Finite Group Databasebeta

← #25101620

Subgroups — #25101620

Order 11008.

1256 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2C2×M16×Dic43C211yesmaximal, characteristic, complemented
3C4×#13063281C211yesmaximal, characteristic, complemented
4#19135537C212yesmaximal, complemented
5#19135512C212yesmaximal, complemented
6#19134898C211yesmaximal, characteristic, complemented
7#19134897C211yesmaximal, characteristic, complemented
8#19134895C211yesmaximal, characteristic, complemented
9#104×Dic43C212yesmaximal, complemented
10#19134399C212yesmaximal, complemented
11C43×#1871C211yesmaximal, characteristic, complemented
12C22×#10621877C2211yescharacteristic
13#14583452C2211yescharacteristic
14#14583451C411yescharacteristic, complemented
15#14583451C411yescharacteristic, complemented
16#14583445C2211yescharacteristic
17#14583444C411yescharacteristic, complemented
18#14583444C411yescharacteristic, complemented
19#14583435C411yescharacteristic, complemented
20#14583435C411yescharacteristic, complemented
21#14583430C411yescharacteristic, complemented
22#14583430C411yescharacteristic, complemented
23#14583429—21no—
24#14583429—21no—
25#14583426—21no—
26#14583426—21no—
27#14583410C2211yescharacteristic
28#14583405—21no—
29#14583405—21no—
30#41×Dic43C2211yescharacteristic
31#14583367C2211yescharacteristic
32C4×#10621900—21no—
33C4×#10621900—21no—
34C2×#13063281—21no—
35C22×C4×Dic43C2211yescharacteristic
36C2×#13063253C2212yes—
37C2×#13063252C2212yes—
38C2×#13063251C2212yes—
39M16×Dic43—21no—
40M16×Dic43—21no—
41M16×Dic43C2212yes—
42M16×Dic43C2212yes—
43C2×#13063235—21no—
44C2×C8×Dic43—21no—
45C4×Dic43⋊C4C2212yes—
46#14582750—21no—
47C22⋊C4×Dic43—21no—
48C4×C22⋊Dic43C2211yescharacteristic
49#14582744—21no—
50C42×Dic43C2212yes—
51#14582660C2212yes—
52#14582659C2212yes—
53#14582658C2212yes—
54C22×M16×C43C2211yescharacteristic
55C43×#525C2211yescharacteristic
56C2×#104×C43C2212yes—
57C4×C22⋊C4×C43C2211yescharacteristic
58C43×#339C2212yes—
59C2×#10621898C2311yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C2×#10621877—21no—
65C2×#10621877—24no—
66C2×#10621877C2312yes—
67C22×C43⋊C8—21no—
68#13063324C2×C411yescharacteristic
69#13063324C2×C411yescharacteristic
70#13063323C2×C411yescharacteristic
71#13063321C2×C411yescharacteristic
72#13063320—21no—
73#13063320—21no—
74#13063318—21no—
75#13063318—21no—
76#13063316C2×C411yescharacteristic
77#13063316C2×C411yescharacteristic
78#13063315—21no—
79#13063315—21no—
80#13063314C2×C411yescharacteristic
81#13063312C2×C411yescharacteristic
82#13063311—21no—
83#13063311—21no—
84#13063309—21no—
85#13063309—21no—
86#13063308—21no—
87#13063306—21no—
88#13063306—21no—
89#13063304C2×C411yescharacteristic
90#13063304C2×C411yescharacteristic
91#13063302—21no—
92#13063302—21no—
93#13063302—21no—
94#13063302—21no—
95#13063299C2×C411yescharacteristic
96#13063299C2×C411yescharacteristic
97#13063297—21no—
98#13063297—21no—
99#13063297—21no—
100#13063297—21no—
101#13063294—21no—
102Q8×Dic43C2×C411yescharacteristic
103Q8×Dic43C2×C411yescharacteristic
104C4×Dic86—21no—
105C4×Dic86—21no—
106#13063290—21no—
107#13063290—21no—
108#13063290C2×C411yescharacteristic
109#13063290C2×C411yescharacteristic
110D4×Dic43—21no—
111D4×Dic43—21no—
112D4×Dic43—21no—
113D4×Dic43—21no—
114D4×Dic43C2×C411yescharacteristic
