Finite Group Databasebeta

← C22×#14300 #72337043

Subgroups — C22×#14300 #72337043

Order 1024.

77917 conjugacy classes of subgroups.

The subgroup lattice has 1095 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D4C211yesmaximal, characteristic
2C23×#394C211yesmaximal, characteristic
3C23×#387C211yesmaximal, characteristic, complemented
4C23×#385C212yesmaximal, complemented
5C2×#14300C2148yesmaximal, direct product factor
6C22×#1444C211yesmaximal, characteristic, complemented
7C22×#1441C211yesmaximal, characteristic, complemented
8C22×#1440C212yesmaximal, complemented
9C22×#1439C212yesmaximal, complemented
10C22×#1438C211yesmaximal, characteristic
11C22×#1434C211yesmaximal, characteristic, complemented
12C22×C22⋊#95C212yesmaximal, complemented
13C25×D4C2211yescharacteristic
14C26×C4C2212yes—
15C23×C4×D4—216no—
16C23×C4×D4—232no—
17C23×C4×D4C22124yes—
18C24×C4⋊C4C2211yescharacteristic
19C24×C4⋊C4C2211yescharacteristic
20C24×C4⋊C4C2211yescharacteristic
21C24×C4⋊C4C2212yes—
22C24×C22⋊C4C2212yes—
23C24×C22⋊C4C2212yes—
24C24×C22⋊C4C2212yes—
25C24×C22⋊C4C2212yes—
26C24×C22⋊C4C2212yes—
27C24×C42C2211yescharacteristic
28C22×#394C4132yescomplemented
29C22×#394C22124yes—
30C22×#387—216no—
31C22×#387C22124yescomplemented
32C22×#385—232no—
33C22×#385C22148yescomplemented
34C23×#95C2212yes—
35C23×#95C2212yes—
36C23×#95C2211yescharacteristic
37C23×#95C2211yescharacteristic
38C23×#95C2211yescharacteristic
39C23×#95C2211yescharacteristic
40C23×#95C2211yescharacteristic
41C23×#95C2212yes—
42C23×#95C2212yes—
43C23×#95C2212yes—
44C23×#95C2211yescharacteristic
45#14300C221256yesdirect product factor
46C2×#1444C22124yescomplemented
47C2×#1441C22124yescomplemented
48C2×#1440C22148yescomplemented
49C2×#1439C22148yescomplemented
50C2×#1438C22124yes—
51C2×#1434C22124yescomplemented
52C2×C22⋊#95C22148yescomplemented
53C27C2312yes—
54C24×D4—216no—
55C24×D4—216no—
56C24×D4—28no—
57C24×D4—28no—
58C24×D4C2×C4116yes—
59C24×D4C23112yes—
60C25×C4—216no—
61C25×C4—216no—
62C25×C4—48no—
63C25×C4—48no—
64C25×C4—48no—
65C25×C4—48no—
66C25×C4D4132yes—
67C25×C4C2311yescharacteristic
68C25×C4C2312yes—
69C25×C4C2311yescharacteristic
70C25×C4C2311yescharacteristic
71C25×C4C2312yes—
72C25×C4C2311yescharacteristic
73C25×C4C2312yes—
74C25×C4C2311yescharacteristic
75C25×C4C2311yescharacteristic
76C25×C4C2311yescharacteristic
77C25×C4C23124yes—
78C22×C4×D4—2512no—
79C22×C4×D4—2192no—
80C22×C4×D4—2384no—
81C22×C4×D4C23164yes—
82C23×C4⋊C4—216no—
83C23×C4⋊C4—28no—
84C23×C4⋊C4—28no—
85C23×C4⋊C4—28no—
86C23×C4⋊C4—216no—
87C23×C4⋊C4—216no—
88C23×C4⋊C4—28no—
89C23×C4⋊C4—48no—
90C23×C4⋊C4—48no—
91C23×C4⋊C4C2×C4116yescomplemented
92C23×C4⋊C4C23112yes—
93C23×C4⋊C4C23112yes—
94C23×C4⋊C4C23112yes—
95C23×C4⋊C4C23124yes—
96C23×C22⋊C4—216no—
97C23×C22⋊C4—216no—
