Finite Group Databasebeta

← #158238

Subgroups — #158238

Order 512.

3284 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic
2C22×#391C211yesmaximal, characteristic
3C2×#1446C211yesmaximal, characteristic
4C2×#1442C212yesmaximal
5C2×#1441C211yesmaximal, characteristic
6C2×#1436C211yesmaximal, characteristic
7C2×#1434C211yesmaximal, characteristic
8#7557C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7556C212yesmaximal
11#7556C212yesmaximal
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C42C2211yescharacteristic
17C2×#395—24no—
18C2×#395—24no—
19C2×#395—24no—
20C2×#391—24no—
21C2×#391—28no—
22C22×#95C2211yescharacteristic
23C22×#95C2212yes—
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2211yescharacteristic
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2211yescharacteristic
40#1446—24no—
41#1442—28no—
42#1441—24no—
43#1436—24no—
44#1434—24no—
45C23×Q8—24no—
46C23×Q8—22no—
47C23×Q8—22no—
48C23×Q8—22no—
49C23×Q8—24no—
50C23×Q8—22no—
51C23×Q8—22no—
52C23×Q8—22no—
53C23×Q8—42no—
54C23×Q8—42no—
55C23×Q8D414yes—
56C24×C4C2311yescharacteristic
57C24×C4C2312yes—
58C24×C4C2312yes—
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2312yes—
63C24×C4C2311yescharacteristic
64C24×C4C2312yes—
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C22×C4⋊C4—24no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—22no—
75C22×C4⋊C4—22no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—24no—
80C22×C4⋊C4—24no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—42no—
83C22×C4⋊C4—42no—
84C22×C4⋊C4—42no—
85C22×C4⋊C4D414yes—
86C22×C42—22no—
87C22×C42—24no—
88C22×C42—22no—
89C22×C42—42no—
90C22×C42D414yes—
91#395—232no—
92#391—232no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—24no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—24no—
120C2×#95—22no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—22no—
128C2×#95—24no—
129C2×#95—22no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—22no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95D414yes—
143C2×#95D418yes—
144C2×#95Q818yescomplemented
145C25C2411yescharacteristic
146C22×Q8—28no—
147C22×Q8—216no—
148C22×Q8—28no—
149C22×Q8—28no—
150C22×Q8—216no—
151C22×Q8—28no—
152C22×Q8—28no—
153C22×Q8—48no—
154C22×Q8—48no—
155C22×Q8—48no—
156C22×Q8—48no—
157C22×Q8—48no—
158C22×Q8—48no—
159C22×Q8—48no—
160C22×Q8—48no—
161C22×Q8—48no—
162C22×Q8—44no—
163C22×Q8—44no—
164C22×Q8—48no—
165C22×Q8—44no—
166C22×Q8—44no—
167C22×Q8—44no—
168C22×Q8—44no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—22no—
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—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—21no—
204C23×C4—21no—
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—21no—
218C23×C4—21no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—22no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—21no—
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—21no—
278C23×C4—21no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4C2×D412yes—
286C23×C4C2×D414yes—
287C23×C4C2×D412yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D412yes—
296C23×C4C2×D412yes—
297C23×C4C2×D412yes—
298C23×C4C2×Q814yes—
299C23×C4C2×Q814yes—
300C23×C4C2×Q814yes—
301C23×C4#4112yes—
302C23×C4#4112yes—
303C23×C4#4114yes—
304C23×C4#4114yes—
305C23×C4#4112yes—
306C23×C4#4112yes—
307C23×C4#4112yes—
308C23×C4#4112yes—
309C23×C4#4112yes—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—216no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—48no—
316C2×C4⋊C4—48no—
317C2×C4⋊C4—48no—
318C2×C4⋊C4—48no—
319C2×C4⋊C4—48no—
320C2×C4⋊C4—48no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—48no—
323C2×C4⋊C4—48no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C42—28no—
330C2×C42—28no—
331C2×C42—44no—
332C2×C42—48no—
333C2×C42—48no—
334#95—28no—
335#95—28no—
336#95—216no—
337#95—216no—
338#95—216no—
339#95—216no—
340#95—28no—
341#95—216no—
342#95—48no—
343#95—48no—
344#95—48no—
345#95—44no—
346#95—48no—
347#95—44no—
348#95—44no—
349#95—48no—
350#95—44no—
351#95—48no—
352C24C22×D411yescharacteristic
353C24C22×D411yescharacteristic
354C24C22×D411yescharacteristic
355C24C22×D411yescharacteristic
356C24C22×D412yes—
357C24C22×Q812yes—
358C24C2×#4111yescharacteristic
359C24C2×#4111yescharacteristic
