Finite Group Databasebeta

← C2×#15043 #608126

Subgroups — C2×#15043 #608126

Order 512.

4606 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#381C211yesmaximal, characteristic
2C22×C4×C22⋊C4C211yesmaximal, characteristic
3#15043C2116yesmaximal, direct product factor
4C2×#1445C211yesmaximal, characteristic, complemented
5C2×#1443C211yesmaximal, characteristic, complemented
6C2×#1443C211yesmaximal, characteristic, complemented
7C2×#1442C211yesmaximal, characteristic, complemented
8C2×#1440C211yesmaximal, characteristic
9C2×#1440C211yesmaximal, characteristic
10C2×#1439C211yesmaximal, characteristic
11C2×#1439C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×#1434C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28C2×#381—28no—
29C2×#381C2218yes—
30C2×C4×C22⋊C4—28no—
31C2×C4×C22⋊C4C2218yes—
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
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1445C2218yescomplemented
57#1443C2218yescomplemented
58#1443C2218yescomplemented
59#1442C2218yescomplemented
60#1440C2218yes—
61#1440C2218yes—
62#1439C2218yes—
63#1439C2218yes—
64#1436C2218yescomplemented
65#1436C2218yescomplemented
66#1434C2218yescomplemented
67#1434C2218yescomplemented
68C22⋊#95C2218yes—
69C26C2311yescharacteristic
70C24×C4—24no—
71C24×C4—24no—
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—42no—
75C24×C4—42no—
76C24×C4D418yes—
77C24×C4C2311yescharacteristic
78C24×C4C2311yescharacteristic
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2314yes—
91C24×C4C2311yescharacteristic
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—42no—
96C22×C4⋊C4—42no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4C2314yes—
99C22×C4⋊C4C2314yes—
100C22×C22⋊C4—24no—
101C22×C22⋊C4—24no—
102C22×C22⋊C4—24no—
103C22×C22⋊C4—24no—
104C22×C22⋊C4—24no—
105C22×C22⋊C4—24no—
106C22×C22⋊C4—24no—
107C22×C22⋊C4—24no—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—42no—
115C22×C22⋊C4—42no—
116C22×C22⋊C4—42no—
117C22×C22⋊C4—42no—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C42—24no—
125C22×C42—24no—
126C22×C42—24no—
127C22×C42—24no—
128C22×C42—42no—
129C22×C42—42no—
130C22×C42C2314yes—
131C22×C42C2314yes—
132#381—232no—
133C4×C22⋊C4—232no—
134C2×#95—24no—
135C2×#95—24no—
136C2×#95—24no—
137C2×#95—24no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—42no—
152C2×#95—42no—
153C2×#95—42no—
154C2×#95—42no—
155C2×#95—42no—
156C2×#95—42no—
157C2×#95—42no—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C25—22no—
183C25—22no—
184C25—22no—
185C25—22no—
186C25—22no—
187C25—22no—
188C25—22no—
189C25—22no—
190C25—22no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25C2×D414yes—
195C25#4114yes—
196C25#4114yes—
197C25C2412yes—
198C25C2411yescharacteristic
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—232no—
204C23×C4—22no—
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—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—28no—
218C23×C4—28no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
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—232no—
249C23×C4—28no—
250C23×C4—28no—
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—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—416no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—416no—
297C23×C4—416no—
298C23×C4—416no—
299C23×C4—416no—
300C23×C4C2×D414yes—
301C23×C4C2×D4116yes—
302C23×C4C2×D414yes—
303C23×C4#4114yes—
304C23×C4#4114yes—
305C23×C4#4114yes—
306C23×C4#4114yes—
307C23×C4#4114yes—
