Finite Group Databasebeta

← #25113308

Subgroups — #25113308

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148173C211yesmaximal, characteristic
2#19143546C211yesmaximal, characteristic, complemented
3#19137072C211yesmaximal, characteristic, complemented
4#19135574C212yesmaximal, complemented
5#19135540C211yesmaximal, characteristic, complemented
6#19135537C212yesmaximal, complemented
7#19134614C212yesmaximal
8#19134612C211yesmaximal, characteristic
9#19134404C212yesmaximal
10C4×#13063253C211yesmaximal, characteristic
11C43×#1994C211yesmaximal, characteristic, complemented
12#14583629C411yescharacteristic, complemented
13#14583626C412yescomplemented
14#14583624C411yescharacteristic, complemented
15#14583610C411yescharacteristic, complemented
16#14583607—21no—
17#14583605C412yescomplemented
18#14583603—22no—
19#14583564C411yescharacteristic, complemented
20#14583562—21no—
21#14583453—21no—
22#14583453—22no—
23#14583452C2212yes—
24C4×#10621898C2211yescharacteristic
25#14583367C2212yes—
26C2×C4×Dic86C2211yescharacteristic
27C4×Q8×D43—21no—
28#14583028—22no—
29#14583026—21no—
30#14583023—21no—
31#14582922C2212yes—
32C2×#13063253C2211yescharacteristic
33C2×#13063253C2211yescharacteristic
34C2×#13063251C2212yes—
35C4×#10621877C2211yescharacteristic
36M16×Dic43C2212yes—
37#14582805—21no—
38#14582797—21no—
39#14582783—22no—
40C4×Dic43⋊C4C2212yes—
41C4×C4⋊Dic43C2211yescharacteristic
42#14582745C2212yes—
43#14582660C2212yes—
44#14582659C2211yescharacteristic
45#14582659C2211yescharacteristic
46#14582658C2212yes—
47#14582658C2212yes—
48C43×#533C2211yescharacteristic
49C43×#423C2211yescharacteristic
50C43×C43C2211yescharacteristic
51C43×#339C2212yes—
52C43×#339C2212yes—
53C2×#10621898C2311yescharacteristic
54C22×Dic86D411yescharacteristic
55C2×Q8×D43—21no—
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2311yescharacteristic
58#13063324—22no—
59#13063324—21no—
60#13063324C2×C412yes—
61#13063324C2×C412yes—
62#13063323—21no—
63#13063323—22no—
64#13063316C2×C412yes—
65#13063316C2×C412yes—
66#13063315—22no—
67#13063315—22no—
68#13063315—22no—
69#13063305—21no—
70#13063305—22no—
71#13063303—22no—
72#13063303—22no—
73#13063303—22no—
74#13063302—22no—
75#13063302—22no—
76#13063301—21no—
77#13063301—22no—
78Q8×Dic43—21no—
79C4×Dic86—22no—
80C4×Dic86—22no—
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2×C412yes—
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86D411yescharacteristic
87C4×Dic86D411yescharacteristic
88C4×Dic86D412yes—
89#13063290—21no—
90#13063290—22no—
91#13063290C2×C412yes—
92#13063290C2×C412yes—
93C4×D172C2×C411yescharacteristic
94C4×D172C2×C411yescharacteristic
95#13063287C2×C412yes—
96#13063287C2×C412yes—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101#13063284C2311yescharacteristic
102#13063282—21no—
103#13063282—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4D412yes—
108C4⋊C4×D43—21no—
109C4⋊C4×D43—22no—
110C2×C4×Dic43C2312yes—
111C2×C4×Dic43C2312yes—
112C42×D43—21no—
113C42×D43—22no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116#13063253—22no—
117#13063253Q814yescomplemented
118#13063251—24no—
119#13063236—21no—
120#13063235—22no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C43⋊#95—21no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C2×M16×C43C2312yes—
128C4⋊Q8×C43C2×C411yescharacteristic
129C4⋊Q8×C43C2×C411yescharacteristic
130#125×C43C2×C412yes—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135#117×C43C2312yes—
136C2×C42×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C4⋊C8×C43—21no—
142C4⋊C8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—21no—
151C22×Dic43—22no—
152C22×Dic43C2×D412yes—
153C22×Dic43C2×D412yes—
154Q8×D43—44no—
155#10621898—21no—
156#10621898—21no—
157#10621898C2×Q812yes—
158#10621898#4112yes—
159C2×D172C22×C411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—22no—
163C2×C4×D43—21no—
164C2×C4×D43—22no—
165C2×Dic86—22no—
166C2×Dic86—22no—
167C2×Dic86—42no—
168C2×Dic86C22⋊C411yescharacteristic
169C2×Dic86C22⋊C411yescharacteristic
170C2×Dic86C22⋊C412yes—
171C2×Dic86C22×C411yescharacteristic
172M16×C43—22no—
173M16×C43—22no—
174C2×C8×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C412yes—
180C4⋊C4×C43C22×C412yes—
181C22⋊C4×C43—22no—
