Finite Group Databasebeta

← C2×#14817 #607759

Subgroups — C2×#14817 #607759

Order 512.

6610 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#394C211yesmaximal, characteristic
2C22×#393C211yesmaximal, characteristic, complemented
3C22×#393C211yesmaximal, characteristic, complemented
4C22×#391C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic
6C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7#14817C2116yesmaximal, direct product factor
8C2×#1443C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1440C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1437C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C22⋊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
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#394—28no—
35C2×#394C2218yes—
36C2×#393—28no—
37C2×#393—28no—
38C2×#393C2218yescomplemented
39C2×#393C2218yescomplemented
40C2×#391—28no—
41C2×#391C2218yescomplemented
42C2×#386—28no—
43C2×#386C2218yes—
44C2×C4×C22⋊C4—28no—
45C2×C4×C22⋊C4C2218yescomplemented
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
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1443C2218yescomplemented
65#1442C2218yescomplemented
66#1440C2218yescomplemented
67#1440C2218yescomplemented
68#1438C2218yes—
69#1437C2218yescomplemented
70#1437C2218yescomplemented
71#1434C2218yescomplemented
72C22⋊#95C2218yescomplemented
73C26C2311yescharacteristic
74C26C2311yescharacteristic
75C23×Q8—24no—
76C23×Q8—24no—
77C23×Q8—24no—
78C23×Q8—24no—
79C23×Q8—24no—
80C23×Q8—42no—
81C23×Q8—42no—
82C23×Q8C2314yes—
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—24no—
86C23×D4—24no—
87C23×D4—24no—
88C23×D4—42no—
89C23×D4—42no—
90C23×D4C2314yes—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—24no—
96C24×C4—42no—
97C24×C4—42no—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2314yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4C2314yes—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
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—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
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⋊C4D418yes—
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—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C42—24no—
161C22×C42—24no—
162C22×C42—24no—
163C22×C42—24no—
164C22×C42—42no—
165C22×C42—42no—
166C22×C42C2314yes—
167C22×C42C2314yes—
168#394—232no—
169#393—232no—
170#393—232no—
171#391—232no—
172#386—232no—
173C4×C22⋊C4—232no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—42no—
188C2×#95—42no—
189C2×#95—42no—
190C2×#95D418yes—
191C2×#95D418yescomplemented
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
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—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—22no—
235C25—22no—
236C25C2×D414yes—
237C25#4114yes—
238C25#4114yes—
239C25#4114yes—
240C25C2412yes—
241C25C2412yes—
242C25C2411yescharacteristic
243C22×Q8—232no—
244C22×Q8—28no—
245C22×Q8—28no—
246C22×Q8—28no—
247C22×Q8—28no—
248C22×Q8—28no—
249C22×Q8—44no—
250C22×Q8—44no—
251C22×Q8—416no—
252C22×Q8—416no—
253C22×Q8—416no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×D4—232no—
258C22×D4—28no—
259C22×D4—28no—
260C22×D4—28no—
261C22×D4—28no—
262C22×D4—28no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—416no—
266C22×D4—416no—
267C22×D4—416no—
268C22×D4—416no—
269C22×D4—416no—
270C22×D4—416no—
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—232no—
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—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—28no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
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—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—28no—
324C23×C4—28no—
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—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—28no—
354C23×C4—28no—
355C23×C4—44no—
356C23×C4—44no—
357C23×C4—416no—
358C23×C4—416no—
359C23×C4—416no—
360C23×C4—416no—
361C23×C4—416no—
362C23×C4—416no—
363C23×C4C2×D414yes—
364C23×C4C2×D414yes—
365C23×C4C2×D414yes—
366C23×C4C2×D414yes—
367C23×C4C2×D414yes—
368C23×C4C2×D414yes—
369C23×C4C2×D414yes—
370C23×C4C2×D414yes—
371C23×C4#4114yes—
372C23×C4#4114yes—
373C23×C4#4114yes—
374C23×C4#4114yes—
375C23×C4#4114yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—416no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—232no—
