Finite Group Databasebeta

← #25101621

Subgroups — #25101621

Order 11008.

1256 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2C4×M16×D43C211yesmaximal, characteristic, complemented
3C4×#13063282C211yesmaximal, characteristic, complemented
4#19135537C212yesmaximal, complemented
5#19135512C212yesmaximal, complemented
6#19134896C212yesmaximal, complemented
7#19134894C212yesmaximal, complemented
8C4×#13063251C211yesmaximal, characteristic, complemented
9C4×#13063253C211yesmaximal, characteristic, complemented
10C4×#13063252C211yesmaximal, characteristic, complemented
11C4×#104×C43C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583453C411yescharacteristic, complemented
14#14583453C411yescharacteristic, complemented
15#14583452C2211yescharacteristic
16#14583446C411yescharacteristic, complemented
17#14583446C411yescharacteristic, complemented
18#14583445C2211yescharacteristic
19#14583436C411yescharacteristic, complemented
20#14583436C411yescharacteristic, complemented
21#14583431C411yescharacteristic, complemented
22#14583431C411yescharacteristic, complemented
23#14583429—21no—
24#14583429—21no—
25#14583427—21no—
26#14583427—21no—
27#14583411C2211yescharacteristic
28#14583408—21no—
29#14583408—21no—
30#14583406C2211yescharacteristic
31C4×#10621898—21no—
32C4×#10621898—21no—
33C4×#10621898C2211yescharacteristic
34C2×#13063282—21no—
35C2×C42×D43C2211yescharacteristic
36C2×#13063253C2212yes—
37C2×#13063252C2212yes—
38C2×#13063251C2212yes—
39C4×#10621877C2211yescharacteristic
40#14582851—21no—
41M16×Dic43C2212yes—
42C4×#10621872—21no—
43#97×D43—21no—
44C4×C8×D43—21no—
45C4×Dic43⋊C4—21no—
46C4×Dic43⋊C4C2212yes—
47C4×(C2×D43)⋊C4—21no—
48C4×(C2×D43)⋊C4C2212yes—
49#14582745—21no—
50C42×Dic43C2211yescharacteristic
51#14582660C2212yes—
52#14582659C2212yes—
53#14582658C2212yes—
54C4×#41×C43C2211yescharacteristic
55C2×#104×C43C2212yes—
56C4×M16×C43C2211yescharacteristic
57C43×C43C2211yescharacteristic
58C43×#339C2212yes—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2311yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877C2312yes—
66C2×#10621872—22no—
67M16×D43—24no—
68M16×D43—24no—
69C2×C8×D43—22no—
70#13063324C2×C411yescharacteristic
71#13063324C2×C411yescharacteristic
72#13063323C2×C411yescharacteristic
73#13063321C2×C411yescharacteristic
74#13063320—21no—
75#13063320—21no—
76#13063318—21no—
77#13063318—21no—
78#13063316C2×C411yescharacteristic
79#13063316C2×C411yescharacteristic
80#13063315—21no—
81#13063315—21no—
82#13063314C2×C411yescharacteristic
83#13063312C2×C411yescharacteristic
84#13063311—21no—
85#13063311—21no—
86#13063310—21no—
87#13063310—21no—
88#13063309—21no—
89#13063307—21no—
90#13063307—21no—
91#13063306—21no—
92#13063305C2×C411yescharacteristic
93#13063305C2×C411yescharacteristic
94#13063303—21no—
95#13063303—21no—
96#13063302—21no—
97#13063302—21no—
98#13063301C2×C411yescharacteristic
99#13063301C2×C411yescharacteristic
100#13063300C2×C411yescharacteristic
101#13063300C2×C411yescharacteristic
102#13063298—21no—
103#13063298—21no—
104#13063297—21no—
105#13063297—21no—
106#13063296C2×C411yescharacteristic
107#13063296C2×C411yescharacteristic
108#13063295—21no—
109#13063293—21no—
110C4×Dic86—21no—
111C4×Dic86—21no—
112C4×Dic86—21no—
113C4×Dic86—21no—
114C4×Dic86C2×C411yescharacteristic
115C4×Dic86C2×C411yescharacteristic
116C4×D172—21no—
117C4×D172—21no—
118C4×D172—21no—
119C4×D172—21no—
120C4×D172C2×C411yescharacteristic
121C4×D172C2×C411yescharacteristic