360C24C2×#4111yescharacteristic
361C24C2×#4112yes—
362C24C2×#4112yes—
363C24C2×#4111yescharacteristic
364C24C2×#4111yescharacteristic
365C24C2×#4111yescharacteristic
366C24C2×#4111yescharacteristic
367C24H(5,𝔽2)12yes—
368C24H(5,𝔽2)12yes—
369C242−1+412yes—
370C242−1+411yescharacteristic
371C242−1+411yescharacteristic
372C242−1+411yescharacteristic
373C242−1+412yes—
374C242−1+411yescharacteristic
375C2×Q8—232no—
376C2×Q8—432no—
377C2×Q8—432no—
378C2×Q8—416no—
379C2×Q8—416no—
380C2×Q8—416no—
381C2×Q8—416no—
382C2×Q8—432no—
383C2×Q8—432no—
384C2×Q8—416no—
385C2×Q8—416no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
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—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
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—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
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—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—41no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—41no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
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—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—42no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—41no—
602C22×C4—41no—
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—41no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—42no—
618C22×C4—41no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—41no—
624C22×C4—41no—
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—41no—
662C22×C4—42no—
663C22×C4—41no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—41no—
670C22×C4—41no—
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#12014yes—
688C22×C4#12014yes—
689C22×C4#12118yes—
690C22×C4#12114yes—
691C22×C4#12114yes—
692C22×C4#12114yes—
693C22×C4C22⋊Q818yes—
694C22×C4#12314yes—
695C22×C4#12314yes—
696C22×C4#12414yes—
697C22×C4#12414yes—
698C22×C4C4⋊Q814yes—
699C4⋊C4—416no—
700C4⋊C4—432no—
701C4⋊C4—416no—
702C42—416no—
703C23C2×#12011yescharacteristic
704C23C2×#12011yescharacteristic
705C23C2×#12111yescharacteristic
706C23C2×#12112yes—
707C23C2×#12111yescharacteristic
708C23C2×#12111yescharacteristic
709C23C2×C22⋊Q812yes—
710C23C2×#12311yescharacteristic
711C23C2×#12311yescharacteristic
712C23#52511yescharacteristic
713C23#52511yescharacteristic
714C23#52512yes—
715C23#52511yescharacteristic
716C23#52512yes—
717C23C2×#12411yescharacteristic
718C23C2×#12411yescharacteristic
719C23#52911yescharacteristic
720C23#52911yescharacteristic
721C23C2×C4⋊Q811yescharacteristic
722C23#53211yescharacteristic
723C23#53211yescharacteristic
724C23#53212yes—
725C23#53312yes—
726C23#53312yes—
727C23#53312yes—
728C23#53411yescharacteristic
729C23#53412yes—
730C23#53511yescharacteristic
731C23#53611yescharacteristic
732C23#53611yescharacteristic
733C23#53611yescharacteristic
734C23#53611yescharacteristic
735C23#53612yes—
736C23#53612yes—
737C23#53612yes—
738C23#53611yescharacteristic
739C23#53611yescharacteristic
740C23#53812yes—
741C23#53912yes—
742C23#53912yes—
743C23#54111yescharacteristic
744C23#54111yescharacteristic
745C23#54112yes—
746C23#54112yes—
747C23#54112yes—
748C23#54212yes—
749C23#54212yes—
750C23#54212yes—
751C23#54212yes—
752C23#54412yes—
753C23#54412yes—
754C23D4212yes—
755C23D4212yes—
756C23#54612yes—
757C23#54612yes—
758C23#54612yes—
759C23#54612yes—
760C23#54712yes—
761C23#54712yes—
762C23#54711yescharacteristic
763C23#54711yescharacteristic
764C23#54812yes—
765C23#54812yes—
766C23#54811yescharacteristic
767C23#54811yescharacteristic
768C23#54811yescharacteristic
769C23#54811yescharacteristic
770C23#54811yescharacteristic
771C23#54811yescharacteristic
772C23D4×Q812yes—
773C23D4×Q812yes—
774C23D4×Q812yes—
775C23D4×Q812yes—
776C23#55112yes—
777C23#55112yes—
778C23#55112yes—
779C23#55212yes—
780C23#55211yescharacteristic
781C23#55212yes—
782C23#55211yescharacteristic
783C23#55211yescharacteristic
784C23#55211yescharacteristic
785C23#55211yescharacteristic
786C23#55211yescharacteristic
787C23#55412yes—
788C23#55412yes—
789C23#55512yes—
790C23#55612yes—
791C23#55612yes—
792C23#55612yes—
793C23#55612yes—
794C23#55611yescharacteristic
795C23#55611yescharacteristic
796C23#55712yes—
797C23#55712yes—
798C23#56312yes—
799C23#56312yes—
800C23#56312yes—
801C23#56312yes—
