Finite Group Databasebeta

← #153757

Subgroups — #153757

Order 512.

4794 conjugacy classes of subgroups.

The subgroup lattice has 1293 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#380C211yesmaximal, characteristic
2C22×C4×C22⋊C4C211yesmaximal, characteristic
3C2×#1437C212yesmaximal
4C2×#1436C212yesmaximal, complemented
5C2×#1434C211yesmaximal, characteristic, complemented
6C2×C22⋊#95C211yesmaximal, characteristic
7C2×C4×#95C211yesmaximal, characteristic, complemented
8#7557C212yesmaximal, complemented
9#7555C212yesmaximal
10#7554C211yesmaximal, characteristic, complemented
11#7554C211yesmaximal, characteristic, complemented
12C25×C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2212yes—
16C23×C22⋊C4C2212yes—
17C23×C22⋊C4C2211yescharacteristic
18C23×C42C2212yes—
19C23×C42C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#380—24no—
22C2×#380—24no—
23C2×#380C418yescomplemented
24C2×C4×C22⋊C4—28no—
25C2×C4×C22⋊C4C418yescomplemented
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2212yes—
37C22×#95C2212yes—
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40#1437—28no—
41#1436—28no—
42#1434—24no—
43C22⋊#95C418yescomplemented
44C4×#95—24no—
45C26C2311yescharacteristic
46C24×C4—24no—
47C24×C4—22no—
48C24×C4—22no—
49C24×C4—24no—
50C24×C4—22no—
51C24×C4—22no—
52C24×C4—42no—
53C24×C4—42no—
54C24×C4C2×C414yes—
55C24×C4C2×C414yes—
56C24×C4C2×C414yes—
57C24×C4C2312yes—
58C24×C4C2312yes—
59C24×C4C2312yes—
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—42no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4C2×C418yes—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—22no—
76C22×C22⋊C4—24no—
77C22×C22⋊C4—24no—
78C22×C22⋊C4—24no—
79C22×C22⋊C4—24no—
80C22×C22⋊C4—24no—
81C22×C22⋊C4—24no—
82C22×C22⋊C4—24no—
83C22×C22⋊C4—24no—
84C22×C22⋊C4—24no—
85C22×C22⋊C4—24no—
86C22×C22⋊C4—24no—
87C22×C22⋊C4—24no—
88C22×C22⋊C4—42no—
89C22×C22⋊C4—42no—
90C22×C22⋊C4—42no—
91C22×C22⋊C4—42no—
92C22×C22⋊C4C2×C414yes—
93C22×C22⋊C4C2×C418yes—
94C22×C22⋊C4C2×C418yes—
95C22×C22⋊C4C2×C414yes—
96C22×C22⋊C4D414yes—
97C22×C22⋊C4Q814yes—
98C22×C42—24no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—24no—
102C22×C42—24no—
103C22×C42—24no—
104C22×C42—24no—
105C22×C42—22no—
106C22×C42—22no—
107C22×C42—24no—
108C22×C42—24no—
109C22×C42—42no—
110C22×C42—42no—
111C22×C42—42no—
112C22×C42—42no—
113C22×C42C2×C414yes—
114C22×C42C2×C414yes—
115#380—232no—
116C4×C22⋊C4—232no—
117C2×#95—24no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—22no—
127C2×#95—24no—
128C2×#95—22no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
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×#95—42no—
147C2×#95C2×C414yes—
148C2×#95C2×C418yes—
149C2×#95C2×C414yes—
150C2×#95C2×C414yes—
151C2×#95C2×C414yes—
152C2×#95C2×C414yes—
153C2×#95C2×C414yes—
154C2×#95D414yes—
155C2×#95D414yes—
156C2×#95D418yes—
157C25—22no—
158C25—21no—
159C25—21no—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—22no—
164C25—22no—
165C25—21no—
166C25—21no—
167C25—21no—
168C25—21no—
169C25—22no—
170C25—22no—
171C25—21no—
172C25—21no—
173C25C22×C412yes—
174C25C22×C412yes—
175C25C22×C412yes—
176C25C2×D412yes—
177C25C2×Q812yes—
178C25#4112yes—
179C25#4112yes—
180C25C2411yescharacteristic
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
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—21no—
225C23×C4—21no—
226C23×C4—21no—
