Finite Group Databasebeta

← #156284

Subgroups — #156284

Order 512.

3446 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#397C211yesmaximal, characteristic
2C2×#1445C211yesmaximal, characteristic, complemented
3C2×#1444C211yesmaximal, characteristic, complemented
4C2×#1439C211yesmaximal, characteristic
5C2×#1439C212yesmaximal
6C2×#1437C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic, complemented
8C2×#1434C211yesmaximal, characteristic, complemented
9#7557C212yesmaximal, complemented
10#7556C212yesmaximal, complemented
11#7555C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2211yescharacteristic
17C23×C22⋊C4C2212yes—
18C23×C22⋊C4C2212yes—
19C23×C22⋊C4C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#397—24no—
22C2×#397—24no—
23C2×#397C418yescomplemented
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2212yes—
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38#1445—24no—
39#1444—24no—
40#1439—24no—
41#1439—28no—
42#1437—24no—
43C4⋊#95—24no—
44#1434—24no—
45C26C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2312yes—
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2312yes—
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—24no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—24no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—24no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—24no—
69C22×C4⋊C4—42no—
70C22×C4⋊C4—42no—
71C22×C4⋊C4—42no—
72C22×C4⋊C4—42no—
73C22×C4⋊C4—42no—
74C22×C4⋊C4C2×C414yes—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—22no—
77C22×C22⋊C4—24no—
78C22×C22⋊C4—24no—
79C22×C22⋊C4—24no—
80C22×C22⋊C4—22no—
81C22×C22⋊C4—22no—
82C22×C22⋊C4—22no—
83C22×C22⋊C4—22no—
84C22×C22⋊C4—22no—
85C22×C22⋊C4—22no—
86C22×C22⋊C4—22no—
87C22×C22⋊C4—22no—
88C22×C22⋊C4—22no—
89C22×C22⋊C4—22no—
90C22×C22⋊C4—24no—
91C22×C22⋊C4—24no—
92C22×C22⋊C4—24no—
93C22×C22⋊C4—24no—
94C22×C22⋊C4—42no—
95C22×C22⋊C4—42no—
96C22×C22⋊C4—42no—
97C22×C22⋊C4—42no—
98C22×C22⋊C4—42no—
99C22×C22⋊C4—42no—
100C22×C22⋊C4—42no—
101C22×C22⋊C4—42no—
102C22×C22⋊C4—42no—
103C22×C22⋊C4C2×C414yes—
104C22×C22⋊C4C2×C418yes—
105C22×C22⋊C4D414yes—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—24no—
109C22×C42—42no—
110C22×C42D414yes—
111#397—232no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—24no—
119C2×#95—24no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—22no—
123C2×#95—24no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—24no—
127C2×#95—24no—
128C2×#95—22no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—22no—
132C2×#95—24no—
133C2×#95—24no—
134C2×#95—24no—
135C2×#95—42no—
136C2×#95—42no—
137C2×#95—42no—
138C2×#95—42no—
139C2×#95—42no—
140C2×#95—42no—
141C2×#95—42no—
142C2×#95—42no—
143C2×#95—42no—
144C2×#95—42no—
145C2×#95—42no—
146C2×#95—42no—
147C2×#95C2×C418yes—
148C2×#95C2×C414yes—
149C2×#95D414yes—
150C2×#95D414yes—
151C2×#95D414yes—
152C25—21no—
153C25—21no—
154C25—21no—
155C25—21no—
156C25—21no—
157C25—21no—
158C25—21no—
159C25—21no—
160C25—22no—
161C25—22no—
162C25—21no—
163C25—21no—
164C25—22no—
165C25—22no—
166C25—21no—
167C25—22no—
168C25—22no—
169C25—22no—
170C25—21no—
171C25—22no—
172C25C22×C412yes—
173C25C2×D412yes—
174C25#4112yes—
175C25C2411yescharacteristic
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
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—22no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—22no—
221C23×C4—21no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—22no—
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—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—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—21no—
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—21no—
270C23×C4—21no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—21no—
281C23×C4C22×C414yes—
282C23×C4C22×C412yes—
283C23×C4C22×C414yes—
284C23×C4C22×C412yes—
285C23×C4C2×D414yes—
286C23×C4C2×D412yes—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2×D412yes—
294C23×C4C2×D412yes—
295C23×C4C2×D412yes—
296C23×C4#4114yes—
297C23×C4#4112yes—
298C23×C4#4112yes—
