Finite Group Databasebeta

← #154031

Subgroups — #154031

Order 512.

4610 conjugacy classes of subgroups.

The subgroup lattice has 1137 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C212yesmaximal
2C22×#385C211yesmaximal, characteristic
3C2×C4⋊#95C212yesmaximal, complemented
4C2×C22⋊#95C212yesmaximal
5#7557C212yesmaximal, complemented
6#7557C212yesmaximal, complemented
7#7555C211yesmaximal, characteristic
8#7555C211yesmaximal, characteristic
9#7554C212yesmaximal, complemented
10C25×C4C2211yescharacteristic
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2212yes—
13C23×C22⋊C4C2212yes—
14C23×C22⋊C4C2212yes—
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2211yescharacteristic
17C23×C42C2212yes—
18C2×#388—28no—
19C2×#388—28no—
20C2×#388C4116yescomplemented
21C2×#385—28no—
22C2×#385C418yescomplemented
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C4⋊#95—28no—
37C22⋊#95—28no—
38C26C2311yescharacteristic
39C24×C4—24no—
40C24×C4—24no—
41C24×C4—24no—
42C24×C4—42no—
43C24×C4—42no—
44C24×C4—41no—
45C24×C4—41no—
46C24×C4—42no—
47C24×C4C2×C414yes—
48C24×C4C2311yescharacteristic
49C24×C4C2312yes—
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2312yes—
53C24×C4C2312yes—
54C24×C4C2312yes—
55C24×C4C2312yes—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—42no—
65C22×C4⋊C4—42no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4C2×C418yes—
69C22×C4⋊C4C2×C418yescomplemented
70C22×C22⋊C4—24no—
71C22×C22⋊C4—24no—
72C22×C22⋊C4—24no—
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—42no—
80C22×C22⋊C4—42no—
81C22×C22⋊C4—42no—
82C22×C22⋊C4—42no—
83C22×C22⋊C4—42no—
84C22×C22⋊C4—41no—
85C22×C22⋊C4—41no—
86C22×C22⋊C4C2×C418yes—
87C22×C22⋊C4C2×C418yes—
88C22×C22⋊C4C2×C414yes—
89C22×C22⋊C4C2×C414yes—
90C22×C22⋊C4C2×C418yes—
91C22×C22⋊C4D418yes—
92C22×C22⋊C4D414yes—
93C22×C22⋊C4Q814yes—
94C22×C42—24no—
95C22×C42—24no—
96C22×C42—24no—
97C22×C42—24no—
98C22×C42—42no—
99C22×C42—42no—
100C22×C42C2×C418yescomplemented
101#388—264no—
102#385—232no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—41no—
123C2×#95—41no—
124C2×#95—42no—
125C2×#95—42no—
126C2×#95—42no—
127C2×#95—42no—
128C2×#95—42no—
129C2×#95—42no—
130C2×#95—42no—
131C2×#95—42no—
132C2×#95—41no—
133C2×#95—41no—
134C2×#95C2×C418yes—
135C2×#95C2×C418yescomplemented
136C2×#95C2×C418yescomplemented
137C2×#95D418yes—
138C25—22no—
139C25—22no—
140C25—22no—
141C25—22no—
142C25—22no—
143C25—22no—
144C25—21no—
145C25—21no—
146C25—22no—
147C25—22no—
148C25—21no—
149C25—21no—
150C25—22no—
151C25—22no—
152C25C22×C414yes—
153C25C22×C412yes—
154C25C2×D412yes—
155C25C2×D414yes—
156C25C2×Q812yes—
157C25C2411yescharacteristic
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—28no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
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—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
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—216no—
248C23×C4—48no—
249C23×C4—44no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—48no—
253C23×C4—44no—
254C23×C4—48no—
255C23×C4—48no—
256C23×C4—48no—
257C23×C4—48no—
258C23×C4—48no—
259C23×C4—48no—
260C23×C4—48no—
261C23×C4—48no—
262C23×C4—48no—
263C23×C4—48no—
264C23×C4—48no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4C22×C412yes—
268C23×C4C22×C414yes—
269C23×C4C22×C412yes—
270C23×C4C22×C414yes—
271C23×C4C22×C414yes—
272C23×C4C22×C414yes—
273C23×C4C22×C414yes—
274C23×C4C22×C414yes—
275C23×C4C22×C414yes—
