Finite Group Databasebeta

← C2×#15631 #609249

Subgroups — C2×#15631 #609249

Order 512.

5922 conjugacy classes of subgroups.

The subgroup lattice has 1160 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×#390C211yesmaximal, characteristic
6C22×#388C211yesmaximal, characteristic, complemented
7#15631C2116yesmaximal, direct product factor
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1440C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1438C211yesmaximal, characteristic
14C2×#1437C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×#1436C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C23×C4⋊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
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#394—28no—
37C2×#394C2218yes—
38C2×#393—28no—
39C2×#393—28no—
40C2×#393C2218yescomplemented
41C2×#393C2218yescomplemented
42C2×#391—28no—
43C2×#391C2218yescomplemented
44C2×#390—28no—
45C2×#390C2218yes—
46C2×#388—28no—
47C2×#388C2218yescomplemented
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#1441C2218yescomplemented
65#1440C2218yescomplemented
66#1440C2218yescomplemented
67#1440C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1437C2218yescomplemented
71#1436C2218yescomplemented
72#1436C2218yescomplemented
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×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
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—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⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
151C22×C22⋊C4D418yes—
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×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C42—24no—
165C22×C42—24no—
166C22×C42—24no—
167C22×C42—42no—
168C22×C42—42no—
169C22×C42—42no—
170C22×C42C2314yes—
171C22×C42C2314yes—
172#394—232no—
173#393—232no—
174#393—232no—
175#391—232no—
176#390—232no—
177#388—232no—
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—24no—
188C2×#95—24no—
189C2×#95—42no—
190C2×#95—42no—
191C2×#95—42no—
192C2×#95D418yes—
193C2×#95D418yescomplemented
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—
236C25—22no—
237C25—22no—
238C25C2×D414yes—
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—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—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
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—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—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×C4C2×D414yes—
350C23×C4C2×D414yes—
351C23×C4C2×D414yes—
352C23×C4C2×D414yes—
353C23×C4C2×D414yes—
354C23×C4C2×D414yes—
355C23×C4C2×D414yes—
356C23×C4C2×D414yes—
357C23×C4#4114yes—
358C23×C4#4114yes—
359C23×C4#4114yes—
360C23×C4#4114yes—
361C23×C4#4114yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—416no—
385C2×C4⋊C4—416no—
386C2×C4⋊C4—416no—
387C2×C22⋊C4—232no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
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—28no—
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—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—416no—
424C2×C22⋊C4—416no—
425C2×C22⋊C4—416no—
426C2×C22⋊C4—416no—
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⋊C4C2×D4116yes—
435C2×C42—28no—
436C2×C42—28no—
437C2×C42—28no—
438C2×C42—44no—
439C2×C42—44no—
440C2×C42—44no—
441C2×C42—416no—
442C2×C42—416no—
443#95—28no—
444#95—28no—
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—44no—
455#95—44no—
456#95—44no—
457#95C2×D4116yes—
458#95C2×D4116yescomplemented
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—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
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—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—44no—
502C24—44no—
503C24—44no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—44no—