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132#13063284—21no—
133#13063284—21no—
134#13063284C2311yescharacteristic
135#13063282—28no—
136#13063282—21no—
137#13063282—21no—
138#13063282—21no—
139#13063282—21no—
140#13063282—21no—
141C2×Dic43⋊C4—22no—
142C2×(C2×D43)⋊C4—22no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43C2312yes—
148C2×C4×Dic43C2311yescharacteristic
149C42×D43—21no—
150C42×D43C2×C411yescharacteristic
151C42×D43C2×C411yescharacteristic
152C42×D43C2×C411yescharacteristic
153C42×D43C2×C411yescharacteristic
154C42×D43D411yescharacteristic
155C42×D43D411yescharacteristic
156C42×D43D411yescharacteristic
157C42×D43D411yescharacteristic
158#13063253—24no—
159#13063252—24no—
160#13063251—24no—
161#13063236—21no—
162#13063235—22no—
163C4×C43⋊C8—21no—
164C8×Dic43—22no—
165C43⋊#95—22no—
166C43⋊#95—22no—
167C2×#41×C43C2311yescharacteristic
168C2×M16×C43C2312yes—
169C4×Q8×C43C2×C411yescharacteristic
170C4×Q8×C43C2×C411yescharacteristic
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173C4×D4×C43C2×C411yescharacteristic
174C4×D4×C43C2×C411yescharacteristic
175#117×C43—21no—
176#117×C43C2311yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2312yes—
181C2×C42×C43C2311yescharacteristic
182#104×C43—24no—
183#97×C43—21no—
184C4×C8×C43—21no—
185C23×D43C2×D411yescharacteristic
186#41×C43—22no—
187#41×C43—22no—
188C2×Q8×C43C22×C411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43C22×C411yescharacteristic
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—22no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—21no—
203C22×Dic43—22no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207#10621898—22no—
208#10621898—22no—
209#10621898—44no—
210#10621898—44no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172C22×C411yescharacteristic
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—24no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—42no—
221C2×C4×D43C22⋊C411yescharacteristic
222C2×C4×D43C22⋊C411yescharacteristic
223C2×C4×D43C22⋊C411yescharacteristic
224C2×C4×D43C22⋊C411yescharacteristic
225C2×C4×D43C22⋊C411yescharacteristic
226C2×C4×D43C22⋊C411yescharacteristic
227C2×C4×D43C22⋊C411yescharacteristic
228C2×C4×D43C22⋊C411yescharacteristic
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C22×C411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86C22×C411yescharacteristic
236M16×C43—22no—
237M16×C43#4114yescomplemented
238C2×C8×C43—22no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43C22×C411yescharacteristic
242C4⋊C4×C43C22×C411yescharacteristic
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C42×C43—24no—
247C42×C43—21no—
248C42×C43—21no—
249C42×C43—21no—
250C42×C43—22no—
251C42×C43—22no—
252C42×C43—42no—
253C42×C43C22×C411yescharacteristic
254C42×C43C22×C411yescharacteristic
255C42×C43C2×D411yescharacteristic
256C42×C43C2×D411yescharacteristic
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43—21no—
262(C2×D43)⋊C4—28no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43C22×C411yescharacteristic
278C4⋊Dic43C22×C411yescharacteristic
279Dic43⋊C4—28no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290C4×Dic43—24no—
291C4×Dic43—21no—
292C4×Dic43—21no—
293C4×Dic43—21no—
294C4×Dic43—22no—
295C4×Dic43—22no—
296C4×Dic43—42no—
297C4×Dic43C22⋊C411yescharacteristic
298C4×Dic43C22⋊C411yescharacteristic
299C4×Dic43C22⋊C411yescharacteristic
300C4×Dic43C22⋊C411yescharacteristic
301C4×Dic43C22⋊C411yescharacteristic
302C4×Dic43C22⋊C411yescharacteristic
303C4×Dic43C22⋊C411yescharacteristic
