Finite Group Databasebeta

← #158491

Subgroups — #158491

Order 512.

3640 conjugacy classes of subgroups.

The subgroup lattice has 1267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic, complemented
2C2×#1442C211yesmaximal, characteristic, complemented
3C2×#1439C211yesmaximal, characteristic
4C2×#1439C212yesmaximal
5C2×#1439C211yesmaximal, characteristic
6C2×#1439C212yesmaximal
7C2×#1437C211yesmaximal, characteristic
8C2×C4⋊#95C211yesmaximal, characteristic, complemented
9#7557C212yesmaximal, complemented
10#7557C212yesmaximal, complemented
11#7557C211yesmaximal, characteristic, complemented
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C4⋊C4C2212yes—
16C23×C22⋊C4C2211yescharacteristic
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2212yes—
19C23×C22⋊C4C2212yes—
20C23×C22⋊C4C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#389—24no—
23C2×#389—28no—
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37#1442—24no—
38#1439—24no—
39#1439—28no—
40#1439—24no—
41#1439—28no—
42#1437—24no—
43C4⋊#95—24no—
44C26C2311yescharacteristic
45C24×C4C2312yes—
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2311yescharacteristic
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2312yes—
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C22×C4⋊C4—24no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—24no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—24no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—24no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4—42no—
75C22×C4⋊C4—42no—
76C22×C4⋊C4—42no—
77C22×C4⋊C4—42no—
78C22×C4⋊C4D414yes—
79C22×C22⋊C4—24no—
80C22×C22⋊C4—22no—
81C22×C22⋊C4—22no—
82C22×C22⋊C4—22no—
83C22×C22⋊C4—24no—
84C22×C22⋊C4—22no—
85C22×C22⋊C4—22no—
86C22×C22⋊C4—24no—
87C22×C22⋊C4—24no—
88C22×C22⋊C4—22no—
89C22×C22⋊C4—22no—
90C22×C22⋊C4—22no—
91C22×C22⋊C4—22no—
92C22×C22⋊C4—22no—
93C22×C22⋊C4—24no—
94C22×C22⋊C4—24no—
95C22×C22⋊C4—24no—
96C22×C22⋊C4—24no—
97C22×C22⋊C4—24no—
98C22×C22⋊C4—24no—
99C22×C22⋊C4—42no—
100C22×C22⋊C4—42no—
101C22×C22⋊C4—42no—
102C22×C22⋊C4—42no—
103C22×C22⋊C4—42no—
104C22×C22⋊C4—42no—
105C22×C22⋊C4—42no—
106C22×C22⋊C4—42no—
107C22×C22⋊C4D414yes—
108C22×C22⋊C4Q814yes—
109C22×C22⋊C4Q814yes—
110C22×C42—22no—
111C22×C42—24no—
112C22×C42—22no—
113C22×C42—42no—
114C22×C42D414yes—
115#389—232no—
116C2×#95—22no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—22no—
120C2×#95—24no—
121C2×#95—22no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—22no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—22no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—22no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—22no—
139C2×#95—22no—
140C2×#95—24no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95—42no—
148C2×#95—42no—
149C2×#95—42no—
150C2×#95—42no—
151C2×#95D414yes—
152C2×#95D418yes—
153C25—21no—
154C25—22no—
155C25—21no—
156C25—21no—
157C25—21no—
158C25—21no—
159C25—21no—
160C25—21no—
161C25—21no—
162C25—22no—
163C25—22no—
164C25—22no—
165C25—22no—
166C25—22no—
167C25—21no—
168C25—22no—
169C25—21no—
170C25—22no—
171C25—21no—
172C25—21no—
173C25C2×D412yes—
174C25C2×Q812yes—
175C25C2×Q812yes—
176C25C2411yescharacteristic
177C23×C4—22no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—21no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—21no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—22no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—22no—
