Finite Group Databasebeta

← #25101484

Subgroups — #25101484

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582954C211yesmaximal, characteristic
2#19136999C211yesmaximal, characteristic
3C4×C4⋊C4×D43C211yesmaximal, characteristic
4#19135357C211yesmaximal, characteristic, complemented
5#19135355C211yesmaximal, characteristic, complemented
6#19135352C211yesmaximal, characteristic, complemented
7#19135350C211yesmaximal, characteristic, complemented
8#19134789C211yesmaximal, characteristic
9#19134786C211yesmaximal, characteristic
10#19134784C211yesmaximal, characteristic
11#19134781C211yesmaximal, characteristic
12#19134493C211yesmaximal, characteristic, complemented
13#19134493C211yesmaximal, characteristic, complemented
14#19134492C211yesmaximal, characteristic, complemented
15C43×#1776C211yesmaximal, characteristic, complemented
16C2×#13063282—21no—
17C2×C4⋊C4×D43C2211yescharacteristic
18C2×C4⋊C4×D43C2211yescharacteristic
19C2×C42×D43—21no—
20C2×C42×D43C2211yescharacteristic
21#14582954C418yescomplemented
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×Dic43⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33#14582768C2211yescharacteristic
34#14582768C2211yescharacteristic
35#14582763—21no—
36#14582758—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×Dic43⋊C4—21no—
42C4×Dic43⋊C4—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582750—21no—
46#95×D43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063282—44no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C4⋊C4×D43—22no—
79C4⋊C4×D43—22no—
80C4⋊C4×D43—22no—
81C4⋊C4×D43—22no—
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×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91C42×D43—44no—
92C42×D43C2×C414yes—
93C42×D43Q814yes—
94#13063259—22no—
95#13063258—22no—
96#13063258—22no—
97#13063257—22no—
98#13063256—22no—
99#13063256—22no—
100Dic43⋊C8C2×C414yescomplemented
101Dic43⋊C8C2×C414yescomplemented
102(C2×D43)⋊C8C2×C414yes—
103(C2×D43)⋊C8C2×C414yes—
104#13063236C2×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×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×C414yescomplemented
123#95×C43—21no—
124#95×C43—21no—
125C23×D43C2×D411yescharacteristic
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×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—24no—
147C2×C4×D43—24no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43C4⋊C414yes—
155C2×C4×D43C4⋊C414yes—
156C2×C4×D43C22×C412yes—
157C2×C4×D43C2×Q812yes—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C412yes—
163C2×C8×C43C22×C412yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43#4112yes—
171C4⋊C4×C43#4112yes—
172C42×C43—42no—
173C42×C43—42no—
174C42×C43C22×C412yes—
175C42×C43C2×Q812yes—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43#4112yes—
185C4⋊Dic43#4112yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—24no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43C4⋊C414yes—
197C4×Dic43C4⋊C414yes—
198C4×Dic43C22×C412yes—
199C4×Dic43C2×Q812yes—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C22×C412yes—
205C2×C43⋊C8C22×C412yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43C2×C4⋊C412yes—
212C22×D43AGL(1,ℤ/8)12yes—
213C22×D43#13712yes—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
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×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C2×C4⋊C412yes—
231C2×C4×C43C2×C4⋊C412yes—
232C2×C4×C43C23×C411yescharacteristic
233C2×C4×C43C22×Q811yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43C2×C4⋊C412yes—
255C2×Dic43C2×C4⋊C412yes—
256C2×Dic43C2×C4⋊C412yes—
257C2×Dic43AGL(1,ℤ/8)12yes—
258C2×Dic43#13712yes—
259C4×D43—28no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—28no—
265C4×D43—48no—
266C4×D43—48no—
267C8×C43—22no—
268C8×C43—22no—
269C43⋊C8—22no—
270C43⋊C8—22no—
271#21365—431nomaximal, Sylow
272C22×C43C22×C4⋊C411yescharacteristic
273C22×C43#52511yescharacteristic
274C22×C43#52511yescharacteristic
275C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C22×C43C2×#13711yescharacteristic
279C2×D43—22no—
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43#42814yes—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43—81no—
292C4×C43C4×#4111yescharacteristic
293C4×C43C4×#4111yescharacteristic
294C4×C43#53311yescharacteristic
295C4×C43#53311yescharacteristic
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—42no—
300Dic43—81no—
301Dic43—81no—
302Dic43#42814yes—
303C2×#432—431no—
304#2285—431no—
305C2×C4×C4⋊C4—431no—
306#1948—431no—
307#1948—431no—
308#1947—431no—
309#1947—431no—
310#1853—431no—
311#1853—431no—
312#1852—431no—
313#1852—431no—
314#1776—431no—
315#1776—431no—
316#1776—431no—
317#1776D4311yescharacteristic, complemented
318C2×C43#229611yescharacteristic
319C2×C43C2×#42811yescharacteristic
320C2×C43C2×#42811yescharacteristic
321C2×C43#310911yescharacteristic
322C2×C43#311011yescharacteristic
323C2×C43#311211yescharacteristic
324C2×C43#311311yescharacteristic
