Finite Group Databasebeta

← #154393

Subgroups — #154393

Order 512.

5454 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#390C211yesmaximal, characteristic
2C22×#390C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic, complemented
5C2×#1439C214yesmaximal, complemented
6C2×C4⋊#95C211yesmaximal, characteristic, complemented
7C2×C4⋊#95C211yesmaximal, characteristic, complemented
8C2×C4×#95C211yesmaximal, characteristic, complemented
9#7555C214yesmaximal, complemented
10C24×D4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C22⋊C4C2212yes—
16C23×C22⋊C4C2214yes—
17C23×C22⋊C4C2212yes—
18C23×C22⋊C4C2214yes—
19C23×C42C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#390—24no—
23C2×#390—24no—
24C2×#390—24no—
25C2×#390—24no—
26C2×#390—24no—
27C2×#390—24no—
28C2×#390—24no—
29C2×#390—24no—
30C2×#390C418yescomplemented
31C2×#389—24no—
32C2×#389—24no—
33C2×#389—24no—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2214yes—
37C22×#95C2214yes—
38C22×#95C2212yes—
39#1439—216no—
40C4⋊#95—24no—
41C4⋊#95—24no—
42C4×#95—24no—
43C26C2312yes—
44C23×D4—22no—
45C23×D4—22no—
46C23×D4—22no—
47C23×D4—22no—
48C23×D4—22no—
49C23×D4—22no—
50C23×D4—22no—
51C23×D4—22no—
52C23×D4—22no—
53C23×D4—22no—
54C23×D4—22no—
55C23×D4—22no—
56C23×D4C2×C414yes—
57C23×D4D414yes—
58C23×D4Q814yes—
59C24×C4C2312yes—
60C24×C4C2312yes—
61C24×C4C2312yes—
62C24×C4C2312yes—
63C24×C4C2311yescharacteristic
64C24×C4C2312yes—
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—22no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—22no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—28no—
87C22×C4⋊C4—44no—
88C22×C4⋊C4C2×C414yes—
89C22×C4⋊C4D414yes—
90C22×C4⋊C4D414yes—
91C22×C4⋊C4D414yes—
92C22×C4⋊C4D414yes—
93C22×C22⋊C4—24no—
94C22×C22⋊C4—28no—
95C22×C22⋊C4—24no—
96C22×C22⋊C4—28no—
97C22×C22⋊C4—28no—
98C22×C22⋊C4—24no—
99C22×C22⋊C4—24no—
100C22×C22⋊C4—28no—
101C22×C22⋊C4—24no—
102C22×C22⋊C4—24no—
103C22×C22⋊C4—28no—
104C22×C22⋊C4—28no—
105C22×C22⋊C4—28no—
106C22×C22⋊C4—28no—
107C22×C22⋊C4—28no—
108C22×C22⋊C4—28no—
109C22×C22⋊C4—28no—
110C22×C22⋊C4—44no—
111C22×C22⋊C4—44no—
112C22×C22⋊C4—44no—
113C22×C22⋊C4—44no—
114C22×C22⋊C4—44no—
115C22×C22⋊C4—44no—
116C22×C22⋊C4C2×C4116yes—
117C22×C42—22no—
118C22×C42—22no—
119C22×C42—22no—
120C22×C42—22no—
121C22×C42—22no—
122C22×C42—22no—
123C22×C42—22no—
124C22×C42—22no—
125C22×C42—22no—
126C22×C42—22no—
127C22×C42—22no—
128C22×C42—22no—
129C22×C42—22no—
130C22×C42—22no—
131C22×C42—22no—
132C22×C42—22no—
133C22×C42—22no—
134C22×C42—22no—
135C22×C42C2×C414yes—
136C22×C42D414yes—
137C22×C42D414yes—
138#390—232no—
139#390—232no—
140#390—232no—
141#389—232no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—28no—
151C2×#95—28no—
152C2×#95—28no—
153C2×#95—28no—
154C2×#95—44no—
155C2×#95—44no—
156C2×#95D418yescomplemented
157C25—24no—
158C25—22no—
159C25—22no—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—22no—
164C25—24no—
165C25—24no—
166C25—24no—
167C25—22no—
168C25—22no—
169C25—22no—
170C25—22no—
171C25—22no—
172C25—22no—
173C25—24no—
174C25—24no—
175C25—24no—
176C25—24no—
