Finite Group Databasebeta

← #156283

Subgroups — #156283

Order 512.

3418 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#399C211yesmaximal, characteristic
2C2×#1445C211yesmaximal, characteristic, complemented
3C2×#1442C211yesmaximal, characteristic, complemented
4C2×#1439C211yesmaximal, characteristic
5C2×#1437C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic, complemented
7C2×#1434C211yesmaximal, characteristic, complemented
8#7557C212yesmaximal, complemented
9#7557C212yesmaximal, complemented
10#7555C212yesmaximal
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×#399—24no—
22C2×#399—24no—
23C2×#399C418yescomplemented
24C22×#95C2211yescharacteristic
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38#1445—24no—
39#1442—24no—
40#1439—24no—
41#1437—24no—
42C4⋊#95—24no—
43#1434—24no—
44C26C2311yescharacteristic
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2312yes—
48C24×C4C2311yescharacteristic
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C22×C4⋊C4—24no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4—42no—
69C22×C4⋊C4—42no—
70C22×C4⋊C4—42no—
71C22×C4⋊C4—42no—
72C22×C4⋊C4C2×C414yes—
73C22×C4⋊C4C2×C418yes—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—24no—
77C22×C22⋊C4—22no—
78C22×C22⋊C4—22no—
79C22×C22⋊C4—22no—
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—24no—
88C22×C22⋊C4—24no—
89C22×C22⋊C4—24no—
90C22×C22⋊C4—24no—
91C22×C22⋊C4—42no—
92C22×C22⋊C4—42no—
93C22×C22⋊C4—42no—
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⋊C4C2×C414yes—
103C22×C22⋊C4C2×C418yes—
104C22×C22⋊C4Q814yes—
105C22×C42—22no—
106C22×C42—22no—
107C22×C42—24no—
108C22×C42—42no—
109C22×C42D414yes—
110#399—232no—
111C2×#95—22no—
112C2×#95—22no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—22no—
124C2×#95—24no—
125C2×#95—24no—
126C2×#95—22no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—42no—
132C2×#95—42no—
133C2×#95—42no—
134C2×#95—42no—
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×C414yes—
148C2×#95D414yes—
149C2×#95D414yes—
150C2×#95D414yes—
151C25—21no—
152C25—21no—
153C25—21no—
154C25—21no—
155C25—21no—
156C25—21no—
157C25—21no—
158C25—21no—
159C25—22no—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—22no—
164C25—22no—
165C25—22no—
166C25—21no—
167C25—21no—
168C25—21no—
169C25—22no—
170C25—21no—
171C25C22×C412yes—
172C25C2×Q812yes—
173C25#4112yes—
174C25C2411yescharacteristic
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
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—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—21no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—22no—
210C23×C4—21no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
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—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—22no—
231C23×C4—22no—
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—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—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—21no—
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—21no—
280C23×C4C22×C412yes—
281C23×C4C22×C414yes—
282C23×C4C22×C414yes—
283C23×C4C22×C412yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4C2×D412yes—
293C23×C4C2×Q812yes—
294C23×C4C2×Q812yes—
295C23×C4#4114yes—
296C23×C4#4112yes—
297C23×C4#4112yes—
298C23×C4#4114yes—
299C23×C4#4112yes—
300C23×C4#4112yes—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—216no—
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—44no—
311C2×C4⋊C4—48no—
312C2×C4⋊C4—48no—
313C2×C4⋊C4—48no—
314C2×C4⋊C4—48no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—216no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—48no—
327C2×C22⋊C4—48no—
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—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—48no—
338C2×C22⋊C4—48no—
339C2×C22⋊C4—48no—
