Finite Group Databasebeta

← C2×#14373 #520673

Subgroups — C2×#14373 #520673

Order 512.

6778 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#386C211yesmaximal, characteristic
2C22×#386C211yesmaximal, characteristic
3C22×#385C211yesmaximal, characteristic, complemented
4C22×#381C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic, complemented
6#14373C2116yesmaximal, direct product factor
7C2×#1443C211yesmaximal, characteristic, complemented
8C2×#1442C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1437C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×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×C42C2211yescharacteristic
34C2×#386—28no—
35C2×#386C4116yescomplemented
36C2×#386C2218yes—
37C2×#386C2218yes—
38C2×#385—28no—
39C2×#385C2218yescomplemented
40C2×#381—28no—
41C2×#381C2218yescomplemented
42C2×#380—28no—
43C2×#380C2218yescomplemented
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
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
62#1443C2218yescomplemented
63#1442C2218yescomplemented
64#1442C2218yescomplemented
65#1439C2218yescomplemented
66#1439C2218yescomplemented
67#1438C2218yes—
68#1437C2218yescomplemented
69#1437C2218yescomplemented
70#1436C2218yescomplemented
71C22⋊#95C2218yescomplemented
72C26C2311yescharacteristic
73C26C2311yescharacteristic
74C23×D4—24no—
75C23×D4—24no—
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—42no—
79C23×D4—42no—
80C23×D4C2×C418yes—
81C23×D4C2314yes—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4—42no—
92C24×C4—42no—
93C24×C4—42no—
94C24×C4—42no—
95C24×C4C2×C418yescomplemented
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2314yes—
109C24×C4C2311yescharacteristic
110C24×C4C2314yes—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
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—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
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⋊C4C2×C418yes—
150C22×C22⋊C4C2×C418yes—
151C22×C22⋊C4C2×C418yescomplemented
152C22×C22⋊C4D418yes—
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×C42—42no—
164C22×C42—42no—
165C22×C42—42no—
166C22×C42C2314yes—
167#386—232no—
168#386C2×C4164yescomplemented
169#385—232no—
170#381—232no—
171#380—232no—
172C2×#95—24no—
173C2×#95—24no—
174C2×#95—24no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95—24no—
180C2×#95—42no—
181C2×#95—42no—
182C2×#95—42no—
183C2×#95—42no—
184C2×#95—42no—
185C2×#95—42no—
186C2×#95—42no—
187C2×#95C2×C418yescomplemented
188C2×#95C2×C418yescomplemented
189C2×#95D418yescomplemented
190C2×#95C2314yes—
191C2×#95C2314yes—
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—
208C25—22no—
209C25—22no—
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—
232C25C22×C414yes—
233C25C22×C414yes—
234C25C2×D414yes—
235C25#4114yes—
236C25#4114yes—
237C25#4114yes—
238C25C2412yes—
239C25C2412yes—
240C25C2411yescharacteristic
241C22×D4—232no—
242C22×D4—232no—
243C22×D4—28no—
244C22×D4—28no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—416no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—416no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4C22×C4116yes—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—232no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—28no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—28no—
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—232no—
311C23×C4—28no—
312C23×C4—28no—
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—28no—
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—28no—
343C23×C4—28no—
344C23×C4—416no—
345C23×C4—44no—
346C23×C4—44no—
347C23×C4—44no—
348C23×C4—44no—
349C23×C4—44no—
350C23×C4—44no—
351C23×C4—416no—
352C23×C4—416no—
353C23×C4—416no—
354C23×C4—416no—
355C23×C4—416no—
356C23×C4—416no—
357C23×C4—416no—
358C23×C4—416no—
359C23×C4—416no—
360C23×C4—416no—
361C23×C4—416no—
362C23×C4C22×C414yes—
363C23×C4C22×C414yes—
364C23×C4C22×C414yes—
365C23×C4C22×C414yes—
366C23×C4C22×C414yes—
367C23×C4C22×C4116yescomplemented
368C23×C4C2×D414yes—
369C23×C4C2×D414yes—
370C23×C4C2×D414yes—
371C23×C4C2×D414yes—
372C23×C4C2×D414yes—
373C23×C4#4114yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—416no—
397C2×C4⋊C4—416no—
398C2×C4⋊C4—416no—
399C2×C22⋊C4—232no—
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—416no—
413C2×C22⋊C4—416no—
