Finite Group Databasebeta

← C2×#14761 #607695

Subgroups — C2×#14761 #607695

Order 512.

7234 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic
2C22×#394C211yesmaximal, characteristic
3C22×#389C211yesmaximal, characteristic, complemented
4C22×#388C211yesmaximal, characteristic, complemented
5C22×#385C211yesmaximal, characteristic, complemented
6C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7#14761C2116yesmaximal, direct product factor
8C2×#1444C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1439C211yesmaximal, characteristic, complemented
14C2×#1438C211yesmaximal, characteristic
15C2×#1437C211yesmaximal, characteristic, complemented
16C2×#1436C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×#123—28no—
20C22×#123—28no—
21C22×#123—28no—
22C22×#123C2218yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C42C2211yescharacteristic
41C23×C42C2211yescharacteristic
42C2×#394—28no—
43C2×#394C2218yes—
44C2×#389—28no—
45C2×#389C2218yescomplemented
46C2×#388—28no—
47C2×#388C2218yescomplemented
48C2×#385—28no—
49C2×#385C2218yescomplemented
50C2×C4×C22⋊C4—28no—
51C2×C4×C22⋊C4C2218yescomplemented
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66#1444C2218yescomplemented
67#1442C2218yescomplemented
68#1440C2218yescomplemented
69#1439C2218yescomplemented
70#1439C2218yescomplemented
71#1439C2218yescomplemented
72#1438C2218yes—
73#1437C2218yescomplemented
74#1436C2218yescomplemented
75C26C2311yescharacteristic
76C26C2311yescharacteristic
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—42no—
83C23×D4—42no—
84C23×D4C2314yes—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4D418yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2314yes—
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C2×#123—2128no—
107C2×#123—232no—
108C2×#123—232no—
109C2×#123—232no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4—42no—
126C22×C4⋊C4—42no—
127C22×C4⋊C4D418yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
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—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—24no—
148C22×C22⋊C4—24no—
149C22×C22⋊C4—24no—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—24no—
158C22×C22⋊C4—24no—
159C22×C22⋊C4—24no—
160C22×C22⋊C4—24no—
161C22×C22⋊C4—24no—
162C22×C22⋊C4—24no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4D418yes—
166C22×C22⋊C4D418yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2314yes—
177C22×C22⋊C4C2314yes—
178C22×C42—24no—
179C22×C42—24no—
180C22×C42—24no—
181C22×C42—24no—
182C22×C42—42no—
183C22×C42—42no—
184C22×C42C2314yes—
185C22×C42C2314yes—
186#394—232no—
187#389—232no—
188#388—232no—
189#385—232no—
190C4×C22⋊C4—232no—
191C2×#95—24no—
192C2×#95—24no—
193C2×#95—24no—
194C2×#95—24no—
195C2×#95—24no—
196C2×#95—24no—
197C2×#95—24no—
198C2×#95—24no—
199C2×#95—24no—
200C2×#95—24no—
201C2×#95—24no—
202C2×#95—24no—
203C2×#95—24no—
204C2×#95—42no—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
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—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25—22no—
243C25—22no—
244C25—22no—
245C25C2×D414yes—
246C25C2×D414yes—
247C25C2×D414yes—
248C25#4114yes—
249C25C2412yes—
250C25C2412yes—
251C25C2411yescharacteristic
252C22×D4—232no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—28no—
256C22×D4—28no—
257C22×D4—28no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4—416no—
263C22×D4—416no—
264C22×D4—416no—
265C22×D4—416no—
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—232no—
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—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—28no—
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—232no—
332C23×C4—28no—
333C23×C4—28no—
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—416no—
349C23×C4—44no—
350C23×C4—44no—
351C23×C4—416no—
352C23×C4—416no—
353C23×C4—416no—
354C23×C4—416no—
355C23×C4C2×D414yes—
356C23×C4C2×D414yes—
357C23×C4C2×D414yes—
358C23×C4C2×D414yes—
359C23×C4C2×D414yes—
360C23×C4C2×D4116yes—
361C23×C4C2×D414yes—
362C23×C4C2×D414yes—
363C23×C4C2×D414yes—
364C23×C4C2×D414yes—
365C23×C4#4114yes—
366C23×C4#4114yes—
367C23×C4#4114yes—
368C23×C4#4114yes—
369C23×C4#4114yes—
370C23×C4#4114yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384#123—2256no—
385C2×C4⋊C4—232no—
386C2×C4⋊C4—232no—
387C2×C4⋊C4—232no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—28no—
398C2×C4⋊C4—28no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—416no—
406C2×C4⋊C4—416no—
407C2×C4⋊C4—416no—
408C2×C4⋊C4C2×D4116yes—
409C2×C22⋊C4—232no—
410C2×C22⋊C4—232no—
411C2×C22⋊C4—232no—
412C2×C22⋊C4—232no—