231C23×C4—21no—
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—21no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—21no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
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—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—22no—
269C23×C4—22no—
270C23×C4—21no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4—22no—
278C23×C4—21no—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D412yes—
282C23×C4C2×D414yes—
283C23×C4C2×D412yes—
284C23×C4C2×D414yes—
285C23×C4C2×D412yes—
286C23×C4C2×D414yes—
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×Q812yes—
292C23×C4C2×Q812yes—
293C23×C4C2×Q812yes—
294C23×C4C2×Q812yes—
295C23×C4#4114yes—
296C23×C4#4112yes—
297C23×C4#4114yes—
298C23×C4#4112yes—
299C23×C4#4112yes—
300C23×C4#4112yes—
301C23×C4#4112yes—
302C23×C4#4114yes—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—216no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—216no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—216no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—216no—
311C2×C4⋊C4—48no—
312C2×C4⋊C4—48no—
313C2×C4⋊C4—48no—
314C2×C4⋊C4—48no—
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—48no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—48no—
327C2×C22⋊C4—216no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—216no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—48no—
335C2×C22⋊C4—48no—
336C2×C22⋊C4—48no—
337C2×C22⋊C4—48no—
338C2×C22⋊C4—48no—
339C2×C22⋊C4—48no—
340C2×C22⋊C4—48no—
341C2×C22⋊C4—48no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—48no—
345C2×C22⋊C4—48no—
346C2×C22⋊C4—48no—
347C2×C22⋊C4—48no—
348C2×C22⋊C4—48no—
349C2×C22⋊C4—48no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—48no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—48no—
357C2×C22⋊C4—44no—
358C2×C42—28no—
359C2×C42—28no—
360C2×C42—44no—
361C2×C42—48no—
362C2×C42—48no—
363#95—216no—
364#95—28no—
365#95—48no—
366#95—48no—
367#95—48no—
368#95—44no—
369#95—48no—
370#95—48no—
371#95—48no—
372#95—48no—
373#95—44no—
374#95—44no—
375#95—44no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—24no—
381C24—22no—
382C24—24no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—24no—
387C24—24no—
388C24—22no—
389C24—22no—
390C24—24no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—22no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—42no—
411C24—41no—
412C24—42no—
413C24—42no—
414C24—41no—
415C24—42no—
416C24—41no—
417C24—42no—
418C24—42no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—42no—
423C24—42no—
424C24—41no—
425C24—41no—
426C24—41no—
427C24—41no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—41no—
438C24—42no—
439C24—41no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24—41no—
448C24—41no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—41no—
453C24—42no—
454C24—41no—
455C24—42no—
456C24—41no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—41no—
461C24—42no—
462C24—41no—
463C24—42no—
464C24—41no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24C4⋊Q814yes—
475C24C22×D411yescharacteristic
476C24C22×D412yes—
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479C24C22×D411yescharacteristic
480C24C22×Q811yescharacteristic
481C24C22×Q811yescharacteristic
482C24C2×#4111yescharacteristic
483C24C2×#4111yescharacteristic
484C24C2×#4111yescharacteristic
485C24C2×#4112yes—
