Finite Group Databasebeta

← #154207

Subgroups — #154207

Order 512.

5650 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#385C211yesmaximal, characteristic
2C23×#95C211yesmaximal, characteristic
3C2×#1442C212yesmaximal, complemented
4C2×C22⋊#95C211yesmaximal, characteristic
5C2×C22⋊#95C211yesmaximal, characteristic
6C2×C22⋊#95C211yesmaximal, characteristic
7C2×C22⋊#95C211yesmaximal, characteristic
8C2×C22⋊#95C211yesmaximal, characteristic
9#7557C212yesmaximal, complemented
10#7556C212yesmaximal, complemented
11#7556C212yesmaximal, complemented
12C25×C4C2211yescharacteristic
13C25×C4C2211yescharacteristic
14C25×C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C22⋊C4C2211yescharacteristic
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2211yescharacteristic
19C23×C22⋊C4C2211yescharacteristic
20C2×#385—24no—
21C2×#385—24no—
22C2×#385—24no—
23C22×#95—28no—
24C22×#95—24no—
25C22×#95C2211yescharacteristic
26C22×#95C2212yes—
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2211yescharacteristic
39C22×#95C2212yes—
40#1442—28no—
41C22⋊#95—24no—
42C22⋊#95—24no—
43C22⋊#95—24no—
44C22⋊#95—24no—
45C22⋊#95C418yescomplemented
46C26C2311yescharacteristic
47C24×C4—22no—
48C24×C4—22no—
49C24×C4—22no—
50C24×C4—22no—
51C24×C4—22no—
52C24×C4—22no—
53C24×C4—24no—
54C24×C4—24no—
55C24×C4—24no—
56C24×C4—24no—
57C24×C4—24no—
58C24×C4—24no—
59C24×C4—22no—
60C24×C4—22no—
61C24×C4—22no—
62C24×C4—22no—
63C24×C4—22no—
64C24×C4—22no—
65C24×C4—22no—
66C24×C4—22no—
67C24×C4—22no—
68C24×C4—22no—
69C24×C4—22no—
70C24×C4—22no—
71C24×C4—42no—
72C24×C4—42no—
73C24×C4—42no—
74C24×C4—42no—
75C24×C4—42no—
76C24×C4—42no—
77C24×C4C2×C414yes—
78C24×C4D414yes—
79C24×C4D414yes—
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2312yes—
85C24×C4C2312yes—
86C24×C4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4—42no—
97C22×C22⋊C4—22no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4—22no—
100C22×C22⋊C4—22no—
101C22×C22⋊C4—22no—
102C22×C22⋊C4—22no—
103C22×C22⋊C4—22no—
104C22×C22⋊C4—22no—
105C22×C22⋊C4—22no—
106C22×C22⋊C4—22no—
107C22×C22⋊C4—22no—
108C22×C22⋊C4—22no—
109C22×C22⋊C4—22no—
110C22×C22⋊C4—22no—
111C22×C22⋊C4—22no—
112C22×C22⋊C4—22no—
113C22×C22⋊C4—22no—
114C22×C22⋊C4—22no—
115C22×C22⋊C4—22no—
116C22×C22⋊C4—22no—
117C22×C22⋊C4—22no—
118C22×C22⋊C4—22no—
119C22×C22⋊C4C2×C414yes—
120C22×C22⋊C4C2×C414yes—
121C22×C22⋊C4D414yes—
122C22×C22⋊C4D414yes—
123C22×C22⋊C4Q814yes—
124C22×C22⋊C4Q814yes—
125#385—232no—
126C2×#95—232no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—22no—
142C2×#95—24no—
143C2×#95—22no—
144C2×#95—22no—
145C2×#95—24no—
146C2×#95—22no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—24no—
152C2×#95—24no—
153C2×#95—24no—
154C2×#95—24no—
155C2×#95—42no—
156C2×#95—42no—
157C2×#95—42no—
158C2×#95—42no—
159C2×#95—42no—
160C2×#95—42no—
161C2×#95—42no—
162C2×#95—42no—
163C2×#95—42no—
164C2×#95—42no—
165C2×#95C2×C418yescomplemented
166C2×#95C2×C418yescomplemented
167C2×#95D418yes—
168C25—22no—
169C25—22no—
170C25—22no—
171C25—22no—
172C25—22no—
173C25—22no—
174C25—22no—
175C25—22no—
176C25C22×C412yes—
