Finite Group Databasebeta

← #25101627

Subgroups — #25101627

Order 11008.

1164 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2C2×M16×Dic43C211yesmaximal, characteristic, complemented
3#19136989C211yesmaximal, characteristic, complemented
4#19135537C212yesmaximal, complemented
5#19135512C212yesmaximal, complemented
6#19134898C211yesmaximal, characteristic, complemented
7#19134897C211yesmaximal, characteristic, complemented
8#19134895C211yesmaximal, characteristic, complemented
9#19134407C212yesmaximal, complemented
10#19134404C212yesmaximal, 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—
34C22×C4×Dic43C2211yescharacteristic
35C2×#13063253C2212yes—
36C2×#13063252C2212yes—
37C2×#13063251C2212yes—
38M16×Dic43—21no—
39M16×Dic43—21no—
40M16×Dic43C2212yes—
41M16×Dic43C2212yes—
42C2×#13063235—21no—
43C2×C8×Dic43—21no—
44#14582766—21no—
45#14582763—21no—
46#14582760—21no—
47#14582757—21no—
48C4×Dic43⋊C4C2212yes—
49C4×C22⋊Dic43C2211yescharacteristic
50#14582745C2212yes—
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—21no—
134#13063281—21no—
135#13063281—21no—
136#13063281—21no—
137C2×Dic43⋊C4—22no—
138C2×C22⋊Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43C2×C411yescharacteristic
142C2×C4×Dic43C2×C411yescharacteristic
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43C2312yes—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153C42×D43—21no—
154#13063253—24no—
155#13063252—24no—
156#13063251—24no—
157#13063235—22no—
158#13063235—22no—
159C8×Dic43—22no—
160C8×Dic43—22no—
161C43⋊#95—21no—
162C43⋊#95—22no—
163C43⋊#95—22no—
164C43⋊#95—22no—
165C2×#41×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×M16×C43—21no—
168C2×M16×C43—24no—
169C2×M16×C43C2312yes—
170C22×C8×C43—21no—
171#123×C43—21no—
172C22⋊Q8×C43C2×C411yescharacteristic
173C22⋊Q8×C43C2×C411yescharacteristic
174#121×C43C2×C411yescharacteristic
175#121×C43C2×C411yescharacteristic
176#120×C43—21no—
177C4×D4×C43—21no—
178C4×D4×C43—21no—
179#117×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C42×C43C2312yes—
182#104×C43—24no—
183#95×C43—21no—
184C24×C43C2×D411yescharacteristic
185#41×C43—22no—
186#41×C43—22no—
187C2×Q8×C43C22×C411yescharacteristic
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43C22×C411yescharacteristic
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—22no—
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—21no—
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C2×C22⋊D43—21no—
206C2×C22⋊D43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—22no—
210C22×Dic43—42no—
211C22×Dic43—42no—
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C22⋊C411yescharacteristic
214C22×Dic43C22⋊C411yescharacteristic
215C22×Dic43C22⋊C411yescharacteristic
216C22×Dic43C22⋊C411yescharacteristic
217C22×Dic43C22⋊C411yescharacteristic
218C22×Dic43C22⋊C411yescharacteristic
219C22×Dic43C22⋊C411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224#10621900—44no—
225#10621900—44no—
226#10621898—22no—
227#10621898—22no—
228C2×D172C22×C411yescharacteristic
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C22×C411yescharacteristic
235M16×C43—24no—
236M16×C43—22no—
237M16×C43#4114yescomplemented
238C2×C8×C43—24no—
239C2×C8×C43—22no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C22×C411yescharacteristic
243C4⋊C4×C43C22×C411yescharacteristic
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—21no—
249C22⋊C4×C43—42no—
250C42×C43—21no—
251C42×C43—22no—
252C42×C43—22no—
253C22⋊Dic43—21no—
254C22⋊Dic43—21no—
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—42no—
261(C2×D43)⋊C4—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—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43C22×C411yescharacteristic
272C4⋊Dic43C22×C411yescharacteristic
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
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—44no—
284C4×Dic43—21no—
285C4×Dic43—21no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288C4×Dic43—21no—
289C4×Dic43—22no—
290C4×Dic43—22no—
291C4×Dic43C22⋊C411yescharacteristic
292C4×Dic43C22⋊C411yescharacteristic
293C4×Dic43C22⋊C411yescharacteristic
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×Dic43C2×D411yescharacteristic
304C4×Dic43C2×D411yescharacteristic
305C4×Dic43C2×D411yescharacteristic
306C4×Dic43C2×D411yescharacteristic
307#10621877—24no—
308#10621877—22no—
309#10621877#4114yescomplemented
310C2×C43⋊C8—24no—
