Finite Group Databasebeta

← #25113493

Subgroups — #25113493

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148192C211yesmaximal, characteristic
2#19143546C211yesmaximal, characteristic, complemented
3C42×Dic86C211yesmaximal, characteristic, complemented
4#19135515C211yesmaximal, characteristic, complemented
5#19135512C212yesmaximal, complemented
6#19135421C212yesmaximal, complemented
7#19134613C212yesmaximal, complemented
8#19134612C211yesmaximal, characteristic, complemented
9#104×Dic43C212yesmaximal, complemented
10C4×#13063253C211yesmaximal, characteristic, complemented
11C43×#1962C211yesmaximal, characteristic, complemented
12#14583635C411yescharacteristic, complemented
13#14583631C412yescomplemented
14#14583624C411yescharacteristic, complemented
15#14583623C411yescharacteristic, complemented
16#14583618C412yescomplemented
17#14583601—21no—
18#14583592—22no—
19#14583569C411yescharacteristic, complemented
20#14583555—21no—
21#14583445C2212yes—
22#14583431—21no—
23#14583429—22no—
24#41×Dic43C2212yes—
25C4×#10621898C2211yescharacteristic
26C4×#10621900—21no—
27C2×C4×Dic86—21no—
28C2×C4×Dic86C2211yescharacteristic
29#14583028—22no—
30#14583026—21no—
31#14583023—21no—
32#14582922C2212yes—
33C2×#13063253C2211yescharacteristic
34C2×#13063253C2211yescharacteristic
35C2×#13063252C2212yes—
36C2×#13063252C2212yes—
37C2×#13063251C2212yes—
38C4×#10621877C2211yescharacteristic
39M16×Dic43C2212yes—
40C4×Dic43⋊C4—22no—
41C4×Dic43⋊C4C2212yes—
42C4×C4⋊Dic43—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C42×Dic43C2212yes—
45#14582660C2212yes—
46#14582659C2211yescharacteristic
47#14582659C2211yescharacteristic
48C43×#532C2211yescharacteristic
49C43×#423C2211yescharacteristic
50C2×#104×C43C2212yes—
51C2×#104×C43C2212yes—
52C43×C43C2211yescharacteristic
53C2×#10621898C2311yescharacteristic
54C2×#10621900—21no—
55C22×Dic86D411yescharacteristic
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2311yescharacteristic
58#13063323C2×C412yes—
59#13063321C2×C412yes—
60#13063320—22no—
61#13063318—22no—
62#13063318—22no—
63#13063316—21no—
64#13063315—22no—
65#13063314C2×C412yes—
66#13063312—21no—
67#13063312C2×C412yes—
68#13063311—22no—
69#13063309—22no—
70#13063307—22no—
71#13063306—22no—
72#13063305—21no—
73#13063302—22no—
74#13063297—22no—
75#13063297—22no—
76#13063297—22no—
77#13063296—21no—
78Q8×Dic43C2×C412yes—
79Q8×Dic43C2×C412yes—
80C4×Dic86—28no—
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2×C412yes—
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86D411yescharacteristic
87C4×Dic86D412yes—
88C4×Dic86D411yescharacteristic
89#13063290—21no—
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92D4×Dic43—22no—
93D4×Dic43—22no—
94D4×Dic43—21no—
95D4×Dic43C2×C412yes—
96D4×Dic43C2×C412yes—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99C4×C22⋊D43—22no—
100C4×C22⋊D43—22no—
101(C22⋊D43)⋊C4—22no—
102#13063284—22no—
103#13063284C2311yescharacteristic
104#13063283—21no—
105#13063282—21no—
106#13063281—22no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43D411yescharacteristic
109C2×Dic43⋊C4—22no—
110C2×Dic43⋊C4D412yes—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—22no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43C2312yes—
115C2×C4×Dic43C2312yes—
116C42×D43—21no—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119#13063253—22no—
120#13063253—22no—
121#13063252—24no—
122#13063252—42no—
123#13063251—42no—
124#13063236—21no—
125#13063235—22no—
126C4×C43⋊C8—21no—
127C8×Dic43—22no—
128C43⋊#95—21no—
129C43⋊#95—22no—
130C2×#41×C43C2312yes—
131C2×M16×C43C2312yes—
132C4⋊Q8×C43C2×C411yescharacteristic
133#127×C43C2×C411yescharacteristic
134#124×C43C2×C412yes—
135#121×C43—21no—