177C25C2×D412yes—
178C25C2×D412yes—
179C25C2×D412yes—
180C25C2×D412yes—
181C25C2×Q812yes—
182C25C2×Q812yes—
183C25#4112yes—
184C25#4112yes—
185C25#4112yes—
186C25#4112yes—
187C25#4112yes—
188C25#4112yes—
189C25#4112yes—
190C25#4112yes—
191C25C2411yescharacteristic
192C23×C4—216no—
193C23×C4—216no—
194C23×C4—216no—
195C23×C4—216no—
196C23×C4—28no—
197C23×C4—28no—
198C23×C4—28no—
199C23×C4—28no—
200C23×C4—28no—
201C23×C4—28no—
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—21no—
215C23×C4—21no—
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—22no—
225C23×C4—22no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—21no—
238C23×C4—21no—
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—216no—
258C23×C4—28no—
259C23×C4—216no—
260C23×C4—28no—
261C23×C4—28no—
262C23×C4—28no—
263C23×C4—28no—
264C23×C4—28no—
265C23×C4—28no—
266C23×C4—28no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—48no—
322C23×C4—48no—
323C23×C4—44no—
324C23×C4—44no—
325C23×C4—48no—
326C23×C4—48no—
327C23×C4—48no—
328C23×C4—48no—
329C23×C4—48no—
330C23×C4—48no—
331C23×C4—48no—
332C23×C4—48no—
333C23×C4—48no—
334C23×C4—48no—
335C23×C4—48no—
336C23×C4—48no—
337C23×C4—48no—
338C23×C4—48no—
339C23×C4—48no—
340C23×C4—48no—
341C23×C4—48no—
342C23×C4—48no—
343C23×C4—48no—
344C23×C4—48no—
345C23×C4—48no—
346C23×C4—48no—
347C23×C4—48no—
348C23×C4—48no—
349C23×C4—44no—
350C23×C4—44no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4—48no—
354C23×C4—48no—
355C23×C4—48no—
356C23×C4—48no—
357C23×C4—44no—
358C23×C4—44no—
359C23×C4—44no—
360C23×C4—44no—
361C23×C4—44no—
362C23×C4—44no—
363C23×C4—44no—
364C23×C4—44no—
365C23×C4—44no—
366C23×C4—44no—
367C23×C4—44no—
368C23×C4—44no—
369C23×C4C22×C412yes—
370C23×C4C22×C412yes—
371C23×C4C22×C414yes—
372C23×C4C22×C414yes—
373C23×C4C2×D412yes—
374C23×C4C2×D412yes—
375C23×C4C2×D414yes—
376C23×C4C2×D414yes—
377C23×C4C2×D414yes—
378C23×C4C2×D412yes—
379C23×C4C2×D414yes—
380C23×C4C2×D414yes—
381C23×C4C2×D412yes—
382C23×C4C2×Q814yes—
383C23×C4C2×Q814yes—
384C23×C4#4114yes—
385C23×C4#4114yes—
386C23×C4#4114yes—
387C2×C4⋊C4—216no—
388C2×C4⋊C4—48no—
389C2×C4⋊C4—48no—
390C2×C4⋊C4—48no—
391C2×C4⋊C4—48no—
392C2×C4⋊C4—48no—
393C2×C4⋊C4—48no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4C4⋊C4116yes—
422#95—216no—
423#95—216no—
424#95—216no—
425#95—216no—
426#95—48no—
427#95—48no—
428#95—48no—
429#95—48no—
430#95—48no—
431#95—44no—
432#95—48no—
433#95—44no—
434#95—44no—
435#95—48no—
436#95—44no—
437C24—24no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—22no—
442C24—24no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—24no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—24no—
465C24—24no—
466C24—24no—
467C24—24no—
468C24—24no—
469C24—24no—
470C24—24no—
471C24—24no—
472C24—24no—
473C24—24no—
474C24—24no—
475C24—24no—
476C24—24no—
477C24—24no—
478C24—24no—
479C24—24no—
480C24—24no—
481C24—24no—
482C24—24no—
483C24—24no—
484C24—24no—
485C24—24no—
486C24—24no—
487C24—24no—
488C24—24no—
489C24—24no—
490C24—24no—
491C24—24no—
492C24—24no—
493C24—24no—
494C24—24no—
495C24—24no—