311C2×C43⋊C8—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—41no—
316C23×C43C2×C22⋊C411yescharacteristic
317C23×C43C2×C22⋊C411yescharacteristic
318C23×C43C22×D411yescharacteristic
319C22×D43—21no—
320Q8×C43—22no—
321D4×C43—22no—
322D4×C43—42no—
323D4×C43—42no—
324D4×C43—42no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—42no—
338C2×C4×C43—42no—
339C2×C4×C43—42no—
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—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—42no—
367C2×Dic43—42no—
368C2×Dic43—42no—
369C2×Dic43—42no—
370C2×Dic43—42no—
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379D172—22no—
380C4×D43—42no—
381C4×D43—42no—
382C4×D43—41no—
383C4×D43—41no—
384Dic86—22no—
385Dic86—42no—
386Dic86—42no—
387C8×C43—24no—
388C43⋊C8—24no—
389#21383—431nomaximal, Sylow
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—21no—
397C22×C43—44no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43#42112yes—
402C22×C43C22×C22⋊C411yescharacteristic
403C22×C43#53212yes—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43—41no—
410C4×C43—41no—
411C4×C43—41no—
412C4×C43—82no—
413C4×C43C4×#4112yes—
414C4×C43#52511yescharacteristic
415C4×C43#52511yescharacteristic
416Dic43—21no—
417Dic43—21no—
418Dic43—21no—
419Dic43—21no—
420Dic43—21no—
421Dic43—21no—
422Dic43—21no—
423Dic43—41no—
424Dic43—41no—
425Dic43—41no—
426Dic43—82no—
427Dic43#42112yes—
428#3444—431no—
429C2×C4×M16—431no—
430#2283—431no—
431#1986—432no—
432#1980—432no—
433#1871—431no—
434#1871—431no—
435#1871—431no—
436#1871D4311yescharacteristic, complemented
437#1759—432no—
438#1759—432no—
439C2×C43—22no—
440C2×C43—22no—
441C2×C43—41no—
442C2×C43—81no—
443C2×C43#229711yescharacteristic
444C2×C43C2×#42111yescharacteristic
445C2×C43C2×#42111yescharacteristic
446D43—81no—
447C22×M16—431no—
448C22×M16C2×D4311yescharacteristic
449#533—431no—
450#533—431no—
451#533—431no—
452#532—431no—
453#532—431no—
454#532—431no—
455#529—431no—
456#529—431no—
457#529—431no—
458#529—431no—
459#529—861no—
460#529—861no—
461#529—861no—
462#529—861no—
463#525—431no—
464#525—861no—
465#525—861no—
466#525C2×D4311yescharacteristic
467C4×#41—431no—
468C4×#41—431no—
469C4×#41—861no—
470C4×#41—861no—
471C22×C42—431no—
472C2×#104—432no—
473C2×#104—432no—
474C2×#104—432no—
475C2×#104C2×D4312yes—
476C4×M16—432no—
477C4×M16—432no—
478C4×M16—861no—
479C4×M16—861no—
480C2×#97—861no—
481C2×C4×C8—861no—
482#383—861no—
483#382—861no—
484#381—861no—
485#380—861no—
486C4×C4⋊C4—432no—
487C4×C22⋊C4—431no—
488C4×C22⋊C4C2×D4311yescharacteristic
489#376—432no—
490#339—432no—
491#339—432no—
492#339—432no—
493#339C2×D4312yes—
494C43#2138311yescharacteristic, complemented, Sylow
495C2×#41—431no—
496C2×#41—861no—
497C2×#41—861no—
498C2×#41C22×D4311yescharacteristic
499C23×C4—431no—
500C23×C4—431no—
501C23×C4C22×D4311yescharacteristic
502C2×M16—21no—
503C2×M16—24no—
504C2×M16—432no—
505C2×M16—864no—
506C2×M16—861no—
507C2×M16C22×D4312yes—
508C22×C8—21no—
509C22×C8—861no—
510C4⋊Q8—431no—
511C4⋊Q8—431no—
512C4⋊Q8—431no—
513#127—431no—
514#126—861no—
515#126—861no—
516#126—861no—
517#126—861no—
518#125—431no—
519#125—431no—
520#125—861no—
521#125—861no—
522#124—431no—
523#124—431no—
524#124—861no—
525#124—861no—
526#123—21no—
527#123—861no—
528#123—861no—
529#123—861no—
530#123—861no—
531#123—861no—
532C22⋊Q8—431no—
533C22⋊Q8—431no—
534C22⋊Q8—861no—
535C22⋊Q8—861no—
536C22⋊Q8—861no—
537C22⋊Q8—861no—
538C22⋊Q8C4×D4311yescharacteristic
539C22⋊Q8C4×D4311yescharacteristic
540#121—431no—
541#121—431no—
542#121—861no—
543#121—861no—
544#121—861no—
545#121—861no—
546#121C4×D4311yescharacteristic
547#121C4×D4311yescharacteristic
548#120—21no—
549#120—861no—
550C4×Q8—431no—
551C4×Q8—431no—
552C4×Q8—431no—
553C4×Q8—431no—
554C4×Q8—861no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×Q8—861no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—431no—
561C4×D4—431no—
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—
578#117—431no—
579#117—861no—
580#117—861no—
581#117—861no—
582#117—861no—
583#117—861no—
584#117—861no—
585#117—861no—
586#117—861no—
587#117C22×D4311yescharacteristic
588C2×C4⋊C4—862no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—861no—
591C2×C42—431no—
592C2×C42—431no—
593C2×C42—431no—
594C2×C42—431no—
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—432no—
604C2×C42—861no—
605C2×C42—861no—
606C2×C42C22×D4312yes—