98C23×C22⋊C4—216no—
99C23×C22⋊C4—216no—
100C23×C22⋊C4—216no—
101C23×C22⋊C4—216no—
102C23×C22⋊C4—216no—
103C23×C22⋊C4—48no—
104C23×C22⋊C4—48no—
105C23×C22⋊C4—48no—
106C23×C22⋊C4—48no—
107C23×C22⋊C4—48no—
108C23×C22⋊C4—48no—
109C23×C22⋊C4C2×C4132yescomplemented
110C23×C22⋊C4C2×C4132yescomplemented
111C23×C22⋊C4C23124yes—
112C23×C22⋊C4C23124yes—
113C23×C22⋊C4C23124yes—
114C23×C22⋊C4C23124yes—
115C23×C22⋊C4C23124yes—
116C23×C42—216no—
117C23×C42D4116yes—
118C23×C42C23112yes—
119C2×#394C2×C41384yescomplemented
120C2×#394C23164yes—
121C2×#387—2192no—
122C2×#387C23164yescomplemented
123C2×#385—2384no—
124C2×#385C231128yescomplemented
125C22×#95—216no—
126C22×#95—216no—
127C22×#95—28no—
128C22×#95—28no—
129C22×#95—28no—
130C22×#95—28no—
131C22×#95—28no—
132C22×#95—48no—
133C22×#95—48no—
134C22×#95—48no—
135C22×#95C2×C4116yescomplemented
136C22×#95C23112yes—
137C22×#95C23112yes—
138C22×#95C23112yes—
139C22×#95C23112yes—
140C22×#95C23124yes—
141C22×#95C23112yes—
142C22×#95C23124yes—
143C22×#95C23124yes—
144C22×#95C23124yes—
145C22×#95C23124yes—
146C22×#95C23112yes—
147#1444C23164yescomplemented
148#1441C23164yescomplemented
149#1440C231128yescomplemented
150#1439C231128yescomplemented
151#1438C23164yes—
152#1434C23164yescomplemented
153C22⋊#95C231128yescomplemented
154C26—28no—
155C26—28no—
156C26—28no—
157C26—28no—
158C26—28no—
159C26—28no—
160C26—28no—
161C26—28no—
162C26—28no—
163C26—28no—
164C26—28no—
165C26—28no—
166C26C22×C4116yes—
167C26C2×D4116yes—
168C26#41116yes—
169C26C24112yes—
170C26C2411yescharacteristic
171C23×D4—2128no—
172C23×D4—2256no—
173C23×D4—2128no—
174C23×D4—2256no—
175C23×D4—296no—
176C23×D4—296no—
177C23×D4—2128no—
178C23×D4—248no—
179C23×D4—248no—
180C23×D4C22×C4196yes—
181C23×D4C24116yes—
182C24×C4—28no—
183C24×C4—28no—
184C24×C4—24no—
185C24×C4—28no—
186C24×C4—24no—
187C24×C4—28no—
188C24×C4—28no—
189C24×C4—28no—
190C24×C4—28no—
191C24×C4—28no—
192C24×C4—24no—
193C24×C4—24no—
194C24×C4—28no—
195C24×C4—28no—
196C24×C4—24no—
197C24×C4—24no—
198C24×C4—28no—
199C24×C4—28no—
200C24×C4—28no—
201C24×C4—28no—
202C24×C4—24no—
203C24×C4—24no—
204C24×C4—28no—
205C24×C4—28no—
206C24×C4—28no—
207C24×C4—24no—
208C24×C4—24no—
209C24×C4—28no—
210C24×C4—24no—
211C24×C4—28no—
212C24×C4—24no—
213C24×C4—2256no—
214C24×C4—296no—
215C24×C4—296no—
216C24×C4—28no—
217C24×C4—28no—
218C24×C4—24no—
219C24×C4—24no—
220C24×C4—28no—
221C24×C4—28no—
222C24×C4—28no—
223C24×C4—24no—
224C24×C4—28no—
225C24×C4—24no—
226C24×C4—28no—
227C24×C4—28no—
228C24×C4—28no—
229C24×C4—28no—
230C24×C4—24no—
231C24×C4—24no—
232C24×C4—28no—
233C24×C4—4128no—
234C24×C4—4128no—
235C24×C4—448no—
236C24×C4—448no—
237C24×C4—448no—
238C24×C4—448no—
239C24×C4—4128no—
240C24×C4—4128no—
241C24×C4—4128no—
242C24×C4—4128no—
243C24×C4C22×C418yes—
