Finite Group Databasebeta

← #157181

Subgroups — #157181

Order 512.

3104 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#391C211yesmaximal, characteristic
2C2×#1446C211yesmaximal, characteristic
3C2×#1446C211yesmaximal, characteristic
4C2×#1444C211yesmaximal, characteristic
5C2×#1434C211yesmaximal, characteristic
6C2×#1434C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7557C212yesmaximal
9#7557C211yesmaximal, characteristic
10#7556C212yesmaximal
11#7556C212yesmaximal
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C2×#391—24no—
17C2×#391—24no—
18C2×#391—24no—
19C22×#95C2211yescharacteristic
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2211yescharacteristic
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38#1446—24no—
39#1446—24no—
40#1444—24no—
41#1434—24no—
42#1434—24no—
43C23×Q8—22no—
44C23×Q8—22no—
45C23×Q8—22no—
46C23×Q8—24no—
47C23×Q8—24no—
48C23×Q8—22no—
49C23×Q8—22no—
50C23×Q8—22no—
51C23×Q8—42no—
52C23×Q8—42no—
53C23×Q8D414yes—
54C24×C4C2312yes—
55C24×C4C2311yescharacteristic
56C24×C4C2312yes—
57C24×C4C2311yescharacteristic
58C24×C4C2311yescharacteristic
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2312yes—
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—42no—
71C22×C4⋊C4—42no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—42no—
76C22×C4⋊C4D414yes—
77C22×C42—22no—
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42D414yes—
84#391—232no—
85C2×#95—22no—
86C2×#95—24no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—22no—
100C2×#95—24no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—24no—
107C2×#95—22no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—22no—
112C2×#95—22no—
113C2×#95—22no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—24no—
123C2×#95—24no—
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—42no—
133C2×#95—42no—
134C2×#95—42no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95D414yes—
138C2×#95Q814yescomplemented
139C2×#95Q818yescomplemented
140C25C2411yescharacteristic
141C22×Q8—216no—
142C22×Q8—28no—
143C22×Q8—28no—
144C22×Q8—28no—
145C22×Q8—28no—
146C22×Q8—216no—
147C22×Q8—28no—
148C22×Q8—48no—
149C22×Q8—48no—
150C22×Q8—48no—
151C22×Q8—48no—
152C22×Q8—48no—
153C22×Q8—48no—
154C22×Q8—48no—
155C22×Q8—48no—
156C22×Q8—48no—
157C22×Q8—48no—
158C22×Q8—44no—
159C22×Q8—44no—
160C22×Q8—44no—
161C22×Q8—44no—
162C22×Q8—44no—
163C22×Q8—44no—
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—21no—
173C23×C4—21no—
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—21no—
187C23×C4—21no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—22no—
210C23×C4—21no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—22no—
226C23×C4—21no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—21no—
231C23×C4—22no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—21no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—21no—
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—21no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—21no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D412yes—
284C23×C4C2×D414yes—
285C23×C4C2×D412yes—
286C23×C4C2×D412yes—
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×Q812yes—
291C23×C4C2×Q814yes—
292C23×C4C2×Q812yes—
293C23×C4C2×Q812yes—
294C23×C4C2×Q814yes—
295C23×C4C2×Q814yes—
296C23×C4#4112yes—
297C23×C4#4112yes—
298C23×C4#4114yes—
299C23×C4#4112yes—
300C23×C4#4114yes—
301C23×C4#4114yes—
302C23×C4#4112yes—
303C23×C4#4112yes—
304C23×C4#4112yes—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4—48no—
308C2×C4⋊C4—48no—
309C2×C4⋊C4—48no—
310C2×C4⋊C4—48no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—48no—
314C2×C4⋊C4—48no—
315C2×C4⋊C4—48no—
316C2×C4⋊C4—48no—
317C2×C42—28no—
318C2×C42—28no—
319C2×C42—28no—
320C2×C42—44no—
321C2×C42—44no—
322C2×C42—44no—
323C2×C42—44no—
324#95—28no—
325#95—216no—
326#95—216no—
327#95—28no—
328#95—216no—
329#95—28no—
330#95—48no—
331#95—48no—
332#95—48no—
333#95—48no—
334#95—48no—
335#95—44no—
336#95—44no—
337#95—48no—
338#95—48no—
339#95—44no—
340#95—44no—
341#95—44no—
342#95—48no—
343C24C22×D411yescharacteristic
344C24C22×D411yescharacteristic