607#104—24no—
608#104—864no—
609#104—864no—
610#104—864no—
611#97—862no—
612#97—862no—
613C4×C8—862no—
614C4×C8—862no—
615#95—21no—
616#95—862no—
617#95—862no—
618#95—862no—
619#95—861no—
620C24D4×D4311yescharacteristic
621#41—22no—
622#41—22no—
623#41—862no—
624#41—862no—
625#41—1724no—
626#41—1724no—
627C2×Q8—431no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8C2×C4×D4311yescharacteristic
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—431no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4C2×C4×D4311yescharacteristic
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—431no—
648C22×C4—431no—
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—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—862no—
663C22×C4—1722no—
664C22×C4—1722no—
665C22×C4C2×C4×D4311yescharacteristic
666C22×C4C2×C4×D4311yescharacteristic
667C22×C4D4×D4311yescharacteristic
668C22×C4D4×D4311yescharacteristic
669C22×C4D4×D4311yescharacteristic
670C22×C4C23×D4311yescharacteristic
671M16—24no—
672M16—22no—
673M16—434no—
674M16—864no—
675M16—862no—
676M16#1062190014yescomplemented
677C2×C8—24no—
678C2×C8—22no—
679C2×C8—864no—
680C2×C8—862no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—431no—
684C4⋊C4—431no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
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—1724no—
700C4⋊C4C2×C4×D4311yescharacteristic
701C4⋊C4C2×C4×D4311yescharacteristic
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—42no—
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—861no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—1722no—
722C42—21no—
723C42—22no—
724C42—22no—
725C42—431no—
726C42—431no—
727C42—431no—
728C42—431no—
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—861no—
742C42—861no—
743C42—861no—
744C42—861no—
745C42—861no—
746C42—862no—
747C42—862no—
748C23—22no—
749C23—22no—
750C23—21no—
751C23—41no—
752C23—861no—
753C23C22⋊C4×D4311yescharacteristic
754C23C22⋊C4×D4311yescharacteristic
755C23C2×D4×D4311yescharacteristic
756Q8—22no—
757Q8—862no—
758Q8—1722no—
759Q8—1722no—
760D4—22no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—862no—
765D4—1722no—
766D4—1722no—
767D4—1722no—
768D4—1722no—
769D4—1722no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—431no—
786C2×C4—431no—
787C2×C4—431no—
788C2×C4—431no—
789C2×C4—431no—
790C2×C4—431no—
791C2×C4—431no—
792C2×C4—431no—
793C2×C4—862no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—1722no—
802C2×C4—1722no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4—1722no—
814C2×C4—1722no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4C22⋊C4×D4311yescharacteristic
818C2×C4C22⋊C4×D4311yescharacteristic
819C2×C4C22×C4×D4311yescharacteristic
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4#41×D4312yes—
822C2×C4C2×#1062190012yes—
823C8—24no—
824C8—864no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—44no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—1721no—
837C22—1721no—
838C22—1721no—
839C22#1458291412yes—
840C22C2×C22⋊C4×D4311yescharacteristic
841C22#1458344412yes—
842C4—21no—
843C4—21no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—82no—
848C4—432no—
849C4—861no—
850C4—861no—
851C4—861no—
852C4—861no—
853C4—861no—
854C4—861no—
855C4—861no—
856C4—3442no—
857C4—1721no—
858C4—1721no—
859C4—1721no—
860C4C4×#1062190012yes—
861C4#1458340511yescharacteristic
862C4#1458340711yescharacteristic
863C2—22no—
864C2—22no—
865C2—41no—
866C2—81no—
867C2—3441no—
868C2#1913708011yescharacteristic
869C2#421×D4311yescharacteristic
870C2C2×#1458291411yescharacteristic
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#21383
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. #19136989C2semidirect
4. #19135537C2semidirect
5. #19135512C2semidirect
6. #19134898C2semidirect
7. #19134897C2semidirect
8. #19134895C2semidirect
9. #19134407C2semidirect
10. #19134404C2semidirect
11. C43×#1871C2semidirect
14. #14583451C4semidirect
15. #14583451C4semidirect
17. #14583444C4semidirect
18. #14583444C4semidirect
19. #14583435C4semidirect
20. #14583435C4semidirect
21. #14583430C4semidirect
22. #14583430C4semidirect
237. M16×C43#41semidirect
309. #10621877#41semidirect
436. #1871D43semidirect
494. C43#21383semidirect
676. 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
#191369892
#191355372
#191355122
#191348982
#191348972
#191348952
#191344072
#191344042
C43×#18712
#2138343