182C42×C43—22no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—42no—
187C42×C43—42no—
188C42×C43C22×C411yescharacteristic
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×Q812yescomplemented
193C22⋊Dic43—21no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43—22no—
200C4⋊Dic43—42no—
201C4⋊Dic43C22⋊C411yescharacteristic
202C4⋊Dic43C22⋊C411yescharacteristic
203C4⋊Dic43C22⋊C412yes—
204C4⋊Dic43C22×C411yescharacteristic
205C4⋊Dic43C22×C411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—44no—
215Dic43⋊C4C22⋊C412yes—
216Dic43⋊C4C22⋊C412yes—
217Dic43⋊C4C22⋊C412yes—
218Dic43⋊C4C22⋊C412yes—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—22no—
223C4×Dic43—22no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C4×Dic43C22×C412yes—
227C4×Dic43C22×C412yes—
228C4×Dic43C2×D412yes—
229C4×Dic43C2×D412yes—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877C2×Q812yescomplemented
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C23×C43C22×D411yescharacteristic
237C22×D43—21no—
238Q8×C43—42no—
239Q8×C43—81no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×Q811yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C432−1+411yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C22⋊D43—22no—
261C22⋊D43—22no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43C2×C22⋊C412yes—
271C2×Dic43C2×C22⋊C412yes—
272C2×Dic43C2×C22⋊C412yes—
273C2×Dic43C2×C22⋊C412yes—
274D172—21no—
275D172C4×Q812yes—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—44no—
279C4×D43—42no—
280C4×D43—82no—
281C4×D43—81no—
282Dic86—21no—
283Dic86—22no—
284Dic86—22no—
285Dic86—42no—
286Dic86—44no—
287Dic86—82no—
288Dic86C4×Q812yes—
289C8×C43—42no—
290C43⋊C8—22no—
291C43⋊C8—41no—
292#22529—431nomaximal, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43#54811yescharacteristic
297C22×C43D4×Q811yescharacteristic
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—42no—
308C4×C43#42112yes—
309C4×C43C2×C4×Q811yescharacteristic
310C4×C43#51911yescharacteristic
311C4×C43#54811yescharacteristic
312C4×C43D4×Q811yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—22no—
316Dic43—22no—
317Dic43—22no—
318Dic43—41no—
319Dic43—41no—
320Dic43—82no—
321Q8×#41—431no—
322Q8×M16—431no—
323#2295—431no—
324#1995—432no—
325#1994D4311yescharacteristic, complemented
326#1986—432no—
327#1986—431no—
328#1806—431no—
329#1806—432no—
330#1759—432no—
331C4×#104—431no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43Q8×C22⋊C411yescharacteristic
335C2×C43C2×#42111yescharacteristic
336C2×C43#290111yescharacteristic
337D43—42no—
338Q82—431no—
339#557—431no—
340#557—432no—
341#554—431no—
342#554—432no—
343#554—862no—
344#554—861no—
345D4×Q8—431no—
346D4×Q8—861no—
347#533—432no—
348#533—862no—
349#533—861no—
350#533C2×D4311yescharacteristic
351C4×#41—432no—
352C4×#41—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8—861no—
355#446—861no—
356#446—862no—
357C8×Q8—861no—
358#423—432no—
359#423C2×D4311yescharacteristic
360C2×#104—431no—
361C2×#104—432no—
362C2×#104—431no—
363C4×M16—432no—
364C4×M16—431no—
365#391—861no—
366#389—861no—
367#387—862no—
368C4×C4⋊C4—432no—
369C4×C4⋊C4—431no—
370#376—432no—
371C43C2×D4311yescharacteristic
372#339—432no—
373#339—432no—
374#339—432no—
375#339—431no—
376#339—431no—
377#339C2×D4312yes—
378#339C2×D4312yes—
379C43#2252911yescharacteristic, complemented, Sylow
380C2×#41—431no—
381C22×Q8—431no—
382C22×Q8—861no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16C22×D4312yes—
386C4⋊Q8—432no—
387C4⋊Q8—432no—
388C4⋊Q8—861no—
389C4⋊Q8—862no—
390C4⋊Q8—862no—
391C4⋊Q8—861no—
392C4⋊Q8C4×D4311yescharacteristic
393C4⋊Q8C4×D4311yescharacteristic
394#125—432no—
395#125—432no—
396#125—862no—
397#125—862no—
398#125—862no—
399#125C4×D4312yes—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—862no—
407C22⋊Q8—862no—
408C22⋊Q8—861no—
409C22⋊Q8—861no—
410C22⋊Q8—862no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—431no—
414C4×Q8—431no—
415C4×Q8—432no—
416C4×Q8—431no—
417C4×Q8—431no—
418C4×Q8—432no—
419C4×Q8—432no—
420C4×Q8—432no—
421C4×Q8—431no—
422C4×Q8—431no—
423C4×Q8—862no—
424C4×Q8—862no—
425C4×Q8—862no—
426C4×Q8—861no—
427C4×Q8—861no—
428C4×D4—432no—
429C4×D4—432no—
430C4×D4—431no—
431C4×D4—431no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—861no—
435C4×D4—861no—
