Finite Group Databasebeta

← C2×#15476 #609049

Subgroups — C2×#15476 #609049

Order 512.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#395C211yesmaximal, characteristic, complemented
2C22×#393C211yesmaximal, characteristic, complemented
3C22×#393C211yesmaximal, characteristic, complemented
4C22×#390C211yesmaximal, characteristic
5C22×#386C211yesmaximal, characteristic
6C22×#380C211yesmaximal, characteristic, complemented
7#15476C2116yesmaximal, direct product factor
8C2×#1442C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1438C211yesmaximal, characteristic
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1434C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊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
36C2×#395—28no—
37C2×#395C2218yescomplemented
38C2×#393—28no—
39C2×#393—28no—
40C2×#393C2218yescomplemented
41C2×#393C2218yescomplemented
42C2×#390—28no—
43C2×#390C2218yes—
44C2×#386—28no—
45C2×#386C2218yes—
46C2×#380—28no—
47C2×#380C2218yescomplemented
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#1442C2218yescomplemented
65#1439C2218yescomplemented
66#1439C2218yescomplemented
67#1439C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1436C2218yescomplemented
71#1434C2218yescomplemented
72C22⋊#95C2218yescomplemented
73C26C2311yescharacteristic
74C26C2311yescharacteristic
75C23×Q8—24no—
76C23×Q8—24no—
77C23×Q8—24no—
78C23×Q8—42no—
79C23×Q8—42no—
80C23×Q8—42no—
81C23×Q8—42no—
82C23×Q8C2314yes—
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—24no—
86C23×D4—24no—
87C23×D4—42no—
88C23×D4—42no—
89C23×D4Q818yescomplemented
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—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
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—24no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4—42no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
151C22×C22⋊C4—42no—
152C22×C22⋊C4—42no—
153C22×C22⋊C4—42no—
154C22×C22⋊C4—42no—
155C22×C22⋊C4—42no—
156C22×C22⋊C4—42no—
157C22×C22⋊C4—42no—
158C22×C22⋊C4—42no—
159C22×C22⋊C4—42no—
160C22×C22⋊C4D418yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C42—24no—
173C22×C42—24no—
174C22×C42—42no—
175C22×C42C2314yes—
176#395—232no—
177#393—232no—
178#393—232no—
179#390—232no—
180#386—232no—
181#380—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—24no—
193C2×#95—24no—
194C2×#95—42no—
195C2×#95—42no—
196C2×#95D418yes—
197C2×#95D418yescomplemented
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
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—
238C25—22no—
239C25—22no—
240C25C2×D414yes—
241C25C2×Q814yes—
242C25C2×Q814yes—
243C25#4114yes—
244C25C2412yes—
245C25C2412yes—
246C25C2411yescharacteristic
247C22×Q8—28no—
248C22×Q8—28no—
249C22×Q8—28no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8—44no—
253C22×Q8—44no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8—416no—
258C22×Q8—416no—
259C22×Q8—416no—
260C22×Q8—416no—
261C22×D4—232no—
262C22×D4—28no—
263C22×D4—28no—
264C22×D4—232no—
265C22×D4—28no—
266C22×D4—28no—
267C22×D4—416no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—416no—
271C22×D4—416no—
272C22×D4—416no—
273C22×D4—416no—
274C22×D4C2×Q8116yescomplemented
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—232no—
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—28no—
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—28no—
328C23×C4—28no—
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—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—28no—
358C23×C4—28no—
359C23×C4—44no—
360C23×C4—44no—
361C23×C4—416no—
362C23×C4—416no—
363C23×C4—416no—
364C23×C4—416no—
365C23×C4—416no—
366C23×C4—416no—
367C23×C4C2×D414yes—
368C23×C4C2×D414yes—
369C23×C4C2×D414yes—
370C23×C4C2×D414yes—
371C23×C4C2×D414yes—
372C23×C4C2×D414yes—
373C23×C4C2×D414yes—
374C23×C4C2×D414yes—
375C23×C4C2×Q814yes—
376C23×C4#4114yes—
377C23×C4#4114yes—
378C23×C4#4114yes—
379C23×C4#4114yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
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—44no—
401C2×C4⋊C4—44no—
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⋊C4—416no—
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—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—416no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—44no—
442C2×C22⋊C4—416no—
443C2×C22⋊C4—416no—
444C2×C22⋊C4—416no—