276C23×C4C22×C414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×Q814yes—
284C23×C4#4114yes—
285C23×C4#4114yes—
286C23×C4#4114yes—
287C2×C4⋊C4—216no—
288C2×C4⋊C4—216no—
289C2×C4⋊C4—216no—
290C2×C4⋊C4—216no—
291C2×C4⋊C4—48no—
292C2×C4⋊C4—48no—
293C2×C4⋊C4—48no—
294C2×C4⋊C4—48no—
295C2×C4⋊C4—48no—
296C2×C4⋊C4—48no—
297C2×C4⋊C4—48no—
298C2×C4⋊C4—48no—
299C2×C4⋊C4—48no—
300C2×C4⋊C4—48no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—216no—
303C2×C22⋊C4—216no—
304C2×C22⋊C4—216no—
305C2×C22⋊C4—216no—
306C2×C22⋊C4—48no—
307C2×C22⋊C4—48no—
308C2×C22⋊C4—44no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—48no—
311C2×C22⋊C4—48no—
312C2×C22⋊C4—48no—
313C2×C22⋊C4—48no—
314C2×C22⋊C4—48no—
315C2×C22⋊C4—48no—
316C2×C22⋊C4—48no—
317C2×C22⋊C4—48no—
318C2×C22⋊C4—48no—
319C2×C22⋊C4—48no—
320C2×C22⋊C4C42116yes—
321C2×C22⋊C4C22⋊C4116yes—
322C2×C22⋊C4C22⋊C4132yes—
323C2×C22⋊C4C4⋊C4116yes—
324C2×C22⋊C4C4⋊C4132yes—
325C2×C42—216no—
326C2×C42—216no—
327C2×C42—48no—
328C2×C42—48no—
329C2×C42—48no—
330C2×C42—48no—
331C2×C42—48no—
332#95—216no—
333#95—216no—
334#95—216no—
335#95—48no—
336#95—44no—
337#95—48no—
338#95—48no—
339#95—44no—
340#95—48no—
341#95—48no—
342#95—48no—
343#95—44no—
344#95—44no—
345C24—24no—
346C24—24no—
347C24—24no—
348C24—24no—
349C24—24no—
350C24—24no—
351C24—22no—
352C24—22no—
353C24—24no—
354C24—24no—
355C24—24no—
356C24—22no—
357C24—22no—
358C24—24no—
359C24—24no—
360C24—24no—
361C24—24no—
362C24—24no—
363C24—24no—
364C24—24no—
365C24—24no—
366C24—24no—
367C24—24no—
368C24—24no—
369C24—24no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—24no—
376C24—24no—
377C24—24no—
378C24—24no—
379C24—24no—
380C24—24no—
381C24—24no—
382C24—24no—
383C24—24no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—24no—
389C24—24no—
390C24—24no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—41no—
412C24—41no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—41no—
417C24—41no—
418C24—42no—
419C24—41no—
420C24—41no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—41no—
426C24—42no—
427C24C2×C4214yes—
428C24C2×C22⋊C418yes—
429C24C2×C22⋊C414yes—
430C24C2×C4⋊C414yes—
431C24C2×C4⋊C418yes—
432C24C23×C411yescharacteristic
433C24C23×C412yes—
434C24C22×D412yes—
435C24C22×D411yescharacteristic
436C24C22×D412yes—
437C24C22×Q811yescharacteristic
438C24C2×#4112yes—
439C24C2×#4112yes—
440C24C2×#4112yes—
441C24H(5,𝔽2)12yes—
442C24H(5,𝔽2)12yes—
443C24H(5,𝔽2)12yes—
444C24H(5,𝔽2)12yes—
445C24H(5,𝔽2)11yescharacteristic
446C24H(5,𝔽2)11yescharacteristic
447C242−1+411yescharacteristic
448C242−1+411yescharacteristic
449C242−1+412yes—
450C242−1+412yes—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
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—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
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—416no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—416no—
561C22×C4—416no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
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—41no—
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—41no—
682C22×C4—41no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—41no—
692C22×C4—42no—
693C22×C4—41no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—41no—
701C22×C4—42no—
702C22×C4C2×C4218yes—
703C22×C4C2×C22⋊C418yes—
704C22×C4C2×C22⋊C418yes—
705C22×C4C2×C22⋊C418yes—
706C22×C4C2×C4⋊C418yes—
707C22×C4C2×C4⋊C418yes—
708C22×C4C2×C4⋊C418yes—
709C22×C4C4×D418yes—
710C22×C4C4×D418yes—
