Finite Group Databasebeta

← #25113501

Subgroups — #25113501

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148188C211yesmaximal, characteristic
2M16×Dic86C211yesmaximal, characteristic, complemented
3#19137072C211yesmaximal, characteristic, complemented
4#19135514C211yesmaximal, characteristic, complemented
5#19135512C212yesmaximal, complemented
6#19135425C212yesmaximal, complemented
7#19135423C211yesmaximal, characteristic, complemented
8#19134615C211yesmaximal, characteristic, complemented
9#19134614C212yesmaximal, complemented
10#19134404C212yesmaximal, complemented
11C4×#104×C43C211yesmaximal, characteristic, complemented
12#14583634C411yescharacteristic, complemented
13#14583632C412yescomplemented
14#14583627C411yescharacteristic, complemented
15#14583621C412yescomplemented
16#14583619C411yescharacteristic, complemented
17#14583598—22no—
18#14583595—21no—
19#14583570C411yescharacteristic, complemented
20#14583558—21no—
21#14583449C2211yescharacteristic
22#14583445C2212yes—
23#14583433—21no—
24#14583427—22no—
25C4×#10621898—21no—
26#14583367C2212yes—
27C2×C4×Dic86C2211yescharacteristic
28#14583029—21no—
29#14583027—22no—
30C8×Dic86—21no—
31#14582923C2211yescharacteristic
32#14582922C2212yes—
33C2×#13063253C2212yes—
34C2×#13063253C2212yes—
35C2×#13063252C2212yes—
36C2×#13063251C2212yes—
37C2×#13063251C2212yes—
38M16×Dic43C2212yes—
39#14582805—21no—
40#14582797—21no—
41#14582783—22no—
42C4×Dic43⋊C4C2212yes—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582745C2212yes—
45#14582658C2212yes—
46C4×#41×C43C2211yescharacteristic
47C2×#104×C43C2211yescharacteristic
48C2×#104×C43C2211yescharacteristic
49C4×M16×C43C2211yescharacteristic
50C43×C43C2211yescharacteristic
51C43×#339C2211yescharacteristic
52C43×#339C2211yescharacteristic
53C2×#10621898—21no—
54C2×#10621898C2312yes—
55C22×Dic86D411yescharacteristic
56C2×#10621877C2312yes—
57#13063325C2×C411yescharacteristic
58#13063323C2×C412yes—
59#13063322C2×C411yescharacteristic
60#13063321C2×C412yes—
61#13063320—22no—
62#13063319—22no—
63#13063318—22no—
64#13063317—21no—
65#13063315—22no—
66#13063314C2×C412yes—
67#13063313—21no—
68#13063313C2×C412yes—
69#13063312C2×C412yes—
70#13063311—22no—
71#13063310—22no—
72#13063308—22no—
73#13063307—22no—
74#13063304—21no—
75#13063303—22no—
76#13063299—21no—
77#13063299—21no—
78#13063299—21no—
79#13063298—22no—
80#13063297—22no—
81#13063297—22no—
82C4×Dic86—21no—
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2×C412yes—
86C4×Dic86D411yescharacteristic
87C4×Dic86D412yes—
88C4×Dic86D411yescharacteristic
89#13063290C2×C412yes—
90#13063290C2×C412yes—
91C4×D172—21no—
92C4×D172—21no—
93C4×D172—21no—
94#13063287C2×C412yes—
95#13063287C2×C412yes—
96C4×C22⋊D43—22no—
97C4×C22⋊D43—22no—
98C4×C22⋊D43—22no—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101#13063284—21no—
102#13063282—22no—
103#13063282—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4D412yes—
108C2×C4×Dic43C2312yes—
109C2×C4×Dic43C2312yes—
110C42×D43—22no—
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)—21no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115#13063253—24no—
116#13063253—42no—
117#13063252—42no—
118#13063251—24no—
119#13063251—42no—
120#13063235—22no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C2×#41×C43C2311yescharacteristic
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C4×Q8×C43C2×C411yescharacteristic
130C4×Q8×C43C2×C411yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43C2×C411yescharacteristic
134C4×D4×C43C2×C411yescharacteristic
135#117×C43—21no—
136#117×C43C2311yescharacteristic
137C2×C42×C43—21no—
