Finite Group Databasebeta

← #25096802

Subgroups — #25096802

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582856C211yesmaximal, characteristic
2#19137220C211yesmaximal, characteristic
3#19137216C211yesmaximal, characteristic
4#19134729C211yesmaximal, characteristic, complemented
5#19134727C211yesmaximal, characteristic, complemented
6#19134727C211yesmaximal, characteristic, complemented
7#19134725C211yesmaximal, characteristic, complemented
8#19134724C211yesmaximal, characteristic, complemented
9#19134722C211yesmaximal, characteristic, complemented
10#19134721C211yesmaximal, characteristic, complemented
11#19134313C211yesmaximal, characteristic
12#19134313C211yesmaximal, characteristic
13#19134310C211yesmaximal, characteristic
14#340×D43C211yesmaximal, characteristic
15C43×#1836C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582856C418yescomplemented
24C2×#13063235C2211yescharacteristic
25C2×C4×C43⋊C8C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582796—21no—
28#14582796—21no—
29#14582794—21no—
30#14582794—21no—
31#14582773—21no—
32#14582773—21no—
33#14582770—21no—
34#14582770—21no—
35#14582769C2211yescharacteristic
36#14582768C2211yescharacteristic
37#14582768C2211yescharacteristic
38#14582765C2211yescharacteristic
39#14582764C2211yescharacteristic
40#14582764C2211yescharacteristic
41#14582662C2211yescharacteristic
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#97×C43C2211yescharacteristic
54C43×#384C2211yescharacteristic
55C43×#382C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C2×#10621872—22no—
64C2×#10621872—22no—
65C2×#10621872C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C2×C8×D43—22no—
69C2×C8×D43—22no—
70C2×C8×D43C2×C414yes—
71#13063283—22no—
72#13063283—22no—
73#13063283—22no—
74#13063283—22no—
75#13063282C2×C414yes—
76#13063282Q814yes—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
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—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C2×Dic43⋊C4D411yescharacteristic
91C4⋊C4×D43—22no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43—22no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4D411yescharacteristic
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063235C2×C414yescomplemented
103C4×C43⋊C8C2×C414yescomplemented
104C8×Dic43C2×C414yescomplemented
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#97×C43C2×C414yescomplemented
121#95×C43—21no—
122#95×C43—21no—
123C23×D43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×C4×D43—42no—
139C2×C4×D43—42no—
140C2×C4×D43—81no—
141C2×C4×D43—81no—
142C2×C4×D43—81no—
143C2×C4×D43—81no—
144C2×C4×D43C22×C412yes—
145C2×C4×D43C2×Q812yes—
146C2×C4×D43#4112yes—
147C2×C4×D43#4112yes—
148C2×C4×D43#4112yes—
149C2×C4×D43#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43C22×C412yes—
155C2×C8×C43C22×C412yes—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—81no—
165C4⋊C4×C43—81no—
166C42×C43C22×C412yes—
167C42×C43C2×Q812yes—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4C4⋊C414yes—
171(C2×D43)⋊C4C4⋊C414yes—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—81no—
181C4⋊Dic43—81no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—81no—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187Dic43⋊C4—81no—
188Dic43⋊C4C4⋊C414yes—
189Dic43⋊C4C4⋊C414yes—
190C4×Dic43—42no—
191C4×Dic43—42no—
192C4×Dic43C22×C412yes—
193C4×Dic43C2×Q812yes—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C2×C43⋊C8C22×C412yes—
200#10621872—28no—
201C8×D43—28no—
202C23×C43C22×D411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43C2×C4⋊C412yes—
208C22×D43#12412yes—
209C22×D43#12412yes—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
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×C43C2×C4⋊C412yes—
227C2×C4×C43C2×C4⋊C412yes—
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×Q811yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43C2×C4⋊C412yes—
251C2×Dic43C2×C4⋊C412yes—
252C2×Dic43C2×C4⋊C412yes—
253C2×Dic43#12412yes—
254C2×Dic43#12412yes—
255C4×D43—84no—
256C4×D43—84no—
257C4×D43#11714yes—
258C4×D43#11714yes—
259C4×D43#12514yes—
260C4×D43#12514yes—
261C8×C43—22no—
262C8×C43—22no—
263C43⋊C8—22no—
264C43⋊C8—22no—
265#20763—431nomaximal, Sylow
266C22×C43C22×C4⋊C411yescharacteristic
267C22×C43C2×#12411yescharacteristic
268C22×C43C2×#12411yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57811yescharacteristic
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C2×D43#38214yes—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43C2×#11711yescharacteristic
287C4×C43C2×#11711yescharacteristic
288C4×C43C2×#12511yescharacteristic
289C4×C43C2×#12511yescharacteristic
290Dic43—22no—
291Dic43—22no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296Dic43#38214yes—
297C2×#405—431no—
298#2317—431no—
299#2317—431no—
300#1836—431no—
301#1836—431no—
302#1836—431no—
303#1836D4311yescharacteristic, complemented
304#1835—431no—
305#1835—431no—
306#1834—431no—
307#1834—431no—
308#1736—431no—
309#1736—431no—
