Finite Group Databasebeta

← #581647

Subgroups — #581647

Order 512.

2586 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2312C211yesmaximal, characteristic
2#14675C211yesmaximal, characteristic, complemented
3#14500C212yesmaximal, complemented
4#14437C212yesmaximal, complemented
5#14434C212yesmaximal, complemented
6#14396C212yesmaximal, complemented
7#14366C212yesmaximal
8#14365C212yesmaximal
9#14129C211yesmaximal, characteristic, complemented
10#14085C212yesmaximal, complemented
11#14079C212yesmaximal, complemented
12#14074C212yesmaximal, complemented
13#14013C212yesmaximal, complemented
14#13913C212yesmaximal, complemented
15#13903C211yesmaximal, characteristic
16#13895C212yesmaximal, complemented
17#13868C211yesmaximal, characteristic
18#13780C211yesmaximal, characteristic, complemented
19#13777C211yesmaximal, characteristic, complemented
20C22×#117C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22#2312C4116yescomplemented
23C2×#389C2212yescomplemented
24C2×#388C2212yes—
25C2×#388C2212yes—
26C2×#388C2212yes—
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#383C2212yescomplemented
33C2×#381C2211yescharacteristic
34C2×#381C2212yes—
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×#379C2212yes—
39C2×#379C2212yes—
40C2×#379C2211yescharacteristic
41C2×#379C2211yescharacteristic
42C2×C4×C4⋊C4C2212yescomplemented
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46C2×#376C2212yescomplemented
47#1444C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1442C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1441C2212yescomplemented
54#1441C2212yescomplemented
55#1440C2212yes—
56#1440C2212yes—
57#1440C2212yes—
58#1440C2212yes—
59#1439C2212yes—
60#1439C2212yes—
61#1439C2212yes—
62#1439C2212yes—
63#1439C2212yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1437C2211yescharacteristic
72#1437C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2211yescharacteristic
81#1437C2211yescharacteristic
82#1437C2211yescharacteristic
83#1437C2211yescharacteristic
84#1437C2211yescharacteristic
85#1437C2211yescharacteristic
86#1437C2211yescharacteristic
87#1436C2212yescomplemented
88#1436C2212yescomplemented
89#1436C2212yescomplemented
90#1436C2212yescomplemented
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95C4⋊#95C2212yescomplemented
96C4⋊#95C2212yescomplemented
97C4⋊#95C2212yescomplemented
98C4⋊#95C2212yescomplemented
99#1434C2212yescomplemented
100#1434C2212yescomplemented
101#1434C2212yescomplemented
102#1434C2212yescomplemented
103#1434C2212yescomplemented
104#1434C2212yescomplemented
105C22⋊#95C2212yes—
106C4×#95C2212yescomplemented
107C4×#95C2212yescomplemented
108C26C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C2×#117—24no—
112C2×#117—44no—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4C2×C418yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158#389—44no—
159#388—44no—
160#388—44no—
161#388—44no—
162#388—44no—
163#388C2×C4116yes—
164#388C2×C4116yes—
165#388C2×C4116yes—
166#388C2×C4116yes—
167#383—44no—
168#381—24no—
169#381—44no—
170#380—24no—
171#380C2×C418yes—
172#380C2×C418yes—
173#379—44no—
174#379—44no—
175#379C2×C418yes—
176#379C2×C418yes—
177C4×C4⋊C4—44no—
178C4×C22⋊C4—24no—
179C4×C22⋊C4C2×C418yes—
180C4×C22⋊C4C2×C418yes—
181#376—44no—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C25—22no—
225C25—22no—
226C25—42no—
227C25—42no—
228C25—42no—
229C25—42no—
230C25—42no—
231C25—42no—
232C25C22×C414yes—
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4C22×C414yes—
243C23×C4C22×C414yes—
244C23×C4#4114yes—
245C23×C4#4114yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262#117—416no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4C22×C418yes—
286C2×C4⋊C4C22×C418yes—
287C2×C22⋊C4—232no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4C22×C414yes—
345C2×C22⋊C4C22×C414yes—
346C2×C22⋊C4C22×C414yes—
347C2×C22⋊C4C22×C414yes—
348C2×C22⋊C4C22×C414yes—
349C2×C22⋊C4C22×C414yes—
350C2×C22⋊C4C22×C414yes—
351C2×C22⋊C4C22×C414yes—
352C2×C22⋊C4C22×C418yes—
353C2×C22⋊C4C22×C418yes—
354C2×C22⋊C4C22×C418yes—
355C2×C22⋊C4C22×C418yes—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42C22×C418yes—
381C2×C42C22×C418yes—
382#95—24no—
383#95—22no—
384#95—22no—
385#95—24no—
386#95—22no—
