Finite Group Databasebeta

← #72257527

Subgroups — #72257527

Order 1024.

248801 conjugacy classes of subgroups.

The subgroup lattice has 1175 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×#41C211yesmaximal, characteristic, complemented
2C2×#34736C216yesmaximal, complemented
3C22×C4×#120C211yesmaximal, characteristic, complemented
4#613434C2112yesmaximal, complemented
5#613321C216yesmaximal, complemented
6#613188C216yesmaximal, complemented
7#613007C212yesmaximal, complemented
8#612792C212yesmaximal, complemented
9#612617C212yesmaximal, complemented
10#612424C212yesmaximal, complemented
11#607926C2112yesmaximal, complemented
12C4×#2846C214yesmaximal, complemented
13#607558C211yesmaximal, characteristic, complemented
14#514204C216yesmaximal, complemented
15C24×#41—296no—
16C24×#41—216no—
17C24×#41C2216yes—
18C24×#41C2216yes—
19C24×#41C2216yescomplemented
20C24×#41C2216yescomplemented
21C25×Q8C2211yescharacteristic, complemented
22C25×D4C2212yes—
23C25×D4C2211yescharacteristic, complemented
24C26×C4C2211yescharacteristic
25C26×C4C2212yescomplemented
26C22×#525C2214yescomplemented
27C23×#120C2211yescharacteristic
28C23×C4×D4C2213yescomplemented
29C2×#2846C2214yes—
30#34736—296no—
31C2×#2406C22112yescomplemented
32C2×#2404C22112yescomplemented
33C2×#2407C22124yescomplemented
34C2×#2409C22112yescomplemented
35C2×#2408C22112yescomplemented
36C2×#2405C22112yescomplemented
37C2×#2403C22112yescomplemented
38C2×#2388C22124yescomplemented
39C2×C4×#120—216no—
40C2×C4×#120C2212yes—
41C2×C4×#120C2212yes—
42C2×C4×#120C2216yescomplemented
43C2×C4×#120C2216yescomplemented
44C2×C4×#120C22124yescomplemented
45C2×#2297C22112yescomplemented
46C22×#386C2213yescomplemented
47C22×#385C2213yescomplemented
48C2×#2280C2216yescomplemented
49C22×#379C2211yescharacteristic
50C22×C4×C22⋊C4C2213yescomplemented
51#14889C22148yescomplemented
52#14885C22148yescomplemented
53#14874C22112yescomplemented
54#14873C22112yescomplemented
55#14724C22124yescomplemented
56#14724C22112yescomplemented
57#14715C22124yescomplemented
58#14715C22112yescomplemented
59#14694C2214yes—
60#14694C22124yescomplemented
61#14693C2214yescomplemented
62#14693C22124yescomplemented
63#14681C2216yescomplemented
64#14680C2212yescomplemented
65#14680C2216yescomplemented
66#14679C2212yes—
67#14679C2214yescomplemented
68#13956C22124yescomplemented
69#13937C22124yescomplemented
70#13922C22112yescomplemented
71#13902C22112yescomplemented
72#13867C22112yescomplemented
73#13867C22112yescomplemented
74#13851C22124yescomplemented
75C4×#379C2212yescomplemented
76C4×#379C2216yescomplemented
77C4×#379C22124yescomplemented
78C27C2312yes—
79C27C2311yescharacteristic
80C23×#41—22048no—
81C23×#41—21536no—
82C23×#41—2192no—
83C23×#41—2192no—
84C23×#41—2192no—
85C23×#41—2192no—
86C23×#41—248no—
87C23×#41—296no—
88C23×#41—248no—
89C23×#41—248no—
90C23×#41—248no—
91C23×#41—248no—
92C23×#41—248no—
93C23×#41—248no—
94C23×#41—296no—
95C23×#41D4196yescomplemented
96C23×#41C23124yes—
97C23×#41C23112yes—
98C23×#41C23112yes—
99C23×#41C23112yes—
100C23×#41C2314yes—
101C24×Q8—248no—
102C24×Q8—28no—
103C24×Q8C2316yes—
104C24×Q8C2316yes—
105C24×D4—216no—
106C24×D4—296no—
107C24×D4—248no—
108C24×D4—28no—
109C24×D4C23112yes—
110C24×D4C2316yes—
111C24×D4C23112yes—
112C24×D4C2316yes—
113C24×D4C2313yes—
114C25×C4—248no—
115C25×C4—216no—
