Finite Group Databasebeta

← #25140961

Subgroups — #25140961

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138912C211yesmaximal, characteristic
2#19136152C211yesmaximal, characteristic, complemented
3#19136072C211yesmaximal, characteristic, complemented
4#19136031C211yesmaximal, characteristic, complemented
5#19136031C211yesmaximal, characteristic, complemented
6#19135180C211yesmaximal, characteristic, complemented
7#19135180C211yesmaximal, characteristic, complemented
8#19134888C211yesmaximal, characteristic
9#19134788C211yesmaximal, characteristic, complemented
10#19134788C211yesmaximal, characteristic, complemented
11#19134683C211yesmaximal, characteristic, complemented
12#19134681C211yesmaximal, characteristic, complemented
13#19134618C211yesmaximal, characteristic, complemented
14C2×#14582661C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C43C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582838—21no—
26#14582835—21no—
27#14582797C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582779—21no—
30#14582771—21no—
31#14582759C2211yescharacteristic
32#14582759C2211yescharacteristic
33#14582759C2211yescharacteristic
34#14582661C2211yescharacteristic
35#14582661C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4×D4×C43—21no—
49C2×C4×D4×C43C2211yescharacteristic
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C43×#389—21no—
53C43×#385—21no—
54C43×#385—21no—
55C43×#384C2211yescharacteristic
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—22no—
62C22×C43⋊C8—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79#13063256—22no—
80#13063256—22no—
81#13063256—41no—
82#13063256—41no—
83C22⋊(C43⋊C8)—22no—
84C22⋊(C43⋊C8)—22no—
85C22⋊(C43⋊C8)—41no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×D4×C43D411yescharacteristic
92C23×C4×C43—21no—
93C23×C4×C43—21no—
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2311yescharacteristic
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43—44no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—41no—
106C2×C4⋊C4×C43—41no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43D411yescharacteristic
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121C24×C43C2×D411yescharacteristic
122C24×C43C2×D411yescharacteristic
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43SD1614yes—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—42no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4112yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—81no—
159C22×Dic43—81no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—42no—
180C22⋊Dic43—42no—
181C22⋊Dic43—81no—
182C22⋊Dic43—81no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—42no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—44no—
206C2×C43⋊C8#4112yes—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43#12312yes—
218C23×C43C2×SD1612yes—
219C23×C43C2×SD1612yes—
220C23×C43#13712yes—
221C23×C43C22×D411yescharacteristic
222D4×C43—28no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—84no—
254C2×C4×C43—84no—
255C2×C4×C43#12312yes—
256C2×C4×C43C2×SD1612yes—
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×C4×C432−1+411yescharacteristic
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—84no—
276C43⋊C8—22no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#24935—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43#48314yes—
295C22×C43C2×#12311yescharacteristic
296C22×C43#54611yescharacteristic
297C22×C43#54711yescharacteristic
298C22×C43C22×SD1611yescharacteristic
299C22×C43C2×#13711yescharacteristic
300C22×C43#57611yescharacteristic
301C22×C43#57711yescharacteristic
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—42no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43#52911yescharacteristic
311C4×C43#53911yescharacteristic
312C4×C43#55111yescharacteristic
313C4×C43#55211yescharacteristic
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318#2487—431no—
319D4×C4⋊C4D4311yescharacteristic
320#2099—431no—
321#2084—431no—
322#2077—431no—
323#2077—431no—
324#1920—431no—
325#1920—431no—
326#1869—431no—
327#1853—431no—
328#1853—431no—
329#1824—431no—
330#1823—431no—
331#1807—431no—
332C2×#340—431no—
333C2×C43—24no—
334C2×C43—42no—
335C2×C43#241911yescharacteristic
336C2×C43C2×#48311yescharacteristic
337C2×C43#309611yescharacteristic
338C2×C43#329511yescharacteristic
339C2×C43#332011yescharacteristic
340C2×C43#333511yescharacteristic