486C24C2×#4111yescharacteristic
487C24C2×#4112yes—
488C24C2×#4111yescharacteristic
489C24C2×#4112yes—
490C24H(5,𝔽2)12yes—
491C24H(5,𝔽2)12yes—
492C24H(5,𝔽2)11yescharacteristic
493C24H(5,𝔽2)12yes—
494C24H(5,𝔽2)11yescharacteristic
495C242−1+412yes—
496C242−1+411yescharacteristic
497C242−1+411yescharacteristic
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
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—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
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—24no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
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—41no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—41no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—41no—
647C22×C4—42no—
648C22×C4—41no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—41no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—41no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—41no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—41no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—41no—
678C22×C4—41no—
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×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—41no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—41no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4#12014yes—
763C22×C4#12118yes—
764C22×C4#12114yes—
765C22×C4#12114yes—
766C22×C4#12114yes—
767C22×C4#12114yes—
768C22×C4C22⋊Q814yes—
769C22×C4C22⋊Q818yes—
770C22×C4C22⋊Q814yes—
771C22×C4C22⋊Q814yes—
772C22×C4C22⋊Q814yes—
773C22×C4#12414yes—
774C22×C4#12418yes—
775C22×C4#12614yes—
776C4⋊C4—232no—
777C4⋊C4—416no—
778C4⋊C4—432no—
779C4⋊C4—432no—
780C22⋊C4—416no—
781C22⋊C4—432no—
782C22⋊C4—432no—
783C22⋊C4—416no—
784C22⋊C4—416no—
785C42—416no—
786C23—28no—
787C23—24no—
788C23—28no—
789C23—24no—
790C23—24no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—44no—
796C23—44no—
797C23—42no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—44no—
810C23—44no—
811C23—42no—
812C23—42no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—42no—
817C23—42no—
818C23—44no—
819C23—42no—
820C23—42no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—42no—
836C23—42no—
837C23—44no—
838C23—44no—
839C23—42no—
840C23—42no—
841C23—44no—
842C23—42no—
843C23—44no—
844C23—44no—
845C23—81no—
846C23—81no—
847C23—82no—
848C23—81no—
849C23—81no—
850C23—82no—
851C23—81no—
852C23—81no—
853C23—81no—
854C23—81no—
855C23—81no—
856C23—81no—
857C23—81no—
858C23—81no—
859C23—82no—
860C23—82no—
861C23—82no—
862C23—82no—
863C23—81no—
864C23—82no—
865C23—82no—
866C23—82no—
867C23—82no—
868C23—82no—
869C23—82no—
870C23—82no—
871C23—82no—
872C23—82no—
873C23—82no—
874C23—82no—
875C23—82no—
876C23—82no—
877C23—82no—
878C23—82no—
879C23—81no—
880C23—82no—
881C23—82no—
882C23—81no—
883C23—82no—
884C23—81no—
885C23C2×#12011yescharacteristic
886C23C2×#12111yescharacteristic
887C23C2×#12112yes—
888C23C2×#12111yescharacteristic
889C23C2×#12111yescharacteristic
890C23C2×#12111yescharacteristic
891C23C2×C22⋊Q811yescharacteristic
892C23C2×C22⋊Q811yescharacteristic
893C23C2×C22⋊Q811yescharacteristic
894C23C2×C22⋊Q812yes—
895C23C2×C22⋊Q811yescharacteristic
896C23#52511yescharacteristic
897C23#52512yes—
898C23#52512yes—
899C23#52512yes—
900C23C2×#12411yescharacteristic
901C23C2×#12412yes—
902C23C2×#12611yescharacteristic
903C23#52912yes—
904C23#52912yes—
905C23C2×C4⋊Q811yescharacteristic