436#117—431no—
437#117—862no—
438#117—861no—
439#117C22×D4312yes—
440C2×C4⋊C4—432no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—862no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—861no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—432no—
449C2×C42—432no—
450C2×C42—862no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453C2×C42C22×D4311yescharacteristic
454C2×C42C22×D4311yescharacteristic
455C4⋊C8—21no—
456C4⋊C8—21no—
457C4⋊C8—862no—
458C4⋊C8—862no—
459#104—434no—
460#104—862no—
461#104—864no—
462#97—862no—
463#97—861no—
464C4×C8—862no—
465C4×C8—861no—
466#95—862no—
467#95—862no—
468#95—862no—
469#95—861no—
470#41—432no—
471#41—432no—
472#41—861no—
473#41—861no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—431no—
477C2×Q8—431no—
478C2×Q8—432no—
479C2×Q8—431no—
480C2×Q8—862no—
481C2×Q8—862no—
482C2×Q8—1722no—
483C2×Q8—1724no—
484C2×D4—431no—
485C2×D4—861no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—862no—
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4C23×D4311yescharacteristic
499M16—22no—
500M16—22no—
501M16—432no—
502M16—861no—
503M16—861no—
504M16—861no—
505C2×C8—22no—
506C2×C8—861no—
507C2×C8—861no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—432no—
513C4⋊C4—431no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—432no—
517C4⋊C4—432no—
518C4⋊C4—431no—
519C4⋊C4—431no—
520C4⋊C4—431no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1724no—
532C4⋊C4—1722no—
533C4⋊C4C2×C4×D4312yes—
534C4⋊C4C2×C4×D4312yes—
535C22⋊C4—22no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C42—22no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—42no—
547C42—432no—
548C42—432no—
549C42—432no—
550C42—432no—
551C42—862no—
552C42—862no—
553C42—861no—
554C42—861no—
555C42—861no—
556C42—862no—
557C42—862no—
558C42C2×C4×D4311yescharacteristic
559C42C2×C4×D4311yescharacteristic
560C42D4×D4311yescharacteristic
561C42D4×D4311yescharacteristic
562C42Q8×D4312yescomplemented
563C23—861no—
564C23C2×D4×D4311yescharacteristic
565Q8—42no—
566Q8—81no—
567Q8—432no—
568Q8—861no—
569Q8—862no—
570Q8—862no—
571Q8—3442no—
572Q8—1722no—
573Q8—1724no—
574D4—432no—
575D4—862no—
576D4—862no—
577D4—861no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—432no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—861no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—3441no—
598C2×C4—3442no—
599C2×C4—1724no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22⋊C4×D4311yescharacteristic
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4C22×C4×D4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C2×C4C2×Q8×D4311yescharacteristic
613C2×C4#41×D4311yescharacteristic
614C2×C4#1306337211yescharacteristic
615C2×C4#1306337311yescharacteristic
616C8—42no—
617C8—862no—
618C8—1721no—
619C22—21no—
620C22—21no—
621C22—862no—
622C22—1721no—
623C22—1721no—
624C22C2×C22⋊C4×D4311yescharacteristic
625C22#1458355911yescharacteristic
626C22#1458356211yescharacteristic
627C4—21no—
628C4—21no—
629C4—21no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—862no—
635C4—862no—
636C4—862no—
637C4—862no—
638C4—862no—
639C4—3442no—
640C4—1721no—
641C4—1721no—
642C4#1458291412yes—
643C4C4×Q8×D4311yescharacteristic
644C4#1458337511yescharacteristic
645C4#1458355711yescharacteristic
646C4#1458356411yescharacteristic
647C2—21no—
648C2—21no—
649C2—1722no—
650C2#1913742911yescharacteristic
651C2C2×#1458291411yescharacteristic
652C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1994C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1994D43
hypocenterC43#22529
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
2. #19143546C2semidirect
3. #19137072C2semidirect
4. #19135574C2semidirect
5. #19135540C2semidirect
6. #19135537C2semidirect
11. C43×#1994C2semidirect
12. #14583629C4semidirect
13. #14583626C4semidirect
14. #14583624C4semidirect
15. #14583610C4semidirect
17. #14583605C4semidirect
19. #14583564C4semidirect
117. #13063253Q8semidirect
192. C42×C43C2×Q8semidirect
233. #10621877C2×Q8semidirect
325. #1994D43semidirect
379. C43#22529semidirect
562. C42Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191481732
#191435462
#191370722
#191355742
#191355402
#191355372
#191346142
#191346122
#191344042
C4×#130632532
C43×#19942
#2252943