Finite Group Databasebeta

← #154103

Subgroups — #154103

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×#1440C212yesmaximal
3C2×#1439C212yesmaximal
4C2×C4⋊#95C211yesmaximal, characteristic, complemented
5C2×#1434C211yesmaximal, characteristic, complemented
6C2×C22⋊#95C211yesmaximal, characteristic
7C2×C22⋊#95C211yesmaximal, characteristic
8#7557C212yesmaximal, complemented
9#7556C212yesmaximal, complemented
10#7554C211yesmaximal, characteristic, complemented
11#7554C211yesmaximal, characteristic, complemented
12C25×C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C22⋊C4C2212yes—
15C23×C22⋊C4C2212yes—
16C23×C22⋊C4C2211yescharacteristic
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#1440—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—22no—
75C22×C22⋊C4—24no—
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—42no—
88C22×C22⋊C4—42no—
89C22×C22⋊C4—42no—
90C22×C22⋊C4—42no—
91C22×C22⋊C4C2×C414yes—
92C22×C22⋊C4C2×C414yes—
93C22×C22⋊C4D418yes—
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—24no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—22no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—22no—
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—22no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—22no—
137C2×#95—22no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95C2×C414yes—
147C2×#95C2×C414yes—
148C2×#95D414yes—
149C2×#95D414yes—
150C25—21no—
151C25—21no—
152C25—22no—
153C25—21no—
154C25—21no—
155C25—22no—
156C25—22no—
157C25—21no—
158C25—21no—
159C25—22no—
160C25—21no—
161C25—21no—
162C25—21no—
163C25—21no—
164C25—22no—
165C25—22no—
166C25—21no—
167C25—21no—
168C25C22×C412yes—
169C25C2×D414yes—
170C25C2×D412yes—
171C25C2×Q812yes—
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—22no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
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×D412yes—
307C23×C4C2×D412yes—
308C23×C4C2×D414yes—
309C23×C4C2×D412yes—
310C23×C4C2×D412yes—
311C23×C4C2×Q812yes—
312C23×C4C2×Q812yes—
313C23×C4#4114yes—
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—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—216no—
333C2×C22⋊C4—216no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—216no—
337C2×C22⋊C4—216no—
338C2×C22⋊C4—216no—
339C2×C22⋊C4—216no—
340C2×C22⋊C4—48no—
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⋊C4C22⋊C4116yes—
353C2×C22⋊C4C4⋊C4116yescomplemented
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—28no—
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—48no—
378#95—44no—
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—22no—
404C24—22no—
405C24—24no—
406C24—24no—
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—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
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—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—41no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—41no—
468C24—42no—
469C24—41no—
470C24—42no—
471C24—41no—
472C24—42no—
473C24C2×C22⋊C414yes—
474C24C2×C4⋊C414yes—
475C24#11714yes—
476C24#12118yes—
477C24C22⋊Q818yes—
478C24C23×C411yescharacteristic
479C24C22×D412yes—
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482C24C22×D411yescharacteristic
483C24C22×Q811yescharacteristic
484C24C2×#4112yes—
485C24C2×#4111yescharacteristic
486C24C2×#4112yes—
487C24C2×#4111yescharacteristic
488C24C2×#4111yescharacteristic
489C24C2×#4111yescharacteristic
490C24C2×#4112yes—
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—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
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—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
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—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—41no—
656C22×C4—41no—
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×C4⋊C414yes—
777C22×C4C2×C4⋊C414yes—
778C22×C4#11714yes—
779C22×C4#11714yes—
780C22×C4#11714yes—
781C22×C4#11714yes—
782C22×C4C4×D414yes—
783C22×C4C4×D414yes—
784C22×C4#12114yes—
785C22×C4#12318yes—
786C22×C4#12318yes—
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—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—28no—
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—42no—
830C23—44no—
831C23—42no—
832C23—44no—
833C23—44no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—42no—