906C23#53211yescharacteristic
907C23#53211yescharacteristic
908C23#53311yescharacteristic
909C23#53311yescharacteristic
910C23#53411yescharacteristic
911C23#53412yes—
912C23#53511yescharacteristic
913C23#53511yescharacteristic
914C23#53512yes—
915C23#53512yes—
916C23#53611yescharacteristic
917C23#53711yescharacteristic
918C23#53711yescharacteristic
919C23#53712yes—
920C23#53712yes—
921C23#53812yes—
922C23#53812yes—
923C23#53812yes—
924C23#53912yes—
925C23#53912yes—
926C23#53912yes—
927C23#53912yes—
928C23#54012yes—
929C23#54011yescharacteristic
930C23#54111yescharacteristic
931C23#54112yes—
932C23#54212yes—
933C23#54412yes—
934C23#54411yescharacteristic
935C23#54411yescharacteristic
936C23D4212yes—
937C23D4212yes—
938C23D4211yescharacteristic
939C23D4211yescharacteristic
940C23#54612yes—
941C23#54612yes—
942C23#54612yes—
943C23#54611yescharacteristic
944C23#54612yes—
945C23#54712yes—
946C23#54711yescharacteristic
947C23#54711yescharacteristic
948C23#54712yes—
949C23#54712yes—
950C23#54711yescharacteristic
951C23#54812yes—
952C23#54811yescharacteristic
953C23D4×Q812yes—
954C23D4×Q811yescharacteristic
955C23D4×Q811yescharacteristic
956C23#55012yes—
957C23#55011yescharacteristic
958C23#55112yes—
959C23#55212yes—
960C23#55211yescharacteristic
961C23#55312yes—
962C23#55312yes—
963C23#55311yescharacteristic
964C23#55412yes—
965C23#55412yes—
966C23#55412yes—
967C23#55412yes—
968C23#55412yes—
969C23#55411yescharacteristic
970C23#55411yescharacteristic
971C23#55512yes—
972C23#55511yescharacteristic
973C23#55611yescharacteristic
974C23#55612yes—
975C23#55612yes—
976C23#55912yes—
977C23#55912yes—
978C23#55912yes—
979C23#55912yes—
980C23#56012yes—
981C23#56212yes—
982C23#56212yes—
983C23#56312yes—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—28no—
999C2×C4—28no—
1000C2×C4—28no—
1001C2×C4—28no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—44no—
1013C2×C4—44no—
1014C2×C4—44no—
1015C2×C4—42no—
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—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—44no—
1033C2×C4—42no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—44no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—42no—
1063C2×C4—44no—
1064C2×C4—42no—
1065C2×C4—42no—
1066C2×C4—81no—
1067C2×C4—81no—
1068C2×C4—82no—
1069C2×C4—81no—
1070C2×C4—81no—
1071C2×C4—82no—
1072C2×C4—81no—
1073C2×C4—82no—
1074C2×C4—81no—
1075C2×C4—81no—
1076C2×C4—82no—
1077C2×C4—81no—
1078C2×C4—82no—
1079C2×C4—82no—
1080C2×C4—82no—
1081C2×C4—82no—
1082C2×C4—82no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4—82no—
1086C2×C4—82no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—82no—
1090C2×C4—82no—
1091C2×C4—82no—
1092C2×C4—82no—
1093C2×C4—82no—
1094C2×C4—82no—
1095C2×C4—82no—
1096C2×C4—82no—
1097C2×C4—81no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4—82no—
1103C2×C4—81no—
1104C2×C4—81no—
1105C2×C4—81no—
1106C2×C4—82no—
1107C2×C4—82no—
1108C2×C4#39318yes—
1109C2×C4#39618yes—
1110C22—44no—
1111C22—44no—
1112C22—48no—
1113C22—44no—
1114C22—48no—
1115C22—84no—
1116C22—84no—
1117C22—84no—
1118C22—82no—
1119C22—82no—
1120C22—84no—
1121C22—82no—
1122C22—82no—
1123C22—82no—
1124C22—84no—
1125C22—82no—
1126C22—82no—
1127C22—84no—
1128C22—82no—
1129C22—82no—
1130C22—82no—
1131C22—82no—
1132C22—82no—
1133C22C2×#39311yescharacteristic
1134C22C2×#39611yescharacteristic
1135C22#239211yescharacteristic
1136C22#240811yescharacteristic
1137C22#240911yescharacteristic