116C25×C4—296no—
117C25×C4D4116yescomplemented
118C25×C4C2312yes—
119C25×C4C23112yes—
120C25×C4C2311yescharacteristic
121C25×C4C2313yes—
122C25×C4C2313yes—
123C25×C4C2311yescharacteristic
124C25×C4C2313yes—
125C25×C4C23112yes—
126C25×C4C2313yes—
127C25×C4C2311yescharacteristic, complemented
128C2×#525—296no—
129C22×#123C2318yescomplemented
130C22×C22⋊Q8C2318yescomplemented
131C22×#121C2318yescomplemented
132C22×#120—28no—
133C22×#120—216no—
134C22×#120C2316yes—
135C22×#120C23124yes—
136C22×#120C2312yes—
137C22×#120C2318yescomplemented
138C22×C4×D4—248no—
139C22×C4×D4—224no—
140C22×C4×D4C2316yes—
141C22×C4×D4C2316yes—
142C22×C4×D4C2316yescomplemented
143C22×C4×D4C2316yescomplemented
144C22×C4×D4C23116yescomplemented
145C22×#117C2314yescomplemented
146C23×C4⋊C4C2313yescomplemented
147C23×C22⋊C4C2313yes—
148C23×C22⋊C4C2313yes—
149C23×C22⋊C4C2313yes—
150C23×C22⋊C4C2313yescomplemented
151C23×C42C2313yescomplemented
152#2846—232no—
153#2409—296no—
154#2408—296no—
155#2407—2192no—
156#2406—296no—
157#2405—296no—
158#2404—296no—
159#2403—296no—
160#2388—2192no—
161C2×#395C23124yescomplemented
162C2×#394C23148yescomplemented
163C2×#394C23124yescomplemented
164C2×#393C23124yescomplemented
165C2×#392C23148yescomplemented
166C2×#392C23124yescomplemented
167C4×#120—216no—
168C4×#120—216no—
169C4×#120—248no—
170C4×#120—248no—
171C4×#120—2192no—
172#2297—296no—
173C2×#391C23124yescomplemented
174C2×#390C23124yescomplemented
175C2×#386—224no—
176C2×#386C2316yes—
177C2×#386C23124yes—
178C2×#386C2316yes—
179C2×#386C23112yescomplemented
180C2×#386C23148yescomplemented
181C2×#386C23124yescomplemented
182C2×#386C23124yescomplemented
183C2×#385—224no—
184C2×#385C2316yes—
185C2×#385C23124yes—
186C2×#385C2316yes—
187C2×#385C23112yescomplemented
188C2×#385C23148yescomplemented
189#2280—248no—
190C2×#381C23112yescomplemented
191C2×#380C23112yes—
192C2×#380C23112yescomplemented
193C2×#379—28no—
194C2×#379C23124yes—
195C2×#379C2314yes—
196C2×#379C23112yes—
197C2×#379C2312yes—
198C2×#379C23124yes—
199C2×#379C2316yes—
200C2×#379C23124yes—
201C2×#379C23112yes—
202C2×C4×C22⋊C4—224no—
203C2×C4×C22⋊C4C2316yes—
204C2×C4×C22⋊C4C2316yes—
205C2×C4×C22⋊C4C23112yes—
206C2×C4×C22⋊C4C2316yescomplemented
207C2×C4×C22⋊C4C23112yescomplemented
208C2×C4×C22⋊C4C23148yescomplemented
209C2×C4×C22⋊C4C2316yescomplemented
210C22×#95C2316yescomplemented
211#1446C23148yescomplemented
212#1438C23148yescomplemented
213#1438C23148yescomplemented
214#1438C23148yescomplemented
215C22⋊#95C23112yes—
216C22⋊#95C23124yes—
217C22⋊#95C23124yes—
218C22⋊#95C23112yes—
219C22⋊#95C23124yescomplemented
220C22⋊#95C23196yescomplemented
221C26—248no—
222C26—224no—
223C26—28no—
224C26—28no—
225C26—216no—
226C26—412no—
227C26—424no—
228C26C2×D418yes—
229C26C2411yescharacteristic
230C26C2413yes—
231C26C24112yes—
232C26C2411yescharacteristic
233C26C2413yes—
234C22×#41—216384no—
235C22×#41—21536no—
236C22×#41—23072no—
237C22×#41—21536no—
238C22×#41—2768no—
239C22×#41—21536no—
240C22×#41—21536no—
241C22×#41—21536no—
242C22×#41—21536no—
243C22×#41—21536no—
244C22×#41—2768no—
245C22×#41—23072no—
246C22×#41—2768no—
247C22×#41—21536no—
248C22×#41—296no—
249C22×#41—296no—
250C22×#41—2192no—
251C22×#41—296no—
252C22×#41—2192no—
253C22×#41—296no—
254C22×#41—2768no—
255C22×#41—2192no—
256C22×#41—296no—
257C22×#41—248no—
258C22×#41—248no—