310#1735—431no—
311C2×#340—431no—
312C2×C43C2×#38211yescharacteristic
313C2×C43#291211yescharacteristic
314C2×C43#291311yescharacteristic
315C2×C43#313611yescharacteristic
316C2×C43#313611yescharacteristic
317C2×C43#313711yescharacteristic
318C2×C43#313711yescharacteristic
319D43—24no—
320C22×M16—431no—
321C23×C8—431no—
322C2×#117—431no—
323C2×#117—431no—
324C2×#117—431no—
325C22×C4⋊C4—431no—
326C22×C4⋊C4—431no—
327#405—438no—
328C2×#97—431no—
329C2×#97C2×D4311yescharacteristic
330C2×C4×C8—431no—
331C2×C4×C8—431no—
332#389—861no—
333#389—861no—
334#389—861no—
335#389—861no—
336#385—861no—
337#385—861no—
338#385—861no—
339#385—861no—
340#384—431no—
341#384—431no—
342#384—431no—
343#384C2×D4311yescharacteristic
344#382—431no—
345#382—431no—
346#382—431no—
347#382C2×D4311yescharacteristic
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340C2×D4311yescharacteristic
361#340C2×D4311yescharacteristic
362#340C2×D4311yescharacteristic
363#340C2×D4311yescharacteristic
364C43#2076311yescharacteristic, complemented, Sylow
365C23×C4—431no—
366C23×C4—861no—
367C23×C4—861no—
368C2×M16—434no—
369C2×M16—862no—
370C2×M16—862no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—434no—
374C22×C8—862no—
375C22×C8—862no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378#117—434no—
379#117—434no—
380#117—862no—
381#117—862no—
382#117—862no—
383#117—862no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—862no—
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⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—431no—
409C2×C22⋊C4—431no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—431no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42C22×D4311yescharacteristic
416#97—434no—
417#97C4×D4314yescomplemented
418C4×C8—434no—
419C4×C8—434no—
420#95—21no—
421#95—21no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428C24—431no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—431no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—3441no—
447C22×C4—3441no—
448C22×C4—3441no—
449C22×C4—3441no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4C23×D4311yescharacteristic
455M16—868no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—432no—
461C2×C8—432no—
462C2×C8—868no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8C2×C4×D4312yes—
468C2×C8C2×C4×D4312yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—434no—
480C4⋊C4—434no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—3441no—
490C4⋊C4—3441no—
491C4⋊C4—3441no—
492C4⋊C4—3441no—
493C4⋊C4—3441no—
494C4⋊C4—3441no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C22⋊C4—434no—
498C22⋊C4—434no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C42—432no—
502C42—432no—
503C42—1722no—
504C42—1722no—
505C42C2×C4×D4312yes—
506C42Q8×D4312yes—
507C23—432no—
508C23—432no—
509C23—432no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—861no—
514C23C2×D4×D4311yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—434no—
535C2×C4—434no—
536C2×C4—434no—
537C2×C4—434no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—3444no—
545C2×C4—3444no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4C4⋊C4×D4312yes—
559C2×C4C4⋊C4×D4312yes—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C2×Q8×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C8—22no—
567C8—22no—
568C8—862no—
569C8—862no—
570C22—434no—
571C22—862no—
572C22—862no—
573C22—862no—
574C22—862no—
575C22—862no—
576C22—862no—
577C22C2×C4⋊C4×D4311yescharacteristic
578C22#124×D4311yescharacteristic
579C22#124×D4311yescharacteristic
580C22#1458370311yescharacteristic
581C22#1458370811yescharacteristic
582C22#1458370911yescharacteristic
583C22#1458371511yescharacteristic
584C4—22no—
585C4—22no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—434no—
591C4—862no—
592C4—862no—
593C4—3441no—
594C4—3441no—
595C4—3441no—
596C4—3441no—
597C4#117×D4311yescharacteristic
598C4#117×D4311yescharacteristic
599C4#125×D4311yescharacteristic
600C4#125×D4311yescharacteristic
601C2—864no—
602C2#382×D4311yescharacteristic
603C2#1914318911yescharacteristic
604C2#1914319411yescharacteristic
605C2#1914494611yescharacteristic
606C2#1914495011yescharacteristic
607C2#1914495711yescharacteristic
608C2#1914496111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1836C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1836D43
hypocenterC43#20763
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #19134729C2semidirect
5. #19134727C2semidirect
6. #19134727C2semidirect
7. #19134725C2semidirect
8. #19134724C2semidirect
9. #19134722C2semidirect
10. #19134721C2semidirect
15. C43×#1836C2semidirect
23. #14582856C4semidirect
102. #13063235C2×C4semidirect
103. C4×C43⋊C8C2×C4semidirect
104. C8×Dic43C2×C4semidirect
120. #97×C43C2×C4semidirect
303. #1836D43semidirect
364. C43#20763semidirect
417. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828562
#191372202
#191372162
#191347292
#191347272
#191347252
#191347242
#191347222
#191347212
#191343132
#191343102
#340×D432
C43×#18362
#2076343