Finite Group Databasebeta

← #25066057

Subgroups — #25066057

Order 11008.

730 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143674C211yesmaximal, characteristic, complemented
2#19143616C211yesmaximal, characteristic
3C4×SD16×D43C211yesmaximal, characteristic
4#19133410C211yesmaximal, characteristic, complemented
5#19133407C211yesmaximal, characteristic, complemented
6#19133405C211yesmaximal, characteristic, complemented
7#19133404C211yesmaximal, characteristic, complemented
8C8×#10621873C211yesmaximal, characteristic, complemented
9SD16×C43⋊C8C211yesmaximal, characteristic, complemented
10#19133394C211yesmaximal, characteristic, complemented
11#19133340C211yesmaximal, characteristic, complemented
12#19132988C211yesmaximal, characteristic, complemented
13#19132984C211yesmaximal, characteristic
14#19132877C211yesmaximal, characteristic, complemented
15C8×SD16×C43C211yesmaximal, characteristic, complemented
16C2×SD16×D43C411yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19Q8×C43⋊C8C2211yescharacteristic, complemented
20C8×Dic86—21no—
21C8×Dic86C2211yescharacteristic, complemented
22#14583023—21no—
23#14583023C2211yescharacteristic, complemented
24#14582990C411yescharacteristic
25C4×#10621873C2211yescharacteristic
26SD16×Dic43C411yescharacteristic
27C4×#10621884C2211yescharacteristic
28#14582986C411yescharacteristic
29C4×#10621883C2211yescharacteristic
30#14582984C411yescharacteristic
31C8×D172C2211yescharacteristic
32D4×C43⋊C8C2211yescharacteristic
33#14582964C2211yescharacteristic
34C8×C22⋊D43—21no—
35(C22⋊D43)⋊C8—21no—
36#14582951—21no—
37#14582951C2211yescharacteristic
38#14582951C2211yescharacteristic
39#14582950—21no—
40#14582950C2211yescharacteristic
41#14582950C2211yescharacteristic
42#106×D43C411yescharacteristic
43#103×D43C411yescharacteristic
44#102×D43C411yescharacteristic
45C2×(C2×D43)⋊C8—21no—
46C22⋊C8×D43—21no—
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582650C2211yescharacteristic, complemented
51#14582631C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53#14582629C2211yescharacteristic, complemented
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic, complemented
58#14582621C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic, complemented
67C2×Q8×D43C2×C411yescharacteristic
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73SD16×D43C818yescomplemented
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43C2×C411yescharacteristic
78C2×C8×D43C2×C411yescharacteristic
79Q8×Dic43C2×C411yescharacteristic
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82#13063290—21no—
83#13063290C2×C411yescharacteristic
84C4×D172C2311yescharacteristic
85D4×Dic43C2×C411yescharacteristic
86#13063287C2×C411yescharacteristic
87C4×C22⋊D43—21no—
88(C22⋊D43)⋊C4—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43C2×C411yescharacteristic
91C4⋊C4×D43C2×C411yescharacteristic
92C22⋊C4×D43—21no—
93C42×D43—21no—
94C42×D43C2311yescharacteristic
95#13063257C2×C411yescharacteristic
96#13063256C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8D411yescharacteristic
105Dic43⋊C8D411yescharacteristic
106#13063250C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063245C2×C411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8D411yescharacteristic
119(C2×D43)⋊C8D411yescharacteristic
120C4×C43⋊C8—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
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
145C23×D43—21no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151Q8×D43—22no—
152Q8×D43C2×C814yescomplemented
153D4×D43—22no—
154D4×D43C2×C814yes—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43C22×C411yescharacteristic
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43#4111yescharacteristic
166C2×Dic86—21no—
167C2×Dic86C22×C411yescharacteristic
168SD16×C43C2×C814yescomplemented
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—81no—
173C2×C8×C43C22×C411yescharacteristic
174C2×C8×C43C22×C411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C4⋊C4×C43—21no—
