Finite Group Databasebeta

← #154641

Subgroups — #154641

Order 512.

3630 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×#1442C211yesmaximal, characteristic, complemented
4C2×#1439C211yesmaximal, characteristic
5C2×#1437C212yesmaximal
6C2×#1437C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic, complemented
8C2×C4×#95C211yesmaximal, characteristic, complemented
9#7556C212yesmaximal, complemented
10#7555C212yesmaximal
11#7554C212yesmaximal, complemented
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2212yes—
17C23×C22⋊C4C2211yescharacteristic
18C23×C22⋊C4C2212yes—
19C23×C42C2212yes—
20C23×C42C2211yescharacteristic
21C2×#397—24no—
22C2×#397—24no—
23C2×#397C418yescomplemented
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2211yescharacteristic
36C22×#95C2212yes—
37C22×#95C2211yescharacteristic
38#1445—24no—
39#1442—24no—
40#1439—24no—
41#1437—24no—
42#1437—28no—
43C4⋊#95—24no—
44C4×#95—24no—
45C26C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2311yescharacteristic
49C24×C4C2312yes—
50C24×C4C2311yescharacteristic
51C24×C4C2312yes—
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—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4C2×C414yes—
68C22×C22⋊C4—24no—
69C22×C22⋊C4—24no—
70C22×C22⋊C4—22no—
71C22×C22⋊C4—24no—
72C22×C22⋊C4—24no—
73C22×C22⋊C4—24no—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—22no—
76C22×C22⋊C4—22no—
77C22×C22⋊C4—22no—
78C22×C22⋊C4—22no—
79C22×C22⋊C4—22no—
80C22×C22⋊C4—24no—
81C22×C22⋊C4—22no—
82C22×C22⋊C4—24no—
83C22×C22⋊C4—22no—
84C22×C22⋊C4—22no—
85C22×C22⋊C4—22no—
86C22×C22⋊C4—24no—
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⋊C4C2×C414yes—
97C22×C22⋊C4C2×C418yes—
98C22×C22⋊C4D414yes—
99C22×C42—24no—
100C22×C42—22no—
101C22×C42—24no—
102C22×C42—24no—
103C22×C42—22no—
104C22×C42—24no—
105C22×C42—24no—
106C22×C42—24no—
107C22×C42—42no—
108C22×C42—42no—
109C22×C42—42no—
110C22×C42D414yes—
111#397—232no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—22no—
116C2×#95—24no—
117C2×#95—24no—
118C2×#95—22no—
119C2×#95—24no—
120C2×#95—24no—
121C2×#95—24no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—22no—
125C2×#95—22no—
126C2×#95—22no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—22no—
131C2×#95—24no—
132C2×#95—24no—
133C2×#95—22no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
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—22no—
160C25—22no—
161C25—22no—
162C25—22no—
163C25—21no—
164C25—22no—
165C25—22no—
166C25—21no—
167C25—21no—
168C25—21no—
169C25—22no—
170C25—21no—
171C25—22no—
172C25C22×C412yes—
173C25C2×D412yes—
174C25#4112yes—
175C25C2411yescharacteristic
176C23×C4—21no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—21no—
184C23×C4—22no—
185C23×C4—21no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—21no—
190C23×C4—22no—
191C23×C4—21no—
192C23×C4—21no—
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—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—21no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—22no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—22no—
229C23×C4—21no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—22no—
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—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4C22×C414yes—
278C23×C4C22×C412yes—
279C23×C4C22×C414yes—
280C23×C4C22×C412yes—
281C23×C4C2×D412yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D412yes—
286C23×C4C2×D412yes—
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D412yes—
290C23×C4C2×D412yes—
291C23×C4C2×D412yes—
292C23×C4#4114yes—
293C23×C4#4112yes—
294C23×C4#4114yes—
295C23×C4#4114yes—
296C23×C4#4114yes—
297C23×C4#4112yes—
298C23×C4#4112yes—
299C23×C4#4112yes—
300C23×C4#4114yes—
301C23×C4#4114yes—
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—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—216no—
316C2×C22⋊C4—216no—
317C2×C22⋊C4—216no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—216no—