244C24×C4C22×C418yes—
245C24×C4C22×C4116yes—
246C24×C4C22×C418yes—
247C24×C4C2×D4116yes—
248C24×C4C2×D418yes—
249C24×C4C2×D418yes—
250C24×C4C2×D418yes—
251C24×C4C2×D4116yes—
252C24×C4C2×D41192yes—
253C24×C4#4118yes—
254C24×C4C2416yes—
255C24×C4C24112yes—
256C24×C4C2416yes—
257C24×C4C2416yes—
258C24×C4C24112yes—
259C24×C4C2416yes—
260C24×C4C24112yes—
261C24×C4C2416yes—
262C24×C4C2416yes—
263C24×C4C2416yes—
264C24×C4C24132yes—
265C2×C4×D4—23072no—
266C2×C4×D4—2512no—
267C2×C4×D4—2256no—
268C22×C4⋊C4—2128no—
269C22×C4⋊C4—2128no—
270C22×C4⋊C4—296no—
271C22×C4⋊C4—248no—
272C22×C4⋊C4—248no—
273C22×C4⋊C4—248no—
274C22×C4⋊C4—296no—
275C22×C4⋊C4—296no—
276C22×C4⋊C4—248no—
277C22×C4⋊C4—448no—
278C22×C4⋊C4—448no—
279C22×C4⋊C4—4128no—
280C22×C4⋊C4—464no—
281C22×C4⋊C4C22×C4196yescomplemented
282C22×C4⋊C4C24116yes—
283C22×C4⋊C4C24116yes—
284C22×C4⋊C4C24116yes—
285C22×C4⋊C4C24132yes—
286C22×C22⋊C4—2256no—
287C22×C22⋊C4—2256no—
288C22×C22⋊C4—296no—
289C22×C22⋊C4—296no—
290C22×C22⋊C4—296no—
291C22×C22⋊C4—296no—
292C22×C22⋊C4—296no—
293C22×C22⋊C4—296no—
294C22×C22⋊C4—296no—
295C22×C22⋊C4—4128no—
296C22×C22⋊C4—448no—
297C22×C22⋊C4—448no—
298C22×C22⋊C4—448no—
299C22×C22⋊C4—448no—
300C22×C22⋊C4—448no—
301C22×C22⋊C4—448no—
302C22×C22⋊C4—4128no—
303C22×C22⋊C4—4128no—
304C22×C22⋊C4C22×C41192yescomplemented
305C22×C22⋊C4C22×C41192yescomplemented
306C22×C22⋊C4C24132yes—
307C22×C22⋊C4C24132yes—
308C22×C22⋊C4C24132yes—
309C22×C22⋊C4C24132yes—
310C22×C22⋊C4C24132yes—
311C22×C42—2128no—
312C22×C42—296no—
313C22×C42C2×D4196yes—
314C22×C42C24116yes—
315#394C22×C41512yescomplemented
316#387—2256no—
317#385—2512no—
318C2×#95—296no—
319C2×#95—296no—
320C2×#95—248no—
321C2×#95—248no—
322C2×#95—248no—
323C2×#95—248no—
324C2×#95—248no—
325C2×#95—448no—
326C2×#95—448no—
327C2×#95—448no—
328C2×#95C22×C4196yescomplemented
329C2×#95C24116yes—
330C2×#95C24132yes—
331C2×#95C24116yes—
332C2×#95C24116yes—
333C2×#95C24116yes—
334C2×#95C24116yes—
335C2×#95C24132yes—
336C2×#95C24132yes—
337C2×#95C24132yes—
338C2×#95C24132yes—
339C2×#95C24116yes—
340C25—264no—
341C25—264no—
342C25—264no—
343C25—264no—
344C25—264no—
345C25—264no—
346C25—264no—
347C25—264no—
348C25—264no—
349C25—264no—
350C25—264no—
351C25—264no—
352C25—264no—
353C25—264no—
354C25—264no—
355C25—264no—
356C25—264no—
357C25—264no—
358C25—224no—
359C25—224no—
360C25—224no—
361C25—224no—
362C25—224no—
363C25—224no—
364C25—224no—
365C25—224no—
366C25—224no—
367C25—224no—
368C25—224no—
369C25—224no—
370C25—432no—
371C25—432no—
372C25—432no—
373C25—432no—
374C25—432no—
375C25—432no—
376C25—432no—
377C25—432no—
378C25—432no—
379C25—432no—
380C25—432no—
381C25—432no—
382C25—432no—
383C25—432no—
384C25—432no—
385C25—432no—
386C25C4×D41128yes—
387C25C23×C4148yes—
388C25C23×C414yes—
389C25C22×D4148yes—