345C24C22×D411yescharacteristic
346C24C22×D411yescharacteristic
347C24C22×Q812yes—
348C24C22×Q811yescharacteristic
349C24C2×#4111yescharacteristic
350C24C2×#4111yescharacteristic
351C24C2×#4111yescharacteristic
352C24C2×#4111yescharacteristic
353C24C2×#4112yes—
354C24C2×#4112yes—
355C24C2×#4112yes—
356C24C2×#4111yescharacteristic
357C24C2×#4111yescharacteristic
358C24H(5,𝔽2)12yes—
359C24H(5,𝔽2)12yes—
360C24H(5,𝔽2)12yes—
361C24H(5,𝔽2)11yescharacteristic
362C242−1+412yes—
363C242−1+411yescharacteristic
364C242−1+411yescharacteristic
365C242−1+411yescharacteristic
366C2×Q8—232no—
367C2×Q8—432no—
368C2×Q8—432no—
369C2×Q8—432no—
370C2×Q8—416no—
371C2×Q8—416no—
372C2×Q8—416no—
373C2×Q8—416no—
374C2×Q8—416no—
375C2×Q8—432no—
376C2×Q8—416no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—24no—
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—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
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—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—42no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—41no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—41no—
544C22×C4—42no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—42no—
591C22×C4—41no—
592C22×C4—41no—
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—41no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—41no—
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—41no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—41no—
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#12014yes—
680C22×C4#12114yes—
681C22×C4#12114yes—
682C22×C4#12114yes—
683C22×C4C22⋊Q814yes—
684C22×C4C22⋊Q818yes—
685C22×C4#12318yes—
686C22×C4#12314yes—
687C22×C4#12314yes—
688C22×C4#12414yes—
689C22×C4C4⋊Q814yes—
690C4⋊C4—416no—
691C4⋊C4—432no—
692C42—416no—
693C23C2×#12011yescharacteristic
694C23C2×#12111yescharacteristic
695C23C2×#12111yescharacteristic
696C23C2×#12111yescharacteristic
697C23C2×C22⋊Q811yescharacteristic
698C23C2×C22⋊Q812yes—
699C23C2×#12312yes—
700C23C2×#12311yescharacteristic
701C23C2×#12311yescharacteristic
702C23#52512yes—
703C23#52511yescharacteristic
704C23#52511yescharacteristic
705C23#52511yescharacteristic
706C23C2×#12411yescharacteristic
707C23#52911yescharacteristic
708C23#52911yescharacteristic
709C23#52912yes—
710C23C2×C4⋊Q811yescharacteristic
711C23#53211yescharacteristic
712C23#53311yescharacteristic
713C23#53311yescharacteristic
714C23#53312yes—
715C23#53312yes—
716C23#53312yes—
717C23#53312yes—
718C23#53412yes—
719C23#53412yes—
720C23#53511yescharacteristic
721C23#53511yescharacteristic
722C23#53511yescharacteristic
723C23#53611yescharacteristic
724C23#53611yescharacteristic
725C23#53711yescharacteristic
726C23#53712yes—
727C23#53812yes—
728C23#53812yes—
729C23#53812yes—
730C23#54111yescharacteristic
731C23#54111yescharacteristic
732C23#54112yes—
733C23#54212yes—
734C23#54211yescharacteristic
735C23#54211yescharacteristic
736C23#54212yes—
737C23#54212yes—
738C23#54212yes—
739C23#54212yes—
740C23#54212yes—
741C23#54412yes—
742C23#54412yes—
743C23#54412yes—
744C23#54611yescharacteristic
745C23#54612yes—
746C23#54612yes—
747C23#54611yescharacteristic
748C23#54612yes—
749C23#54711yescharacteristic
750C23#54711yescharacteristic
751C23#54811yescharacteristic
752C23#54811yescharacteristic
753C23#54811yescharacteristic
754C23#54811yescharacteristic
755C23D4×Q811yescharacteristic
756C23D4×Q811yescharacteristic
757C23D4×Q811yescharacteristic
758C23D4×Q812yes—
759C23D4×Q812yes—
760C23#55011yescharacteristic
761C23#55012yes—
762C23#55112yes—
763C23#55112yes—
764C23#55112yes—
765C23#55112yes—
766C23#55112yes—
767C23#55112yes—
768C23#55112yes—
769C23#55212yes—
770C23#55212yes—
771C23#55211yescharacteristic
772C23#55212yes—
773C23#55211yescharacteristic
774C23#55412yes—
775C23#55412yes—
776C23#55412yes—
777C23#55411yescharacteristic
778C23#55412yes—
779C23#55412yes—
780C23#55512yes—
781C23#55612yes—
782C23#55612yes—
783C23#55611yescharacteristic
784C23#55612yes—
785C23#55712yes—
786C23Q8212yes—
787C23#55912yes—
788C23H(3,𝔽4)12yes—
789C23#56212yes—
790C23#56312yes—
791C23#56312yes—
