Finite Group Databasebeta

← C2×#15954 #609887

Subgroups — C2×#15954 #609887

Order 512.

6378 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#386C211yesmaximal, characteristic
2C22×#386C211yesmaximal, characteristic
3C22×#385C211yesmaximal, characteristic, complemented
4C22×#381C211yesmaximal, characteristic, complemented
5#15954C2116yesmaximal, direct product factor
6C2×#1445C211yesmaximal, characteristic, complemented
7C2×#1443C211yesmaximal, characteristic, complemented
8C2×#1443C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1440C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1439C211yesmaximal, characteristic, complemented
14C2×#1438C211yesmaximal, characteristic
15C2×C22⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C2×#386—28no—
33C2×#386—28no—
34C2×#386C2218yes—
35C2×#386C2218yes—
36C2×#385—28no—
37C2×#385C2218yescomplemented
38C2×#381—28no—
39C2×#381C2218yescomplemented
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1445C2218yescomplemented
61#1443C2218yescomplemented
62#1443C2218yescomplemented
63#1442C2218yescomplemented
64#1440C2218yescomplemented
65#1440C2218yescomplemented
66#1439C2218yescomplemented
67#1439C2218yescomplemented
68#1438C2218yes—
69C22⋊#95C2218yescomplemented
70C22⋊#95C2218yescomplemented
71C26C2311yescharacteristic
72C26C2311yescharacteristic
73C23×D4—24no—
74C23×D4—24no—
75C23×D4—24no—
76C23×D4—24no—
77C23×D4—42no—
78C23×D4—42no—
79C23×D4D418yes—
80C23×D4C2314yes—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4—42no—
92C24×C4—42no—
93C24×C4—42no—
94C24×C4—42no—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2314yes—
109C24×C4C2314yes—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4—42no—
143C22×C22⋊C4—42no—
144C22×C22⋊C4—42no—
145C22×C22⋊C4—42no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4—42no—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158#386—232no—
159#386—232no—
160#385—232no—
161#381—232no—
162C2×#95—24no—
163C2×#95—24no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95—42no—
176C2×#95—42no—
177C2×#95—42no—
178C2×#95—42no—
179C2×#95—42no—
180C2×#95—42no—
181C2×#95D418yescomplemented
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25C2×D414yes—
227C25C2×D414yes—
228C25#4114yes—
229C25#4114yes—
230C25#4114yes—
231C25#4114yes—
232C25C2412yes—
233C25C2412yes—
234C25C2411yescharacteristic
235C22×D4—232no—
236C22×D4—232no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—28no—
240C22×D4—28no—
241C22×D4—416no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—416no—
245C22×D4—416no—
246C22×D4—416no—
247C22×D4—416no—
248C22×D4C2×D4116yes—
249C23×C4—232no—
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—28no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
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—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—28no—
294C23×C4—28no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—28no—
303C23×C4—28no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—28no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—28no—
341C23×C4—28no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—44no—
345C23×C4—44no—
346C23×C4—44no—
347C23×C4—44no—
348C23×C4—416no—
349C23×C4—416no—
350C23×C4—416no—
351C23×C4—416no—
352C23×C4—416no—
353C23×C4—416no—
354C23×C4—416no—
355C23×C4—416no—
356C23×C4—416no—
357C23×C4—416no—
358C23×C4—416no—
359C23×C4—416no—
360C23×C4—416no—
361C23×C4C2×D414yes—
362C23×C4C2×D414yes—
363C23×C4C2×D414yes—
364C23×C4C2×D414yes—
365C23×C4#4114yes—
366C23×C4#4114yes—
367C23×C4#4114yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—416no—
388C2×C4⋊C4—416no—
389C2×C22⋊C4—232no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—416no—
421C2×C22⋊C4—416no—
422C2×C22⋊C4—416no—
423C2×C22⋊C4—416no—
424C2×C22⋊C4—416no—
425C2×C22⋊C4—416no—