259C22×#41—248no—
260C22×#41—248no—
261C22×#41—248no—
262C22×#41—248no—
263C22×#41—2192no—
264C22×#41—248no—
265C22×#41—216no—
266C22×#41C2×D4196yes—
267C22×#41C2×D4196yes—
268C22×#41C2×D4196yescomplemented
269C22×#41C2×D4196yescomplemented
270C23×Q8—2512no—
271C23×Q8—2384no—
272C23×Q8—296no—
273C23×Q8—296no—
274C23×Q8—248no—
275C23×Q8—224no—
276C23×Q8—224no—
277C23×Q8—224no—
278C23×Q8C2×D4148yescomplemented
279C23×Q8C24112yes—
280C23×Q8C2414yes—
281C23×D4—2768no—
282C23×D4—21024no—
283C23×D4—2512no—
284C23×D4—2384no—
285C23×D4—248no—
286C23×D4—248no—
287C23×D4—248no—
288C23×D4—248no—
289C23×D4—248no—
290C23×D4—2192no—
291C23×D4—296no—
292C23×D4—2192no—
293C23×D4—296no—
294C23×D4—212no—
295C23×D4—224no—
296C23×D4—224no—
297C23×D4—248no—
298C23×D4—224no—
299C23×D4—224no—
300C23×D4—224no—
301C23×D4—412no—
302C23×D4C2×D4196yes—
303C23×D4C2×D4148yescomplemented
304C23×D4C24124yes—
305C23×D4C24112yes—
306C23×D4C2416yes—
307C23×D4C2416yes—
308C23×D4C24116yes—
309C23×D4C2418yes—
310C23×D4C2414yes—
311C24×C4—2512no—
312C24×C4—21024no—
313C24×C4—2768no—
314C24×C4—28no—
315C24×C4—248no—
316C24×C4—224no—
317C24×C4—2384no—
318C24×C4—224no—
319C24×C4—248no—
320C24×C4—224no—
321C24×C4—248no—
322C24×C4—248no—
323C24×C4—2192no—
324C24×C4—224no—
325C24×C4—224no—
326C24×C4—248no—
327C24×C4—248no—
328C24×C4—248no—
329C24×C4—248no—
330C24×C4—248no—
331C24×C4—2192no—
332C24×C4—248no—
333C24×C4—24no—
334C24×C4—224no—
335C24×C4C2×D418yes—
336C24×C4C2×D418yes—
337C24×C4C2×D4124yes—
338C24×C4C2×D4124yes—
339C24×C4C2×D4124yes—
340C24×C4C2×D4148yes—
341C24×C4C2×D4124yes—
342C24×C4C2×D4196yescomplemented
343C24×C4C2411yescharacteristic
344C24×C4C2412yes—
345C24×C4C2412yes—
346C24×C4C2413yes—
347C24×C4C24112yes—
348C24×C4C2413yes—
349C24×C4C24124yes—
350C24×C4C2416yes—
351C24×C4C2413yes—
352C24×C4C2413yes—
353C24×C4C2413yes—
354C24×C4C2413yes—
355C24×C4C2413yes—
356C24×C4C2413yes—
357C24×C4C2418yes—
358C24×C4C2413yes—
359C24×C4C2411yescharacteristic
360#525—4256no—
361C2×#123—296no—
362C2×C22⋊Q8—296no—
363C2×#121—296no—
364C2×#120—2128no—
365C2×#120—224no—
366C2×#120—28no—
367C2×#120—28no—
368C2×#120—224no—
369C2×#120—296no—
370C2×#120—296no—
371C2×#120—296no—
372C2×#120—224no—
373C2×#120—448no—
374C2×#120#41116yescomplemented
375C2×C4×D4—248no—
376C2×C4×D4—2192no—
377C2×C4×D4—248no—
378C2×C4×D4—224no—
379C2×C4×D4—248no—
380C2×C4×D4—224no—
381C2×C4×D4—248no—
382C2×C4×D4—224no—
383C2×C4×D4—224no—
384C2×C4×D4—4192no—
385C2×#117—248no—
386C22×C4⋊C4—224no—
387C22×C4⋊C4—212no—
388C22×C4⋊C4C2416yes—
389C22×C4⋊C4C24116yes—
390C22×C4⋊C4C2416yes—
391C22×C4⋊C4C2418yes—
392C22×C22⋊C4—212no—
393C22×C22⋊C4—224no—
394C22×C22⋊C4—224no—
395C22×C22⋊C4—212no—
396C22×C22⋊C4—212no—
397C22×C22⋊C4—224no—
398C22×C22⋊C4—212no—
399C22×C22⋊C4—412no—
400C22×C22⋊C4C2416yes—
401C22×C22⋊C4C24116yes—
402C22×C22⋊C4C2416yes—
403C22×C22⋊C4C24116yes—
404C22×C22⋊C4C2416yes—
405C22×C22⋊C4C2416yes—
406C22×C22⋊C4C2416yes—
407C22×C22⋊C4C2416yes—
408C22×C22⋊C4C2418yes—
409C22×C22⋊C4C24124yes—
410C22×C22⋊C4C24148yes—
411C22×C22⋊C4C2416yes—
412C22×C22⋊C4C24124yes—
413C22×C22⋊C4C24148yes—
414C22×C22⋊C4C2416yes—
415C22×C42—212no—
416C22×C42—224no—
417C22×C42C2416yes—
418C22×C42C2416yes—
419C22×C42C2418yes—
420#395—296no—
421#394—2192no—
422#394—296no—
423#393—296no—
424#392—2192no—
425#392—296no—
426#391—296no—
