Finite Group Databasebeta

← #153752

Subgroups — #153752

Order 512.

6166 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×#380C211yesmaximal, characteristic
2C22×C4×C22⋊C4C211yesmaximal, characteristic
3C23×#95C211yesmaximal, characteristic
4C2×#1436C212yesmaximal, complemented
5C2×C22⋊#95C211yesmaximal, characteristic
6C2×C22⋊#95C211yesmaximal, characteristic
7C2×C22⋊#95C211yesmaximal, characteristic
8C2×C22⋊#95C211yesmaximal, characteristic
9#7557C212yesmaximal, complemented
10#7556C212yesmaximal, complemented
11#7554C212yesmaximal, complemented
12C25×C4C2211yescharacteristic
13C25×C4C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C22⋊C4C2211yescharacteristic
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C23×C42C2212yes—
21C2×#380—24no—
22C2×#380—24no—
23C2×#380C418yescomplemented
24C2×C4×C22⋊C4—24no—
25C2×C4×C22⋊C4—24no—
26C2×C4×C22⋊C4—24no—
27C22×#95—28no—
28C22×#95C418yescomplemented
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2212yes—
39C22×#95C2212yes—
40C22×#95C2212yes—
41C22×#95C2212yes—
42C22×#95C2211yescharacteristic
43#1436—28no—
44C22⋊#95—24no—
45C22⋊#95—24no—
46C22⋊#95—24no—
47C22⋊#95C418yescomplemented
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—22no—
58C24×C4—22no—
59C24×C4—24no—
60C24×C4—24no—
61C24×C4—24no—
62C24×C4—24no—
63C24×C4—24no—
64C24×C4—24no—
65C24×C4—22no—
66C24×C4—22no—
67C24×C4—22no—
68C24×C4—22no—
69C24×C4—42no—
70C24×C4—42no—
71C24×C4—42no—
72C24×C4—42no—
73C24×C4—42no—
74C24×C4—42no—
75C24×C4C2×C414yes—
76C24×C4C2×C414yes—
77C24×C4C2×C414yes—
78C24×C4C2×C414yes—
79C24×C4C2×C414yes—
80C24×C4D414yes—
81C24×C4Q814yes—
82C24×C4C2312yes—
83C24×C4C2312yes—
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4C2×C418yescomplemented
99C22×C22⋊C4—22no—
100C22×C22⋊C4—22no—
101C22×C22⋊C4—22no—
102C22×C22⋊C4—22no—
103C22×C22⋊C4—22no—
104C22×C22⋊C4—22no—
105C22×C22⋊C4—22no—
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⋊C4C2×C414yes—
120C22×C22⋊C4C2×C414yes—
121C22×C22⋊C4C2×C414yes—
122C22×C22⋊C4C2×C414yes—
123C22×C22⋊C4D414yes—
124C22×C22⋊C4D414yes—
125C22×C22⋊C4D414yes—
126C22×C22⋊C4Q814yes—
127C22×C42—24no—
128C22×C42—24no—
129C22×C42—24no—
130C22×C42—24no—
131C22×C42—24no—
132C22×C42—42no—
133C22×C42—42no—
134#380—232no—
135C4×C22⋊C4—232no—
136C2×#95—24no—
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—232no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—24no—
152C2×#95—24no—
153C2×#95—24no—
154C2×#95—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—42no—
160C2×#95—42no—
161C2×#95—42no—
162C2×#95—42no—
163C2×#95—42no—
164C2×#95—42no—
165C2×#95—42no—
166C2×#95—42no—
167C2×#95C2×C414yes—
168C2×#95C2×C414yes—
169C2×#95C2×C414yes—
170C2×#95C2×C414yes—
171C2×#95C2×C418yescomplemented
172C2×#95C2×C418yescomplemented
173C2×#95C2×C418yescomplemented
174C2×#95D418yes—
175C25—22no—
176C25—22no—
177C25—22no—
178C25—22no—
179C25—22no—
180C25—22no—
181C25—22no—
182C25—22no—
183C25C22×C412yes—
184C25C22×C412yes—
185C25C22×C412yes—
186C25C2×D412yes—
187C25C2×D412yes—
188C25C2×D412yes—
189C25C2×D412yes—
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—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—216no—
212C23×C4—216no—
213C23×C4—28no—
214C23×C4—28no—
215C23×C4—28no—
216C23×C4—28no—
217C23×C4—28no—
218C23×C4—28no—
219C23×C4—28no—
220C23×C4—28no—
221C23×C4—28no—
222C23×C4—28no—
223C23×C4—28no—
224C23×C4—28no—
225C23×C4—28no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—22no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—28no—
