Finite Group Databasebeta

← #154035

Subgroups — #154035

Order 512.

3982 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1437C211yesmaximal, characteristic
2C2×#1437C211yesmaximal, characteristic
3C2×#1434C212yesmaximal, complemented
4C2×C22⋊#95C212yesmaximal
5C2×C22⋊#95C211yesmaximal, characteristic
6#7556C212yesmaximal, complemented
7#7556C212yesmaximal, complemented
8#7555C212yesmaximal
9#7554C212yesmaximal, complemented
10C25×C4C2211yescharacteristic
11C23×C22⋊C4C2212yes—
12C23×C22⋊C4C2212yes—
13C23×C22⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31#1437C418yescomplemented
32#1437C418yescomplemented
33#1434—28no—
34C22⋊#95—28no—
35C22⋊#95C418yescomplemented
36C26C2311yescharacteristic
37C24×C4—24no—
38C24×C4—24no—
39C24×C4—24no—
40C24×C4—41no—
41C24×C4—41no—
42C24×C4—42no—
43C24×C4—42no—
44C24×C4—42no—
45C24×C4C2×C414yes—
46C24×C4C2312yes—
47C24×C4C2312yes—
48C24×C4C2312yes—
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
52C24×C4C2312yes—
53C24×C4C2312yes—
54C22×C22⋊C4—24no—
55C22×C22⋊C4—24no—
56C22×C22⋊C4—24no—
57C22×C22⋊C4—24no—
58C22×C22⋊C4—24no—
59C22×C22⋊C4—24no—
60C22×C22⋊C4—24no—
61C22×C22⋊C4—24no—
62C22×C22⋊C4—24no—
63C22×C22⋊C4—41no—
64C22×C22⋊C4—41no—
65C22×C22⋊C4—41no—
66C22×C22⋊C4—41no—
67C22×C22⋊C4—42no—
68C22×C22⋊C4—42no—
69C22×C22⋊C4—42no—
70C22×C22⋊C4—42no—
71C22×C22⋊C4—41no—
72C22×C22⋊C4—41no—
73C22×C22⋊C4—42no—
74C22×C22⋊C4C2×C418yes—
75C22×C22⋊C4C2×C418yes—
76C22×C22⋊C4C2×C414yes—
77C22×C22⋊C4C2×C414yes—
78C22×C22⋊C4C2×C414yes—
79C22×C22⋊C4C2×C414yes—
80C22×C42—24no—
81C22×C42—24no—
82C22×C42—41no—
83C22×C42—41no—
84C22×C42—41no—
85C22×C42—42no—
86C22×C42—41no—
87C22×C42—42no—
88C22×C42C2×C414yescomplemented
89C22×C42C2×C414yescomplemented
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—42no—
104C2×#95—42no—
105C2×#95—42no—
106C2×#95—42no—
107C2×#95—41no—
108C2×#95—41no—
109C2×#95—41no—
110C2×#95—41no—
111C2×#95—42no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95—42no—
115C2×#95—42no—
116C2×#95—42no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—42no—
123C2×#95—42no—
124C2×#95—42no—
125C2×#95C2×C418yes—
126C2×#95C2×C418yes—
127C2×#95C2×C418yescomplemented
128C2×#95C2×C414yescomplemented
129C2×#95C2×C414yescomplemented
130C2×#95C2×C418yescomplemented
131C2×#95D418yes—
132C25—22no—
133C25—22no—
134C25—22no—
135C25—22no—
136C25—21no—
137C25—21no—
138C25—22no—
139C25—21no—
140C25—21no—
141C25—22no—
142C25—22no—
143C25—22no—
144C25—22no—
145C25—22no—
146C25C22×C412yes—
147C25C22×C412yes—
148C25C22×C412yes—
149C25#4114yes—
150C25#4114yes—
151C25C2411yescharacteristic
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
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—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
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—22no—
203C23×C4—22no—
204C23×C4—28no—
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—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—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×C414yes—
268C23×C4C22×C414yes—
269C23×C4C22×C414yes—
270C23×C4C22×C412yes—
271C23×C4C22×C412yes—
272C23×C4C22×C412yes—