427#390—296no—
428#386—296no—
429#386—296no—
430#386—296no—
431#386—2192no—
432#386—224no—
433#386—224no—
434#386—248no—
435#385—296no—
436#385—2192no—
437#385—224no—
438#385—224no—
439#385—248no—
440#381—248no—
441#380—248no—
442#380—248no—
443#379—248no—
444#379—296no—
445#379—28no—
446#379—224no—
447#379—216no—
448#379—296no—
449#379—448no—
450#379—424no—
451C4×C22⋊C4—248no—
452C4×C22⋊C4—2192no—
453C4×C22⋊C4—224no—
454C4×C22⋊C4—224no—
455C4×C22⋊C4—224no—
456C4×C22⋊C4—224no—
457C4×C22⋊C4—248no—
458C2×#95—224no—
459C2×#95C24124yes—
460C2×#95C24148yes—
461C2×#95C24148yes—
462C2×#95C24124yes—
463C2×#95C24112yes—
464C2×#95C24112yes—
465C25—212no—
466C25—212no—
467C25—2256no—
468C25—2128no—
469C25—2192no—
470C25—296no—
471C25—296no—
472C25—224no—
473C25—224no—
474C25—224no—
475C25—224no—
476C25—212no—
477C25—212no—
478C25—212no—
479C25—232no—
480C25—22no—
481C25—212no—
482C25—248no—
483C25—24no—
484C25—248no—
485C25—212no—
486C25—212no—
487C25—448no—
488C25—412no—
489C25—412no—
490C25—448no—
491C25—46no—
492C25—4192no—
493C25—4384no—
494C25—4192no—
495C25—4384no—
496C25—496no—
497C25—432no—
498C25C22×D414yes—
499C25C22×D4148yes—
500C25C22×D4112yes—
501C25C22×D4112yes—
502C25C22×D4124yes—
503C25C2×#4118yes—
504C25C2512yes—
505C25C2518yes—
506C25C2513yes—
507C25C2511yescharacteristic
508C25C2513yes—
509C2×#41—212288no—
510C2×#41—212288no—
511C2×#41—212288no—
512C2×#41—21536no—
513C2×#41—2768no—
514C2×#41—2768no—
515C2×#41—2768no—
516C2×#41—212288no—
517C2×#41—21536no—
518C2×#41—2768no—
519C2×#41—2768no—
520C2×#41—2768no—
521C2×#41—2768no—
522C2×#41—2768no—
523C2×#41—2768no—
524C2×#41—2384no—
525C2×#41—2768no—
526C2×#41—2384no—
527C2×#41—2384no—
528C2×#41—2384no—
529C2×#41—2384no—
530C2×#41—2384no—
531C2×#41—2384no—
532C2×#41—2768no—
533C2×#41#1201256yescomplemented
534C22×Q8—22048no—
535C22×Q8—2768no—
536C22×Q8—2384no—
537C22×Q8—2384no—
538C22×Q8—2384no—
539C22×Q8—2192no—
540C22×Q8—2384no—
541C22×Q8—2192no—
542C22×Q8—296no—
543C22×Q8—224no—
544C22×Q8—224no—
545C22×Q8—28no—
546C22×Q8—224no—
547C22×Q8C22×D4148yes—
548C22×Q8C22×D4148yes—
549C22×D4—24096no—
550C22×D4—22048no—
551C22×D4—2768no—
552C22×D4—2768no—
553C22×D4—2768no—
554C22×D4—2768no—
555C22×D4—2768no—
556C22×D4—2384no—
557C22×D4—2192no—
558C22×D4—2768no—
559C22×D4—2384no—
560C22×D4—2384no—
561C22×D4—2384no—
562C22×D4—2384no—
563C22×D4—296no—
564C22×D4—296no—
565C22×D4—248no—
566C22×D4—248no—
567C22×D4—248no—
568C22×D4—216no—
569C22×D4—2768no—
570C22×D4—2384no—
571C22×D4—296no—
572C22×D4—212no—
573C22×D4—212no—
574C22×D4—224no—
575C22×D4—212no—
576C22×D4—212no—
577C22×D4—224no—
578C22×D4—224no—
579C22×D4—232no—
580C22×D4—296no—
581C22×D4—2192no—
582C22×D4—296no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—28no—
586C22×D4—224no—
587C22×D4—212no—
588C22×D4—412no—
589C22×D4—448no—
590C22×D4—4192no—
591C22×D4—448no—
592C22×D4—448no—
593C22×D4C22×D4196yes—
594C22×D4C22×D4148yes—
595C22×D4C22×D4196yes—
596C22×D4C22×D4148yes—
597C22×D4C2×#41124yescomplemented
598C23×C4—2128no—
599C23×C4—2192no—
600C23×C4—2256no—
601C23×C4—2128no—
602C23×C4—24096no—
603C23×C4—2768no—
604C23×C4—2384no—
605C23×C4—22048no—
606C23×C4—2768no—
607C23×C4—2384no—
608C23×C4—2768no—
609C23×C4—2384no—
610C23×C4—2768no—
611C23×C4—2768no—
612C23×C4—2384no—
613C23×C4—296no—
614C23×C4—212no—
615C23×C4—224no—
616C23×C4—224no—
