Finite Group Databasebeta

← #158222

Subgroups — #158222

Order 512.

3124 conjugacy classes of subgroups.

The subgroup lattice has 1044 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×#1445C212yesmaximal
5C2×#1444C211yesmaximal, characteristic
6C2×#1442C211yesmaximal, characteristic
7C2×#1434C211yesmaximal, characteristic
8#7557C212yesmaximal
9#7556C212yesmaximal
10#7556C212yesmaximal
11#7554C211yesmaximal, characteristic
12C24×Q8C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C42C2211yescharacteristic
16C2×#391—24no—
17C2×#391—28no—
18C22×#95C2211yescharacteristic
19C22×#95C2211yescharacteristic
20C22×#95C2212yes—
21C22×#95C2211yescharacteristic
22C22×#95C2212yes—
23C22×#95C2211yescharacteristic
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37#1446—24no—
38#1446—24no—
39#1445—28no—
40#1444—24no—
41#1442—24no—
42#1434—24no—
43C23×Q8—24no—
44C23×Q8—22no—
45C23×Q8—22no—
46C23×Q8—22no—
47C23×Q8—24no—
48C23×Q8—22no—
49C23×Q8—22no—
50C23×Q8—22no—
51C23×Q8—42no—
52C23×Q8—42no—
53C23×Q8Q814yes—
54C24×C4C2312yes—
55C24×C4C2312yes—
56C24×C4C2311yescharacteristic
57C24×C4C2311yescharacteristic
58C24×C4C2311yescharacteristic
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2312yes—
62C24×C4C2311yescharacteristic
63C24×C4C2312yes—
64C24×C4C2311yescharacteristic
65C22×C4⋊C4—24no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—42no—
76C22×C4⋊C4—42no—
77C22×C42—24no—
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—42no—
81C22×C42D414yes—
82#391—232no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—24no—
105C2×#95—22no—
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—22no—
116C2×#95—22no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—24no—
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×#95D414yes—
135C2×#95D414yes—
136C2×#95D418yes—
137C2×#95Q814yescomplemented
138C25C2411yescharacteristic
139C22×Q8—28no—
140C22×Q8—216no—
141C22×Q8—28no—
142C22×Q8—216no—
143C22×Q8—28no—
144C22×Q8—28no—
145C22×Q8—28no—
146C22×Q8—48no—
147C22×Q8—48no—
148C22×Q8—48no—
149C22×Q8—48no—
150C22×Q8—48no—
151C22×Q8—48no—
152C22×Q8—48no—
153C22×Q8—48no—
154C22×Q8—48no—
155C22×Q8—44no—
156C22×Q8—44no—
157C22×Q8—48no—
158C22×Q8—44no—
159C22×Q8—44no—
160C22×Q8—44no—
161C22×Q8—44no—
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—21no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
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—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—21no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—22no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—22no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—21no—
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—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—21no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—21no—
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—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—22no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—22no—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D412yes—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4C2×D412yes—
281C23×C4C2×D414yes—
282C23×C4C2×D412yes—
283C23×C4C2×D412yes—
284C23×C4C2×D412yes—
285C23×C4C2×Q812yes—
286C23×C4C2×Q812yes—
287C23×C4C2×Q814yes—
288C23×C4C2×Q812yes—
289C23×C4C2×Q812yes—
290C23×C4#4112yes—
291C23×C4#4112yes—
292C23×C4#4114yes—
293C23×C4#4112yes—
294C23×C4#4114yes—
295C23×C4#4114yes—
296C23×C4#4112yes—
297C23×C4#4112yes—
298C23×C4#4112yes—
299C2×C4⋊C4—216no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—48no—
302C2×C4⋊C4—48no—
303C2×C4⋊C4—48no—
304C2×C4⋊C4—48no—
305C2×C4⋊C4—48no—
306C2×C4⋊C4—48no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—48no—
309C2×C4⋊C4—48no—
310C2×C4⋊C4—44no—
311C2×C42—28no—
312C2×C42—28no—
313C2×C42—44no—
314C2×C42—48no—
315C2×C42—48no—
316#95—28no—
317#95—216no—
318#95—216no—
319#95—28no—
320#95—28no—
321#95—28no—
322#95—48no—
323#95—48no—
324#95—48no—
325#95—48no—
326#95—48no—
327#95—48no—
328#95—48no—
329#95—48no—
330#95—44no—
331#95—44no—
332#95—48no—
333#95—44no—
334#95—44no—