136#121×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144C4⋊C8×C43—21no—
145C4⋊C8×C43—21no—
146#104×C43—24no—
147#104×C43—42no—
148#41×C43—22no—
149#41×C43—22no—
150#41×C43—22no—
151#41×C43—22no—
152C2×Q8×C43C22×C412yes—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—22no—
156C2×D4×C43C22×C412yes—
157C22×C4×C43—22no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—21no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43C2×D412yes—
170C22×Dic43C2×D412yes—
171#10621900—44no—
172#10621898—21no—
173#10621898—21no—
174#10621898—21no—
175#10621898—21no—
176C2×D172C22×C411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×Dic86—24no—
181C2×Dic86C22⋊C412yes—
182C2×Dic86C22⋊C411yescharacteristic
183C2×Dic86C22⋊C411yescharacteristic
184C2×Dic86C22×C411yescharacteristic
185M16×C43—22no—
186M16×C43—22no—
187C2×C8×C43—22no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C42×C43—24no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—42no—
197C42×C43C22×C411yescharacteristic
198C42×C43C22×C411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43#4112yescomplemented
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206C22⋊Dic43—21no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211C4⋊Dic43—24no—
212C4⋊Dic43—22no—
213C4⋊Dic43—22no—
214C4⋊Dic43C22⋊C411yescharacteristic
215C4⋊Dic43C22⋊C411yescharacteristic
216C4⋊Dic43C22⋊C412yes—
217C4⋊Dic43C22×C411yescharacteristic
218C4⋊Dic43C22×C411yescharacteristic
219Dic43⋊C4—28no—
220Dic43⋊C4—21no—
221Dic43⋊C4—21no—
222Dic43⋊C4—22no—
223Dic43⋊C4—22no—
224Dic43⋊C4C22⋊C412yes—
225Dic43⋊C4C22⋊C412yes—
226Dic43⋊C4C22⋊C412yes—
227Dic43⋊C4C22⋊C412yes—
228C4×Dic43—28no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—22no—
233C4×Dic43—22no—
234C4×Dic43—22no—
235C4×Dic43—22no—
236C4×Dic43—44no—
237C4×Dic43C22×C412yes—
238C4×Dic43C22×C412yes—
239C4×Dic43C2×D412yes—
240C4×Dic43C2×D412yes—
241#10621877—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877#4112yescomplemented
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C23×C43—22no—
248C23×C43C22×D411yescharacteristic
249C22×D43—21no—
250Q8×C43—22no—
251Q8×C43—22no—
252D4×C43—22no—
253D4×C43—22no—
254D4×C43—42no—
255D4×C43—42no—
256D4×C43—42no—
257D4×C43—81no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43C2×C22⋊C411yescharacteristic
271C2×C4×C43C2×C22⋊C411yescharacteristic
272C2×C4×C43C2×C22⋊C411yescharacteristic
273C2×C4×C43C23×C411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43H(5,𝔽2)11yescharacteristic
278C2×C4×C432−1+411yescharacteristic
279C22⋊D43—41no—
280C22⋊D43—41no—
281C22⋊D43—44no—
282C22⋊D43—82no—
283C2×Dic43—24no—
284C2×Dic43—24no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—42no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—44no—
292C2×Dic43—82no—
293C2×Dic43C2×C22⋊C412yes—
294C2×Dic43C2×C22⋊C412yes—
295C2×Dic43C2×C22⋊C412yes—
296C2×Dic43C2×C22⋊C412yes—
297D172—21no—
298D172—21no—
299C4×D43—41no—
300C4×D43—41no—
301C4×D43—42no—
302C4×D43—81no—
303Dic86—22no—
304Dic86—24no—
305Dic86—21no—
306Dic86—21no—
307Dic86#10414yescomplemented
308C8×C43—42no—
309C43⋊C8—22no—
310C43⋊C8—41no—
311#22550—431nomaximal, Sylow
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—42no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43C22×C22⋊C411yescharacteristic
318C22×C43#54811yescharacteristic
319C22×C43#55011yescharacteristic
320C2×D43—41no—
321C2×D43—41no—
322C2×D43—41no—
323C4×C43—24no—
324C4×C43—21no—
325C4×C43—21no—
326C4×C43—21no—
327C4×C43—42no—
328C4×C43—42no—
329C4×C43C2×#10412yes—
330C4×C43C4×#4111yescharacteristic
331C4×C43#52011yescharacteristic
332C4×C43#54811yescharacteristic
333C4×C43#55011yescharacteristic
334Dic43—22no—
