Finite Group Databasebeta

← #25159540

Subgroups — #25159540

Order 11008.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583205C211yesmaximal, characteristic, complemented
2C2×#14582938C211yesmaximal, characteristic
3#19138322C211yesmaximal, characteristic
4#19137624C211yesmaximal, characteristic
5#19136146C211yesmaximal, characteristic, complemented
6#19136092C211yesmaximal, characteristic, complemented
7#19135989C211yesmaximal, characteristic, complemented
8#19135936C211yesmaximal, characteristic, complemented
9#19135173C211yesmaximal, characteristic, complemented
10#19135027C211yesmaximal, characteristic
11#19134901C211yesmaximal, characteristic
12#19134860C211yesmaximal, characteristic, complemented
13#19134791C211yesmaximal, characteristic
14#19134776C211yesmaximal, characteristic
15C43×#1949C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14583205—24no—
23#14582938—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34#14582840—21no—
35#14582833—21no—
36#14582805C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582791—21no—
41#14582790—21no—
42#14582784—21no—
43#14582773—21no—
44#14582758—21no—
45#14582756C2211yescharacteristic
46C4×C4⋊Dic43—21no—
47C4×(C2×D43)⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C2×#10621872—22no—
65C2×#10621872—22no—
66C2×#10621872—22no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063316—22no—
70#13063316—41no—
71#13063305—22no—
72#13063305Q814yes—
73#13063290—22no—
74#13063290—41no—
75#13063283—22no—
76#13063283—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—41no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×(C2×D43)⋊C4D411yescharacteristic
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063259—22no—
99#13063258—22no—
100#13063256—41no—
101#13063256D414yes—
102Dic43⋊C8—22no—
103#13063250—22no—
104#13063250—22no—
105#13063248—22no—
106#13063248—41no—
107(C2×D43)⋊C8—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#107×C43—22no—
125#106×C43—22no—
126C4⋊C8×C43—22no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130C23×D43C2×D411yescharacteristic
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—81no—
152C2×C4×D43C2×Q812yes—
153C2×C4×D43#4112yes—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C2×Q812yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43#4112yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D412yes—
173C4⋊C4×C43C2×Q812yes—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—41no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182C4⋊Dic43—21no—
183C4⋊Dic43—24no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189C4⋊Dic43—42no—
190C4⋊Dic43C2×D412yes—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—81no—
195Dic43⋊C4—81no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—42no—
199C4×Dic43—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D412yes—
206#10621872—28no—
207C23×C43C22×D411yescharacteristic
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43C22⋊Q812yes—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×Q811yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—22no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43C22⋊Q812yes—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—84no—
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—22no—
270C8×C43—41no—
271C43⋊C8—22no—
272C43⋊C8—41no—
273#26367—431nomaximal, Sylow
274C22×C43C2×C22⋊Q811yescharacteristic
275C22×C43D4211yescharacteristic
276C22×C43#54711yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57811yescharacteristic
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43#52511yescharacteristic
295C4×C43#53911yescharacteristic
296C4×C43D4×Q811yescharacteristic
297C4×C43#55411yescharacteristic
298Dic43—22no—
299Dic43—42no—
300Dic43—41no—
301Dic43—42no—
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305C2×#479—431no—
306C2×#428—431no—
307#2442—431no—
308#2362—431no—
309#2097—431no—
310#2087—431no—
311#2068—431no—
312#2059—431no—
313#1949D4311yescharacteristic, complemented
314#1919—431no—
315#1894—431no—
316#1872—431no—
317#1865—431no—
318#1854—431no—
319#1851—431no—
320C2×C43#244911yescharacteristic
321C2×C43#308011yescharacteristic
322C2×C43#308211yescharacteristic
323C2×C43#326911yescharacteristic
324C2×C43#327511yescharacteristic
325C2×C43#334911yescharacteristic
326C2×C43#335111yescharacteristic
327D43—42no—
328C22×M16—431no—
329C2×#125—431no—
330C2×C22⋊Q8—431no—
331C2×C4×Q8—431no—
332C2×#117—431no—
333C22×C4⋊C4—431no—
334#479—864no—