177C25C22×C414yes—
178C25C2×D414yes—
179C25C2×Q814yes—
180C25C2411yescharacteristic
181C22×D4—28no—
182C22×D4—28no—
183C22×D4—28no—
184C22×D4—28no—
185C22×D4—28no—
186C22×D4—28no—
187C22×D4—28no—
188C22×D4—28no—
189C22×D4—28no—
190C22×D4—28no—
191C22×D4—28no—
192C22×D4—28no—
193C22×D4—28no—
194C22×D4—28no—
195C22×D4—28no—
196C22×D4—28no—
197C22×D4—28no—
198C22×D4—28no—
199C22×D4—44no—
200C22×D4—44no—
201C22×D4—44no—
202C22×D4—44no—
203C22×D4—44no—
204C22×D4—44no—
205C22×D4—44no—
206C22×D4—44no—
207C22×D4—44no—
208C22×D4—44no—
209C22×D4—44no—
210C22×D4—44no—
211C22×D4—44no—
212C22×D4—44no—
213C22×D4—44no—
214C22×D4—44no—
215C22×D4C4⋊C4116yescomplemented
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—22no—
236C23×C4—24no—
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—21no—
248C23×C4—21no—
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—22no—
258C23×C4—24no—
259C23×C4—24no—
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—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4C22×C414yes—
287C23×C4C22×C414yes—
288C23×C4C22×C412yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2×D412yes—
297C23×C4C2×D414yes—
298C23×C4C2×D412yes—
299C23×C4C2×D412yes—
300C23×C4C2×D412yes—
301C23×C4C2×D412yes—
302C23×C4C2×D412yes—
303C23×C4C2×D412yes—
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×Q812yes—
307C23×C4#4114yes—
308C23×C4#4114yes—
309C23×C4#4114yes—
310C23×C4#4112yes—
311C23×C4#4112yes—
312C23×C4#4112yes—
313C23×C4#4112yes—
314C23×C4#4112yes—
315C23×C4#4112yes—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—216no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—416no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—48no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—48no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4C22⋊C4116yescomplemented
342C2×C22⋊C4—232no—
343C2×C22⋊C4—216no—
344C2×C22⋊C4—216no—
345C2×C22⋊C4—232no—
346C2×C22⋊C4—232no—
347C2×C22⋊C4—416no—
348C2×C22⋊C4—416no—
349C2×C22⋊C4—416no—
350C2×C22⋊C4—416no—
351C2×C22⋊C4—416no—
352C2×C22⋊C4—416no—
353C2×C22⋊C4—416no—
354C2×C22⋊C4—416no—
355C2×C22⋊C4—416no—
356C2×C22⋊C4—416no—
357C2×C22⋊C4—416no—
358C2×C22⋊C4—416no—
359C2×C22⋊C4—416no—
360C2×C22⋊C4—416no—
361C2×C22⋊C4—48no—
362C2×C22⋊C4—48no—
363C2×C22⋊C4—416no—
364C2×C22⋊C4—48no—
365C2×C22⋊C4—48no—
366C2×C42—28no—
367C2×C42—28no—
368C2×C42—28no—
369C2×C42—28no—
370C2×C42—28no—
371C2×C42—28no—
372C2×C42—28no—
373C2×C42—28no—
374C2×C42—28no—
375C2×C42—44no—
376C2×C42—44no—
377C2×C42—44no—
378C2×C42—44no—
379C2×C42—44no—
380C2×C42—44no—
381C2×C42—44no—
382C2×C42—44no—
383C2×C42—44no—
384C2×C42—44no—
385C2×C42—44no—
386C2×C42—44no—
387#95—216no—
388#95—216no—
389#95—216no—
390#95—416no—
391#95—416no—
392C24—24no—
393C24—24no—
394C24—28no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—28no—
400C24—28no—
401C24—28no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—24no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—24no—
413C24—24no—
414C24—28no—
415C24—28no—
416C24—28no—
417C24—28no—
418C24—28no—
419C24—28no—
420C24—28no—