138C2×C42×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#104×C43—22no—
144#104×C43—22no—
145#97×C43—21no—
146C4×C8×C43—21no—
147#41×C43—21no—
148#41×C43—21no—
149#41×C43—21no—
150#41×C43—21no—
151C2×Q8×C43C22×C411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43C22×C411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C22×Dic43—22no—
166C22×Dic43C2×D412yes—
167C22×Dic43C2×D412yes—
168#10621898—22no—
169#10621898—22no—
170#10621898—22no—
171#10621898—22no—
172#10621898—44no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C22×C412yes—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×Dic86—42no—
180C2×Dic86C22⋊C411yescharacteristic
181C2×Dic86C22⋊C411yescharacteristic
182C2×Dic86C22⋊C412yes—
183C2×Dic86C22×C412yes—
184M16×C43—21no—
185M16×C43—21no—
186M16×C43—21no—
187M16×C43#4112yescomplemented
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43C22×C411yescharacteristic
193C4⋊C4×C43C22×C411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—42no—
204C42×C43—42no—
205C42×C43C22×C411yescharacteristic
206C42×C43C22×C411yescharacteristic
207C42×C43C2×D411yescharacteristic
208C42×C43C2×D411yescharacteristic
209C42×C43#4112yescomplemented
210C22⋊Dic43—22no—
211C22⋊Dic43—22no—
212(C2×D43)⋊C4—22no—
213(C2×D43)⋊C4—22no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—22no—
216(C2×D43)⋊C4—22no—
217(C2×D43)⋊C4—22no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—42no—
221C4⋊Dic43C22⋊C411yescharacteristic
222C4⋊Dic43C22⋊C411yescharacteristic
223C4⋊Dic43C22⋊C412yes—
224Dic43⋊C4—22no—
225Dic43⋊C4—22no—
226Dic43⋊C4—22no—
227Dic43⋊C4—22no—
228Dic43⋊C4—44no—
229Dic43⋊C4C22⋊C412yes—
230Dic43⋊C4C22⋊C412yes—
231Dic43⋊C4C22⋊C412yes—
232Dic43⋊C4C22⋊C412yes—
233C4×Dic43—22no—
234C4×Dic43—22no—
235C4×Dic43—22no—
236C4×Dic43—22no—
237C4×Dic43C22×C412yes—
238C4×Dic43C22×C412yes—
239C4×Dic43C2×D412yes—
240C4×Dic43C2×D412yes—
241#10621877—22no—
242#10621877—22no—
243C2×C43⋊C8—22no—
244C23×C43—21no—
245C23×C43C22×D411yescharacteristic
246C22×D43—22no—
247Q8×C43—21no—
248Q8×C43—21no—
249D4×C43—21no—
250D4×C43—21no—
251D4×C43—41no—
252D4×C43—41no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—22no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—42no—
267C2×C4×C43—81no—
268C2×C4×C43C2×C22⋊C411yescharacteristic
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43C2×C22⋊C411yescharacteristic
271C2×C4×C43C2×C22⋊C411yescharacteristic
272C2×C4×C43C23×C411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C22⋊D43—44no—
279C22⋊D43—42no—
280C22⋊D43—42no—
281C22⋊D43—82no—
282C2×Dic43—22no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—42no—
288C2×Dic43C2×C22⋊C412yes—
289C2×Dic43C2×C22⋊C412yes—
290C2×Dic43C2×C22⋊C412yes—
291C2×Dic43C2×C22⋊C412yes—
292D172—22no—
293D172—22no—
294D172—42no—
295D172—81no—
296C4×D43—44no—
297C4×D43—42no—
298C4×D43—42no—
299C4×D43—82no—
300Dic86—22no—
301Dic86—22no—
302Dic86—22no—
303Dic86—22no—
304Dic86—42no—
305C8×C43—22no—
306C8×C43—41no—
307C43⋊C8—42no—
308#22551—431nomaximal, Sylow
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43C22×C22⋊C411yescharacteristic
315C22×C43#54811yescharacteristic
316C22×C43#55011yescharacteristic
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—42no—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—21no—
323C4×C43—42no—
324C4×C43—42no—
325C4×C43—41no—
326C4×C43—41no—
327C4×C43—41no—
328C4×C43#42112yes—
329C4×C43C4×#4111yescharacteristic
330C4×C43#52011yescharacteristic
331C4×C43#54811yescharacteristic
332C4×C43#55011yescharacteristic
333Dic43—22no—
334Dic43—22no—
335Dic43—22no—
336Dic43—22no—
337Dic43—42no—