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—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—22no—
247C23×C4—28no—
248C23×C4—28no—
249C23×C4—28no—
250C23×C4—28no—
251C23×C4—216no—
252C23×C4—28no—
253C23×C4—28no—
254C23×C4—28no—
255C23×C4—28no—
256C23×C4—216no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
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—22no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—48no—
288C23×C4—48no—
289C23×C4—48no—
290C23×C4—48no—
291C23×C4—48no—
292C23×C4—48no—
293C23×C4—48no—
294C23×C4—48no—
295C23×C4—48no—
296C23×C4—48no—
297C23×C4C42116yescomplemented
298C23×C4C22×C414yes—
299C23×C4C22×C414yes—
300C23×C4C22×C414yes—
301C23×C4C22×C412yes—
302C23×C4C22×C412yes—
303C23×C4C22×C414yes—
304C23×C4C22×C412yes—
305C23×C4C22×C412yes—
306C23×C4C22×C412yes—
307C23×C4C22×C412yes—
308C23×C4C22×C412yes—
309C23×C4C22×C412yes—
310C23×C4C22×C412yes—
311C23×C4C22×C412yes—
312C23×C4C2×D414yes—
313C23×C4C2×D414yes—
314C23×C4C2×D414yes—
315C23×C4C2×D412yes—
316C23×C4C2×D414yes—
317C23×C4C2×D412yes—
318C23×C4C2×D412yes—
319C23×C4C2×D414yes—
320C23×C4C2×D412yes—
321C23×C4C2×Q812yes—
322C23×C4C2×Q812yes—
323C23×C4#4114yes—
324C23×C4#4114yes—
325C23×C4#4114yes—
326C23×C4#4114yes—
327C23×C4#4112yes—
328C23×C4#4112yes—
329C23×C4#4114yes—
330C2×C4⋊C4—216no—
331C2×C4⋊C4—216no—
332C2×C4⋊C4—48no—
333C2×C4⋊C4—48no—
334C2×C4⋊C4—48no—
335C2×C4⋊C4—48no—
336C2×C4⋊C4—48no—
337C2×C22⋊C4—216no—
338C2×C22⋊C4—216no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—216no—
345C2×C22⋊C4—216no—
346C2×C22⋊C4—216no—
347C2×C22⋊C4—216no—
348C2×C22⋊C4—216no—
349C2×C22⋊C4—216no—
350C2×C22⋊C4—48no—
351C2×C22⋊C4—48no—
352C2×C22⋊C4—48no—
353C2×C22⋊C4—48no—
354C2×C22⋊C4—48no—
355C2×C22⋊C4—48no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—48no—
358C2×C22⋊C4—48no—
359C2×C22⋊C4—48no—
360C2×C22⋊C4C4⋊C4116yescomplemented
361C2×C42—216no—
362C2×C42—28no—
363C2×C42—28no—
364C2×C42—28no—
365C2×C42—28no—
366C2×C42—44no—
367C2×C42—44no—
368C2×C42—48no—
369C2×C42—48no—
370C2×C42—48no—
371C2×C42—48no—
372C2×C42—48no—
373C2×C42—48no—
374C2×C42—48no—
375C2×C42—48no—
376C2×C42—48no—
377C2×C42—48no—
378#95—216no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—216no—
383#95—28no—
384#95—48no—
385#95—48no—
386#95—48no—
387#95—48no—
388#95—48no—
389#95—48no—
390#95C22⋊C4116yescomplemented
391#95C22⋊C4116yescomplemented
392C24—22no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—22no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—24no—
448C24—22no—
449C24—22no—
450C24—24no—
451C24—24no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—42no—
483C24—42no—
484C24C2×C4214yes—
485C24C2×C4⋊C414yes—
486C24#11714yes—
487C24C4×D414yes—
488C24C4×D414yes—
489C24C4×Q814yes—
490C24C4×Q814yes—
491C24C23×C411yescharacteristic
492C24C23×C411yescharacteristic
493C24C23×C411yescharacteristic
494C24C22×D412yes—
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498C24C22×Q811yescharacteristic
499C24C2×#4111yescharacteristic
500C24C2×#4111yescharacteristic
501C24C2×#4112yes—
502C24C2×#4111yescharacteristic
503C24C2×#4111yescharacteristic
504C24C2×#4112yes—
505C24C2×#4112yes—
506C24C2×#4112yes—
507C24C2×#4112yes—
508C24H(5,𝔽2)12yes—
509C24H(5,𝔽2)12yes—
510C24H(5,𝔽2)11yescharacteristic
511C24H(5,𝔽2)11yescharacteristic
512C242−1+411yescharacteristic
513C242−1+411yescharacteristic
