Finite Group Databasebeta

← #4342179

Subgroups — #4342179

Order 512.

2354 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2736C211yesmaximal, characteristic
2C2×#2735C211yesmaximal, characteristic
3#16859C212yesmaximal, complemented
4#16831C211yesmaximal, characteristic, complemented
5#16830C211yesmaximal, characteristic, complemented
6#16788C212yesmaximal, complemented
7#16391C212yesmaximal
8#15845C212yesmaximal, complemented
9#15697C212yesmaximal, complemented
10#15648C212yesmaximal, complemented
11#15645C212yesmaximal, complemented
12#15161C211yesmaximal, characteristic, complemented
13#15150C211yesmaximal, characteristic, complemented
14#14983C212yesmaximal, complemented
15#14953C212yesmaximal, complemented
16#14820C212yesmaximal
17#14576C212yesmaximal, complemented
18#14108C212yesmaximal, complemented
19#13775C211yesmaximal, characteristic
20C23×C22⋊C4C2211yescharacteristic
21#2736—28no—
22#2735—28no—
23C2×#399C2211yescharacteristic
24C2×#397C2212yes—
25C2×#397C2212yes—
26C2×#397C2211yescharacteristic
27C2×#397C2211yescharacteristic
28C2×#397C2212yes—
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#396C2212yes—
32C2×#393C2211yescharacteristic
33C2×#393C2212yes—
34C2×#391C2211yescharacteristic, complemented
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#387C2212yescomplemented
42C2×#384C2211yescharacteristic, complemented
43C2×#380C2212yes—
44C2×#379C2211yescharacteristic
45C2×#379C2212yes—
46C2×#379C2212yes—
47C2×#379C2211yescharacteristic
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2211yescharacteristic
50#1446C2211yescharacteristic, complemented
51#1446C2212yescomplemented
52#1445C2212yescomplemented
53#1445C2212yescomplemented
54#1445C2211yescharacteristic, complemented
55#1445C2211yescharacteristic, complemented
56#1445C2211yescharacteristic, complemented
57#1444C2212yescomplemented
58#1443C2212yescomplemented
59#1443C2212yescomplemented
60#1443C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96#1436C2212yescomplemented
97#1436C2212yescomplemented
98C4⋊#95C2211yescharacteristic, complemented
99C4⋊#95C2212yescomplemented
100C4⋊#95C2211yescharacteristic, complemented
101#1434C2212yescomplemented
102#1434C2212yescomplemented
103C22⋊#95C2212yes—
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2211yescharacteristic
108C4×#95C2212yescomplemented
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—42no—
125C22×C22⋊C4—42no—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153#399—24no—
154#397—24no—
155#397—28no—
156#397—24no—
157#397—28no—
158#397—28no—
159#397—44no—
160#397—44no—
161#396—28no—
162#393—24no—
163#393—28no—
164#391—42no—
165#388—28no—
166#388—28no—
167#388—28no—
168#388—28no—
169#388—28no—
170#388—28no—
171#387—44no—
172#384—42no—
173#380—28no—
174#379—28no—
175#379—28no—
176#379—24no—
177#379D418yes—
178C4×C22⋊C4—42no—
179C4×C22⋊C4—42no—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2311yescharacteristic
185C2×#95C2312yes—
186C2×#95C2311yescharacteristic
187C2×#95C2311yescharacteristic
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2311yescharacteristic
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—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C25—22no—
227C25—22no—
228C25—41no—
229C25—41no—
230C25—41no—
231C25—41no—
232C25—42no—
233C25—42no—
234C25—42no—
235C25—42no—
236C25C2×D414yes—
237C25C2412yes—
238C25C2411yescharacteristic
239C22×Q8—22no—
240C22×Q8—42no—
241C22×Q8—41no—
242C22×Q8—42no—
243C22×Q8—41no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—41no—
248C23×C4—41no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4#4114yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—41no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—416no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4C2×D414yes—
364C2×C22⋊C4C2×D418yes—
365C2×C22⋊C4C2×D418yes—
366C2×C22⋊C4C2×D414yes—
367C2×C22⋊C4#4114yes—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—22no—
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×C42—42no—
381#95—24no—
382#95—22no—
383#95—24no—
384#95—22no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—22no—
391#95—22no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
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—41no—
419#95—41no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