335Dic43—22no—
336Dic43—22no—
337Dic43—44no—
338Dic43—41no—
339Dic43—41no—
340Dic43—41no—
341Dic43C2×#10414yes—
342#3480—431no—
343Q8×M16—431no—
344C42×Q8—431no—
345#1980—432no—
346#1980—431no—
347#1962—432no—
348#1962D4311yescharacteristic, complemented
349#1806—431no—
350#1806—432no—
351C4×#104—432no—
352C4×#104—431no—
353C2×C43—21no—
354C2×C43—21no—
355C2×C43—82no—
356C2×C43#234111yescharacteristic
357C2×C43C22×#10411yescharacteristic
358C2×C43#290111yescharacteristic
359D43—81no—
360#559—431no—
361#559—432no—
362#557—431no—
363#556—431no—
364#556—432no—
365#553—862no—
366#553—861no—
367#550—431no—
368#548—861no—
369#532—432no—
370#532C2×D4311yescharacteristic
371#529—862no—
372#529—861no—
373C4×#41—432no—
374C4×#41—431no—
375C4×#41—861no—
376C2×C4×Q8—431no—
377C2×C4×Q8—861no—
378#446—861no—
379#446—862no—
380C8×Q8—861no—
381#423—432no—
382#423C2×D4311yescharacteristic
383C2×#104—432no—
384C2×#104—431no—
385C2×#104—431no—
386C2×#104—432no—
387C2×#104—432no—
388C2×#104C2×D4312yes—
389C2×#104C2×D4312yes—
390C4×M16—432no—
391C4×M16—431no—
392C4×C4⋊C4—432no—
393C4×C4⋊C4—431no—
394C4×C4⋊C4—861no—
395C4×C4⋊C4—862no—
396C43—432no—
397C43C2×D4311yescharacteristic
398#339—432no—
399#339—431no—
400#339—431no—
401C43#2255011yescharacteristic, complemented, Sylow
402C2×#41—431no—
403C2×#41—861no—
404C2×#41C22×D4312yes—
405C22×Q8—431no—
406C2×M16—431no—
407C2×M16—431no—
408C2×M16C22×D4312yes—
409C4⋊Q8—432no—
410C4⋊Q8C4×D4311yescharacteristic
411#127—432no—
412#127C4×D4311yescharacteristic
413#126—862no—
414#126—862no—
415#126—862no—
416#125—862no—
417#125—861no—
418#124—432no—
419#124—432no—
420#124—862no—
421#124—861no—
422#124C4×D4312yes—
423#123—862no—
424#123—862no—
425#123—862no—
426C22⋊Q8—862no—
427C22⋊Q8—861no—
428#121—21no—
429#121—21no—
430#121—861no—
431#121—862no—
432#121—862no—
433#121—862no—
434C4×Q8—431no—
435C4×Q8—431no—
436C4×Q8—432no—
437C4×Q8—431no—
438C4×Q8—432no—
439C4×Q8—431no—
440C4×Q8—432no—
441C4×Q8—432no—
442C4×Q8—431no—
443C4×Q8—431no—
444C4×Q8—868no—
445C4×Q8—861no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—432no—
449C4×D4—432no—
450C4×D4—431no—
451C4×D4—431no—
452C4×D4—862no—
453C4×D4—862no—
454C4×D4—862no—
455C4×D4—861no—
456C4×D4—862no—
457C4×D4—862no—
458C4×D4—861no—
459C4×D4—861no—
460#117—431no—
461#117—862no—
462#117—862no—
463#117—861no—
464#117—861no—
465C2×C4⋊C4—432no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—861no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—432no—
472C2×C42—432no—
473C2×C42—862no—
474C2×C42—862no—
475C2×C42—861no—
476C2×C42—862no—
477C2×C42C22×D4311yescharacteristic
478C2×C42C22×D4311yescharacteristic
479C2×C42C22×D4311yescharacteristic
480C4⋊C8—21no—
481C4⋊C8—21no—
482C4⋊C8—862no—
483C4⋊C8—862no—
484#104—24no—
485#104—42no—
486#104—862no—
487#104—864no—
488#104—862no—
489#104—1722no—
490#104—1722no—
491#97—862no—
492#97—861no—
493C4×C8—862no—
494C4×C8—861no—
495#95—862no—
496#95—861no—
497#41—22no—
498#41—22no—
499#41—22no—
500#41—22no—
501#41—861no—
502#41—861no—
503#41—861no—
504#41—861no—
505#41—1724no—
506C2×Q8—431no—
507C2×Q8—432no—
508C2×Q8—431no—
509C2×Q8—431no—
510C2×Q8—864no—
511C2×Q8C2×C4×D4312yes—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—431no—
516C2×D4—862no—
517C2×D4—862no—
518C2×D4—861no—
519C2×D4C2×C4×D4312yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—432no—
524C22×C4—432no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4D4×D4311yescharacteristic
532C22×C4D4×D4311yescharacteristic
533C22×C4C23×D4311yescharacteristic
534M16—22no—
535M16—22no—
536M16—432no—
537M16—861no—
538M16—861no—
539M16—861no—
540C2×C8—22no—
541C2×C8—861no—
542C2×C8—861no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—432no—
