Finite Group Databasebeta

← C2×#14999 #608049

Subgroups — C2×#14999 #608049

Order 512.

5734 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C211yesmaximal, characteristic, complemented
2C22×#394C211yesmaximal, characteristic
3C22×#390C211yesmaximal, characteristic
4C22×#388C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6C22×#388C211yesmaximal, characteristic, complemented
7#14999C2116yesmaximal, direct product factor
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1438C211yesmaximal, characteristic
14C2×#1437C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C4×#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊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×C22⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C23×C42C2211yescharacteristic
37C23×C42C2211yescharacteristic
38C2×#398—28no—
39C2×#398C2218yescomplemented
40C2×#394—28no—
41C2×#394C2218yes—
42C2×#390—28no—
43C2×#390C2218yes—
44C2×#388—28no—
45C2×#388—28no—
46C2×#388—28no—
47C2×#388C2218yescomplemented
48C2×#388C2218yescomplemented
49C2×#388C2218yescomplemented
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#1439C2218yescomplemented
67#1439C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1437C2218yescomplemented
71#1436C2218yescomplemented
72C4×#95C2218yescomplemented
73C26C2311yescharacteristic
74C26C2311yescharacteristic
75C23×D4—24no—
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—42no—
81C23×D4—42no—
82C23×D4C2314yes—
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
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—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
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—24no—
168C22×C42—24no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—42no—
172C22×C42—42no—
173C22×C42C2314yes—
174C22×C42C2314yes—
175C22×C42C2314yes—
176#398—232no—
177#394—232no—
178#390—232no—
179#388—232no—
180#388—232no—
181#388—232no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—42no—
193C2×#95—42no—
194C2×#95D418yes—
195C2×#95D418yescomplemented
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×D4—232no—
244C22×D4—28no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—28no—
248C22×D4—28no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4—416no—
255C22×D4—416no—
256C22×D4—416no—
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—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×C4C2×D414yes—
334C23×C4C2×D414yes—
335C23×C4C2×D414yes—
336C23×C4C2×D414yes—
337C23×C4C2×D414yes—
338C23×C4C2×D414yes—
339C23×C4C2×D414yes—
340C23×C4C2×D414yes—
341C23×C4#4114yes—
342C23×C4#4114yes—
343C23×C4#4114yes—
344C23×C4#4114yes—
345C23×C4#4114yes—
346C23×C4#4114yes—
347C23×C4#4114yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—416no—
377C2×C4⋊C4—416no—
378C2×C4⋊C4—416no—
379C2×C4⋊C4—416no—
380C2×C4⋊C4—416no—
381C2×C22⋊C4—232no—
382C2×C22⋊C4—232no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—232no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
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—416no—
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⋊C4C2×D4116yes—
429C2×C42—28no—
430C2×C42—28no—
431C2×C42—28no—
432C2×C42—28no—
433C2×C42—28no—
434C2×C42—28no—
435C2×C42—28no—
436C2×C42—44no—
437C2×C42—44no—
438C2×C42—416no—
439C2×C42—416no—
440C2×C42—416no—
441#95—28no—
442#95—28no—
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—44no—
452#95—44no—
453#95C2×D4116yes—
454#95C2×D4116yescomplemented
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—22no—
470C24—22no—
471C24—22no—
472C24—22no—
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—44no—
498C24—44no—
499C24—44no—
500C24—44no—
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—
553C24C22×D414yes—
554C24C22×D412yes—
555C24C22×D412yes—
556C24C22×D412yes—
557C24C2×#4114yes—
558C24C2×#4112yes—
559C24C2×#4112yes—
560C24C2×#4112yes—
561C24C2×#4112yes—
562C24C2×#4112yes—
563C24C2×#4112yes—
564C24C2×#4112yes—
565C24C2×#4112yes—
566C24H(5,𝔽2)12yes—
567C24H(5,𝔽2)12yes—
568C24H(5,𝔽2)12yes—
569C242−1+412yes—
570C24C2511yescharacteristic
571C2×D4—232no—
572C2×D4—416no—
573C2×D4—416no—
574C2×D4—416no—
575C2×D4—416no—
576C2×D4—416no—
577C2×D4—4128no—
578C2×D4—416no—
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—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
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—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—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—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—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#121116yes—
745C22×C4#124116yes—
746C22×C4C22×D414yes—
747C22×C4C22×D414yes—
748C22×C4C22×D414yes—
749C22×C4C22×D414yes—
750C22×C4C22×D414yes—
751C22×C4C22×D414yes—
752C22×C4C22×D414yes—
753C22×C4C22×D414yes—
754C22×C4C2×#4114yes—
755C22×C4C2×#4114yes—
756C22×C4C2×#4114yes—
757C22×C4C2×#4114yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C4⋊C4—416no—
762C4⋊C4—416no—
763C4⋊C4—416no—
764C4⋊C4—416no—
765C4⋊C4—416no—
766C22⋊C4—232no—
767C22⋊C4—232no—
768C22⋊C4—232no—
769C22⋊C4—416no—
770C22⋊C4—416no—
771C22⋊C4—416no—
772C22⋊C4—416no—
773C22⋊C4—416no—
774C22⋊C4—416no—
775C22⋊C4—416no—
776C22⋊C4—416no—
777C22⋊C4—416no—
778C42—416no—
779C42—416no—