390C25C22×D418yes—
391C25C22×D414yes—
392C25C2×#41148yes—
393C25C2×#4118yes—
394C25C2×#4114yes—
395C25H(5,𝔽2)14yes—
396C25H(5,𝔽2)14yes—
397C25H(5,𝔽2)18yes—
398C25H(5,𝔽2)14yes—
399C252−1+414yes—
400C252−1+418yes—
401C25C2518yes—
402C25C2513yes—
403C22×D4—2384no—
404C22×D4—2384no—
405C22×D4—2768no—
406C22×D4—22048no—
407C22×D4—2768no—
408C22×D4—264no—
409C22×D4—264no—
410C22×D4—2384no—
411C22×D4—232no—
412C22×D4—232no—
413C22×D4C23×C4164yes—
414C23×C4—264no—
415C23×C4—232no—
416C23×C4—232no—
417C23×C4—264no—
418C23×C4—264no—
419C23×C4—264no—
420C23×C4—232no—
421C23×C4—232no—
422C23×C4—224no—
423C23×C4—224no—
424C23×C4—212no—
425C23×C4—224no—
426C23×C4—212no—
427C23×C4—264no—
428C23×C4—264no—
429C23×C4—232no—
430C23×C4—232no—
431C23×C4—232no—
432C23×C4—264no—
433C23×C4—232no—
434C23×C4—264no—
435C23×C4—232no—
436C23×C4—264no—
437C23×C4—264no—
438C23×C4—264no—
439C23×C4—232no—
440C23×C4—232no—
441C23×C4—224no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—224no—
445C23×C4—224no—
446C23×C4—212no—
447C23×C4—212no—
448C23×C4—224no—
449C23×C4—224no—
450C23×C4—212no—
451C23×C4—212no—
452C23×C4—212no—
453C23×C4—212no—
454C23×C4—224no—
455C23×C4—224no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—224no—
460C23×C4—224no—
461C23×C4—212no—
462C23×C4—212no—
463C23×C4—224no—
464C23×C4—212no—
465C23×C4—224no—
466C23×C4—212no—
467C23×C4—2768no—
468C23×C4—264no—
469C23×C4—264no—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—212no—
473C23×C4—212no—
474C23×C4—224no—
475C23×C4—224no—
476C23×C4—224no—
477C23×C4—212no—
478C23×C4—224no—
479C23×C4—212no—
480C23×C4—224no—
481C23×C4—224no—
482C23×C4—224no—
483C23×C4—224no—
484C23×C4—212no—
485C23×C4—212no—
486C23×C4—224no—
487C23×C4—4384no—
488C23×C4—4384no—
489C23×C4—432no—
490C23×C4—432no—
491C23×C4—432no—
492C23×C4—432no—
493C23×C4—42048no—
494C23×C4—4384no—
495C23×C4—4384no—
496C23×C4—4384no—
497C23×C4—4384no—
498C23×C4—416no—
499C23×C4—432no—
500C23×C4—416no—
501C23×C4—432no—
502C23×C4—432no—
503C23×C4—432no—
504C23×C4—416no—
505C23×C4—432no—
506C23×C4—432no—
507C23×C4—432no—
508C23×C4—416no—
509C23×C4—432no—
510C23×C4—432no—
511C23×C4—432no—
512C23×C4—432no—
513C23×C4—416no—
514C23×C4—416no—
515C23×C4—416no—
516C23×C4—432no—
517C23×C4—416no—
518C23×C4—432no—
519C23×C4—432no—
520C23×C4—432no—
521C23×C4—416no—
522C23×C4—416no—
523C23×C4—416no—
524C23×C4—432no—
525C23×C4—416no—
526C23×C4—432no—
527C23×C4—432no—
528C23×C4—432no—
529C23×C4—432no—
530C23×C4—432no—
531C23×C4—432no—
532C23×C4C4×D4164yes—
533C23×C4#120164yes—
534C23×C4C23×C4124yes—
535C23×C4C23×C4124yes—
536C23×C4C23×C4148yes—
537C23×C4C23×C4124yes—
538C23×C4C22×D4124yes—
539C23×C4C22×D4148yes—
540C23×C4C22×D4124yes—
541C23×C4C22×D4124yes—
542C23×C4C22×D4148yes—
543C23×C4C22×D41128yes—
544C23×C4C2×#41124yes—