299C23×C4#4114yes—
300C23×C4#4112yes—
301C23×C4#4112yes—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
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—48no—
313C2×C4⋊C4—48no—
314C2×C4⋊C4—48no—
315C2×C4⋊C4—48no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—216no—
323C2×C22⋊C4—216no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—48no—
329C2×C22⋊C4—48no—
330C2×C22⋊C4—48no—
331C2×C22⋊C4—48no—
332C2×C22⋊C4—48no—
333C2×C22⋊C4—48no—
334C2×C22⋊C4—48no—
335C2×C22⋊C4—48no—
336C2×C22⋊C4—48no—
337C2×C22⋊C4—48no—
338C2×C22⋊C4—48no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—48no—
343C2×C22⋊C4—48no—
344C2×C22⋊C4—48no—
345C2×C22⋊C4—48no—
346C2×C22⋊C4—48no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C42—28no—
353C2×C42—28no—
354C2×C42—44no—
355C2×C42—48no—
356C2×C42—48no—
357#95—216no—
358#95—28no—
359#95—48no—
360#95—48no—
361#95—48no—
362#95—48no—
363#95—48no—
364#95—44no—
365#95—44no—
366#95—48no—
367#95—48no—
368#95—48no—
369#95—44no—
370#95C22⋊C4116yescomplemented
371C24—22no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—22no—
376C24—22no—
377C24—24no—
378C24—24no—
379C24—24no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—24no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—22no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—42no—
411C24—41no—
412C24—42no—
413C24—41no—
414C24—42no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—41no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—41no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—41no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—41no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—41no—
458C24—42no—
459C24—41no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24C4×D414yes—
470C24C23×C411yescharacteristic
471C24C22×D411yescharacteristic
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476C24C2×#4111yescharacteristic
477C24C2×#4111yescharacteristic
478C24C2×#4111yescharacteristic
479C24C2×#4111yescharacteristic
480C24C2×#4112yes—
481C24C2×#4112yes—
482C24C2×#4111yescharacteristic
483C24H(5,𝔽2)11yescharacteristic
484C24H(5,𝔽2)11yescharacteristic
485C24H(5,𝔽2)12yes—
486C24H(5,𝔽2)12yes—
487C24H(5,𝔽2)12yes—
488C24H(5,𝔽2)11yescharacteristic
489C242−1+412yes—
490C242−1+412yes—
491C242−1+412yes—
492C242−1+411yescharacteristic
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
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—41no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—41no—
614C22×C4—41no—
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—41no—
626C22×C4—41no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—42no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—41no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—41no—
650C22×C4—41no—
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—41no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—41no—
669C22×C4—42no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—42no—
673C22×C4—41no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—41no—
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—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—41no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—41no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—41no—
740C22×C4—41no—
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×C4C2×C22⋊C418yes—
762C22×C4C2×C22⋊C414yes—
763C22×C4C4×D414yes—
764C22×C4C4×D414yes—
765C22×C4#12114yes—
766C22×C4#12114yes—
767C22×C4#12114yes—
768C22×C4#12314yes—
769C22×C4#12414yes—
770C22×C4#12714yes—
771C4⋊C4—416no—
772C4⋊C4—432no—
773C4⋊C4—416no—
774C22⋊C4—432no—
775C22⋊C4—416no—
776C22⋊C4—416no—
777C22⋊C4—432no—
778C22⋊C4—416no—
779C42—416no—
780C23—28no—
781C23—24no—
782C23—28no—
783C23—24no—
784C23—24no—
785C23—44no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—44no—
790C23—42no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—44no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—44no—
802C23—44no—
803C23—42no—
804C23—42no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—42no—
