Finite Group Databasebeta

← #72281699

Subgroups — #72281699

Order 1024.

15221 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#34936C211yesmaximal, characteristic
2#6408574C2116yesmaximal, complemented
3#6408573C2116yesmaximal, complemented
4#6407628C214yesmaximal, complemented
5#6382734C214yesmaximal, complemented
6#6378988C218yesmaximal, complemented
7#6376471C218yesmaximal, complemented
8#6374114C212yesmaximal, complemented
9#6374111C212yesmaximal, complemented
10#6371086C212yesmaximal, complemented
11C22×#532C2211yescharacteristic
12C22×#525C2214yes—
13C23×C4×D4C2211yescharacteristic
14C2×D4×M16C22116yescomplemented
15C2×#2879C2214yes—
16C22×#407C2214yes—
17#34936C418yes—
18#34936C418yes—
19#34936C2218yes—
20#34936C2218yes—
21C2×#2542C412yes—
22C2×#2541C412yes—
23C2×#2540C414yes—
24C2×#2539C414yes—
25C2×#2501C412yes—
26C2×#2433C412yes—
27C2×#2397C2212yes—
28C2×#2397C2212yes—
29C2×C4×#127C2214yes—
30C2×C4×#117C2211yescharacteristic
31#23359C22116yescomplemented
32#23359C22116yescomplemented
33#23358C22116yescomplemented
34#23358C22116yescomplemented
35#23178C22116yescomplemented
36#23178C22116yescomplemented
37#23177C22116yescomplemented
38#23177C22116yescomplemented
39#22400C22132yescomplemented
40#22400C22132yescomplemented
41#22398C22132yescomplemented
42#22398C22132yescomplemented
43#22266C22116yescomplemented
44#22266C22132yescomplemented
45#22266C22116yescomplemented
46#22264C22116yescomplemented
47#22262C22132yescomplemented
48#22260C22116yescomplemented
49#21745C22132yescomplemented
50#21742C2218yescomplemented
51#21740C2218yescomplemented
52#21740C2218yescomplemented
53#21738C2218yescomplemented
54#21190C22116yescomplemented
55#20898C2218yes—
56#20898C2218yes—
57#20898C2218yescomplemented
58#20898C22116yescomplemented
59#20898C22116yescomplemented
60#20898C2218yescomplemented
61#20780C22132yescomplemented
62#20773C2214yescomplemented
63#20752C2214yescomplemented
64#20682C2214yes—
65#20627C2214yes—
66#20580C2214yes—
67#20579C2214yes—
68#20429C2214yescomplemented
69#20377C2214yes—
70#20364C2214yescomplemented
71C23×#41C2312yes—
72C24×D4C2×C411yescharacteristic
73C25×C4C2312yes—
74C23×M16C2318yes—
75C23×M16C2318yes—
76C2×#532—48no—
77C2×#532C2×C418yes—
78C2×#532C2318yes—
79C22×C4⋊Q8C2×C411yescharacteristic
80C22×#127C2×C411yescharacteristic
81C22×#127C2×C414yes—
82C22×#124C2×C412yes—
83C2×#525—432no—
84C2×#525C2×C418yes—
85C2×#525C2×C4116yes—
86C2×#525C2×C418yes—
87C2×#525C2318yes—
88C2×#525C23116yes—
89C2×#525C2318yes—
90C22×#123C2×C418yes—
91C22×C22⋊Q8C2×C418yes—
92C22×#121C2×C412yes—
93C22×#121C2×C418yes—
94C22×#121C2×C412yes—
95C22×#120C2×C418yes—
96C22×C4×D4—48no—
97C22×C4×D4C2×C412yes—
98C22×C4×D4C2×C412yes—
99C22×C4×D4C2×C414yes—
100C22×C4×D4C2×C414yes—
101C22×C4×D4C2318yes—
102C22×C4×D4C2314yes—
103C22×C4×D4C2314yes—
104C22×C4×D4C2312yes—
105C22×C4×D4C2312yes—
106C22×C4×D4C2318yes—
107C22×C4×D4C2312yes—
108C22×C4×D4C2312yes—
109C22×#117C2312yes—
110C23×C4⋊C4C2×C411yescharacteristic
111C23×C22⋊C4C2×C412yes—
112C23×C42C2311yescharacteristic
113D4×M16—464no—
114C2×#436C23132yescomplemented
115C2×#435C23132yescomplemented
116C2×#435C23132yescomplemented
117C2×C8×D4C23132yescomplemented
118C2×#423C2318yes—
119#2879—416no—
120C2×#408C23132yes—
121C2×#407—416no—
122C2×#407C2318yes—