802Q8—464no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—24no—
821C2×C4—28no—
822C2×C4—28no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—28no—
827C2×C4—24no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—42no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—44no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—44no—
896C2×C4—44no—
897C2×C4—44no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—44no—
908C2×C4—42no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—82no—
913C2×C4—82no—
914C2×C4—81no—
915C2×C4—82no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—82no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4—82no—
923C2×C4—81no—
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—82no—
934C2×C4—82no—
935C2×C4—82no—
936C2×C4—82no—
937C2×C4—82no—
938C2×C4—81no—
939C2×C4—82no—
940C2×C4—81no—
941C2×C4—82no—
942C2×C4—82no—
943C2×C4#39418yes—
944C22C2×#39411yescharacteristic
945C22#238811yescharacteristic
946C22#239911yescharacteristic
947C22#240611yescharacteristic
948C22#240811yescharacteristic
949C22#240912yes—
950C22#241011yescharacteristic
951C22#241012yes—
952C22#241111yescharacteristic
953C22#241212yes—
954C22#241511yescharacteristic
955C22#241511yescharacteristic
956C22#241812yes—
957C22#242111yescharacteristic
958C22#242111yescharacteristic
959C22#242912yes—
960C22#242912yes—
961C22#243211yescharacteristic
962C22#243411yescharacteristic
963C22#243611yescharacteristic
964C22#243812yes—
965C22#243912yes—
966C22#244612yes—
967C22#244612yes—
968C22#244912yes—
969C22#245212yes—
970C22#246112yes—
971C22#246212yes—
972C22#246212yes—
973C22#246512yes—
974C22#247212yes—
975C22#247412yes—
976C22#248911yescharacteristic
977C22#248911yescharacteristic
978C22#249112yes—
979C22#249212yes—
980C22#249911yescharacteristic
981C22#250311yescharacteristic
982C22#252012yes—
983C22#252112yes—
984C22#253411yescharacteristic
985C22#253611yescharacteristic
986C22#253611yescharacteristic
987C22#253612yes—
988C22#254511yescharacteristic
989C22#254512yes—
990C22#254511yescharacteristic
991C22#254611yescharacteristic
992C22#254611yescharacteristic
993C22#255612yes—
994C22#255612yes—
995C22#256812yes—
996C22#258311yescharacteristic
997C22#258812yes—
998C22#259912yes—
999C22#259911yescharacteristic
1000C22#260412yes—
1001C22#260411yescharacteristic
1002C22#260512yes—
1003C22#261011yescharacteristic
1004C22#261212yes—
1005C22#261411yescharacteristic
1006C22#261711yescharacteristic
1007C22#262111yescharacteristic
1008C22#262111yescharacteristic
1009C22#263211yescharacteristic
1010C22#263411yescharacteristic
1011C22#263811yescharacteristic
1012C22#266011yescharacteristic
1013C22#266311yescharacteristic
1014C22#267412yes—
1015C22#267712yes—
1016C22#267712yes—
1017C22#268012yes—
1018C22#268912yes—
1019C22#269012yes—
1020C22#269812yes—
1021C22#269812yes—
1022C22#271312yes—
1023C22#271312yes—
1024C22#271612yes—
1025C22#271612yes—
1026C22#272812yes—
1027C22#272912yes—
1028C22#272912yes—
1029C22#273112yes—
1030C22#274512yes—
1031C22#275812yes—
1032C22#275812yes—
1033C22#276212yes—
1034C22#277412yes—
1035C22#277412yes—
1036C22#277512yes—
1037C22#278912yes—
1038C22#281711yescharacteristic
1039C22#282111yescharacteristic
1040C22#284711yescharacteristic
1041C22#285011yescharacteristic
1042C22#285711yescharacteristic
1043C4—28no—
1044C4—44no—
1045C4—48no—
1046C4—44no—
1047C4—44no—
1048C4—48no—
1049C4—82no—
1050C4—82no—
1051C4—82no—
1052C4—84no—
1053C4—84no—
1054C2#1472511yescharacteristic
1055C2#1476311yescharacteristic
1056C2#1488011yescharacteristic
1057C2#1490111yescharacteristic
1058C2#1507011yescharacteristic
1059C2#1509711yescharacteristic
1060C2#1517611yescharacteristic
1061C2#1518011yescharacteristic
1062C2#1523611yescharacteristic
1063C2#1527912yes—
1064C2#1532212yes—
1065C2#1537412yes—
1066C2#1543712yes—
1067C2#1550312yes—
1068C2#1563812yes—
1069C2#1569912yes—
1070C2#1585312yes—
1071C2#1626211yescharacteristic
1072C2#1650711yescharacteristic
1073C2#1666311yescharacteristic
1074C2#1680411yescharacteristic
1075C2#1699311yescharacteristic
1076C2#1702311yescharacteristic
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
144. C2×#95Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#3952
C22×#3912
C2×#14462
C2×#14422
C2×#14412
C2×#14362
C2×#14342
#75572
#75562