340C2×C22⋊C4—48no—
341C2×C22⋊C4—48no—
342C2×C22⋊C4—48no—
343C2×C22⋊C4—48no—
344C2×C22⋊C4—48no—
345C2×C22⋊C4—48no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C42—28no—
352C2×C42—28no—
353C2×C42—44no—
354C2×C42—48no—
355C2×C42—48no—
356#95—28no—
357#95—48no—
358#95—48no—
359#95—48no—
360#95—48no—
361#95—48no—
362#95—48no—
363#95—44no—
364#95—44no—
365#95—48no—
366#95—48no—
367#95—48no—
368#95—44no—
369#95C22⋊C4116yescomplemented
370C24—22no—
371C24—22no—
372C24—22no—
373C24—24no—
374C24—22no—
375C24—24no—
376C24—24no—
377C24—22no—
378C24—24no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—41no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—42no—
406C24—41no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—41no—
413C24—41no—
414C24—42no—
415C24—41no—
416C24—41no—
417C24—42no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—41no—
435C24—41no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—41no—
442C24—42no—
443C24—42no—
444C24—41no—
445C24—41no—
446C24—42no—
447C24—42no—
448C24—41no—
449C24—42no—
450C24—41no—
451C24—41no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—41no—
456C24—42no—
457C24—42no—
458C24—41no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24C4×Q814yes—
469C24C23×C411yescharacteristic
470C24C22×D411yescharacteristic
471C24C22×D411yescharacteristic
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×Q811yescharacteristic
475C24C2×#4111yescharacteristic
476C24C2×#4111yescharacteristic
477C24C2×#4111yescharacteristic
478C24C2×#4111yescharacteristic
479C24C2×#4112yes—
480C24C2×#4112yes—
481C24C2×#4111yescharacteristic
482C24H(5,𝔽2)12yes—
483C24H(5,𝔽2)12yes—
484C24H(5,𝔽2)12yes—
485C24H(5,𝔽2)12yes—
486C24H(5,𝔽2)12yes—
487C24H(5,𝔽2)11yescharacteristic
488C242−1+411yescharacteristic
489C242−1+411yescharacteristic
490C242−1+412yes—
491C242−1+411yescharacteristic
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
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—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
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—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
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—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
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—41no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—41no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—41no—
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—41no—
623C22×C4—41no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—42no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—41no—
639C22×C4—42no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—41no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—41no—
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—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—42no—
669C22×C4—42no—
670C22×C4—41no—
671C22×C4—41no—
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—41no—
683C22×C4—41no—
684C22×C4—42no—
685C22×C4—41no—
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—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—41no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—41no—
735C22×C4—41no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
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×C4C2×C22⋊C418yes—
761C22×C4C2×C22⋊C414yes—
762C22×C4C4×D414yes—
763C22×C4C4×D414yes—
764C22×C4#12114yes—
765C22×C4#12114yes—
766C22×C4C22⋊Q814yes—
767C22×C4#12314yes—
768C22×C4#12414yes—
769C22×C4#12714yes—
770C4⋊C4—416no—
771C4⋊C4—432no—
772C4⋊C4—416no—
773C22⋊C4—432no—
774C22⋊C4—416no—
775C22⋊C4—416no—
776C22⋊C4—432no—
777C22⋊C4—416no—
778C42—416no—
779C23—28no—
780C23—24no—
781C23—24no—
782C23—28no—
783C23—24no—
784C23—44no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—44no—
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—44no—