496C24—24no—
497C24—24no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24C2×C4⋊C414yes—
502C24#11714yes—
503C24#11714yes—
504C24C4×D414yes—
505C24C4×D414yes—
506C24C4×D414yes—
507C24C4×Q814yes—
508C24#12014yes—
509C24#12114yes—
510C24#12114yes—
511C24#12114yes—
512C24C22⋊Q814yes—
513C24C22⋊Q814yes—
514C24C22⋊Q814yes—
515C24C22⋊Q814yes—
516C24C22⋊Q814yes—
517C24#12314yes—
518C24#12314yes—
519C24#12314yes—
520C24#12314yes—
521C24#12314yes—
522C24#12414yes—
523C24#12414yes—
524C24#12414yes—
525C24#12414yes—
526C24#12514yes—
527C24#12514yes—
528C24#12514yes—
529C24#12514yes—
530C24#12514yes—
531C24#12614yes—
532C24#12614yes—
533C24#12614yes—
534C24#12614yes—
535C24C4⋊Q814yes—
536C24C23×C411yescharacteristic
537C24C22×D411yescharacteristic
538C24C22×D411yescharacteristic
539C24C22×D411yescharacteristic
540C24C22×D411yescharacteristic
541C24C22×D412yes—
542C24C22×Q811yescharacteristic
543C24C22×Q811yescharacteristic
544C24C2×#4111yescharacteristic
545C24C2×#4111yescharacteristic
546C24C2×#4111yescharacteristic
547C24C2×#4111yescharacteristic
548C24C2×#4111yescharacteristic
549C24C2×#4111yescharacteristic
550C24C2×#4111yescharacteristic
551C24C2×#4112yes—
552C24C2×#4111yescharacteristic
553C24C2×#4112yes—
554C24C2×#4112yes—
555C24H(5,𝔽2)12yes—
556C24H(5,𝔽2)12yes—
557C24H(5,𝔽2)12yes—
558C242−1+412yes—
559C22×C4—232no—
560C22×C4—232no—
561C22×C4—232no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—22no—
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—22no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—22no—
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—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—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—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—432no—
668C22×C4—432no—
669C22×C4—416no—
670C22×C4—432no—
671C22×C4—416no—
672C22×C4—432no—
673C22×C4—416no—
674C22×C4—416no—
675C22×C4—416no—
676C22×C4—416no—
677C22×C4—416no—
678C22×C4—416no—
679C22×C4—416no—
680C22×C4—416no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—432no—
686C22×C4—432no—
687C22×C4—432no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—416no—
692C22×C4—416no—
693C22×C4—416no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—42no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
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—416no—
763C22×C4—416no—
764C22×C4—416no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—42no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—41no—
792C22×C4—42no—
793C22×C4—41no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—42no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4C2×C4⋊C418yes—
866C22×C4C4×D418yes—
867C22×C4#12014yes—
868C22×C4#12118yes—
869C22×C4#12314yes—
870C4⋊C4—432no—
871C22⋊C4—232no—
872C22⋊C4—416no—
873C22⋊C4—416no—
874C22⋊C4—416no—
875C23—28no—
876C23—28no—
877C23—28no—
878C23—24no—
879C23—24no—
880C23—28no—
881C23—24no—
882C23—24no—
883C23—24no—
884C23—24no—
885C23—28no—
886C23—28no—
887C23—24no—
888C23—28no—
889C23—24no—
890C23—28no—
891C23—28no—
892C23—28no—
