Finite Group Databasebeta

← #153755

Subgroups — #153755

Order 512.

4598 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#381C211yesmaximal, characteristic
2C22×C4×C22⋊C4C211yesmaximal, characteristic
3C2×#1437C212yesmaximal
4C2×#1434C211yesmaximal, characteristic, complemented
5C2×C22⋊#95C211yesmaximal, characteristic
6C2×C4×#95C211yesmaximal, characteristic, complemented
7#7556C212yesmaximal, complemented
8#7555C212yesmaximal
9#7554C212yesmaximal, complemented
10#7554C211yesmaximal, characteristic, complemented
11#7554C211yesmaximal, characteristic, complemented
12C25×C4C2211yescharacteristic
13C23×C22⋊C4C2211yescharacteristic
14C23×C22⋊C4C2212yes—
15C23×C22⋊C4C2212yes—
16C23×C22⋊C4C2211yescharacteristic
17C23×C42C2212yes—
18C23×C42C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C2×#381—24no—
21C2×#381—24no—
22C2×#381C418yescomplemented
23C2×C4×C22⋊C4—28no—
24C2×C4×C22⋊C4C418yescomplemented
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2211yescharacteristic
40#1437—28no—
41#1434—24no—
42C22⋊#95C418yescomplemented
43C4×#95—24no—
44C26C2311yescharacteristic
45C24×C4—24no—
46C24×C4—24no—
47C24×C4—22no—
48C24×C4—22no—
49C24×C4—22no—
50C24×C4—22no—
51C24×C4—42no—
52C24×C4—42no—
53C24×C4C2×C414yes—
54C24×C4C2×C414yes—
55C24×C4C2×C414yes—
56C24×C4C2312yes—
57C24×C4C2312yes—
58C24×C4C2311yescharacteristic
59C24×C4C2312yes—
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C22×C22⋊C4—24no—
67C22×C22⋊C4—24no—
68C22×C22⋊C4—22no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4—22no—
71C22×C22⋊C4—24no—
72C22×C22⋊C4—22no—
73C22×C22⋊C4—24no—
74C22×C22⋊C4—24no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—24no—
77C22×C22⋊C4—24no—
78C22×C22⋊C4—24no—
79C22×C22⋊C4—24no—
80C22×C22⋊C4—24no—
81C22×C22⋊C4—42no—
82C22×C22⋊C4—42no—
83C22×C22⋊C4—42no—
84C22×C22⋊C4—42no—
85C22×C22⋊C4C2×C414yes—
86C22×C22⋊C4C2×C418yes—
87C22×C22⋊C4C2×C418yes—
88C22×C22⋊C4C2×C414yes—
89C22×C22⋊C4D418yes—
90C22×C42—24no—
91C22×C42—22no—
92C22×C42—22no—
93C22×C42—24no—
94C22×C42—24no—
95C22×C42—24no—
96C22×C42—24no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—24no—
100C22×C42—24no—
101C22×C42—42no—
102C22×C42—42no—
103C22×C42—42no—
104C22×C42—42no—
105C22×C42C2×C414yes—
106C22×C42C2×C414yes—
107#381—232no—
108C4×C22⋊C4—232no—
109C2×#95—24no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—22no—
121C2×#95—22no—
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—42no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95C2×C414yes—
143C2×#95C2×C414yes—
144C2×#95C2×C414yes—
145C2×#95C2×C414yes—
146C2×#95C2×C414yes—
147C2×#95C2×C418yes—
148C2×#95C2×C418yes—
149C2×#95C2×C414yes—
150C2×#95D414yes—
151C2×#95D414yes—
152C25—21no—
153C25—21no—
154C25—22no—
155C25—21no—
156C25—21no—
157C25—22no—
158C25—21no—
159C25—21no—
160C25—22no—
161C25—22no—
162C25—21no—
163C25—21no—
164C25—21no—
165C25—21no—
166C25—22no—
167C25—22no—
168C25—21no—
169C25—21no—
170C25C22×C412yes—
171C25C22×C412yes—
172C25C22×C412yes—
173C25C2×D414yes—
174C25#4114yes—
175C25C2411yescharacteristic
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—28no—
187C23×C4—28no—
188C23×C4—216no—
189C23×C4—216no—
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—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—22no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—22no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—22no—
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—21no—
222C23×C4—21no—
223C23×C4—21no—
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—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—21no—
245C23×C4—22no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—28no—
249C23×C4—28no—
250C23×C4—28no—
251C23×C4—28no—
252C23×C4—28no—
253C23×C4—28no—
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—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—44no—
283C23×C4—44no—
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—48no—