123C2×#407C23116yes—
124C2×#407C23116yes—
125C2×#407C2318yes—
126C2×#407C2318yes—
127C2×#407C2318yes—
128C2×#407C2318yes—
129C22×C22⋊C8C2318yes—
130C22×C22⋊C8C2318yes—
131C2×C4×M16C2318yes—
132#2542C2×C418yes—
133#2542C2×C418yes—
134#2542C2×C418yes—
135#2542C2×C418yes—
136#2541C2×C418yes—
137#2541C2×C418yes—
138#2541C2×C418yes—
139#2541C2×C418yes—
140#2540C2×C4116yes—
141#2540C2×C4116yes—
142#2540C2×C4116yes—
143#2540C2×C4116yes—
144#2539C2×C418yes—
145#2539C2×C418yes—
146#2539C2×C418yes—
147#2539C2×C418yes—
148#2539C2×C418yes—
149#2539C2×C418yes—
150#2539C2×C418yes—
151#2539C2×C418yes—
152#2501C2×C4116yes—
153#2501C2×C4116yes—
154#2433C2×C4116yes—
155#2433C2×C4116yes—
156#2397C2×C414yes—
157#2397C2×C418yes—
158#2397C2×C414yes—
159#2397C2×C414yes—
160#2397C2×C418yes—
161#2397C2×C414yes—
162#2397C2314yes—
163#2397C2318yes—
164#2397C2314yes—
165#2397C2314yes—
166#2397C2318yes—
167#2397C2314yes—
168C2×#399C2×C414yes—
169C2×#399C2×C414yes—
170C2×#399C2×C414yes—
171C2×#399C2×C414yes—
172C2×#392C2×C414yes—
173C2×#392C2×C414yes—
174C2×#392C2×C414yes—
175C2×#392C2×C414yes—
176C4×#127C2×C418yes—
177C4×#127C2×C4116yes—
178C4×#127C2×C418yes—
179C4×#127C2318yes—
180C4×#127C23116yes—
181C4×#127C2318yes—
182C2×#390C2×C418yes—
183C2×#390C2×C418yes—
184C2×#390C2×C414yes—
185C2×#390C2×C414yes—
186C2×#384C2×C414yes—
187C4×#117C2×C418yes—
188C4×#117C2318yes—
189C2×C4×C4⋊C4C2×C412yes—
190C2×C4×C4⋊C4C2×C412yes—
191C2×C4×C22⋊C4C2×C412yes—
192C2×C4×C22⋊C4C2×C412yes—
193C2×#376C2311yescharacteristic
194C2×#376C2311yescharacteristic
195C2×C43C2312yes—
196#1955C23132yescomplemented
197#1955C23132yescomplemented
198#1954C23132yescomplemented
199#1954C23132yescomplemented
200#1870C23116yes—
201#1870C23116yes—
202#1870C23116yes—
203#1870C23116yes—
204#1870C23132yescomplemented
205#1870C23132yescomplemented
206#1870C23116yescomplemented
207#1870C23132yescomplemented
208#1870C23132yescomplemented
209#1870C23116yescomplemented
210#1870C23132yescomplemented
211#1869C23116yes—
212#1869C23116yes—
213#1869C23116yes—
214#1869C23116yes—
215#1869C23132yescomplemented
216#1869C23132yescomplemented
217#1869C23116yescomplemented
218#1869C23132yescomplemented
219#1869C23132yescomplemented
220#1869C23116yescomplemented
221#1869C23132yescomplemented
222#1840C23132yescomplemented
223#1831C23116yescomplemented
224#1831C23116yescomplemented
225#1817C23116yes—
226#1817C23116yes—
227#1798C23132yes—
228#1780C23132yes—
229#1779C2318yes—
230#1779C23116yes—
231#1779C2318yes—
232#1768C23132yescomplemented
233#1750C23132yes—
234#1745C23116yescomplemented
235#1744C23116yescomplemented
236#1728C2318yes—
237#1728C2318yes—
238#1728C2318yes—
239#1728C2318yes—
240C26C22×C412yes—
241C22×#41—216no—
242C22×#41—416no—
243C22×#41C22×C418yes—
244C22×#41C2418yes—
245C23×Q8C22×C412yes—
246C23×D4—44no—
247C23×D4—48no—
248C23×D4C22×C412yes—
249C23×D4C22×C414yes—
250C23×D4C22×C414yes—
251C23×D4C22×C412yes—
252C23×D4C22×C418yes—
253C23×D4C22×C412yes—
254C23×D4C22×C414yes—
255C23×D4C22×C412yes—
256C23×D4C22×C418yes—
257C23×D4C22×C412yes—
258C24×C4—216no—
259C24×C4—416no—
260C24×C4C22×C412yes—
261C24×C4C22×C414yes—
262C24×C4C22×C412yes—
263C24×C4C22×C414yes—
264C24×C4C22×C412yes—
265C24×C4C22×C411yescharacteristic
266C24×C4C22×C411yescharacteristic
267C24×C4C2414yes—