325D43—24no—
326C2×#117—861no—
327C22×C4⋊C4—431no—
328C22×C4⋊C4—431no—
329C22×C42—431no—
330C22×C42—861no—
331#432—438no—
332C2×#107—431no—
333C2×#107—431no—
334C2×#107—431no—
335C2×#107C2×D4311yescharacteristic
336C2×#106—431no—
337C2×#106—431no—
338C2×#106—431no—
339C2×#106C2×D4311yescharacteristic
340C2×C4⋊C8—431no—
341C2×C4⋊C8—431no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×#97—431no—
345C2×#97C2×D4311yescharacteristic
346#384—431no—
347#384—431no—
348#382—861no—
349#380—431no—
350#380—431no—
351#380—861no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—861no—
357C4×C4⋊C4—861no—
358C4×C4⋊C4—861no—
359C4×C4⋊C4C2×D4311yescharacteristic
360C4×C4⋊C4C2×D4311yescharacteristic
361C2×#95—861no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#340C2×D4311yescharacteristic
370C43#2136511yescharacteristic, complemented, Sylow
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—861no—
375C23×C4—861no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380#117—1724no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—861no—
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×C4⋊C4C22×D4311yescharacteristic
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—431no—
406C2×C42—434no—
407C2×C42—434no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—1724no—
413C2×C42C22×D4311yescharacteristic
414#107—22no—
415#107—862no—
416#107—862no—
417#107—862no—
418#106—22no—
419#106—862no—
420#106—862no—
421#106—862no—
422C4⋊C8—434no—
423C4⋊C8—434no—
424C22⋊C8—434no—
425C22⋊C8—434no—
426#97—434no—
427#97C4×D4314yescomplemented
428#95—21no—
429#95—21no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—431no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—434no—
445C22×C4—434no—
446C22×C4—432no—
447C22×C4—432no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—864no—
453C22×C4—864no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4D4×D4311yescharacteristic
467C22×C4D4×D4311yescharacteristic
468C22×C4C23×D4311yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—432no—
474C2×C8—432no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8C2×C4×D4312yes—
480C2×C8C2×C4×D4312yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C4⋊C4—864no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4#1062189812yes—
502C4⋊C4#1062189812yes—
503C22⋊C4—1722no—
504C22⋊C4—1722no—
505C42—42no—
506C42—42no—
507C42—434no—
508C42—434no—
509C42—432no—
510C42—432no—
511C42—1722no—
512C42—1722no—
513C42—1722no—
514C42—1722no—
515C42C2×C4×D4312yes—
516C42Q8×D4312yes—
517C23—432no—
518C23—432no—
519C23—432no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23C2×D4×D4311yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
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—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—432no—
546C2×C4—868no—
547C2×C4—868no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—1728no—
559C2×C4—1728no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C4⋊C4×D4312yes—
571C2×C4C4⋊C4×D4312yes—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4C2×Q8×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4#41×D4311yescharacteristic
576C2×C4C2×#1062189811yescharacteristic
577C2×C4C2×#1062189811yescharacteristic
578C8—22no—
579C8—22no—
580C8—862no—
581C8—862no—
582C22—434no—
583C22—862no—
584C22—862no—
585C22—862no—
586C22—862no—
587C22—862no—
588C22—862no—
589C22C2×C4⋊C4×D4311yescharacteristic
590C22#1458340811yescharacteristic
591C22#1458340811yescharacteristic
592C22AGL(1,ℤ/8)×D4311yescharacteristic
593C22AGL(1,ℤ/8)×D4311yescharacteristic
594C22#137×D4311yescharacteristic
595C22#137×D4311yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—434no—
603C4—862no—
604C4—862no—
605C4—3441no—
606C4—3441no—
607C4—1722no—
608C4—1722no—
609C4#1458336711yescharacteristic
610C4C4×#1062189811yescharacteristic
611C4#1458345311yescharacteristic
612C4#1458345311yescharacteristic
613C2—864no—
614C2#1913707511yescharacteristic
615C2#428×D4311yescharacteristic
616C2#428×D4311yescharacteristic
617C2#1914468411yescharacteristic
618C2#1914469211yescharacteristic
619C2#1914471511yescharacteristic
620C2#1914472311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1776C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1776D43
hypocenterC43#21365
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
4. #19135357C2semidirect
5. #19135355C2semidirect
6. #19135352C2semidirect
7. #19135350C2semidirect
12. #19134493C2semidirect
13. #19134493C2semidirect
14. #19134492C2semidirect
15. C43×#1776C2semidirect
21. #14582954C4semidirect
100. Dic43⋊C8C2×C4semidirect
101. Dic43⋊C8C2×C4semidirect
104. #13063236C2×C4semidirect
122. #97×C43C2×C4semidirect
317. #1776D43semidirect
370. C43#21365semidirect
427. #97C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829542
#191369992
C4×C4⋊C4×D432
#191353572
#191353552
#191353522
#191353502
#191347892
#191347862
#191347842
#191347812
#191344932
#191344922
C43×#17762
#2136543