Finite Group Databasebeta

← #154841

Subgroups — #154841

Order 512.

2334 conjugacy classes of subgroups.

The subgroup lattice has 1595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1434C211yesmaximal, characteristic
2C2×#1434C211yesmaximal, characteristic
3C2×#1434C211yesmaximal, characteristic
4#7556C211yesmaximal, characteristic
5#7556C211yesmaximal, characteristic
6#7556C211yesmaximal, characteristic
7#7556C211yesmaximal, characteristic
8#7556C211yesmaximal, characteristic
9#7556C211yesmaximal, characteristic
10#7556C211yesmaximal, characteristic
11#7556C211yesmaximal, characteristic
12#7556C211yesmaximal, characteristic
13#7554C211yesmaximal, characteristic
14#7554C211yesmaximal, characteristic
15#7554C211yesmaximal, characteristic
16C23×C42C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C22×#95C2211yescharacteristic
19C22×#95C2211yescharacteristic
20C22×#95C2211yescharacteristic
21C22×#95C2211yescharacteristic
22C22×#95C2211yescharacteristic
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51#1434—24no—
52#1434—24no—
53#1434C418yescomplemented
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C24×C4C2311yescharacteristic
57C24×C4C2311yescharacteristic
58C24×C4C2311yescharacteristic
59C24×C4C2311yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C24×C4C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C24×C4C2311yescharacteristic
65C24×C4C2311yescharacteristic
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C22×C42—22no—
70C22×C42—22no—
71C22×C42—22no—
72C22×C42—22no—
73C22×C42—22no—
74C22×C42—22no—
75C22×C42—22no—
76C22×C42—22no—
77C22×C42—22no—
78C22×C42—41no—
79C22×C42—41no—
80C22×C42—41no—
81C22×C42—41no—
82C22×C42C2×C414yes—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95—22no—
113C2×#95—22no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—22no—
123C2×#95—22no—
124C2×#95—22no—
125C2×#95—22no—
126C2×#95—22no—
127C2×#95—22no—
128C2×#95—22no—
129C2×#95—22no—
130C2×#95—22no—
131C2×#95—22no—
132C2×#95—22no—
133C2×#95—22no—
134C2×#95—22no—
135C2×#95—22no—
136C2×#95—22no—
137C2×#95—41no—
138C2×#95—41no—
139C2×#95—41no—
140C2×#95—41no—
141C2×#95—41no—
142C2×#95—41no—
143C2×#95—41no—
144C2×#95—41no—
145C2×#95—41no—
146C2×#95—41no—
147C2×#95—41no—
148C2×#95—41no—
149C2×#95—41no—
150C2×#95—41no—
151C2×#95—41no—
152C2×#95—41no—
153C2×#95—41no—
154C2×#95—41no—
155C2×#95—41no—
156C2×#95—41no—
157C2×#95—41no—
158C2×#95—41no—
159C2×#95—41no—
160C2×#95—41no—
161C2×#95—41no—
162C2×#95—41no—
163C2×#95—41no—
164C2×#95—41no—
165C2×#95—41no—
166C2×#95—41no—
167C2×#95—41no—
168C2×#95—41no—
169C2×#95—41no—
170C2×#95—41no—
171C2×#95—41no—
172C2×#95—41no—
173C2×#95—41no—
174C2×#95—41no—
175C2×#95C2×C414yes—
176C2×#95C2×C414yes—
177C2×#95C2×C414yes—
178C2×#95C2×C414yes—
179C2×#95C2×C414yes—
180C2×#95C2×C414yes—
181C2×#95D414yes—
182C25C2411yescharacteristic
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
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—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—21no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—21no—
381C23×C4C22×C412yes—