617C23×C4—212no—
618C23×C4—296no—
619C23×C4—224no—
620C23×C4—224no—
621C23×C4—296no—
622C23×C4—296no—
623C23×C4—296no—
624C23×C4—296no—
625C23×C4—2192no—
626C23×C4—2192no—
627C23×C4—2192no—
628C23×C4—2192no—
629C23×C4—2384no—
630C23×C4—2384no—
631C23×C4—2768no—
632C23×C4—224no—
633C23×C4—224no—
634C23×C4—296no—
635C23×C4—224no—
636C23×C4—224no—
637C23×C4—296no—
638C23×C4—224no—
639C23×C4—248no—
640C23×C4—224no—
641C23×C4—248no—
642C23×C4—224no—
643C23×C4—224no—
644C23×C4—248no—
645C23×C4—216no—
646C23×C4—26no—
647C23×C4—212no—
648C23×C4—26no—
649C23×C4—22no—
650C23×C4—212no—
651C23×C4—212no—
652C23×C4—212no—
653C23×C4—224no—
654C23×C4—24no—
655C23×C4—24no—
656C23×C4—224no—
657C23×C4—46no—
658C23×C4—412no—
659C23×C4—448no—
660C23×C4—464no—
661C23×C4#1201192yescomplemented
662C23×C4C22×D4112yes—
663C23×C4C22×D4148yes—
664C23×C4C22×D4196yes—
665C23×C4C22×D4112yes—
666C23×C4C22×D4124yes—
667C23×C4C22×D4124yes—
668C23×C4C22×D4112yes—
669C23×C4C22×D4112yes—
670C23×C4C22×D4124yes—
671C23×C4C22×D4124yes—
672C23×C4C22×D4124yes—
673C23×C4C22×D4124yes—
674C23×C4C22×D4112yes—
675C23×C4C22×D4112yes—
676C23×C4C22×D4112yes—
677C23×C4C22×D4196yes—
678C23×C4C22×D4124yes—
679C23×C4C22×D414yes—
680C23×C4C2516yes—
681C23×C4C25116yes—
682C23×C4C2512yes—
683C23×C4C2516yes—
684C23×C4C2513yes—
685C23×C4C2518yes—
686C23×C4C2513yes—
687C23×C4C2511yescharacteristic
688C23×C4C2511yescharacteristic
689#123—4128no—
690C22⋊Q8—4128no—
691#121—4128no—
692#120—2192no—
693#120—264no—
694#120—4384no—
695#120—4128no—
696C4×D4—496no—
697C4×D4—496no—
698C4×D4—496no—
699C4×D4—496no—
700C4×D4—4256no—
701#117—464no—
702C2×C4⋊C4—224no—
703C2×C4⋊C4—212no—
704C2×C4⋊C4—212no—
705C2×C4⋊C4—224no—
706C2×C4⋊C4—248no—
707C2×C4⋊C4—296no—
708C2×C4⋊C4—448no—
709C2×C22⋊C4—296no—
710C2×C22⋊C4—212no—
711C2×C22⋊C4—212no—
712C2×C22⋊C4—212no—
713C2×C22⋊C4—224no—
714C2×C22⋊C4—212no—
715C2×C22⋊C4—212no—
716C2×C22⋊C4—224no—
717C2×C22⋊C4—224no—
718C2×C22⋊C4—212no—
719C2×C22⋊C4—212no—
720C2×C22⋊C4—248no—
721C2×C22⋊C4—296no—
722C2×C22⋊C4—248no—
723C2×C22⋊C4—296no—
724C2×C22⋊C4—248no—
725C2×C22⋊C4—224no—
726C2×C22⋊C4—248no—
727C2×C22⋊C4—224no—
728C2×C22⋊C4—212no—
729C2×C22⋊C4—212no—
730C2×C22⋊C4—224no—
731C2×C22⋊C4—296no—
732C2×C22⋊C4—296no—
733C2×C22⋊C4—248no—
734C2×C22⋊C4—296no—
735C2×C22⋊C4—412no—
736C2×C22⋊C4—448no—
737C2×C22⋊C4—448no—
738C2×C22⋊C4—448no—
739C2×C22⋊C4—448no—
740C2×C22⋊C4—496no—
741C2×C22⋊C4—448no—
742C2×C22⋊C4C2×#41124yescomplemented
743C2×C42—248no—
744C2×C42—224no—
745C2×C42—212no—
746C2×C42—212no—
747C2×C42—224no—
748C2×C42—448no—
749#95—224no—
750#95—224no—
751#95—248no—
752#95—248no—
753#95—296no—
754#95—296no—
755C24—232no—
756C24—296no—
757C24—212no—
758C24—22no—
759C24—26no—
760C24—212no—
761C24—224no—
762C24—224no—
763C24—296no—
764C24—2512no—
765C24—2256no—
766C24—2192no—
767C24—2192no—
768C24—296no—
769C24—224no—
770C24—212no—
771C24—28no—
772C24—216no—
773C24—26no—
774C24—212no—
775C24—248no—
776C24—26no—
777C24—2192no—
778C24—248no—
779C24—296no—
780C24—248no—
781C24—296no—
782C24—224no—
783C24—224no—
784C24—224no—
785C24—296no—
786C24—28no—
787C24—22no—
788C24—212no—
789C24—22no—
790C24—212no—
791C24—224no—
792C24—224no—
793C24—2192no—
794C24—448no—
795C24—496no—
796C24—424no—
797C24—424no—
798C24—496no—
799C24—496no—
800C24—4384no—
801C24—4384no—
802C24—496no—
803C24—4384no—
804C24—496no—