304C4×Dic43C22⋊C411yescharacteristic
305C4×Dic43C22×C411yescharacteristic
306C4×Dic43C22×C411yescharacteristic
307C4×Dic43C2×D411yescharacteristic
308C4×Dic43C2×D411yescharacteristic
309#10621877—22no—
310#10621877#4114yescomplemented
311C2×C43⋊C8—22no—
312#10621872—28no—
313C8×D43—28no—
314C23×C43—21no—
315C23×C43C22×D411yescharacteristic
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—21no—
319C22×D43—41no—
320C22×D43C2×C22⋊C411yescharacteristic
321C22×D43C2×C22⋊C411yescharacteristic
322Q8×C43—21no—
323Q8×C43—21no—
324D4×C43—21no—
325D4×C43—21no—
326D4×C43—42no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—24no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—42no—
334C2×C4×C43—42no—
335C2×C4×C43—42no—
336C2×C4×C43—42no—
337C2×C4×C43—42no—
338C2×C4×C43C2×C22⋊C411yescharacteristic
339C2×C4×C43C2×C22⋊C411yescharacteristic
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C23×C411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4112yes—
345C2×C4×C43C2×#4112yes—
346C22⋊D43—42no—
347C22⋊D43—42no—
348C22⋊D43—42no—
349C22⋊D43—42no—
350C22⋊D43—42no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—24no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—41no—
358C2×Dic43—42no—
359C2×Dic43—42no—
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362C2×Dic43C2×C22⋊C411yescharacteristic
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366D172—21no—
367D172—21no—
368D172—42no—
369D172—42no—
370C4×D43—22no—
371C4×D43—21no—
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—41no—
382C4×D43—41no—
383C4×D43—42no—
384C4×D43—42no—
385C4×D43—42no—
386C4×D43#10414yescomplemented
387Dic86—21no—
388Dic86—21no—
389Dic86—42no—
390Dic86—42no—
391C8×C43—24no—
392C43⋊C8—24no—
393#21382—431nomaximal, Sylow
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43#53212yes—
401C2×D43—21no—
402C2×D43—21no—
403C2×D43—21no—
404C2×D43—21no—
405C2×D43—21no—
406C2×D43—44no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43C2×#10412yes—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—44no—
414C4×C43—41no—
415C4×C43—41no—
416C4×C43—41no—
417C4×C43C2×#10412yes—
418C4×C43#42112yes—
419C4×C43C4×#4111yescharacteristic
420C4×C43C4×#4111yescharacteristic
421C4×C43#52512yes—
422Dic43—21no—
423Dic43—21no—
424Dic43—21no—
425Dic43—21no—
426Dic43—21no—
427Dic43—44no—
428Dic43—41no—
429Dic43—41no—
430Dic43—41no—
431Dic43C2×#10412yes—
432#3444—431no—
433C2×C4×M16—431no—
434C4×#117—431no—
435#1986—432no—
436#1980—432no—
437#1871—432no—
438#1871—432no—
439C4×#104—431no—
440C4×#104—431no—
441C4×#104—431no—
442C4×#104D4311yescharacteristic, complemented
443C2×C43—22no—
444C2×C43—81no—
445C2×C43#229711yescharacteristic
446C2×C43C22×#10411yescharacteristic
447C2×C43C2×#42111yescharacteristic
448D43—22no—
449D43—41no—
450D43—81no—
451C22×M16—432no—
452#533—431no—
453#533—431no—
454#533—431no—
455#532—431no—
456#532—431no—
457#532—431no—
458#529—431no—
459#529—431no—
460#529—431no—
461#529—431no—
462#529—861no—
463#529—861no—
464#529—861no—
465#529—861no—
466#525—431no—
467#525—431no—
468#525—861no—
469#525—861no—
470C4×#41—431no—
471C4×#41—861no—
472C4×#41—861no—
473C4×#41C2×D4311yescharacteristic
474C2×#117—861no—
475C22×C42—431no—
476C2×#104—432no—
477C2×#104—432no—
478C2×#104—432no—
479C2×#104C2×D4312yes—
480C4×M16—432no—
481C4×M16—431no—
482C4×M16—861no—
483C4×M16—861no—
484C4×M16C2×D4311yescharacteristic
485C2×#97—861no—
486C2×C4×C8—861no—
487C4×C4⋊C4—432no—
488C4×C4⋊C4—861no—
489C4×C22⋊C4—432no—
490C4×C22⋊C4—861no—
491#376—861no—