308C23×C4#4114yes—
309C23×C4#4114yes—
310C23×C4#4114yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—416no—
332C2×C4⋊C4—416no—
333C2×C22⋊C4—232no—
334C2×C22⋊C4—232no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—416no—
354C2×C22⋊C4—416no—
355C2×C22⋊C4—416no—
356C2×C22⋊C4—416no—
357C2×C42—28no—
358C2×C42—28no—
359C2×C42—28no—
360C2×C42—28no—
361C2×C42—44no—
362C2×C42—44no—
363C2×C42—416no—
364C2×C42—416no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—28no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389C24—28no—
390C24—28no—
391C24—28no—
392C24—28no—
393C24—28no—
394C24—28no—
395C24—28no—
396C24—28no—
397C24—28no—
398C24—28no—
399C24—28no—
400C24—28no—
401C24—28no—
402C24—28no—
403C24—28no—
404C24—28no—
405C24—28no—
406C24—28no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—44no—
420C24—44no—
421C24—44no—
422C24—44no—
423C24—44no—
424C24—44no—
425C24—44no—
426C24—44no—
427C24—44no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—44no—
432C24—44no—
433C24—44no—
434C24—44no—
435C24#123116yes—
436C24C22×D414yes—
437C24C22×D412yes—
438C24C2×#4114yes—
439C24C2×#4114yes—
440C24C2×#4112yes—
441C24C2×#4112yes—
442C24C2×#4112yes—
443C24C2×#4112yes—
444C24C2×#4112yes—
445C24C2×#4112yes—
446C24C2×#4112yes—
447C24C2×#4112yes—
448C24C2×#4112yes—
449C24C2×#4112yes—
450C24H(5,𝔽2)12yes—
451C24H(5,𝔽2)12yes—
452C24H(5,𝔽2)12yes—
453C242−1+412yes—
454C24C2511yescharacteristic
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—232no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
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—232no—
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—416no—
573C22×C4—416no—
574C22×C4—416no—
575C22×C4—416no—
576C22×C4—416no—
577C22×C4—4128no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4#123116yes—
649C22×C4C22×D414yes—
650C22×C4C22×D414yes—
651C22×C4C2×#4114yes—
652C22×C4C2×#4114yes—
653C22×C4C2×#4114yes—
654C22×C4C2×#4114yes—
655C22×C4C2×#4114yes—
656C22×C4C2×#4114yes—
657C22×C4C2×#4114yes—
658C22×C4C2×#4114yes—
659C4⋊C4—416no—
660C4⋊C4—416no—
661C22⋊C4—232no—
662C22⋊C4—232no—
663C22⋊C4—416no—
664C22⋊C4—416no—
665C22⋊C4—416no—
666C22⋊C4—416no—
667C42—416no—
668C42—416no—
669C23—232no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—232no—
689C23—232no—
690C23—416no—
691C23—416no—
692C23—416no—
693C23—416no—
694C23—416no—
695C23—416no—
696C23—416no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—416no—
714C23—416no—
715C23—416no—
716C23—416no—
717C23—416no—
718C23C2×#12318yes—
719C23C2×#12314yes—
720C23C2×#12314yes—
721C23#52514yes—
722C23#52514yes—
723C23#52914yes—
724C23#52914yes—
725C23#52914yes—
726C23#52914yes—
727C23#52914yes—
728C23#52914yes—
729C23#52914yes—
730C23#52914yes—
731C23#53214yes—
732C23#53414yes—
733C23#53714yes—
734C23#53814yes—
735C23#53914yes—
736C23#54014yes—
737C23#54214yes—
738C23#55114yes—
739C23#55114yes—
740C23#55114yes—
741C23#55114yes—
742C23#55114yes—
743C23#55114yes—
744C23#55114yes—
745C23#55214yes—
746C23#55214yes—
747C23#55214yes—
748C23#55314yes—
749C23#55314yes—
750C23#55314yes—
751C23#55514yes—
752C23#55614yes—
753C23#55914yes—
754C23C23×D411yescharacteristic
755C23C22×#4111yescharacteristic
756C23C22×#4111yescharacteristic
757C23C22×#4111yescharacteristic
758C23C22×#4111yescharacteristic
759C23C22×#4111yescharacteristic
760C23C22×#4111yescharacteristic
761C23C22×#4111yescharacteristic
762C23C22×#4111yescharacteristic
763C23C22×#4111yescharacteristic
764C23C22×#4111yescharacteristic