413C2×C22⋊C4—232no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—232no—
420C2×C22⋊C4—232no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—28no—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—28no—
438C2×C22⋊C4—28no—
439C2×C22⋊C4—28no—
440C2×C22⋊C4—28no—
441C2×C22⋊C4—28no—
442C2×C22⋊C4—28no—
443C2×C22⋊C4—28no—
444C2×C22⋊C4—28no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—416no—
448C2×C22⋊C4—416no—
449C2×C22⋊C4—416no—
450C2×C22⋊C4—416no—
451C2×C22⋊C4C2×D4116yes—
452C2×C22⋊C4C2×D4116yes—
453C2×C42—28no—
454C2×C42—28no—
455C2×C42—28no—
456C2×C42—28no—
457C2×C42—44no—
458C2×C42—44no—
459C2×C42—416no—
460C2×C42—416no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—28no—
469#95—28no—
470#95—28no—
471#95—28no—
472#95—28no—
473#95—28no—
474#95—44no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—28no—
485C24—28no—
486C24—28no—
487C24—28no—
488C24—28no—
489C24—28no—
490C24—28no—
491C24—28no—
492C24—28no—
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—28no—
506C24—28no—
507C24—28no—
508C24—28no—
509C24—28no—
510C24—28no—
511C24—28no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
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—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—44no—
564C24—44no—
565C24—44no—
566C24—44no—
567C24—44no—
568C24—44no—
569C24—44no—
570C24#121116yes—
571C24C22×D414yes—
572C24C22×D414yes—
573C24C22×D414yes—
574C24C22×D412yes—
575C24C22×D412yes—
576C24C22×D412yes—
577C24C22×D412yes—
578C24C2×#4114yes—
579C24C2×#4112yes—
580C24C2×#4112yes—
581C24C2×#4112yes—
582C24C2×#4112yes—
583C24C2×#4112yes—
584C24C2×#4112yes—
585C24C2×#4112yes—
586C24H(5,𝔽2)12yes—
587C24H(5,𝔽2)12yes—
588C242−1+412yes—
589C242−1+412yes—
590C24C2511yescharacteristic
591C2×D4—232no—
592C2×D4—416no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—416no—
596C2×D4—4128no—
597C2×D4—416no—
598C2×D4—416no—
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—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
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—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—232no—
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—28no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
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—232no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—416no—
717C22×C4—4128no—
718C22×C4—416no—
719C22×C4—416no—
720C22×C4—416no—
721C22×C4—416no—
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×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4#120116yes—
773C22×C4#123116yescomplemented
774C22×C4C22×D414yes—
775C22×C4C22×D414yes—
776C22×C4C22×D414yes—
777C22×C4C22×D414yes—
778C22×C4C22×D414yes—
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C22×D414yes—
782C22×C4C22×D414yes—
783C22×C4C2×#4114yes—
784C22×C4C2×#4114yes—
785C22×C4C2×#4114yes—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C4C2×#4114yes—
789C4⋊C4—232no—
790C4⋊C4—232no—
791C4⋊C4—232no—
792C4⋊C4—416no—
793C4⋊C4—416no—
794C4⋊C4—416no—
795C22⋊C4—232no—
796C22⋊C4—232no—
797C22⋊C4—232no—
798C22⋊C4—232no—
799C22⋊C4—232no—
800C22⋊C4—232no—
801C22⋊C4—232no—
802C22⋊C4—416no—
803C22⋊C4—416no—
804C22⋊C4—416no—
805C22⋊C4—416no—
806C42—416no—
807C42—416no—
808C23—232no—
809C23—24no—
810C23—232no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—232no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—416no—
837C23—416no—
838C23—416no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—416no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—416no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—416no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—416no—
858C23—42no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—42no—
866C23—416no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—416no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—416no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—416no—
896C23—42no—
897C23—416no—
898C23—416no—
899C23—88no—
900C23—88no—
901C23—88no—
902C23—88no—
903C23—88no—
904C23—88no—
905C23—88no—
906C23—88no—
907C23C2×#12014yes—
908C23C2×#12118yes—
909C23C2×#12114yes—
910C23C2×#12314yes—
911C23#52514yes—
912C23#52514yes—
913C23#52514yes—
914C23#52514yes—
915C23#52914yes—
916C23#52914yes—
917C23#53214yes—
918C23#53214yes—
919C23#53214yes—
920C23#53214yes—
921C23#53414yes—
922C23#53614yes—
923C23#53914yes—
924C23#53914yes—
925C23#54214yes—
926C23#54214yes—
927C23D4214yes—
928C23D4214yes—
929C23#54614yes—
930C23#54614yes—
931C23#54714yes—
932C23#54714yes—
933C23#54714yes—
934C23#54714yes—
935C23#54814yes—
936C23#54814yes—
937C23#55114yes—
938C23#55214yes—
939C23#55214yes—
940C23#55314yes—