285C23×C4—28no—
286C23×C4—28no—
287C23×C4—28no—
288C23×C4—28no—
289C23×C4—28no—
290C23×C4—216no—
291C23×C4—216no—
292C23×C4—216no—
293C23×C4—216no—
294C23×C4—28no—
295C23×C4—28no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
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—48no—
325C23×C4—48no—
326C23×C4—44no—
327C23×C4—44no—
328C23×C4—44no—
329C23×C4—44no—
330C23×C4—44no—
331C23×C4—44no—
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—48no—
358C23×C4—48no—
359C23×C4—48no—
360C23×C4—44no—
361C23×C4—44no—
362C23×C4—44no—
363C23×C4—44no—
364C23×C4C42116yescomplemented
365C23×C4C4⋊C4116yescomplemented
366C23×C4C22×C414yes—
367C23×C4C22×C414yes—
368C23×C4C22×C412yes—
369C23×C4C22×C412yes—
370C23×C4C22×C412yes—
371C23×C4C22×C414yes—
372C23×C4C22×C412yes—
373C23×C4C22×C414yes—
374C23×C4C22×C412yes—
375C23×C4C22×C412yes—
376C23×C4C22×C412yes—
377C23×C4C22×C412yes—
378C23×C4C22×C412yes—
379C23×C4C22×C412yes—
380C23×C4C2×D414yes—
381C23×C4C2×D414yes—
382C23×C4C2×D414yes—
383C23×C4C2×D414yes—
384C23×C4C2×D412yes—
385C23×C4C2×D414yes—
386C23×C4C2×D414yes—
387C23×C4C2×D412yes—
388C23×C4C2×Q814yes—
389C23×C4C2×Q812yes—
390C23×C4C2×Q812yes—
391C23×C4#4114yes—
392C23×C4#4114yes—
393C23×C4#4114yes—
394C2×C4⋊C4—216no—
395C2×C4⋊C4—216no—
396C2×C4⋊C4—48no—
397C2×C4⋊C4—48no—
398C2×C4⋊C4—48no—
399C2×C4⋊C4—48no—
400C2×C4⋊C4—48no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
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—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4C22⋊C4116yes—
428C2×C22⋊C4C4⋊C4116yescomplemented
429C2×C42—216no—
430C2×C42—48no—
431C2×C42—48no—
432C2×C42—48no—
433C2×C42—48no—
434C2×C42—48no—
435C2×C42—48no—
436#95—216no—
437#95—28no—
438#95—28no—
439#95—28no—
440#95—216no—
441#95—216no—
442#95—48no—
443#95—48no—
444#95—48no—
445#95—48no—
446#95—48no—
447#95—48no—
448#95—48no—
449#95C22⋊C4116yescomplemented
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—24no—
462C24—24no—
463C24—22no—
464C24—24no—
465C24—24no—
466C24—24no—
467C24—24no—
468C24—24no—
469C24—24no—
470C24—24no—
471C24—24no—
472C24—24no—
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×C4214yes—
515C24C2×C22⋊C414yes—
516C24C2×C4⋊C414yes—
517C24C2×C4⋊C414yes—
518C24#11714yes—
519C24#11714yes—
520C24#11714yes—
521C24C4×D414yes—
522C24C4×D414yes—
523C24C4×D414yes—
524C24C4×D414yes—
525C24C4×D414yes—
526C24C4×D414yes—
527C24C4×D414yes—
528C24C4×D414yes—
529C24C4×Q814yes—
530C24C4×Q814yes—
531C24C4×Q814yes—
532C24C4×Q814yes—
533C24#12014yes—
534C24#12114yes—
535C24#12114yes—
536C24C22⋊Q814yes—
537C24C22⋊Q814yes—
538C24C22⋊Q814yes—
539C24C22⋊Q814yes—
540C24#12314yes—
541C24#12314yes—
542C24#12314yes—
543C24#12414yes—
544C24#12514yes—
545C24#12514yes—
546C24#12614yes—
547C24#12614yes—
548C24C4⋊Q814yes—
549C24C23×C411yescharacteristic
550C24C23×C411yescharacteristic
551C24C23×C411yescharacteristic
552C24C22×D411yescharacteristic
553C24C22×D411yescharacteristic
554C24C22×D412yes—
555C24C22×D411yescharacteristic
556C24C22×D411yescharacteristic
557C24C22×Q811yescharacteristic
558C24C22×Q811yescharacteristic
559C24C2×#4111yescharacteristic
560C24C2×#4111yescharacteristic
561C24C2×#4112yes—
562C24C2×#4111yescharacteristic
563C24C2×#4111yescharacteristic
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—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