421C24—28no—
422C24—42no—
423C24—44no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—44no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—44no—
448C24—42no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—42no—
453C24—42no—
454C24—44no—
455C24—42no—
456C24—42no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24—44no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24—44no—
469C24—44no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—44no—
477C24—44no—
478C24—44no—
479C24—44no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24C2×C4⋊C418yes—
491C24C23×C411yescharacteristic
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494C24C22×D411yescharacteristic
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498C24C22×D411yescharacteristic
499C24C22×D412yes—
500C24C22×Q811yescharacteristic
501C24C2×#4111yescharacteristic
502C24C2×#4111yescharacteristic
503C24C2×#4111yescharacteristic
504C24C2×#4111yescharacteristic
505C24C2×#4111yescharacteristic
506C24C2×#4111yescharacteristic
507C24C2×#4112yes—
508C24C2×#4112yes—
509C24C2×#4112yes—
510C24H(5,𝔽2)12yes—
511C24H(5,𝔽2)12yes—
512C24H(5,𝔽2)12yes—
513C242−1+412yes—
514C2×D4—232no—
515C2×D4—232no—
516C2×D4—232no—
517C2×D4—416no—
518C2×D4—416no—
519C2×D4—416no—
520C2×D4—416no—
521C2×D4—416no—
522C2×D4—416no—
523C2×D4—416no—
524C2×D4—416no—
525C2×D4—416no—
526C2×D4—416no—
527C2×D4—416no—
528C2×D4—416no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—28no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—28no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—28no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—28no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—28no—
592C22×C4—28no—
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—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
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—41no—
625C22×C4—41no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—44no—
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—44no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—44no—
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—44no—
662C22×C4—44no—
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—44no—
673C22×C4—42no—
674C22×C4—44no—
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—44no—
686C22×C4—44no—
687C22×C4—42no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4C2×C22⋊C418yes—
710C22×C4C2×C22⋊C414yes—
711C22×C4C2×C4⋊C414yes—
712C22×C4#11714yes—
713C22×C4C4×D418yes—
714C22×C4C4×D414yes—
715C22×C4C4×D414yes—
716C22×C4C4×D414yes—
717C22×C4C4×D414yes—
718C22×C4#12014yes—
719C22×C4#12014yes—
720C22×C4#12014yes—
721C22×C4#12118yes—
722C22×C4#12114yes—
723C22×C4#12114yes—
724C22×C4#12114yes—
725C22×C4#12114yes—
726C22×C4#12114yes—
727C22×C4#12114yes—
728C22×C4#12114yes—
729C22×C4#12114yes—
730C22×C4C22⋊Q814yes—
731C22×C4C22⋊Q814yes—
732C22×C4C22⋊Q814yes—
733C22×C4C22⋊Q814yes—
734C22×C4C22⋊Q814yes—
735C22×C4C22⋊Q814yes—
736C22×C4#12314yes—
737C22×C4#12314yes—
738C22×C4#12314yes—
739C22×C4#12314yes—
740C22×C4#12314yes—
741C22×C4#12414yes—