711C22×C4C4×D418yes—
712C4⋊C4—432no—
713C4⋊C4—432no—
714C22⋊C4—432no—
715C22⋊C4—432no—
716C22⋊C4—416no—
717C22⋊C4#95164yescomplemented
718C42—432no—
719C23—24no—
720C23—24no—
721C23—28no—
722C23—28no—
723C23—24no—
724C23—24no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—28no—
733C23—28no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—24no—
741C23—24no—
742C23—28no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—42no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—42no—
762C23—42no—
763C23—44no—
764C23—42no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—42no—
776C23—44no—
777C23—42no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—42no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—42no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—42no—
798C23—44no—
799C23—42no—
800C23—42no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—42no—
805C23C2×#9518yes—
806C23C22×C4211yescharacteristic
807C23C22×C22⋊C411yescharacteristic
808C23C22×C22⋊C412yes—
809C23C22×C4⋊C411yescharacteristic
810C23C22×C4⋊C412yes—
811C23C2×C4×D412yes—
812C23C2×C4×D412yes—
813C23C2×C4×D412yes—
814C23C4×#4112yes—
815C23C4×#4112yes—
816C23C4×#4112yes—
817C23#51811yescharacteristic
818C23#51811yescharacteristic
819C23#51812yes—
820C23#51812yes—
821C23#51812yes—
822C23#51911yescharacteristic
823C23#51911yescharacteristic
824C23#52012yes—
825C23#52012yes—
826C23#52012yes—
827C23#52012yes—
828C23#52012yes—
829C23#52012yes—
830C23#52012yes—
831C23#53412yes—
832C23#53512yes—
833C23#53512yes—
834C23#53512yes—
835C23#53612yes—
836C23#53612yes—
837C23#53612yes—
838C23#53712yes—
839C23#53711yescharacteristic
840C23#53711yescharacteristic
841C23#53712yes—
842C23#53812yes—
843C23#53812yes—
844C23#53812yes—
845C23#53912yes—
846C23#53912yes—
847C23#53912yes—
848C23#54012yes—
849C23#54112yes—
850C23#54212yes—
851C23#54212yes—
852C23#54212yes—
853C23#54212yes—
854C23#54411yescharacteristic
855C23#54411yescharacteristic
856C23#54412yes—
857C23D4212yes—
858C23D4212yes—
859C23D4212yes—
860C23D4211yescharacteristic
861C23#54612yes—
862C23#54612yes—
863C23#54612yes—
864C23#54612yes—
865C23#54612yes—
866C23#54612yes—
867C23#54612yes—
868C23#54712yes—
869C23#54712yes—
870C23#54712yes—
871C23#54712yes—
872C23#54812yes—
873C23D4×Q812yes—
874C23#55111yescharacteristic
875C23#55111yescharacteristic
876C23#55212yes—
877C23#55312yes—
878C23#55412yes—
879C23#55412yes—
880C23#55412yes—
881C23#55612yes—
882C23#55911yescharacteristic
883C23#56011yescharacteristic
884C23#56012yes—
885C23#56011yescharacteristic
886C23H(3,𝔽4)11yescharacteristic
887C23#56212yes—
888C23#56212yes—
889C23#56212yes—
890C23#56312yes—
891C23#56311yescharacteristic
892C23#56312yes—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—28no—
898C2×C4—28no—
899C2×C4—28no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—464no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—44no—
938C2×C4—44no—
939C2×C4—44no—
940C2×C4—44no—
941C2×C4—44no—
942C2×C4—44no—
943C2×C4—44no—
944C2×C4—44no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—44no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—44no—
960C2×C4—44no—
961C2×C4—44no—
962C2×C4—44no—
963C2×C4—44no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—42no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—82no—
978C2×C4—82no—
979C2×C4—82no—
980C2×C4—82no—
981C2×C4—82no—
982C2×C4—82no—
983C2×C4—82no—
984C2×C4—82no—
985C2×C4—82no—
986C2×C4—82no—
987C2×C4—82no—
988C2×C4—82no—
