Finite Group Databasebeta

← #25196768

Subgroups — #25196768

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140422C211yesmaximal, characteristic
2#19137271C211yesmaximal, characteristic
3#19136165C211yesmaximal, characteristic, complemented
4#19136141C211yesmaximal, characteristic, complemented
5#19135921C211yesmaximal, characteristic, complemented
6#19135734C211yesmaximal, characteristic, complemented
7#19135170C211yesmaximal, characteristic, complemented
8#19135167C211yesmaximal, characteristic, complemented
9#19135025C211yesmaximal, characteristic
10#19135015C211yesmaximal, characteristic
11#19134849C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic
13#19134621C211yesmaximal, characteristic
14#19134290C211yesmaximal, characteristic
15C43×#1863C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26#14582840—21no—
27#14582834—21no—
28#14582819—21no—
29#14582812—21no—
30#14582806C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582794—21no—
34#14582790—21no—
35#14582789—21no—
36#14582783—21no—
37#14582764C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×C4×D43C2311yescharacteristic
61C2×#10621872—22no—
62C2×#10621872—22no—
63C2×#10621872—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43—41no—
69#13063324—41no—
70#13063324—41no—
71#13063301—22no—
72#13063301Q814yescomplemented
73#13063282—41no—
74#13063282—41no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4D411yescharacteristic
84C2×Dic43⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063258—41no—
95#13063256—22no—
96#13063249—22no—
97#13063249—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C4×Q8×C43—41no—
112C4×Q8×C43—41no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#107×C43—41no—
121#103×C43—22no—
122#103×C43—41no—
123#95×C43—21no—
124C23×D43C2×D411yescharacteristic
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43C2×Q812yes—
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×D43C2×Q812yes—
150C2×C4×D43#4112yes—
151C2×Dic86—42no—
152C2×Dic86—81no—
153C2×Dic86—81no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43#4112yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—42no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—41no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×Q812yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188Dic43⋊C4—42no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—81no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8#4112yes—
200#10621872—44no—
201C8×D43—44no—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43C22⋊Q812yes—
210Q8×C43—22no—
211Q8×C43—22no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
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×C43C22×Q811yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—22no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
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×Dic43C22⋊Q812yes—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263Dic86—84no—
264C8×C43—22no—
265C8×C43—41no—
266C43⋊C8—22no—
267C43⋊C8—41no—
268#29171—431nomaximal, Sylow
269C22×C43C2×C22⋊Q811yescharacteristic
270C22×C43#53211yescharacteristic
271C22×C43#53411yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C22×C43#57811yescharacteristic
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43#55111yescharacteristic
290C4×C43#55111yescharacteristic
291C4×C43#55411yescharacteristic
292C4×C43#55411yescharacteristic
293Dic43—22no—
294Dic43—42no—
295Dic43—41no—
296Dic43—41no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300#2628—431no—
301#2323—431no—
302#2101—431no—
303#2097—431no—
304#2057—431no—
305#2024—431no—
306#1919—431no—
307#1918—431no—
308#1894—431no—
309#1892—431no—
310#1863—431no—
311#1863D4311yescharacteristic, complemented
312#1809—431no—
313#1808—431no—
314#1729—431no—
315C2×C43#256411yescharacteristic
316C2×C43#308211yescharacteristic
317C2×C43#308311yescharacteristic
318C2×C43#317511yescharacteristic
319C2×C43#317811yescharacteristic
320C2×C43#319811yescharacteristic
321C2×C43#320211yescharacteristic
322D43—42no—
323C22×M16—431no—
324C23×C8—431no—
325C2×C4⋊Q8—431no—
326C2×C22⋊Q8—431no—
327C2×C4×Q8C2×D4311yescharacteristic