341C2×C43#334611yescharacteristic
342C23×C8—431no—
343C2×C4×D4—21no—
344C2×C4×D4C2×D4311yescharacteristic
345C22×C4⋊C4—431no—
346C22×C4⋊C4C2×D4311yescharacteristic
347C22×C4⋊C4C2×D4311yescharacteristic
348C2×#106—431no—
349C2×#106—431no—
350C2×#106—431no—
351C2×#106—431no—
352C2×C22⋊C8—431no—
353C2×C22⋊C8—431no—
354C2×C22⋊C8—431no—
355#400—861no—
356#399—861no—
357#389—21no—
358#389—431no—
359#389—431no—
360#386—861no—
361#385—21no—
362#385—21no—
363#385—861no—
364#384C2×D4311yescharacteristic
365#380—431no—
366#380—431no—
367#380—431no—
368#380C2×D4311yescharacteristic
369#380C2×D4311yescharacteristic
370C4×C4⋊C4C2×D4311yescharacteristic
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#336—431no—
384#336—431no—
385C43#2493511yescharacteristic, complemented, Sylow
386C22×D4C22⋊D4311yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—861no—
390C23×C4C22×D4311yescharacteristic
391C23×C4C22×D4311yescharacteristic
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8—431no—
396C22×C8—862no—
397C22×C8—862no—
398C22×C8—1721no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—44no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—862no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22⋊D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4C22⋊D4311yescharacteristic
430C2×C22⋊C4C22⋊D4311yescharacteristic
431C2×C42—21no—
432C2×C42C22×D4311yescharacteristic
433#106—862no—
434#106—862no—
435#106—1721no—
436#106—1721no—
437C22⋊C8—862no—
438C22⋊C8—862no—
439C22⋊C8—1721no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448C24C2×C22⋊D4311yescharacteristic
449C24C2×C22⋊D4311yescharacteristic
450C2×D4—22no—
451C2×D4—22no—
452C2×D4#1062188314yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—3441no—
478C22×C4—3441no—
479C22×C4—1722no—
480C22×C4#1062189812yes—
481C22×C4#1062189812yes—
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C22×C4C2×C22⋊D4311yescharacteristic
486C22×C4C23×D4311yescharacteristic
487C2×C8—432no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—1724no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—81no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1722no—
523C4⋊C4#1062190012yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C22⋊C4—1722no—
531C42—21no—
532C42—21no—
533C42—42no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23#1306330812yes—
545C23C2×#1062188312yes—
546C23C2×#1062188312yes—
547C23#1306335612yes—
548C23C22×C22⋊D4311yescharacteristic
549D4—28no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—84no—
582C2×C4—3444no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4#1306330812yes—
596C2×C4C2×#1062188312yes—
597C2×C4#41×D4311yescharacteristic
598C2×C4C2×#1062190011yescharacteristic
599C2×C4C2×#1062189811yescharacteristic
600C2×C4C2×#1062189811yescharacteristic
601C2×C4#1306337011yescharacteristic
602C2×C4#1306337211yescharacteristic
603C8—862no—
604C8—1721no—
605C8—1721no—
606C8—1721no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22#1458322914yes—
621C22C2×#1306330811yescharacteristic
622C22#1458354311yescharacteristic
623C22#1458354811yescharacteristic
624C22C22×#1062188311yescharacteristic
625C22C2×#1306335611yescharacteristic
626C22#1458370211yescharacteristic
627C22#1458370711yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—3441no—
637C4—3441no—
638C4—3441no—
639C4—3441no—
640C4#1458342911yescharacteristic
641C4#1458349111yescharacteristic
642C4#1458357811yescharacteristic
643C4#1458358911yescharacteristic
644C2—24no—
645C2—42no—
646C2#1913806611yescharacteristic
647C2C2×#1458322911yescharacteristic
648C2#1914455311yescharacteristic
649C2#1914641911yescharacteristic
650C2#1914676611yescharacteristic
651C2#1914695211yescharacteristic
652C2#1914707411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterD4×C4⋊C4D43
hypocenterC43#24935
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #19136152C2semidirect
3. #19136072C2semidirect
4. #19136031C2semidirect
5. #19136031C2semidirect
6. #19135180C2semidirect
7. #19135180C2semidirect
9. #19134788C2semidirect
10. #19134788C2semidirect
11. #19134683C2semidirect
12. #19134681C2semidirect
13. #19134618C2semidirect
14. C2×#14582661C2semidirect
385. C43#24935semidirect

Maximal subgroups

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

subgroupindex
#191389122
#191361522
#191360722
#191360312
#191351802
#191348882
#191347882
#191346832
#191346812
#191346182
C2×#145826612
D4×C4⋊C4×C432
#2493543