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—28no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—416no—
428C2×C22⋊C4—416no—
429C2×C22⋊C4—416no—
430C2×C22⋊C4—416no—
431C2×C22⋊C4—416no—
432C2×C22⋊C4—416no—
433C2×C22⋊C4—416no—
434C2×C22⋊C4—416no—
435C2×C22⋊C4—416no—
436C2×C22⋊C4C2×D4116yes—
437C2×C42—28no—
438C2×C42—28no—
439C2×C42—28no—
440C2×C42—28no—
441C2×C42—44no—
442C2×C42—44no—
443C2×C42—416no—
444C2×C42—416no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—28no—
455#95—28no—
456#95—28no—
457#95—28no—
458#95—44no—
459#95—44no—
460#95—44no—
461#95C2×D4116yes—
462#95C2×D4116yescomplemented
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—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—28no—
494C24—28no—
495C24—28no—
496C24—28no—
497C24—28no—
498C24—28no—
499C24—28no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
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—44no—
542C24—44no—
543C24—44no—
544C24—44no—
545C24—44no—
546C24—44no—
547C24—44no—
548C24—44no—
549C24—44no—
550C24—44no—
551C24—44no—
552C24—44no—
553C24—44no—
554C24—44no—
555C24—44no—
556C24—44no—
557C24—44no—
558C24#124116yes—
559C24C22×D414yes—
560C24C22×D412yes—
561C24C22×D412yes—
562C24C22×D412yes—
563C24C2×#4114yes—
564C24C2×#4114yes—
565C24C2×#4114yes—
566C24C2×#4112yes—
567C24C2×#4112yes—
568C24C2×#4112yes—
569C24C2×#4112yes—
570C24C2×#4112yes—
571C24C2×#4112yes—
572C24C2×#4112yes—
573C24C2×#4112yes—
574C24H(5,𝔽2)12yes—
575C24H(5,𝔽2)12yes—
576C24H(5,𝔽2)12yes—
577C242−1+412yes—
578C24C2511yescharacteristic
579C2×Q8—232no—
580C2×Q8—416no—
581C2×Q8—416no—
582C2×Q8—416no—
583C2×Q8—416no—
584C2×Q8—4128no—
585C2×Q8—416no—
586C2×Q8—416no—
587C2×D4—232no—
588C2×D4—416no—
589C2×D4—416no—
590C2×D4—416no—
591C2×D4—416no—
592C2×D4—416no—
593C2×D4—4128no—
594C2×D4—416no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
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—232no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—28no—
627C22×C4—28no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—28no—
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—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—416no—
708C22×C4—416no—
709C22×C4—416no—
710C22×C4—416no—
711C22×C4—416no—
712C22×C4—4128no—
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—416no—
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×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4#121116yes—
771C22×C4#124116yes—
772C22×C4C22×D414yes—
773C22×C4C22×D414yes—
774C22×C4C22×D414yes—
775C22×C4C22×D414yes—
776C22×C4C22×D414yes—
777C22×C4C22×D414yes—
778C22×C4C22×D414yes—
779C22×C4C22×D414yes—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4C2×#4114yes—
783C22×C4C2×#4114yes—
784C22×C4C2×#4114yes—
785C4⋊C4—416no—
786C22⋊C4—232no—
787C22⋊C4—232no—
788C22⋊C4—416no—
789C22⋊C4—416no—
790C22⋊C4—416no—
791C22⋊C4—416no—
792C22⋊C4—416no—
793C22⋊C4—416no—
794C22⋊C4—416no—
795C22⋊C4—416no—
796C22⋊C4—416no—
797C42—416no—
798C42—416no—
799C23—232no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—232no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—416no—
828C23—416no—
829C23—416no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—416no—
835C23—42no—
836C23—42no—
837C23—416no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—416no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—416no—
853C23—416no—
854C23—416no—
855C23—416no—
856C23—416no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—416no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—416no—
887C23—416no—
888C23—416no—
889C23—416no—
890C23—88no—
891C23—88no—
892C23—88no—
893C23—88no—
894C23—88no—
895C23—88no—
896C23—88no—
897C23—88no—
898C23C2×#12114yes—
899C23#52514yes—
900C23#52514yes—
901C23#52514yes—
902C23#52514yes—
903C23C2×#12418yes—
904C23C2×#12414yes—
905C23C2×#12414yes—
906C23#52914yes—
907C23#52914yes—
908C23#52914yes—
909C23#52914yes—
910C23#52914yes—
911C23#53214yes—
912C23#53814yes—
913C23#53814yes—
914C23#53814yes—
915C23#53914yes—
916C23#54214yes—
917C23#54214yes—
918C23D4214yes—
919C23D4214yes—
920C23#54614yes—
921C23#54614yes—
922C23#54614yes—
923C23#54614yes—
924C23#54614yes—
925C23#54714yes—
926C23#54814yes—
927C23#54814yes—
928C23#55114yes—
929C23#55114yes—
930C23#55114yes—
931C23#55214yes—
932C23#55514yes—
933C23#55914yes—
934C23C23×D411yescharacteristic
935C23C23×D411yescharacteristic
936C23C23×D411yescharacteristic
937C23C22×#4111yescharacteristic
938C23C22×#4111yescharacteristic