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—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—232no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—24no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
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—24no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—232no—
698C22×C4—232no—
699C22×C4—232no—
700C22×C4—232no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—416no—
716C22×C4—416no—
717C22×C4—432no—
718C22×C4—416no—
719C22×C4—416no—
720C22×C4—416no—
721C22×C4—416no—
722C22×C4—416no—
723C22×C4—416no—
724C22×C4—416no—
725C22×C4—416no—
726C22×C4—432no—
727C22×C4—432no—
728C22×C4—432no—
729C22×C4—432no—
730C22×C4—432no—
731C22×C4—432no—
732C22×C4—432no—
733C22×C4—416no—
734C22×C4—416no—
735C22×C4—416no—
736C22×C4—416no—
737C22×C4—416no—
738C22×C4—432no—
739C22×C4—432no—
740C22×C4—432no—
741C22×C4—432no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—41no—
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—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—416no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
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×C4C2×C4214yes—
868C22×C4C2×C4214yes—
869C22×C4C2×C22⋊C414yes—
870C22×C4C2×C22⋊C418yes—
871C22×C4C2×C22⋊C414yes—
872C22×C4C2×C22⋊C414yes—
873C22×C4C2×C4⋊C418yes—
874C22×C4C2×C4⋊C414yes—
875C22×C4C2×C4⋊C414yes—
876C22×C4#11714yes—
877C22×C4#11714yes—
878C22×C4#11714yes—
879C22×C4C4×D418yes—
880C22×C4C4×D418yes—
881C22×C4#12118yes—
882C22×C4C22⋊Q818yes—
883C4⋊C4—432no—
884C22⋊C4—232no—
885C22⋊C4—232no—
886C22⋊C4—416no—
887C22⋊C4—416no—
888C42—432no—
889C23—28no—
890C23—24no—
891C23—24no—
892C23—28no—
893C23—24no—
894C23—24no—
895C23—28no—
896C23—28no—
897C23—28no—
898C23—28no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23—28no—
903C23—28no—
904C23—24no—
905C23—28no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—28no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—28no—
920C23—28no—
921C23—28no—
922C23—28no—
923C23—28no—
924C23—28no—
925C23—28no—
926C23—28no—
927C23—28no—
928C23—28no—
929C23—28no—
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—28no—
958C23—28no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—28no—
968C23—28no—
969C23—28no—
970C23—28no—
971C23—28no—
972C23—28no—
973C23C4×C22⋊C418yes—
974C23C4×C4⋊C418yes—
975C23C4×C4⋊C418yes—
976C23#38518yes—
977C23#38518yes—
978C23#38618yes—
979C23#38718yes—
980C23#38718yes—
981C23#38718yes—
982C23#38718yes—
983C23#38818yes—
984C23#38818yes—
985C23#38918yes—
986C23#38918yes—
987C23#39118yes—
988C23C22×C4211yescharacteristic
989C23C22×C22⋊C411yescharacteristic
990C23C22×C22⋊C411yescharacteristic
991C23C22×C4⋊C411yescharacteristic
992C23C22×C4⋊C411yescharacteristic
993C23C2×#11711yescharacteristic
994C23C2×#11711yescharacteristic
995C23C2×#11711yescharacteristic
996C23C2×#11711yescharacteristic
997C23C2×#11711yescharacteristic
998C23C2×#11711yescharacteristic
999C23C2×C4×D411yescharacteristic
1000C23C2×C4×D411yescharacteristic
1001C23C2×C4×D411yescharacteristic
1002C23C2×C4×D411yescharacteristic
1003C23C2×C4×D411yescharacteristic
1004C23C2×C4×D412yes—
1005C23C2×C4×D412yes—
1006C23C2×C4×D411yescharacteristic
1007C23C2×C4×D411yescharacteristic
1008C23C2×C4×D411yescharacteristic
1009C23C2×C4×Q811yescharacteristic
1010C23C2×C4×Q811yescharacteristic
1011C23C2×C4×Q811yescharacteristic
1012C23C2×C4×Q811yescharacteristic
1013C23C4×#4112yes—
1014C23C4×#4112yes—
1015C23#51811yescharacteristic