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—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—
557C24C22×D414yes—
558C24C22×D412yes—
559C24C22×D412yes—
560C24C22×D412yes—
561C24C2×#4114yes—
562C24C2×#4112yes—
563C24C2×#4112yes—
564C24C2×#4112yes—
565C24C2×#4112yes—
566C24C2×#4112yes—
567C24C2×#4112yes—
568C24H(5,𝔽2)12yes—
569C24H(5,𝔽2)12yes—
570C24H(5,𝔽2)12yes—
571C24H(5,𝔽2)12yes—
572C242−1+412yes—
573C242−1+412yes—
574C24C2511yescharacteristic
575C2×Q8—232no—
576C2×Q8—416no—
577C2×Q8—416no—
578C2×Q8—416no—
579C2×Q8—416no—
580C2×Q8—4128no—
581C2×Q8—416no—
582C2×Q8—416no—
583C2×D4—232no—
584C2×D4—416no—
585C2×D4—416no—
586C2×D4—416no—
587C2×D4—416no—
588C2×D4—416no—
589C2×D4—4128no—
590C2×D4—416no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
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—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—28no—
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—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—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—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#121116yes—
759C22×C4#124116yes—
760C22×C4C22×D414yes—
761C22×C4C22×D414yes—
762C22×C4C22×D414yes—
763C22×C4C22×D414yes—
764C22×C4C22×D414yes—
765C22×C4C22×D414yes—
766C22×C4C22×D414yes—
767C22×C4C22×D414yes—
768C22×C4C2×#4114yes—
769C22×C4C2×#4114yes—
770C22×C4C2×#4114yes—
771C22×C4C2×#4114yes—
772C22×C4C2×#4114yes—
773C4⋊C4—416no—
774C4⋊C4—416no—
775C4⋊C4—416no—
776C22⋊C4—232no—
777C22⋊C4—416no—
778C22⋊C4—416no—
779C22⋊C4—416no—
780C22⋊C4—416no—
781C22⋊C4—416no—
782C22⋊C4—416no—
783C22⋊C4—416no—
784C22⋊C4—416no—
785C22⋊C4—416no—
786C22⋊C4—416no—
787C22⋊C4—416no—
788C42—416no—
789C42—416no—
790C23—24no—
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—416no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—416no—
811C23—416no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—416no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—416no—
820C23—42no—
821C23—42no—
822C23—416no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—416no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—416no—
864C23—416no—
865C23—416no—
866C23—416no—
867C23—416no—
868C23—416no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—416no—
874C23—88no—
875C23—88no—
876C23—88no—
877C23—88no—
878C23—88no—
879C23—88no—
880C23—88no—
881C23—88no—
882C23—88no—
883C23—88no—
884C23—88no—
885C23—88no—
886C23—88no—
887C23—88no—
888C23—88no—
889C23—88no—
890C23C2×#12114yes—
891C23#52514yes—
892C23#52514yes—
893C23C2×#12414yes—
894C23#52914yes—
895C23#53214yes—
896C23#53514yes—
897C23#53614yes—
898C23#53714yes—
899C23#53814yes—
900C23#53814yes—
901C23#53814yes—
902C23#53914yes—
903C23#54214yes—
904C23#54214yes—
905C23D4214yes—
906C23D4214yes—
907C23#54614yes—
908C23#54614yes—
909C23#54614yes—
910C23#54614yes—
911C23#54614yes—
912C23#54714yes—
913C23#54814yes—
914C23#54814yes—
915C23#55114yes—
916C23#55214yes—
917C23#55514yes—
918C23#55614yes—
919C23#55614yes—
920C23#55914yes—
921C23#55914yes—
922C23#55914yes—
923C23#56214yes—
924C23#56214yes—
925C23C23×D411yescharacteristic
926C23C23×D411yescharacteristic
927C23C23×D411yescharacteristic
928C23C22×#4111yescharacteristic
929C23C22×#4111yescharacteristic
930C23C22×#4111yescharacteristic
931C23C22×#4111yescharacteristic
932C23C22×#4111yescharacteristic
933C23C22×#4111yescharacteristic
934C23C2×H(5,𝔽2)11yescharacteristic
935C23C2×H(5,𝔽2)11yescharacteristic
936C23C2×H(5,𝔽2)11yescharacteristic
937C23C2×H(5,𝔽2)11yescharacteristic
938C23C2×2−1+411yescharacteristic
939C23C2×2−1+411yescharacteristic
940Q8—464no—
941D4—464no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—232no—
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—232no—
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—24no—
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—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—416no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—416no—
