes—
530C24C22⋊Q814yes—
531C24C22⋊Q814yes—
532C24C22⋊Q814yes—
533C24C22⋊Q814yes—
534C24C22⋊Q814yes—
535C24C22⋊Q814yes—
536C24#12314yes—
537C24#12314yes—
538C24#12314yes—
539C24#12414yes—
540C24#12514yes—
541C24#12514yes—
542C24#12514yes—
543C24#12514yes—
544C24#12614yes—
545C24#12614yes—
546C24C4⋊Q814yes—
547C24C4⋊Q814yes—
548C24C4⋊Q814yes—
549C24C23×C411yescharacteristic
550C24C22×D411yescharacteristic
551C24C22×D411yescharacteristic
552C24C22×D411yescharacteristic
553C24C22×D411yescharacteristic
554C24C22×D411yescharacteristic
555C24C22×D412yes—
556C24C22×Q811yescharacteristic
557C24C22×Q811yescharacteristic
558C24C22×Q811yescharacteristic
559C24C2×#4111yescharacteristic
560C24C2×#4111yescharacteristic
561C24C2×#4111yescharacteristic
562C24C2×#4111yescharacteristic
563C24C2×#4112yes—
564C24C2×#4111yescharacteristic
565C24C2×#4111yescharacteristic
566C24C2×#4112yes—
567C24C2×#4112yes—
568C24H(5,𝔽2)12yes—
569C24H(5,𝔽2)12yes—
570C24H(5,𝔽2)12yes—
571C242−1+412yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—232no—
591C22×C4—232no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—232no—
661C22×C4—232no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—416no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—416no—
693C22×C4—416no—
694C22×C4—416no—
695C22×C4—416no—
696C22×C4—432no—
697C22×C4—432no—
698C22×C4—432no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—416no—
703C22×C4—416no—
704C22×C4—416no—
705C22×C4—416no—
706C22×C4—416no—
707C22×C4—416no—
708C22×C4—416no—
709C22×C4—416no—
710C22×C4—432no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—416no—
715C22×C4—416no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4—42no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—42no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—42no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—42no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4C2×C22⋊C418yes—
875C22×C4C2×C4⋊C414yes—
876C22×C4C2×C4⋊C414yes—
877C22×C4C4×D418yes—
878C22×C4#12014yes—
879C22×C4#12118yes—
880C22×C4C22⋊Q818yes—
881C22×C4C22⋊Q818yes—
882C22×C4#12314yes—
883C4⋊C4—432no—
884C4⋊C4—432no—
885C22⋊C4—232no—
886C22⋊C4—416no—
887C22⋊C4—416no—
888C22⋊C4—416no—
889C23—28no—
890C23—28no—
891C23—28no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—24no—
896C23—28no—
897C23—28no—
898C23—24no—
899C23—24no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—28no—
904C23—24no—
905C23—28no—
906C23—24no—
907C23—28no—
908C23—28no—
909C23—28no—
910C23—24no—
911C23—24no—
912C23—28no—
913C23—28no—
914C23—24no—
915C23—24no—
916C23—28no—
917C23—28no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—28no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—28no—
928C23—24no—
929C23—24no—
930C23—28no—
931C23—28no—
932C23—28no—
933C23—28no—
934C23—28no—
935C23—28no—
936C23—28no—
937C23—28no—
938C23—28no—
939C23—28no—
940C23—28no—
941C23—28no—
942C23—28no—
943C23—28no—
944C23—28no—
945C23—28no—
946C23—28no—
947C23—28no—
948C23—28no—
949C23—28no—
950C23—28no—
951C23—28no—
952C23—28no—
953C23—28no—
954C23—28no—
955C23—28no—
956C23—28no—
957C23—24no—
958C23—24no—
959C23—28no—
960C23—28no—
961C23—28no—
962C23—28no—
963C23—28no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—28no—
968C23—28no—
969C23—28no—
970C23—24no—
971C23—28no—
972C23—28no—
973C23#38018yes—
974C23#38618yes—
975C23#38718yes—
976C23#38718yes—
977C23#38918yes—
978C23#38918yes—
979C23#39118yes—
980C23#39418yes—
981C23#39518yes—
982C23#39618yes—
983C23#39618yes—
984C23#39818yes—
985C23#39818yes—
986C23#39818yes—
987C23#40018yes—
988C23C22×C22⋊C411yescharacteristic
989C23C22×C4⋊C411yescharacteristic
990C23C2×#11711yescharacteristic
991C23C2×C4×D411yescharacteristic
992C23C2×C4×D412yes—
993C23C2×C4×D411yescharacteristic
994C23C2×C4×Q811yescharacteristic
995C23C2×C4×Q811yescharacteristic
996C23C4×#4112yes—
997C23#51812yes—
998C23#52012yes—
999C23C2×#12011yescharacteristic
1000C23C2×#12011yescharacteristic
1001C23C2×#12111yescharacteristic