855C23—44no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—44no—
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—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—44no—
881C23—44no—
882C23—44no—
883C23—44no—
884C23—44no—
885C23—44no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—44no—
890C23—42no—
891C23—44no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23#38018yes—
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×#12312yes—
915C23C2×#12312yes—
916C23C2×#12311yescharacteristic
917C23#52512yes—
918C23#52512yes—
919C23#52512yes—
920C23#52512yes—
921C23#52512yes—
922C23C2×#12411yescharacteristic
923C23C2×#12611yescharacteristic
924C23#52912yes—
925C23#52912yes—
926C23#52912yes—
927C23#52912yes—
928C23#52912yes—
929C23#52912yes—
930C23#52912yes—
931C23#52912yes—
932C23#52912yes—
933C23#52912yes—
934C23#53211yescharacteristic
935C23#53211yescharacteristic
936C23#53212yes—
937C23#53212yes—
938C23#53312yes—
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#54612yes—
967C23#54611yescharacteristic
968C23#54712yes—
969C23#54712yes—
970C23#54711yescharacteristic
971C23#54711yescharacteristic
972C23#54711yescharacteristic
973C23#54811yescharacteristic
974C23D4×Q811yescharacteristic
975C23D4×Q811yescharacteristic
976C23#55011yescharacteristic
977C23#55112yes—
978C23#55112yes—
979C23#55112yes—
980C23#55212yes—
981C23#55211yescharacteristic
982C23#55312yes—
983C23#55312yes—
984C23#55312yes—
985C23#55311yescharacteristic
986C23#55411yescharacteristic
987C23#55412yes—
988C23#55412yes—
989C23#55411yescharacteristic
990C23#55512yes—
991C23#55511yescharacteristic
992C23#55612yes—
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#38118yes—
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
1146C22C2×#38111yescharacteristic
1147C22#228011yescharacteristic
1148C22#228311yescharacteristic
1149C22#228311yescharacteristic
1150C22#228511yescharacteristic
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#233911yescharacteristic
1168C22#234211yescharacteristic
1169C22#234211yescharacteristic
1170C22#234611yescharacteristic
1171C22#234711yescharacteristic
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#241812yes—
1186C22#241912yes—
1187C22#242012yes—
1188C22#242211yescharacteristic
1189C22#242212yes—
1190C22#242311yescharacteristic
1191C22#242412yes—
1192C22#242412yes—
1193C22#242412yes—
1194C22#242512yes—
1195C22#242512yes—
1196C22#242811yescharacteristic
1197C22#242911yescharacteristic
1198C22#244312yes—
1199C22#244412yes—
1200C22#244512yes—
1201C22#244712yes—
1202C22#244912yes—
1203C22#244912yes—
1204C22#245012yes—
1205C22#245012yes—
1206C22#245912yes—
1207C22#246012yes—
1208C22#246412yes—
1209C22#246512yes—
1210C22#246612yes—
1211C22#246712yes—
1212C22#247012yes—
1213C22#247212yes—
1214C22#247412yes—
1215C22#247612yes—
1216C22#247812yes—
1217C22#248012yes—
1218C22#249111yescharacteristic
1219C22#249211yescharacteristic
1220C22#249611yescharacteristic
1221C22#249711yescharacteristic
1222C22#251712yes—
1223C22#251812yes—
1224C22#251812yes—
1225C22#252112yes—
1226C22#252212yes—
1227C22#252312yes—
1228C22#255312yes—
1229C22#255512yes—
1230C22#255612yes—
1231C22#255712yes—
1232C22#255912yes—
1233C22#257412yes—
1234C22#258712yes—
1235C22#258912yes—
1236C22#264812yes—
1237C22#264912yes—
1238C22#265212yes—
1239C22#265312yes—
1240C22#285412yes—
1241C22#285412yes—
1242C22#285512yes—
1243C22#285512yes—
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#1388811yescharacteristic
1259C2#1389111yescharacteristic
1260C2#1389211yescharacteristic
1261C2#1389411yescharacteristic
1262C2#1389911yescharacteristic
1263C2#1389911yescharacteristic
1264C2#1391511yescharacteristic
1265C2#1391611yescharacteristic
1266C2#1394311yescharacteristic
1267C2#1394811yescharacteristic
1268C2#1435111yescharacteristic
1269C2#1468511yescharacteristic
1270C2#1474112yes—
1271C2#1474212yes—
1272C2#1475112yes—
1273C2#1475212yes—
1274C2#1479712yes—
1275C2#1480212yes—
1276C2#1483012yes—
1277C2#1483112yes—
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×C4⋊#95C2semidirect
5. C2×#1434C2semidirect
8. #7557C2semidirect
9. #7556C2semidirect
10. #7554C2semidirect
11. #7554C2semidirect
21. C2×C4×C22⋊C4C4semidirect
353. C2×C22⋊C4C4⋊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×#14402
C2×#14392
C2×C4⋊#952
C2×#14342
C2×C22⋊#952
#75572
#75562
#75542