382C23×C4C22×C412yes—
383C23×C4C22×C412yes—
384C23×C4C22×C412yes—
385C23×C4C22×C412yes—
386C23×C4C22×C412yes—
387C23×C4C22×C412yes—
388C23×C4C2×D412yes—
389C23×C4C2×D412yes—
390C23×C4C2×D412yes—
391C23×C4#4112yes—
392C23×C4#4112yes—
393C23×C4#4112yes—
394C23×C4#4112yes—
395C23×C4#4112yes—
396C23×C4#4112yes—
397C23×C4#4112yes—
398C23×C4#4112yes—
399C23×C4#4112yes—
400C23×C4#4112yes—
401C23×C4#4112yes—
402C23×C4#4112yes—
403C23×C4#4112yes—
404C23×C4#4112yes—
405C23×C4#4112yes—
406C23×C4#4112yes—
407C23×C4#4112yes—
408C2×C42—28no—
409C2×C42—28no—
410C2×C42—28no—
411C2×C42—44no—
412C2×C42—44no—
413C2×C42—44no—
414C2×C42—44no—
415C2×C42—44no—
416C2×C42—44no—
417C2×C42—44no—
418C2×C42—44no—
419C2×C42—44no—
420C2×C42—44no—
421C2×C42—44no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95—44no—
452#95—44no—
453#95—44no—
454#95—44no—
455C24C23×C411yescharacteristic
456C24C22×D411yescharacteristic
457C24C2×#4111yescharacteristic
458C24C2×#4111yescharacteristic
459C24C2×#4111yescharacteristic
460C24C2×#4111yescharacteristic
461C24C2×#4111yescharacteristic
462C24C2×#4111yescharacteristic
463C24C2×#4111yescharacteristic
464C24C2×#4111yescharacteristic
465C24C2×#4111yescharacteristic
466C24C2×#4111yescharacteristic
467C24C2×#4111yescharacteristic
468C24C2×#4111yescharacteristic
469C24C2×#4111yescharacteristic
470C24C2×#4111yescharacteristic
471C24C2×#4111yescharacteristic
472C24C2×#4111yescharacteristic
473C24C2×#4111yescharacteristic
474C24H(5,𝔽2)11yescharacteristic
475C24H(5,𝔽2)11yescharacteristic
476C24H(5,𝔽2)11yescharacteristic
477C24H(5,𝔽2)11yescharacteristic
478C24H(5,𝔽2)11yescharacteristic
479C24H(5,𝔽2)11yescharacteristic
480C24H(5,𝔽2)11yescharacteristic
481C242−1+411yescharacteristic
482C242−1+411yescharacteristic
483C242−1+411yescharacteristic
484C242−1+411yescharacteristic
485C242−1+411yescharacteristic
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—41no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—41no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—41no—
779C22×C4—41no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—41no—
791C22×C4—41no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—41no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—41no—
977C22×C4—41no—
978C22×C4—41no—
979C22×C4—41no—
980C22×C4—41no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—41no—
990C22×C4—41no—
991C22×C4—41no—
992C22×C4—41no—
993C22×C4—41no—
994C22×C4—41no—
995C22×C4—41no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4#11714yes—
1006C22×C4#11714yes—
1007C22×C4#11714yes—
1008C22×C4C4×D414yes—
1009C22×C4#12314yes—
1010C22×C4#12614yes—
1011C42—416no—
1012C42—416no—
1013C23C2×#11711yescharacteristic
1014C23C2×#11711yescharacteristic
1015C23C2×#11711yescharacteristic
1016C23C2×C4×D411yescharacteristic
1017C23C4×#4111yescharacteristic
1018C23C4×#4111yescharacteristic
1019C23C4×#4111yescharacteristic
1020C23C4×#4111yescharacteristic
1021C23C4×#4111yescharacteristic
1022C23#51811yescharacteristic
1023C23#51811yescharacteristic
1024C23#51911yescharacteristic
1025C23#52011yescharacteristic
1026C23#52011yescharacteristic