268C24×C4C2414yes—
269C24×C4C2411yescharacteristic
270C24×C4C2412yes—
271C24×C4C2414yes—
272C24×C4C2412yes—
273C22×M16—416no—
274C22×M16—416no—
275C22×M16—432no—
276C22×M16—432no—
277C22×M16C24116yes—
278C22×M16C24116yes—
279C22×M16C24116yes—
280C23×C8C24116yes—
281C23×C8C24116yes—
282#532—432no—
283#532—416no—
284#532—416no—
285C2×C4⋊Q8—44no—
286C2×C4⋊Q8C22×C418yes—
287C2×#127—44no—
288C2×#127—416no—
289C2×#127C22×C418yes—
290C2×#127C22×C418yes—
291C2×#127C22×C4116yes—
292C2×#127C22×C418yes—
293C2×#124—48no—
294C2×#124C22×C4116yes—
295#525—432no—
296#525—464no—
297#525—432no—
298#525—432no—
299#525—432no—
300#525—432no—
301#525—432no—
302C2×#123—432no—
303C2×#123C22×C4116yes—
304C2×#123C22×C4116yes—
305C2×#123C22×C4116yes—
306C2×#123C22×C4116yes—
307C2×C22⋊Q8—432no—
308C2×C22⋊Q8C22×C4116yes—
309C2×C22⋊Q8C22×C4116yes—
310C2×C22⋊Q8C22×C4116yes—
311C2×C22⋊Q8C22×C4116yes—
312C2×#121—432no—
313C2×#121—48no—
314C2×#121—48no—
315C2×#121C22×C4116yes—
316C2×#121C22×C4116yes—
317C2×#121C22×C4116yes—
318C2×#121C22×C4116yes—
319C2×#121C22×C4116yes—
320C2×#121C22×C418yes—
321C2×#121C22×C418yes—
322C2×#120—432no—
323C2×#120C22×C4116yes—
324C2×#120C22×C4116yes—
325C2×#120C22×C4116yes—
326C2×#120C22×C4116yes—
327C2×C4×D4—264no—
328C2×C4×D4—48no—
329C2×C4×D4—48no—
330C2×C4×D4—416no—
331C2×C4×D4—416no—
332C2×C4×D4—44no—
333C2×C4×D4—48no—
334C2×C4×D4—44no—
335C2×C4×D4—48no—
336C2×C4×D4—48no—
337C2×C4×D4—48no—
338C2×C4×D4—48no—
339C2×C4×D4—432no—
340C2×C4×D4—44no—
341C2×C4×D4—48no—
342C2×C4×D4—44no—
343C2×C4×D4C22×C4116yes—
344C2×C4×D4C22×C4116yes—
345C2×C4×D4C22×C414yes—
346C2×C4×D4C22×C412yes—
347C2×C4×D4C22×C412yes—
348C2×C4×D4C22×C418yes—
349C2×C4×D4C22×C4116yes—
350C2×C4×D4C22×C4116yes—
351C2×C4×D4C22×C412yes—
352C2×C4×D4C22×C414yes—
353C2×C4×D4C22×C412yes—
354C2×C4×D4C22×C414yes—
355C2×C4×D4C22×C414yes—
356C2×C4×D4C22×C414yes—
357C2×C4×D4C22×C414yes—
358C2×C4×D4C22×C414yes—
359C2×C4×D4C22×C414yes—
360C2×C4×D4C22×C414yes—
361C2×C4×D4C22×C414yes—
362C2×C4×D4C22×C414yes—
363C2×C4×D4C22×C414yes—
364C2×C4×D4C24116yes—
365C2×C4×D4C24116yes—
366C2×C4×D4C2412yes—
367C2×C4×D4C2414yes—
368C2×C4×D4C2418yes—
369C2×C4×D4C2412yes—
370C2×C4×D4C24116yes—
371C2×C4×D4C24116yes—
372C2×C4×D4C2412yes—
373C2×C4×D4C2414yes—
374C2×C4×D4C2414yes—
375C2×C4×D4C2414yes—
376C2×C4×D4C2412yes—
377C2×#117—216no—
378C2×#117C22×C418yes—
379C2×#117C2418yes—
380C22×C4⋊C4—44no—
381C22×C4⋊C4C22×C418yes—
382C22×C4⋊C4C22×C414yes—
383C22×C4⋊C4C22×C412yes—
384C22×C4⋊C4C22×C412yes—
385C22×C4⋊C4C22×C418yes—
386C22×C4⋊C4C22×C414yes—
387C22×C4⋊C4C22×C414yes—
388C22×C4⋊C4C22×C412yes—
389C22×C4⋊C4C22×C412yes—
390C22×C22⋊C4—48no—
391C22×C22⋊C4C22×C418yes—
392C22×C22⋊C4C22×C418yes—
393C22×C22⋊C4C22×C414yes—
394C22×C22⋊C4C22×C414yes—
395C22×C22⋊C4C22×C414yes—
396C22×C22⋊C4C22×C418yes—
397C22×C22⋊C4C22×C418yes—
398C22×C22⋊C4C22×C414yes—
399C22×C22⋊C4C22×C414yes—
400C22×C22⋊C4C22×C414yes—
401C22×C22⋊C4C22×C414yes—
402C22×C22⋊C4C22×C414yes—
403C22×C22⋊C4C22×C414yes—
404C22×C42—28no—
405C22×C42C22×C411yescharacteristic
406C22×C42C22×C411yescharacteristic
407C22×C42C22×C414yes—
408C22×C42C22×C414yes—
409C22×C42C22×C414yes—
410C22×C42C2414yes—
411C22×C42C2411yescharacteristic
412C22×C42C2411yescharacteristic
413C22×C42C2412yes—
414C22×C42C2412yes—
415#436—464no—
416#435—464no—