335C24C22×D411yescharacteristic
336C24C22×D412yes—
337C24C22×D411yescharacteristic
338C24C22×D411yescharacteristic
339C24C22×Q811yescharacteristic
340C24C22×Q811yescharacteristic
341C24C2×#4111yescharacteristic
342C24C2×#4111yescharacteristic
343C24C2×#4111yescharacteristic
344C24C2×#4112yes—
345C24C2×#4111yescharacteristic
346C24C2×#4111yescharacteristic
347C24C2×#4112yes—
348C24C2×#4111yescharacteristic
349C24C2×#4112yes—
350C24H(5,𝔽2)12yes—
351C24H(5,𝔽2)12yes—
352C24H(5,𝔽2)11yescharacteristic
353C242−1+412yes—
354C242−1+411yescharacteristic
355C242−1+412yes—
356C242−1+411yescharacteristic
357C242−1+411yescharacteristic
358C2×Q8—232no—
359C2×Q8—432no—
360C2×Q8—432no—
361C2×Q8—416no—
362C2×Q8—416no—
363C2×Q8—432no—
364C2×Q8—432no—
365C2×Q8—416no—
366C2×Q8—416no—
367C2×Q8—416no—
368C2×Q8—416no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
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—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
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—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
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—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—41no—
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—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—42no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—41no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—42no—
582C22×C4—41no—
583C22×C4—41no—
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—41no—
620C22×C4—41no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—41no—
632C22×C4—41no—
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#12014yes—
660C22×C4C22⋊Q814yes—
661C22×C4C22⋊Q818yes—
662C22×C4C22⋊Q814yes—
663C22×C4C22⋊Q814yes—
664C22×C4C22⋊Q814yes—
665C22×C4#12314yes—
666C22×C4#12314yes—
667C22×C4#12314yes—
668C22×C4#12418yes—
669C22×C4#12714yes—
670C4⋊C4—416no—
671C4⋊C4—432no—
672C42—416no—
673C23C2×#12011yescharacteristic
674C23C2×C22⋊Q811yescharacteristic
675C23C2×C22⋊Q811yescharacteristic
676C23C2×C22⋊Q811yescharacteristic
677C23C2×C22⋊Q812yes—
678C23C2×C22⋊Q811yescharacteristic
679C23C2×#12311yescharacteristic
680C23C2×#12311yescharacteristic
681C23C2×#12311yescharacteristic
682C23#52511yescharacteristic
683C23#52512yes—
684C23#52511yescharacteristic
685C23#52512yes—
686C23C2×#12412yes—
687C23#52911yescharacteristic
688C23#52911yescharacteristic
689C23#52912yes—
690C23C2×#12711yescharacteristic
691C23#53212yes—
692C23#53211yescharacteristic
693C23#53211yescharacteristic
694C23#53212yes—
695C23#53311yescharacteristic
696C23#53311yescharacteristic
697C23#53312yes—
698C23#53411yescharacteristic
699C23#53511yescharacteristic
700C23#53611yescharacteristic
701C23#53611yescharacteristic
702C23#53612yes—
703C23#53612yes—
704C23#53611yescharacteristic
705C23#53612yes—
706C23#53612yes—
707C23#53711yescharacteristic
708C23#53812yes—
709C23#53812yes—
710C23#53912yes—
711C23#53912yes—
712C23#54111yescharacteristic
713C23#54111yescharacteristic
714C23#54112yes—
715C23#54211yescharacteristic
716C23#54211yescharacteristic
717C23#54212yes—
718C23#54212yes—
719C23#54212yes—
720C23#54212yes—
721C23#54212yes—
722C23#54312yes—
723C23#54412yes—
724C23D4212yes—
725C23D4212yes—
726C23#54612yes—
727C23#54612yes—
728C23#54612yes—
729C23#54612yes—
730C23#54612yes—
731C23#54611yescharacteristic
732C23#54611yescharacteristic
733C23#54711yescharacteristic
734C23#54711yescharacteristic
735C23#54712yes—
736C23#54812yes—
737C23#54811yescharacteristic
738C23#54811yescharacteristic
739C23D4×Q812yes—
740C23D4×Q811yescharacteristic
741C23D4×Q811yescharacteristic
742C23#55112yes—
743C23#55112yes—
744C23#55112yes—
745C23#55112yes—
746C23#55212yes—
747C23#55212yes—
748C23#55212yes—
749C23#55212yes—
750C23#55212yes—
751C23#55212yes—
752C23#55412yes—
753C23#55512yes—
754C23#55612yes—
755C23#55612yes—
756C23#55612yes—
757C23#55611yescharacteristic
758C23#55611yescharacteristic
759C23#55612yes—
760C23#55712yes—
761C23#55712yes—
762C23#55711yescharacteristic
763C23#55711yescharacteristic
764C23#55711yescharacteristic
