Finite Group Databasebeta

← #25103772

Subgroups — #25103772

Order 11008.

888 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583239C211yesmaximal, characteristic
2#19137133C211yesmaximal, characteristic
3C4×#13063283C211yesmaximal, characteristic
4#19135226C211yesmaximal, characteristic, complemented
5#19135173C211yesmaximal, characteristic, complemented
6#19135167C211yesmaximal, characteristic, complemented
7#19134904C211yesmaximal, characteristic
8#19134791C211yesmaximal, characteristic
9#19134689C211yesmaximal, characteristic
10#107×Dic43C211yesmaximal, characteristic, complemented
11#19134483C211yesmaximal, characteristic, complemented
12#103×Dic43C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic
15C43×#1928C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×C42×D43C2211yescharacteristic
21#14583239C418yescomplemented
22C2×#13063259C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582786—21no—
33#14582773—21no—
34#14582756C2211yescharacteristic
35C4⋊C4×Dic43C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4×C4⋊Dic43C2211yescharacteristic
39#14582750—21no—
40C4×(C2×D43)⋊C4—21no—
41#14582746—21no—
42#14582746—21no—
43#14582744—21no—
44C42×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063301—22no—
66#13063301C2×C414yes—
67Q8×Dic43—22no—
68Q8×Dic43—22no—
69#13063283—22no—
70#13063283—22no—
71#13063283—22no—
72#13063283C2×C414yes—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C42×D43—22no—
95C42×D43—22no—
96#13063259C2×C414yescomplemented
97#13063256—22no—
98#13063256C2×C414yescomplemented
99#13063249—22no—
100#13063249C2×C414yescomplemented
101(C2×D43)⋊C8—22no—
102(C2×D43)⋊C8C2×C414yes—
103C8×Dic43—22no—
104C8×Dic43—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×Q8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#107×C43—22no—
120#103×C43—22no—
121#103×C43C2×C414yescomplemented
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43C2×D411yescharacteristic
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—41no—
156C2×C4×D43C22×C412yes—
157C2×C4×D43#4112yes—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C412yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C412yes—
169C4⋊C4×C43#4112yes—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—42no—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—42no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43C22×C412yes—
184C4⋊Dic43C22×C412yes—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—42no—
188C4×Dic43—24no—
189C4×Dic43—24no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43#4112yes—
198C4×Dic43#4112yes—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C22×C412yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43C4×D412yes—
213Q8×C43—22no—
214Q8×C43—22no—
215Q8×C43—41no—
216Q8×C43—41no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
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×C43—41no—
234C2×C4×C43#13512yes—
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
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×Dic43C4×D412yes—
258C2×Dic43#12312yes—
259C2×Dic43#12312yes—
260C2×Dic43#13512yes—
261C2×Dic43#13712yes—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—44no—
267C4×D43—44no—
268C8×C43—22no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272C4×#485—431nomaximal, Sylow
273C22×C43C2×C4×D411yescharacteristic
274C22×C43C2×#12311yescharacteristic
275C22×C43#52511yescharacteristic
276C22×C43C2×#13511yescharacteristic
277C22×C43C2×#13511yescharacteristic
278C22×C43C2×#13711yescharacteristic
279C22×C43#57511yescharacteristic
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C4×C43—22no—
288C4×C43—41no—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43C4×#4111yescharacteristic
294C4×C43C4×#4111yescharacteristic
295C4×C43#52911yescharacteristic
296C4×C43#52911yescharacteristic
297Dic43—22no—
298Dic43—22no—
299Dic43—42no—
300Dic43—42no—
301Dic43—42no—
302Dic43—81no—
303Dic43#48514yescomplemented
304C2×#485—431no—
305C4×C22⋊Q8—431no—
306C4×#117—431no—
307#1928D4311yescharacteristic, complemented
308#1927—431no—
309#1919—431no—
310#1918—431no—
311#1873—431no—
312#1854—431no—
313#1825—431no—
314C4×#107—431no—
315C4×#106—431no—
316C4×#103—431no—
317C4×#103—431no—
318C4×C22⋊C8—431no—
319C2×C43C4×#12311yescharacteristic
320C2×C43C4×#13511yescharacteristic
321C2×C43C4×#13711yescharacteristic
322C2×C43C2×#48511yescharacteristic
323C2×C43#309111yescharacteristic