417#435—464no—
418C8×D4—464no—
419#423—232no—
420C2×C4⋊C8C24132yes—
421#408—464no—
422#407—232no—
423#407—416no—
424#407—416no—
425#407—416no—
426#407—416no—
427#407—432no—
428#407—432no—
429C2×C22⋊C8—416no—
430C2×C22⋊C8—416no—
431C2×C22⋊C8C24116yes—
432C2×C22⋊C8C24116yes—
433C2×C22⋊C8C24116yes—
434C2×C22⋊C8C24116yes—
435C2×C22⋊C8C24116yes—
436C2×C22⋊C8C24116yes—
437C2×C22⋊C8C24132yes—
438C2×C22⋊C8C24132yes—
439C2×C22⋊C8C24132yes—
440C2×C22⋊C8C24132yes—
441C4×M16—232no—
442C2×#97C24116yes—
443C2×C4×C8C24116yes—
444#399C22×C418yes—
445#399C22×C4116yes—
446#399C22×C418yes—
447#399C22×C418yes—
448#399C22×C4116yes—
449#399C22×C418yes—
450#399C22×C418yes—
451#399C22×C418yes—
452#399C22×C418yes—
453#399C22×C418yes—
454#399C22×C418yes—
455#399C22×C418yes—
456#399C22×C418yes—
457#399C22×C418yes—
458#392C22×C418yes—
459#392C22×C4116yes—
460#392C22×C418yes—
461#392C22×C418yes—
462#392C22×C4116yes—
463#392C22×C418yes—
464#392C22×C418yes—
465#392C22×C418yes—
466#392C22×C418yes—
467#392C22×C418yes—
468#392C22×C418yes—
469#392C22×C418yes—
470#392C22×C418yes—
471#392C22×C418yes—
472#390C22×C4116yes—
473#390C22×C418yes—
474#390C22×C418yes—
475#390C22×C4116yes—
476#390C22×C418yes—
477#390C22×C418yes—
478#390C22×C4116yes—
479#390C22×C4116yes—
480#390C22×C4116yes—
481#390C22×C4116yes—
482#390C22×C4116yes—
483#390C22×C4116yes—
484#390C22×C4116yes—
485#390C22×C4116yes—
486#384C22×C418yes—
487#384C22×C418yes—
488#384C22×C4116yes—
489C4×C4⋊C4C22×C4116yes—
490C4×C4⋊C4C22×C418yes—
491C4×C4⋊C4C22×C418yes—
492C4×C22⋊C4C22×C4116yes—
493C4×C22⋊C4C22×C418yes—
494C4×C22⋊C4C22×C418yes—
495#376C22×C414yes—
496#376C22×C414yes—
497#376C2414yes—
498#376C2414yes—
499C2×#95C22×C412yes—
500C2×#95C22×C412yes—
501C2×#95C22×C412yes—
502C2×#95C22×C412yes—
503C43C22×C418yes—
504C43C2418yes—
505#336C24132yes—
506#336C24132yes—
507#336C24132yes—
508#336C24116yes—
509#336C24116yes—
510C25—28no—
511C25—48no—
512C25—48no—
513C25—84no—
514C25C23×C414yes—
515C25C23×C414yes—
516C25C23×C412yes—
517C25C23×C414yes—
518C25C23×C411yescharacteristic
519C25C23×C412yes—
520C2×#41—232no—
521C2×#41—232no—
522C2×#41—416no—
523C2×#41—416no—
524C2×#41—48no—
525C2×#41—416no—
526C2×#41—48no—
527C2×#41—864no—
528C22×Q8—28no—
529C22×Q8—48no—
530C22×Q8C23×C418yes—
531C22×D4—216no—
532C22×D4—28no—
533C22×D4—216no—
534C22×D4—232no—
535C22×D4—28no—
536C22×D4—44no—
537C22×D4—48no—
538C22×D4—48no—
539C22×D4—44no—
540C22×D4—44no—
541C22×D4—48no—
542C22×D4—48no—
543C22×D4—416no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4—416no—
547C22×D4—48no—
548C22×D4—48no—
549C22×D4—48no—
550C22×D4—48no—
551C22×D4—416no—
552C22×D4—416no—
553C22×D4—464no—
554C22×D4—88no—
555C22×D4—88no—
556C22×D4—84no—
557C22×D4C23×C414yes—
558C22×D4C23×C412yes—
559C22×D4C23×C4116yes—
560C22×D4C23×C412yes—
561C22×D4C23×C414yes—
562C22×D4C23×C4116yes—
563C22×D4C23×C4116yes—
564C22×D4C23×C418yes—
565C22×D4C23×C4116yes—
566C22×D4C23×C418yes—
567C22×D4C23×C412yes—
568C22×D4C23×C4116yes—
569C22×D4C23×C414yes—
570C22×D4C23×C414yes—
571C22×D4C23×C412yes—
572C23×C4—28no—
573C23×C4—24no—
574C23×C4—24no—
575C23×C4—28no—
576C23×C4—232no—
577C23×C4—232no—
578C23×C4—28no—
579C23×C4—28no—
580C23×C4—28no—
581C23×C4—28no—
582C23×C4—216no—
583C23×C4—28no—
584C23×C4—216no—
585C23×C4—28no—
586C23×C4—28no—