1016C23#51811yescharacteristic
1017C23#51811yescharacteristic
1018C23#51812yes—
1019C23#51812yes—
1020C23#51911yescharacteristic
1021C23#52012yes—
1022C23#52012yes—
1023C23C2×#12011yescharacteristic
1024C23C2×#12112yes—
1025C23C2×#12111yescharacteristic
1026C23C2×#12111yescharacteristic
1027C23C2×C22⋊Q811yescharacteristic
1028C23C2×C22⋊Q811yescharacteristic
1029C23C2×C22⋊Q811yescharacteristic
1030C23C2×C22⋊Q812yes—
1031C23C2×C22⋊Q811yescharacteristic
1032C23C2×#12311yescharacteristic
1033C23C2×#12311yescharacteristic
1034C23C2×#12311yescharacteristic
1035C23#52512yes—
1036C23#52512yes—
1037C23C2×#12411yescharacteristic
1038C23C2×#12511yescharacteristic
1039C23C2×#12511yescharacteristic
1040C23C2×#12611yescharacteristic
1041C23C2×#12611yescharacteristic
1042C23#52912yes—
1043C23#52912yes—
1044C23C2×C4⋊Q811yescharacteristic
1045C23#53212yes—
1046C23#53312yes—
1047C23#53412yes—
1048C23#53712yes—
1049C23#53812yes—
1050C23#53812yes—
1051C23#53912yes—
1052C23#53912yes—
1053C23#54312yes—
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—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—28no—
1098C2×C4—28no—
1099C2×C4—28no—
1100C2×C4—28no—
1101C2×C4—28no—
1102C2×C4—28no—
1103C2×C4—28no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—28no—
1115C2×C4—28no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—28no—
1123C2×C4—24no—
1124C2×C4—28no—
1125C2×C4—464no—
1126C2×C4—464no—
1127C2×C4—464no—
1128C2×C4—44no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—44no—
1132C2×C4—44no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—44no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
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—44no—
1158C2×C4—44no—
1159C2×C4—44no—
1160C2×C4—44no—
1161C2×C4—44no—
1162C2×C4—44no—
1163C2×C4—44no—
1164C2×C4—44no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—44no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—44no—
1175C2×C4—44no—
1176C2×C4—44no—
1177C2×C4—44no—
1178C2×C4—44no—
1179C2×C4—44no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—44no—
1183C2×C4—44no—
1184C2×C4—44no—
1185C2×C4—44no—
1186C2×C4—44no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—44no—
1191C2×C4—44no—
1192C2×C4—44no—
1193C2×C4—44no—
1194C2×C4—44no—
1195C2×C4—44no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—82no—
1199C2×C4—82no—
1200C2×C4—82no—
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×C4C4×C22⋊C418yescomplemented
1215C2×C4#38018yescomplemented
1216C22—28no—
1217C22—28no—
1218C22—28no—
1219C22—28no—
1220C22—28no—
1221C22—28no—
1222C22—28no—
1223C22—28no—
1224C22—216no—
1225C22—216no—
1226C22—216no—
1227C22—216no—
1228C22—216no—
1229C22—28no—
1230C22—216no—
1231C22—28no—
1232C22—216no—
1233C22—216no—
1234C22—28no—
1235C22—28no—
1236C22—28no—
1237C22—28no—
1238C22#1436116yescomplemented
1239C22C2×C4×C22⋊C411yescharacteristic
1240C22C2×C4×C22⋊C411yescharacteristic
1241C22C2×C4×C4⋊C411yescharacteristic
1242C22C2×C4×C4⋊C411yescharacteristic
1243C22C4×#11711yescharacteristic
1244C22#227311yescharacteristic
1245C22#227411yescharacteristic
1246C22C2×#38011yescharacteristic
1247C22#228011yescharacteristic
1248C22#228311yescharacteristic
1249C22#228511yescharacteristic
1250C22C2×#38511yescharacteristic
1251C22C2×#38511yescharacteristic
1252C22C2×#38611yescharacteristic
1253C22C2×#38711yescharacteristic
1254C22C2×#38711yescharacteristic
1255C22C2×#38711yescharacteristic
1256C22C2×#38711yescharacteristic