742C22×C4#12414yes—
743C22×C4#12414yes—
744C22×C4#12414yes—
745C22×C4#12614yes—
746C22×C4#12614yes—
747C22×C4#12714yes—
748C22×C4#12714yes—
749C4⋊C4—232no—
750C4⋊C4—432no—
751C4⋊C4—416no—
752C4⋊C4—416no—
753C22⋊C4—464no—
754C22⋊C4—464no—
755C22⋊C4—432no—
756C22⋊C4—432no—
757C42—416no—
758C42—416no—
759C42—416no—
760C23—216no—
761C23—216no—
762C23—28no—
763C23—28no—
764C23—28no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—48no—
770C23—48no—
771C23—48no—
772C23—44no—
773C23—44no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—48no—
779C23—48no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—48no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—48no—
793C23—48no—
794C23—48no—
795C23—48no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—48no—
801C23—48no—
802C23—48no—
803C23—48no—
804C23—48no—
805C23—48no—
806C23—48no—
807C23—48no—
808C23—48no—
809C23—48no—
810C23—48no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—48no—
817C23—48no—
818C23—44no—
819C23—82no—
820C23—84no—
821C23—82no—
822C23—82no—
823C23—84no—
824C23—82no—
825C23—82no—
826C23—82no—
827C23—84no—
828C23—82no—
829C23—82no—
830C23—84no—
831C23—84no—
832C23—84no—
833C23—84no—
834C23—84no—
835C23—84no—
836C23—84no—
837C23—84no—
838C23—84no—
839C23—82no—
840C23—82no—
841C23—82no—
842C23—82no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23—82no—
856C23—82no—
857C23—82no—
858C23—82no—
859C23C22×C22⋊C411yescharacteristic
860C23C22×C4⋊C411yescharacteristic
861C23C2×#11711yescharacteristic
862C23C2×C4×D411yescharacteristic
863C23C2×C4×D412yes—
864C23C2×C4×D411yescharacteristic
865C23C2×C4×D411yescharacteristic
866C23C2×C4×D411yescharacteristic
867C23C4×#4112yes—
868C23#51812yes—
869C23#52012yes—
870C23C2×#12011yescharacteristic
871C23C2×#12011yescharacteristic
872C23C2×#12011yescharacteristic
873C23C2×#12111yescharacteristic
874C23C2×#12112yes—
875C23C2×#12111yescharacteristic
876C23C2×#12111yescharacteristic
877C23C2×#12111yescharacteristic
878C23C2×#12111yescharacteristic
879C23C2×#12111yescharacteristic
880C23C2×#12111yescharacteristic
881C23C2×#12111yescharacteristic
882C23C2×C22⋊Q811yescharacteristic
883C23C2×C22⋊Q811yescharacteristic
884C23C2×C22⋊Q811yescharacteristic
885C23C2×C22⋊Q811yescharacteristic
886C23C2×C22⋊Q811yescharacteristic
887C23C2×C22⋊Q811yescharacteristic
888C23C2×#12311yescharacteristic
889C23C2×#12311yescharacteristic
890C23C2×#12311yescharacteristic
891C23C2×#12311yescharacteristic
892C23C2×#12311yescharacteristic
893C23#52512yes—
894C23C2×#12411yescharacteristic
895C23C2×#12411yescharacteristic
896C23C2×#12411yescharacteristic
897C23C2×#12411yescharacteristic
898C23C2×#12611yescharacteristic
899C23C2×#12611yescharacteristic
900C23#52912yes—
901C23#52912yes—
902C23#52912yes—
903C23#52912yes—
904C23C2×#12711yescharacteristic
905C23C2×#12711yescharacteristic
906C23#53211yescharacteristic
907C23#53212yes—
908C23#53211yescharacteristic
909C23#53212yes—
910C23#53212yes—
911C23#53212yes—
912C23#53511yescharacteristic
913C23#53511yescharacteristic
914C23#53511yescharacteristic