986C2×C4—416no—
987C2×C4—42no—
988C2×C4—416no—
989C2×C4—42no—
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—416no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—42no—
1007C2×C4—416no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—416no—
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—42no—
1035C2×C4—42no—
1036C2×C4—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—88no—
1041C2×C4—88no—
1042C2×C4—88no—
1043C2×C4—88no—
1044C2×C4C2×#12118yes—
1045C2×C4C2×#12418yes—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—82no—
1061C22—832no—
1062C22—832no—
1063C22—82no—
1064C22—82no—
1065C22—82no—
1066C22—82no—
1067C22—82no—
1068C22—82no—
1069C22—82no—
1070C22—82no—
1071C22—82no—
1072C22—82no—
1073C22—82no—
1074C22—82no—
1075C22—82no—
1076C22—82no—
1077C22—82no—
1078C22#241518yes—
1079C22#242418yes—
1080C22#245818yes—
1081C22#245918yes—
1082C22#247218yes—
1083C22#249118yes—
1084C22#254418yes—
1085C22#256018yes—
1086C22#259218yes—
1087C22#267618yes—
1088C22#268118yes—
1089C22#270018yes—
1090C22#271018yes—
1091C22#275118yes—
1092C22#280818yes—
1093C22C22×#12111yescharacteristic
1094C22C2×#52511yescharacteristic
1095C22C2×#52511yescharacteristic
1096C22C22×#12411yescharacteristic
1097C22C2×#52911yescharacteristic
1098C22C2×#53211yescharacteristic
1099C22C2×#53511yescharacteristic
1100C22C2×#53611yescharacteristic
1101C22C2×#53711yescharacteristic
1102C22C2×#53811yescharacteristic
1103C22C2×#53811yescharacteristic
1104C22C2×#53811yescharacteristic
1105C22C2×#53911yescharacteristic
1106C22C2×#54211yescharacteristic
1107C22C2×#54211yescharacteristic
1108C22C2×D4211yescharacteristic
1109C22C2×D4211yescharacteristic
1110C22C2×#54611yescharacteristic
1111C22C2×#54611yescharacteristic
1112C22C2×#54611yescharacteristic
1113C22C2×#54611yescharacteristic
1114C22C2×#54611yescharacteristic
1115C22C2×#54711yescharacteristic
1116C22C2×#54811yescharacteristic
1117C22C2×#54811yescharacteristic
1118C22C2×#55111yescharacteristic
1119C22C2×#55211yescharacteristic
1120C22C2×#55511yescharacteristic
1121C22C2×#55611yescharacteristic
1122C22C2×#55611yescharacteristic
1123C22C2×#55911yescharacteristic
1124C22C2×#55911yescharacteristic
1125C22C2×#55911yescharacteristic
1126C22C2×#56211yescharacteristic
1127C22C2×#56211yescharacteristic
1128C4—28no—
1129C4—28no—
1130C4—44no—
1131C4—44no—
1132C4—44no—
1133C4—44no—
1134C4—44no—
1135C4—44no—
1136C4—44no—
1137C4—82no—
1138C4—82no—
1139C4—82no—
1140C4—82no—
1141C2—84no—
1142C2—84no—
1143C2#15631116yesdirect product factor
1144C2C2×#242411yescharacteristic
1145C2C2×#247211yescharacteristic
1146C2C2×#245911yescharacteristic
1147C2C2×#245811yescharacteristic
1148C2C2×#241511yescharacteristic
1149C2C2×#249111yescharacteristic
1150C2C2×#256011yescharacteristic
1151C2C2×#254411yescharacteristic
1152C2C2×#259211yescharacteristic
1153C2C2×#267611yescharacteristic
1154C2C2×#268111yescharacteristic
1155C2C2×#270011yescharacteristic
1156C2C2×#271011yescharacteristic
1157C2C2×#275111yescharacteristic
1158C2C2×#280811yescharacteristic
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×#388C2semidirect
7. #15631C2direct (N × H)
8. C2×#1441C2semidirect
9. C2×#1440C2semidirect
10. C2×#1440C2semidirect
11. C2×#1440C2semidirect
12. C2×#1439C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×#1436C2semidirect
40. C2×#393C22semidirect
41. C2×#393C22semidirect
43. C2×#391C22semidirect
47. C2×#388C22semidirect
64. #1441C22semidirect
65. #1440C22semidirect
66. #1440C22semidirect
67. #1440C22semidirect
68. #1439C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. #1436C22semidirect
193. C2×#95D4semidirect
458. #95C2×D4semidirect
1143. C2#15631direct (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×#3902
C22×#3882
#156312
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362