893C23—28no—
894C23—28no—
895C23—28no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—28no—
907C23—24no—
908C23—24no—
909C23—28no—
910C23—24no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—28no—
917C23—28no—
918C23—24no—
919C23—28no—
920C23—28no—
921C23—28no—
922C23—28no—
923C23—28no—
924C23—28no—
925C23—28no—
926C23—28no—
927C23—28no—
928C23—28no—
929C23—28no—
930C23—28no—
931C23—28no—
932C23—28no—
933C23—28no—
934C23—28no—
935C23—28no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—28no—
941C23—28no—
942C23—28no—
943C23—28no—
944C23—28no—
945C23—28no—
946C23—28no—
947C23—24no—
948C23—28no—
949C23—28no—
950C23—28no—
951C23—28no—
952C23—28no—
953C23—24no—
954C23—24no—
955C23—28no—
956C23—24no—
957C23—28no—
958C23—24no—
959C23#38218yes—
960C23#38518yes—
961C23#38718yes—
962C23#38718yes—
963C23#38818yes—
964C23#38818yes—
965C23#38918yes—
966C23#39318yes—
967C23#39418yes—
968C23#39718yes—
969C23#39818yes—
970C23#39818yes—
971C23#40018yes—
972C23#40018yes—
973C23#40018yes—
974C23C22×C4⋊C411yescharacteristic
975C23C2×#11711yescharacteristic
976C23C2×#11711yescharacteristic
977C23C2×C4×D411yescharacteristic
978C23C2×C4×D411yescharacteristic
979C23C2×C4×D412yes—
980C23C2×C4×D411yescharacteristic
981C23C2×C4×Q811yescharacteristic
982C23C4×#4112yes—
983C23#51812yes—
984C23#52012yes—
985C23C2×#12011yescharacteristic
986C23C2×#12011yescharacteristic
987C23C2×#12112yes—
988C23C2×#12111yescharacteristic
989C23C2×#12111yescharacteristic
990C23C2×#12111yescharacteristic
991C23C2×C22⋊Q811yescharacteristic
992C23C2×C22⋊Q811yescharacteristic
993C23C2×C22⋊Q811yescharacteristic
994C23C2×C22⋊Q811yescharacteristic
995C23C2×C22⋊Q811yescharacteristic
996C23C2×#12311yescharacteristic
997C23C2×#12311yescharacteristic
998C23C2×#12311yescharacteristic
999C23C2×#12311yescharacteristic
1000C23C2×#12311yescharacteristic
1001C23C2×#12311yescharacteristic
1002C23#52511yescharacteristic
1003C23#52511yescharacteristic
1004C23#52512yes—
1005C23#52512yes—
1006C23#52512yes—
1007C23#52512yes—
1008C23C2×#12411yescharacteristic
1009C23C2×#12411yescharacteristic
1010C23C2×#12411yescharacteristic
1011C23C2×#12411yescharacteristic
1012C23C2×#12511yescharacteristic
1013C23C2×#12511yescharacteristic
1014C23C2×#12511yescharacteristic
1015C23C2×#12511yescharacteristic
1016C23C2×#12511yescharacteristic
1017C23C2×#12611yescharacteristic
1018C23C2×#12611yescharacteristic
1019C23C2×#12611yescharacteristic
1020C23C2×#12611yescharacteristic
1021C23#52912yes—
1022C23#52912yes—
1023C23#52912yes—
1024C23#52912yes—
1025C23C2×C4⋊Q811yescharacteristic
1026C23#53212yes—
1027C23#53412yes—
1028C23#53411yescharacteristic
1029C23#53411yescharacteristic
1030C23#53511yescharacteristic
1031C23#53611yescharacteristic
1032C23#53712yes—
1033C23#53812yes—
1034C23#53812yes—
1035C23#53812yes—
1036C23#53812yes—
1037C23#53912yes—
1038C23#53912yes—
1039C23#53912yes—
1040C23#53912yes—
1041C23D4212yes—
1042C23D4212yes—
1043C23#54612yes—
1044C23#54612yes—
1045C23#54612yes—
1046C23#54612yes—
1047C23#54612yes—
1048C23#54612yes—
1049C23#54612yes—
1050C23#54612yes—
1051C23#54712yes—