587C23×C4—28no—
588C23×C4—28no—
589C23×C4—28no—
590C23×C4—44no—
591C23×C4—48no—
592C23×C4—416no—
593C23×C4—48no—
594C23×C4—48no—
595C23×C4—416no—
596C23×C4—48no—
597C23×C4—416no—
598C23×C4—48no—
599C23×C4—864no—
600C23×C4—82no—
601C23×C4C23×C414yes—
602C23×C4C23×C414yes—
603C23×C4C23×C411yescharacteristic
604C23×C4C23×C414yes—
605C23×C4C23×C414yes—
606C23×C4C23×C418yes—
607C23×C4C23×C414yes—
608C23×C4C23×C411yescharacteristic
609C23×C4C23×C412yes—
610C23×C4C23×C411yescharacteristic
611C23×C4C23×C414yes—
612C23×C4C23×C411yescharacteristic
613C23×C4C23×C411yescharacteristic
614C23×C4C23×C414yes—
615C23×C4C23×C412yes—
616C23×C4C23×C414yes—
617C23×C4C23×C412yes—
618C23×C4C23×C414yes—
619C23×C4C23×C414yes—
620C23×C4C23×C414yes—
621C23×C4C23×C414yes—
622C23×C4C23×C414yes—
623C23×C4H(5,𝔽2)18yes—
624C23×C4C2514yes—
625C23×C4C2518yes—
626C23×C4C2514yes—
627C23×C4C2512yes—
628C23×C4C2511yescharacteristic
629C2×M16—232no—
630C2×M16—232no—
631C2×M16—232no—
632C2×M16—416no—
633C2×M16—416no—
634C2×M16—432no—
635C2×M16—432no—
636C2×M16—864no—
637C2×M16—864no—
638C22×C8—416no—
639C22×C8—416no—
640C22×C8—432no—
641C22×C8—432no—
642C22×C8C25132yes—
643C4⋊Q8—416no—
644#127—232no—
645#127—416no—
646#127—416no—
647#127—432no—
648#124—432no—
649#123—432no—
650#123—432no—
651#123—432no—
652#123—432no—
653C22⋊Q8—432no—
654C22⋊Q8—432no—
655C22⋊Q8—432no—
656C22⋊Q8—432no—
657#121—432no—
658#121—432no—
659#121—432no—
660#121—432no—
661#121—432no—
662#121—416no—
663#121—416no—
664#120—432no—
665#120—432no—
666#120—432no—
667#120—432no—
668C4×D4—264no—
669C4×D4—264no—
670C4×D4—232no—
671C4×D4—232no—
672C4×D4—232no—
673C4×D4—232no—
674C4×D4—44no—
675C4×D4—48no—
676C4×D4—44no—
677C4×D4—44no—
678C4×D4—48no—
679C4×D4—44no—
680C4×D4—48no—
681C4×D4—48no—
682C4×D4—48no—
683C4×D4—48no—
684C4×D4—48no—
685C4×D4—48no—
686C4×D4—48no—
687C4×D4—48no—
688C4×D4—42no—
689C4×D4—44no—
690C4×D4—42no—
691C4×D4—44no—
692C4×D4—44no—
693C4×D4—44no—
694C4×D4—44no—
695C4×D4—42no—
696C4×D4—44no—
697C4×D4—42no—
698C4×D4—432no—
699C4×D4—432no—
700C4×D4—416no—
701C4×D4—48no—
702C4×D4—48no—
703C4×D4—416no—
704C4×D4—416no—
705C4×D4—416no—
706C4×D4—416no—
707C4×D4—44no—
708C4×D4—44no—
709C4×D4—416no—
710C4×D4—44no—
711C4×D4—44no—
712#117—232no—
713#117—232no—
714C2×C4⋊C4—216no—
715C2×C4⋊C4—232no—
716C2×C4⋊C4—44no—
717C2×C4⋊C4—44no—
718C2×C4⋊C4—48no—
719C2×C4⋊C4—48no—
720C2×C4⋊C4—44no—
721C2×C4⋊C4—44no—
722C2×C4⋊C4—416no—
723C2×C4⋊C4C23×C4116yes—
724C2×C4⋊C4C23×C4116yes—
725C2×C4⋊C4C23×C4116yes—
726C2×C4⋊C4C23×C412yes—
727C2×C4⋊C4C23×C414yes—
728C2×C4⋊C4C23×C412yes—
729C2×C4⋊C4C23×C412yes—
730C2×C4⋊C4C23×C414yes—
731C2×C4⋊C4C23×C412yes—
732C2×C4⋊C4C23×C418yes—
733C2×C4⋊C4C23×C414yes—
734C2×C4⋊C4C23×C414yes—
735C2×C4⋊C4C23×C4116yes—
736C2×C4⋊C4C23×C4116yes—
737C2×C22⋊C4—216no—
738C2×C22⋊C4—232no—
739C2×C22⋊C4—232no—
740C2×C22⋊C4—48no—
741C2×C22⋊C4—48no—
742C2×C22⋊C4—48no—
743C2×C22⋊C4—48no—
744C2×C22⋊C4—48no—
745C2×C22⋊C4—48no—
746C2×C22⋊C4—416no—
747C2×C22⋊C4—416no—
748C2×C22⋊C4—48no—
749C2×C22⋊C4—48no—
750C2×C22⋊C4C23×C4116yes—
751C2×C22⋊C4C23×C4116yes—
752C2×C22⋊C4C23×C4116yes—
753C2×C22⋊C4C23×C4116yes—
754C2×C22⋊C4C23×C4116yes—
755C2×C22⋊C4C23×C414yes—
756C2×C22⋊C4C23×C414yes—
757C2×C22⋊C4C23×C414yes—
758C2×C22⋊C4C23×C414yes—
759C2×C22⋊C4C23×C414yes—
