Finite Group Databasebeta

← #25068032

Subgroups — #25068032

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621872C211yesmaximal, characteristic, complemented
2C4×SD16×D43C211yesmaximal, characteristic
3#19143331C211yesmaximal, characteristic
4#19133488C211yesmaximal, characteristic, complemented
5#19133483C211yesmaximal, characteristic, complemented
6#19133439C211yesmaximal, characteristic, complemented
7#19133433C211yesmaximal, characteristic, complemented
8#19133430C211yesmaximal, characteristic, complemented
9C8×#10621884C211yesmaximal, characteristic, complemented
10#19133392C211yesmaximal, characteristic, complemented
11#19133349C211yesmaximal, characteristic, complemented
12#19133022C211yesmaximal, characteristic, complemented
13#19133018C211yesmaximal, characteristic
14#19132874C211yesmaximal, characteristic, complemented
15C43×#1583C211yesmaximal, characteristic, complemented
16C2×SD16×D43C411yescharacteristic
17C2×M16×D43—21no—
18C4×Q8×D43C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583029—21no—
21#14583029C2211yescharacteristic, complemented
22#14583026—21no—
23#14583026C2211yescharacteristic, complemented
24Q8×C43⋊C8C2211yescharacteristic, complemented
25#14582990C411yescharacteristic
26C4×#10621873C2211yescharacteristic
27SD16×Dic43C411yescharacteristic
28C4×#10621884C2211yescharacteristic
29#14582986C411yescharacteristic
30C4×#10621883C2211yescharacteristic
31#14582984C411yescharacteristic
32#14582977C2211yescharacteristic
33#14582973—21no—
34#14582968—21no—
35C8×D172C2211yescharacteristic
36#14582964C2211yescharacteristic
37#14582950C2211yescharacteristic
38#106×D43C411yescharacteristic
39#14582921—21no—
40#14582921C2211yescharacteristic
41#14582921C2211yescharacteristic
42#103×D43C411yescharacteristic
43#102×D43C411yescharacteristic
44#14582861—21no—
45C4×#10621872—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582650C2211yescharacteristic, complemented
49#14582649C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51#14582631C2211yescharacteristic, complemented
52Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
53#14582629C2211yescharacteristic, complemented
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic, complemented
58C8×C43⋊C8C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×Q8×D43C2×C411yescharacteristic
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70C2×#10621873C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73SD16×D43—24no—
74C2×#10621877—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C2×#10621872D411yescharacteristic
78C2×#10621872D411yescharacteristic
79M16×D43—44no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43C2×C411yescharacteristic
83C2×C8×D43C2×C411yescharacteristic
84Q8×Dic43C2×C411yescharacteristic
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290C2×C411yescharacteristic
89C4×D172C2311yescharacteristic
90D4×Dic43C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92C4×C22⋊D43—21no—
93(C22⋊D43)⋊C4—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43C2×C411yescharacteristic
96C4⋊C4×D43C2×C411yescharacteristic
97C22⋊C4×D43—21no—
98C42×D43—21no—
99C42×D43C2311yescharacteristic
100#13063257C2×C411yescharacteristic
101#13063256C2×C411yescharacteristic
102#13063256C2×C411yescharacteristic
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250C2×C411yescharacteristic
112#13063249C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063247C2×C411yescharacteristic
115#13063246C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43C2×C411yescharacteristic
130C8×Dic43C2×C411yescharacteristic
131C2×SD16×C43C2×C411yescharacteristic
132C2×M16×C43—21no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43C2×C411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141C22⋊C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C22×Dic43—21no—
152Q8×D43—22no—
153Q8×D43—41no—