338Dic43—82no—
339#3480—431no—
340Q8×M16—431no—
341#2295—431no—
342#1980—432no—
343#1980—431no—
344#1963—432no—
345#1962—431no—
346#1806—432no—
347#1806—431no—
348#1759—432no—
349C4×#104D4311yescharacteristic, complemented
350C2×C43—21no—
351C2×C43—21no—
352C2×C43—81no—
353C2×C43#234111yescharacteristic
354C2×C43C2×#42111yescharacteristic
355C2×C43#290111yescharacteristic
356D43—82no—
357#559—431no—
358#559—432no—
359#557—431no—
360#556—432no—
361#556—431no—
362#553—861no—
363#553—862no—
364#550—431no—
365#548—861no—
366#532—432no—
367#532—431no—
368#529—861no—
369#529—862no—
370C4×#41—432no—
371C4×#41—861no—
372C4×#41C2×D4311yescharacteristic
373C2×C4×Q8—431no—
374#446—861no—
375#446—862no—
376C8×Q8—861no—
377#423—432no—
378#423—431no—
379C2×#104—432no—
380C2×#104—432no—
381C2×#104—432no—
382C2×#104—432no—
383C2×#104—432no—
384C2×#104C2×D4311yescharacteristic
385C2×#104C2×D4311yescharacteristic
386C4×M16—432no—
387C4×M16C2×D4311yescharacteristic
388#391—861no—
389#389—861no—
390#387—862no—
391C4×C4⋊C4—432no—
392C4×C4⋊C4—431no—
393#376—432no—
394C43C2×D4311yescharacteristic
395#339—432no—
396#339C2×D4311yescharacteristic
397#339C2×D4311yescharacteristic
398C43#2255111yescharacteristic, complemented, Sylow
399C2×#41—432no—
400C2×#41—861no—
401C2×#41C22×D4311yescharacteristic
402C22×Q8—431no—
403C2×M16—432no—
404C2×M16C22×D4311yescharacteristic
405C2×M16C22×D4311yescharacteristic
406C4⋊Q8—432no—
407C4⋊Q8—431no—
408#127—432no—
409#127—431no—
410#126—862no—
411#126—862no—
412#126—862no—
413#125—861no—
414#125—862no—
415#124—432no—
416#124—432no—
417#124—432no—
418#124—861no—
419#124—862no—
420#123—862no—
421#123—862no—
422#123—862no—
423C22⋊Q8—862no—
424C22⋊Q8—861no—
425#121—862no—
426#121—861no—
427#121—862no—
428#121—862no—
429#121—861no—
430#121—861no—
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—432no—
434C4×Q8—431no—
435C4×Q8—431no—
436C4×Q8—432no—
437C4×Q8—432no—
438C4×Q8—432no—
439C4×Q8—861no—
440C4×Q8C4×D4311yescharacteristic
441C4×Q8C4×D4311yescharacteristic
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—432no—
445C4×D4—432no—
446C4×D4—861no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—862no—
450C4×D4—862no—
451C4×D4—862no—
452C4×D4—861no—
453C4×D4—861no—
454C4×D4C4×D4311yescharacteristic
455C4×D4C4×D4311yescharacteristic
456#117—21no—
457#117—862no—
458#117—862no—
459#117—861no—
460#117C22×D4311yescharacteristic
461C2×C4⋊C4—432no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—862no—
464C2×C4⋊C4—861no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—432no—
469C2×C42—432no—
470C2×C42—862no—
471C2×C42C22×D4311yescharacteristic
472C2×C42C22×D4311yescharacteristic
473C2×C42C22×D4311yescharacteristic
474C4⋊C8—862no—
475C4⋊C8—862no—
476C4⋊C8—861no—
477C4⋊C8—861no—
478#104—22no—
479#104—22no—
480#104—864no—
481#104—864no—
482#104—1722no—
483#104—1722no—
484#104—1722no—
485#97—21no—
486#97—862no—
487C4×C8—21no—
488C4×C8—862no—
489#95—862no—
490#95—862no—
491#95—862no—
492#95—861no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—862no—
498#41—862no—
499#41—862no—
500#41—862no—
501#41—1724no—
502C2×Q8—431no—
503C2×Q8—431no—
504C2×Q8—432no—
505C2×Q8—432no—
506C2×Q8—1722no—
507C2×Q8C2×C4×D4311yescharacteristic
508C2×D4—21no—
509C2×D4—432no—
510C2×D4—862no—
511C2×D4—862no—
512C2×D4—862no—
513C2×D4—861no—
514C2×D4—861no—
515C2×D4C2×C4×D4311yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—432no—
522C22×C4—432no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—862no—
534M16—862no—
535M16#1062189812yescomplemented
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—862no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—432no—