387#95—22no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95C22×C418yes—
421#95C22×C418yes—
422#95C22×C418yes—
423#95C22×C418yes—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—28no—
447C24—44no—
448C24—44no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—82no—
454C24—82no—
455C24—84no—
456C24—84no—
457C24—82no—
458C24—82no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—84no—
463C24—84no—
464C24—84no—
465C24—84no—
466C24—84no—
467C24C23×C412yes—
468C24C23×C412yes—
469C24C23×C412yes—
470C24C2×#4112yes—
471C24C2×#4112yes—
472C24C2511yescharacteristic
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—84no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4#117116yes—
573C22×C4C23×C412yes—
574C22×C4C23×C412yes—
575C22×C4C23×C414yes—
576C22×C4C23×C414yes—
577C22×C4C23×C414yes—
578C22×C4C23×C414yes—
579C22×C4C23×C412yes—
580C22×C4C23×C412yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4H(5,𝔽2)14yes—
586C22×C4H(5,𝔽2)14yes—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—84no—
592C4⋊C4—84no—
593C4⋊C4—84no—
594C4⋊C4—84no—
595C22⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—28no—
598C22⋊C4—28no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C22⋊C4—84no—
614C22⋊C4—84no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C42—28no—
620C42—48no—
621C42—48no—
622C42—48no—
623C42—48no—
624C42—44no—
625C42—82no—
626C42—82no—
627C42—84no—
628C42—84no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—416no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—88no—
693C23—88no—
694C23—816no—
695C23—816no—
696C23—816no—
697C23—816no—
698C23—816no—
699C23—816no—
700C23C2×#11714yes—
701C23C24×C411yescharacteristic
702C23C22×#4111yescharacteristic
703C23C22×#4111yescharacteristic
704C23C2×H(5,𝔽2)12yes—
705C23C2×H(5,𝔽2)12yes—
706C23#58512yes—
707C23#58512yes—
708C23#58512yes—
709C23#58512yes—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—416no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—88no—
814C2×C4C2×#11714yes—
815C2×C4C2×#11714yes—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—832no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22C22×#11711yescharacteristic
845C22#342811yescharacteristic
846C22#342811yescharacteristic
847C22C4×H(5,𝔽2)12yes—
848C22C4×H(5,𝔽2)12yes—
849C22#349011yescharacteristic
850C22#349111yescharacteristic
851C22#349312yes—
852C22#349312yes—
853C22#349412yes—
854C22#350512yes—
855C22#350811yescharacteristic
856C22#351011yescharacteristic
857C22#353312yes—
858C22#354212yes—
859C22#354512yes—
860C22#354612yes—
861C22#355112yes—
862C22#356012yes—
863C22#356612yes—
864C22#356812yes—
865C4—24no—
866C4—24no—
867C4—44no—
868C4—44no—
869C4—44no—
870C4—44no—
871C4—44no—
872C4—44no—
873C4—42no—
874C4—42no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C2—44no—
882C2—82no—
883C2—82no—
884C2#3417911yescharacteristic
885C2#3425111yescharacteristic
886C2#3425511yescharacteristic
887C2#3444612yes—
888C2#3445112yes—
889C2#4720212yes—
890C2#4723612yes—
891C2#4723712yes—
892C2#4756512yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14675C2semidirect
3. #14500C2semidirect
4. #14437C2semidirect
5. #14434C2semidirect
6. #14396C2semidirect
9. #14129C2semidirect
10. #14085C2semidirect
11. #14079C2semidirect
12. #14074C2semidirect
13. #14013C2semidirect
14. #13913C2semidirect
16. #13895C2semidirect
18. #13780C2semidirect
19. #13777C2semidirect
22. #2312C4semidirect
23. C2×#389C22semidirect
32. C2×#383C22semidirect
42. C2×C4×C4⋊C4C22semidirect
46. C2×#376C22semidirect
47. #1444C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1442C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1441C22semidirect
54. #1441C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. #1436C22semidirect
90. #1436C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. C4⋊#95C22semidirect
96. C4⋊#95C22semidirect
97. C4⋊#95C22semidirect
98. C4⋊#95C22semidirect
99. #1434C22semidirect
100. #1434C22semidirect
101. #1434C22semidirect
102. #1434C22semidirect
103. #1434C22semidirect
104. #1434C22semidirect
106. C4×#95C22semidirect
107. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#23122
#146752
#145002
#144372
#144342
#143962
#143662
#143652
#141292
#140852
#140792
#140742
#140132
#139132
#139032
#138952
#138682
#137802
#137772