Finite Group Databasebeta

← #25066075

Subgroups — #25066075

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143705C211yesmaximal, characteristic, complemented
2#19143702C211yesmaximal, characteristic, complemented
3C4×#13063346C211yesmaximal, characteristic
4#19133409C211yesmaximal, characteristic, complemented
5SD16⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#19133406C211yesmaximal, characteristic, complemented
7C8×#10621885C211yesmaximal, characteristic, complemented
8#19133399C211yesmaximal, characteristic, complemented
9C8×#10621882C211yesmaximal, characteristic, complemented
10#19133387C211yesmaximal, characteristic, complemented
11#335×D43C211yesmaximal, characteristic, complemented
12#19132981C211yesmaximal, characteristic, complemented
13#19132979C211yesmaximal, characteristic, complemented
14#19132880C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#13063346C411yescharacteristic
17C4×#10621902C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19Q8×C43⋊C8C2211yescharacteristic
20C8×Dic86C2211yescharacteristic
21#14583023C2211yescharacteristic
22C4×#10621885C2211yescharacteristic
23#14582991C411yescharacteristic
24C4×#10621873C2211yescharacteristic
25SD16×Dic43C411yescharacteristic
26#14582986C411yescharacteristic
27C4×#10621882C2211yescharacteristic
28#14582979C411yescharacteristic
29C8×D172—21no—
30C8×D172C2211yescharacteristic
31D4×C43⋊C8C2211yescharacteristic
32#14582964—21no—
33#14582964C2211yescharacteristic
34C8×C22⋊D43—21no—
35(C22⋊D43)⋊C8—21no—
36#14582950—21no—
37#14582950C2211yescharacteristic
38#14582950C2211yescharacteristic
39#14582949—21no—
40#14582934C411yescharacteristic
41C2×Dic43⋊C8—21no—
42C4⋊C8×D43—21no—
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#14582894C411yescharacteristic
46#14582892C411yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582651C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582620C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×#10621900C2×C411yescharacteristic
69#13063346C818yescomplemented
70C2×#10621885C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621882C2×C411yescharacteristic
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43C2×C411yescharacteristic
79C2×C8×D43C2×C411yescharacteristic
80Q8×Dic43C2×C411yescharacteristic
81C4×Dic86C2311yescharacteristic
82#13063290C2×C411yescharacteristic
83C4×D172—21no—
84C4×D172C2311yescharacteristic
85D4×Dic43C2×C411yescharacteristic
86#13063287—21no—
87#13063287C2×C411yescharacteristic
88C4×C22⋊D43—21no—
89(C22⋊D43)⋊C4—21no—
90#13063283—21no—
91#13063283C2×C411yescharacteristic
92#13063283C2×C411yescharacteristic
93#13063281—21no—
94C2×C4×Dic43—21no—
95C42×D43—21no—
96C42×D43C2311yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99#13063257C2×C411yescharacteristic
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8D411yescharacteristic
109Dic43⋊C8D411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43C2×C411yescharacteristic
129C8×Dic43C2×C411yescharacteristic
130C2×SD16×C43C2×C411yescharacteristic
131C22×C8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621902—22no—
152#10621902C2×C814yescomplemented
153#10621900—22no—
154#10621900C2×C814yescomplemented
155C2×D172—21no—
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43C22×C411yescharacteristic
161C2×C4×D43C2×D411yescharacteristic
162C2×C4×D43#4111yescharacteristic
163C2×Dic86C22×C411yescharacteristic
164SD16×C43C2×C814yescomplemented
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C22⋊C4×C43—21no—
177C42×C43—21no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621885C2×C814yescomplemented
181#10621882C2×C814yescomplemented
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621873C2×C814yescomplemented
208C8×D43—22no—
209C8×D43—81no—