939C23C22×#4111yescharacteristic
940C23C22×#4111yescharacteristic
941C23C22×#4111yescharacteristic
942C23C22×#4111yescharacteristic
943C23C22×#4111yescharacteristic
944C23C22×#4111yescharacteristic
945C23C2×H(5,𝔽2)11yescharacteristic
946C23C2×H(5,𝔽2)11yescharacteristic
947C23C2×H(5,𝔽2)11yescharacteristic
948C23C2×2−1+411yescharacteristic
949Q8—464no—
950D4—464no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—232no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—232no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—464no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—416no—
995C2×C4—416no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—416no—
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—416no—
1019C2×C4—416no—
1020C2×C4—416no—
1021C2×C4—416no—
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—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—88no—
1051C2×C4—88no—
1052C2×C4—88no—
1053C2×C4—88no—
1054C2×C4C2×#12118yes—
1055C2×C4C2×#12418yes—
1056C22—28no—
1057C22—28no—
1058C22—28no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—464no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—82no—
1080C22—82no—
1081C22—82no—
1082C22—82no—
1083C22—82no—
1084C22—82no—
1085C22—82no—
1086C22—82no—
1087C22—832no—
1088C22#239818yes—
1089C22#242418yes—
1090C22#242718yes—
1091C22#245818yes—
1092C22#245918yes—
1093C22#246318yes—
1094C22#247218yes—
1095C22#247218yes—
1096C22#247718yes—
1097C22#248818yes—
1098C22#249118yes—
1099C22#255718yes—
1100C22#257218yes—
1101C22#265318yes—
1102C22#285018yes—
1103C22C22×#12111yescharacteristic
1104C22C2×#52511yescharacteristic
1105C22C2×#52511yescharacteristic
1106C22C2×#52511yescharacteristic
1107C22C2×#52511yescharacteristic
1108C22C22×#12411yescharacteristic
1109C22C22×#12411yescharacteristic
1110C22C2×#52911yescharacteristic
1111C22C2×#52911yescharacteristic
1112C22C2×#52911yescharacteristic
1113C22C2×#52911yescharacteristic
1114C22C2×#52911yescharacteristic
1115C22C2×#53211yescharacteristic
1116C22C2×#53811yescharacteristic
1117C22C2×#53811yescharacteristic
1118C22C2×#53811yescharacteristic
1119C22C2×#53911yescharacteristic
1120C22C2×#54211yescharacteristic
1121C22C2×#54211yescharacteristic
1122C22C2×D4211yescharacteristic
1123C22C2×D4211yescharacteristic
1124C22C2×#54611yescharacteristic
1125C22C2×#54611yescharacteristic
1126C22C2×#54611yescharacteristic
1127C22C2×#54611yescharacteristic
1128C22C2×#54611yescharacteristic
1129C22C2×#54711yescharacteristic
1130C22C2×#54811yescharacteristic
1131C22C2×#54811yescharacteristic
1132C22C2×#55111yescharacteristic
1133C22C2×#55111yescharacteristic
1134C22C2×#55111yescharacteristic
1135C22C2×#55211yescharacteristic
1136C22C2×#55511yescharacteristic
1137C22C2×#55911yescharacteristic
1138C4—28no—
1139C4—28no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—44no—
1146C4—44no—
1147C4—82no—
1148C4—82no—
1149C4—82no—
1150C4—82no—
1151C2—48no—
1152C2—84no—
1153C2#14817116yesdirect product factor
1154C2C2×#239811yescharacteristic
1155C2C2×#265311yescharacteristic
1156C2C2×#242411yescharacteristic
1157C2C2×#246311yescharacteristic
1158C2C2×#247211yescharacteristic
1159C2C2×#247211yescharacteristic
1160C2C2×#245911yescharacteristic
1161C2C2×#242711yescharacteristic
1162C2C2×#245811yescharacteristic
1163C2C2×#247711yescharacteristic
1164C2C2×#248811yescharacteristic
1165C2C2×#249111yescharacteristic
1166C2C2×#255711yescharacteristic
1167C2C2×#257211yescharacteristic
1168C2C2×#285011yescharacteristic
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
2. C22×#393C2semidirect
3. C22×#393C2semidirect
4. C22×#391C2semidirect
6. C22×C4×C22⋊C4C2semidirect
7. #14817C2direct (N × H)
8. C2×#1443C2semidirect
9. C2×#1442C2semidirect
10. C2×#1440C2semidirect
11. C2×#1440C2semidirect
13. C2×#1437C2semidirect
14. C2×#1437C2semidirect
15. C2×#1434C2semidirect
16. C2×C22⋊#95C2semidirect
38. C2×#393C22semidirect
39. C2×#393C22semidirect
41. C2×#391C22semidirect
45. C2×C4×C22⋊C4C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1440C22semidirect
67. #1440C22semidirect
69. #1437C22semidirect
70. #1437C22semidirect
71. #1434C22semidirect
72. C22⋊#95C22semidirect
191. C2×#95D4semidirect
462. #95C2×D4semidirect
1153. C2#14817direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3942
C22×#3932
C22×#3912
C22×#3862
C22×C4×C22⋊C42
#148172
C2×#14432
C2×#14422
C2×#14402
C2×#14382
C2×#14372
C2×#14342
C2×C22⋊#952