1027C23#52011yescharacteristic
1028C23C2×#12311yescharacteristic
1029C23#52511yescharacteristic
1030C23#52511yescharacteristic
1031C23#52511yescharacteristic
1032C23C2×#12611yescharacteristic
1033C23#52911yescharacteristic
1034C23#52911yescharacteristic
1035C23#52911yescharacteristic
1036C23#52911yescharacteristic
1037C23#52911yescharacteristic
1038C23#52911yescharacteristic
1039C23#52911yescharacteristic
1040C23#52911yescharacteristic
1041C23#52911yescharacteristic
1042C23#52911yescharacteristic
1043C23#52911yescharacteristic
1044C23#52911yescharacteristic
1045C23#52911yescharacteristic
1046C23#52911yescharacteristic
1047C23#52911yescharacteristic
1048C23#52911yescharacteristic
1049C23#52911yescharacteristic
1050C23#52911yescharacteristic
1051C23#52911yescharacteristic
1052C23#53511yescharacteristic
1053C23#53711yescharacteristic
1054C23#53811yescharacteristic
1055C23#53811yescharacteristic
1056C23#53811yescharacteristic
1057C23#53811yescharacteristic
1058C23#53911yescharacteristic
1059C23#53911yescharacteristic
1060C23#53911yescharacteristic
1061C23#53911yescharacteristic
1062C23#53911yescharacteristic
1063C23#53911yescharacteristic
1064C23#53911yescharacteristic
1065C23#53911yescharacteristic
1066C23#53911yescharacteristic
1067C23#53911yescharacteristic
1068C23#54011yescharacteristic
1069C23#54011yescharacteristic
1070C23#54011yescharacteristic
1071C23#54011yescharacteristic
1072C23#54011yescharacteristic
1073C23#54011yescharacteristic
1074C23#54011yescharacteristic
1075C23#54111yescharacteristic
1076C23#54111yescharacteristic
1077C23#54111yescharacteristic
1078C23#54111yescharacteristic
1079C23#54111yescharacteristic
1080C23#54111yescharacteristic
1081C23#54211yescharacteristic
1082C23#54211yescharacteristic
1083C23#54211yescharacteristic
1084C23#54211yescharacteristic
1085C23#54211yescharacteristic
1086C23#54211yescharacteristic
1087C23#54211yescharacteristic
1088C23#54611yescharacteristic
1089C23#54611yescharacteristic
1090C23#54611yescharacteristic
1091C23#54611yescharacteristic
1092C23#54711yescharacteristic
1093C23#54711yescharacteristic
1094C23#54811yescharacteristic
1095C23#54811yescharacteristic
1096C23#55111yescharacteristic
1097C23#55111yescharacteristic
1098C23#55111yescharacteristic
1099C23#55111yescharacteristic
1100C23#55111yescharacteristic
1101C23#55111yescharacteristic
1102C23#55111yescharacteristic
1103C23#55111yescharacteristic
1104C23#55111yescharacteristic
1105C23#55111yescharacteristic
1106C23#55111yescharacteristic
1107C23#55111yescharacteristic
1108C23#55111yescharacteristic
1109C23#55111yescharacteristic
1110C23#55111yescharacteristic
1111C23#55111yescharacteristic
1112C23#55211yescharacteristic
1113C23#55211yescharacteristic
1114C23#55211yescharacteristic
1115C23#55211yescharacteristic
1116C23#55211yescharacteristic
1117C23#55211yescharacteristic
1118C23#55211yescharacteristic
1119C23#55211yescharacteristic
1120C23#55211yescharacteristic
1121C23#55211yescharacteristic
1122C23#55211yescharacteristic
1123C23#55211yescharacteristic
1124C23#55211yescharacteristic
1125C23#55211yescharacteristic
1126C23#55211yescharacteristic