542C4⋊C4—431no—
543C4⋊C4—432no—
544C4⋊C4—431no—
545C4⋊C4—432no—
546C4⋊C4—432no—
547C4⋊C4—432no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—862no—
551C4⋊C4—862no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—1724no—
555C4⋊C4—1722no—
556C4⋊C4C2×C4×D4311yescharacteristic
557C4⋊C4C2×C4×D4311yescharacteristic
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—862no—
564C22⋊C4—862no—
565C22⋊C4—862no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C22⋊C4—862no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—42no—
577C42—432no—
578C42—432no—
579C42—432no—
580C42—432no—
581C42—862no—
582C42—862no—
583C42—862no—
584C42—862no—
585C42C2×C4×D4311yescharacteristic
586C42C2×C4×D4311yescharacteristic
587C42#1062189812yescomplemented
588C42D4×D4311yescharacteristic
589C42D4×D4311yescharacteristic
590C23—21no—
591C23—862no—
592C23C2×D4×D4311yescharacteristic
593Q8—21no—
594Q8—21no—
595Q8—862no—
596Q8—862no—
597Q8—862no—
598Q8—862no—
599Q8—1722no—
600D4—21no—
601D4—21no—
602D4—41no—
603D4—41no—
604D4—862no—
605D4—862no—
606D4—3441no—
607D4—3442no—
608D4—1724no—
609D4—1722no—
610D4—1722no—
611D4—1722no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—81no—
627C2×C4—432no—
628C2×C4—432no—
629C2×C4—432no—
630C2×C4—432no—
631C2×C4—862no—
632C2×C4—3442no—
633C2×C4—1724no—
634C2×C4—1722no—
635C2×C4—1722no—
636C2×C4—1722no—
637C2×C4—1722no—
638C2×C4—1722no—
639C2×C4—1722no—
640C2×C4—1722no—
641C2×C4C22⋊C4×D4311yescharacteristic
642C2×C4C22⋊C4×D4311yescharacteristic
643C2×C4C22⋊C4×D4311yescharacteristic
644C2×C4C22⋊C4×D4311yescharacteristic
645C2×C4C22×C4×D4311yescharacteristic
646C2×C4C2×D4×D4311yescharacteristic
647C2×C4C2×#1062189811yescharacteristic
648C2×C4C2×#1062189811yescharacteristic
649C2×C4#1306337111yescharacteristic
650C2×C4#1306337211yescharacteristic
651C8—22no—
652C8—41no—
653C8—1722no—
654C22—21no—
655C22—21no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—1722no—
660C22—1722no—
661C22—1722no—
662C22C2×C22⋊C4×D4311yescharacteristic
663C22#1458355811yescharacteristic
664C22#1458357011yescharacteristic
665C4—21no—
666C4—21no—
667C4—21no—
668C4—42no—
669C4—42no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—862no—
674C4—862no—
675C4—862no—
676C4—862no—
677C4—3442no—
678C4—1722no—
679C4#1458291412yes—
680C4C4×#1062189811yescharacteristic
681C4#1458337911yescharacteristic
682C4#1458355811yescharacteristic
683C4#1458357011yescharacteristic
684C2—21no—
685C2—21no—
686C2—81no—
687C2—3442no—
688C2#1913743511yescharacteristic
689C2C2×#1458291411yescharacteristic
690C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#104×C43C2
socleC22×C43C22×C22⋊C4
prime radical#19148188C2
cosocleC22×C4×C43C24
hypercenterC4×#104D43
hypocenterC43#22551
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
3. #19137072C2semidirect
4. #19135514C2semidirect
5. #19135512C2semidirect
6. #19135425C2semidirect
7. #19135423C2semidirect
8. #19134615C2semidirect
9. #19134614C2semidirect
10. #19134404C2semidirect
11. C4×#104×C43C2semidirect
12. #14583634C4semidirect
13. #14583632C4semidirect
14. #14583627C4semidirect
15. #14583621C4semidirect
16. #14583619C4semidirect
19. #14583570C4semidirect
187. M16×C43#41semidirect
209. C42×C43#41semidirect
349. C4×#104D43semidirect
398. C43#22551semidirect
535. M16#10621898semidirect
587. C42#10621898semidirect

Maximal subgroups

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

subgroupindex
#191481882
M16×Dic862
#191370722
#191355142
#191355122
#191354252
#191354232
#191346152
#191346142
#191344042
C4×#104×C432
#2255143