545C23×C4C2514yes—
546C23×C4C2514yes—
547C23×C4C2518yes—
548C23×C4C2514yes—
549C23×C4C2514yes—
550C23×C4C2518yes—
551C23×C4C2514yes—
552C23×C4C2518yes—
553C23×C4C2514yes—
554C23×C4C2514yes—
555C4×D4—22048no—
556C2×C4⋊C4—2384no—
557C2×C4⋊C4—2384no—
558C2×C4⋊C4—264no—
559C2×C4⋊C4—232no—
560C2×C4⋊C4—232no—
561C2×C4⋊C4—232no—
562C2×C4⋊C4—264no—
563C2×C4⋊C4—264no—
564C2×C4⋊C4—232no—
565C2×C4⋊C4—432no—
566C2×C4⋊C4—432no—
567C2×C4⋊C4—4384no—
568C2×C4⋊C4—4192no—
569C2×C4⋊C4C23×C4164yescomplemented
570C2×C22⋊C4—2768no—
571C2×C22⋊C4—2768no—
572C2×C22⋊C4—264no—
573C2×C22⋊C4—264no—
574C2×C22⋊C4—264no—
575C2×C22⋊C4—264no—
576C2×C22⋊C4—264no—
577C2×C22⋊C4—264no—
578C2×C22⋊C4—264no—
579C2×C22⋊C4—4384no—
580C2×C22⋊C4—432no—
581C2×C22⋊C4—432no—
582C2×C22⋊C4—432no—
583C2×C22⋊C4—432no—
584C2×C22⋊C4—432no—
585C2×C22⋊C4—432no—
586C2×C22⋊C4—4384no—
587C2×C22⋊C4—4384no—
588C2×C22⋊C4C23×C41128yescomplemented
589C2×C22⋊C4C23×C41128yescomplemented
590C2×C42—2384no—
591C2×C42—264no—
592C2×C42C22×D4164yes—
593#95—264no—
594#95—264no—
595#95—232no—
596#95—232no—
597#95—232no—
598#95—232no—
599#95—232no—
600#95—432no—
601#95—432no—
602#95—432no—
603#95C23×C4164yescomplemented
604C24—28no—
605C24—28no—
606C24—28no—
607C24—28no—
608C24—28no—
609C24—28no—
610C24—28no—
611C24—28no—
612C24—28no—
613C24—28no—
614C24—28no—
615C24—28no—
616C24—2512no—
617C24—2512no—
618C24—296no—
619C24—296no—
620C24—296no—
621C24—296no—
622C24—296no—
623C24—296no—
624C24—296no—
625C24—296no—
626C24—296no—
627C24—296no—
628C24—296no—
629C24—296no—
630C24—296no—
631C24—296no—
632C24—296no—
633C24—296no—
634C24—296no—
635C24—296no—
636C24—2512no—
637C24—4256no—
638C24—4256no—
639C24—4256no—
640C24—4256no—
641C24—4256no—
642C24—4256no—
643C24—4256no—
644C24—4256no—
645C24—4256no—
646C24—4256no—
647C24—4256no—
648C24—4256no—
649C24—448no—
650C24—448no—
651C24—448no—
652C24—448no—
653C24—448no—
654C24—448no—
655C24—448no—
656C24—448no—
657C24—448no—
658C24—448no—
659C24—448no—
660C24—448no—
661C24—448no—
662C24—448no—
663C24—448no—
664C24—448no—
665C24C2×C4×D41192yes—
666C24C2×C4×D4132yes—
667C24C2×C4×D4116yes—
668C24#518116yes—
669C24#520116yes—
670C24#520132yes—
671C24C2×#120116yes—
672C24#525132yes—
673C24#525116yes—
674C24#534132yes—
675C24#534132yes—
676C24#535116yes—
677C24#535116yes—
678C24#536132yes—
679C24#536116yes—
680C24#537116yes—
681C24#537132yes—
682C24#538132yes—
683C24#539132yes—
684C24#539132yes—
685C24#539132yes—
686C24#540116yes—
687C24#542116yes—
688C24#542132yes—
689C24C24×C4116yes—
690C24C24×C416yes—
691C24C23×D4116yes—
692C24C23×D4112yes—
693C24C23×D416yes—
694C24C22×#41116yes—
695C24C22×#41112yes—
696C24C22×#4116yes—
697C24C2×H(5,𝔽2)16yes—
698C24C2×H(5,𝔽2)16yes—
699C24C2×H(5,𝔽2)112yes—
700C24C2×H(5,𝔽2)16yes—
701C24C2×2−1+416yes—