1127C23#55211yescharacteristic
1128C23#55211yescharacteristic
1129C23#55311yescharacteristic
1130C23#55311yescharacteristic
1131C23#55311yescharacteristic
1132C23#55311yescharacteristic
1133C23#55311yescharacteristic
1134C23#55311yescharacteristic
1135C23#55311yescharacteristic
1136C23#55311yescharacteristic
1137C23#55311yescharacteristic
1138C23#55311yescharacteristic
1139C23#55311yescharacteristic
1140C23#55311yescharacteristic
1141C23#55311yescharacteristic
1142C23#55511yescharacteristic
1143C23#55511yescharacteristic
1144C23#55511yescharacteristic
1145C23#55511yescharacteristic
1146C23#55511yescharacteristic
1147C23#55511yescharacteristic
1148C23#55611yescharacteristic
1149C23#55611yescharacteristic
1150C23#55611yescharacteristic
1151C23#55611yescharacteristic
1152C23#55611yescharacteristic
1153C23#55611yescharacteristic
1154C23#55611yescharacteristic
1155C23#55611yescharacteristic
1156C23#55611yescharacteristic
1157C23#55911yescharacteristic
1158C23#55911yescharacteristic
1159C23#55911yescharacteristic
1160C23H(3,𝔽4)11yescharacteristic
1161C23#56211yescharacteristic
1162C23#56211yescharacteristic
1163C23#56211yescharacteristic
1164C23#56211yescharacteristic
1165C23#56311yescharacteristic
1166C23#56311yescharacteristic
1167C23#56311yescharacteristic
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—42no—
1281C2×C4—42no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—42no—
1297C2×C4—42no—
1298C2×C4—42no—
1299C2×C4—42no—
1300C2×C4—42no—
1301C2×C4—42no—
1302C2×C4—42no—
1303C2×C4—42no—
1304C2×C4—42no—
1305C2×C4—42no—
1306C2×C4—42no—
1307C2×C4—42no—
1308C2×C4—42no—
1309C2×C4—42no—
1310C2×C4—42no—
1311C2×C4—42no—
1312C2×C4—42no—
1313C2×C4—42no—
1314C2×C4—42no—
1315C2×C4—42no—
1316C2×C4—42no—
1317C2×C4—42no—
1318C2×C4—42no—
1319C2×C4—42no—
1320C2×C4—42no—
1321C2×C4—81no—
1322C2×C4—81no—
1323C2×C4—81no—
1324C2×C4—81no—
1325C2×C4—81no—
1326C2×C4—81no—
1327C2×C4—81no—
1328C2×C4—81no—
1329C2×C4—81no—
1330C2×C4—81no—
1331C2×C4—81no—
1332C2×C4—81no—
1333C2×C4—81no—
1334C2×C4—81no—
1335C2×C4—81no—
1336C2×C4—81no—
1337C2×C4—81no—
1338C2×C4—81no—
1339C2×C4—81no—
1340C2×C4—81no—
1341C2×C4—81no—
1342C2×C4—81no—
1343C2×C4—81no—
1344C2×C4—81no—
1345C2×C4—81no—
1346C2×C4—81no—
1347C2×C4—81no—
1348C2×C4—81no—
1349C2×C4—81no—
1350C2×C4—81no—
1351C2×C4—81no—
1352C2×C4—81no—
1353C2×C4—81no—
1354C2×C4—81no—
1355C2×C4—81no—
1356C2×C4—81no—
1357C2×C4—81no—
1358C2×C4—81no—
1359C2×C4—81no—
1360C2×C4—81no—
1361C2×C4—81no—
1362C2×C4—81no—
1363C2×C4—81no—
1364C2×C4—81no—
1365C2×C4—81no—
1366C2×C4—81no—
1367C2×C4—81no—
1368C2×C4—81no—
1369C2×C4—81no—
1370C2×C4—81no—
1371C2×C4—81no—
1372C2×C4—81no—
1373C2×C4—81no—
1374C2×C4—81no—
1375C2×C4—81no—
1376C2×C4—81no—
1377C2×C4—81no—
1378C2×C4—81no—
1379C2×C4—81no—
1380C2×C4—81no—
1381C2×C4—81no—
1382C2×C4—81no—
1383C2×C4—81no—
1384C2×C4—81no—
1385C2×C4—81no—
1386C2×C4—81no—
1387C2×C4—81no—
1388C2×C4—81no—
1389C2×C4—81no—
1390C2×C4—81no—
1391C2×C4—81no—
1392C2×C4—81no—
1393C22#228311yescharacteristic
1394C22#229011yescharacteristic
1395C22#229811yescharacteristic
1396C22#229811yescharacteristic