323C2×C22⋊C4—48no—
324C2×C22⋊C4—48no—
325C2×C22⋊C4—48no—
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—48no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—48no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—48no—
344C2×C22⋊C4—44no—
345C2×C42—216no—
346C2×C42—28no—
347C2×C42—28no—
348C2×C42—44no—
349C2×C42—48no—
350C2×C42—48no—
351C2×C42—48no—
352C2×C42—48no—
353C2×C42—48no—
354C2×C42—48no—
355C2×C42—48no—
356C2×C42—48no—
357#95—216no—
358#95—216no—
359#95—28no—
360#95—48no—
361#95—48no—
362#95—48no—
363#95—48no—
364#95—48no—
365#95—48no—
366#95—44no—
367#95—48no—
368#95—44no—
369#95—44no—
370#95C22⋊C4116yescomplemented
371C24—22no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—22no—
376C24—24no—
377C24—24no—
378C24—22no—
379C24—24no—
380C24—22no—
381C24—22no—
382C24—24no—
383C24—24no—
384C24—22no—
385C24—22no—
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—22no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24—42no—
406C24—42no—
407C24—41no—
408C24—41no—
409C24—42no—
410C24—41no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—41no—
421C24—42no—
422C24—41no—
423C24—41no—
424C24—42no—
425C24—42no—
426C24—41no—
427C24—41no—
428C24—41no—
429C24—41no—
430C24—42no—
431C24—42no—
432C24—42no—
433C24—42no—
434C24—42no—
435C24—41no—
436C24—42no—
437C24—42no—
438C24—41no—
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—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—41no—
463C24—42no—
464C24—42no—
465C24—41no—
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×#4112yes—
483C24C2×#4112yes—
484C24C2×#4112yes—
485C24C2×#4112yes—
486C24C2×#4111yescharacteristic
487C24H(5,𝔽2)11yescharacteristic
488C24H(5,𝔽2)11yescharacteristic
489C24H(5,𝔽2)12yes—
490C24H(5,𝔽2)11yescharacteristic
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—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
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—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
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—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
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—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
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—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—41no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—41no—
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—41no—
649C22×C4—41no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—41no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—41no—
659C22×C4—42no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—42no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—42no—
667C22×C4—41no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
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—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—42no—
703C22×C4—41no—
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—41no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—41no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—41no—
741C22×C4—41no—
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×C4C2×C22⋊C418yes—
757C22×C4C2×C22⋊C414yes—
758C22×C4C4×D414yes—
759C22×C4C4×D414yes—
760C22×C4#12114yes—
761C22×C4#12114yes—
762C22×C4#12114yes—
763C22×C4#12314yes—
764C22×C4#12318yes—
765C22×C4#12414yes—
766C22×C4#12418yes—
767C22×C4#12414yes—
768C22×C4#12414yes—
769C22×C4#12618yes—
770C22×C4#12714yes—
771C4⋊C4—416no—
772C4⋊C4—416no—
773C22⋊C4—432no—
774C22⋊C4—416no—
775C22⋊C4—432no—
776C22⋊C4—416no—
777C22⋊C4—416no—
778C42—416no—
779C42—432no—
780C23—24no—
781C23—28no—
782C23—24no—
783C23—24no—
784C23—28no—
785C23—44no—
786C23—44no—
787C23—42no—
788C23—44no—
789C23—42no—
790C23—44no—
791C23—42no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—44no—
798C23—42no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—42no—
803C23—42no—