792Q8—464no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—24no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—44no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—81no—
894C2×C4—82no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—82no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—82no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—82no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4—82no—
912C2×C4—82no—
913C2×C4—82no—
914C2×C4—81no—
915C2×C4—81no—
916C2×C4—82no—
917C2×C4—82no—
918C2×C4—82no—
919C2×C4—82no—
920C2×C4—82no—
921C2×C4—82no—
922C2×C4—82no—
923C2×C4—82no—
924C2×C4—82no—
925C2×C4—82no—
926C2×C4—82no—
927C2×C4—82no—
928C2×C4—82no—
929C2×C4—82no—
930C2×C4—82no—
931C2×C4—82no—
932C2×C4—82no—
933C2×C4#39418yes—
934C22C2×#39411yescharacteristic
935C22#239611yescharacteristic
936C22#239911yescharacteristic
937C22#240711yescharacteristic
938C22#240911yescharacteristic
939C22#241111yescharacteristic
940C22#241111yescharacteristic
941C22#241212yes—
942C22#241511yescharacteristic
943C22#241711yescharacteristic
944C22#241712yes—
945C22#242111yescharacteristic
946C22#242312yes—
947C22#242312yes—
948C22#242311yescharacteristic
949C22#242312yes—
950C22#242611yescharacteristic
951C22#242711yescharacteristic
952C22#242911yescharacteristic
953C22#242911yescharacteristic
954C22#243111yescharacteristic
955C22#243411yescharacteristic
956C22#243812yes—
957C22#243912yes—
958C22#244612yes—
959C22#244812yes—
960C22#245012yes—
961C22#245112yes—
962C22#245812yes—
963C22#246212yes—
964C22#246512yes—
965C22#246512yes—
966C22#248211yescharacteristic
967C22#248211yescharacteristic
968C22#248312yes—
969C22#248911yescharacteristic
970C22#249211yescharacteristic
971C22#249212yes—
972C22#249911yescharacteristic
973C22#250211yescharacteristic
974C22#252012yes—
975C22#252712yes—
976C22#253212yes—
977C22#253412yes—
978C22#253812yes—
979C22#256112yes—
980C22#256711yescharacteristic
981C22#258011yescharacteristic
982C22#258411yescharacteristic
983C22#258612yes—
984C22#258612yes—
985C22#258612yes—
986C22#258912yes—
987C22#258912yes—
988C22#259911yescharacteristic
989C22#260411yescharacteristic
990C22#260512yes—
991C22#260512yes—
992C22#261011yescharacteristic
993C22#261212yes—
994C22#261212yes—
995C22#261311yescharacteristic
996C22#262011yescharacteristic
997C22#262511yescharacteristic
998C22#262811yescharacteristic
999C22#263111yescharacteristic
1000C22#263211yescharacteristic
1001C22#263711yescharacteristic
1002C22#266011yescharacteristic
1003C22#266211yescharacteristic
1004C22#268412yes—
1005C22#268612yes—
1006C22#270212yes—
1007C22#270412yes—
1008C22#271212yes—
1009C22#271512yes—
1010C22#272912yes—
1011C22#272912yes—
1012C22#273012yes—
1013C22#273312yes—
1014C22#273412yes—
1015C22#273412yes—
1016C22#275412yes—
1017C22#275512yes—
1018C22#275512yes—
1019C22#275812yes—
1020C22#275912yes—
1021C22#275912yes—
1022C22#276212yes—
1023C22#276312yes—
1024C22#276312yes—
1025C22#276312yes—
1026C22#276412yes—
1027C22#276412yes—
1028C22#281911yescharacteristic
1029C22#282111yescharacteristic
1030C22#284911yescharacteristic
1031C22#285511yescharacteristic
1032C22#285711yescharacteristic
1033C4—28no—
1034C4—48no—
1035C4—44no—
1036C4—44no—
1037C4—48no—
1038C4—82no—
1039C4—82no—
1040C4—82no—
1041C4—84no—
1042C4—82no—
1043C4—84no—
1044C2#1487211yescharacteristic
1045C2#1487511yescharacteristic
1046C2#1487911yescharacteristic
1047C2#1490111yescharacteristic
1048C2#1491811yescharacteristic
1049C2#1510411yescharacteristic
1050C2#1511911yescharacteristic
1051C2#1517911yescharacteristic
1052C2#1518211yescharacteristic
1053C2#1582412yes—
1054C2#1585112yes—
1055C2#1585212yes—
1056C2#1585412yes—
1057C2#1585712yes—
1058C2#1586012yes—
1059C2#1610812yes—
1060C2#1611012yes—
1061C2#1656611yescharacteristic
1062C2#1660311yescharacteristic
1063C2#1666511yescharacteristic
1064C2#1668011yescharacteristic
1065C2#1669411yescharacteristic
1066C2#1669611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
138. C2×#95Q8semidirect
139. C2×#95Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#3912
C2×#14462
C2×#14442
C2×#14342
#75572
#75562