989C2×C4—82no—
990C2×C4—82no—
991C2×C4—82no—
992C2×C4—82no—
993C2×C4—82no—
994C2×C4—82no—
995C2×C4—82no—
996C2×C4—82no—
997C2×C4—82no—
998C2×C4—82no—
999C2×C4—82no—
1000C2×C4—82no—
1001C2×C4C2×#95116yes—
1002C22—28no—
1003C22—216no—
1004C22—44no—
1005C22—44no—
1006C22—48no—
1007C22—48no—
1008C22—48no—
1009C22—44no—
1010C22—48no—
1011C22—48no—
1012C22—48no—
1013C22—48no—
1014C22—48no—
1015C22—48no—
1016C22—48no—
1017C22—44no—
1018C22—44no—
1019C22—48no—
1020C22—44no—
1021C22C22×#9511yescharacteristic
1022C22C42×D412yes—
1023C22#227411yescharacteristic
1024C22#227411yescharacteristic
1025C22#227512yes—
1026C22#230911yescharacteristic
1027C22#231011yescharacteristic
1028C22#231112yes—
1029C22#231112yes—
1030C22#231611yescharacteristic
1031C22#231611yescharacteristic
1032C22#231712yes—
1033C22#231712yes—
1034C22#232112yes—
1035C22#232212yes—
1036C22#232312yes—
1037C22#232412yes—
1038C22#232512yes—
1039C22#232612yes—
1040C22#233212yes—
1041C22#233412yes—
1042C22#233412yes—
1043C22#233512yes—
1044C22#233512yes—
1045C22#233712yes—
1046C22D4×C22⋊C412yes—
1047C22D4×C22⋊C412yes—
1048C22D4×C22⋊C412yes—
1049C22#233912yes—
1050C22#233912yes—
1051C22#233912yes—
1052C22D4×C4⋊C412yes—
1053C22D4×C4⋊C412yes—
1054C22D4×C4⋊C412yes—
1055C22#234912yes—
1056C22#234912yes—
1057C22#234912yes—
1058C22#235811yescharacteristic
1059C22#235912yes—
1060C22#236112yes—
1061C22#236212yes—
1062C22#236712yes—
1063C22#237312yes—
1064C22#237411yescharacteristic
1065C22#237511yescharacteristic
1066C22#237612yes—
1067C22#237611yescharacteristic
1068C22#237712yes—
1069C22#237812yes—
1070C22#237912yes—
1071C22#238312yes—
1072C22#266912yes—
1073C22#267012yes—
1074C22#267112yes—
1075C22#267212yes—
1076C22#267212yes—
1077C22#267412yes—
1078C22#267511yescharacteristic
1079C22#267612yes—
1080C22#267711yescharacteristic
1081C22#267812yes—
1082C22#268012yes—
1083C22#268112yes—
1084C22#268512yes—
1085C22#268712yes—
1086C22#268912yes—
1087C22#269112yes—
1088C22#269311yescharacteristic
1089C22#269512yes—
1090C22#269812yes—
1091C22#270012yes—
1092C22#270312yes—
1093C22#270412yes—
1094C22#270612yes—
1095C22#271012yes—
1096C22#271211yescharacteristic
1097C22#271512yes—
1098C22#271812yes—
1099C22#272012yes—
1100C22#272211yescharacteristic
1101C22#272912yes—
1102C22#274211yescharacteristic
1103C22#276311yescharacteristic
1104C22#276812yes—
1105C22#278812yes—
1106C22#279012yes—
1107C22#280711yescharacteristic
1108C4—216no—
1109C4—48no—
1110C4—48no—
1111C4—48no—
1112C4—82no—
1113C4—84no—
1114C4—84no—
1115C4—82no—
1116C2—48no—
1117C2#1378912yes—
1118C2#1379511yescharacteristic
1119C2D4×#9512yes—
1120C2#1382311yescharacteristic
1121C2#1383111yescharacteristic
1122C2#1435811yescharacteristic
1123C2#1435912yes—
1124C2#1436112yes—
1125C2#1436412yes—
1126C2#1440211yescharacteristic
1127C2#1440312yes—
1128C2#1440512yes—
1129C2#1440812yes—
1130C2#1442112yes—
1131C2#1444212yes—
1132C2#1447512yes—
1133C2#1448812yes—
1134C2#1450611yescharacteristic
1135C2#1451411yescharacteristic
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
3. C2×C4⋊#95C2semidirect
5. #7557C2semidirect
6. #7557C2semidirect
9. #7554C2semidirect
20. C2×#388C4semidirect
22. C2×#385C4semidirect
69. C22×C4⋊C4C2×C4semidirect
100. C22×C42C2×C4semidirect
135. C2×#95C2×C4semidirect
136. C2×#95C2×C4semidirect
717. C22⋊C4#95semidirect

Maximal subgroups

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

subgroupindex
C22×#3882
C22×#3852
C2×C4⋊#952
C2×C22⋊#952
#75572
#75552
#75542