760C2×C22⋊C4C23×C414yes—
761C2×C22⋊C4C23×C414yes—
762C2×C22⋊C4C23×C414yes—
763C2×C22⋊C4C23×C4116yes—
764C2×C22⋊C4C23×C4116yes—
765C2×C22⋊C4C23×C4116yes—
766C2×C22⋊C4C23×C4116yes—
767C2×C22⋊C4C23×C4116yes—
768C2×C22⋊C4C23×C418yes—
769C2×C22⋊C4C23×C418yes—
770C2×C42—24no—
771C2×C42—24no—
772C2×C42—216no—
773C2×C42—28no—
774C2×C42—24no—
775C2×C42—24no—
776C2×C42—28no—
777C2×C42—28no—
778C2×C42—48no—
779C2×C42—84no—
780C2×C42C23×C414yes—
781C2×C42C23×C412yes—
782C2×C42C23×C412yes—
783C2×C42C23×C414yes—
784C2×C42C23×C414yes—
785C2×C42C23×C418yes—
786C2×C42C23×C418yes—
787C2×C42C23×C418yes—
788C2×C42C23×C418yes—
789C2×C42C23×C414yes—
790C2×C42H(5,𝔽2)116yes—
791C2×C42C2514yes—
792C2×C42C2512yes—
793C2×C42C2512yes—
794C2×C42C2514yes—
795C4⋊C8—264no—
796C22⋊C8—232no—
797C22⋊C8—232no—
798C22⋊C8—416no—
799C22⋊C8—416no—
800C22⋊C8—416no—
801C22⋊C8—416no—
802C22⋊C8—432no—
803C22⋊C8—432no—
804C22⋊C8—432no—
805C22⋊C8—432no—
806#97—232no—
807C4×C8—232no—
808#95C23×C418yes—
809#95C23×C418yes—
810#95C23×C418yes—
811#95C23×C418yes—
812C24—24no—
813C24—24no—
814C24—28no—
815C24—28no—
816C24—216no—
817C24—28no—
818C24—28no—
819C24—216no—
820C24—24no—
821C24—28no—
822C24—28no—
823C24—42no—
824C24—42no—
825C24—44no—
826C24—44no—
827C24—44no—
828C24—48no—
829C24—48no—
830C24—44no—
831C24—48no—
832C24—44no—
833C24—48no—
834C24—44no—
835C24—44no—
836C24—44no—
837C24—44no—
838C24—432no—
839C24—816no—
840C24—816no—
841C24—864no—
842C24#51814yes—
843C24C24×C414yes—
844C24C24×C418yes—
845C24C24×C412yes—
846C24C24×C414yes—
847C24C24×C411yescharacteristic
848#41—832no—
849#41—832no—
850#41—864no—
851C2×Q8—216no—
852C2×Q8—48no—
853C2×Q8—48no—
854C2×Q8—816no—
855C2×D4—232no—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—232no—
860C2×D4—232no—
861C2×D4—232no—
862C2×D4—232no—
863C2×D4—216no—
864C2×D4—24no—
865C2×D4—28no—
866C2×D4—216no—
867C2×D4—42no—
868C2×D4—44no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—44no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—416no—
878C2×D4—432no—
879C2×D4—416no—
880C2×D4—416no—
881C2×D4—48no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—416no—
885C2×D4—416no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—416no—
889C2×D4—48no—
890C2×D4—416no—
891C2×D4—416no—
892C2×D4—416no—
893C2×D4—416no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—464no—
897C2×D4—464no—
898C2×D4—432no—
899C2×D4—816no—
900C2×D4—816no—
901C2×D4—864no—
902C2×D4—832no—
903C2×D4—864no—
904C2×D4—816no—
905C2×D4#56818yes—
906C22×C4—22no—
907C22×C4—24no—
908C22×C4—28no—
909C22×C4—28no—
910C22×C4—232no—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—28no—
916C22×C4—28no—
917C22×C4—216no—
918C22×C4—216no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—24no—
923C22×C4—28no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—28no—
928C22×C4—216no—
929C22×C4—216no—
930C22×C4—216no—
931C22×C4—216no—
932C22×C4—24no—
933C22×C4—28no—
934C22×C4—24no—
935C22×C4—216no—
936C22×C4—216no—
937C22×C4—232no—
938C22×C4—28no—
939C22×C4—28no—
940C22×C4—216no—
941C22×C4—28no—
942C22×C4—28no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—42no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—48no—
955C22×C4—48no—
956C22×C4—48no—
957C22×C4—48no—
958C22×C4—44no—
959C22×C4—48no—
960C22×C4—44no—
961C22×C4—48no—