335#428—864no—
336C2×#107—431no—
337C2×#107—431no—
338C2×#107C2×D4311yescharacteristic
339C2×#106—431no—
340C2×#106—431no—
341C2×#106C2×D4311yescharacteristic
342C2×C4⋊C8—431no—
343C2×C4⋊C8C2×D4311yescharacteristic
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×C22⋊C8—431no—
349#400—861no—
350#398—861no—
351#391—431no—
352#389—431no—
353#389—431no—
354#389—431no—
355#388—861no—
356#388—861no—
357#387—861no—
358#385—861no—
359#382C2×D4311yescharacteristic
360#380—431no—
361#380—861no—
362C4×C4⋊C4—861no—
363C4×C4⋊C4C2×D4311yescharacteristic
364C4×C22⋊C4—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340C2×D4311yescharacteristic
370#340C2×D4311yescharacteristic
371#336—431no—
372#336—431no—
373C43#2636711yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C23×C4—431no—
376C23×C4—861no—
377C2×M16—862no—
378C2×M16—862no—
379C2×M16—862no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384#125—862no—
385#125—1721no—
386C22⋊Q8—434no—
387C22⋊Q8—862no—
388C4×Q8—862no—
389C4×Q8—1721no—
390#117—862no—
391#117—1721no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—862no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—1721no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C22⋊C4—431no—
410C2×C22⋊C4—431no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—21no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42C22×D4311yescharacteristic
419#107—22no—
420#107—862no—
421#107—862no—
422#106—22no—
423#106—434no—
424#106—1721no—
425C4⋊C8—22no—
426C4⋊C8—862no—
427#103—862no—
428#103—862no—
429#103—862no—
430#103—1721no—
431C22⋊C8—862no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—431no—
436#95—431no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443C24—431no—
444C2×Q8—432no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—3441no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473M16—868no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—432no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8#1062189812yes—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—432no—
493C4⋊C4—864no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—3441no—
500C4⋊C4—3441no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C4⋊C4D4×D4312yes—
507C4⋊C4Q8×D4312yes—
508C22⋊C4—864no—
509C22⋊C4—1721no—
510C22⋊C4—1721no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—861no—
517C42—861no—
518C42—1722no—
519C42—1722no—
520C23—432no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—861no—
526C23—861no—
527C23C2×D4×D4311yescharacteristic
528Q8—862no—
529Q8—862no—
530Q8—1721no—
531Q8—1721no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—432no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—3444no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C2×Q8×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C2×C4#1306337111yescharacteristic
581C2×C4#1306337311yescharacteristic
582C8—22no—
583C8—41no—
584C8—862no—
585C8—1721no—
586C22—862no—
587C22—862no—
588C22—862no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22C22⋊Q8×D4311yescharacteristic
594C22#1458353311yescharacteristic
595C22#1458355011yescharacteristic
596C22#1458369511yescharacteristic
597C22#1458369611yescharacteristic
598C22#1458370811yescharacteristic
599C22#1458371311yescharacteristic
600C4—41no—
601C4—41no—
602C4—42no—
603C4—42no—
604C4—81no—
605C4—81no—
606C4—862no—
607C4—3441no—
608C4—3441no—
609C4—1722no—
610C4—1721no—
611C4—1721no—
612C4—1722no—
613C4#1458340811yescharacteristic
614C4#1458349711yescharacteristic
615C4#1458356411yescharacteristic
616C4#1458360911yescharacteristic
617C2—1722no—
618C2#1913841111yescharacteristic
619C2#1914441211yescharacteristic
620C2#1914443611yescharacteristic
621C2#1914615611yescharacteristic
622C2#1914622111yescharacteristic
623C2#1914712111yescharacteristic
624C2#1914715111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1949C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1949D43
hypocenterC43#26367
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. C2×#14583205C2semidirect
5. #19136146C2semidirect
6. #19136092C2semidirect
7. #19135989C2semidirect
8. #19135936C2semidirect
9. #19135173C2semidirect
12. #19134860C2semidirect
15. C43×#1949C2semidirect
313. #1949D43semidirect
373. C43#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#145832052
C2×#145829382
#191383222
#191376242
#191361462
#191360922
#191359892
#191359362
#191351732
#191350272
#191349012
#191348602
#191347912
#191347762
C43×#19492
#2636743