941C23#55314yes—
942C23#55914yes—
943C23C23×D411yescharacteristic
944C23C23×D411yescharacteristic
945C23C23×D411yescharacteristic
946C23C23×D411yescharacteristic
947C23C22×#4111yescharacteristic
948C23C22×#4111yescharacteristic
949C23C22×#4111yescharacteristic
950C23C22×#4111yescharacteristic
951C23C22×#4111yescharacteristic
952C23C22×#4111yescharacteristic
953C23C22×#4111yescharacteristic
954C23C2×H(5,𝔽2)11yescharacteristic
955C23C2×H(5,𝔽2)11yescharacteristic
956C23C2×2−1+411yescharacteristic
957C23C2×2−1+411yescharacteristic
958D4—464no—
959C2×C4—24no—
960C2×C4—232no—
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—232no—
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—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—464no—
1001C2×C4—416no—
1002C2×C4—416no—
1003C2×C4—416no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—416no—
1007C2×C4—416no—
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—416no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—416no—
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—416no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—416no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—88no—
1061C2×C4—88no—
1062C2×C4C2×#12018yes—
1063C2×C4C2×#12318yescomplemented
1064C22—28no—
1065C22—28no—
1066C22—28no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—464no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—82no—
1088C22—82no—
1089C22—82no—
1090C22—82no—
1091C22—82no—
1092C22—82no—
1093C22—82no—
1094C22—832no—
1095C22—82no—
1096C22#238818yes—
1097C22#241018yes—
1098C22#241318yes—
1099C22#242218yes—
1100C22#243218yes—
1101C22#244318yes—
1102C22#245518yes—
1103C22#245818yes—
1104C22#246118yes—
1105C22#247018yes—
1106C22#255318yes—
1107C22#255818yes—
1108C22#260218yes—
1109C22#266318yes—
1110C22#285418yes—
1111C22C22×#12011yescharacteristic
1112C22C22×#12111yescharacteristic
1113C22C22×#12311yescharacteristic
1114C22C2×#52511yescharacteristic
1115C22C2×#52511yescharacteristic
1116C22C2×#52511yescharacteristic
1117C22C2×#52511yescharacteristic
1118C22C2×#52911yescharacteristic
1119C22C2×#52911yescharacteristic
1120C22C2×#53211yescharacteristic
1121C22C2×#53211yescharacteristic
1122C22C2×#53211yescharacteristic
1123C22C2×#53211yescharacteristic
1124C22C2×#53411yescharacteristic
1125C22C2×#53611yescharacteristic
1126C22C2×#53911yescharacteristic
1127C22C2×#53911yescharacteristic
1128C22C2×#54211yescharacteristic
1129C22C2×#54211yescharacteristic
1130C22C2×D4211yescharacteristic
1131C22C2×D4211yescharacteristic
1132C22C2×#54611yescharacteristic
1133C22C2×#54611yescharacteristic
1134C22C2×#54711yescharacteristic
1135C22C2×#54711yescharacteristic
1136C22C2×#54711yescharacteristic
1137C22C2×#54711yescharacteristic
1138C22C2×#54811yescharacteristic
1139C22C2×#54811yescharacteristic
1140C22C2×#55111yescharacteristic
1141C22C2×#55211yescharacteristic
1142C22C2×#55211yescharacteristic
1143C22C2×#55311yescharacteristic
1144C22C2×#55311yescharacteristic
1145C22C2×#55911yescharacteristic
1146C4—28no—
1147C4—28no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—44no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—44no—
1157C4—82no—
1158C4—82no—
1159C2—48no—
1160C2—84no—
1161C2#14761116yesdirect product factor
1162C2C2×#238811yescharacteristic
1163C2C2×#266311yescharacteristic
1164C2C2×#241011yescharacteristic
1165C2C2×#244311yescharacteristic
1166C2C2×#245511yescharacteristic
1167C2C2×#246111yescharacteristic
1168C2C2×#242211yescharacteristic
1169C2C2×#245811yescharacteristic
1170C2C2×#243211yescharacteristic
1171C2C2×#247011yescharacteristic
1172C2C2×#241311yescharacteristic
1173C2C2×#255311yescharacteristic
1174C2C2×#255811yescharacteristic
1175C2C2×#260211yescharacteristic
1176C2C2×#285411yescharacteristic
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×#389C2semidirect
4. C22×#388C2semidirect
5. C22×#385C2semidirect
6. C22×C4×C22⋊C4C2semidirect
7. #14761C2direct (N × H)
8. C2×#1444C2semidirect
9. C2×#1442C2semidirect
10. C2×#1440C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
13. C2×#1439C2semidirect
15. C2×#1437C2semidirect
16. C2×#1436C2semidirect
45. C2×#389C22semidirect
47. C2×#388C22semidirect
49. C2×#385C22semidirect
51. C2×C4×C22⋊C4C22semidirect
66. #1444C22semidirect
67. #1442C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
73. #1437C22semidirect
74. #1436C22semidirect
773. C22×C4#123semidirect
1063. C2×C4C2×#123semidirect
1161. C2#14761direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1232
C22×#3942
C22×#3892
C22×#3882
C22×#3852
C22×C4×C22⋊C42
#147612
C2×#14442
C2×#14422
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362