765C23#55711yescharacteristic
766C23Q8211yescharacteristic
767C23#55911yescharacteristic
768C23#56212yes—
769C23#56312yes—
770C23#56312yes—
771C23#56312yes—
772Q8—464no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—82no—
870C2×C4—81no—
871C2×C4—82no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—82no—
875C2×C4—81no—
876C2×C4—82no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—82no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—82no—
885C2×C4—82no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—82no—
890C2×C4—82no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—82no—
900C2×C4—82no—
901C2×C4—82no—
902C2×C4—82no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—82no—
907C2×C4—82no—
908C2×C4—81no—
909C2×C4#39918yes—
910C22#238811yescharacteristic
911C22C2×#39911yescharacteristic
912C22#239611yescharacteristic
913C22#240511yescharacteristic
914C22#240911yescharacteristic
915C22#241812yes—
916C22#241812yes—
917C22#243011yescharacteristic
918C22#243311yescharacteristic
919C22#243712yes—
920C22#243712yes—
921C22#244611yescharacteristic
922C22#244611yescharacteristic
923C22#244711yescharacteristic
924C22#244711yescharacteristic
925C22#245112yes—
926C22#245111yescharacteristic
927C22#245111yescharacteristic
928C22#245312yes—
929C22#245311yescharacteristic
930C22#245311yescharacteristic
931C22#245812yes—
932C22#246112yes—
933C22#246212yes—
934C22#246512yes—
935C22#247212yes—
936C22#247712yes—
937C22#248211yescharacteristic
938C22#248812yes—
939C22#249112yes—
940C22#249212yes—
941C22#249912yes—
942C22#249911yescharacteristic
943C22#249911yescharacteristic
944C22#250312yes—
945C22#252112yes—
946C22#252712yes—
947C22#253212yes—
948C22#253911yescharacteristic
949C22#254011yescharacteristic
950C22#254211yescharacteristic
951C22#255512yes—
952C22#255612yes—
953C22#255612yes—
954C22#256012yes—
955C22#256411yescharacteristic
956C22#256511yescharacteristic
957C22#256511yescharacteristic
958C22#256512yes—
959C22#256512yes—
960C22#256812yes—
961C22#258111yescharacteristic
962C22#258112yes—
963C22#258211yescharacteristic
964C22#259912yes—
965C22#259911yescharacteristic
966C22#260411yescharacteristic
967C22#260412yes—
968C22#260512yes—
969C22#261011yescharacteristic
970C22#261212yes—
971C22#261411yescharacteristic
972C22#262511yescharacteristic
973C22#262611yescharacteristic
974C22#262811yescharacteristic
975C22#263711yescharacteristic
976C22#263811yescharacteristic
977C22#265811yescharacteristic
978C22#266211yescharacteristic
979C22#266311yescharacteristic
980C22#267412yes—
981C22#267412yes—
982C22#267712yes—
983C22#267712yes—
984C22#268712yes—
985C22#268712yes—
986C22#268912yes—
987C22#269012yes—
988C22#269812yes—
989C22#270012yes—
990C22#270012yes—
991C22#271612yes—
992C22#274512yes—
993C22#275112yes—
994C22#275812yes—
995C22#275912yes—
996C22#276212yes—
997C22#276412yes—
998C22#277412yes—
999C22#277512yes—
1000C22#279912yes—
1001C22#279912yes—
1002C22#280612yes—
1003C22#280912yes—
1004C22#281411yescharacteristic
1005C22#282111yescharacteristic
1006C22#284811yescharacteristic
1007C22#285511yescharacteristic
1008C22#285811yescharacteristic
1009C4—28no—
1010C4—48no—
1011C4—48no—
1012C4—44no—
1013C4—44no—
1014C4—82no—
1015C4—84no—
1016C4—84no—
1017C4—82no—
1018C4—82no—
1019C4—82no—
1020C2#1473411yescharacteristic
1021C2#1487811yescharacteristic
1022C2#1492811yescharacteristic
1023C2#1500111yescharacteristic
1024C2#1506511yescharacteristic
1025C2#1511911yescharacteristic
1026C2#1519311yescharacteristic
1027C2#1521411yescharacteristic
1028C2#1524011yescharacteristic
1029C2#1533212yes—
1030C2#1533612yes—
1031C2#1537112yes—
1032C2#1537412yes—
1033C2#1550912yes—
1034C2#1551112yes—
1035C2#1569912yes—
1036C2#1570012yes—
1037C2#1636411yescharacteristic
1038C2#1651111yescharacteristic
1039C2#1669611yescharacteristic
1040C2#1681211yescharacteristic
1041C2#1689811yescharacteristic
1042C2#1702511yescharacteristic
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
137. 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×#14452
C2×#14442
C2×#14422
C2×#14342
#75572
#75562
#75542