294C23×C4C42116yescomplemented
295C23×C4C22×C414yes—
296C23×C4C22×C414yes—
297C23×C4C22×C412yes—
298C23×C4C22×C412yes—
299C23×C4C22×C412yes—
300C23×C4C22×C414yes—
301C23×C4C22×C412yes—
302C23×C4C22×C414yes—
303C23×C4C22×C412yes—
304C23×C4C22×C412yes—
305C23×C4C22×C412yes—
306C23×C4C22×C412yes—
307C23×C4C22×C412yes—
308C23×C4C22×C412yes—
309C23×C4C2×D414yes—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2×D412yes—
313C23×C4C2×D412yes—
314C23×C4C2×D414yes—
315C23×C4#4114yes—
316C23×C4#4114yes—
317C23×C4#4112yes—
318C23×C4#4112yes—
319C23×C4#4114yes—
320C23×C4#4112yes—
321C23×C4#4112yes—
322C23×C4#4112yes—
323C23×C4#4114yes—
324C23×C4#4112yes—
325C2×C22⋊C4—216no—
326C2×C22⋊C4—216no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—216no—
333C2×C22⋊C4—216no—
334C2×C22⋊C4—216no—
335C2×C22⋊C4—216no—
336C2×C22⋊C4—216no—
337C2×C22⋊C4—216no—
338C2×C22⋊C4—48no—
339C2×C22⋊C4—48no—
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⋊C4C22⋊C4116yes—
349C2×C42—216no—
350C2×C42—28no—
351C2×C42—28no—
352C2×C42—28no—
353C2×C42—28no—
354C2×C42—44no—
355C2×C42—44no—
356C2×C42—48no—
357C2×C42—48no—
358C2×C42—48no—
359C2×C42—48no—
360C2×C42—48no—
361C2×C42—48no—
362C2×C42—48no—
363C2×C42—48no—
364C2×C42—48no—
365C2×C42—48no—
366#95—216no—
367#95—28no—
368#95—28no—
369#95—216no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—48no—
374#95—48no—
375#95—48no—
376#95—48no—
377#95—48no—
378#95—48no—
379#95—48no—
380#95C22⋊C4116yescomplemented
381C24—22no—
382C24—24no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—42no—
460C24—42no—
461C24—41no—
462C24—41no—
463C24—42no—
464C24—41no—
465C24—42no—
466C24—41no—
467C24—42no—
468C24—42no—
469C24—41no—
470C24—41no—
471C24—41no—
472C24—41no—
473C24—42no—
474C24—42no—
475C24C2×C4214yes—
476C24C2×C22⋊C414yes—
477C24#11714yes—
478C24C4×D418yes—
479C24C4×D418yes—
480C24C23×C411yescharacteristic
481C24C23×C411yescharacteristic
482C24C23×C411yescharacteristic
483C24C22×D412yes—
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486C24C2×#4112yes—
487C24C2×#4111yescharacteristic
488C24C2×#4111yescharacteristic
489C24C2×#4112yes—
490C24C2×#4111yescharacteristic
491C24C2×#4111yescharacteristic
492C24C2×#4112yes—
493C24C2×#4111yescharacteristic
494C24C2×#4111yescharacteristic
495C24C2×#4112yes—
496C24C2×#4112yes—
497C24H(5,𝔽2)12yes—
498C24H(5,𝔽2)12yes—
499C24H(5,𝔽2)11yescharacteristic
500C24H(5,𝔽2)11yescharacteristic
501C242−1+411yescharacteristic
502C242−1+411yescharacteristic
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
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—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—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—22no—
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—22no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—232no—
626C22×C4—232no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—416no—
642C22×C4—416no—
643C22×C4—416no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—416no—
647C22×C4—416no—
648C22×C4—432no—
649C22×C4—432no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
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—41no—
694C22×C4—41no—
695C22×C4—42no—
696C22×C4—41no—
697C22×C4—41no—
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—41no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
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×C4214yes—
775C22×C4C2×C4214yes—
776C22×C4C2×C22⋊C418yes—
777C22×C4C2×C22⋊C414yes—
778C22×C4C2×C22⋊C414yes—
779C22×C4C2×C22⋊C414yes—
780C22×C4#11714yes—
781C22×C4#11718yes—
782C22×C4#11714yes—
783C22×C4#11714yes—
784C22×C4#11714yes—
785C22×C4#11714yes—
786C22×C4C4×D414yes—
787C22×C4C4×D414yes—
788C22×C4C4×D414yes—
789C22×C4C4×D414yes—
790C22×C4#12318yes—
791C22×C4#12318yes—
792C22⋊C4—232no—
793C22⋊C4—232no—
794C22⋊C4—432no—
795C22⋊C4—432no—
796C42—416no—
797C42—416no—
798C42—432no—