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
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—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—22no—
639C22×C4—24no—
640C22×C4—232no—
641C22×C4—232no—
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—416no—
657C22×C4—416no—
658C22×C4—416no—
659C22×C4—432no—
660C22×C4—432no—
661C22×C4—416no—
662C22×C4—416no—
663C22×C4—432no—
664C22×C4—432no—
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—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
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×C4—41no—
698C22×C4—41no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—42no—
717C22×C4—41no—
718C22×C4—41no—
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—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×C4C2×C4214yes—
782C22×C4C2×C4214yes—
783C22×C4C2×C22⋊C414yes—
784C22×C4C2×C22⋊C418yes—
785C22×C4C2×C22⋊C414yes—
786C22×C4C2×C22⋊C414yes—
787C22×C4C2×C22⋊C414yes—
788C22×C4C2×C4⋊C414yes—
789C22×C4C2×C4⋊C414yes—
790C22×C4#11714yes—
791C22×C4#11718yes—
792C22×C4#11714yes—
793C22×C4#11714yes—
794C22×C4#11714yes—
795C22×C4C4×D418yes—
796C22×C4C4×D414yes—
797C22×C4C4×D414yes—
798C22×C4C4×D414yes—
799C22×C4C4×D414yes—
800C22×C4C4×D418yes—
801C22×C4#12118yes—
802C22×C4C22⋊Q818yes—
803C4⋊C4—432no—
804C22⋊C4—232no—
805C22⋊C4—232no—
806C22⋊C4—432no—
807C22⋊C4—432no—
808C42—416no—
809C42—416no—
810C42—432no—
811C23—24no—
812C23—24no—
813C23—28no—
814C23—24no—
815C23—24no—
816C23—28no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—28no—
830C23—28no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—28no—
842C23—28no—
843C23—28no—
844C23—28no—
845C23—44no—
846C23—42no—
847C23—42no—
848C23—44no—
849C23—42no—
850C23—42no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23—44no—
856C23—44no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—44no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—44no—
868C23—44no—
869C23—44no—
870C23—44no—
871C23—44no—
872C23—44no—
873C23—44no—
874C23—44no—
875C23—44no—
876C23—44no—
877C23—44no—
878C23—44no—
879C23—44no—
880C23—44no—
881C23—44no—
882C23—44no—
883C23—44no—
884C23—44no—
885C23—44no—
886C23—44no—
887C23—44no—
888C23—44no—
889C23—44no—
890C23—44no—
891C23—44no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23—44no—
896C23—44no—
897C23—42no—
898C23—42no—
899C23—44no—
900C23—42no—
901C23—42no—
902C23—44no—
903C23—44no—
904C23—44no—
905C23—44no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23C4×C4⋊C418yes—
910C23C22×C4211yescharacteristic
911C23C22×C22⋊C411yescharacteristic
912C23C22×C22⋊C411yescharacteristic
913C23C22×C4⋊C411yescharacteristic
914C23C2×#11711yescharacteristic
915C23C2×#11711yescharacteristic
916C23C2×#11711yescharacteristic
917C23C2×#11711yescharacteristic
918C23C2×#11712yes—
919C23C2×#11711yescharacteristic
920C23C2×C4×D411yescharacteristic
921C23C2×C4×D411yescharacteristic
922C23C2×C4×D412yes—
923C23C2×C4×D411yescharacteristic
924C23C2×C4×D411yescharacteristic
925C23C2×C4×D412yes—
926C23C2×C4×D411yescharacteristic
927C23C2×C4×D411yescharacteristic
928C23C2×C4×Q811yescharacteristic
929C23C2×C4×Q811yescharacteristic
930C23C4×#4112yes—
931C23C4×#4112yes—
932C23C4×#4111yescharacteristic
933C23C4×#4111yescharacteristic
934C23C4×#4112yes—
935C23#51811yescharacteristic
936C23#51811yescharacteristic
937C23#51812yes—
938C23#51811yescharacteristic