804C23—44no—
805C23—42no—
806C23—42no—
807C23—44no—
808C23—42no—
809C23—42no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—42no—
815C23—42no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—42no—
824C23—42no—
825C23—44no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—42no—
835C23—44no—
836C23—42no—
837C23—44no—
838C23—42no—
839C23—82no—
840C23—81no—
841C23—82no—
842C23—81no—
843C23—81no—
844C23—82no—
845C23—81no—
846C23—81no—
847C23—81no—
848C23—82no—
849C23—81no—
850C23—81no—
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—81no—
866C23—81no—
867C23—81no—
868C23—82no—
869C23—82no—
870C23—82no—
871C23—82no—
872C23—82no—
873C23—82no—
874C23—82no—
875C23—82no—
876C23—81no—
877C23—82no—
878C23—82no—
879C23C22×C22⋊C411yescharacteristic
880C23C2×C4×D411yescharacteristic
881C23C2×C4×D411yescharacteristic
882C23C2×C4×D411yescharacteristic
883C23C4×#4111yescharacteristic
884C23C4×#4112yes—
885C23C4×#4112yes—
886C23C4×#4112yes—
887C23#51811yescharacteristic
888C23#52012yes—
889C23#52011yescharacteristic
890C23C2×#12111yescharacteristic
891C23C2×#12111yescharacteristic
892C23C2×#12111yescharacteristic
893C23C2×#12311yescharacteristic
894C23C2×#12312yes—
895C23#52511yescharacteristic
896C23#52511yescharacteristic
897C23#52512yes—
898C23#52512yes—
899C23#52512yes—
900C23C2×#12411yescharacteristic
901C23C2×#12411yescharacteristic
902C23C2×#12412yes—
903C23C2×#12411yescharacteristic
904C23C2×#12612yes—
905C23#52912yes—
906C23#52912yes—
907C23#52912yes—
908C23#52912yes—
909C23#52911yescharacteristic
910C23#52912yes—
911C23#52912yes—
912C23#52912yes—
913C23#52912yes—
914C23#52912yes—
915C23#52912yes—
916C23C2×#12711yescharacteristic
917C23#53212yes—
918C23#53212yes—
919C23#53211yescharacteristic
920C23#53211yescharacteristic
921C23#53212yes—
922C23#53211yescharacteristic
923C23#53411yescharacteristic
924C23#53511yescharacteristic
925C23#53611yescharacteristic
926C23#53711yescharacteristic
927C23#53812yes—
928C23#53812yes—
929C23#53912yes—
930C23#53912yes—
931C23#53912yes—
932C23#54011yescharacteristic
933C23#54012yes—
934C23#54112yes—
935C23#54211yescharacteristic
936C23#54212yes—
937C23#54212yes—
938C23D4211yescharacteristic
939C23D4211yescharacteristic
940C23D4211yescharacteristic
941C23#54612yes—
942C23#54612yes—
943C23#54611yescharacteristic
944C23#54611yescharacteristic
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#55112yes—
963C23#55112yes—
964C23#55212yes—
965C23#55212yes—
966C23#55212yes—
967C23#55212yes—
968C23#55312yes—
969C23#55311yescharacteristic
970C23#55312yes—
971C23#55311yescharacteristic
972C23#55312yes—
973C23#55312yes—
974C23#55511yescharacteristic
975C23#55612yes—
976C23#55612yes—
977C23#55912yes—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—28no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—28no—
1001C2×C4—24no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—28no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
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—44no—
1030C2×C4—44no—
1031C2×C4—44no—
1032C2×C4—44no—
1033C2×C4—44no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—44no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—42no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—44no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—42no—
1048C2×C4—44no—
1049C2×C4—42no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—44no—
1065C2×C4—42no—
1066C2×C4—44no—
1067C2×C4—42no—
1068C2×C4—82no—
1069C2×C4—81no—
1070C2×C4—82no—
1071C2×C4—81no—
1072C2×C4—81no—
1073C2×C4—81no—
1074C2×C4—81no—
1075C2×C4—81no—
1076C2×C4—81no—
1077C2×C4—82no—
1078C2×C4—82no—
1079C2×C4—81no—
1080C2×C4—81no—
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—81no—
1092C2×C4—81no—
1093C2×C4—82no—
1094C2×C4—82no—
1095C2×C4—81no—
1096C2×C4—82no—
1097C2×C4—82no—
1098C2×C4—82no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4#39018yes—
1103C2×C4#39718yescomplemented
1104C22—48no—