210C8×D43—81no—
211C8×D43—81no—
212C8×D43—81no—
213C8×D43C2×C814yescomplemented
214C23×C43—21no—
215C22×D43—21no—
216C22×D43C4×D411yescharacteristic
217Q8×C43—21no—
218Q8×C43C22×C812yes—
219D4×C43—21no—
220D4×C43C22×C812yes—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—24no—
230C2×Dic43—21no—
231C2×Dic43—24no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—81no—
235C2×Dic43C4×D411yescharacteristic
236C2×Dic43C4×D411yescharacteristic
237C2×Dic43C4×D411yescharacteristic
238D172—24no—
239D172—21no—
240D172C22×C812yes—
241C4×D43—21no—
242C4×D43—21no—
243C4×D43—24no—
244C4×D43—41no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—81no—
248C4×D43C22×C812yes—
249C4×D43#13112yes—
250Dic86—21no—
251Dic86C22×C812yes—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43C22×C812yes—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8C22×C812yes—
266#17857—431nomaximal, Sylow
267C22×C43—22no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43C2×C4×D411yescharacteristic
271C2×D43—21no—
272C2×D43—21no—
273C2×D43—22no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43C8×D412yes—
277C4×C43—22no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43C23×C811yescharacteristic
282C4×C43C2×#13111yescharacteristic
283C4×C43#57611yescharacteristic
284C4×C43#57811yescharacteristic
285Dic43—22no—
286Dic43—21no—
287Dic43—21no—
288Dic43—41no—
289Dic43—41no—
290Dic43C8×D412yes—
291#2988—431no—
292#2988—431no—
293C4×#135—431no—
294SD16⋊C8—431no—
295SD16⋊C8—431no—
296SD16⋊C8—431no—
297SD16⋊C8D4311yescharacteristic, complemented
298C8×Q16—431no—
299C8×Q16—431no—
300C8×D8—431no—
301C8×D8—431no—
302C2×#335—431no—
303#1477—431no—
304#1477—431no—
305#1450—431no—
306C2×C43—42no—
307C2×C43C2×C8×D411yescharacteristic
308C2×C43#295111yescharacteristic
309C2×C43#295711yescharacteristic
310D43—22no—
311D43—42no—
312C2×#135—431no—
313C4×#41—431no—
314C4×#41—431no—
315C8×Q8—431no—
316C8×Q8—431no—
317C8×Q8—431no—
318C8×Q8C2×D4311yescharacteristic
319C4×Q16—431no—
320C4×Q16—431no—
321C4×SD16—431no—
322C4×SD16—431no—
323C4×SD16—431no—
324C4×SD16C2×D4311yescharacteristic
325C4×D8—431no—
326C4×D8—431no—
327C8×D4—431no—
328C8×D4—431no—
329C8×D4—431no—
330C8×D4—861no—
331C8×D4—861no—
332C8×D4—861no—
333C8×D4—861no—
334C8×D4C2×D4311yescharacteristic
335#431—431no—
336#431—431no—
337#431—861no—
338#431—861no—
339#427—431no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8—431no—
342C2×C4⋊C8—861no—
343C2×C4⋊C8—861no—
344#416—431no—
345#416—431no—
346C2×C4×C8—431no—
347#335—431no—
348#335—431no—
349#335—431no—
350#335C2×D4311yescharacteristic
351Q8⋊C8—431no—
352Q8⋊C8—431no—
353Q8⋊C8—431no—
354Q8⋊C8C2×D4311yescharacteristic
355D4⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8C2×D4311yescharacteristic
359#322—431no—
360#322C2×D4311yescharacteristic
361C82—431no—
362C82—431no—
363C43#1785711yescharacteristic, complemented, Sylow
364C2×#41—431no—
365C2×#41—431no—
366#135—438no—
367C2×Q16—431no—
368C2×SD16—431no—
369C2×SD16C4×D4311yescharacteristic
370C2×D8—431no—
371C22×C8—21no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—861no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8—861no—
378C22×C8—861no—
379C4×Q8—431no—
380C4×Q8—431no—
381C4×Q8—431no—
382C4×Q8C22×D4311yescharacteristic
383C4×D4—431no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4—861no—
390C4×D4C22×D4311yescharacteristic
391#117—431no—
392#117—431no—
393#117—861no—
394#117—861no—
395C2×C42—431no—
396C2×C42—861no—
397C2×C42—861no—
398#107—431no—
399#107—431no—
400#106—431no—
401#106C4×D4311yescharacteristic
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—431no—
416#103—431no—
417#103—431no—
418#103C4×D4311yescharacteristic
419#102—431no—
420#102—431no—
421#102—431no—
422#102C4×D4311yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—431no—