799C23—28no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—28no—
805C23—24no—
806C23—24no—
807C23—28no—
808C23—24no—
809C23—24no—
810C23—28no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—44no—
830C23—44no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—44no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—44no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—44no—
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—44no—
877C23—44no—
878C23—44no—
879C23—44no—
880C23—44no—
881C23—44no—
882C23—44no—
883C23—44no—
884C23—44no—
885C23—42no—
886C23—42no—
887C23—44no—
888C23—42no—
889C23—42no—
890C23—44no—
891C23—44no—
892C23—44no—
893C23—44no—
894C23—44no—
895C23—44no—
896C23—44no—
897C23C4×C22⋊C418yes—
898C23C22×C4211yescharacteristic
899C23C22×C22⋊C411yescharacteristic
900C23C22×C22⋊C411yescharacteristic
901C23C2×#11711yescharacteristic
902C23C2×#11711yescharacteristic
903C23C2×#11711yescharacteristic
904C23C2×#11711yescharacteristic
905C23C2×#11712yes—
906C23C2×#11711yescharacteristic
907C23C2×#11711yescharacteristic
908C23C2×C4×D411yescharacteristic
909C23C2×C4×D411yescharacteristic
910C23C2×C4×D412yes—
911C23C2×C4×D412yes—
912C23C2×C4×D411yescharacteristic
913C23C2×C4×D411yescharacteristic
914C23C4×#4112yes—
915C23C4×#4112yes—
916C23C4×#4111yescharacteristic
917C23C4×#4111yescharacteristic
918C23C4×#4111yescharacteristic
919C23C4×#4111yescharacteristic
920C23C4×#4111yescharacteristic
921C23C4×#4111yescharacteristic
922C23C4×#4112yes—
923C23#51811yescharacteristic
924C23#51811yescharacteristic
925C23#51812yes—
926C23#51811yescharacteristic
927C23#51812yes—
928C23#51911yescharacteristic
929C23#52011yescharacteristic
930C23#52011yescharacteristic
931C23#52011yescharacteristic
932C23#52011yescharacteristic
933C23C2×#12312yes—
934C23C2×#12312yes—
935C23#52512yes—
936C23#52512yes—
937C23#52512yes—
938C23#52512yes—
939C23#52912yes—
940C23#52912yes—
941C23#52912yes—
942C23#52912yes—
943C23#52912yes—
944C23#52912yes—
945C23#52912yes—
946C23#52912yes—
947C23#53212yes—
948C23#53212yes—
949C23#53812yes—
950C23#53812yes—
951C23#53912yes—
952C23#53912yes—
953C23#54012yes—
954C23#54012yes—
955C23#54212yes—
956C23#54212yes—
957C23D4212yes—
958C23D4212yes—
959C23#54612yes—
960C23#54612yes—
961C23#54612yes—
962C23#54612yes—
963C23#54612yes—
964C23#54612yes—
965C23#54611yescharacteristic
966C23#54611yescharacteristic
967C23#54712yes—
968C23#54712yes—
969C23#54711yescharacteristic
970C23#54711yescharacteristic
971C23#54811yescharacteristic
972C23#54811yescharacteristic
973C23#55011yescharacteristic
974C23#55011yescharacteristic
975C23#55112yes—
976C23#55112yes—
977C23#55112yes—
978C23#55112yes—
979C23#55112yes—
980C23#55112yes—
981C23#55212yes—
982C23#55211yescharacteristic
983C23#55212yes—
984C23#55211yescharacteristic
985C23#55312yes—
986C23#55311yescharacteristic
987C23#55312yes—
988C23#55311yescharacteristic
989C23#55312yes—
990C23#55312yes—
991C23#55511yescharacteristic
992C23#55511yescharacteristic
993C23#55611yescharacteristic
994C23#55611yescharacteristic
995C23#55912yes—
996C23#55912yes—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—28no—
1020C2×C4—28no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—28no—
1034C2×C4—28no—
1035C2×C4—464no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—44no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—44no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
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—42no—
1087C2×C4—42no—
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—44no—
1097C2×C4—44no—
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—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—82no—
1121C2×C4—82no—
1122C2×C4C4×C22⋊C418yes—
1123C2×C4#38118yescomplemented
1124C22—28no—
1125C22—28no—
1126C22—28no—
1127C22—48no—
1128C22—48no—
1129C22—48no—
1130C22—48no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—48no—