273C23×C4C22×C412yes—
274C23×C4C22×C412yes—
275C23×C4C22×C412yes—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4#4114yes—
283C23×C4#4114yes—
284C23×C4#4114yes—
285C2×C22⋊C4—216no—
286C2×C22⋊C4—216no—
287C2×C22⋊C4—28no—
288C2×C22⋊C4—216no—
289C2×C22⋊C4—216no—
290C2×C22⋊C4—44no—
291C2×C22⋊C4—44no—
292C2×C22⋊C4—44no—
293C2×C22⋊C4—44no—
294C2×C22⋊C4—44no—
295C2×C22⋊C4—44no—
296C2×C22⋊C4—48no—
297C2×C22⋊C4—48no—
298C2×C22⋊C4—44no—
299C2×C22⋊C4—44no—
300C2×C22⋊C4—48no—
301C2×C22⋊C4—48no—
302C2×C22⋊C4—48no—
303C2×C22⋊C4—48no—
304C2×C22⋊C4—48no—
305C2×C22⋊C4—48no—
306C2×C22⋊C4—48no—
307C2×C22⋊C4—48no—
308C2×C22⋊C4—48no—
309C2×C22⋊C4—48no—
310C2×C22⋊C4C42116yes—
311C2×C42—216no—
312C2×C42—44no—
313C2×C42—48no—
314C2×C42—44no—
315C2×C42—44no—
316C2×C42—48no—
317C2×C42—44no—
318C2×C42—44no—
319C2×C42—48no—
320C2×C42—44no—
321#95—216no—
322#95—216no—
323#95—48no—
324#95—48no—
325#95—44no—
326#95—44no—
327#95—48no—
328#95—48no—
329#95—48no—
330#95—48no—
331#95—48no—
332#95—48no—
333#95—48no—
334#95—48no—
335C24—24no—
336C24—24no—
337C24—24no—
338C24—24no—
339C24—24no—
340C24—24no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—22no—
347C24—22no—
348C24—24no—
349C24—24no—
350C24—24no—
351C24—22no—
352C24—24no—
353C24—24no—
354C24—24no—
355C24—24no—
356C24—24no—
357C24—24no—
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—24no—
371C24—24no—
372C24—24no—
373C24—24no—
374C24—24no—
375C24—24no—
376C24—24no—
377C24—24no—
378C24—24no—
379C24—24no—
380C24—24no—
381C24—42no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24—42no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—41no—
398C24—42no—
399C24—42no—
400C24—42no—
401C24—41no—
402C24—41no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—41no—
407C24—41no—
408C24—42no—
409C24—41no—
410C24—42no—
411C24—42no—
412C24—41no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—41no—
417C24C2×C4214yes—
418C24#11714yes—
419C24#11718yes—
420C24#11718yes—
421C24#11714yes—
422C24C23×C411yescharacteristic
423C24C23×C411yescharacteristic
424C24C23×C411yescharacteristic
425C24C22×D412yes—
426C24C2×#4112yes—
427C24C2×#4112yes—
428C24C2×#4112yes—
429C24C2×#4112yes—
430C24C2×#4112yes—
431C24H(5,𝔽2)11yescharacteristic
432C24H(5,𝔽2)11yescharacteristic
433C24H(5,𝔽2)11yescharacteristic
434C24H(5,𝔽2)11yescharacteristic
435C24H(5,𝔽2)12yes—
436C24H(5,𝔽2)12yes—
437C24H(5,𝔽2)12yes—
438C24H(5,𝔽2)12yes—
439C242−1+412yes—
440C242−1+412yes—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
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—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—416no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—416no—
544C22×C4—416no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—41no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—41no—
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—41no—
595C22×C4—41no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—41no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—41no—
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—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—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4C2×C4214yes—