1052C23#54712yes—
1053C23D4×Q812yes—
1054C23D4×Q812yes—
1055C23#55112yes—
1056C23#55112yes—
1057C23#55112yes—
1058C23#55112yes—
1059C23#55112yes—
1060C23#55112yes—
1061C23#55112yes—
1062C23#55112yes—
1063C23#55212yes—
1064C23#55212yes—
1065C23#55212yes—
1066C23#55212yes—
1067C23#55412yes—
1068C23#55412yes—
1069C23#55412yes—
1070C23#55412yes—
1071C23#55412yes—
1072C23#55412yes—
1073C2×C4—28no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—28no—
1077C2×C4—28no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—24no—
1081C2×C4—28no—
1082C2×C4—24no—
1083C2×C4—28no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—28no—
1087C2×C4—28no—
1088C2×C4—464no—
1089C2×C4—464no—
1090C2×C4—464no—
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—42no—
1100C2×C4—42no—
1101C2×C4—44no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—44no—
1106C2×C4—44no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—42no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—42no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—44no—
1121C2×C4—44no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—44no—
1129C2×C4—44no—
1130C2×C4—44no—
1131C2×C4—44no—
1132C2×C4—44no—
1133C2×C4—44no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—42no—
1139C2×C4—44no—
1140C2×C4—44no—
1141C2×C4—44no—
1142C2×C4—44no—
1143C2×C4—44no—
1144C2×C4—44no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—44no—
1155C2×C4—44no—
1156C2×C4—44no—
1157C2×C4—44no—
1158C2×C4—44no—
1159C2×C4—44no—
1160C2×C4—44no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—44no—
1167C2×C4—42no—
1168C2×C4—44no—
1169C2×C4—42no—
1170C2×C4—81no—
1171C2×C4—81no—
1172C2×C4—81no—
1173C2×C4—82no—
1174C2×C4—82no—
1175C2×C4—82no—
1176C2×C4—81no—
1177C2×C4—81no—
1178C2×C4—81no—
1179C2×C4—81no—
1180C2×C4—81no—
1181C2×C4—81no—
1182C2×C4—81no—
1183C2×C4—81no—
1184C2×C4—81no—
1185C2×C4—82no—
1186C2×C4—82no—
1187C2×C4—82no—
1188C2×C4—81no—
1189C2×C4—82no—
1190C2×C4—81no—
1191C2×C4—81no—
1192C2×C4—82no—
1193C2×C4—81no—
1194C2×C4—82no—
1195C2×C4—82no—
1196C2×C4—82no—
1197C2×C4—82no—
1198C2×C4—82no—
1199C2×C4—82no—
1200C2×C4—82no—
1201C2×C4—82no—
1202C22—216no—
1203C22—28no—
1204C22—216no—
1205C22—28no—
1206C22—28no—
1207C22—28no—
1208C22—28no—
1209C22—28no—
1210C22—216no—
1211C22—216no—
1212C22—216no—
1213C22—28no—
1214C22—28no—
1215C22—216no—
1216C22—28no—
1217C22—28no—
1218C22—28no—
1219C22—28no—
1220C22—28no—
1221C22—216no—
1222C22—28no—
1223C22—216no—
1224C22#1442116yescomplemented
1225C22C2×#38211yescharacteristic
1226C22C2×#38511yescharacteristic
1227C22C2×#38711yescharacteristic
1228C22C2×#38711yescharacteristic
1229C22C2×#38811yescharacteristic
1230C22C2×#38811yescharacteristic
1231C22#229012yes—
1232C22C2×#38911yescharacteristic
1233C22C4×#12011yescharacteristic
1234C22C4×#12112yes—
1235C22C4×#12311yescharacteristic
1236C22#231812yes—
1237C22#232111yescharacteristic
1238C22#232211yescharacteristic
1239C22#232512yes—
1240C22#234212yes—
1241C22#234312yes—
1242C22D4×C4⋊C412yes—
1243C22#234912yes—
1244C22#235812yes—
1245C22#235912yes—
1246C22#236012yes—