178C4⋊C4×C43C22×C411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C22⋊C4×C43—21no—
181C42×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184#10621884C2×C814yescomplemented
185#10621883C2×C814yescomplemented
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43C22×C411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209#10621873C2×C814yescomplemented
210C8×D43—22no—
211C8×D43—81no—
212C8×D43—81no—
213C8×D43C2×C814yescomplemented
214C23×C43—21no—
215C22×D43—21no—
216C22×D43—24no—
217C22×D43—81no—
218C22×D43—81no—
219C22×D43C4×D411yescharacteristic
220Q8×C43—21no—
221Q8×C43C22×C812yes—
222D4×C43—21no—
223D4×C43C22×C812yes—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—24no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—81no—
237C2×Dic43C4×D411yescharacteristic
238C2×Dic43C4×D411yescharacteristic
239C2×Dic43C4×D411yescharacteristic
240D172—21no—
241D172C22×C812yes—
242C4×D43—24no—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—81no—
249C4×D43—81no—
250C4×D43—81no—
251C4×D43C22×C812yes—
252C4×D43#13112yes—
253Dic86—21no—
254Dic86—24no—
255Dic86C22×C812yes—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43C22×C812yes—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8C22×C812yes—
270#17855—431nomaximal, Sylow
271C22×C43—22no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C2×C4×D411yescharacteristic
275C2×D43—21no—
276C2×D43—21no—
277C2×D43—22no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—84no—
281C2×D43C8×D412yes—
282C4×C43—22no—
283C4×C43—21no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43C23×C811yescharacteristic
287C4×C43C2×#13111yescharacteristic
288C4×C43#57711yescharacteristic
289C4×C43#57711yescharacteristic
290Dic43—22no—
291Dic43—21no—
292Dic43—21no—
293Dic43—41no—
294Dic43—41no—
295Dic43C8×D412yes—
296#2982—431no—
297#2972—431no—
298C2×C4×SD16—431no—
299SD16⋊C8—431no—
300SD16⋊C8—431no—
301SD16⋊C8—431no—
302SD16⋊C8—431no—
303C8×SD16—431no—
304C8×SD16—431no—
305C8×SD16—431no—
306C8×SD16D4311yescharacteristic, complemented
307#1564—431no—
308#1479—431no—
309#1478—431no—
310#1450—431no—
311C2×C43—42no—
312C2×C43C2×C8×D411yescharacteristic
313C2×C43#294911yescharacteristic
314C2×C43#295711yescharacteristic
315D43—22no—
316D43—42no—
317C22×SD16—431no—
318C2×C4×Q8—431no—
319C2×C4×D4—431no—
320C8×Q8—431no—
321C8×Q8—431no—
322C8×Q8—431no—
323C8×Q8—861no—
324C8×Q8—861no—
325C8×Q8C2×D4311yescharacteristic, complemented
326C4×SD16—431no—
327C4×SD16—431no—
328C4×SD16—431no—
329C4×SD16—431no—
330C4×SD16—431no—
331C4×SD16—431no—
332C4×SD16—431no—
333C4×SD16C2×D4311yescharacteristic
334C8×D4—431no—
335C8×D4—431no—
336C8×D4—431no—
337C8×D4—861no—
338C8×D4—861no—
339C8×D4C2×D4311yescharacteristic
340#431—431no—
341#431—431no—
342#431—431no—
343#431—431no—
344#431—861no—
345#431—861no—
346C2×#106—431no—
347C2×#103—431no—
348C2×#102—431no—
349C2×C22⋊C8—861no—
350C2×C22⋊C8—861no—
351C2×C4×C8—431no—
352#335—431no—
353#335—431no—
354#334—431no—
355#334C2×D4311yescharacteristic, complemented
356Q8⋊C8—431no—
357Q8⋊C8—431no—
358Q8⋊C8—431no—
359Q8⋊C8C2×D4311yescharacteristic, complemented
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8C2×D4311yescharacteristic
364#322—431no—
365#322—431no—
366C82—431no—
367C82C2×D4311yescharacteristic, complemented
368C43#1785511yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×D4—431no—
371C23×C4—861no—
372C2×SD16—431no—
373C2×SD16—431no—
374C2×SD16—438no—
375C2×SD16—431no—
376C2×SD16C4×D4311yescharacteristic
377C22×C8—21no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C4×Q8—431no—
384C4×Q8—431no—
385C4×Q8—431no—
386C4×Q8—861no—
387C4×Q8—861no—
388C4×Q8C22×D4311yescharacteristic
389C4×D4—431no—
390C4×D4—431no—
391C4×D4—431no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C42—431no—
400C2×C42—861no—
401#106—431no—
402#106—431no—
403#106—431no—
404#106C4×D4311yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416#103—431no—
417#103—431no—
418#103—431no—
419#103C4×D4311yescharacteristic
420#102—431no—
421#102—431no—
422#102—431no—
423#102C4×D4311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—431no—
