Finite Group Databasebeta

← #25067229

Subgroups — #25067229

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143744C211yesmaximal, characteristic, complemented
2#19143671C211yesmaximal, characteristic, complemented
3#19133509C211yesmaximal, characteristic, complemented
4#19133498C211yesmaximal, characteristic, complemented
5#19133486C211yesmaximal, characteristic, complemented
6#19133480C211yesmaximal, characteristic, complemented
7#19133419C211yesmaximal, characteristic, complemented
8SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
9SD16×C43⋊C8C211yesmaximal, characteristic, complemented
10D8×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133362C211yesmaximal, characteristic, complemented
12#19133055C211yesmaximal, characteristic, complemented
13#19133046C211yesmaximal, characteristic, complemented
14M16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3171C211yesmaximal, characteristic
16#14583030C2211yescharacteristic
17Q8×C43⋊C8C2211yescharacteristic
18#14582977—21no—
19#14582977C2211yescharacteristic
20#14582977C2211yescharacteristic
21#14582977C2211yescharacteristic
22#14582971—21no—
23#14582971—21no—
24#14582971—21no—
25D4×C43⋊C8C2211yescharacteristic
26D4×C43⋊C8C2211yescharacteristic
27D4×C43⋊C8C2211yescharacteristic
28#14582960—21no—
29#14582956C2211yescharacteristic
30#14582952C2211yescharacteristic
31#14582926—21no—
32#14582923C2211yescharacteristic
33#14582866—21no—
34#14582866—21no—
35C2×C4×C43⋊C8C2211yescharacteristic
36#14582652C2211yescharacteristic
37#14582652C2211yescharacteristic
38#14582650C2211yescharacteristic
39#14582650C2211yescharacteristic
40Q8⋊(C43⋊C8)C2211yescharacteristic
41Q8⋊(C43⋊C8)C2211yescharacteristic
42D4⋊(C43⋊C8)C2211yescharacteristic
43D4⋊(C43⋊C8)C2211yescharacteristic
44D4⋊(C43⋊C8)C2211yescharacteristic
45D4⋊(C43⋊C8)C2211yescharacteristic
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48#14582620C2211yescharacteristic
49#14582620C2211yescharacteristic
50C8×C43⋊C8C2211yescharacteristic
51C8×C43⋊C8C2211yescharacteristic
52C43×#532C2211yescharacteristic
53C43×#529C2211yescharacteristic
54C43×#501C411yescharacteristic
55C43×#496C411yescharacteristic
56C43×#490C411yescharacteristic
57C43×#489C411yescharacteristic
58C43×#469C411yescharacteristic
59C43×#469C411yescharacteristic
60C43×#468C411yescharacteristic
61C43×#468C411yescharacteristic
62C4×SD16×C43C2211yescharacteristic
63C4×SD16×C43C2211yescharacteristic
64C4×D8×C43C2211yescharacteristic
65C4×D8×C43C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)D411yescharacteristic
79C4⋊(C43⋊C8)D411yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82C4⋊(C43⋊C8)C2311yescharacteristic
83C4⋊(C43⋊C8)C2311yescharacteristic
84C22⋊(C43⋊C8)—21no—
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)—21no—
88C22⋊(C43⋊C8)—21no—
89C22⋊(C43⋊C8)—21no—
90C22⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)D411yescharacteristic
92C22⋊(C43⋊C8)D411yescharacteristic
93#13063236—21no—
94#13063236—21no—
95C4×C43⋊C8—21no—
96C4×C43⋊C8—21no—
97C4×C43⋊C8C2311yescharacteristic
98C4×C43⋊C8C2311yescharacteristic
99C4×C43⋊C8C2311yescharacteristic
100C4×C43⋊C8C2311yescharacteristic
101C2×#41×C43—21no—
102C2×SD16×C43C2×C411yescharacteristic
103C2×SD16×C43C2×C411yescharacteristic
104C2×D8×C43C2×C411yescharacteristic
105C2×D8×C43C2×C411yescharacteristic
106C2×M16×C43C2×C411yescharacteristic
107C2×M16×C43C2×C411yescharacteristic
108C4⋊Q8×C43C2×C411yescharacteristic
109#127×C43C2×C411yescharacteristic
110#126×C43—21no—
111#125×C43C2×C411yescharacteristic
112#124×C43—21no—
113#124×C43C2×C411yescharacteristic
114#123×C43—21no—
115C22⋊Q8×C43C2×C411yescharacteristic
116#121×C43—21no—
117#121×C43C2×C411yescharacteristic
118#121×C43C2×C411yescharacteristic
119#121×C43C2×C411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43C2311yescharacteristic
124C4×D4×C43C2311yescharacteristic
125C4×D4×C43C2311yescharacteristic
126#117×C43—21no—
127C2×C42×C43C2311yescharacteristic
128#107×C43C2×C411yescharacteristic
129#107×C43C2×C411yescharacteristic
130#106×C43C2×C411yescharacteristic
131#106×C43C2×C411yescharacteristic