805C24—448no—
806C24—4384no—
807C24—41024no—
808C24—42048no—
809C24—4768no—
810C24—448no—
811C24—496no—
812C24—4768no—
813C24—496no—
814C24—412no—
815C24—448no—
816C24—448no—
817C24—448no—
818C24—496no—
819C24—412no—
820C24—416no—
821C24—824no—
822C24C2×#120148yes—
823C24#525116yescomplemented
824C24C23×D4112yes—
825C24C23×D4148yes—
826C24C23×D416yes—
827C24C23×D4112yes—
828C24C23×D412yes—
829C24C23×D416yes—
830C24C23×D4112yes—
831C24C22×#41112yes—
832C24C22×#4114yescomplemented
833C24#585112yes—
834C24C2611yescharacteristic
835#41—26144no—
836#41—23072no—
837#41—23072no—
838#41—23072no—
839#41—21024no—
840C2×Q8—21536no—
841C2×Q8—21536no—
842C2×Q8—2192no—
843C2×Q8—2192no—
844C2×Q8—2192no—
845C2×Q8—296no—
846C2×Q8—296no—
847C2×Q8—296no—
848C2×Q8C2×#120164yescomplemented
849C2×D4—23072no—
850C2×D4—21536no—
851C2×D4—23072no—
852C2×D4—2384no—
853C2×D4—2192no—
854C2×D4—2384no—
855C2×D4—2192no—
856C2×D4—21536no—
857C2×D4—2192no—
858C2×D4—2192no—
859C2×D4—2192no—
860C2×D4—2192no—
861C2×D4—2192no—
862C2×D4—248no—
863C2×D4—248no—
864C2×D4—296no—
865C2×D4—2192no—
866C2×D4—296no—
867C2×D4—296no—
868C2×D4—296no—
869C2×D4—448no—
870C2×D4—448no—
871C2×D4—4384no—
872C2×D4—424no—
873C2×D4—424no—
874C2×D4—424no—
875C2×D4—424no—
876C2×D4—448no—
877C2×D4—4192no—
878C2×D4—464no—
879C2×D4—896no—
880C2×D4C2×#1201128yes—
881C2×D4C2×#120164yescomplemented
882C22×C4—296no—
883C22×C4—2256no—
884C22×C4—2512no—
885C22×C4—2192no—
886C22×C4—2192no—
887C22×C4—296no—
888C22×C4—2256no—
889C22×C4—23072no—
890C22×C4—2768no—
891C22×C4—2768no—
892C22×C4—2768no—
893C22×C4—23072no—
894C22×C4—2384no—
895C22×C4—2384no—
896C22×C4—2192no—
897C22×C4—212no—
898C22×C4—224no—
899C22×C4—212no—
900C22×C4—28no—
901C22×C4—224no—
902C22×C4—296no—
903C22×C4—224no—
904C22×C4—2192no—
905C22×C4—248no—
906C22×C4—296no—
907C22×C4—248no—
908C22×C4—2768no—
909C22×C4—248no—
910C22×C4—248no—
911C22×C4—296no—
912C22×C4—2192no—
913C22×C4—248no—
914C22×C4—248no—
915C22×C4—296no—
916C22×C4—2192no—
917C22×C4—248no—
918C22×C4—2192no—
919C22×C4—248no—
920C22×C4—248no—
921C22×C4—296no—
922C22×C4—248no—
923C22×C4—296no—
924C22×C4—2192no—
925C22×C4—2192no—
926C22×C4—224no—
927C22×C4—26no—
928C22×C4—212no—
929C22×C4—26no—
930C22×C4—212no—
931C22×C4—212no—
932C22×C4—26no—
933C22×C4—248no—
934C22×C4—212no—
935C22×C4—22no—
936C22×C4—216no—
937C22×C4—224no—
938C22×C4—248no—
939C22×C4—448no—
940C22×C4—412no—
941C22×C4—412no—
942C22×C4—424no—
943C22×C4—412no—
944C22×C4—412no—
945C22×C4—416no—
946C22×C4—424no—
947C22×C4—432no—
948C22×C4—424no—
949C22×C4—432no—
950C22×C4—824no—
951C22×C4—864no—
952C22×C4C2×#120148yes—
953C22×C4C2×#120148yes—
954C22×C4C2×#120148yes—
955C22×C4C2×#120148yes—
956C22×C4C2×#120148yes—
957C22×C4C2×#120148yes—
958C22×C4C2×#120164yes—
959C22×C4C2×#1201128yescomplemented
960C22×C4C23×D4112yes—
961C22×C4C23×D416yes—
962C22×C4C23×D4148yes—
963C22×C4C23×D4112yes—
964C22×C4C23×D416yes—
965C22×C4C23×D412yes—
966C22×C4C23×D4112yes—
967C22×C4C23×D412yes—
968C22×C4C23×D4112yes—
969C22×C4C22×#41112yescomplemented
970C4⋊C4—424no—
971C4⋊C4—424no—
972C4⋊C4—432no—
973C4⋊C4—464no—
974C22⋊C4—248no—
975C22⋊C4—248no—
976C22⋊C4—4192no—
977C22⋊C4—424no—
978C22⋊C4—424no—
979C22⋊C4—424no—
980C22⋊C4—432no—
981C22⋊C4—464no—
982C22⋊C4—424no—
983C22⋊C4—496no—
984C22⋊C4—424no—
985C22⋊C4—424no—
986C22⋊C4—464no—
987C22⋊C4—896no—