962C22×C4—416no—
963C22×C4—432no—
964C22×C4—432no—
965C22×C4—432no—
966C22×C4—432no—
967C22×C4—816no—
968C22×C4—816no—
969C22×C4—816no—
970C22×C4—816no—
971C22×C4—816no—
972C22×C4—832no—
973C22×C4—816no—
974C22×C4—832no—
975C22×C4—816no—
976C22×C4—88no—
977C22×C4#51814yes—
978C22×C4#51818yes—
979C22×C4#518116yes—
980C22×C4C24×C412yes—
981C22×C4C24×C412yes—
982C22×C4C24×C418yes—
983C22×C4C24×C412yes—
984C22×C4C24×C414yes—
985C22×C4C24×C414yes—
986C22×C4C24×C418yes—
987C22×C4C24×C418yes—
988C22×C4C24×C412yes—
989C22×C4C24×C412yes—
990C22×C4C24×C411yescharacteristic
991C22×C4C2×H(5,𝔽2)18yes—
992C22×C4C2×H(5,𝔽2)14yes—
993C22×C4C2×H(5,𝔽2)18yes—
994C22×C4C2611yescharacteristic
995M16—464no—
996M16—832no—
997M16—832no—
998C2×C8—232no—
999C2×C8—232no—
1000C2×C8—232no—
1001C2×C8—832no—
1002C2×C8—832no—
1003C4⋊C4—232no—
1004C4⋊C4—232no—
1005C4⋊C4—232no—
1006C4⋊C4—42no—
1007C4⋊C4—44no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—44no—
1011C4⋊C4—42no—
1012C4⋊C4—48no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—416no—
1016C4⋊C4—416no—
1017C22⋊C4—232no—
1018C22⋊C4—232no—
1019C22⋊C4—232no—
1020C22⋊C4—232no—
1021C22⋊C4—232no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—416no—
1031C22⋊C4—416no—
1032C22⋊C4—416no—
1033C22⋊C4—416no—
1034C22⋊C4—416no—
1035C22⋊C4—48no—
1036C22⋊C4—48no—
1037C42—24no—
1038C42—22no—
1039C42—22no—
1040C42—28no—
1041C42—24no—
1042C42—24no—
1043C42—28no—
1044C42—28no—
1045C42—28no—
1046C42—216no—
1047C42—48no—
1048C42—48no—
1049C42—48no—
1050C42#518116yes—
1051C42C2×H(5,𝔽2)116yes—
1052C23—22no—
1053C23—22no—
1054C23—216no—
1055C23—28no—
1056C23—24no—
1057C23—24no—
1058C23—24no—
1059C23—28no—
1060C23—24no—
1061C23—28no—
1062C23—24no—
1063C23—216no—
1064C23—24no—
1065C23—24no—
1066C23—28no—
1067C23—28no—
1068C23—28no—
1069C23—28no—
1070C23—216no—
1071C23—24no—
1072C23—28no—
1073C23—44no—
1074C23—44no—
1075C23—416no—
1076C23—416no—
1077C23—432no—
1078C23—416no—
1079C23—48no—
1080C23—416no—
1081C23—416no—
1082C23—416no—
1083C23—84no—
1084C23—88no—
1085C23—84no—
1086C23—88no—
1087C23—816no—
1088C23—84no—
1089C23—84no—
1090C23—816no—
1091C23—816no—
1092C23—88no—
1093C23—88no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23—816no—
1098C23—8128no—
1099C23C2×#51814yes—
1100C23C2×#51812yes—
1101C23C2×#51814yes—
1102C23C2×#56818yes—
1103C23C25×C411yescharacteristic
1104Q8—816no—
1105D4—48no—
1106D4—416no—
1107D4—464no—
1108D4—48no—
1109D4—48no—
1110D4—416no—
1111D4—48no—
1112D4—816no—
1113D4—832no—
1114D4—816no—
1115D4—832no—
1116D4—832no—
1117D4—88no—
1118D4—88no—
1119D4—832no—
1120C2×C4—28no—
1121C2×C4—28no—
1122C2×C4—28no—
1123C2×C4—22no—
1124C2×C4—28no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—216no—
1128C2×C4—216no—
1129C2×C4—28no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—28no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—28no—
1138C2×C4—28no—
1139C2×C4—28no—
1140C2×C4—216no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—28no—
1144C2×C4—416no—
1145C2×C4—416no—
1146C2×C4—44no—
1147C2×C4—44no—
1148C2×C4—44no—
1149C2×C4—416no—
1150C2×C4—416no—
1151C2×C4—416no—
1152C2×C4—48no—
1153C2×C4—48no—
1154C2×C4—48no—
1155C2×C4—48no—
1156C2×C4—48no—
1157C2×C4—48no—
1158C2×C4—416no—
1159C2×C4—416no—
1160C2×C4—416no—
1161C2×C4—432no—
1162C2×C4—88no—