132#103×C43C2×C411yescharacteristic
133#103×C43C2×C411yescharacteristic
134#102×C43C2×C411yescharacteristic
135#102×C43C2×C411yescharacteristic
136#102×C43C2×C411yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140#97×C43C2×C411yescharacteristic
141#97×C43C2×C411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43C22×C411yescharacteristic
154C2×D4×C43C22×C411yescharacteristic
155C2×D4×C43C22×C411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162SD16×C43—22no—
163SD16×C43—22no—
164D8×C43—22no—
165D8×C43—22no—
166M16×C43—22no—
167M16×C43—22no—
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43C22×C411yescharacteristic
178C4⋊C4×C43C22×C411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C42×C43—21no—
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43#4111yescharacteristic
194C42×C43C2411yescharacteristic
195#10621877—81no—
196#10621877—81no—
197#10621877—81no—
198#10621877—81no—
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—42no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8—81no—
208C2×C43⋊C8—81no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C2×C43⋊C8C2×D411yescharacteristic
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43C4×D411yescharacteristic
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—81no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—81no—
227D4×C43—81no—
228D4×C43—81no—
229D4×C43—81no—
230D4×C43—81no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
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×C43C4×D411yescharacteristic
248C2×C4×C43C4×D411yescharacteristic
249C2×C4×C43C4×D411yescharacteristic
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C8×C43—21no—
254C8×C43—21no—
255C8×C43#13112yes—
256C8×C43#13112yes—
257C43⋊C8—22no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#17968—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43C2×C4×D411yescharacteristic
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43C2×#13111yescharacteristic
291C4×C43C2×#13111yescharacteristic
292C4×C43#57611yescharacteristic
293C4×C43#57711yescharacteristic
294#3171D4311yescharacteristic
295#2993—431no—
296#2981—431no—
297#1594—431no—
298#1592—431no—
299#1590—431no—
300#1589—431no—
301#1580—431no—
302SD16⋊C8—431no—
303C8×SD16—431no—
304C8×D8—431no—
305#1569—431no—
306#1494—431no—
307#1492—431no—
308C8×M16—431no—
309C2×C43—41no—
310C2×C43—81no—
311C2×C43—81no—
312C2×C43—81no—
313C2×C43#293111yescharacteristic
314C2×C43#294611yescharacteristic
315C2×C43#295611yescharacteristic
316#532C2×D4311yescharacteristic
317#529C2×D4311yescharacteristic
318#501Dic4311yescharacteristic
319#496Dic4311yescharacteristic
320#490Dic4311yescharacteristic
321#489Dic4311yescharacteristic
322#469Dic4311yescharacteristic
323#469Dic4311yescharacteristic
324#468Dic4311yescharacteristic
325#468Dic4311yescharacteristic
326#446—431no—
327C8×Q8—431no—
328C4×SD16C2×D4311yescharacteristic
329C4×SD16C2×D4311yescharacteristic
330C4×D8C2×D4311yescharacteristic
331C4×D8C2×D4311yescharacteristic
332#436—431no—
333#436—431no—
334#436—431no—
335#436—861no—
336#435—861no—
337#435—861no—
338#435—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—431no—
342#433—861no—
343#432—431no—
344#431—431no—
345#424—861no—
346#423—431no—
347#408—861no—
348#408—861no—
349C4×M16C2×D4311yescharacteristic
350C2×C4×C8—431no—
351#335—431no—
352#335—431no—
353#334—431no—
354#334—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363#322—431no—
364#322—431no—
365C82—431no—
366C82—431no—
367C43#1796811yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×SD16C2×Dic4311yescharacteristic
370C2×SD16C2×Dic4311yescharacteristic
371C2×D8C2×Dic4311yescharacteristic
372C2×D8C2×Dic4311yescharacteristic
373C2×M16—861no—
374C2×M16—861no—
375C2×M16—861no—
376C2×M16—861no—
377C2×M16C2×Dic4311yescharacteristic
378C2×M16C2×Dic4311yescharacteristic
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8C2×Dic4311yescharacteristic
384#127C2×Dic4311yescharacteristic
385#126—21no—
386#125C2×Dic4311yescharacteristic
387#124—21no—
388#124C2×Dic4311yescharacteristic
