Finite Group Databasebeta

← #154104

Subgroups — #154104

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊C4C211yesmaximal, characteristic
2C2×#1442C212yesmaximal, complemented
3C2×#1439C212yesmaximal
4C2×C4⋊#95C211yesmaximal, characteristic, complemented
5C2×#1434C211yesmaximal, characteristic, complemented
6C2×C22⋊#95C211yesmaximal, characteristic
7C2×C22⋊#95C211yesmaximal, characteristic
8#7556C212yesmaximal, 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×C42C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C2×C4×C22⋊C4—28no—
21C2×C4×C22⋊C4C418yescomplemented
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37#1442—28no—
38#1439—28no—
39C4⋊#95—24no—
40#1434—24no—
41C22⋊#95—24no—
42C22⋊#95—24no—
43C26C2311yescharacteristic
44C24×C4—24no—
45C24×C4—24no—
46C24×C4—22no—
47C24×C4—22no—
48C24×C4—22no—
49C24×C4—22no—
50C24×C4—22no—
51C24×C4—22no—
52C24×C4—42no—
53C24×C4—42no—
54C24×C4C2×C414yes—
55C24×C4C2312yes—
56C24×C4C2312yes—
57C24×C4C2312yes—
58C24×C4C2312yes—
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C22×C4⋊C4—24no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—42no—
71C22×C4⋊C4—42no—
72C22×C22⋊C4—24no—
73C22×C22⋊C4—24no—
74C22×C22⋊C4—24no—
75C22×C22⋊C4—22no—
76C22×C22⋊C4—22no—
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×C414yes—
94C22×C22⋊C4D414yes—
95C22×C22⋊C4Q814yes—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—24no—
99C22×C42—24no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—42no—
103C22×C42—42no—
104C22×C42C2×C414yes—
105C22×C42C2×C414yes—
106C4×C22⋊C4—232no—
107C2×#95—22no—
108C2×#95—24no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—22no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—22no—
135C2×#95—22no—
136C2×#95—22no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95C2×C414yes—
146C2×#95C2×C414yes—
147C2×#95D414yes—
148C2×#95D414yes—
149C2×#95D418yes—
150C25—22no—
151C25—21no—
152C25—21no—
153C25—22no—
154C25—21no—
155C25—21no—
156C25—22no—
157C25—22no—
158C25—21no—
159C25—21no—
160C25—21no—
161C25—21no—
162C25—21no—
163C25—21no—
164C25—22no—
165C25—22no—
166C25—21no—
167C25—21no—
168C25C22×C412yes—
169C25C2×D412yes—
170C25C2×Q812yes—
171C25#4114yes—
172C25#4114yes—
173C25C2411yescharacteristic
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—21no—
184C23×C4—216no—
185C23×C4—216no—
186C23×C4—28no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—22no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—22no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—28no—
222C23×C4—28no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×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—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—28no—
280C23×C4—28no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4—48no—
284C23×C4—48no—
285C23×C4—48no—
286C23×C4—48no—
287C23×C4—48no—
288C23×C4—48no—
289C23×C4—48no—
290C23×C4—48no—
291C23×C4—48no—
292C23×C4—48no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4C22×C412yes—
298C23×C4C22×C412yes—
299C23×C4C22×C412yes—
300C23×C4C22×C412yes—
301C23×C4C22×C412yes—
302C23×C4C22×C412yes—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4C2×D414yes—
306C23×C4C2×D414yes—
307C23×C4C2×D412yes—
308C23×C4C2×D414yes—
309C23×C4C2×D412yes—
310C23×C4C2×D412yes—
311C23×C4C2×D412yes—
312C23×C4C2×Q812yes—
313C23×C4C2×Q812yes—
314C23×C4#4114yes—
315C23×C4#4114yes—
316C23×C4#4112yes—
317C23×C4#4112yes—
318C23×C4#4114yes—
319C23×C4#4112yes—
320C23×C4#4112yes—
321C23×C4#4112yes—
322C23×C4#4112yes—
323C2×C4⋊C4—216no—
324C2×C4⋊C4—48no—
325C2×C4⋊C4—48no—
326C2×C4⋊C4—48no—
327C2×C4⋊C4—48no—
328C2×C4⋊C4—48no—
329C2×C4⋊C4—48no—