988C22⋊C4—848no—
989C42—424no—
990C42—424no—
991C42—432no—
992C23—232no—
993C23—296no—
994C23—2256no—
995C23—224no—
996C23—224no—
997C23—248no—
998C23—296no—
999C23—212no—
1000C23—224no—
1001C23—22no—
1002C23—26no—
1003C23—212no—
1004C23—224no—
1005C23—248no—
1006C23—2384no—
1007C23—296no—
1008C23—296no—
1009C23—224no—
1010C23—296no—
1011C23—296no—
1012C23—248no—
1013C23—212no—
1014C23—248no—
1015C23—224no—
1016C23—26no—
1017C23—26no—
1018C23—212no—
1019C23—296no—
1020C23—224no—
1021C23—24no—
1022C23—224no—
1023C23—448no—
1024C23—496no—
1025C23—496no—
1026C23—496no—
1027C23—496no—
1028C23—4384no—
1029C23—4768no—
1030C23—41024no—
1031C23—42048no—
1032C23—4192no—
1033C23—448no—
1034C23—4384no—
1035C23—4384no—
1036C23—4384no—
1037C23—4768no—
1038C23—448no—
1039C23—424no—
1040C23—448no—
1041C23—448no—
1042C23—4192no—
1043C23—48no—
1044C23—424no—
1045C23—448no—
1046C23—424no—
1047C23—424no—
1048C23—46no—
1049C23—48no—
1050C23—46no—
1051C23—412no—
1052C23—864no—
1053C23—824no—
1054C23—88no—
1055C23C22×#120132yes—
1056C23C22×#120112yes—
1057C23C22×#120116yes—
1058C23C22×#120112yes—
1059C23C22×#120112yes—
1060C23C2×#525112yes—
1061C23#3449112yes—
1062C23D4×#41148yes—
1063C23C24×D416yes—
1064C23C24×D411yescharacteristic
1065C23C23×#4112yes—
1066C23C2×#58516yes—
1067Q8—2384no—
1068Q8—2128no—
1069D4—2768no—
1070D4—2384no—
1071D4—2256no—
1072D4—2128no—
1073D4—496no—
1074D4—496no—
1075D4—8128no—
1076C2×C4—296no—
1077C2×C4—2384no—
1078C2×C4—296no—
1079C2×C4—2768no—
1080C2×C4—2192no—
1081C2×C4—296no—
1082C2×C4—212no—
1083C2×C4—224no—
1084C2×C4—248no—
1085C2×C4—212no—
1086C2×C4—248no—
1087C2×C4—224no—
1088C2×C4—296no—
1089C2×C4—296no—
1090C2×C4—296no—
1091C2×C4—296no—
1092C2×C4—2256no—
1093C2×C4—212no—
1094C2×C4—224no—
1095C2×C4—448no—
1096C2×C4—46no—
1097C2×C4—46no—
1098C2×C4—412no—
1099C2×C4—424no—
1100C2×C4—448no—
1101C2×C4—46no—
1102C2×C4—416no—
1103C2×C4—46no—
1104C2×C4—48no—
1105C2×C4—412no—
1106C2×C4—448no—
1107C2×C4—824no—
1108C2×C4—88no—
1109C2×C4—816no—
1110C2×C4—816no—
1111C2×C4#2846164yescomplemented
1112C2×C4C22×#120112yes—
1113C2×C4C22×#120132yes—
1114C2×C4C22×#120112yes—
1115C2×C4C22×#120112yes—
1116C2×C4C22×#120116yes—
1117C2×C4C22×#120112yes—
1118C2×C4C22×#120116yes—
1119C22—2128no—
1120C22—212no—
1121C22—212no—
1122C22—224no—
1123C22—212no—
1124C22—224no—
1125C22—212no—
1126C22—296no—
1127C22—232no—
1128C22—212no—
1129C22—212no—
1130C22—232no—
1131C22—212no—
1132C22—264no—
1133C22—4192no—
1134C22—4192no—
1135C22—4768no—
1136C22—448no—
1137C22—412no—
1138C22—412no—
1139C22—448no—
1140C22—448no—
1141C22—496no—
1142C22—412no—
1143C22—416no—
1144C22—832no—
1145C22—86no—
1146C22—82no—
1147C22—88no—
1148C22#34736124yescomplemented
1149C22C2×#284618yes—
1150C22C23×#12013yes—
1151C22C23×#12014yes—
1152C22C22×#52511yescharacteristic
1153C22C2×#344913yes—
1154C22C2×D4×#41112yes—
1155C22#62811112yes—
1156C4—212no—
1157C4—232no—
1158C4—212no—
1159C4—412no—
1160C4—86no—
1161C4—82no—
1162C4—816no—
1163C4C2×#284618yes—
1164C4C2×#284618yes—
1165C2—224no—
1166C2—28no—
1167C2—412no—
1168C2—432no—
1169C2—84no—
1170C2C2×#3473613yes—
1171C2#762864913yes—
1172C2#41×#12018yes—
1173C2C22×#284611yescharacteristic
subgroupG/H
centerC23×C4C25
commutator, Frattini, socle, cosocleC24C26
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C25×#41C2semidirect