809C23—44no—
810C23—42no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—42no—
817C23—42no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—44no—
830C23—42no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—81no—
840C23—81no—
841C23—82no—
842C23—82no—
843C23—81no—
844C23—81no—
845C23—82no—
846C23—81no—
847C23—81no—
848C23—81no—
849C23—81no—
850C23—82no—
851C23—82no—
852C23—82no—
853C23—81no—
854C23—81no—
855C23—81no—
856C23—81no—
857C23—82no—
858C23—82no—
859C23—82no—
860C23—82no—
861C23—82no—
862C23—82no—
863C23—82no—
864C23—82no—
865C23—82no—
866C23—82no—
867C23—82no—
868C23—82no—
869C23—82no—
870C23—82no—
871C23—82no—
872C23—82no—
873C23—81no—
874C23—82no—
875C23—82no—
876C23—81no—
877C23—81no—
878C23—81no—
879C23C22×C22⋊C411yescharacteristic
880C23C2×C4×D411yescharacteristic
881C23C2×C4×D411yescharacteristic
882C23C2×C4×D411yescharacteristic
883C23C4×#4111yescharacteristic
884C23C4×#4112yes—
885C23#51811yescharacteristic
886C23#52012yes—
887C23#52012yes—
888C23#52012yes—
889C23#52011yescharacteristic
890C23C2×#12111yescharacteristic
891C23C2×#12111yescharacteristic
892C23C2×#12111yescharacteristic
893C23C2×#12311yescharacteristic
894C23#52511yescharacteristic
895C23#52511yescharacteristic
896C23C2×#12411yescharacteristic
897C23#52912yes—
898C23#52911yescharacteristic
899C23C2×#12711yescharacteristic
900C23#53211yescharacteristic
901C23#53411yescharacteristic
902C23#53412yes—
903C23#53511yescharacteristic
904C23#53511yescharacteristic
905C23#53512yes—
906C23#53511yescharacteristic
907C23#53512yes—
908C23#53611yescharacteristic
909C23#53611yescharacteristic
910C23#53612yes—
911C23#53612yes—
912C23#53611yescharacteristic
913C23#53612yes—
914C23#53711yescharacteristic
915C23#53712yes—
916C23#53712yes—
917C23#53812yes—
918C23#53812yes—
919C23#53812yes—
920C23#53912yes—
921C23#53912yes—
922C23#53912yes—
923C23#53912yes—
924C23#53912yes—
925C23#53912yes—
926C23#54011yescharacteristic
927C23#54012yes—
928C23#54112yes—
929C23#54112yes—
930C23#54211yescharacteristic
931C23#54212yes—
932C23#54212yes—
933C23#54212yes—
934C23#54212yes—
935C23#54212yes—
936C23#54212yes—
937C23#54212yes—
938C23D4211yescharacteristic
939C23D4211yescharacteristic
940C23D4211yescharacteristic
941C23#54611yescharacteristic
942C23#54611yescharacteristic
943C23#54612yes—
944C23#54612yes—
945C23#54612yes—
946C23#54612yes—
947C23#54611yescharacteristic
948C23#54712yes—
949C23#54712yes—
950C23#54712yes—
951C23#54712yes—
952C23#54711yescharacteristic
953C23#54811yescharacteristic
954C23#54811yescharacteristic
955C23#54811yescharacteristic
956C23#55011yescharacteristic
957C23#55011yescharacteristic
958C23#55011yescharacteristic
959C23#55112yes—
960C23#55112yes—
961C23#55112yes—
962C23#55212yes—
963C23#55212yes—
964C23#55212yes—
965C23#55311yescharacteristic
966C23#55311yescharacteristic
967C23#55312yes—
968C23#55511yescharacteristic
969C23#55612yes—
970C23#56012yes—
971C23#56012yes—
972C23#56212yes—
973C23#56212yes—
974C23#56312yes—
975C23#56312yes—
976C23#56312yes—
977C23#56312yes—
978C2×C4—24no—
979C2×C4—28no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—44no—
998C2×C4—44no—
999C2×C4—44no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—44no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—44no—
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—42no—
1024C2×C4—42no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—44no—
1029C2×C4—42no—
1030C2×C4—44no—
1031C2×C4—44no—
1032C2×C4—44no—
1033C2×C4—42no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—44no—
1039C2×C4—44no—
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—42no—
1053C2×C4—42no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—81no—
1062C2×C4—82no—
1063C2×C4—82no—
1064C2×C4—81no—
1065C2×C4—81no—
1066C2×C4—82no—
1067C2×C4—81no—
1068C2×C4—81no—
1069C2×C4—82no—
1070C2×C4—82no—
1071C2×C4—81no—
1072C2×C4—81no—
1073C2×C4—82no—
1074C2×C4—81no—
1075C2×C4—81no—
1076C2×C4—82no—
1077C2×C4—82no—
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—81no—
1096C2×C4—82no—
1097C2×C4—81no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—81no—