805C23—42no—
806C23—44no—
807C23—44no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—42no—
825C23—44no—
826C23—42no—
827C23—44no—
828C23—42no—
829C23—42no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—81no—
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—
878C23C22×C22⋊C411yescharacteristic
879C23C2×C4×D411yescharacteristic
880C23C2×C4×D411yescharacteristic
881C23C2×C4×Q811yescharacteristic
882C23C4×#4112yes—
883C23C4×#4111yescharacteristic
884C23#51812yes—
885C23#51812yes—
886C23#51911yescharacteristic
887C23#52012yes—
888C23#52011yescharacteristic
889C23C2×#12111yescharacteristic
890C23C2×#12111yescharacteristic
891C23C2×C22⋊Q811yescharacteristic
892C23C2×#12311yescharacteristic
893C23#52511yescharacteristic
894C23#52511yescharacteristic
895C23C2×#12411yescharacteristic
896C23#52911yescharacteristic
897C23#52912yes—
898C23C2×#12711yescharacteristic
899C23#53311yescharacteristic
900C23#53411yescharacteristic
901C23#53511yescharacteristic
902C23#53512yes—
903C23#53512yes—
904C23#53512yes—
905C23#53512yes—
906C23#53511yescharacteristic
907C23#53511yescharacteristic
908C23#53511yescharacteristic
909C23#53512yes—
910C23#53512yes—
911C23#53611yescharacteristic
912C23#53611yescharacteristic
913C23#53711yescharacteristic
914C23#53812yes—
915C23#53812yes—
916C23#53812yes—
917C23#53912yes—
918C23#53912yes—
919C23#53912yes—
920C23#53912yes—
921C23#53912yes—
922C23#53912yes—
923C23#54012yes—
924C23#54012yes—
925C23#54012yes—
926C23#54012yes—
927C23#54012yes—
928C23#54012yes—
929C23#54111yescharacteristic
930C23#54211yescharacteristic
931C23#54212yes—
932C23#54212yes—
933C23#54212yes—
934C23#54212yes—
935C23#54312yes—
936C23#54412yes—
937C23#54612yes—
938C23#54611yescharacteristic
939C23#54612yes—
940C23#54611yescharacteristic
941C23#54612yes—
942C23#54611yescharacteristic
943C23#54712yes—
944C23#54711yescharacteristic
945C23#54712yes—
946C23#54711yescharacteristic
947C23#54712yes—
948C23#54711yescharacteristic
949C23#54811yescharacteristic
950C23#54811yescharacteristic
951C23#54811yescharacteristic
952C23D4×Q811yescharacteristic
953C23D4×Q811yescharacteristic
954C23D4×Q811yescharacteristic
955C23#55112yes—
956C23#55112yes—
957C23#55112yes—
958C23#55112yes—
959C23#55212yes—
960C23#55211yescharacteristic
961C23#55211yescharacteristic
962C23#55312yes—
963C23#55312yes—
964C23#55412yes—
965C23#55411yescharacteristic
966C23#55412yes—
967C23#55611yescharacteristic
968C23#55912yes—
969C23#56012yes—
970C23#56212yes—
971C23#56212yes—
972C23#56212yes—
973C23#56212yes—
974C23#56312yes—
975C23#56312yes—
976C23#56312yes—
977C2×C4—24no—
978C2×C4—28no—
979C2×C4—28no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—28no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—28no—
989C2×C4—28no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—42no—
997C2×C4—44no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
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—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—44no—
1030C2×C4—42no—
1031C2×C4—44no—
1032C2×C4—44no—
1033C2×C4—44no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—42no—
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—44no—
1053C2×C4—44no—
1054C2×C4—42no—
1055C2×C4—44no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—44no—
1060C2×C4—81no—
1061C2×C4—81no—
1062C2×C4—82no—
1063C2×C4—81no—
1064C2×C4—82no—
1065C2×C4—81no—
1066C2×C4—82no—
1067C2×C4—82no—
1068C2×C4—82no—
1069C2×C4—82no—
1070C2×C4—81no—
1071C2×C4—81no—
1072C2×C4—82no—
1073C2×C4—82no—
1074C2×C4—82no—
1075C2×C4—82no—
1076C2×C4—82no—
1077C2×C4—82no—
1078C2×C4—81no—
1079C2×C4—82no—
1080C2×C4—81no—
1081C2×C4—81no—
1082C2×C4—82no—
1083C2×C4—81no—
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—81no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4#39018yes—
1103C22—48no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22—48no—