492C43—431no—
493C43C2×D4311yescharacteristic
494#339—432no—
495#339—432no—
496#339—432no—
497#339C2×D4312yes—
498C43#2138211yescharacteristic, complemented, Sylow
499C2×#41—431no—
500C2×#41—861no—
501C2×#41—861no—
502C2×#41C22×D4311yescharacteristic
503C23×C4—431no—
504C23×C4—431no—
505C23×C4—431no—
506C2×M16—432no—
507C2×M16—862no—
508C2×M16—864no—
509C2×M16—864no—
510C2×M16C22×D4312yes—
511C22×C8—862no—
512C4⋊Q8—431no—
513C4⋊Q8—431no—
514C4⋊Q8—431no—
515#127—431no—
516#126—861no—
517#126—861no—
518#126—861no—
519#126—861no—
520#125—431no—
521#125—431no—
522#125—861no—
523#125—861no—
524#124—431no—
525#124—431no—
526#124—861no—
527#124—861no—
528#123—861no—
529#123—861no—
530#123—861no—
531#123—861no—
532#123—861no—
533#123—861no—
534C22⋊Q8—431no—
535C22⋊Q8—431no—
536C22⋊Q8—431no—
537C22⋊Q8—431no—
538C22⋊Q8—861no—
539C22⋊Q8—861no—
540C22⋊Q8—861no—
541C22⋊Q8—861no—
542#121—431no—
543#121—431no—
544#121—431no—
545#121—431no—
546#121—861no—
547#121—861no—
548#121—861no—
549#121—861no—
550#120—861no—
551#120—861no—
552C4×Q8—431no—
553C4×Q8—431no—
554C4×Q8—861no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×Q8—861no—
558C4×Q8C4×D4311yescharacteristic
559C4×Q8C4×D4311yescharacteristic
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—431no—
563C4×D4—431no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—861no—
569C4×D4—861no—
570C4×D4—861no—
571C4×D4—861no—
572C4×D4—861no—
573C4×D4—861no—
574C4×D4—861no—
575C4×D4—861no—
576C4×D4—861no—
577C4×D4—861no—
578C4×D4C4×D4311yescharacteristic
579C4×D4C4×D4311yescharacteristic
580#117—21no—
581#117—431no—
582#117—861no—
583#117—861no—
584#117—861no—
585#117—861no—
586#117—868no—
587#117—861no—
588#117—861no—
589#117—861no—
590#117C22×D4311yescharacteristic
591C2×C4⋊C4—862no—
592C2×C22⋊C4—862no—
593C2×C42—21no—
594C2×C42—21no—
595C2×C42—21no—
596C2×C42—431no—
597C2×C42—431no—
598C2×C42—431no—
599C2×C42—431no—
600C2×C42—431no—
601C2×C42—431no—
602C2×C42—431no—
603C2×C42—431no—
604C2×C42—431no—
605C2×C42—431no—
606C2×C42—431no—
607C2×C42—432no—
608C2×C42—861no—
609C2×C42—861no—
610C2×C42—861no—
611C2×C42C22×D4312yes—
612C2×C42C22×D4311yescharacteristic
613#104—24no—
614#104—864no—
615#104—864no—
616#104—864no—
617#97—21no—
618#97—862no—
619#97—861no—
620C4×C8—21no—
621C4×C8—862no—
622C4×C8—861no—
623#95—862no—
624#95—862no—
625C24—431no—
626#41—22no—
627#41—22no—
628#41—862no—
629#41—862no—
630#41—1724no—
631#41—1724no—
632C2×Q8—431no—
633C2×Q8—861no—
634C2×Q8—861no—
635C2×Q8C2×C4×D4311yescharacteristic
636C2×D4—21no—
637C2×D4—431no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4C2×C4×D4311yescharacteristic
646C22×C4—22no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—864no—
666C22×C4—862no—
667C22×C4—862no—
668C22×C4—862no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—1722no—
673C22×C4D4×D4311yescharacteristic
674C22×C4D4×D4311yescharacteristic
675C22×C4C23×D4311yescharacteristic
676M16—22no—
677M16—434no—
678M16—868no—
679M16—862no—
680M16#1062189814yescomplemented
681C2×C8—22no—
682C2×C8—868no—
683C2×C8—862no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—431no—
687C4⋊C4—431no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—868no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4C2×C4×D4311yescharacteristic
704C4⋊C4C2×C4×D4311yescharacteristic
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—861no—
709C22⋊C4—861no—
710C22⋊C4—861no—
711C22⋊C4—861no—
712C22⋊C4—861no—
713C22⋊C4—861no—
714C22⋊C4—861no—
715C22⋊C4—861no—