324C2×C43#310211yescharacteristic
325C2×C43#310711yescharacteristic
326D43—42no—
327C2×C22⋊Q8—431no—
328C2×C4×Q8—431no—
329C2×#117—431no—
330C2×#117—431no—
331C22×C42—431no—
332#485—438no—
333C2×#107—431no—
334C2×#107C2×D4311yescharacteristic
335C2×#106—431no—
336C2×#106—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103C2×D4311yescharacteristic
340C2×#103C2×D4311yescharacteristic
341C2×C22⋊C8—431no—
342C2×C22⋊C8—431no—
343C2×C4×C8—431no—
344C2×C4×C8—431no—
345#391C2×D4311yescharacteristic
346#389—431no—
347#387—861no—
348#385—861no—
349#380—431no—
350C4×C4⋊C4—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—861no—
355C4×C4⋊C4C2×D4311yescharacteristic
356C4×C22⋊C4—861no—
357C4×C22⋊C4—861no—
358C4×C22⋊C4—861no—
359#376—861no—
360C43—861no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336C2×D4311yescharacteristic
371C43C4×#48511yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C22⋊Q8—434no—
381C22⋊Q8—862no—
382C4×Q8—862no—
383C4×Q8—862no—
384#117—434no—
385#117—862no—
386#117—862no—
387#117—862no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—21no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—431no—
406C2×C42—862no—
407C2×C42—862no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42C22×D4311yescharacteristic
416#107—22no—
417#107—434no—
418#106—434no—
419#106—862no—
420#103—22no—
421#103—434no—
422#103—862no—
423#103C4×D4314yescomplemented
424C22⋊C8—434no—
425C22⋊C8—862no—
426C4×C8—862no—
427C4×C8—862no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437C24—431no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8C2×C4×D4312yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—862no—
465C22×C4—861no—
466C22×C4—1721no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8C2×C4×D4312yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—432no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C4⋊C4—864no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C4⋊C4C2×C4×D4312yes—
498C4⋊C4#1062190012yes—
499C22⋊C4—864no—
500C22⋊C4—864no—
501C22⋊C4—864no—
502C22⋊C4—1722no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—432no—
507C42—432no—
508C42—862no—
509C42—862no—
510C42—864no—
511C42—864no—
512C42—1722no—
513C42—1722no—
514C42—1722no—
515C42—1722no—
516C42—1722no—
517C23—432no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23C2×D4×D4311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—1724no—
563C2×C4—1724no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4#1306334812yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C8—22no—
581C8—41no—
582C8—862no—
583C8—1721no—
584C22—862no—
585C22—862no—
586C22—862no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22C4×D4×D4311yescharacteristic
592C22#123×D4311yescharacteristic
593C22#1458340911yescharacteristic
594C22#135×D4311yescharacteristic
595C22C2×#1306334811yescharacteristic
596C22#137×D4311yescharacteristic
597C22#1458369511yescharacteristic
598C4—22no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—81no—
604C4—434no—
605C4—862no—
606C4—862no—
607C4—3441no—
608C4—1722no—
609C4—1722no—
610C4—1722no—
611C4C4×#1062190011yescharacteristic
612C4#1458336711yescharacteristic
613C4#1458342811yescharacteristic
614C4#1458343211yescharacteristic
615C2—1722no—
616C2#1913712211yescharacteristic
617C2C4×#1306334811yescharacteristic
618C2#1914341711yescharacteristic
619C2#485×D4311yescharacteristic
620C2#1914451111yescharacteristic
621C2#1914461011yescharacteristic
622C2#1914466511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1928C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1928D43
hypocenterC43C4×#485
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1928

Complements

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

NH ≅ G/Ntype
4. #19135226C2semidirect
5. #19135173C2semidirect
6. #19135167C2semidirect
10. #107×Dic43C2semidirect
11. #19134483C2semidirect
12. #103×Dic43C2semidirect
13. #103×Dic43C2semidirect
15. C43×#1928C2semidirect
21. #14583239C4semidirect
96. #13063259C2×C4semidirect
98. #13063256C2×C4semidirect
100. #13063249C2×C4semidirect
121. #103×C43C2×C4semidirect
303. Dic43#485semidirect
307. #1928D43semidirect
371. C43C4×#485semidirect
423. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832392
#191371332
C4×#130632832
#191352262
#191351732
#191351672
#191349042
#191347912
#191346892
#107×Dic432
#191344832
#103×Dic432
#191343522
C43×#19282
C4×#48543