1108C22—82no—
1109C22—82no—
1110C22—82no—
1111C22—82no—
1112C22—82no—
1113C22—84no—
1114C22—84no—
1115C22—84no—
1116C22—84no—
1117C22—82no—
1118C22—82no—
1119C22—84no—
1120C22—82no—
1121C22—82no—
1122C22—82no—
1123C22—82no—
1124C22—82no—
1125C22—84no—
1126C22C2×#39011yescharacteristic
1127C22C4×#12311yescharacteristic
1128C22C4×C22⋊Q811yescharacteristic
1129C22#230912yes—
1130C22#232211yescharacteristic
1131C22#232311yescharacteristic
1132C22#232811yescharacteristic
1133C22#232811yescharacteristic
1134C22#232812yes—
1135C22#232912yes—
1136C22#233212yes—
1137C22#233512yes—
1138C22#233512yes—
1139C22#233912yes—
1140C22#233911yescharacteristic
1141C22Q8×C22⋊C411yescharacteristic
1142C22#235912yes—
1143C22#236011yescharacteristic
1144C22#236211yescharacteristic
1145C22#236812yes—
1146C22#237412yes—
1147C22#237612yes—
1148C22#237812yes—
1149C22#241211yescharacteristic
1150C22#241311yescharacteristic
1151C22#241511yescharacteristic
1152C22#241711yescharacteristic
1153C22#242512yes—
1154C22#242711yescharacteristic
1155C22#242911yescharacteristic
1156C22#248211yescharacteristic
1157C22#248711yescharacteristic
1158C22#248812yes—
1159C22#248911yescharacteristic
1160C22#249211yescharacteristic
1161C22#250111yescharacteristic
1162C22#251612yes—
1163C22#252212yes—
1164C22#253911yescharacteristic
1165C22#254011yescharacteristic
1166C22#254211yescharacteristic
1167C22#258011yescharacteristic
1168C22#259811yescharacteristic
1169C22#261911yescharacteristic
1170C22#261911yescharacteristic
1171C22#261912yes—
1172C22#262311yescharacteristic
1173C22#262411yescharacteristic
1174C22#262611yescharacteristic
1175C22#262811yescharacteristic
1176C22#263211yescharacteristic
1177C22#263311yescharacteristic
1178C22#263511yescharacteristic
1179C22#263611yescharacteristic
1180C22#264112yes—
1181C22#264912yes—
1182C22#265112yes—
1183C22#265412yes—
1184C22#265711yescharacteristic
1185C22#265711yescharacteristic
1186C22#266712yes—
1187C22#268512yes—
1188C22#269212yes—
1189C22#269212yes—
1190C22#269212yes—
1191C22#269612yes—
1192C22#269612yes—
1193C22#270312yes—
1194C22#270312yes—
1195C22#270612yes—
1196C22#270612yes—
1197C22#270612yes—
1198C22#271012yes—
1199C22#271012yes—
1200C22#271012yes—
1201C22#271112yes—
1202C22#271812yes—
1203C22#271812yes—
1204C22#271812yes—
1205C22#272012yes—
1206C22#272012yes—
1207C22#272012yes—
1208C22#272312yes—
1209C22#272312yes—
1210C22#272312yes—
1211C22#273812yes—
1212C22#274012yes—
1213C22#274112yes—
1214C22#274312yes—
1215C22#274812yes—
1216C22#276812yes—
1217C22#277312yes—
1218C22#277712yes—
1219C22#281311yescharacteristic
1220C22#281611yescharacteristic
1221C22#282011yescharacteristic
1222C22#282111yescharacteristic
1223C22#283612yes—
1224C22#283712yes—
1225C4—28no—
1226C4—44no—
1227C4—44no—
1228C4—48no—
1229C4—82no—
1230C4—84no—
1231C4—84no—
1232C4—82no—
1233C4—84no—
1234C4—82no—
1235C2—84no—
1236C2#1399611yescharacteristic
1237C2#1399711yescharacteristic
1238C2#1424011yescharacteristic
1239C2#1427211yescharacteristic
1240C2#1430511yescharacteristic
1241C2#1431711yescharacteristic
1242C2#1444812yes—
1243C2#1450612yes—
1244C2#1457812yes—
1245C2#1458412yes—
1246C2#1462811yescharacteristic
1247C2#1639211yescharacteristic
1248C2#1639811yescharacteristic
1249C2#1646312yes—
1250C2#1646812yes—
1251C2#1656411yescharacteristic
1252C2#1667611yescharacteristic
1253C2#1669211yescharacteristic
1254C2#1676212yes—
1255C2#1679412yes—
1256C2#1680911yescharacteristic
1257C2#1681411yescharacteristic
1258C2#1706411yescharacteristic
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×#1442C2semidirect
6. C2×C4⋊#95C2semidirect
7. C2×#1434C2semidirect
8. #7557C2semidirect
9. #7557C2semidirect
23. C2×#399C4semidirect
369. #95C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3992
C2×#14452
C2×#14422
C2×#14392
C2×#14372
C2×C4⋊#952
C2×#14342
#75572
#75552