939C23#51812yes—
940C23#51911yescharacteristic
941C23#52011yescharacteristic
942C23#52011yescharacteristic
943C23#52011yescharacteristic
944C23#52011yescharacteristic
945C23C2×#12112yes—
946C23C2×C22⋊Q812yes—
947C23#52512yes—
948C23#52512yes—
949C23#52512yes—
950C23#52512yes—
951C23#52912yes—
952C23#52912yes—
953C23#52912yes—
954C23#52912yes—
955C23#52912yes—
956C23#52912yes—
957C23#53212yes—
958C23#53212yes—
959C23#53212yes—
960C23#53312yes—
961C23#53812yes—
962C23#53812yes—
963C23#53912yes—
964C23#53912yes—
965C23#54012yes—
966C23#54012yes—
967C23#54212yes—
968C23#54212yes—
969C23D4212yes—
970C23D4212yes—
971C23D4211yescharacteristic
972C23D4211yescharacteristic
973C23#54612yes—
974C23#54612yes—
975C23#54612yes—
976C23#54612yes—
977C23#54611yescharacteristic
978C23#54611yescharacteristic
979C23#54612yes—
980C23#54612yes—
981C23#54612yes—
982C23#54712yes—
983C23#54711yescharacteristic
984C23#54711yescharacteristic
985C23#54811yescharacteristic
986C23#54811yescharacteristic
987C23#54812yes—
988C23D4×Q811yescharacteristic
989C23D4×Q811yescharacteristic
990C23#55012yes—
991C23#55112yes—
992C23#55112yes—
993C23#55112yes—
994C23#55112yes—
995C23#55211yescharacteristic
996C23#55211yescharacteristic
997C23#55212yes—
998C23#55312yes—
999C23#55311yescharacteristic
1000C23#55312yes—
1001C23#55311yescharacteristic
1002C23#55312yes—
1003C23#55411yescharacteristic
1004C23#55412yes—
1005C23#55411yescharacteristic
1006C23#55412yes—
1007C23#55512yes—
1008C23#55612yes—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—28no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—28no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—28no—
1042C2×C4—28no—
1043C2×C4—24no—
1044C2×C4—28no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—28no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—28no—
1053C2×C4—28no—
1054C2×C4—464no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—42no—
1063C2×C4—42no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—44no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—44no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—44no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—44no—
1099C2×C4—44no—
1100C2×C4—44no—
1101C2×C4—44no—
1102C2×C4—44no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4—82no—
1121C2×C4—82no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4—82no—
1125C2×C4—82no—
1126C2×C4—82no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—82no—
1130C2×C4—82no—
1131C2×C4—82no—
1132C2×C4—82no—
1133C2×C4C4×C22⋊C418yes—
1134C2×C4C4×C22⋊C418yes—
1135C2×C4#38018yescomplemented
1136C22—28no—
1137C22—28no—
1138C22—28no—
1139C22—48no—
1140C22—48no—
1141C22—48no—
1142C22—48no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22—44no—
1148C22—44no—
1149C22—44no—
1150C22—44no—
1151C22—48no—
1152C22—48no—
1153C22—48no—
1154C22—48no—
1155C22—44no—
1156C22—44no—
1157C22—44no—
1158C22—44no—
1159C22C2×C4×C22⋊C411yescharacteristic
1160C22C2×C4×C22⋊C411yescharacteristic
1161C22C2×C4×C4⋊C411yescharacteristic
1162C22C4×#11711yescharacteristic
1163C22C4×#11711yescharacteristic
1164C22#227311yescharacteristic
1165C22#227411yescharacteristic
1166C22C2×#38011yescharacteristic
1167C22#228011yescharacteristic
1168C22#228311yescharacteristic
1169C22#228511yescharacteristic
1170C22#229011yescharacteristic
1171C22#229011yescharacteristic
1172C22#229012yes—