330C2×C22⋊C4—216no—
331C2×C22⋊C4—216no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—216no—
338C2×C22⋊C4—216no—
339C2×C22⋊C4—216no—
340C2×C22⋊C4—216no—
341C2×C22⋊C4—48no—
342C2×C22⋊C4—48no—
343C2×C22⋊C4—48no—
344C2×C22⋊C4—48no—
345C2×C22⋊C4—48no—
346C2×C22⋊C4—48no—
347C2×C22⋊C4—48no—
348C2×C22⋊C4—48no—
349C2×C22⋊C4—48no—
350C2×C22⋊C4—48no—
351C2×C22⋊C4—48no—
352C2×C22⋊C4—48no—
353C2×C22⋊C4C4⋊C4116yes—
354C2×C42—28no—
355C2×C42—28no—
356C2×C42—28no—
357C2×C42—28no—
358C2×C42—44no—
359C2×C42—44no—
360C2×C42—48no—
361C2×C42—48no—
362C2×C42—48no—
363C2×C42—48no—
364#95—28no—
365#95—28no—
366#95—28no—
367#95—48no—
368#95—48no—
369#95—48no—
370#95—48no—
371#95—48no—
372#95—48no—
373#95—48no—
374#95—48no—
375#95—48no—
376#95—44no—
377#95—44no—
378#95C22⋊C4116yescomplemented
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—24no—
393C24—24no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—41no—
434C24—41no—
435C24—42no—
436C24—41no—
437C24—41no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—41no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—41no—
459C24—42no—
460C24—41no—
461C24—42no—
462C24—41no—
463C24—42no—
464C24—41no—
465C24—42no—
466C24—41no—
467C24—42no—
468C24—42no—
469C24—41no—
470C24—41no—
471C24—41no—
472C24—42no—
473C24C2×C4⋊C414yes—
474C24#11714yes—
475C24#11714yes—
476C24#12418yes—
477C24#12518yes—
478C24C23×C411yescharacteristic
479C24C22×D412yes—
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482C24C22×D411yescharacteristic
483C24C22×Q811yescharacteristic
484C24C2×#4112yes—
485C24C2×#4111yescharacteristic
486C24C2×#4111yescharacteristic
487C24C2×#4112yes—
488C24C2×#4112yes—
489C24C2×#4111yescharacteristic
490C24C2×#4111yescharacteristic
491C24C2×#4111yescharacteristic
492C24C2×#4111yescharacteristic
493C24C2×#4112yes—
494C24C2×#4112yes—
495C24H(5,𝔽2)12yes—
496C24H(5,𝔽2)12yes—
497C24H(5,𝔽2)11yescharacteristic
498C24H(5,𝔽2)11yescharacteristic
499C242−1+411yescharacteristic
500C242−1+411yescharacteristic
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—232no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
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—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—416no—
617C22×C4—416no—
618C22×C4—416no—
619C22×C4—416no—
620C22×C4—416no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—41no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—42no—
661C22×C4—416no—
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—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—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
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—42no—
773C22×C4—42no—
774C22×C4C2×C22⋊C414yes—
775C22×C4C2×C22⋊C414yes—
776C22×C4C2×C22⋊C414yes—
777C22×C4C2×C4⋊C414yes—
778C22×C4C2×C4⋊C414yes—
779C22×C4#11714yes—
780C22×C4#11714yes—
781C22×C4#11714yes—
782C22×C4C4×D414yes—
783C22×C4C4×D414yes—
784C22×C4#12118yes—
785C22×C4#12114yes—
786C22×C4C22⋊Q818yes—
787C22×C4#12314yes—
788C22×C4#12414yes—
789C22×C4#12614yes—
790C4⋊C4—432no—
791C22⋊C4—232no—
792C22⋊C4—232no—
793C22⋊C4—432no—
794C22⋊C4—432no—
795C42—416no—
796C42—416no—
797C23—24no—
798C23—24no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—28no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—28no—
818C23—28no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—42no—
828C23—42no—
829C23—44no—
830C23—44no—
831C23—42no—
832C23—42no—
833C23—44no—
834C23—44no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—42no—
853C23—42no—
854C23—44no—
855C23—44no—
856C23—44no—
857C23—44no—
858C23—42no—
859C23—44no—
860C23—42no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