115D4×Dic43C2×C411yescharacteristic
116#13063287C2×C411yescharacteristic
117#13063287C2×C411yescharacteristic
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127(C22⋊D43)⋊C4—21no—
128#13063284—21no—
129#13063284C2311yescharacteristic
130#13063283—21no—
131#13063283—21no—
132#13063282—21no—
133#13063281—28no—
134#13063281—21no—
135#13063281—21no—
136#13063281—21no—
137#13063281—21no—
138C2×Dic43⋊C4—22no—
139C2×C22⋊Dic43—21no—
140C2×C4×Dic43—22no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43—22no—
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43C2×C411yescharacteristic
145C2×C4×Dic43C2×C411yescharacteristic
146C2×C4×Dic43C2×C411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43D411yescharacteristic
152C2×C4×Dic43D411yescharacteristic
153C2×C4×Dic43C2312yes—
154C2×C4×Dic43C2311yescharacteristic
155C2×C4×Dic43C2311yescharacteristic
156C42×D43—21no—
157#13063253—24no—
158#13063252—24no—
159#13063251—24no—
160#13063235—22no—
161#13063235—22no—
162C8×Dic43—22no—
163C8×Dic43—22no—
164C43⋊#95—21no—
165C43⋊#95—22no—
166C2×#41×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C2×M16×C43—21no—
169C2×M16×C43—24no—
170C2×M16×C43C2312yes—
171C22×C8×C43—21no—
172#123×C43—21no—
173C22⋊Q8×C43C2×C411yescharacteristic
174C22⋊Q8×C43C2×C411yescharacteristic
175#121×C43C2×C411yescharacteristic
176#121×C43C2×C411yescharacteristic
177#120×C43—21no—
178C4×D4×C43—21no—
179C4×D4×C43—21no—
180#117×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C42×C43C2312yes—
183#104×C43—24no—
184#95×C43—21no—
185C24×C43C2×D411yescharacteristic
186#41×C43—22no—
187#41×C43—22no—
188C2×Q8×C43C22×C411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43C22×C411yescharacteristic
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—21no—
196C22×C4×C43—22no—
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C22×C411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C2×C22⋊D43—21no—
206C2×C22⋊D43—21no—
207C2×C22⋊D43—21no—
208C22×Dic43—24no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—22no—
212C22×Dic43—42no—
213C22×Dic43C22⋊C411yescharacteristic
214C22×Dic43C22⋊C411yescharacteristic
215C22×Dic43C22⋊C411yescharacteristic
216C22×Dic43C22⋊C411yescharacteristic
217C22×Dic43C22⋊C411yescharacteristic
218C22×Dic43C22⋊C411yescharacteristic
219C22×Dic43C22⋊C411yescharacteristic
220C22×Dic43C22⋊C411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225#10621900—44no—
226#10621900—44no—
227#10621898—22no—
228#10621898—22no—
229C2×D172C22×C411yescharacteristic
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86C22×C411yescharacteristic
236M16×C43—24no—
237M16×C43—22no—
238M16×C43#4114yescomplemented
239C2×C8×C43—24no—
240C2×C8×C43—22no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43C22×C411yescharacteristic
244C4⋊C4×C43C22×C411yescharacteristic
245C22⋊C4×C43—24no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—21no—
249C22⋊C4×C43—21no—
250C22⋊C4×C43—21no—
251C42×C43—21no—
252C42×C43—22no—
253C42×C43—22no—
254C22⋊Dic43—24no—
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43—21no—
262(C2×D43)⋊C4—21no—
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—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43C22×C411yescharacteristic
273C4⋊Dic43C22×C411yescharacteristic