426C2×C22⋊C4—416no—
427C2×C22⋊C4—416no—
428C2×C22⋊C4—416no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—28no—
436#95—28no—
437#95—28no—
438#95—28no—
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#95C2×D4116yescomplemented
449C24—28no—
450C24—28no—
451C24—28no—
452C24—28no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—28no—
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—28no—
466C24—28no—
467C24—28no—
468C24—28no—
469C24—28no—
470C24—28no—
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—28no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24#123116yes—
542C24#123116yes—
543C24C22×D414yes—
544C24C22×D414yes—
545C24C22×D412yes—
546C24C22×D412yes—
547C24C2×#4114yes—
548C24C2×#4114yes—
549C24C2×#4114yes—
550C24C2×#4114yes—
551C24C2×#4112yes—
552C24C2×#4112yes—
553C24C2×#4112yes—
554C24C2×#4112yes—
555C24C2×#4112yes—
556C24C2×#4112yes—
557C24C2×#4112yes—
558C24H(5,𝔽2)12yes—
559C24H(5,𝔽2)12yes—
560C24H(5,𝔽2)12yes—
561C24H(5,𝔽2)12yes—
562C24H(5,𝔽2)12yes—
563C242−1+412yes—
564C24C2511yescharacteristic
565C2×D4—232no—
566C2×D4—232no—
567C2×D4—416no—
568C2×D4—416no—
569C2×D4—416no—
570C2×D4—416no—
571C2×D4—416no—
572C2×D4—4128no—
573C22×C4—232no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
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—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—416no—
680C22×C4—416no—
681C22×C4—416no—
682C22×C4—416no—
683C22×C4—416no—
684C22×C4—416no—
685C22×C4—416no—
686C22×C4—416no—
687C22×C4—416no—
688C22×C4—4128no—
689C22×C4—416no—
690C22×C4—416no—
691C22×C4—4128no—
692C22×C4—416no—
693C22×C4—416no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4C22×D414yes—
765C22×C4C22×D414yes—
766C22×C4C22×D414yes—
767C22×C4C22×D414yes—
768C22×C4C2×#4114yes—
769C22×C4C2×#4114yes—
770C22×C4C2×#4114yes—
771C4⋊C4—416no—
772C4⋊C4—416no—
773C22⋊C4—232no—
774C22⋊C4—416no—
775C22⋊C4—416no—
776C22⋊C4—416no—
777C22⋊C4—416no—
778C22⋊C4—416no—
779C22⋊C4—416no—
780C22⋊C4—416no—
781C22⋊C4—416no—
782C22⋊C4—416no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—232no—
790C23—232no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—232no—
808C23—232no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—232no—
824C23—232no—
825C23—416no—
826C23—416no—
827C23—416no—
828C23—416no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—416no—
834C23—416no—
835C23—416no—
836C23—416no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—416no—
853C23—416no—
854C23—42no—
855C23—416no—
856C23—416no—
857C23—416no—
858C23—416no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—416no—
868C23—416no—
869C23—416no—
870C23—416no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—416no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23C2×#12318yes—
882C23C2×#12318yes—
883C23C2×#12314yes—
884C23C2×#12314yes—
885C23#52514yes—
886C23#52514yes—
887C23#52914yes—
888C23#52914yes—
889C23#53414yes—
890C23#53514yes—
891C23#53814yes—
892C23#53814yes—
893C23#53814yes—
894C23#53914yes—
895C23#53914yes—
896C23#54014yes—
897C23#54214yes—
898C23D4214yes—
899C23#54614yes—
900C23#54614yes—
901C23#54614yes—
902C23#54614yes—
903C23#54714yes—
904C23#54814yes—
905C23#55114yes—
906C23#55114yes—
907C23#55114yes—
908C23#55114yes—
909C23#55114yes—
910C23#55114yes—
911C23#55214yes—
912C23#55314yes—
913C23#55314yes—
914C23#55314yes—
915C23#55314yes—
916C23#56014yes—
917C23#56214yes—
918C23C23×D411yescharacteristic
919C23C23×D411yescharacteristic
920C23C22×#4111yescharacteristic
921C23C22×#4111yescharacteristic
922C23C22×#4111yescharacteristic
923C23C22×#4111yescharacteristic
924C23C22×#4111yescharacteristic
925C23C22×#4111yescharacteristic
926C23C22×#4111yescharacteristic
927C23C2×H(5,𝔽2)11yescharacteristic
928C23C2×H(5,𝔽2)11yescharacteristic
929C23C2×H(5,𝔽2)11yescharacteristic
930C23C2×H(5,𝔽2)11yescharacteristic