1102C2×C4—82no—
1103C2×C4#39018yes—
1104C22—48no—
1105C22—44no—
1106C22—44no—
1107C22—48no—
1108C22—44no—
1109C22—82no—
1110C22—82no—
1111C22—82no—
1112C22—82no—
1113C22—82no—
1114C22—84no—
1115C22—84no—
1116C22—84no—
1117C22—82no—
1118C22—84no—
1119C22—84no—
1120C22—82no—
1121C22—82no—
1122C22—82no—
1123C22—82no—
1124C22—82no—
1125C22—82no—
1126C22—84no—
1127C22C2×#39011yescharacteristic
1128C22C4×#12111yescharacteristic
1129C22C4×#12311yescharacteristic
1130C22#231112yes—
1131C22#232212yes—
1132C22#232211yescharacteristic
1133C22#232411yescharacteristic
1134C22#232611yescharacteristic
1135C22#232612yes—
1136C22#232611yescharacteristic
1137C22#233412yes—
1138C22#233412yes—
1139C22#233512yes—
1140C22D4×C22⋊C411yescharacteristic
1141C22#233912yes—
1142C22#234111yescharacteristic
1143C22#235912yes—
1144C22#235912yes—
1145C22#236111yescharacteristic
1146C22#236311yescharacteristic
1147C22#237312yes—
1148C22#237612yes—
1149C22#238312yes—
1150C22#241211yescharacteristic
1151C22#241311yescharacteristic
1152C22#241411yescharacteristic
1153C22#241611yescharacteristic
1154C22#242512yes—
1155C22#242611yescharacteristic
1156C22#242811yescharacteristic
1157C22#248211yescharacteristic
1158C22#248611yescharacteristic
1159C22#248812yes—
1160C22#249011yescharacteristic
1161C22#249111yescharacteristic
1162C22#250111yescharacteristic
1163C22#251512yes—
1164C22#252112yes—
1165C22#253511yescharacteristic
1166C22#253911yescharacteristic
1167C22#254011yescharacteristic
1168C22#254111yescharacteristic
1169C22#259911yescharacteristic
1170C22#261711yescharacteristic
1171C22#262011yescharacteristic
1172C22#262011yescharacteristic
1173C22#262012yes—
1174C22#262111yescharacteristic
1175C22#262311yescharacteristic
1176C22#262411yescharacteristic
1177C22#263111yescharacteristic
1178C22#263311yescharacteristic
1179C22#263711yescharacteristic
1180C22#263811yescharacteristic
1181C22#264012yes—
1182C22#265012yes—
1183C22#265112yes—
1184C22#265212yes—
1185C22#265711yescharacteristic
1186C22#265811yescharacteristic
1187C22#266312yes—
1188C22#267112yes—
1189C22#267212yes—
1190C22#267812yes—
1191C22#267812yes—
1192C22#268012yes—
1193C22#268012yes—
1194C22#268712yes—
1195C22#269012yes—
1196C22#269312yes—
1197C22#269512yes—
1198C22#269812yes—
1199C22#270012yes—
1200C22#270212yes—
1201C22#270512yes—
1202C22#270612yes—
1203C22#270612yes—
1204C22#271412yes—
1205C22#271412yes—
1206C22#271612yes—
1207C22#271712yes—
1208C22#272112yes—
1209C22#272112yes—
1210C22#272312yes—
1211C22#272312yes—
1212C22#272512yes—
1213C22#272712yes—
1214C22#273712yes—
1215C22#274112yes—
1216C22#274612yes—
1217C22#277012yes—
1218C22#277212yes—
1219C22#277512yes—
1220C22#281411yescharacteristic
1221C22#281511yescharacteristic
1222C22#282011yescharacteristic
1223C22#282111yescharacteristic
1224C22#283712yes—
1225C22#283812yes—
1226C4—28no—
1227C4—44no—
1228C4—44no—
1229C4—48no—
1230C4—82no—
1231C4—84no—
1232C4—82no—
1233C4—84no—
1234C4—84no—
1235C4—82no—
1236C2—84no—
1237C2#1399611yescharacteristic
1238C2#1399811yescharacteristic
1239C2#1422511yescharacteristic
1240C2#1427311yescharacteristic
1241C2#1430611yescharacteristic
1242C2#1431311yescharacteristic
1243C2#1435912yes—
1244C2#1449312yes—
1245C2#1454112yes—
1246C2#1457912yes—
1247C2#1463011yescharacteristic
1248C2#1639511yescharacteristic
1249C2#1640111yescharacteristic
1250C2#1646712yes—
1251C2#1647212yes—
1252C2#1651811yescharacteristic
1253C2#1667911yescharacteristic
1254C2#1669211yescharacteristic
1255C2#1675812yes—
1256C2#1678712yes—
1257C2#1681011yescharacteristic
1258C2#1681211yescharacteristic
1259C2#1706211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC25C24
commutatorC24C23×C4
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1445C2semidirect
3. C2×#1444C2semidirect
7. C2×C4⋊#95C2semidirect
8. C2×#1434C2semidirect
9. #7557C2semidirect
10. #7556C2semidirect
23. C2×#397C4semidirect
370. #95C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3972
C2×#14452
C2×#14442
C2×#14392
C2×#14372
C2×C4⋊#952
C2×#14342
#75572
#75562
#75552