1163C2×C4—88no—
1164C2×C4—88no—
1165C2×C4—88no—
1166C2×C4—88no—
1167C2×C4—84no—
1168C2×C4—88no—
1169C2×C4—84no—
1170C2×C4C2×#51814yes—
1171C2×C4C2×#518116yes—
1172C2×C4C2×#51812yes—
1173C2×C4C2×#51814yes—
1174C2×C4#3543116yes—
1175C2×C4C2×#56814yes—
1176C2×C4C22×H(5,𝔽2)12yes—
1177C2×C4C22×H(5,𝔽2)14yes—
1178C8—432no—
1179C22—22no—
1180C22—22no—
1181C22—28no—
1182C22—24no—
1183C22—28no—
1184C22—24no—
1185C22—216no—
1186C22—24no—
1187C22—416no—
1188C22—44no—
1189C22—48no—
1190C22—48no—
1191C22—44no—
1192C22—44no—
1193C22—48no—
1194C22—48no—
1195C22—44no—
1196C22—416no—
1197C22—48no—
1198C22—416no—
1199C22—48no—
1200C22—44no—
1201C22—48no—
1202C22—832no—
1203C22—816no—
1204C22—832no—
1205C22—816no—
1206C22—1616no—
1207C22#3436414yes—
1208C22C22×#51811yescharacteristic
1209C22C22×#51812yes—
1210C22C22×#56812yes—
1211C22#6307612yes—
1212C4—24no—
1213C4—216no—
1214C4—24no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—48no—
1219C4—44no—
1220C4—44no—
1221C4—48no—
1222C4#3436414yes—
1223C4C2×#354314yes—
1224C2—24no—
1225C2—44no—
1226C2—48no—
1227C2—84no—
1228C2—88no—
1229C2C2×#3436411yescharacteristic
1230C2#1057429411yescharacteristic
1231C2#1057429511yescharacteristic
1232C2#1057430514yes—
subgroupG/H
center, Frattini, cosocleC22×C4C26
commutator, socleC23C25×C4
prime radicalC2×#34936C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6408574C2semidirect
3. #6408573C2semidirect
4. #6407628C2semidirect
5. #6382734C2semidirect
6. #6378988C2semidirect
7. #6376471C2semidirect
8. #6374114C2semidirect
9. #6374111C2semidirect
10. #6371086C2semidirect
14. C2×D4×M16C22semidirect
31. #23359C22semidirect
32. #23359C22semidirect
33. #23358C22semidirect
34. #23358C22semidirect
35. #23178C22semidirect
36. #23178C22semidirect
37. #23177C22semidirect
38. #23177C22semidirect
39. #22400C22semidirect
40. #22400C22semidirect
41. #22398C22semidirect
42. #22398C22semidirect
43. #22266C22semidirect
44. #22266C22semidirect
45. #22266C22semidirect
46. #22264C22semidirect
47. #22262C22semidirect
48. #22260C22semidirect
49. #21745C22semidirect
50. #21742C22semidirect
51. #21740C22semidirect
52. #21740C22semidirect
53. #21738C22semidirect
54. #21190C22semidirect
57. #20898C22semidirect
58. #20898C22semidirect
59. #20898C22semidirect
60. #20898C22semidirect
61. #20780C22semidirect
62. #20773C22semidirect
63. #20752C22semidirect
68. #20429C22semidirect
70. #20364C22semidirect
114. C2×#436C23semidirect
115. C2×#435C23semidirect
116. C2×#435C23semidirect
117. C2×C8×D4C23semidirect
196. #1955C23semidirect
197. #1955C23semidirect
198. #1954C23semidirect
199. #1954C23semidirect
204. #1870C23semidirect
205. #1870C23semidirect
206. #1870C23semidirect
207. #1870C23semidirect
208. #1870C23semidirect
209. #1870C23semidirect
210. #1870C23semidirect
215. #1869C23semidirect
216. #1869C23semidirect
217. #1869C23semidirect
218. #1869C23semidirect
219. #1869C23semidirect
220. #1869C23semidirect
221. #1869C23semidirect
222. #1840C23semidirect
223. #1831C23semidirect
224. #1831C23semidirect
232. #1768C23semidirect
234. #1745C23semidirect
235. #1744C23semidirect

Maximal subgroups

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

subgroupindex
C2×#349362
#64085742
#64085732
#64076282
#63827342
#63789882
#63764712
#63741142
#63741112
#63710862