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—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—44no—
886C23—44no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—44no—
891C23—42no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23#38218yes—
896C23C22×C22⋊C411yescharacteristic
897C23C22×C4⋊C411yescharacteristic
898C23C2×#11711yescharacteristic
899C23C2×#11711yescharacteristic
900C23C2×#11711yescharacteristic
901C23C2×#11711yescharacteristic
902C23C2×#11711yescharacteristic
903C23C2×C4×D411yescharacteristic
904C23C2×C4×D411yescharacteristic
905C23C4×#4111yescharacteristic
906C23C4×#4111yescharacteristic
907C23#51811yescharacteristic
908C23#51811yescharacteristic
909C23#52011yescharacteristic
910C23#52011yescharacteristic
911C23C2×#12112yes—
912C23C2×#12111yescharacteristic
913C23C2×C22⋊Q812yes—
914C23C2×#12311yescharacteristic
915C23#52512yes—
916C23#52512yes—
917C23#52512yes—
918C23#52512yes—
919C23#52512yes—
920C23#52512yes—
921C23#52512yes—
922C23C2×#12412yes—
923C23C2×#12411yescharacteristic
924C23C2×#12512yes—
925C23C2×#12611yescharacteristic
926C23#52912yes—
927C23#52912yes—
928C23#52912yes—
929C23#52912yes—
930C23#52912yes—
931C23#52912yes—
932C23#52912yes—
933C23#52912yes—
934C23#52912yes—
935C23#52912yes—
936C23#53211yescharacteristic
937C23#53211yescharacteristic
938C23#53212yes—
939C23#53311yescharacteristic
940C23#53311yescharacteristic
941C23#53812yes—
942C23#53812yes—
943C23#53812yes—
944C23#53812yes—
945C23#53812yes—
946C23#53912yes—
947C23#53912yes—
948C23#53912yes—
949C23#54011yescharacteristic
950C23#54012yes—
951C23#54111yescharacteristic
952C23#54211yescharacteristic
953C23#54211yescharacteristic
954C23#54212yes—
955C23D4212yes—
956C23D4212yes—
957C23D4211yescharacteristic
958C23D4211yescharacteristic
959C23#54612yes—
960C23#54612yes—
961C23#54612yes—
962C23#54612yes—
963C23#54612yes—
964C23#54612yes—
965C23#54612yes—
966C23#54611yescharacteristic
967C23#54712yes—
968C23#54711yescharacteristic
969C23#54711yescharacteristic
970C23#54711yescharacteristic
971C23#54812yes—
972C23#54811yescharacteristic
973C23D4×Q811yescharacteristic
974C23D4×Q811yescharacteristic
975C23#55012yes—
976C23#55011yescharacteristic
977C23#55112yes—
978C23#55112yes—
979C23#55112yes—
980C23#55112yes—
981C23#55112yes—
982C23#55212yes—
983C23#55212yes—
984C23#55211yescharacteristic
985C23#55312yes—
986C23#55312yes—
987C23#55311yescharacteristic
988C23#55412yes—
989C23#55412yes—
990C23#55411yescharacteristic
991C23#55411yescharacteristic
992C23#55511yescharacteristic
993C23#55611yescharacteristic
994C23#55912yes—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—28no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—464no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—44no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—44no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—44no—
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—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4—82no—
1092C2×C4—82no—
1093C2×C4—82no—
1094C2×C4—82no—
1095C2×C4—82no—
1096C2×C4—82no—
1097C2×C4—82no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4—82no—
1103C2×C4—82no—
1104C2×C4—82no—
1105C2×C4—82no—
1106C2×C4—82no—
1107C2×C4—82no—
1108C2×C4—82no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—82no—
1112C2×C4—82no—
1113C2×C4—82no—
1114C2×C4—82no—
1115C2×C4—82no—
1116C2×C4—82no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—82no—
1120C2×C4#38018yes—
1121C2×C4#38818yes—
1122C22—28no—
1123C22—28no—
1124C22—28no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22—44no—
1137C22—48no—
1138C22—48no—
1139C22—48no—
1140C22—48no—
1141C22—48no—