716C22⋊C4—868no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C42—24no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—22no—
729C42—22no—
730C42—42no—
731C42—431no—
732C42—431no—
733C42—431no—
734C42—431no—
735C42—431no—
736C42—431no—
737C42—431no—
738C42—431no—
739C42—431no—
740C42—431no—
741C42—431no—
742C42—431no—
743C42—864no—
744C42—861no—
745C42—861no—
746C42—861no—
747C42—862no—
748C42—862no—
749C42—1722no—
750C42C2×C4×D4311yescharacteristic
751C42C2×C4×D4311yescharacteristic
752C42D4×D4311yescharacteristic
753C42D4×D4311yescharacteristic
754C23—21no—
755C23—431no—
756C23—431no—
757C23—862no—
758C23—862no—
759C23—861no—
760C23—1721no—
761C23C2×D4×D4311yescharacteristic
762Q8—21no—
763Q8—21no—
764Q8—861no—
765Q8—861no—
766Q8—1722no—
767Q8—1722no—
768D4—21no—
769D4—21no—
770D4—42no—
771D4—861no—
772D4—861no—
773D4—1722no—
774D4—1722no—
775D4—1722no—
776D4—1722no—
777D4—1722no—
778D4—1722no—
779D4—1722no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—431no—
792C2×C4—434no—
793C2×C4—431no—
794C2×C4—431no—
795C2×C4—431no—
796C2×C4—431no—
797C2×C4—431no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—864no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1722no—
819C2×C4—1722no—
820C2×C4—1722no—
821C2×C4—1722no—
822C2×C4—1722no—
823C2×C4C22⋊C4×D4311yescharacteristic
824C2×C4C22⋊C4×D4311yescharacteristic
825C2×C4C22⋊C4×D4311yescharacteristic
826C2×C4C22⋊C4×D4311yescharacteristic
827C2×C4C22×C4×D4311yescharacteristic
828C2×C4C2×D4×D4311yescharacteristic
829C2×C4#41×D4312yes—
830C2×C4C2×#1062189812yes—
831C8—24no—
832C8—864no—
833C22—21no—
834C22—21no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—432no—
839C22—861no—
840C22—861no—
841C22—861no—
842C22—861no—
843C22—861no—
844C22—1724no—
845C22—1721no—
846C22—1721no—
847C22—1721no—
848C22C2×C22⋊C4×D4311yescharacteristic
849C22#1458344612yes—
850C4—21no—
851C4—21no—
852C4—44no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—432no—
857C4—861no—
858C4—861no—
859C4—861no—
860C4—861no—
861C4—861no—
862C4—1724no—
863C4—1721no—
864C4—1721no—
865C4—1721no—
866C4#104×D4312yes—
867C4#1458291412yes—
868C4#1458336711yescharacteristic
869C4C4×#1062189811yescharacteristic
870C4#1458340812yes—
871C2—22no—
872C2—81no—
873C2—862no—
874C2—3441no—
875C2—1721no—
876C2#1913708111yescharacteristic
877C2C2×#104×D4311yescharacteristic
878C2C2×#1458291411yescharacteristic
subgroupG/H
centerC42D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#104×C43C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC22×C4×C43C24
hypercenterC4×#104D43
hypocenterC43#21382
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. C4×M16×D43C2semidirect
3. C4×#13063282C2semidirect
4. #19135537C2semidirect
5. #19135512C2semidirect
6. #19134896C2semidirect
7. #19134894C2semidirect
8. C4×#13063251C2semidirect
9. C4×#13063253C2semidirect
10. C4×#13063252C2semidirect
11. C4×#104×C43C2semidirect
13. #14583453C4semidirect
14. #14583453C4semidirect
16. #14583446C4semidirect
17. #14583446C4semidirect
19. #14583436C4semidirect
20. #14583436C4semidirect
21. #14583431C4semidirect
22. #14583431C4semidirect
237. M16×C43#41semidirect
310. #10621877#41semidirect
386. C4×D43#104semidirect
442. C4×#104D43semidirect
498. C43#21382semidirect
680. M16#10621898semidirect

Maximal subgroups

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

subgroupindex
#191478882
C4×M16×D432
C4×#130632822
#191355372
#191355122
#191348962
#191348942
C4×#130632512
C4×#130632532
C4×#130632522
C4×#104×C432
#2138243