445C2×C22⋊C4—416no—
446C2×C22⋊C4—416no—
447C2×C22⋊C4—416no—
448C2×C22⋊C4—416no—
449C2×C22⋊C4—416no—
450C2×C22⋊C4—416no—
451C2×C22⋊C4—416no—
452C2×C22⋊C4C2×D4116yes—
453C2×C42—28no—
454C2×C42—28no—
455C2×C42—44no—
456C2×C42—416no—
457#95—28no—
458#95—28no—
459#95—28no—
460#95—28no—
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—44no—
470#95—44no—
471#95C2×D4116yes—
472#95C2×D4116yescomplemented
473C24—28no—
474C24—28no—
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—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—28no—
504C24—28no—
505C24—28no—
506C24—28no—
507C24—28no—
508C24—28no—
509C24—28no—
510C24—22no—
511C24—22no—
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—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—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—44no—
564C24—44no—
565C24—44no—
566C24—44no—
567C24—44no—
568C24C22⋊Q8116yes—
569C24C22×D414yes—
570C24C22×D412yes—
571C24C22×D412yes—
572C24C22×D412yes—
573C24C22×Q814yes—
574C24C22×Q814yes—
575C24C22×Q812yes—
576C24C2×#4114yes—
577C24C2×#4112yes—
578C24C2×#4112yes—
579C24C2×#4112yes—
580C24C2×#4112yes—
581C24C2×#4112yes—
582C24H(5,𝔽2)12yes—
583C24H(5,𝔽2)12yes—
584C24H(5,𝔽2)12yes—
585C24H(5,𝔽2)12yes—
586C24H(5,𝔽2)12yes—
587C242−1+412yes—
588C24C2511yescharacteristic
589C2×Q8—416no—
590C2×Q8—416no—
591C2×Q8—416no—
592C2×Q8—416no—
593C2×Q8—416no—
594C2×Q8—416no—
595C2×Q8—4128no—
596C2×Q8—416no—
597C2×D4—232no—
598C2×D4—232no—
599C2×D4—416no—
600C2×D4—4128no—
601C2×D4—416no—
602C2×D4—416no—
603C2×D4—416no—
604C2×D4—416no—
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—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—232no—
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—22no—
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—22no—
717C22×C4—416no—
718C22×C4—416no—
719C22×C4—416no—
720C22×C4—416no—
721C22×C4—416no—
722C22×C4—4128no—
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—416no—
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—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4C22⋊Q8116yes—
781C22×C4#124116yes—
782C22×C4C22×D414yes—
783C22×C4C22×D414yes—
784C22×C4C22×D414yes—
785C22×C4C22×D414yes—
786C22×C4C22×D414yes—
787C22×C4C22×D414yes—
788C22×C4C22×D414yes—
789C22×C4C22×D414yes—
790C22×C4C22×Q814yes—
791C22×C4C2×#4114yes—
792C22×C4C2×#4114yes—
793C22×C4C2×#4114yes—
794C22×C4C2×#4114yes—
795C4⋊C4—416no—
796C4⋊C4—416no—
797C4⋊C4—416no—
798C4⋊C4—416no—
799C22⋊C4—416no—
800C22⋊C4—416no—
801C22⋊C4—416no—
802C22⋊C4—416no—
803C22⋊C4—416no—
804C22⋊C4—416no—
805C22⋊C4—416no—
806C22⋊C4—416no—
807C22⋊C4—416no—
808C22⋊C4—416no—
809C22⋊C4—416no—
810C42—416no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—232no—
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—232no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—416no—
840C23—416no—
841C23—42no—
842C23—416no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—416no—
849C23—42no—
850C23—42no—
851C23—416no—
852C23—42no—
853C23—42no—
854C23—416no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—42no—
864C23—42no—
865C23—416no—
866C23—416no—
867C23—416no—
868C23—416no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—416no—
882C23—416no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—416no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—416no—
899C23—42no—
900C23—42no—
901C23—416no—
902C23—88no—
903C23—88no—
904C23—88no—
905C23—88no—
906C23—88no—
907C23—88no—
908C23—88no—
909C23—88no—
910C23C2×C22⋊Q818yes—
911C23C2×C22⋊Q814yes—
912C23C2×C22⋊Q814yes—
913C23#52514yes—
914C23C2×#12414yes—
915C23#53214yes—
916C23#53214yes—
917C23#53414yes—
918C23#53514yes—
919C23#53514yes—
920C23#53814yes—
921C23#53814yes—
922C23#53914yes—
923C23#54214yes—
924C23#54214yes—
925C23#54314yes—
926C23D4214yes—
927C23D4214yes—
928C23D4214yes—
929C23#54614yes—
930C23#54614yes—
931C23#54614yes—
932C23#54714yes—
933C23#54814yes—
934C23D4×Q814yes—
935C23#55114yes—
936C23#55114yes—
937C23#55114yes—
938C23#55414yes—
939C23#55414yes—
940C23#55414yes—
941C23#55514yes—
942C23#55514yes—
943C23#55514yes—
944C23#56014yes—
945C23#56214yes—
946C23C23×D411yescharacteristic
947C23C23×D411yescharacteristic
948C23C23×D411yescharacteristic
949C23C23×Q811yescharacteristic
950C23C22×#4111yescharacteristic
951C23C22×#4111yescharacteristic
952C23C22×#4111yescharacteristic
953C23C22×#4111yescharacteristic