702C24C2×2−1+4112yes—
703C24C2611yescharacteristic
704C2×D4—2128no—
705C2×D4—2128no—
706C2×D4—2256no—
707C2×D4—23072no—
708C2×D4—2256no—
709C2×D4—2128no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—2256no—
716C22×C4—296no—
717C22×C4—248no—
718C22×C4—248no—
719C22×C4—296no—
720C22×C4—296no—
721C22×C4—296no—
722C22×C4—248no—
723C22×C4—248no—
724C22×C4—2256no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—296no—
752C22×C4—296no—
753C22×C4—248no—
754C22×C4—248no—
755C22×C4—248no—
756C22×C4—296no—
757C22×C4—248no—
758C22×C4—296no—
759C22×C4—248no—
760C22×C4—296no—
761C22×C4—296no—
762C22×C4—296no—
763C22×C4—248no—
764C22×C4—248no—
765C22×C4—2256no—
766C22×C4—24no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—24no—
777C22×C4—28no—
778C22×C4—24no—
779C22×C4—28no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—28no—
783C22×C4—4128no—
784C22×C4—4128no—
785C22×C4—4128no—
786C22×C4—4128no—
787C22×C4—4128no—
788C22×C4—4128no—
789C22×C4—43072no—
790C22×C4—4128no—
791C22×C4—4256no—
792C22×C4—4256no—
793C22×C4—4128no—
794C22×C4—424no—
795C22×C4—448no—
796C22×C4—424no—
797C22×C4—448no—
798C22×C4—448no—
799C22×C4—448no—
800C22×C4—424no—
801C22×C4—448no—
802C22×C4—448no—
803C22×C4—448no—
804C22×C4—424no—
805C22×C4—448no—
806C22×C4—448no—
807C22×C4—448no—
808C22×C4—448no—
809C22×C4—424no—
810C22×C4—424no—
811C22×C4—4128no—
812C22×C4—424no—
813C22×C4—424no—
814C22×C4—448no—
815C22×C4—448no—
816C22×C4—448no—
817C22×C4—448no—
818C22×C4—424no—
819C22×C4—424no—
820C22×C4—424no—
821C22×C4—424no—
822C22×C4—448no—
823C22×C4—448no—
824C22×C4—448no—
825C22×C4—448no—
826C22×C4—448no—
827C22×C4—448no—
828C22×C4—448no—
829C22×C4—864no—
830C22×C4—8128no—
831C22×C4—864no—
832C22×C4C2×C4×D4196yes—
833C22×C4C2×#120196yes—
834C22×C4C24×C4116yes—
835C22×C4C24×C418yes—
836C22×C4C24×C418yes—
837C22×C4C24×C418yes—
838C22×C4C23×D418yes—
839C22×C4C23×D4116yes—
840C22×C4C23×D418yes—
841C22×C4C23×D4116yes—
842C22×C4C23×D418yes—
843C22×C4C22×#4118yes—
844C4⋊C4—2128no—
845C4⋊C4—2128no—
846C4⋊C4—4128no—
847C4⋊C4—464no—
848C22⋊C4—2256no—
849C22⋊C4—2256no—
850C22⋊C4—4128no—
851C22⋊C4—4128no—
852C22⋊C4—4128no—
853C42—2128no—
854C23—2384no—
855C23—2384no—
856C23—216no—
857C23—216no—
858C23—216no—
859C23—216no—
860C23—216no—
861C23—216no—
862C23—216no—
863C23—216no—
864C23—216no—
865C23—216no—
866C23—216no—
867C23—216no—
868C23—216no—
869C23—216no—
870C23—216no—
871C23—216no—
872C23—216no—
873C23—216no—
874C23—2384no—
875C23—4192no—
876C23—4192no—
877C23—4192no—
878C23—4192no—
879C23—4192no—
880C23—4192no—
881C23—4192no—
882C23—4192no—
883C23—4192no—
884C23—48no—
885C23—48no—
886C23—48no—
887C23—48no—
888C23—48no—
889C23—48no—
890C23—48no—
891C23—48no—
892C23—48no—
893C23—48no—
894C23—48no—
895C23—48no—
896C23—48no—
897C23—48no—