1397C22C4×#12311yescharacteristic
1398C22C4×#12611yescharacteristic
1399C22#231311yescharacteristic
1400C22#231411yescharacteristic
1401C22#231911yescharacteristic
1402C22#232411yescharacteristic
1403C22#233311yescharacteristic
1404C22#233411yescharacteristic
1405C22#233511yescharacteristic
1406C22#233611yescharacteristic
1407C22#233611yescharacteristic
1408C22#234211yescharacteristic
1409C22#234311yescharacteristic
1410C22#234311yescharacteristic
1411C22#234611yescharacteristic
1412C22#234611yescharacteristic
1413C22#234711yescharacteristic
1414C22#235211yescharacteristic
1415C22#235311yescharacteristic
1416C22#235311yescharacteristic
1417C22#235611yescharacteristic
1418C22#235611yescharacteristic
1419C22#235711yescharacteristic
1420C22#235911yescharacteristic
1421C22#236211yescharacteristic
1422C22#237211yescharacteristic
1423C22#237311yescharacteristic
1424C22#237311yescharacteristic
1425C22#237411yescharacteristic
1426C22#237811yescharacteristic
1427C22#237911yescharacteristic
1428C22#241911yescharacteristic
1429C22#241911yescharacteristic
1430C22#242011yescharacteristic
1431C22#242111yescharacteristic
1432C22#245911yescharacteristic
1433C22#246011yescharacteristic
1434C22#246611yescharacteristic
1435C22#246811yescharacteristic
1436C22#246911yescharacteristic
1437C22#246911yescharacteristic
1438C22#247611yescharacteristic
1439C22#247611yescharacteristic
1440C22#247711yescharacteristic
1441C22#247711yescharacteristic
1442C22#247811yescharacteristic
1443C22#248111yescharacteristic
1444C22#248211yescharacteristic
1445C22#248511yescharacteristic
1446C22#249311yescharacteristic
1447C22#249511yescharacteristic
1448C22#251011yescharacteristic
1449C22#251311yescharacteristic
1450C22#251411yescharacteristic
1451C22#251511yescharacteristic
1452C22#251611yescharacteristic
1453C22#251611yescharacteristic
1454C22#251811yescharacteristic
1455C22#251811yescharacteristic
1456C22#252411yescharacteristic
1457C22#252411yescharacteristic
1458C22#252411yescharacteristic
1459C22#252411yescharacteristic
1460C22#252611yescharacteristic
1461C22#252611yescharacteristic
1462C22#252711yescharacteristic
1463C22#252711yescharacteristic
1464C22#252711yescharacteristic
1465C22#252811yescharacteristic
1466C22#252911yescharacteristic
1467C22#252911yescharacteristic
1468C22#253011yescharacteristic
1469C22#253011yescharacteristic
1470C22#253011yescharacteristic
1471C22#253111yescharacteristic
1472C22#253111yescharacteristic
1473C22#253111yescharacteristic
1474C22#253111yescharacteristic
1475C22#253111yescharacteristic
1476C22#253111yescharacteristic
1477C22#253211yescharacteristic
1478C22#253311yescharacteristic
1479C22#253311yescharacteristic
1480C22#257211yescharacteristic
1481C22#257211yescharacteristic
1482C22#257311yescharacteristic
1483C22#257311yescharacteristic
1484C22#257511yescharacteristic
1485C22#257511yescharacteristic
1486C22#257511yescharacteristic
1487C22#257711yescharacteristic
1488C22#257711yescharacteristic
1489C22#257711yescharacteristic
1490C22#257711yescharacteristic
1491C22#259311yescharacteristic
1492C22#259411yescharacteristic
1493C22#259411yescharacteristic