915C23#53512yes—
916C23#53611yescharacteristic
917C23#53712yes—
918C23#54012yes—
919C23#54012yes—
920C23#54012yes—
921C23#54012yes—
922C23#54212yes—
923C23#54212yes—
924C23#54212yes—
925C23#54212yes—
926C23D4212yes—
927C23D4212yes—
928C23D4212yes—
929C23D4212yes—
930C23D4212yes—
931C23#54612yes—
932C23#54612yes—
933C23#54612yes—
934C23#54612yes—
935C23#54612yes—
936C23#54612yes—
937C23#54712yes—
938C23#54712yes—
939C23#54812yes—
940C23#54812yes—
941C23#54812yes—
942C23#54812yes—
943C23D4×Q812yes—
944C23#55012yes—
945C23#55012yes—
946C23#55012yes—
947C23#55012yes—
948C23#55012yes—
949C23#55312yes—
950C23#55312yes—
951C23#55412yes—
952C23#55412yes—
953C23#55412yes—
954C23#55512yes—
955C23#55612yes—
956C23#55912yes—
957C23#55912yes—
958D4—464no—
959C2×C4—28no—
960C2×C4—216no—
961C2×C4—24no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—28no—
972C2×C4—28no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—48no—
981C2×C4—44no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—44no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—44no—
992C2×C4—44no—
993C2×C4—44no—
994C2×C4—44no—
995C2×C4—44no—
996C2×C4—44no—
997C2×C4—44no—
998C2×C4—44no—
999C2×C4—44no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—44no—
1008C2×C4—42no—
1009C2×C4—44no—
1010C2×C4—48no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—44no—
1018C2×C4—44no—
1019C2×C4—44no—
1020C2×C4—44no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—44no—
1024C2×C4—48no—
1025C2×C4—48no—
1026C2×C4—48no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—44no—
1031C2×C4—48no—
1032C2×C4—82no—
1033C2×C4—82no—
1034C2×C4—82no—
1035C2×C4—82no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4—82no—
1043C2×C4—82no—
1044C2×C4#38018yes—
1045C2×C4#38518yes—
1046C2×C4#38518yes—
1047C2×C4#38618yes—
1048C2×C4#38818yes—
1049C2×C4#38818yes—
1050C2×C4#39018yes—
1051C2×C4#39218yes—
1052C2×C4#39318yes—
1053C2×C4#39418yes—
1054C2×C4#39418yes—
1055C2×C4#39618yes—
1056C2×C4#39618yes—
1057C2×C4#39718yes—
1058C2×C4#39918yes—
1059C22—48no—
1060C22—416no—
1061C22—48no—
1062C22—48no—
1063C22—416no—
1064C22—84no—
1065C22—88no—
1066C22—84no—
1067C22—88no—
1068C22—84no—
1069C22—88no—
1070C22—84no—
1071C22—88no—
1072C22—88no—
1073C22—84no—
1074C22—84no—
1075C22—84no—
1076C22—84no—
1077C22—84no—
1078C22—88no—
1079C22—84no—
1080C22—84no—
1081C22—84no—
1082C22C2×#38011yescharacteristic
1083C22C2×#38511yescharacteristic
1084C22C2×#38511yescharacteristic
1085C22C2×#38611yescharacteristic
1086C22C2×#38811yescharacteristic
1087C22C2×#38811yescharacteristic
1088C22C2×#39011yescharacteristic
1089C22#229312yes—
1090C22C4×#12112yes—
1091C22C4×#12411yescharacteristic
1092C22C4×#12711yescharacteristic
1093C22#231912yes—
1094C22#232412yes—
1095C22#232611yescharacteristic
1096C22#232811yescharacteristic
1097C22D4×C22⋊C412yes—
1098C22#234112yes—
1099C22D4×C4⋊C412yes—
1100C22#234912yes—
1101C22#236112yes—
1102C22#236312yes—
1103C22#236612yes—
1104C22#236712yes—
1105C22C2×#39211yescharacteristic
1106C22C2×#39311yescharacteristic
1107C22C2×#39411yescharacteristic