898C23—48no—
899C23—48no—
900C23—42048no—
901C23—4192no—
902C23—4192no—
903C23—4192no—
904C23C4×#120164yes—
905C23#23221128yes—
906C23#2324164yes—
907C23#23251128yes—
908C23#2326164yes—
909C23#2613164yes—
910C23#2616164yes—
911C23#26301128yes—
912C23#2633164yes—
913C23#2636164yes—
914C23#26381128yes—
915C23C22×C4×D4132yes—
916C23C22×C4×D4124yes—
917C23C22×C4×D4112yes—
918C23C2×#518112yes—
919C23C2×#520112yes—
920C23C2×#520124yes—
921C23C22×#120112yes—
922C23C2×#525124yes—
923C23C2×#525112yes—
924C23C2×#534124yes—
925C23C2×#534124yes—
926C23C2×#535112yes—
927C23C2×#535112yes—
928C23C2×#536124yes—
929C23C2×#536112yes—
930C23C2×#537112yes—
931C23C2×#537124yes—
932C23C2×#538124yes—
933C23C2×#539124yes—
934C23C2×#539124yes—
935C23C2×#539124yes—
936C23C2×#540112yes—
937C23C2×#542112yes—
938C23C2×#542124yes—
939C23C25×C411yescharacteristic
940C23C24×D412yes—
941C23C24×D411yescharacteristic
942C23C23×#4112yes—
943C23C23×#4111yescharacteristic
944C23C22×H(5,𝔽2)11yescharacteristic
945C23C22×H(5,𝔽2)11yescharacteristic
946C23C22×H(5,𝔽2)12yes—
947C23C22×H(5,𝔽2)11yescharacteristic
948C23C22×2−1+412yes—
949C23C22×2−1+411yescharacteristic
950D4—2512no—
951C2×C4—216no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—216no—
955C2×C4—216no—
956C2×C4—216no—
957C2×C4—28no—
958C2×C4—28no—
959C2×C4—2192no—
960C2×C4—2192no—
961C2×C4—216no—
962C2×C4—216no—
963C2×C4—28no—
964C2×C4—28no—
965C2×C4—28no—
966C2×C4—216no—
967C2×C4—216no—
968C2×C4—28no—
969C2×C4—28no—
970C2×C4—216no—
971C2×C4—216no—
972C2×C4—216no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—4512no—
976C2×C4—496no—
977C2×C4—4192no—
978C2×C4—496no—
979C2×C4—44no—
980C2×C4—48no—
981C2×C4—44no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—48no—
986C2×C4—48no—
987C2×C4—44no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—44no—
992C2×C4—48no—
993C2×C4—44no—
994C2×C4—44no—
995C2×C4—48no—
996C2×C4—496no—
997C2×C4—4192no—
998C2×C4—44no—
999C2×C4—48no—
1000C2×C4—44no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—48no—
1005C2×C4—48no—
1006C2×C4—48no—
1007C2×C4—48no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—48no—
1012C2×C4—44no—
1013C2×C4—48no—
1014C2×C4—48no—
1015C2×C4—848no—
1016C2×C4—848no—
1017C2×C4—896no—
1018C2×C4C22×C4×D4116yes—
1019C2×C4C22×#120116yes—
1020C22—232no—
1021C22—232no—
1022C22—232no—
1023C22—4768no—
1024C22—416no—
1025C22—416no—
1026C22—416no—
1027C22—416no—
1028C22—416no—
1029C22—416no—
1030C22—416no—
1031C22—416no—
1032C22—416no—
1033C22—416no—
1034C22—416no—
1035C22—416no—
1036C22#143001256yesdirect product factor
1037C22C2×C4×#120124yes—
1038C22C2×#2322148yes—
1039C22C2×#2324124yes—
1040C22C2×#2325148yes—
1041C22C2×#2326124yes—
1042C22C2×#2613124yes—
1043C22C2×#2630148yes—
1044C22C2×#2638148yes—
1045C22C2×#2636124yes—