780C42—416no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—416no—
796C23—416no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—416no—
818C23—42no—
819C23—42no—
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—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—416no—
856C23—416no—
857C23—416no—
858C23—416no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—88no—
866C23—88no—
867C23—88no—
868C23—88no—
869C23—88no—
870C23—88no—
871C23—88no—
872C23—88no—
873C23—88no—
874C23—88no—
875C23—88no—
876C23—88no—
877C23—88no—
878C23—88no—
879C23—88no—
880C23—88no—
881C23C2×#12114yes—
882C23#52514yes—
883C23#52514yes—
884C23#52514yes—
885C23C2×#12414yes—
886C23#52914yes—
887C23#52914yes—
888C23#52914yes—
889C23#52914yes—
890C23#52914yes—
891C23#53214yes—
892C23#53214yes—
893C23#53214yes—
894C23#53814yes—
895C23#53914yes—
896C23#54014yes—
897C23#54014yes—
898C23#54214yes—
899C23#54214yes—
900C23D4214yes—
901C23D4214yes—
902C23#54614yes—
903C23#54614yes—
904C23#54614yes—
905C23#54614yes—
906C23#54714yes—
907C23#54714yes—
908C23#54814yes—
909C23#55014yes—
910C23#55114yes—
911C23#55114yes—
912C23#55214yes—
913C23#55314yes—
914C23#55314yes—
915C23#55514yes—
916C23C23×D411yescharacteristic
917C23C23×D411yescharacteristic
918C23C23×D411yescharacteristic
919C23C22×#4111yescharacteristic
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
930C23C2×2−1+411yescharacteristic
931D4—464no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—232no—
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—232no—
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—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—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—416no—
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—416no—
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—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—416no—
1013C2×C4—416no—
1014C2×C4—416no—
1015C2×C4—416no—
1016C2×C4—416no—
1017C2×C4—416no—
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—88no—
1033C2×C4—88no—
1034C2×C4C2×#12118yes—
1035C2×C4C2×#12418yes—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—44no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—82no—
1055C22—82no—
1056C22—82no—
1057C22—82no—
1058C22—82no—
1059C22—82no—
1060C22—82no—
1061C22—832no—
1062C22—832no—
1063C22—82no—
1064C22—82no—
1065C22—82no—
1066C22—82no—
1067C22—82no—
1068C22#239218yes—
1069C22#242518yes—
1070C22#242818yes—
1071C22#246118yes—
1072C22#246418yes—
1073C22#246818yes—
1074C22#247218yes—
1075C22#247618yes—
1076C22#247918yes—
1077C22#249118yes—
1078C22#253118yes—
1079C22#255418yes—
1080C22#255818yes—
1081C22#265118yes—
1082C22#286118yes—
1083C22C22×#12111yescharacteristic
1084C22C2×#52511yescharacteristic
1085C22C2×#52511yescharacteristic
1086C22C2×#52511yescharacteristic
1087C22C22×#12411yescharacteristic
1088C22C2×#52911yescharacteristic
1089C22C2×#52911yescharacteristic
1090C22C2×#52911yescharacteristic
1091C22C2×#52911yescharacteristic
1092C22C2×#52911yescharacteristic
1093C22C2×#53211yescharacteristic
1094C22C2×#53211yescharacteristic
1095C22C2×#53211yescharacteristic
1096C22C2×#53811yescharacteristic
1097C22C2×#53911yescharacteristic
1098C22C2×#54011yescharacteristic
1099C22C2×#54011yescharacteristic
1100C22C2×#54211yescharacteristic
1101C22C2×#54211yescharacteristic
1102C22C2×D4211yescharacteristic
1103C22C2×D4211yescharacteristic
1104C22C2×#54611yescharacteristic
1105C22C2×#54611yescharacteristic
1106C22C2×#54611yescharacteristic
1107C22C2×#54611yescharacteristic
1108C22C2×#54711yescharacteristic
1109C22C2×#54711yescharacteristic
1110C22C2×#54811yescharacteristic
1111C22C2×#55011yescharacteristic
1112C22C2×#55111yescharacteristic
1113C22C2×#55111yescharacteristic
1114C22C2×#55211yescharacteristic
1115C22C2×#55311yescharacteristic
1116C22C2×#55311yescharacteristic
1117C22C2×#55511yescharacteristic
1118C4—28no—
1119C4—28no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—82no—
1130C4—82no—
1131C2—84no—
1132C2—84no—
1133C2#14999116yesdirect product factor
1134C2C2×#239211yescharacteristic
1135C2C2×#265111yescharacteristic
1136C2C2×#247211yescharacteristic
1137C2C2×#242511yescharacteristic
1138C2C2×#246411yescharacteristic
1139C2C2×#246111yescharacteristic
1140C2C2×#242811yescharacteristic
1141C2C2×#246811yescharacteristic
1142C2C2×#247611yescharacteristic
1143C2C2×#247911yescharacteristic
1144C2C2×#249111yescharacteristic
1145C2C2×#253111yescharacteristic
1146C2C2×#255411yescharacteristic
1147C2C2×#255811yescharacteristic
1148C2C2×#286111yescharacteristic
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
1. C22×#398C2semidirect
4. C22×#388C2semidirect
5. C22×#388C2semidirect
6. C22×#388C2semidirect
7. #14999C2direct (N × H)
8. C2×#1441C2semidirect
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×C4×#95C2semidirect
39. C2×#398C22semidirect
47. C2×#388C22semidirect
48. C2×#388C22semidirect
49. C2×#388C22semidirect
64. #1441C22semidirect
65. #1440C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. C4×#95C22semidirect
195. C2×#95D4semidirect
454. #95C2×D4semidirect
1133. C2#14999direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3982
C22×#3942
C22×#3902
C22×#3882
#149992
C2×#14412
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C4×#952