954C23C22×#4111yescharacteristic
955C23C2×H(5,𝔽2)11yescharacteristic
956C23C2×H(5,𝔽2)11yescharacteristic
957C23C2×H(5,𝔽2)11yescharacteristic
958C23C2×H(5,𝔽2)11yescharacteristic
959C23C2×H(5,𝔽2)11yescharacteristic
960C23C2×2−1+411yescharacteristic
961Q8—464no—
962D4—464no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—232no—
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—232no—
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—464no—
999C2×C4—42no—
1000C2×C4—416no—
1001C2×C4—416no—
1002C2×C4—416no—
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—416no—
1016C2×C4—42no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—416no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—416no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—416no—
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—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—42no—
1061C2×C4—42no—
1062C2×C4—88no—
1063C2×C4—88no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4C2×C22⋊Q818yes—
1067C2×C4C2×#12418yes—
1068C22—28no—
1069C22—28no—
1070C22—28no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—464no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—82no—
1092C22—82no—
1093C22—82no—
1094C22—832no—
1095C22—82no—
1096C22—82no—
1097C22—82no—
1098C22—82no—
1099C22—82no—
1100C22#243718yes—
1101C22#244918yes—
1102C22#245218yes—
1103C22#247218yes—
1104C22#249118yes—
1105C22#255518yes—
1106C22#256318yes—
1107C22#256418yes—
1108C22#261018yes—
1109C22#266918yes—
1110C22#268618yes—
1111C22#269218yes—
1112C22#269618yes—
1113C22#273718yes—
1114C22#278418yes—
1115C22C22×C22⋊Q811yescharacteristic
1116C22C22×C22⋊Q811yescharacteristic
1117C22C2×#52511yescharacteristic
1118C22C22×#12411yescharacteristic
1119C22C2×#53211yescharacteristic
1120C22C2×#53211yescharacteristic
1121C22C2×#53411yescharacteristic
1122C22C2×#53511yescharacteristic
1123C22C2×#53511yescharacteristic
1124C22C2×#53811yescharacteristic
1125C22C2×#53811yescharacteristic
1126C22C2×#53911yescharacteristic
1127C22C2×#54211yescharacteristic
1128C22C2×#54211yescharacteristic
1129C22C2×#54311yescharacteristic
1130C22C2×D4211yescharacteristic
1131C22C2×D4211yescharacteristic
1132C22C2×D4211yescharacteristic
1133C22C2×#54611yescharacteristic
1134C22C2×#54611yescharacteristic
1135C22C2×#54611yescharacteristic
1136C22C2×#54711yescharacteristic
1137C22C2×#54811yescharacteristic
1138C22C2×D4×Q811yescharacteristic
1139C22C2×#55111yescharacteristic
1140C22C2×#55111yescharacteristic
1141C22C2×#55111yescharacteristic
1142C22C2×#55411yescharacteristic
1143C22C2×#55411yescharacteristic
1144C22C2×#55411yescharacteristic
1145C22C2×#55511yescharacteristic
1146C22C2×#55511yescharacteristic
1147C22C2×#55511yescharacteristic
1148C22C2×#56011yescharacteristic
1149C22C2×#56211yescharacteristic
1150C4—28no—
1151C4—28no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—82no—
1160C4—82no—
1161C4—82no—
1162C4—82no—
1163C2—48no—
1164C2—84no—
1165C2#15476116yesdirect product factor
1166C2C2×#243711yescharacteristic
1167C2C2×#244911yescharacteristic
1168C2C2×#247211yescharacteristic
1169C2C2×#245211yescharacteristic
1170C2C2×#249111yescharacteristic
1171C2C2×#255511yescharacteristic
1172C2C2×#256411yescharacteristic
1173C2C2×#261011yescharacteristic
1174C2C2×#256311yescharacteristic
1175C2C2×#266911yescharacteristic
1176C2C2×#268611yescharacteristic
1177C2C2×#269211yescharacteristic
1178C2C2×#269611yescharacteristic
1179C2C2×#273711yescharacteristic
1180C2C2×#278411yescharacteristic
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×#395C2semidirect
2. C22×#393C2semidirect
3. C22×#393C2semidirect
6. C22×#380C2semidirect
7. #15476C2direct (N × H)
8. C2×#1442C2semidirect
9. C2×#1439C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
14. C2×#1436C2semidirect
15. C2×#1434C2semidirect
16. C2×C22⋊#95C2semidirect
37. C2×#395C22semidirect
40. C2×#393C22semidirect
41. C2×#393C22semidirect
47. C2×#380C22semidirect
64. #1442C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
70. #1436C22semidirect
71. #1434C22semidirect
72. C22⋊#95C22semidirect
89. C23×D4Q8semidirect
197. C2×#95D4semidirect
274. C22×D4C2×Q8semidirect
472. #95C2×D4semidirect
1165. C2#15476direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3952
C22×#3932
C22×#3902
C22×#3862
C22×#3802
#154762
C2×#14422
C2×#14392
C2×#14382
C2×#14362
C2×#14342
C2×C22⋊#952