414C2×C22⋊C4—416no—
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—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
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⋊C4C22×C4116yes—
436C2×C22⋊C4C22×C4116yes—
437C2×C22⋊C4C22×C4116yescomplemented
438C2×C22⋊C4C2×D4116yes—
439C2×C42—44no—
440C2×C42—44no—
441C2×C42—44no—
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—44no—
452#95—44no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95—44no—
457#95—44no—
458#95C22×C4116yescomplemented
459#95C22×C4116yescomplemented
460#95C2×D4116yescomplemented
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—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—28no—
492C24—28no—
493C24—28no—
494C24—28no—
495C24—28no—
496C24—28no—
497C24—22no—
498C24—22no—
499C24—22no—
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—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
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#117116yes—
554C24C4×D4116yes—
555C24C23×C414yes—
556C24C23×C414yes—
557C24C23×C412yes—
558C24C22×D414yes—
559C24C22×D412yes—
560C24C22×D412yes—
561C24C2×#4114yes—
562C24C2×#4114yes—
563C24C2×#4114yes—
564C24C2×#4112yes—
565C24C2×#4112yes—
566C24C2×#4112yes—
567C24C2×#4112yes—
568C24H(5,𝔽2)12yes—
569C24H(5,𝔽2)12yes—
570C24H(5,𝔽2)12yes—
571C24H(5,𝔽2)12yes—
572C24H(5,𝔽2)12yes—
573C24H(5,𝔽2)12yes—
574C242−1+412yes—
575C242−1+412yes—
576C24C2511yescharacteristic
577C2×D4—232no—
578C2×D4—232no—
579C2×D4—416no—
580C2×D4—4128no—
581C2×D4—416no—
582C2×D4—416no—
583C2×D4—416no—
584C2×D4—416no—
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—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—232no—
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—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
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—232no—
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—416no—
698C22×C4—416no—
699C22×C4—4128no—
700C22×C4—416no—
701C22×C4—416no—
702C22×C4—416no—
703C22×C4—416no—
704C22×C4—416no—
705C22×C4—416no—
706C22×C4—416no—
707C22×C4—416no—
708C22×C4—416no—
709C22×C4—4128no—
710C22×C4—416no—
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—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×C4C4×D4116yes—
772C22×C4C23×C414yes—
773C22×C4C23×C414yes—
774C22×C4C23×C414yes—
775C22×C4C23×C414yes—
776C22×C4C23×C414yes—
777C22×C4C22×D414yes—
778C22×C4C22×D414yes—
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C22×D414yes—
782C22×C4C2×#4114yes—
783C4⋊C4—416no—
784C4⋊C4—416no—
785C4⋊C4—416no—
786C22⋊C4—232no—
787C22⋊C4—416no—
788C22⋊C4—416no—
789C22⋊C4—416no—
790C22⋊C4—416no—
791C22⋊C4—416no—
792C22⋊C4—416no—
793C22⋊C4—416no—
794C22⋊C4—416no—
795C22⋊C4—416no—
796C42—416no—
797C23—232no—
798C23—232no—
799C23—232no—
800C23—232no—
801C23—232no—
802C23—232no—
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—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—24no—
837C23—24no—
838C23—24no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—416no—
843C23—416no—
844C23—416no—
845C23—416no—
846C23—416no—
847C23—42no—
848C23—416no—
849C23—416no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
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—416no—
868C23—416no—
869C23—416no—
870C23—416no—
871C23—416no—
872C23—416no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—416no—
878C23—416no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—416no—
884C23—416no—
885C23—416no—
886C23—416no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23C2×#11718yes—
896C23C2×#11714yes—
897C23C2×C4×D418yes—
898C23C2×C4×D414yes—
899C23C2×C4×D414yes—
900C23#51814yes—
901C23#51814yes—
902C23#52014yes—
903C23#52014yes—
904C23#53414yes—
905C23#53514yes—
906C23#53614yes—
907C23#53714yes—
908C23#53814yes—
909C23#53814yes—
910C23#53914yes—
911C23#53914yes—
912C23#53914yes—
913C23#53914yes—
914C23#54014yes—
915C23#54214yes—
916C23D4214yes—
917C23#54614yes—
918C23#54614yes—
919C23#54614yes—
920C23#54614yes—
921C23#54614yes—
922C23#54814yes—
923C23#55114yes—
924C23#55114yes—
925C23#55114yes—
926C23#55214yes—
927C23#55314yes—
928C23#56014yes—
929C23#56014yes—
930C23#56214yes—
931C23#56214yes—
932C23C24×C411yescharacteristic
933C23C23×D411yescharacteristic
934C23C23×D411yescharacteristic
935C23C22×#4111yescharacteristic
936C23C22×#4111yescharacteristic