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—22no—
447C24—22no—
448C24—22no—
449C24—28no—
450C24—44no—
451C24—44no—
452C24—48no—
453C24—48no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—84no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—82no—
463C24—82no—
464C24—82no—
465C24—82no—
466C24—84no—
467C24—84no—
468C24—84no—
469C24—84no—
470C24—84no—
471C24—84no—
472C24C22×D414yes—
473C24C22×D412yes—
474C24C2×#4112yes—
475C24C2×#4112yes—
476C24C2511yescharacteristic
477C2×Q8—44no—
478C2×Q8—84no—
479C2×Q8—82no—
480C2×Q8—82no—
481C2×Q8—84no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
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—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—28no—
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—22no—
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—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—84no—
590C22×C4C22×D412yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C4⋊C4—48no—
600C4⋊C4—84no—
601C4⋊C4—84no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C4⋊C4—82no—
607C4⋊C4—84no—
608C4⋊C4—84no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—84no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C42—44no—
632C42—82no—
633C42—84no—
634C42—84no—
635C42—84no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—416no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
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—42no—
693C23—42no—
694C23—816no—
695C23—816no—
696C23—88no—
697C23—88no—
698C23—88no—
699C23—88no—
700C23—816no—
701C23—816no—
702C23—88no—
703C23—88no—
704C23#53214yes—
705C23C23×D411yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4111yescharacteristic
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)11yescharacteristic
710C23#58511yescharacteristic
711C23#58511yescharacteristic
712C23#58512yes—
713C23#58512yes—
714C23#58512yes—
715C23#58512yes—
716Q8—88no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
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—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—88no—
824C2×C4—88no—
825C2×C4#53814yes—
826C22—28no—
827C22—24no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—832no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22C2×#53211yescharacteristic
854C22C2×#53811yescharacteristic
855C22#345511yescharacteristic
856C22#348512yes—
857C22#348512yes—
858C22#349112yes—
859C22#349611yescharacteristic
860C22#349611yescharacteristic
861C22#350511yescharacteristic
862C22#350611yescharacteristic
863C22#351012yes—
864C22#352112yes—
865C22#352112yes—
866C22#353311yescharacteristic
867C22#354011yescharacteristic
868C22#354511yescharacteristic
869C22#355111yescharacteristic
870C22#356012yes—
871C22#356212yes—
872C22#356612yes—
873C22#356612yes—
874C22#356812yes—
875C22#356812yes—
876C4—24no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C2—44no—
894C2—84no—
895C2#3500511yescharacteristic
896C2#3601212yes—
897C2#3702012yes—
898C2#4142711yescharacteristic
899C2#4298311yescharacteristic
900C2#4637012yes—
901C2#4719311yescharacteristic
902C2#4745211yescharacteristic
903C2#4881111yescharacteristic
904C2#4881211yescharacteristic
905C2#5029412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #16859C2semidirect
4. #16831C2semidirect
5. #16830C2semidirect
6. #16788C2semidirect
8. #15845C2semidirect
9. #15697C2semidirect
10. #15648C2semidirect
11. #15645C2semidirect
12. #15161C2semidirect
13. #15150C2semidirect
14. #14983C2semidirect
15. #14953C2semidirect
17. #14576C2semidirect
18. #14108C2semidirect
34. C2×#391C22semidirect
41. C2×#387C22semidirect
42. C2×#384C22semidirect
50. #1446C22semidirect
51. #1446C22semidirect
52. #1445C22semidirect
53. #1445C22semidirect
54. #1445C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1444C22semidirect
58. #1443C22semidirect
59. #1443C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1436C22semidirect
97. #1436C22semidirect
98. C4⋊#95C22semidirect
99. C4⋊#95C22semidirect
100. C4⋊#95C22semidirect
101. #1434C22semidirect
102. #1434C22semidirect
108. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#27362
C2×#27352
#168592
#168312
#168302
#167882
#163912
#158452
#156972
#156482
#156452
#151612
#151502
#149832
#149532
#148202
#145762
#141082
#137752