425C22⋊C8—431no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C4×C8—21no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8—861no—
438C4×C8—861no—
439C4×C8C22×D4311yescharacteristic
440C4×C8C22×D4311yescharacteristic
441C4×C8C22×D4311yescharacteristic
442#41—434no—
443#41—434no—
444#41—862no—
445#41—862no—
446C2×Q8—431no—
447C2×Q8C2×C4×D4311yescharacteristic
448C2×D4—431no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4C2×C4×D4311yescharacteristic
452C22×C4—21no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461Q16—434no—
462SD16—434no—
463SD16C8×D4314yescomplemented
464D8—434no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—81no—
469C2×C8—431no—
470C2×C8—434no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—862no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—3441no—
479C2×C8—3441no—
480C2×C8—3441no—
481C2×C8—3441no—
482C2×C8—3441no—
483C2×C8C2×C4×D4311yescharacteristic
484C2×C8C2×C4×D4311yescharacteristic
485C2×C8D4×D4311yescharacteristic
486C2×C8D4×D4311yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—431no—
489C4⋊C4—431no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4C2×C4×D4311yescharacteristic
494C4⋊C4C2×C4×D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C42—21no—
502C42—431no—
503C42—431no—
504C42—431no—
505C42—861no—
506C42—861no—
507C42—861no—
508C42—861no—
509C42—861no—
510C42C23×D4311yescharacteristic
511C23—21no—
512C23—431no—
513C23—861no—
514Q8—21no—
515Q8—432no—
516Q8—861no—
517Q8C2×C8×D4312yes—
518D4—21no—
519D4—432no—
520D4—864no—
521D4—864no—
522D4—861no—
523D4C2×C8×D4312yes—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—431no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—431no—
533C2×C4—431no—
534C2×C4—864no—
535C2×C4—864no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3441no—
542C2×C4—3441no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C22×C4×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—432no—
556C8—861no—
557C8—861no—
558C8—861no—
559C8—1721no—
560C8—1721no—
561C8—1721no—
562C8C2×C8×D4312yes—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—432no—
567C22—861no—
568C22—861no—
569C22—862no—
570C22—1721no—
571C22—1721no—
572C22C4×D4×D4311yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—432no—
578C4—861no—
579C4—861no—
580C4—862no—
581C4—1721no—
582C4—1721no—
583C4C22×C8×D4311yescharacteristic
584C4#131×D4311yescharacteristic
585C4#1458370311yescharacteristic
586C4#1458371511yescharacteristic
587C2—42no—
588C2—862no—
589C2—1722no—
590C2C8×D4×D4311yescharacteristic
591C2#1914346711yescharacteristic
592C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC43×SD16⋊C8C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063346C4
cosocleC42×C43C24
hypercenterSD16⋊C8D43
hypocenterC43#17857
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
1. #19143705C2semidirect
2. #19143702C2semidirect
4. #19133409C2semidirect
5. SD16⋊(C43⋊C8)C2semidirect
6. #19133406C2semidirect
7. C8×#10621885C2semidirect
8. #19133399C2semidirect
9. C8×#10621882C2semidirect
10. #19133387C2semidirect
11. #335×D43C2semidirect
12. #19132981C2semidirect
13. #19132979C2semidirect
14. #19132880C2semidirect
15. C43×SD16⋊C8C2semidirect
69. #13063346C8semidirect
152. #10621902C2×C8semidirect
154. #10621900C2×C8semidirect
164. SD16×C43C2×C8semidirect
180. #10621885C2×C8semidirect
181. #10621882C2×C8semidirect
207. #10621873C2×C8semidirect
213. C8×D43C2×C8semidirect
297. SD16⋊C8D43semidirect
363. C43#17857semidirect
463. SD16C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191437052
#191437022
C4×#130633462
#191334092
SD16⋊(C43⋊C8)2
#191334062
C8×#106218852
#191333992
C8×#106218822
#191333872
#335×D432
#191329812
#191329792
#191328802
C43×SD16⋊C82
#1785743