Finite Group Databasebeta

← #545162

Subgroups — #545162

Order 512.

2192 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2625C211yesmaximal, characteristic
2#14647C212yesmaximal, complemented
3#14615C212yesmaximal
4#14598C212yesmaximal, complemented
5#14585C212yesmaximal, complemented
6#14579C212yesmaximal
7#14332C212yesmaximal
8#14324C212yesmaximal
9#14247C212yesmaximal, complemented
10#14142C211yesmaximal, characteristic, complemented
11#14133C211yesmaximal, characteristic, complemented
12#14046C211yesmaximal, characteristic, complemented
13#14041C211yesmaximal, characteristic, complemented
14#14021C211yesmaximal, characteristic, complemented
15#14017C211yesmaximal, characteristic, complemented
16#13997C211yesmaximal, characteristic
17#13994C211yesmaximal, characteristic
18#13973C211yesmaximal, characteristic
19#13969C211yesmaximal, characteristic
20#13852C211yesmaximal, characteristic
21#13818C211yesmaximal, characteristic, complemented
22#13817C211yesmaximal, characteristic, complemented
23#13777C211yesmaximal, characteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2625C4116yescomplemented
28C2×#400C2212yes—
29C2×#398C2212yes—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2212yes—
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#388C2212yes—
44C2×#387C2212yes—
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57#1445C2212yes—
58#1445C2212yes—
59#1444C2212yes—
60#1443C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1441C2211yescharacteristic
72#1441C2212yes—
73#1441C2211yescharacteristic
74#1441C2211yescharacteristic
75#1441C2211yescharacteristic
76#1441C2212yes—
77#1440C2212yes—
78#1439C2211yescharacteristic
79#1439C2212yes—
80#1439C2211yescharacteristic
81#1439C2211yescharacteristic
82#1439C2211yescharacteristic
83#1439C2212yes—
84#1439C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105C4⋊#95C2212yes—
106C4⋊#95C2211yescharacteristic
107C4⋊#95C2211yescharacteristic
108C4⋊#95C2211yescharacteristic
109C4⋊#95C2211yescharacteristic
110C4⋊#95C2211yescharacteristic
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2212yes—
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115#1434C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118#1434C2212yes—
119#1434C2212yes—
120C4×#95C2211yescharacteristic
121C4×#95C2211yescharacteristic
122C4×#95C2212yes—
123C4×#95C2212yes—
124C23×Q8C2311yescharacteristic
125C24×C4C2311yescharacteristic
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8C2×C418yes—
129C2×C4×Q8—24no—
130C2×C4×Q8—42no—
131C2×C4×Q8—42no—
132C2×#117—42no—
133C2×#117—42no—
134C2×#117C2×C418yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2312yes—
176C22×C42C2312yes—
177#400C2×C4116yes—
178#398C2×C4116yes—
179#397C2×C4116yes—
180#397C2×C4116yes—
181#391—24no—
182#391—42no—
183#391—42no—
184#391C2×C418yes—
185#391C2×C418yes—
186#389—24no—
187#389—42no—
188#389—42no—
189#389—44no—
190#389C2×C418yes—
191#389C2×C418yes—
192#388—44no—
193#387—44no—
194#380—24no—
195#380—24no—
196#380C2×C418yes—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—42no—
199C4×C4⋊C4—42no—
200C4×C4⋊C4—42no—
201C4×C4⋊C4—42no—
202C4×C4⋊C4—42no—
203C4×C4⋊C4—42no—
204C4×C22⋊C4—42no—
205C4×C22⋊C4—42no—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2311yescharacteristic
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2311yescharacteristic
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C25C2411yescharacteristic
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8C22×C414yes—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4C22×C414yes—
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C22⋊Q8—416no—
299C4×Q8—416no—
300#117—416no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4C22×C414yes—
352C2×C4⋊C4C22×C414yes—
353C2×C4⋊C4C22×C414yes—
354C2×C4⋊C4C22×C414yes—
355C2×C4⋊C4C22×C414yes—
356C2×C4⋊C4C22×C418yes—
357C2×C4⋊C4C22×C418yes—
358C2×C4⋊C4C22×C418yes—
359C2×C4⋊C4#4114yes—
360C2×C4⋊C4#4114yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4C22×C414yes—
388C2×C22⋊C4C22×C414yes—
389C2×C22⋊C4C22×C418yes—
390C2×C22⋊C4C22×C418yes—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42C22×C414yes—
426C2×C42C22×C414yes—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—22no—
434#95—24no—
435#95—22no—
436#95—22no—
437#95—24no—
438#95—22no—
439#95—24no—
440#95—24no—
441#95—42no—
442#95—41no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—41no—
448#95—41no—
449#95—41no—
450#95—42no—
451#95—42no—
452#95—41no—
453#95—41no—
454#95—41no—
455#95—41no—
456#95—41no—
457#95—42no—
458#95—41no—
459#95—41no—
460#95—41no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95C22×C418yes—
476#95C22×C418yes—