1002C23C2×#12112yes—
1003C23C2×#12111yescharacteristic
1004C23C2×#12111yescharacteristic
1005C23C2×#12111yescharacteristic
1006C23C2×#12111yescharacteristic
1007C23C2×#12111yescharacteristic
1008C23C2×C22⋊Q811yescharacteristic
1009C23C2×C22⋊Q811yescharacteristic
1010C23C2×C22⋊Q811yescharacteristic
1011C23C2×C22⋊Q812yes—
1012C23C2×C22⋊Q812yes—
1013C23C2×C22⋊Q811yescharacteristic
1014C23C2×C22⋊Q811yescharacteristic
1015C23C2×C22⋊Q811yescharacteristic
1016C23C2×C22⋊Q811yescharacteristic
1017C23C2×C22⋊Q811yescharacteristic
1018C23C2×#12311yescharacteristic
1019C23C2×#12311yescharacteristic
1020C23C2×#12311yescharacteristic
1021C23C2×#12311yescharacteristic
1022C23#52511yescharacteristic
1023C23#52511yescharacteristic
1024C23#52512yes—
1025C23#52512yes—
1026C23C2×#12411yescharacteristic
1027C23C2×#12511yescharacteristic
1028C23C2×#12511yescharacteristic
1029C23C2×#12511yescharacteristic
1030C23C2×#12511yescharacteristic
1031C23C2×#12611yescharacteristic
1032C23C2×#12611yescharacteristic
1033C23#52912yes—
1034C23#52912yes—
1035C23C2×C4⋊Q811yescharacteristic
1036C23C2×C4⋊Q811yescharacteristic
1037C23C2×C4⋊Q811yescharacteristic
1038C23#53212yes—
1039C23#53312yes—
1040C23#53312yes—
1041C23#53412yes—
1042C23#53411yescharacteristic
1043C23#53411yescharacteristic
1044C23#53511yescharacteristic
1045C23#53611yescharacteristic
1046C23#53712yes—
1047C23#53812yes—
1048C23#53812yes—
1049C23#53912yes—
1050C23#53912yes—
1051C23#54312yes—
1052C23#54312yes—
1053C23#54412yes—
1054C23#54412yes—
1055C23D4212yes—
1056C23D4212yes—
1057C23D4212yes—
1058C23#54612yes—
1059C23#54612yes—
1060C23#54612yes—
1061C23#54612yes—
1062C23#54612yes—
1063C23#54612yes—
1064C23#54612yes—
1065C23#54612yes—
1066C23#54612yes—
1067C23#54712yes—
1068C23#54712yes—
1069C23#54712yes—
1070C23#54812yes—
1071C23D4×Q812yes—
1072C23#55112yes—
1073C23#55112yes—
1074C23#55112yes—
1075C23#55112yes—
1076C23#55112yes—
1077C23#55112yes—
1078C23#55212yes—
1079C23#55212yes—
1080C23#55212yes—
1081C23#55312yes—
1082C23#55312yes—
1083C23#55312yes—
1084C23#55412yes—
1085C23#55412yes—
1086C23#55412yes—
1087C2×C4—24no—
1088C2×C4—28no—
1089C2×C4—28no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—28no—
1095C2×C4—28no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—28no—
1099C2×C4—28no—
1100C2×C4—28no—
1101C2×C4—28no—
1102C2×C4—28no—
1103C2×C4—28no—
1104C2×C4—28no—
1105C2×C4—28no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—464no—
1110C2×C4—464no—
1111C2×C4—464no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—44no—
1121C2×C4—44no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—44no—
1129C2×C4—44no—
1130C2×C4—44no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—44no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—44no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—44no—
1150C2×C4—44no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—44no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—44no—
1160C2×C4—44no—
1161C2×C4—44no—
1162C2×C4—44no—
1163C2×C4—44no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—44no—
1171C2×C4—44no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—44no—
1175C2×C4—44no—
1176C2×C4—44no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—44no—
1182C2×C4—44no—
1183C2×C4—81no—
1184C2×C4—81no—
1185C2×C4—81no—
1186C2×C4—81no—
1187C2×C4—81no—
1188C2×C4—81no—
1189C2×C4—81no—
1190C2×C4—81no—
1191C2×C4—81no—
1192C2×C4—81no—
1193C2×C4—82no—
1194C2×C4—81no—
1195C2×C4—81no—
1196C2×C4—81no—
1197C2×C4—81no—
1198C2×C4—82no—
1199C2×C4—81no—
1200C2×C4—81no—
1201C2×C4—82no—
1202C2×C4—82no—
1203C2×C4—82no—
1204C2×C4—82no—
1205C2×C4—82no—
1206C2×C4—82no—
1207C2×C4—82no—
1208C2×C4—82no—
1209C2×C4—82no—
1210C2×C4—82no—
1211C2×C4—82no—
1212C2×C4—82no—
1213C2×C4—82no—
1214C2×C4—82no—
1215C2×C4#38518yescomplemented
1216C22—28no—
1217C22—28no—
1218C22—28no—
1219C22—28no—
1220C22—28no—
1221C22—28no—
1222C22—28no—
1223C22—28no—
1224C22—28no—
1225C22—28no—
1226C22—28no—