702C22×C4C2×C4214yes—
703C22×C4C4×D418yes—
704C22×C4C4×D418yes—
705C22×C4C4×D418yes—
706C22⋊C4—416no—
707C22⋊C4—432no—
708C22⋊C4—432no—
709C22⋊C4—416no—
710C42—416no—
711C42—416no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—28no—
722C23—28no—
723C23—28no—
724C23—28no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—28no—
733C23—24no—
734C23—24no—
735C23—28no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—42no—
749C23—42no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—42no—
765C23—42no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23#37618yes—
799C23C22×C4211yescharacteristic
800C23C2×#11711yescharacteristic
801C23C2×#11711yescharacteristic
802C23C2×#11712yes—
803C23C2×#11712yes—
804C23C2×C4×D412yes—
805C23C2×C4×D412yes—
806C23C2×C4×D412yes—
807C23C4×#4112yes—
808C23C4×#4112yes—
809C23C4×#4112yes—
810C23#51811yescharacteristic
811C23#51811yescharacteristic
812C23#51811yescharacteristic
813C23#51811yescharacteristic
814C23#51811yescharacteristic
815C23#51811yescharacteristic
816C23#51811yescharacteristic
817C23#51812yes—
818C23#51812yes—
819C23#51812yes—
820C23#51911yescharacteristic
821C23#52012yes—
822C23#52012yes—
823C23#52012yes—
824C23#52012yes—
825C23#52012yes—
826C23#53412yes—
827C23#53512yes—
828C23#53612yes—
829C23#53712yes—
830C23#53812yes—
831C23#53812yes—
832C23#53812yes—
833C23#53812yes—
834C23#53812yes—
835C23#53812yes—
836C23#53812yes—
837C23#53912yes—
838C23#53912yes—
839C23#53912yes—
840C23#53912yes—
841C23#53912yes—
842C23#53912yes—
843C23#53912yes—
844C23#54012yes—
845C23#54112yes—
846C23#54212yes—
847C23#54212yes—
848C23#54212yes—
849C23#54212yes—
850C23D4211yescharacteristic
851C23#54612yes—
852C23#54612yes—
853C23#54612yes—
854C23#54612yes—
855C23#54612yes—
856C23#54812yes—
857C23#55012yes—
858C23#55112yes—
859C23#55112yes—
860C23#55112yes—
861C23#55112yes—
862C23#55112yes—
863C23#55112yes—
864C23#55111yescharacteristic
865C23#55111yescharacteristic
866C23#55212yes—
867C23#55212yes—
868C23#55212yes—
869C23#55312yes—
870C23#55312yes—
871C23#55312yes—
872C23#55312yes—
873C23#55312yes—
874C23#55512yes—
875C23#55911yescharacteristic
876C23#56011yescharacteristic
877C23#56011yescharacteristic
878C23#56012yes—
879C23#56012yes—
880C23#56012yes—
881C23H(3,𝔽4)11yescharacteristic
882C23#56212yes—
883C23#56212yes—
884C23#56212yes—
885C23#56311yescharacteristic
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—464no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—44no—
912C2×C4—44no—
913C2×C4—44no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—44no—
920C2×C4—42no—
921C2×C4—44no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—42no—
929C2×C4—42no—
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—44no—
954C2×C4—44no—
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—44no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—82no—
976C2×C4—82no—
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—
999C22—28no—
1000C22—216no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—48no—
1005C22—48no—
1006C22—48no—
1007C22—48no—