2. C2×#34736C2semidirect
3. C22×C4×#120C2semidirect
4. #613434C2semidirect
5. #613321C2semidirect
6. #613188C2semidirect
7. #613007C2semidirect
8. #612792C2semidirect
9. #612617C2semidirect
10. #612424C2semidirect
11. #607926C2semidirect
12. C4×#2846C2semidirect
13. #607558C2semidirect
14. #514204C2semidirect
19. C24×#41C22semidirect
20. C24×#41C22semidirect
21. C25×Q8C22semidirect
23. C25×D4C22semidirect
25. C26×C4C22semidirect
26. C22×#525C22semidirect
28. C23×C4×D4C22semidirect
31. C2×#2406C22semidirect
32. C2×#2404C22semidirect
33. C2×#2407C22semidirect
34. C2×#2409C22semidirect
35. C2×#2408C22semidirect
36. C2×#2405C22semidirect
37. C2×#2403C22semidirect
38. C2×#2388C22semidirect
42. C2×C4×#120C22semidirect
43. C2×C4×#120C22semidirect
44. C2×C4×#120C22semidirect
45. C2×#2297C22semidirect
46. C22×#386C22semidirect
47. C22×#385C22semidirect
48. C2×#2280C22semidirect
50. C22×C4×C22⋊C4C22semidirect
51. #14889C22semidirect
52. #14885C22semidirect
53. #14874C22semidirect
54. #14873C22semidirect
55. #14724C22semidirect
56. #14724C22semidirect
57. #14715C22semidirect
58. #14715C22semidirect
60. #14694C22semidirect
61. #14693C22semidirect
62. #14693C22semidirect
63. #14681C22semidirect
64. #14680C22semidirect
65. #14680C22semidirect
67. #14679C22semidirect
68. #13956C22semidirect
69. #13937C22semidirect
70. #13922C22semidirect
71. #13902C22semidirect
72. #13867C22semidirect
73. #13867C22semidirect
74. #13851C22semidirect
75. C4×#379C22semidirect
76. C4×#379C22semidirect
77. C4×#379C22semidirect
95. C23×#41D4semidirect
117. C25×C4D4semidirect
127. C25×C4C23semidirect
129. C22×#123C23semidirect
130. C22×C22⋊Q8C23semidirect
131. C22×#121C23semidirect
137. C22×#120C23semidirect
142. C22×C4×D4C23semidirect
143. C22×C4×D4C23semidirect
144. C22×C4×D4C23semidirect
145. C22×#117C23semidirect
146. C23×C4⋊C4C23semidirect
150. C23×C22⋊C4C23semidirect
151. C23×C42C23semidirect
161. C2×#395C23semidirect
162. C2×#394C23semidirect
163. C2×#394C23semidirect
164. C2×#393C23semidirect
165. C2×#392C23semidirect
166. C2×#392C23semidirect
173. C2×#391C23semidirect
174. C2×#390C23semidirect
179. C2×#386C23semidirect
180. C2×#386C23semidirect
181. C2×#386C23semidirect
182. C2×#386C23semidirect
187. C2×#385C23semidirect
188. C2×#385C23semidirect
190. C2×#381C23semidirect
192. C2×#380C23semidirect
206. C2×C4×C22⋊C4C23semidirect
207. C2×C4×C22⋊C4C23semidirect
208. C2×C4×C22⋊C4C23semidirect
209. C2×C4×C22⋊C4C23semidirect
210. C22×#95C23semidirect
211. #1446C23semidirect
212. #1438C23semidirect
213. #1438C23semidirect
214. #1438C23semidirect
219. C22⋊#95C23semidirect
220. C22⋊#95C23semidirect
268. C22×#41C2×D4semidirect
269. C22×#41C2×D4semidirect
278. C23×Q8C2×D4semidirect
303. C23×D4C2×D4semidirect
342. C24×C4C2×D4semidirect
374. C2×#120#41semidirect
533. C2×#41#120semidirect
597. C22×D4C2×#41semidirect
661. C23×C4#120semidirect
742. C2×C22⋊C4C2×#41semidirect
823. C24#525semidirect
832. C24C22×#41semidirect
848. C2×Q8C2×#120semidirect
881. C2×D4C2×#120semidirect
959. C22×C4C2×#120semidirect
969. C22×C4C22×#41semidirect
1111. C2×C4#2846semidirect
1148. C22#34736semidirect

Maximal subgroups

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

subgroupindex
C25×#412
C2×#347362
C22×C4×#1202
#6134342
#6133212
#6131882
#6130072
#6127922
#6126172
#6124242
#6079262
C4×#28462
#6075582
#5142042