1140C22—48no—
1141C22—48no—
1142C22—48no—
1143C22—44no—
1144C22—44no—
1145C22—44no—
1146C22—44no—
1147C22C2×C4×C22⋊C411yescharacteristic
1148C22C2×C4×C22⋊C411yescharacteristic
1149C22C4×#11711yescharacteristic
1150C22C4×#11711yescharacteristic
1151C22C4×#11711yescharacteristic
1152C22#227311yescharacteristic
1153C22#227411yescharacteristic
1154C22C2×#38111yescharacteristic
1155C22#228011yescharacteristic
1156C22#228311yescharacteristic
1157C22#228311yescharacteristic
1158C22#229011yescharacteristic
1159C22#229011yescharacteristic
1160C22#229012yes—
1161C22#229311yescharacteristic
1162C22#229311yescharacteristic
1163C22#229312yes—
1164C22#229712yes—
1165C22#229812yes—
1166C22C4×#12312yes—
1167C22C4×#12312yes—
1168C22C4×#12312yes—
1169C22C4×#12312yes—
1170C22#231811yescharacteristic
1171C22#231811yescharacteristic
1172C22#231911yescharacteristic
1173C22#231911yescharacteristic
1174C22#233212yes—
1175C22#233312yes—
1176C22#233512yes—
1177C22#233512yes—
1178C22D4×C22⋊C412yes—
1179C22D4×C22⋊C411yescharacteristic
1180C22D4×C22⋊C411yescharacteristic
1181C22#233911yescharacteristic
1182C22#233911yescharacteristic
1183C22#233911yescharacteristic
1184C22#234111yescharacteristic
1185C22#234212yes—
1186C22#234211yescharacteristic
1187C22#234211yescharacteristic
1188C22#234212yes—
1189C22#234311yescharacteristic
1190C22#234311yescharacteristic
1191C22#234412yes—
1192C22#234611yescharacteristic
1193C22#234711yescharacteristic
1194C22#235211yescharacteristic
1195C22#235211yescharacteristic
1196C22#235311yescharacteristic
1197C22#235311yescharacteristic
1198C22#235312yes—
1199C22#235411yescharacteristic
1200C22#235411yescharacteristic
1201C22#235711yescharacteristic
1202C22#235711yescharacteristic
1203C22#235712yes—
1204C22#235812yes—
1205C22#235812yes—
1206C22#235912yes—
1207C22#235912yes—
1208C22#236211yescharacteristic
1209C22#236211yescharacteristic
1210C22#236311yescharacteristic
1211C22#236311yescharacteristic
1212C22#237412yes—
1213C22#237412yes—
1214C22#241812yes—
1215C22#241912yes—
1216C22#242012yes—
1217C22#242212yes—
1218C22#244312yes—
1219C22#244412yes—
1220C22#244512yes—
1221C22#244712yes—
1222C22#245512yes—
1223C22#245612yes—
1224C22#245712yes—
1225C22#245712yes—
1226C22#245812yes—
1227C22#245912yes—
1228C22#246112yes—
1229C22#246412yes—
1230C22#246612yes—
1231C22#246812yes—
1232C22#247012yes—
1233C22#247112yes—
1234C22#251512yes—
1235C22#251612yes—
1236C22#252612yes—
1237C22#252712yes—
1238C22#255312yes—
1239C22#255412yes—
1240C22#255712yes—
1241C22#255812yes—
1242C22#257212yes—
1243C22#257312yes—
1244C22#257512yes—
1245C22#257612yes—
1246C4—28no—
1247C4—28no—
1248C4—48no—
1249C4—44no—
1250C4—44no—
1251C4—44no—
1252C4—48no—
1253C4—44no—
1254C4—84no—
1255C4—84no—
1256C2—48no—
1257C2#1376111yescharacteristic
1258C2C4×#38111yescharacteristic
1259C2#1378011yescharacteristic
1260C2C22⋊C4211yescharacteristic
1261C2#1379911yescharacteristic
1262C2#1380111yescharacteristic
1263C2#1380711yescharacteristic
1264C2#1388611yescharacteristic
1265C2#1388711yescharacteristic
1266C2#1389411yescharacteristic
1267C2#1389511yescharacteristic
1268C2#1391211yescharacteristic
1269C2#1391311yescharacteristic
1270C2#1391611yescharacteristic
1271C2#1391711yescharacteristic
1272C2#1398312yes—
1273C2#1398412yes—
1274C2#1400712yes—
1275C2#1400812yes—
1276C2#1409512yes—
1277C2#1409612yes—
1278C2#1410312yes—
1279C2#1410412yes—
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×#1434C2semidirect
6. C2×C4×#95C2semidirect
7. #7556C2semidirect
9. #7554C2semidirect
10. #7554C2semidirect
11. #7554C2semidirect
22. C2×#381C4semidirect
24. C2×C4×C22⋊C4C4semidirect
42. C22⋊#95C4semidirect
294. C23×C4C42semidirect
380. #95C22⋊C4semidirect
1123. C2×C4#381semidirect

Maximal subgroups

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

subgroupindex
C22×#3812
C22×C4×C22⋊C42
C2×#14372
C2×#14342
C2×C22⋊#952
C2×C4×#952
#75562
#75552
#75542