546C4⋊C4—431no—
547C4⋊C4—432no—
548C4⋊C4—431no—
549C4⋊C4—432no—
550C4⋊C4—432no—
551C4⋊C4—432no—
552C4⋊C4—431no—
553C4⋊C4—431no—
554C4⋊C4—862no—
555C4⋊C4—862no—
556C4⋊C4—862no—
557C4⋊C4—862no—
558C4⋊C4—868no—
559C4⋊C4—864no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—862no—
565C22⋊C4—862no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C22⋊C4—862no—
569C22⋊C4—862no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C22⋊C4—861no—
573C42—24no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—432no—
579C42—432no—
580C42—432no—
581C42—432no—
582C42—862no—
583C42—862no—
584C42—868no—
585C42—861no—
586C42—861no—
587C42—861no—
588C42—862no—
589C42—862no—
590C42—1724no—
591C42C2×C4×D4311yescharacteristic
592C42C2×C4×D4311yescharacteristic
593C42D4×D4311yescharacteristic
594C42D4×D4311yescharacteristic
595C42#1062190012yescomplemented
596C23—22no—
597C23—861no—
598C23C2×D4×D4311yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—434no—
602Q8—864no—
603Q8—862no—
604Q8—861no—
605Q8—861no—
606D4—22no—
607D4—22no—
608D4—42no—
609D4—42no—
610D4—42no—
611D4—81no—
612D4—861no—
613D4—861no—
614D4—3442no—
615D4—1724no—
616D4—1721no—
617D4—1721no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—432no—
630C2×C4—432no—
631C2×C4—432no—
632C2×C4—432no—
633C2×C4—864no—
634C2×C4—864no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—3441no—
639C2×C4—3442no—
640C2×C4—1724no—
641C2×C4—1722no—
642C2×C4—1722no—
643C2×C4—1722no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1722no—
647C2×C4C22⋊C4×D4311yescharacteristic
648C2×C4C22⋊C4×D4311yescharacteristic
649C2×C4C22⋊C4×D4311yescharacteristic
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4C22×C4×D4311yescharacteristic
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4#41×D4311yescharacteristic
654C2×C4C2×#1062190011yescharacteristic
655C2×C4#1306337011yescharacteristic
656C2×C4#1306337211yescharacteristic
657C8—42no—
658C8—862no—
659C8—1721no—
660C22—21no—
661C22—21no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—1721no—
666C22—1721no—
667C22—1721no—
668C22C2×C22⋊C4×D4311yescharacteristic
669C22#1458355511yescharacteristic
670C22#1458356711yescharacteristic
671C4—24no—
672C4—21no—
673C4—21no—
674C4—21no—
675C4—42no—
676C4—42no—
677C4—434no—
678C4—862no—
679C4—862no—
680C4—862no—
681C4—1724no—
682C4—1721no—
683C4—1721no—
684C4—1721no—
685C4#104×D4312yes—
686C4C4×#1062190011yescharacteristic
687C4#1458337811yescharacteristic
688C4#1458355711yescharacteristic
689C4#1458356911yescharacteristic
690C2—21no—
691C2—21no—
692C2—82no—
693C2—3441no—
694C2#1913743411yescharacteristic
695C2C2×#104×D4311yescharacteristic
696C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1962C2
socleC22×C43C22×C22⋊C4
prime radical#19148192C2
cosocleC22×C4×C43C24
hypercenter#1962D43
hypocenterC43#22550
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #19143546C2semidirect
3. C42×Dic86C2semidirect
4. #19135515C2semidirect
5. #19135512C2semidirect
6. #19135421C2semidirect
7. #19134613C2semidirect
8. #19134612C2semidirect
9. #104×Dic43C2semidirect
10. C4×#13063253C2semidirect
11. C43×#1962C2semidirect
12. #14583635C4semidirect
13. #14583631C4semidirect
14. #14583624C4semidirect
15. #14583623C4semidirect
16. #14583618C4semidirect
19. #14583569C4semidirect
201. C42×C43#41semidirect
244. #10621877#41semidirect
307. Dic86#104semidirect
348. #1962D43semidirect
401. C43#22550semidirect
595. C42#10621900semidirect

Maximal subgroups

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

subgroupindex
#191481922
#191435462
C42×Dic862
#191355152
#191355122
#191354212
#191346132
#191346122
#104×Dic432
C4×#130632532
C43×#19622
#2255043