1142C22—48no—
1143C22—48no—
1144C22—48no—
1145C22C2×#38011yescharacteristic
1146C22#228011yescharacteristic
1147C22#228011yescharacteristic
1148C22C2×#38211yescharacteristic
1149C22#228311yescharacteristic
1150C22#228311yescharacteristic
1151C22#228511yescharacteristic
1152C22C2×#38811yescharacteristic
1153C22#229011yescharacteristic
1154C22#229011yescharacteristic
1155C22#229011yescharacteristic
1156C22#229311yescharacteristic
1157C22#229811yescharacteristic
1158C22#231211yescharacteristic
1159C22#231411yescharacteristic
1160C22#231811yescharacteristic
1161C22#231811yescharacteristic
1162C22#231811yescharacteristic
1163C22#231911yescharacteristic
1164C22D4×C22⋊C411yescharacteristic
1165C22D4×C22⋊C411yescharacteristic
1166C22#233911yescharacteristic
1167C22#234111yescharacteristic
1168C22#234211yescharacteristic
1169C22#234211yescharacteristic
1170C22#234311yescharacteristic
1171C22#234311yescharacteristic
1172C22D4×C4⋊C411yescharacteristic
1173C22D4×C4⋊C411yescharacteristic
1174C22#234911yescharacteristic
1175C22#234911yescharacteristic
1176C22#235211yescharacteristic
1177C22#235311yescharacteristic
1178C22#235411yescharacteristic
1179C22#235711yescharacteristic
1180C22#239212yes—
1181C22#239512yes—
1182C22#239812yes—
1183C22#240112yes—
1184C22#241812yes—
1185C22#242211yescharacteristic
1186C22#242311yescharacteristic
1187C22#242412yes—
1188C22#242412yes—
1189C22#242512yes—
1190C22#242712yes—
1191C22#242811yescharacteristic
1192C22#242812yes—
1193C22#242911yescharacteristic
1194C22#244912yes—
1195C22#245012yes—
1196C22#245212yes—
1197C22#245412yes—
1198C22#245512yes—
1199C22#245612yes—
1200C22#245612yes—
1201C22#245712yes—
1202C22#245812yes—
1203C22#245912yes—
1204C22#246012yes—
1205C22#246312yes—
1206C22#246612yes—
1207C22#246712yes—
1208C22#247112yes—
1209C22#247212yes—
1210C22#247212yes—
1211C22#247212yes—
1212C22#247312yes—
1213C22#247312yes—
1214C22#247512yes—
1215C22#247712yes—
1216C22#247912yes—
1217C22#248012yes—
1218C22#248812yes—
1219C22#248812yes—
1220C22#249111yescharacteristic
1221C22#249211yescharacteristic
1222C22#249611yescharacteristic
1223C22#249711yescharacteristic
1224C22#250512yes—
1225C22#250512yes—
1226C22#251512yes—
1227C22#251612yes—
1228C22#255312yes—
1229C22#255412yes—
1230C22#255712yes—
1231C22#255912yes—
1232C22#257212yes—
1233C22#257312yes—
1234C22#258712yes—
1235C22#258912yes—
1236C22#264812yes—
1237C22#264912yes—
1238C22#265212yes—
1239C22#265312yes—
1240C22#285012yes—
1241C22#285012yes—
1242C22#285112yes—
1243C22#285112yes—
1244C4—28no—
1245C4—28no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—84no—
1251C4—84no—
1252C4—84no—
1253C4—84no—
1254C2—48no—
1255C2#1384211yescharacteristic
1256C2#1387311yescharacteristic
1257C2#1387611yescharacteristic
1258C2#1388611yescharacteristic
1259C2#1388711yescharacteristic
1260C2#1389011yescharacteristic
1261C2#1389611yescharacteristic
1262C2#1389611yescharacteristic
1263C2#1389911yescharacteristic
1264C2#1391311yescharacteristic
1265C2#1392011yescharacteristic
1266C2#1394411yescharacteristic
1267C2#1394811yescharacteristic
1268C2#1435111yescharacteristic
1269C2#1468211yescharacteristic
1270C2#1474312yes—
1271C2#1474412yes—
1272C2#1475312yes—
1273C2#1475412yes—
1274C2#1481712yes—
1275C2#1481912yes—
1276C2#1483212yes—
1277C2#1483312yes—
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
2. C2×#1442C2semidirect
4. C2×C4⋊#95C2semidirect
5. C2×#1434C2semidirect
8. #7556C2semidirect
10. #7554C2semidirect
11. #7554C2semidirect
21. C2×C4×C22⋊C4C4semidirect
378. #95C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊C42
C2×#14422
C2×#14392
C2×C4⋊#952
C2×#14342
C2×C22⋊#952
#75562
#75552
#75542