1008C22—44no—
1009C22—48no—
1010C22—48no—
1011C22—48no—
1012C22—48no—
1013C22—48no—
1014C22—44no—
1015C22—48no—
1016C22—44no—
1017C22—48no—
1018C22C2×#37611yescharacteristic
1019C22C42×D412yes—
1020C22#227311yescharacteristic
1021C22#227411yescharacteristic
1022C22#227512yes—
1023C22#231211yescharacteristic
1024C22#231211yescharacteristic
1025C22#231311yescharacteristic
1026C22#231311yescharacteristic
1027C22#231812yes—
1028C22#231812yes—
1029C22#231812yes—
1030C22#231812yes—
1031C22#232112yes—
1032C22#232212yes—
1033C22#232312yes—
1034C22#232412yes—
1035C22#232512yes—
1036C22#232612yes—
1037C22#233212yes—
1038C22#233412yes—
1039C22#233412yes—
1040C22#233512yes—
1041C22#233512yes—
1042C22#233712yes—
1043C22#234212yes—
1044C22#234212yes—
1045C22#234212yes—
1046C22#234312yes—
1047C22#234312yes—
1048C22#234312yes—
1049C22#235212yes—
1050C22#235212yes—
1051C22#235212yes—
1052C22#235312yes—
1053C22#235312yes—
1054C22#235312yes—
1055C22#235811yescharacteristic
1056C22#235811yescharacteristic
1057C22#236312yes—
1058C22#236312yes—
1059C22#236412yes—
1060C22#236611yescharacteristic
1061C22#237211yescharacteristic
1062C22#237411yescharacteristic
1063C22#237411yescharacteristic
1064C22#237511yescharacteristic
1065C22#237511yescharacteristic
1066C22#237611yescharacteristic
1067C22#237611yescharacteristic
1068C22#237712yes—
1069C22#237712yes—
1070C22#237712yes—
1071C22#237911yescharacteristic
1072C22#238011yescharacteristic
1073C22#267812yes—
1074C22#268112yes—
1075C22#268412yes—
1076C22#268512yes—
1077C22#268712yes—
1078C22#268812yes—
1079C22#269012yes—
1080C22#269112yes—
1081C22#269312yes—
1082C22#269412yes—
1083C22#269612yes—
1084C22#270512yes—
1085C22#271412yes—
1086C22#273012yes—
1087C22#273512yes—
1088C22#273712yes—
1089C22#273912yes—
1090C22#274312yes—
1091C22#274412yes—
1092C22#274612yes—
1093C22#274612yes—
1094C22#274712yes—
1095C22#274912yes—
1096C22#275112yes—
1097C22#275612yes—
1098C22#275712yes—
1099C22#276512yes—
1100C22#277812yes—
1101C22#277912yes—
1102C22#278112yes—
1103C22#278212yes—
1104C22#279612yes—
1105C4—44no—
1106C4—44no—
1107C4—48no—
1108C4—48no—
1109C4—48no—
1110C4—84no—
1111C4—84no—
1112C4—84no—
1113C2—48no—
1114C2#1378912yes—
1115C2#1379611yescharacteristic
1116C2#1380912yes—
1117C2#1382411yescharacteristic
1118C2#1383211yescharacteristic
1119C2#1436511yescharacteristic
1120C2#1437112yes—
1121C2#1437312yes—
1122C2#1437912yes—
1123C2#1439312yes—
1124C2#1440911yescharacteristic
1125C2#1441512yes—
1126C2#1442712yes—
1127C2#1442912yes—
1128C2#1443312yes—
1129C2#1447912yes—
1130C2#1450711yescharacteristic
1131C2#1450912yes—
1132C2#1451511yescharacteristic
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×#1434C2semidirect
6. #7556C2semidirect
7. #7556C2semidirect
9. #7554C2semidirect
31. #1437C4semidirect
32. #1437C4semidirect
35. C22⋊#95C4semidirect
88. C22×C42C2×C4semidirect
89. C22×C42C2×C4semidirect
127. C2×#95C2×C4semidirect
128. C2×#95C2×C4semidirect
129. C2×#95C2×C4semidirect
130. C2×#95C2×C4semidirect

Maximal subgroups

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

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