937C23C22×#4111yescharacteristic
938C23C22×#4111yescharacteristic
939C23C2×H(5,𝔽2)11yescharacteristic
940C23C2×H(5,𝔽2)11yescharacteristic
941C23C2×H(5,𝔽2)11yescharacteristic
942C23C2×H(5,𝔽2)11yescharacteristic
943C23C2×H(5,𝔽2)11yescharacteristic
944C23C2×H(5,𝔽2)11yescharacteristic
945C23C2×2−1+411yescharacteristic
946C23C2×2−1+411yescharacteristic
947D4—464no—
948C2×C4—232no—
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—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—464no—
980C2×C4—464no—
981C2×C4—416no—
982C2×C4—416no—
983C2×C4—416no—
984C2×C4—416no—
985C2×C4—42no—
986C2×C4—416no—
987C2×C4—416no—
988C2×C4—42no—
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—416no—
1000C2×C4—416no—
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—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—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—88no—
1050C2×C4—88no—
1051C2×C4—88no—
1052C2×C4—88no—
1053C2×C4C2×C4×D418yes—
1054C22—28no—
1055C22—28no—
1056C22—28no—
1057C22—28no—
1058C22—28no—
1059C22—28no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—464no—
1067C22—464no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22#231818yes—
1087C22#232218yes—
1088C22#232418yes—
1089C22#234218yes—
1090C22#235218yes—
1091C22#235818yes—
1092C22#237718yes—
1093C22#267818yes—
1094C22#268118yes—
1095C22#268718yes—
1096C22#268818yes—
1097C22#269318yes—
1098C22#269618yes—
1099C22#274318yes—
1100C22#274618yes—
1101C22C22×#11711yescharacteristic
1102C22C22×C4×D411yescharacteristic
1103C22C22×C4×D411yescharacteristic
1104C22C2×#51811yescharacteristic
1105C22C2×#51811yescharacteristic
1106C22C2×#52011yescharacteristic
1107C22C2×#52011yescharacteristic
1108C22C2×#53411yescharacteristic
1109C22C2×#53511yescharacteristic
1110C22C2×#53611yescharacteristic
1111C22C2×#53711yescharacteristic
1112C22C2×#53811yescharacteristic
1113C22C2×#53811yescharacteristic
1114C22C2×#53911yescharacteristic
1115C22C2×#53911yescharacteristic
1116C22C2×#53911yescharacteristic
1117C22C2×#53911yescharacteristic
1118C22C2×#54011yescharacteristic
1119C22C2×#54211yescharacteristic
1120C22C2×D4211yescharacteristic
1121C22C2×#54611yescharacteristic
1122C22C2×#54611yescharacteristic
1123C22C2×#54611yescharacteristic
1124C22C2×#54611yescharacteristic
1125C22C2×#54611yescharacteristic
1126C22C2×#54811yescharacteristic
1127C22C2×#55111yescharacteristic
1128C22C2×#55111yescharacteristic
1129C22C2×#55111yescharacteristic
1130C22C2×#55211yescharacteristic
1131C22C2×#55311yescharacteristic
1132C22C2×#56011yescharacteristic
1133C22C2×#56011yescharacteristic
1134C22C2×#56211yescharacteristic
1135C22C2×#56211yescharacteristic
1136C4—28no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—82no—
1146C4—82no—
1147C4—82no—
1148C4—82no—
1149C2—48no—
1150C2—48no—
1151C2#14373116yesdirect product factor
1152C2C2×#231811yescharacteristic
1153C2C2×#232211yescharacteristic
1154C2C2×#232411yescharacteristic
1155C2C2×#234211yescharacteristic
1156C2C2×#235211yescharacteristic
1157C2C2×#235811yescharacteristic
1158C2C2×#237711yescharacteristic
1159C2C2×#267811yescharacteristic
1160C2C2×#268111yescharacteristic
1161C2C2×#268711yescharacteristic
1162C2C2×#268811yescharacteristic
1163C2C2×#269311yescharacteristic
1164C2C2×#269611yescharacteristic
1165C2C2×#274311yescharacteristic
1166C2C2×#274611yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C22×#385C2semidirect
4. C22×#381C2semidirect
5. C22×#380C2semidirect
6. #14373C2direct (N × H)
7. C2×#1443C2semidirect
8. C2×#1442C2semidirect
9. C2×#1442C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×C22⋊#95C2semidirect
35. C2×#386C4semidirect
39. C2×#385C22semidirect
41. C2×#381C22semidirect
43. C2×#380C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
68. #1437C22semidirect
69. #1437C22semidirect
70. #1436C22semidirect
71. C22⋊#95C22semidirect
95. C24×C4C2×C4semidirect
151. C22×C22⋊C4C2×C4semidirect
168. #386C2×C4semidirect
187. C2×#95C2×C4semidirect
188. C2×#95C2×C4semidirect
189. C2×#95D4semidirect
367. C23×C4C22×C4semidirect
437. C2×C22⋊C4C22×C4semidirect
458. #95C22×C4semidirect
459. #95C22×C4semidirect
460. #95C2×D4semidirect
1151. C2#14373direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3862
C22×#3852
C22×#3812
C22×#3802
#143732
C2×#14432
C2×#14422
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C22⋊#952