1046C22C2×#2633124yes—
1047C22C2×#2616124yes—
1048C22C23×C4×D412yes—
1049C22C23×C4×D411yescharacteristic
1050C22C22×#51811yescharacteristic
1051C22C22×#52012yes—
1052C22C22×#52011yescharacteristic
1053C22C23×#12011yescharacteristic
1054C22C22×#52512yes—
1055C22C22×#52511yescharacteristic
1056C22C22×#53412yes—
1057C22C22×#53412yes—
1058C22C22×#53812yes—
1059C22C22×#53912yes—
1060C22C22×#53912yes—
1061C22C22×#53912yes—
1062C22C22×#53511yescharacteristic
1063C22C22×#53511yescharacteristic
1064C22C22×#53712yes—
1065C22C22×#53711yescharacteristic
1066C22C22×#54011yescharacteristic
1067C22C22×#54212yes—
1068C22C22×#54211yescharacteristic
1069C22C22×#53612yes—
1070C22C22×#53611yescharacteristic
1071C4—216no—
1072C4—216no—
1073C4—48no—
1074C4—416no—
1075C4—48no—
1076C4—416no—
1077C4—48no—
1078C4—84no—
1079C4—88no—
1080C4—84no—
1081C2—432no—
1082C2C2×#14300148yesdirect product factor
1083C2C22×C4×#12011yescharacteristic
1084C2C22×#232512yes—
1085C2C22×#232212yes—
1086C2C22×#232611yescharacteristic
1087C2C22×#232411yescharacteristic
1088C2C22×#261311yescharacteristic
1089C2C22×#263012yes—
1090C2C22×#263812yes—
1091C2C22×#263611yescharacteristic
1092C2C22×#263311yescharacteristic
1093C2C22×#261611yescharacteristic
subgroupG/H
center, socleC26C24
commutatorC23C25×C4
Frattini, cosocleC24C26
prime radicalC25×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C26 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C23×#387C2semidirect
4. C23×#385C2semidirect
5. C2×#14300C2direct (N × H)
6. C22×#1444C2semidirect
7. C22×#1441C2semidirect
8. C22×#1440C2semidirect
9. C22×#1439C2semidirect
11. C22×#1434C2semidirect
12. C22×C22⋊#95C2semidirect
28. C22×#394C4semidirect
31. C22×#387C22semidirect
33. C22×#385C22semidirect
45. #14300C22direct (N × H)
46. C2×#1444C22semidirect
47. C2×#1441C22semidirect
48. C2×#1440C22semidirect
49. C2×#1439C22semidirect
51. C2×#1434C22semidirect
52. C2×C22⋊#95C22semidirect
91. C23×C4⋊C4C2×C4semidirect
109. C23×C22⋊C4C2×C4semidirect
110. C23×C22⋊C4C2×C4semidirect
119. C2×#394C2×C4semidirect
122. C2×#387C23semidirect
124. C2×#385C23semidirect
135. C22×#95C2×C4semidirect
147. #1444C23semidirect
148. #1441C23semidirect
149. #1440C23semidirect
150. #1439C23semidirect
152. #1434C23semidirect
153. C22⋊#95C23semidirect
281. C22×C4⋊C4C22×C4semidirect
304. C22×C22⋊C4C22×C4semidirect
305. C22×C22⋊C4C22×C4semidirect
315. #394C22×C4semidirect
328. C2×#95C22×C4semidirect
569. C2×C4⋊C4C23×C4semidirect
588. C2×C22⋊C4C23×C4semidirect
589. C2×C22⋊C4C23×C4semidirect
603. #95C23×C4semidirect
1036. C22#14300direct (N × H)
1082. C2C2×#14300direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D42
C23×#3942
C23×#3872
C23×#3852
C2×#143002
C22×#14442
C22×#14412
C22×#14402
C22×#14392
C22×#14382
C22×#14342
C22×C22⋊#952