274Dic43⋊C4—28no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285C4×Dic43—28no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288C4×Dic43—21no—
289C4×Dic43—21no—
290C4×Dic43—21no—
291C4×Dic43—22no—
292C4×Dic43—22no—
293C4×Dic43—44no—
294C4×Dic43C22⋊C411yescharacteristic
295C4×Dic43C22⋊C411yescharacteristic
296C4×Dic43C22⋊C411yescharacteristic
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×Dic43C2×D411yescharacteristic
307C4×Dic43C2×D411yescharacteristic
308C4×Dic43C2×D411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310#10621877—24no—
311#10621877—22no—
312#10621877#4114yescomplemented
313C2×C43⋊C8—24no—
314C2×C43⋊C8—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—21no—
318C23×C43—41no—
319C23×C43C2×C22⋊C411yescharacteristic
320C23×C43C2×C22⋊C411yescharacteristic
321C23×C43C22×D411yescharacteristic
322C22×D43—21no—
323Q8×C43—22no—
324D4×C43—22no—
325D4×C43—42no—
326D4×C43—42no—
327D4×C43—42no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—24no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—42no—
340C2×C4×C43—42no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C23×C411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C2×#4112yes—
348C2×C4×C43C2×#4112yes—
349C22⋊D43—42no—
350C22⋊D43—42no—
351C22⋊D43—42no—
352C22⋊D43—42no—
353C22⋊D43—42no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—24no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—42no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43#10414yescomplemented
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382D172—22no—
383C4×D43—41no—
384C4×D43—41no—
385C4×D43—42no—
386C4×D43—42no—
387Dic86—22no—
388Dic86—42no—
389Dic86—42no—
390C8×C43—24no—
391C43⋊C8—24no—
392#21382—431nomaximal, Sylow
393C22×C43—21no—
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—21no—
397C22×C43—21no—
398C22×C43—21no—
399C22×C43—21no—
400C22×C43—44no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43C2×#10412yes—
405C22×C43C22×C22⋊C411yescharacteristic
406C22×C43#53212yes—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—41no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—44no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43—41no—
416C4×C43C4×#4112yes—
417C4×C43#52511yescharacteristic
418C4×C43#52511yescharacteristic
419Dic43—21no—
420Dic43—21no—
421Dic43—21no—
422Dic43—21no—
423Dic43—21no—
424Dic43—44no—
425Dic43—41no—
426Dic43—41no—
427Dic43—41no—
428Dic43C2×#10412yes—
429Dic43C2×#10412yes—
430Dic43#42112yes—
431#3444—431no—
432C2×C4×M16—431no—
433C4×#117—431no—
434#1986—432no—
435#1980—432no—
436#1871—431no—
437#1871—431no—
438#1871—431no—
439#1871D4311yescharacteristic, complemented
440C4×#104—432no—
441C4×#104—432no—
442C2×C43—22no—
443C2×C43—22no—
444C2×C43—41no—
445C2×C43—81no—
446C2×C43#229711yescharacteristic
447C2×C43C22×#10411yescharacteristic
448C2×C43C2×#42111yescharacteristic
449D43—81no—
450C22×M16—431no—
451C22×M16C2×D4311yescharacteristic
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—861no—
468#525—861no—
469#525C2×D4311yescharacteristic
470C4×#41—431no—
471C4×#41—431no—
472C4×#41—861no—
473C4×#41—861no—
474C2×#117—861no—
475C22×C42—431no—
476C2×#104—432no—
477C2×#104—432no—
478C2×#104—432no—
479C2×#104C2×D4312yes—
480C4×M16—432no—
481C4×M16—432no—
482C4×M16—861no—
483C4×M16—861no—
484C2×#97—861no—
485C2×C4×C8—861no—
486C4×C4⋊C4—432no—