765C23C2×H(5,𝔽2)11yescharacteristic
766C23C2×H(5,𝔽2)11yescharacteristic
767C23C2×H(5,𝔽2)11yescharacteristic
768C23C2×2−1+411yescharacteristic
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—232no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—464no—
798C2×C4—416no—
799C2×C4—416no—
800C2×C4—416no—
801C2×C4—416no—
802C2×C4—416no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—416no—
832C2×C4—416no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—88no—
876C2×C4—88no—
877C2×C4—88no—
878C2×C4—88no—
879C2×C4—88no—
880C2×C4—88no—
881C2×C4C2×#12318yes—
882C22—28no—
883C22—28no—
884C22—28no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—464no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22#239518yes—
899C22#248318yes—
900C22#248518yes—
901C22#249818yes—
902C22#251518yes—
903C22#251618yes—
904C22#252618yes—
905C22#252718yes—
906C22#257218yes—
907C22#257318yes—
908C22#257518yes—
909C22#257618yes—
910C22#260218yes—
911C22#263018yes—
912C22#285318yes—
913C22C22×#12311yescharacteristic
914C22C22×#12311yescharacteristic
915C22C2×#52511yescharacteristic
916C22C2×#52511yescharacteristic
917C22C2×#52911yescharacteristic
918C22C2×#52911yescharacteristic
919C22C2×#52911yescharacteristic
920C22C2×#52911yescharacteristic
921C22C2×#52911yescharacteristic
922C22C2×#52911yescharacteristic
923C22C2×#52911yescharacteristic
924C22C2×#52911yescharacteristic
925C22C2×#53211yescharacteristic
926C22C2×#53411yescharacteristic
927C22C2×#53711yescharacteristic
928C22C2×#53811yescharacteristic
929C22C2×#53911yescharacteristic
930C22C2×#54011yescharacteristic
931C22C2×#54211yescharacteristic
932C22C2×#55111yescharacteristic
933C22C2×#55111yescharacteristic
934C22C2×#55111yescharacteristic
935C22C2×#55111yescharacteristic
936C22C2×#55111yescharacteristic
937C22C2×#55111yescharacteristic
938C22C2×#55111yescharacteristic
939C22C2×#55211yescharacteristic
940C22C2×#55211yescharacteristic
941C22C2×#55211yescharacteristic
942C22C2×#55311yescharacteristic
943C22C2×#55311yescharacteristic
944C22C2×#55311yescharacteristic
945C22C2×#55511yescharacteristic
946C22C2×#55611yescharacteristic
947C22C2×#55911yescharacteristic
948C4—28no—
949C4—44no—
950C4—44no—
951C4—44no—
952C4—44no—
953C4—44no—
954C4—44no—
955C4—44no—
956C4—82no—
957C4—82no—
958C4—82no—
959C4—82no—
960C4—82no—
961C4—82no—
962C2—48no—
963C2#15043116yesdirect product factor
964C2C2×#239511yescharacteristic
965C2C2×#263011yescharacteristic
966C2C2×#248311yescharacteristic
967C2C2×#251511yescharacteristic
968C2C2×#251611yescharacteristic
969C2C2×#248511yescharacteristic
970C2C2×#252611yescharacteristic
971C2C2×#252711yescharacteristic
972C2C2×#249811yescharacteristic
973C2C2×#257211yescharacteristic
974C2C2×#257311yescharacteristic
975C2C2×#257511yescharacteristic
976C2C2×#257611yescharacteristic
977C2C2×#260211yescharacteristic
978C2C2×#285311yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #15043C2direct (N × H)
4. C2×#1445C2semidirect
5. C2×#1443C2semidirect
6. C2×#1443C2semidirect
7. C2×#1442C2semidirect
12. C2×#1436C2semidirect
13. C2×#1436C2semidirect
14. C2×#1434C2semidirect
15. C2×#1434C2semidirect
56. #1445C22semidirect
57. #1443C22semidirect
58. #1443C22semidirect
59. #1442C22semidirect
64. #1436C22semidirect
65. #1436C22semidirect
66. #1434C22semidirect
67. #1434C22semidirect
963. C2#15043direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3812
C22×C4×C22⋊C42
#150432
C2×#14452
C2×#14432
C2×#14422
C2×#14402
C2×#14392
C2×#14362
C2×#14342
C2×C22⋊#952