1173C22#229311yescharacteristic
1174C22#229311yescharacteristic
1175C22#229312yes—
1176C22#229712yes—
1177C22#229812yes—
1178C22C4×#12112yes—
1179C22C4×#12112yes—
1180C22C4×C22⋊Q812yes—
1181C22C4×C22⋊Q812yes—
1182C22#231811yescharacteristic
1183C22#231811yescharacteristic
1184C22#231911yescharacteristic
1185C22#231911yescharacteristic
1186C22#233212yes—
1187C22#233312yes—
1188C22#233512yes—
1189C22#233512yes—
1190C22D4×C22⋊C412yes—
1191C22D4×C22⋊C411yescharacteristic
1192C22D4×C22⋊C411yescharacteristic
1193C22D4×C22⋊C411yescharacteristic
1194C22#233911yescharacteristic
1195C22Q8×C22⋊C411yescharacteristic
1196C22#234111yescharacteristic
1197C22#234212yes—
1198C22#234211yescharacteristic
1199C22#234211yescharacteristic
1200C22#234212yes—
1201C22#234411yescharacteristic
1202C22#234511yescharacteristic
1203C22#234512yes—
1204C22#234611yescharacteristic
1205C22#234711yescharacteristic
1206C22D4×C4⋊C411yescharacteristic
1207C22D4×C4⋊C411yescharacteristic
1208C22#234911yescharacteristic
1209C22#234911yescharacteristic
1210C22#235211yescharacteristic
1211C22#235211yescharacteristic
1212C22#235212yes—
1213C22#235311yescharacteristic
1214C22#235311yescharacteristic
1215C22#235412yes—
1216C22#235812yes—
1217C22#235812yes—
1218C22#236011yescharacteristic
1219C22#236011yescharacteristic
1220C22#236111yescharacteristic
1221C22#236111yescharacteristic
1222C22#236212yes—
1223C22#236312yes—
1224C22#236412yes—
1225C22#236812yes—
1226C22#242412yes—
1227C22#242512yes—
1228C22#242712yes—
1229C22#242812yes—
1230C22#244912yes—
1231C22#245012yes—
1232C22#245212yes—
1233C22#245412yes—
1234C22#245612yes—
1235C22#245712yes—
1236C22#246012yes—
1237C22#246112yes—
1238C22#246312yes—
1239C22#246412yes—
1240C22#246412yes—
1241C22#246512yes—
1242C22#246712yes—
1243C22#246812yes—
1244C22#247612yes—
1245C22#247712yes—
1246C22#252112yes—
1247C22#252212yes—
1248C22#253012yes—
1249C22#253112yes—
1250C22#255312yes—
1251C22#255512yes—
1252C22#255612yes—
1253C22#255912yes—
1254C22#256012yes—
1255C22#257412yes—
1256C22#257712yes—
1257C22#257812yes—
1258C4—28no—
1259C4—28no—
1260C4—28no—
1261C4—48no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C4—48no—
1266C4—84no—
1267C4—84no—
1268C2—48no—
1269C2#1376111yescharacteristic
1270C2C4×#38011yescharacteristic
1271C2#1378011yescharacteristic
1272C2C22⋊C4211yescharacteristic
1273C2C22⋊C4×C4⋊C411yescharacteristic
1274C2#1380111yescharacteristic
1275C2#1380211yescharacteristic
1276C2#1389011yescharacteristic
1277C2#1389111yescharacteristic
1278C2#1389811yescharacteristic
1279C2#1389911yescharacteristic
1280C2#1391211yescharacteristic
1281C2#1391511yescharacteristic
1282C2#1391911yescharacteristic
1283C2#1392011yescharacteristic
1284C2#1398712yes—
1285C2#1398812yes—
1286C2#1401112yes—
1287C2#1401212yes—
1288C2#1409912yes—
1289C2#1410012yes—
1290C2#1410712yes—
1291C2#1410812yes—
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
5. C2×#1434C2semidirect
7. C2×C4×#95C2semidirect
8. #7557C2semidirect
10. #7554C2semidirect
11. #7554C2semidirect
23. C2×#380C4semidirect
25. C2×C4×C22⋊C4C4semidirect
43. C22⋊#95C4semidirect
297. C23×C4C42semidirect
360. C2×C22⋊C4C4⋊C4semidirect
390. #95C22⋊C4semidirect
391. #95C22⋊C4semidirect
1135. C2×C4#380semidirect

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
C2×#14372
C2×#14362
C2×#14342
C2×C22⋊#952
C2×C4×#952
#75572
#75552
#75542