1257C22C2×#38811yescharacteristic
1258C22C2×#38811yescharacteristic
1259C22C2×#38911yescharacteristic
1260C22C2×#38911yescharacteristic
1261C22C2×#39111yescharacteristic
1262C22C4×#12112yes—
1263C22C4×#12112yes—
1264C22C4×C22⋊Q812yes—
1265C22C4×C22⋊Q812yes—
1266C22#231211yescharacteristic
1267C22#231311yescharacteristic
1268C22#231511yescharacteristic
1269C22#231611yescharacteristic
1270C22#232512yes—
1271C22#232512yes—
1272C22#232912yes—
1273C22#232912yes—
1274C22D4×C22⋊C411yescharacteristic
1275C22D4×C22⋊C411yescharacteristic
1276C22D4×C22⋊C411yescharacteristic
1277C22D4×C22⋊C412yes—
1278C22#233912yes—
1279C22Q8×C22⋊C411yescharacteristic
1280C22#234211yescharacteristic
1281C22#234211yescharacteristic
1282C22#234211yescharacteristic
1283C22#234211yescharacteristic
1284C22#234211yescharacteristic
1285C22#234211yescharacteristic
1286C22#234212yes—
1287C22#234312yes—
1288C22#234411yescharacteristic
1289C22#234411yescharacteristic
1290C22#234411yescharacteristic
1291C22#234511yescharacteristic
1292C22#234511yescharacteristic
1293C22#234511yescharacteristic
1294C22D4×C4⋊C412yes—
1295C22#234912yes—
1296C22#235212yes—
1297C22#235312yes—
1298C22#235812yes—
1299C22#235812yes—
1300C22#235912yes—
1301C22#235912yes—
1302C22#236012yes—
1303C22#236112yes—
1304C22#236412yes—
1305C22#236812yes—
1306C22#241012yes—
1307C22#241212yes—
1308C22#241612yes—
1309C22#241712yes—
1310C22#241812yes—
1311C22#241912yes—
1312C22#242412yes—
1313C22#242512yes—
1314C22#243012yes—
1315C22#243712yes—
1316C22#243712yes—
1317C22#243812yes—
1318C22#243812yes—
1319C22#244012yes—
1320C22#244212yes—
1321C22#244312yes—
1322C22#244412yes—
1323C22#244912yes—
1324C22#245012yes—
1325C22#247212yes—
1326C22#247312yes—
1327C22#248012yes—
1328C22#248112yes—
1329C22#248812yes—
1330C22#249312yes—
1331C22#249812yes—
1332C22#250512yes—
1333C22#251012yes—
1334C22#254312yes—
1335C22#254912yes—
1336C22#256412yes—
1337C22#256912yes—
1338C4—28no—
1339C4—28no—
1340C4—44no—
1341C4—44no—
1342C4—44no—
1343C4—48no—
1344C4—48no—
1345C4—44no—
1346C4—84no—
1347C4—84no—
1348C2—216no—
1349C2C2×#143611yescharacteristic
1350C2C4×#38011yescharacteristic
1351C2#1377811yescharacteristic
1352C2C22⋊C4211yescharacteristic
1353C2#1379911yescharacteristic
1354C2C22⋊C4×C4⋊C411yescharacteristic
1355C2#1380211yescharacteristic
1356C2#1387311yescharacteristic
1357C2#1387411yescharacteristic
1358C2#1387711yescharacteristic
1359C2#1387811yescharacteristic
1360C2#1388211yescharacteristic
1361C2#1388311yescharacteristic
1362C2#1390711yescharacteristic
1363C2#1390811yescharacteristic
1364C2#1397512yes—
1365C2#1398012yes—
1366C2#1399912yes—
1367C2#1400412yes—
1368C2#1402312yes—
1369C2#1402812yes—
1370C2#1404712yes—
1371C2#1405212yes—
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC23C22×C42
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1436C2semidirect
9. #7557C2semidirect
10. #7556C2semidirect
11. #7554C2semidirect
23. C2×#380C4semidirect
28. C22×#95C4semidirect
47. C22⋊#95C4semidirect
98. C22×C4⋊C4C2×C4semidirect
171. C2×#95C2×C4semidirect
172. C2×#95C2×C4semidirect
173. C2×#95C2×C4semidirect
364. C23×C4C42semidirect
365. C23×C4C4⋊C4semidirect
428. C2×C22⋊C4C4⋊C4semidirect
449. #95C22⋊C4semidirect
1214. C2×C4C4×C22⋊C4semidirect
1215. C2×C4#380semidirect
1238. C22#1436semidirect

Maximal subgroups

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

subgroupindex
C22×#3802
C22×C4×C22⋊C42
C23×#952
C2×#14362
C2×C22⋊#952
#75572
#75562
#75542