1108C22C2×#39411yescharacteristic
1109C22C2×#39611yescharacteristic
1110C22C2×#39611yescharacteristic
1111C22C2×#39711yescharacteristic
1112C22C2×#39911yescharacteristic
1113C22#240712yes—
1114C22#240812yes—
1115C22#241412yes—
1116C22#241612yes—
1117C22#242012yes—
1118C22#242212yes—
1119C22#242612yes—
1120C22#242612yes—
1121C22#242612yes—
1122C22#242712yes—
1123C22#242712yes—
1124C22#242812yes—
1125C22#242812yes—
1126C22#242812yes—
1127C22#242812yes—
1128C22#242812yes—
1129C22#243111yescharacteristic
1130C22#243111yescharacteristic
1131C22#243111yescharacteristic
1132C22#243211yescharacteristic
1133C22#243311yescharacteristic
1134C22#243311yescharacteristic
1135C22#243511yescharacteristic
1136C22#243611yescharacteristic
1137C22#244512yes—
1138C22#244512yes—
1139C22#244512yes—
1140C22#244712yes—
1141C22#244812yes—
1142C22#244812yes—
1143C22#245212yes—
1144C22#245212yes—
1145C22#245212yes—
1146C22#245212yes—
1147C22#245412yes—
1148C22#245412yes—
1149C22#245412yes—
1150C22#245412yes—
1151C22#249012yes—
1152C22#249012yes—
1153C22#249112yes—
1154C22#249112yes—
1155C22#251212yes—
1156C22#251312yes—
1157C22#253812yes—
1158C22#254012yes—
1159C22#254112yes—
1160C22#254111yescharacteristic
1161C22#254211yescharacteristic
1162C22#254411yescharacteristic
1163C22#254511yescharacteristic
1164C22#254811yescharacteristic
1165C22#256311yescharacteristic
1166C22#256611yescharacteristic
1167C22#256611yescharacteristic
1168C22#258012yes—
1169C22#261911yescharacteristic
1170C22#262011yescharacteristic
1171C22#262412yes—
1172C22#264011yescharacteristic
1173C22#264111yescharacteristic
1174C22#264412yes—
1175C22#285011yescharacteristic
1176C22#285412yes—
1177C22#285611yescharacteristic
1178C22#285811yescharacteristic
1179C22#286012yes—
1180C22#286111yescharacteristic
1181C4—44no—
1182C4—48no—
1183C4—44no—
1184C4—48no—
1185C4—48no—
1186C4—84no—
1187C4—84no—
1188C4#1439116yescomplemented
1189C2—88no—
1190C2C2×#143911yescharacteristic
1191C2#1392012yes—
1192C2#1397711yescharacteristic
1193C2#1397911yescharacteristic
1194C2#1399812yes—
1195C2#1401812yes—
1196C2#1402511yescharacteristic
1197C2#1402611yescharacteristic
1198C2#1414112yes—
1199C2#1426011yescharacteristic
1200C2#1470011yescharacteristic
1201C2#1512411yescharacteristic
1202C2#1512612yes—
1203C2#1513411yescharacteristic
1204C2#1513812yes—
1205C2#1514011yescharacteristic
1206C2#1514112yes—
1207C2#1514411yescharacteristic
1208C2#1514812yes—
1209C2#1521511yescharacteristic
1210C2#1522211yescharacteristic
1211C2#1522611yescharacteristic
1212C2#1522911yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC24C23×C4
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C22×#389C2semidirect
5. C2×#1439C2semidirect
6. C2×C4⋊#95C2semidirect
7. C2×C4⋊#95C2semidirect
8. C2×C4×#95C2semidirect
9. #7555C2semidirect
30. C2×#390C4semidirect
156. C2×#95D4semidirect
215. C22×D4C4⋊C4semidirect
341. C2×C4⋊C4C22⋊C4semidirect
1188. C4#1439semidirect

Maximal subgroups

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

subgroupindex
C22×#3902
C22×#3892
C2×#14392
C2×C4⋊#952
C2×C4×#952
#75552