931C23C2×H(5,𝔽2)11yescharacteristic
932C23C2×2−1+411yescharacteristic
933D4—464no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—464no—
956C2×C4—464no—
957C2×C4—416no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—416no—
963C2×C4—416no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—416no—
967C2×C4—416no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—416no—
989C2×C4—416no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—42no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—88no—
1035C2×C4—88no—
1036C2×C4—88no—
1037C2×C4—88no—
1038C2×C4—88no—
1039C2×C4—88no—
1040C22—28no—
1041C22—28no—
1042C22—28no—
1043C22—28no—
1044C22—28no—
1045C22—28no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—464no—
1051C22—464no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22#241818yes—
1073C22#241918yes—
1074C22#244318yes—
1075C22#244418yes—
1076C22#245718yes—
1077C22#247718yes—
1078C22#248318yes—
1079C22#257618yes—
1080C22#259818yes—
1081C22#267818yes—
1082C22#269618yes—
1083C22#270118yes—
1084C22#274618yes—
1085C22#274918yes—
1086C22#275018yes—
1087C22C22×#12311yescharacteristic
1088C22C22×#12311yescharacteristic
1089C22C2×#52511yescharacteristic
1090C22C2×#52511yescharacteristic
1091C22C2×#52911yescharacteristic
1092C22C2×#52911yescharacteristic
1093C22C2×#53411yescharacteristic
1094C22C2×#53511yescharacteristic
1095C22C2×#53811yescharacteristic
1096C22C2×#53811yescharacteristic
1097C22C2×#53811yescharacteristic
1098C22C2×#53911yescharacteristic
1099C22C2×#53911yescharacteristic
1100C22C2×#54011yescharacteristic
1101C22C2×#54211yescharacteristic
1102C22C2×D4211yescharacteristic
1103C22C2×#54611yescharacteristic
1104C22C2×#54611yescharacteristic
1105C22C2×#54611yescharacteristic
1106C22C2×#54611yescharacteristic
1107C22C2×#54711yescharacteristic
1108C22C2×#54811yescharacteristic
1109C22C2×#55111yescharacteristic
1110C22C2×#55111yescharacteristic
1111C22C2×#55111yescharacteristic
1112C22C2×#55111yescharacteristic
1113C22C2×#55111yescharacteristic
1114C22C2×#55111yescharacteristic
1115C22C2×#55211yescharacteristic
1116C22C2×#55311yescharacteristic
1117C22C2×#55311yescharacteristic
1118C22C2×#55311yescharacteristic
1119C22C2×#55311yescharacteristic
1120C22C2×#56011yescharacteristic
1121C22C2×#56211yescharacteristic
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—82no—
1130C4—82no—
1131C4—82no—
1132C4—82no—
1133C4—82no—
1134C4—82no—
1135C2—48no—
1136C2—48no—
1137C2#15954116yesdirect product factor
1138C2C2×#241811yescharacteristic
1139C2C2×#244311yescharacteristic
1140C2C2×#241911yescharacteristic
1141C2C2×#244411yescharacteristic
1142C2C2×#245711yescharacteristic
1143C2C2×#247711yescharacteristic
1144C2C2×#248311yescharacteristic
1145C2C2×#257611yescharacteristic
1146C2C2×#259811yescharacteristic
1147C2C2×#267811yescharacteristic
1148C2C2×#269611yescharacteristic
1149C2C2×#270111yescharacteristic
1150C2C2×#274611yescharacteristic
1151C2C2×#274911yescharacteristic
1152C2C2×#275011yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#385C2semidirect
4. C22×#381C2semidirect
5. #15954C2direct (N × H)
6. C2×#1445C2semidirect
7. C2×#1443C2semidirect
8. C2×#1443C2semidirect
9. C2×#1442C2semidirect
10. C2×#1440C2semidirect
11. C2×#1440C2semidirect
12. C2×#1439C2semidirect
13. C2×#1439C2semidirect
15. C2×C22⋊#95C2semidirect
16. C2×C22⋊#95C2semidirect
37. C2×#385C22semidirect
39. C2×#381C22semidirect
60. #1445C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1440C22semidirect
65. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
69. C22⋊#95C22semidirect
70. C22⋊#95C22semidirect
181. C2×#95D4semidirect
448. #95C2×D4semidirect
1137. C2#15954direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3862
C22×#3852
C22×#3812
#159542
C2×#14452
C2×#14432
C2×#14422
C2×#14402
C2×#14392
C2×#14382
C2×C22⋊#952