426C22⋊C8—431no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C4×C8—21no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—861no—
440C4×C8—861no—
441C4×C8—861no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447C24—861no—
448C2×Q8—434no—
449C2×Q8—431no—
450C2×Q8—861no—
451C2×Q8—862no—
452C2×Q8C2×C4×D4311yescharacteristic
453C2×D4—434no—
454C2×D4—431no—
455C2×D4—862no—
456C2×D4—861no—
457C2×D4C2×C4×D4311yescharacteristic
458C22×C4—21no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—3441no—
469C22×C4—3441no—
470SD16—434no—
471SD16—434no—
472SD16—434no—
473SD16C8×D4314yescomplemented
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—431no—
479C2×C8—434no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—862no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8C2×C4×D4311yescharacteristic
491C2×C8C2×C4×D4311yescharacteristic
492C2×C8D4×D4311yescharacteristic
493C2×C8D4×D4311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4C2×C4×D4311yescharacteristic
503C4⋊C4C2×C4×D4311yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C42—21no—
509C42—431no—
510C42—431no—
511C42—431no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—431no—
518C23—864no—
519C23—861no—
520C23—3441no—
521C23—3441no—
522Q8—21no—
523Q8—432no—
524Q8—864no—
525Q8—861no—
526Q8C2×C8×D4312yes—
527D4—21no—
528D4—432no—
529D4—864no—
530D4—861no—
531D4C2×C8×D4312yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—431no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—431no—
541C2×C4—431no—
542C2×C4—864no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—3441no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—3441no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4C22×C4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—432no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C8—1721no—
571C8C2×C8×D4312yes—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—432no—
576C22—861no—
577C22—861no—
578C22—862no—
579C22—3444no—
580C22—1721no—
581C22—1721no—
582C22C4×D4×D4311yescharacteristic
583C4—21no—
584C4—22no—
585C4—41no—
586C4—41no—
587C4—432no—
588C4—861no—
589C4—861no—
590C4—862no—
591C4—1721no—
592C4—1721no—
593C4C22×C8×D4311yescharacteristic
594C4#131×D4311yescharacteristic
595C4#1458370511yescharacteristic
596C4#1458370611yescharacteristic
597C2—42no—
598C2—862no—
599C2—1722no—
600C2C8×D4×D4311yescharacteristic
601C2#1914344911yescharacteristic
602C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC8×SD16×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×D4×D43C2×C4
cosocleC42×C43C24
hypercenterC8×SD16D43
hypocenterC43#17855
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
1. #19143674C2semidirect
4. #19133410C2semidirect
5. #19133407C2semidirect
6. #19133405C2semidirect
7. #19133404C2semidirect
8. C8×#10621873C2semidirect
9. SD16×C43⋊C8C2semidirect
10. #19133394C2semidirect
11. #19133340C2semidirect
12. #19132988C2semidirect
14. #19132877C2semidirect
15. C8×SD16×C43C2semidirect
19. Q8×C43⋊C8C22semidirect
21. C8×Dic86C22semidirect
23. #14583023C22semidirect
48. #14582651C22semidirect
49. #14582651C22semidirect
50. #14582650C22semidirect
51. #14582631C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
53. #14582629C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. C8×C43⋊C8C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#334C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C82×C43C22semidirect
73. SD16×D43C8semidirect
152. Q8×D43C2×C8semidirect
168. SD16×C43C2×C8semidirect
184. #10621884C2×C8semidirect
185. #10621883C2×C8semidirect
209. #10621873C2×C8semidirect
213. C8×D43C2×C8semidirect
306. C8×SD16D43semidirect
325. C8×Q8C2×D43semidirect
355. #334C2×D43semidirect
359. Q8⋊C8C2×D43semidirect
367. C82C2×D43semidirect
368. C43#17855semidirect
473. SD16C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191436742
#191436162
C4×SD16×D432
#191334102
#191334072
#191334052
#191334042
C8×#106218732
SD16×C43⋊C82
#191333942
#191333402
#191329882
#191329842
#191328772
C8×SD16×C432
#1785543