389#123—21no—
390C22⋊Q8C2×Dic4311yescharacteristic
391#121—21no—
392#121C2×Dic4311yescharacteristic
393#121C2×Dic4311yescharacteristic
394#121C2×Dic4311yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C22×D4311yescharacteristic
399C4×D4C22×D4311yescharacteristic
400C4×D4C22×D4311yescharacteristic
401#117—21no—
402C2×C42C22×D4311yescharacteristic
403#107C2×Dic4311yescharacteristic
404#107C2×Dic4311yescharacteristic
405#106C2×Dic4311yescharacteristic
406#106C2×Dic4311yescharacteristic
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8—861no—
416#103C2×Dic4311yescharacteristic
417#103C2×Dic4311yescharacteristic
418#102C2×Dic4311yescharacteristic
419#102C2×Dic4311yescharacteristic
420#102C2×Dic4311yescharacteristic
421#102C2×Dic4311yescharacteristic
422#102C2×Dic4311yescharacteristic
423#102C2×Dic4311yescharacteristic
424C22⋊C8—431no—
425C22⋊C8—431no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—861no—
434#97—861no—
435#97C2×Dic4311yescharacteristic
436#97C2×Dic4311yescharacteristic
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—861no—
442C4×C8—861no—
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8C22×Dic4311yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4C22×Dic4311yescharacteristic
455C2×D4C22×Dic4311yescharacteristic
456C2×D4C22×Dic4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4D4×D4311yescharacteristic
461C22×C4#1062190011yescharacteristic
462C22×C4C22×Dic4311yescharacteristic
463SD16—22no—
464SD16—22no—
465D8—22no—
466D8—22no—
467M16—22no—
468M16—22no—
469M16—3441no—
470M16—3441no—
471M16—3441no—
472M16—3441no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—3441no—
484C2×C8—3441no—
485C2×C8—3441no—
486C2×C8—1722no—
487C2×C8C22×Dic4311yescharacteristic
488C2×C8C22×Dic4311yescharacteristic
489C2×C8C22×Dic4311yescharacteristic
490C2×C8C22×Dic4311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C22×Dic4311yescharacteristic
497C4⋊C4C22×Dic4311yescharacteristic
498C4⋊C4C22×Dic4311yescharacteristic
499C4⋊C4C22×Dic4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C42—21no—
510C42D4×D4311yescharacteristic
511C42#1062190011yescharacteristic
512C42C22×Dic4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic4311yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—81no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4D4×Dic4311yescharacteristic
549C2×C4D4×Dic4311yescharacteristic
550C2×C4D4×Dic4311yescharacteristic
551C2×C4C23×Dic4311yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×#1062190011yescharacteristic
554C8—21no—
555C8—21no—
556C8—862no—
557C8—861no—
558C8—861no—
559C8—861no—
560C8—861no—
561C8—1721no—
562C8—1721no—
563C8—1721no—
564C8—1721no—
565C8—1721no—
566C8#1306333212yes—
567C8#1306333212yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22C2×D4×Dic4311yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4C2×#1306333211yescharacteristic
591C4C2×#1306333211yescharacteristic
592C4#1458370311yescharacteristic
593C4#1458370911yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—81no—
598C2#1914330711yescharacteristic
599C2#1914342811yescharacteristic
600C2#1914350511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
Fitting, prime radicalC43×#3171C2
socleC22×C43C2×C4×D4
cosocleC42×C43C24
hypercenter#3171D43
hypocenterC43#17968
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3171

Complements

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

NH ≅ G/Ntype
1. #19143744C2semidirect
2. #19143671C2semidirect
3. #19133509C2semidirect
4. #19133498C2semidirect
5. #19133486C2semidirect
6. #19133480C2semidirect
7. #19133419C2semidirect
8. SD16⋊(C43⋊C8)C2semidirect
9. SD16×C43⋊C8C2semidirect
10. D8×C43⋊C8C2semidirect
11. #19133362C2semidirect
12. #19133055C2semidirect
13. #19133046C2semidirect
14. M16×C43⋊C8C2semidirect
367. C43#17968semidirect

Maximal subgroups

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

subgroupindex
#191437442
#191436712
#191335092
#191334982
#191334862
#191334802
#191334192
SD16⋊(C43⋊C8)2
SD16×C43⋊C82
D8×C43⋊C82
#191333622
#191330552
#191330462
M16×C43⋊C82
C43×#31712
#1796843