1494C22#259411yescharacteristic
1495C22#259611yescharacteristic
1496C22#259611yescharacteristic
1497C22#259711yescharacteristic
1498C22#259811yescharacteristic
1499C22#260911yescharacteristic
1500C22#269511yescharacteristic
1501C22#269611yescharacteristic
1502C22#270611yescharacteristic
1503C22#270711yescharacteristic
1504C22#271011yescharacteristic
1505C22#271111yescharacteristic
1506C22#271211yescharacteristic
1507C22#272511yescharacteristic
1508C22#273811yescharacteristic
1509C22#273911yescharacteristic
1510C22#274011yescharacteristic
1511C22#274011yescharacteristic
1512C22#274011yescharacteristic
1513C22#274111yescharacteristic
1514C22#274311yescharacteristic
1515C22#274311yescharacteristic
1516C22#274411yescharacteristic
1517C22#274411yescharacteristic
1518C22#274411yescharacteristic
1519C22#274411yescharacteristic
1520C22#274511yescharacteristic
1521C22#274711yescharacteristic
1522C22#275311yescharacteristic
1523C22#275311yescharacteristic
1524C22#275311yescharacteristic
1525C22#275411yescharacteristic
1526C22#275811yescharacteristic
1527C22#275911yescharacteristic
1528C22#276211yescharacteristic
1529C22#276511yescharacteristic
1530C22#276611yescharacteristic
1531C22#276911yescharacteristic
1532C22#276911yescharacteristic
1533C22#277211yescharacteristic
1534C22#277211yescharacteristic
1535C22#277311yescharacteristic
1536C22#277311yescharacteristic
1537C22#277711yescharacteristic
1538C22#278511yescharacteristic
1539C22#278511yescharacteristic
1540C22#278611yescharacteristic
1541C22#278611yescharacteristic
1542C22#278911yescharacteristic
1543C22#279311yescharacteristic
1544C22#279311yescharacteristic
1545C22#279811yescharacteristic
1546C22#280011yescharacteristic
1547C22#280011yescharacteristic
1548C4—44no—
1549C4—44no—
1550C4—44no—
1551C4—44no—
1552C4—44no—
1553C4—44no—
1554C4—82no—
1555C4—82no—
1556C4—82no—
1557C4—82no—
1558C4—82no—
1559C4—82no—
1560C4—82no—
1561C4—82no—
1562C4—82no—
1563C2#1389811yescharacteristic
1564C2#1394611yescharacteristic
1565C2#1395011yescharacteristic
1566C2#1398911yescharacteristic
1567C2#1406611yescharacteristic
1568C2#1410311yescharacteristic
1569C2#1411011yescharacteristic
1570C2#1412211yescharacteristic
1571C2#1412611yescharacteristic
1572C2#1437211yescharacteristic
1573C2#1441211yescharacteristic
1574C2#1447611yescharacteristic
1575C2#1449111yescharacteristic
1576C2#1449711yescharacteristic
1577C2#1451011yescharacteristic
1578C2#1602111yescharacteristic
1579C2#1602311yescharacteristic
1580C2#1603611yescharacteristic
1581C2#1603811yescharacteristic
1582C2#1607611yescharacteristic
1583C2#1607711yescharacteristic
1584C2#1608211yescharacteristic
1585C2#1608311yescharacteristic
1586C2#1613611yescharacteristic
1587C2#1613911yescharacteristic
1588C2#1615311yescharacteristic
1589C2#1615411yescharacteristic
1590C2#1615911yescharacteristic
1591C2#1615911yescharacteristic
1592C2#1619411yescharacteristic
1593C2#1622011yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
53. #1434C4semidirect

Maximal subgroups

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

subgroupindex
C2×#14342
#75562
#75542