477#95C22×C418yes—
478#95C22×C418yes—
479#95C22×C418yes—
480#95C22×C418yes—
481#95C22×C418yes—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24C23×C412yes—
497C24C2511yescharacteristic
498C2×Q8—28no—
499C2×Q8—28no—
500C2×Q8—28no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4C23×C412yes—
645C22×C4C23×C412yes—
646C22×C4C23×C414yes—
647C22×C4C23×C414yes—
648C22×C4C23×C414yes—
649C22×C4C23×C412yes—
650C22×C4C23×C412yes—
651C22×C4C23×C414yes—
652C22×C4C23×C412yes—
653C22×C4C23×C412yes—
654C22×C4C2×#4114yes—
655C22×C4C2×#4114yes—
656C22×C4C2×#4112yes—
657C22×C4C2×#4112yes—
658C22×C4H(5,𝔽2)12yes—
659C22×C4H(5,𝔽2)12yes—
660C22×C4H(5,𝔽2)12yes—
661C22×C4H(5,𝔽2)12yes—
662C22×C42−1+412yes—
663C22×C42−1+412yes—
664C22×C42−1+412yes—
665C22×C42−1+412yes—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—28no—
670C4⋊C4—28no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—48no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—48no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—84no—
684C4⋊C4—84no—
685C4⋊C4—84no—
686C22⋊C4—48no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—48no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—84no—
695C22⋊C4—84no—
696C42—28no—
697C42—28no—
698C42—48no—
699C42—44no—
700C42—44no—
701C42—44no—
702C42—44no—
703C42—84no—
704C42—84no—
705C42—84no—
706C42—84no—
707C42—84no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23C24×C411yescharacteristic
744C23C22×#4111yescharacteristic
745C23C22×#4111yescharacteristic
746C23C2×H(5,𝔽2)11yescharacteristic
747C23C2×H(5,𝔽2)11yescharacteristic
748C23C2×H(5,𝔽2)11yescharacteristic
749C23C2×H(5,𝔽2)11yescharacteristic
750C23C2×2−1+411yescharacteristic
751C23C2×2−1+411yescharacteristic
752C23C2×2−1+411yescharacteristic
753C23C2×2−1+411yescharacteristic
754C23#58511yescharacteristic
755C23#58511yescharacteristic
756C23#58511yescharacteristic
757C23#58511yescharacteristic
758Q8—416no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—416no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—42no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4C4×#4114yes—
908C2×C4#51814yes—
909C2×C4#52014yes—
910C2×C4#53814yes—
911C2×C4#53914yes—
912C2×C4#54014yes—
913C2×C4#54214yes—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22C2×C4×#4111yescharacteristic
930C22C2×#51811yescharacteristic
931C22C2×#52011yescharacteristic
932C22C4×H(5,𝔽2)11yescharacteristic
933C22C4×2−1+411yescharacteristic
934C22C4×2−1+411yescharacteristic
935C22C4×2−1+411yescharacteristic
936C22C2×#53811yescharacteristic
937C22C2×#53911yescharacteristic
938C22C2×#54011yescharacteristic
939C22C2×#54211yescharacteristic
940C22#351411yescharacteristic
941C22#351511yescharacteristic
942C22#351611yescharacteristic
943C22#351611yescharacteristic
944C22#352111yescharacteristic
945C22#352111yescharacteristic
946C22#352211yescharacteristic
947C22#352311yescharacteristic
948C22#353811yescharacteristic
949C22#354011yescharacteristic
950C22#354111yescharacteristic
951C22#354111yescharacteristic
952C22#354111yescharacteristic
953C22#354111yescharacteristic
954C22#354211yescharacteristic
955C22#354211yescharacteristic
956C22#354711yescharacteristic
957C22#354711yescharacteristic
958C22#354811yescharacteristic
959C22#355011yescharacteristic
960C22#355111yescharacteristic
961C22#355611yescharacteristic
962C22#355711yescharacteristic
963C22#355711yescharacteristic
964C4—42no—
965C4—44no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—44no—
973C4—44no—
974C4—44no—
975C4—44no—
976C4—42no—
977C4—44no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—81no—
982C4—82no—
983C4—81no—
984C4—82no—
985C4#233518yes—
986C2—82no—
987C2C2×#233511yescharacteristic
988C2#3428511yescharacteristic
989C2#3428611yescharacteristic
990C2#3441211yescharacteristic
991C2#3441411yescharacteristic
992C2#3442111yescharacteristic
993C2#3442211yescharacteristic
994C2#4271211yescharacteristic
995C2#4271311yescharacteristic
996C2#4272411yescharacteristic
997C2#4272611yescharacteristic
998C2#4273511yescharacteristic
999C2#4274611yescharacteristic
1000C2#4283111yescharacteristic
1001C2#4284011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14647C2semidirect
4. #14598C2semidirect
5. #14585C2semidirect
9. #14247C2semidirect
10. #14142C2semidirect
11. #14133C2semidirect
12. #14046C2semidirect
13. #14041C2semidirect
14. #14021C2semidirect
15. #14017C2semidirect
21. #13818C2semidirect
22. #13817C2semidirect
27. #2625C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26252
#146472
#146152
#145982
#145852
#145792
#143322
#143242
#142472
#141422
#141332
#140462
#140412
#140212
#140172
#139972
#139942
#139732
#139692
#138522
#138182
#138172
#137772