1138C22#241011yescharacteristic
1139C22#241311yescharacteristic
1140C22#241412yes—
1141C22#241612yes—
1142C22#241611yescharacteristic
1143C22#241711yescharacteristic
1144C22#241712yes—
1145C22#242412yes—
1146C22#242512yes—
1147C22#242811yescharacteristic
1148C22#242911yescharacteristic
1149C22#243011yescharacteristic
1150C22#243912yes—
1151C22#243911yescharacteristic
1152C22#244012yes—
1153C22#244011yescharacteristic
1154C22#244011yescharacteristic
1155C22#244111yescharacteristic
1156C22#244912yes—
1157C22#244912yes—
1158C22#245012yes—
1159C22#245412yes—
1160C22#245512yes—
1161C22#245512yes—
1162C22#245912yes—
1163C22#246912yes—
1164C22#247212yes—
1165C22#247812yes—
1166C22#248112yes—
1167C22#248812yes—
1168C22#249112yes—
1169C22#249212yes—
1170C22#249611yescharacteristic
1171C22#249711yescharacteristic
1172C22#251312yes—
1173C22#253711yescharacteristic
1174C22#253812yes—
1175C22#253811yescharacteristic
1176C22#254411yescharacteristic
1177C22#254711yescharacteristic
1178C22#254812yes—
1179C22#254811yescharacteristic
1180C22#256311yescharacteristic
1181C22#256411yescharacteristic
1182C22#256611yescharacteristic
1183C22#257911yescharacteristic
1184C22#258012yes—
1185C22#258012yes—
1186C22#258011yescharacteristic
1187C22#258312yes—
1188C22#258712yes—
1189C22#258912yes—
1190C22#259212yes—
1191C22#259211yescharacteristic
1192C22#259612yes—
1193C22#260212yes—
1194C22#261511yescharacteristic
1195C22#261711yescharacteristic
1196C22#261811yescharacteristic
1197C22#261911yescharacteristic
1198C22#262811yescharacteristic
1199C22#262911yescharacteristic
1200C22#263611yescharacteristic
1201C22#263911yescharacteristic
1202C22#266411yescharacteristic
1203C22#266912yes—
1204C22#267112yes—
1205C22#267612yes—
1206C22#268212yes—
1207C22#270312yes—
1208C22#270412yes—
1209C22#270412yes—
1210C22#270512yes—
1211C22#271012yes—
1212C22#271112yes—
1213C22#272012yes—
1214C22#272012yes—
1215C22#272412yes—
1216C22#272512yes—
1217C22#272712yes—
1218C22#276812yes—
1219C22#277312yes—
1220C22#278312yes—
1221C22#278812yes—
1222C22#279812yes—
1223C22#280312yes—
1224C22#280712yes—
1225C22#280712yes—
1226C22#280812yes—
1227C22#281311yescharacteristic
1228C22#282011yescharacteristic
1229C22#284711yescharacteristic
1230C22#285011yescharacteristic
1231C22#285711yescharacteristic
1232C4—28no—
1233C4—28no—
1234C4—44no—
1235C4—48no—
1236C4—84no—
1237C4—84no—
1238C4—82no—
1239C4—82no—
1240C4—84no—
1241C4—82no—
1242C2—84no—
1243C2#1472911yescharacteristic
1244C2#1475911yescharacteristic
1245C2#1480611yescharacteristic
1246C2#1480811yescharacteristic
1247C2#1512511yescharacteristic
1248C2#1513111yescharacteristic
1249C2#1515711yescharacteristic
1250C2#1520411yescharacteristic
1251C2#1522211yescharacteristic
1252C2#1530512yes—
1253C2#1536112yes—
1254C2#1536212yes—
1255C2#1540612yes—
1256C2#1553212yes—
1257C2#1561712yes—
1258C2#1567512yes—
1259C2#1600812yes—
1260C2#1626011yescharacteristic
1261C2#1656411yescharacteristic
1262C2#1660411yescharacteristic
1263C2#1689911yescharacteristic
1264C2#1698011yescharacteristic
1265C2#1706911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC25C24
prime radicalC26C23
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#389C2semidirect
2. C2×#1442C2semidirect
8. C2×C4⋊#95C2semidirect
9. #7557C2semidirect
10. #7557C2semidirect
11. #7557C2semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C2×#14422
C2×#14392
C2×#14372
C2×C4⋊#952
#75572