487C4×C4⋊C4—861no—
488C4×C22⋊C4—431no—
489C4×C22⋊C4—861no—
490C4×C22⋊C4C2×D4311yescharacteristic
491#376—861no—
492C43—432no—
493#339—432no—
494#339—432no—
495#339—432no—
496#339C2×D4312yes—
497C43#2138211yescharacteristic, complemented, Sylow
498C2×#41—431no—
499C2×#41—861no—
500C2×#41—861no—
501C2×#41C22×D4311yescharacteristic
502C23×C4—431no—
503C23×C4—431no—
504C23×C4C22×D4311yescharacteristic
505C2×M16—21no—
506C2×M16—24no—
507C2×M16—432no—
508C2×M16—864no—
509C2×M16—861no—
510C2×M16C22×D4312yes—
511C22×C8—21no—
512C22×C8—861no—
513C4⋊Q8—431no—
514C4⋊Q8—431no—
515C4⋊Q8—431no—
516#127—431no—
517#126—861no—
518#126—861no—
519#126—861no—
520#126—861no—
521#125—431no—
522#125—431no—
523#125—861no—
524#125—861no—
525#124—431no—
526#124—431no—
527#124—861no—
528#124—861no—
529#123—21no—
530#123—861no—
531#123—861no—
532#123—861no—
533#123—861no—
534#123—861no—
535C22⋊Q8—431no—
536C22⋊Q8—431no—
537C22⋊Q8—861no—
538C22⋊Q8—861no—
539C22⋊Q8—861no—
540C22⋊Q8—861no—
541C22⋊Q8C4×D4311yescharacteristic
542C22⋊Q8C4×D4311yescharacteristic
543#121—431no—
544#121—431no—
545#121—861no—
546#121—861no—
547#121—861no—
548#121—861no—
549#121C4×D4311yescharacteristic
550#121C4×D4311yescharacteristic
551#120—21no—
552#120—861no—
553C4×Q8—431no—
554C4×Q8—431no—
555C4×Q8—431no—
556C4×Q8—431no—
557C4×Q8—861no—
558C4×Q8—861no—
559C4×Q8—861no—
560C4×Q8—861no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—431no—
564C4×D4—431no—
565C4×D4—431no—
566C4×D4—431no—
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×D4—861no—
579C4×D4—861no—
580C4×D4—861no—
581#117—431no—
582#117—861no—
583#117—861no—
584#117—861no—
585#117—861no—
586#117—861no—
587#117—861no—
588#117—861no—
589#117—861no—
590#117—868no—
591#117C22×D4311yescharacteristic
592C2×C4⋊C4—862no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—861no—
595C2×C42—431no—
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—862no—
611C2×C42—862no—
612C2×C42C22×D4312yes—
613#104—24no—
614#104—864no—
615#104—864no—
616#104—864no—
617#97—862no—
618#97—862no—
619C4×C8—862no—
620C4×C8—862no—
621#95—21no—
622#95—862no—
623#95—861no—
624C24D4×D4311yescharacteristic
625#41—22no—
626#41—22no—
627#41—862no—
628#41—862no—
629#41—1724no—
630#41—1724no—
631C2×Q8—431no—
632C2×Q8—861no—
633C2×Q8—861no—
634C2×Q8C2×C4×D4311yescharacteristic
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—431no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4C2×C4×D4311yescharacteristic
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—431no—
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—861no—
662C22×C4—861no—
663C22×C4—864no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—862no—
667C22×C4—861no—
668C22×C4—1722no—
669C22×C4C2×C4×D4311yescharacteristic
670C22×C4C2×C4×D4311yescharacteristic
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4D4×D4311yescharacteristic
674C22×C4C23×D4311yescharacteristic
675M16—24no—
676M16—22no—
677M16—434no—
678M16—864no—
679M16—862no—
680M16#1062190014yescomplemented
681C2×C8—24no—
682C2×C8—22no—
683C2×C8—864no—
684C2×C8—862no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—431no—
688C4⋊C4—431no—
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—861no—
701C4⋊C4—868no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4C2×C4×D4311yescharacteristic
