Finite Group Databasebeta

← #25099716

Subgroups — #25099716

Order 11008.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583001C211yesmaximal, characteristic
2#19137233C211yesmaximal, characteristic
3#19136959C211yesmaximal, characteristic, complemented
4#19135221C211yesmaximal, characteristic
5#19135214C211yesmaximal, characteristic
6#19135186C211yesmaximal, characteristic, complemented
7#19135165C211yesmaximal, characteristic, complemented
8#19134951C211yesmaximal, characteristic
9#19134951C211yesmaximal, characteristic
10#19134860C211yesmaximal, characteristic, complemented
11#19134846C211yesmaximal, characteristic, complemented
12C4×#13063248C211yesmaximal, characteristic, complemented
13C4×#13063245C211yesmaximal, characteristic
14#19134348C211yesmaximal, characteristic, complemented
15C43×#1776C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583001C418yescomplemented
22C2×#13063259C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582800C2211yescharacteristic
31#14582800C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582790—21no—
35#14582790—21no—
36#14582761—21no—
37#14582758—21no—
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×Dic43⋊C4—21no—
41C4×Dic43⋊C4—21no—
42#14582750—21no—
43#14582745C2211yescharacteristic
44#14582744—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621873—22no—
64C2×#10621873—22no—
65C2×#10621873C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C4×Dic86—22no—
69C4×Dic86C2×C414yes—
70#13063290—22no—
71#13063290—22no—
72#13063290—22no—
73#13063290—22no—
74C4×D172—22no—
75C4×D172C2×C414yes—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063259C2×C414yes—
96#13063250C2×C414yes—
97#13063248—22no—
98#13063248—22no—
99#13063247C2×C414yes—
100#13063245—22no—
101#13063245—22no—
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#107×C43—22no—
121#106×C43—22no—
122#97×C43C2×C414yes—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172C22×C412yes—
146C2×C4×D43—24no—
147C2×C4×D43—81no—
148C2×C4×D43—81no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86C22×C412yes—
153C2×Dic86#4112yes—
154C2×Dic86#4112yes—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C22×C412yes—
160C2×C8×C43C22×C412yes—
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#4112yes—
168C4⋊C4×C43#4112yes—
169C42×C43—81no—
170C42×C43—81no—
171C42×C43C22×C412yes—
172C42×C43#4112yes—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43C22×C412yes—
181C4⋊Dic43C22×C412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—24no—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187C4×Dic43—24no—
188C4×Dic43—24no—
189C4×Dic43—24no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—81no—
195C4×Dic43—81no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202#10621873—28no—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
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×C43C4×D412yes—
228C2×C4×C43C4×D412yes—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256D172—22no—
257D172—22no—
258D172—41no—
259D172—41no—
260C4×D43—84no—
261Dic86—22no—
262Dic86—22no—
263Dic86—22no—
264Dic86#11714yes—
265C8×C43—22no—
266C8×C43—22no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#21128—431nomaximal, Sylow
270C22×C43C2×C4×D411yescharacteristic
271C22×C43#52511yescharacteristic
272C22×C43#52511yescharacteristic
273C22×C43#57611yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57711yescharacteristic
276C22×C43#57811yescharacteristic
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—42no—
287C4×C43—42no—
288C4×C43—81no—
289C4×C43—81no—
290C4×C43C2×#11711yescharacteristic
291C4×C43C4×#4111yescharacteristic
292C4×C43#52911yescharacteristic
293C4×C43#52911yescharacteristic
294Dic43—24no—
295Dic43—41no—
296Dic43—41no—
297Dic43—41no—
298Dic43—41no—
299Dic43—42no—
300Dic43—42no—
301C2×#440—431no—
302#2319—431no—
303#2276—431no—
304#1926—431no—
305#1925—431no—
306#1921—431no—
307#1918—431no—
308#1880—431no—
309#1880—431no—
310#1865—431no—
311#1863—431no—
312#1776D4311yescharacteristic, complemented
313C4×#103—431no—
314C4×#102—431no—
315#1746—431no—
316C2×C43#229011yescharacteristic
317C2×C43#294611yescharacteristic
318C2×C43#294711yescharacteristic
319C2×C43#311911yescharacteristic
320C2×C43#312111yescharacteristic
321C2×C43#312411yescharacteristic
322C2×C43#312611yescharacteristic
323D43—82no—
324C22×SD16—431no—
325C2×C4×Q8—431no—
326C2×C4×Q8—431no—
327C2×C4×Q8—431no—
328C2×C4×D4—431no—
329#440—438no—
330C2×#107—431no—
331C2×#107C2×D4311yescharacteristic
332C2×#106C2×D4311yescharacteristic
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#97C2×D4311yescharacteristic
340C2×C4×C8—431no—
341#390—431no—
342#390—431no—