1105C22—44no—
1106C22—48no—
1107C22—44no—
1108C22—44no—
1109C22—84no—
1110C22—84no—
1111C22—82no—
1112C22—82no—
1113C22—82no—
1114C22—82no—
1115C22—82no—
1116C22—84no—
1117C22—84no—
1118C22—84no—
1119C22—82no—
1120C22—82no—
1121C22—82no—
1122C22—82no—
1123C22—84no—
1124C22—82no—
1125C22—82no—
1126C22—82no—
1127C22C2×#39011yescharacteristic
1128C22#229712yes—
1129C22C4×#12111yescharacteristic
1130C22C4×#12312yes—
1131C22C4×#12311yescharacteristic
1132C22C4×#12411yescharacteristic
1133C22C4×#12412yes—
1134C22C4×#12411yescharacteristic
1135C22C4×#12612yes—
1136C22#232211yescharacteristic
1137C22#232411yescharacteristic
1138C22#233412yes—
1139C22#233512yes—
1140C22D4×C22⋊C411yescharacteristic
1141C22#233912yes—
1142C22#234111yescharacteristic
1143C22#235912yes—
1144C22#235912yes—
1145C22#236111yescharacteristic
1146C22#236311yescharacteristic
1147C22#237312yes—
1148C22#237312yes—
1149C22#237412yes—
1150C22C2×#39711yescharacteristic
1151C22#239211yescharacteristic
1152C22#239512yes—
1153C22#239511yescharacteristic
1154C22#239811yescharacteristic
1155C22#240112yes—
1156C22#241211yescharacteristic
1157C22#241311yescharacteristic
1158C22#241411yescharacteristic
1159C22#241611yescharacteristic
1160C22#241812yes—
1161C22#241912yes—
1162C22#242212yes—
1163C22#242212yes—
1164C22#242512yes—
1165C22#242611yescharacteristic
1166C22#242811yescharacteristic
1167C22#245512yes—
1168C22#245712yes—
1169C22#246412yes—
1170C22#246712yes—
1171C22#246912yes—
1172C22#247012yes—
1173C22#247212yes—
1174C22#247812yes—
1175C22#247912yes—
1176C22#248112yes—
1177C22#248812yes—
1178C22#248812yes—
1179C22#248912yes—
1180C22#249012yes—
1181C22#249011yescharacteristic
1182C22#249111yescharacteristic
1183C22#249811yescharacteristic
1184C22#250111yescharacteristic
1185C22#250411yescharacteristic
1186C22#251012yes—
1187C22#251212yes—
1188C22#251212yes—
1189C22#251612yes—
1190C22#251912yes—
1191C22#252512yes—
1192C22#252912yes—
1193C22#253012yes—
1194C22#253112yes—
1195C22#253911yescharacteristic
1196C22#254011yescharacteristic
1197C22#254111yescharacteristic
1198C22#254311yescharacteristic
1199C22#254711yescharacteristic
1200C22#255312yes—
1201C22#255312yes—
1202C22#255412yes—
1203C22#255712yes—
1204C22#255712yes—
1205C22#256012yes—
1206C22#256012yes—
1207C22#256111yescharacteristic
1208C22#257312yes—
1209C22#257812yes—
1210C22#259211yescharacteristic
1211C22#259612yes—
1212C22#260311yescharacteristic
1213C22#261111yescharacteristic
1214C22#263911yescharacteristic
1215C22#264011yescharacteristic
1216C22#264912yes—
1217C22#265412yes—
1218C22#266111yescharacteristic
1219C22#266411yescharacteristic
1220C22#285012yes—
1221C22#285011yescharacteristic
1222C22#285011yescharacteristic
1223C22#285811yescharacteristic
1224C22#285811yescharacteristic
1225C22#286112yes—
1226C4—28no—
1227C4—28no—
1228C4—48no—
1229C4—48no—
1230C4—44no—
1231C4—82no—
1232C4—82no—
1233C4—82no—
1234C4—84no—
1235C4—84no—
1236C2—84no—
1237C2C4×#39711yescharacteristic
1238C2#1399611yescharacteristic
1239C2#1399811yescharacteristic
1240C2#1409612yes—
1241C2#1410112yes—
1242C2#1418312yes—
1243C2#1422911yescharacteristic
1244C2#1423312yes—
1245C2#1424911yescharacteristic
1246C2#1432411yescharacteristic
1247C2#1470811yescharacteristic
1248C2#1473511yescharacteristic
1249C2#1474312yes—
1250C2#1480811yescharacteristic
1251C2#1484211yescharacteristic
1252C2#1485412yes—
1253C2#1489411yescharacteristic
1254C2#1500612yes—
1255C2#1500711yescharacteristic
1256C2#1502011yescharacteristic
1257C2#1503512yes—
1258C2#1513611yescharacteristic
1259C2#1516711yescharacteristic
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
7. C2×C4⋊#95C2semidirect
8. C2×C4×#95C2semidirect
9. #7556C2semidirect
11. #7554C2semidirect
23. C2×#397C4semidirect
370. #95C22⋊C4semidirect
1103. C2×C4#397semidirect

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×#14422
C2×#14392
C2×#14372
C2×C4⋊#952
C2×C4×#952
#75562
#75552
#75542