705C4⋊C4C2×C4×D4311yescharacteristic
706C22⋊C4—24no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—861no—
713C22⋊C4—861no—
714C22⋊C4—861no—
715C22⋊C4—861no—
716C22⋊C4—861no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—864no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C42—21no—
727C42—22no—
728C42—22no—
729C42—431no—
730C42—431no—
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—431no—
744C42—431no—
745C42—861no—
746C42—861no—
747C42—861no—
748C42—861no—
749C42—868no—
750C42—861no—
751C42—862no—
752C42—862no—
753C42—1724no—
754C23—22no—
755C23—22no—
756C23—21no—
757C23—41no—
758C23—861no—
759C23C22⋊C4×D4311yescharacteristic
760C23C22⋊C4×D4311yescharacteristic
761C23C2×D4×D4311yescharacteristic
762Q8—22no—
763Q8—862no—
764Q8—1722no—
765Q8—1722no—
766D4—22no—
767D4—42no—
768D4—42no—
769D4—42no—
770D4—862no—
771D4—1722no—
772D4—1722no—
773D4—1722no—
774D4—1722no—
775D4—1722no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—24no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—431no—
792C2×C4—431no—
793C2×C4—431no—
794C2×C4—434no—
795C2×C4—431no—
796C2×C4—431no—
797C2×C4—431no—
798C2×C4—431no—
799C2×C4—431no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—864no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—1722no—
813C2×C4—1722no—
814C2×C4—1722no—
815C2×C4—1722no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1722no—
820C2×C4—1722no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4C22⋊C4×D4311yescharacteristic
824C2×C4C22⋊C4×D4311yescharacteristic
825C2×C4C22×C4×D4311yescharacteristic
826C2×C4C2×D4×D4311yescharacteristic
827C2×C4#41×D4312yes—
828C2×C4C2×#1062190012yes—
829C8—24no—
830C8—864no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—44no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—1721no—
843C22—1721no—
844C22—1721no—
845C22#104×D4312yes—
846C22C2×C22⋊C4×D4311yescharacteristic
847C22#1458344412yes—
848C4—21no—
849C4—21no—
850C4—44no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—432no—
855C4—432no—
856C4—432no—
857C4—861no—
858C4—861no—
859C4—861no—
860C4—861no—
861C4—861no—
862C4—1724no—
863C4—1721no—
864C4—1721no—
865C4—1721no—
866C4C4×#1062190012yes—
867C4#1458340511yescharacteristic
868C4#1458340711yescharacteristic
869C2—22no—
870C2—22no—
871C2—41no—
872C2—81no—
873C2—3441no—
874C2#1913708011yescharacteristic
875C2C2×#104×D4311yescharacteristic
876C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43#21382
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×M16×Dic43C2semidirect
3. C4×#13063281C2semidirect
4. #19135537C2semidirect
5. #19135512C2semidirect
6. #19134898C2semidirect
7. #19134897C2semidirect
8. #19134895C2semidirect
9. #104×Dic43C2semidirect
10. #19134399C2semidirect
11. C43×#1871C2semidirect
14. #14583451C4semidirect
15. #14583451C4semidirect
17. #14583444C4semidirect
18. #14583444C4semidirect
19. #14583435C4semidirect
20. #14583435C4semidirect
21. #14583430C4semidirect
22. #14583430C4semidirect
238. M16×C43#41semidirect
312. #10621877#41semidirect
373. C2×Dic43#104semidirect
439. #1871D43semidirect
497. C43#21382semidirect
680. M16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191478872
C2×M16×Dic432
C4×#130632812
#191355372
#191355122
#191348982
#191348972
#191348952
#104×Dic432
#191343992
C43×#18712
#2138243