343#389—431no—
344#389—431no—
345#388—861no—
346#388—861no—
347#381—861no—
348#380—861no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—431no—
351C4×C4⋊C4—861no—
352C4×C4⋊C4—861no—
353C4×C4⋊C4—861no—
354C4×C4⋊C4C2×D4311yescharacteristic
355C4×C4⋊C4C2×D4311yescharacteristic
356#376—431no—
357#376—861no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340C2×D4311yescharacteristic
363#340C2×D4311yescharacteristic
364#336—431no—
365#336—431no—
366#336—431no—
367#336—431no—
368C43#2112811yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×D4—431no—
371C23×C4—861no—
372C2×SD16—434no—
373C2×SD16—862no—
374C2×SD16—862no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8C22×D4311yescharacteristic
378C22×C8C22×D4311yescharacteristic
379C4×Q8—434no—
380C4×Q8—862no—
381C4×Q8—862no—
382C4×Q8—862no—
383C4×Q8—862no—
384C4×Q8—862no—
385C4×D4—434no—
386C4×D4—862no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4C22×D4311yescharacteristic
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×C22⋊C4—861no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—861no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#107—22no—
414#107—434no—
415#106—22no—
416#103—434no—
417#103—862no—
418#103—862no—
419#102—434no—
420#102—862no—
421#102—862no—
422#97C4×D4314yes—
423C4×C8—862no—
424#95—21no—
425#95—21no—
426#95—431no—
427#95—431no—
428#95—431no—
429#95—431no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434C24—861no—
435C2×Q8—432no—
436C2×Q8—432no—
437C2×Q8—432no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×D4—432no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—864no—
459C22×C4—3441no—
460C22×C4—3441no—
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4C23×D4311yescharacteristic
464SD16—868no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8C2×C4×D4312yes—
476C2×C8C2×C4×D4312yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—432no—
484C4⋊C4—432no—
485C4⋊C4—864no—
486C4⋊C4—864no—
487C4⋊C4—864no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—3441no—
491C4⋊C4—3441no—
492C4⋊C4#1062189812yes—
493C4⋊C4#1062189812yes—
494C22⋊C4—864no—
495C22⋊C4—3441no—
496C22⋊C4—3441no—
497C22⋊C4—3441no—
498C22⋊C4—3441no—
499C42—81no—
500C42—81no—
501C42—864no—
502C42—864no—
503C42—864no—
504C42—861no—
505C42—861no—
506C42—861no—
507C42—861no—
508C42—3441no—
509C42—3441no—
510C42C2×C4×D4312yes—
511C42#1062190212yes—
512C23—862no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23—1721no—
519C23C2×D4×D4311yescharacteristic
520Q8—434no—
521Q8—862no—
522Q8—862no—
523Q8—862no—
524D4—862no—
525D4—862no—
526D4—1721no—
527D4—1721no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
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—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—3444no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4#1306328712yes—
567C2×C4#1306328712yes—
568C2×C4C22×C4×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C2×C4#41×D4311yescharacteristic
571C2×C4C2×#1062189811yescharacteristic
572C2×C4C2×#1062189811yescharacteristic
573C2×C4C2×#1062190211yescharacteristic
574C8—22no—
575C8—22no—
576C8—1721no—
577C8—1721no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—1722no—
583C22—1722no—
584C22—1722no—
585C22C2×#1306328711yescharacteristic
586C22#1458340811yescharacteristic
587C22#1458340811yescharacteristic
588C22#1458370311yescharacteristic
589C22#1458370811yescharacteristic
590C22#1458370911yescharacteristic
591C22#1458371511yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—864no—
599C4—1722no—
600C4—1722no—
601C4—1721no—
602C4—1721no—
603C4—1721no—
604C4—1721no—
605C4#117×D4311yescharacteristic
606C4C4×#1062189811yescharacteristic
607C4#1458343611yescharacteristic
608C4#1458343611yescharacteristic
609C2—3442no—
610C2#1913703611yescharacteristic
611C2#1914342511yescharacteristic
612C2#1914343611yescharacteristic
613C2#1914479811yescharacteristic
614C2#1914482811yescharacteristic
615C2#1914486111yescharacteristic
616C2#1914488511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1776C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1776D43
hypocenterC43#21128
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
3. #19136959C2semidirect
6. #19135186C2semidirect
7. #19135165C2semidirect
10. #19134860C2semidirect
11. #19134846C2semidirect
12. C4×#13063248C2semidirect
14. #19134348C2semidirect
15. C43×#1776C2semidirect
21. #14583001C4semidirect
312. #1776D43semidirect
368. C43#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#145830012
#191372332
#191369592
#191352212
#191352142
#191351862
#191351652
#191349512
#191348602
#191348462
C4×#130632482
C4×#130632452
#191343482
C43×#17762
#2112843