1247C22#236812yes—
1248C22C2×#39311yescharacteristic
1249C22C2×#39411yescharacteristic
1250C22C2×#39711yescharacteristic
1251C22C2×#39811yescharacteristic
1252C22C2×#39811yescharacteristic
1253C22C2×#40011yescharacteristic
1254C22C2×#40011yescharacteristic
1255C22C2×#40011yescharacteristic
1256C22#240511yescharacteristic
1257C22#240811yescharacteristic
1258C22#241011yescharacteristic
1259C22#241012yes—
1260C22#241111yescharacteristic
1261C22#241211yescharacteristic
1262C22#241212yes—
1263C22#241311yescharacteristic
1264C22#241712yes—
1265C22#241712yes—
1266C22#241812yes—
1267C22#241812yes—
1268C22#241912yes—
1269C22#241912yes—
1270C22#243012yes—
1271C22#243411yescharacteristic
1272C22#244912yes—
1273C22#244912yes—
1274C22#244912yes—
1275C22#245012yes—
1276C22#245012yes—
1277C22#245012yes—
1278C22#247212yes—
1279C22#247212yes—
1280C22#247212yes—
1281C22#247312yes—
1282C22#247312yes—
1283C22#247312yes—
1284C22#247312yes—
1285C22#247312yes—
1286C22#248012yes—
1287C22#248012yes—
1288C22#248012yes—
1289C22#248211yescharacteristic
1290C22#248311yescharacteristic
1291C22#248411yescharacteristic
1292C22#248611yescharacteristic
1293C22#248812yes—
1294C22#248812yes—
1295C22#248812yes—
1296C22#249312yes—
1297C22#249312yes—
1298C22#249312yes—
1299C22#249812yes—
1300C22#250211yescharacteristic
1301C22#250512yes—
1302C22#250512yes—
1303C22#250512yes—
1304C22#250512yes—
1305C22#250512yes—
1306C22#253411yescharacteristic
1307C22#253411yescharacteristic
1308C22#256412yes—
1309C22#256412yes—
1310C22#258311yescharacteristic
1311C22#258311yescharacteristic
1312C22#261711yescharacteristic
1313C22#261811yescharacteristic
1314C22#262211yescharacteristic
1315C22#262311yescharacteristic
1316C22#263912yes—
1317C22#264312yes—
1318C22#284711yescharacteristic
1319C22#284911yescharacteristic
1320C22#285012yes—
1321C22#285212yes—
1322C22#285311yescharacteristic
1323C22#285411yescharacteristic
1324C4—48no—
1325C4—44no—
1326C4—44no—
1327C4—48no—
1328C4—48no—
1329C4—82no—
1330C4—82no—
1331C4—82no—
1332C4—84no—
1333C4—82no—
1334C2—216no—
1335C2C2×#144211yescharacteristic
1336C2#1389612yes—
1337C2#1397512yes—
1338C2#1399111yescharacteristic
1339C2#1399211yescharacteristic
1340C2#1404311yescharacteristic
1341C2#1404411yescharacteristic
1342C2#1404712yes—
1343C2#1413112yes—
1344C2#1425911yescharacteristic
1345C2#1469611yescharacteristic
1346C2#1472511yescharacteristic
1347C2#1472711yescharacteristic
1348C2#1473812yes—
1349C2#1473812yes—
1350C2#1475912yes—
1351C2#1478611yescharacteristic
1352C2#1482111yescharacteristic
1353C2#1482612yes—
1354C2#1491911yescharacteristic
1355C2#1492711yescharacteristic
1356C2#1495511yescharacteristic
1357C2#1501411yescharacteristic
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
3. C2×#1442C2semidirect
9. #7557C2semidirect
10. #7556C2semidirect
11. #7556C2semidirect
45. C22⋊#95C4semidirect
165. C2×#95C2×C4semidirect
166. C2×#95C2×C4semidirect
1224. C22#1442semidirect

Maximal subgroups

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

subgroupindex
C22×#3852
C23×#952
C2×#14422
C2×C22⋊#952
#75572
#75562