328C2×#117—431no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#107C2×D4311yescharacteristic
332C2×#106—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103C2×D4311yescharacteristic
336C2×#103C2×D4311yescharacteristic
337#400—861no—
338#399—861no—
339#395—861no—
340#393—861no—
341#391—431no—
342#389—431no—
343#389—431no—
344#389—861no—
345#389C2×D4311yescharacteristic
346#388—861no—
347#388—861no—
348#387—861no—
349#382—431no—
350#380—431no—
351#380—431no—
352#380—431no—
353C4×C4⋊C4—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340C2×D4311yescharacteristic
362#336—431no—
363#336—431no—
364#336—431no—
365#336C2×D4311yescharacteristic
366C43#2917111yescharacteristic, complemented, Sylow
367C22×Q8—861no—
368C22×Q8C22×D4311yescharacteristic
369C23×C4—431no—
370C2×M16—862no—
371C2×M16—862no—
372C2×M16—1721no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—862no—
376C22×C8—862no—
377C22×C8—1721no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C4⋊Q8—1721no—
381C4⋊Q8—1721no—
382C22⋊Q8—434no—
383C22⋊Q8—862no—
384C4×Q8—41no—
385C4×Q8—41no—
386#117—1721no—
387#117—1721no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—431no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—21no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#107—41no—
414#107—862no—
415#107—1721no—
416#106—862no—
417#103—22no—
418#103—41no—
419#103—862no—
420#103—1721no—
421#95—21no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432C24—431no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—3441no—
439C2×Q8—3441no—
440C2×Q8—1722no—
441C2×Q8Q8×D4312yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4C23×D4311yescharacteristic
462M16—1724no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—1724no—
475C2×C8#1062189812yes—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—42no—
483C4⋊C4—81no—
484C4⋊C4—432no—
485C4⋊C4—864no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—1721no—
496C4⋊C4—1721no—
497C4⋊C4—1722no—
498C22⋊C4—864no—
499C22⋊C4—3441no—
500C22⋊C4—3441no—
501C22⋊C4—3441no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—861no—
508C42—861no—
509C42—3441no—
510C23—432no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23C2×D4×D4311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—3444no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—432no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4C2×Q8×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4C2×#1062189811yescharacteristic
570C2×C4#1306337011yescharacteristic
571C2×C4#1306337011yescharacteristic
572C8—22no—
573C8—41no—
574C8—862no—
575C8—1721no—
576C22—862no—
577C22—862no—
578C22—862no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22—1721no—
583C22C22⋊Q8×D4311yescharacteristic
584C22#1458344611yescharacteristic
585C22#1458345911yescharacteristic
586C22#1458370111yescharacteristic
587C22#1458370911yescharacteristic
588C22#1458371211yescharacteristic
589C22#1458371511yescharacteristic
590C4—41no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—862no—
597C4—3441no—
598C4—3441no—
599C4—3441no—
600C4—1722no—
601C4—1721no—
602C4—1721no—
603C4#1458357711yescharacteristic
604C4#1458357811yescharacteristic
605C4#1458360311yescharacteristic
606C4#1458360411yescharacteristic
607C2—1722no—
608C2#1913978011yescharacteristic
609C2#1914443211yescharacteristic
610C2#1914444911yescharacteristic
611C2#1914523611yescharacteristic
612C2#1914526111yescharacteristic
613C2#1914544411yescharacteristic
614C2#1914548811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1863C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1863D43
hypocenterC43#29171
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
3. #19136165C2semidirect
4. #19136141C2semidirect
5. #19135921C2semidirect
6. #19135734C2semidirect
7. #19135170C2semidirect
8. #19135167C2semidirect
11. #19134849C2semidirect
15. C43×#1863C2semidirect
72. #13063301Q8semidirect
311. #1863D43semidirect
366. C43#29171semidirect

Maximal subgroups

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

subgroupindex
#191404222
#191372712
#191361652
#191361412
#191359212
#191357342
#191351702
#191351672
#191350252
#191350152
#191348492
#191346272
#191346212
#191342902
C43×#18632
#2917143