1227C22—28no—
1228C22—28no—
1229C22—216no—
1230C22—216no—
1231C22—216no—
1232C22—216no—
1233C22—28no—
1234C22—216no—
1235C22—216no—
1236C22—216no—
1237C22—216no—
1238C22#1441116yescomplemented
1239C22C2×#38011yescharacteristic
1240C22C2×#38511yescharacteristic
1241C22C2×#38611yescharacteristic
1242C22C2×#38711yescharacteristic
1243C22C2×#38711yescharacteristic
1244C22C2×#38911yescharacteristic
1245C22C2×#38911yescharacteristic
1246C22C2×#39111yescharacteristic
1247C22#229611yescharacteristic
1248C22C4×#12112yes—
1249C22C4×C22⋊Q812yes—
1250C22#231511yescharacteristic
1251C22#231711yescharacteristic
1252C22#232512yes—
1253C22#232912yes—
1254C22D4×C22⋊C412yes—
1255C22#233912yes—
1256C22#234212yes—
1257C22#234312yes—
1258C22#236012yes—
1259C22#236112yes—
1260C22#236412yes—
1261C22#236812yes—
1262C22C2×#39411yescharacteristic
1263C22C2×#39511yescharacteristic
1264C22C2×#39611yescharacteristic
1265C22C2×#39611yescharacteristic
1266C22C2×#39811yescharacteristic
1267C22C2×#39811yescharacteristic
1268C22C2×#39811yescharacteristic
1269C22C2×#40011yescharacteristic
1270C22#240811yescharacteristic
1271C22#240911yescharacteristic
1272C22#241011yescharacteristic
1273C22#241011yescharacteristic
1274C22#241012yes—
1275C22#241111yescharacteristic
1276C22#241111yescharacteristic
1277C22#241211yescharacteristic
1278C22#241211yescharacteristic
1279C22#241212yes—
1280C22#241311yescharacteristic
1281C22#241311yescharacteristic
1282C22#241612yes—
1283C22#241712yes—
1284C22#241812yes—
1285C22#241912yes—
1286C22#242412yes—
1287C22#242512yes—
1288C22#243012yes—
1289C22#243712yes—
1290C22#243712yes—
1291C22#243712yes—
1292C22#243712yes—
1293C22#243812yes—
1294C22#243812yes—
1295C22#243812yes—
1296C22#243812yes—
1297C22#244012yes—
1298C22#244012yes—
1299C22#244212yes—
1300C22#244212yes—
1301C22#244312yes—
1302C22#244412yes—
1303C22#244912yes—
1304C22#245012yes—
1305C22#247212yes—
1306C22#247312yes—
1307C22#248012yes—
1308C22#248112yes—
1309C22#248611yescharacteristic
1310C22#248711yescharacteristic
1311C22#248812yes—
1312C22#249312yes—
1313C22#249812yes—
1314C22#250512yes—
1315C22#251012yes—
1316C22#253411yescharacteristic
1317C22#253411yescharacteristic
1318C22#254312yes—
1319C22#254912yes—
1320C22#254912yes—
1321C22#256412yes—
1322C22#256912yes—
1323C22#256912yes—
1324C22#257911yescharacteristic
1325C22#257911yescharacteristic
1326C22#261711yescharacteristic
1327C22#261811yescharacteristic
1328C22#262611yescharacteristic
1329C22#262711yescharacteristic
1330C22#264612yes—
1331C22#265912yes—
1332C22#284711yescharacteristic
1333C22#284811yescharacteristic
1334C22#285112yes—
1335C22#285411yescharacteristic
1336C22#285511yescharacteristic
1337C22#285712yes—
1338C4—28no—
1339C4—44no—
1340C4—48no—
1341C4—48no—
1342C4—48no—
1343C4—82no—
1344C4—82no—
1345C4—82no—
1346C4—82no—
1347C4—84no—
1348C2—216no—
1349C2C2×#144111yescharacteristic
1350C2#1387711yescharacteristic
1351C2#1396211yescharacteristic
1352C2#1402312yes—
1353C2#1402812yes—
1354C2#1404712yes—
1355C2#1405212yes—
1356C2#1413011yescharacteristic
1357C2#1414911yescharacteristic
1358C2#1427511yescharacteristic
1359C2#1469711yescharacteristic
1360C2#1472511yescharacteristic
1361C2#1472611yescharacteristic
1362C2#1472811yescharacteristic
1363C2#1472911yescharacteristic
1364C2#1473612yes—
1365C2#1475812yes—
1366C2#1476612yes—
1367C2#1476712yes—
1368C2#1492011yescharacteristic
1369C2#1492111yescharacteristic
1370C2#1492711yescharacteristic
1371C2#1493511yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC24C23×C4
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1441C2semidirect
9. #7557C2semidirect
10. #7557C2semidirect
11. #7556C2semidirect
26. C2×#380C4semidirect
105. C22×C4⋊C4C2×C4semidirect
173. C2×#95C2×C4semidirect
371. C23×C4C4⋊C4semidirect
1215. C2×C4#385semidirect
1238. C22#1441semidirect

Maximal subgroups

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

subgroupindex
C22×#3852
C22×#3802
C23×#952
C2×#14412
C2×C22⋊#952
#75572
#75562