154D4×D43—22no—
155D4×D43—41no—
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43C22×C411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43#4111yescharacteristic
167C2×Dic86—21no—
168C2×Dic86C22×C411yescharacteristic
169SD16×C43—22no—
170M16×C43—42no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C22×C411yescharacteristic
175C2×C8×C43C22×C411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C42×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621884M1614yescomplemented
186#10621883—22no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C411yescharacteristic
191C4⋊Dic43C22×C411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43C22×C411yescharacteristic
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43#4111yescharacteristic
202#10621877—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210#10621873—22no—
211#10621872—22no—
212#10621872—42no—
213#10621872—42no—
214#10621872SD1614yescomplemented
215C8×D43—22no—
216C8×D43—41no—
217C8×D43—42no—
218C8×D43—42no—
219C23×C43—21no—
220C22×D43—21no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—81no—
224C22×D43C4×D411yescharacteristic
225Q8×C43—21no—
226Q8×C43C2×M1612yescomplemented
227D4×C43—21no—
228D4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C22⋊D43—42no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—42no—
242C2×Dic43C4×D411yescharacteristic
243C2×Dic43C4×D411yescharacteristic
244C2×Dic43C4×D411yescharacteristic
245D172—21no—
246D172C2×M1612yes—
247C4×D43—21no—
248C4×D43—21no—
249C4×D43—41no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—41no—
253C4×D43—41no—
254C4×D43—42no—
255C4×D43—81no—
256C4×D43C2×SD1612yes—
257C4×D43#13512yes—
258Dic86—21no—
259Dic86—21no—
260Dic86—42no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43C2×SD1612yescomplemented
268C43⋊C8—21no—
269C43⋊C8—21no—
270C43⋊C8—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8C2×M1612yescomplemented
274C43⋊C8C2×SD1612yescomplemented
275M16×SD16—431nomaximal, Sylow
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43C2×C4×D411yescharacteristic
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—22no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—84no—
286C2×D43C4×SD1612yes—
287C4×C43—22no—
288C4×C43—21no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43C22×M1611yescharacteristic
292C4×C43#56811yescharacteristic
293C4×C43C22×SD1611yescharacteristic
294C4×C43C2×#13511yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—41no—
298Dic43—41no—
299Dic43—41no—
300Dic43C4×SD1612yes—
301Q8×M16—431no—
302C2×C4×SD16—431no—
303D4×M16—431no—
304#1590—431no—
305#1590—431no—
306#1583—431no—
307#1583D4311yescharacteristic, complemented
308#1582—431no—
309#1582—431no—
310C8×SD16—431no—
311C8×SD16—431no—
312#1566—431no—
313#1487—431no—
314#1486—431no—
315C8×M16—431no—
316C2×C43—81no—
317C2×C43D4×M1611yescharacteristic
318C2×C43C2×C4×SD1611yescharacteristic
319C2×C43#295711yescharacteristic
320D43—22no—
321D43—42no—
322C22×SD16—431no—
323C22×M16—861no—
324C2×C4×Q8—431no—
325C2×C4×D4—431no—
326#446—431no—
327#446—431no—
328#446—861no—
329#446—861no—
330C8×Q8—431no—
331C8×Q8C2×D4311yescharacteristic, complemented
332C4×SD16—431no—
333C4×SD16—431no—
334C4×SD16—431no—
335C4×SD16—431no—
336C4×SD16—431no—
337C4×SD16—431no—
338C4×SD16—431no—
339C4×SD16C2×D4311yescharacteristic
340#436—431no—
341#436C2×D4311yescharacteristic
342#435—861no—
343#435—861no—
344C8×D4—431no—
345C8×D4—431no—
346#431—431no—
347C2×#106—431no—
348#423—431no—
349#423—431no—
350#423—861no—
351C2×#103—431no—
352C2×#102—431no—
353#407—861no—
354C4×M16—431no—
355C4×M16—861no—
356C2×C4×C8—431no—
357#334—431no—
358#334—431no—
359#334—431no—
360#334C2×D4311yescharacteristic, complemented
361Q8⋊C8—431no—
362Q8⋊C8—431no—
363Q8⋊C8—431no—
364Q8⋊C8C2×D4311yescharacteristic, complemented
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8C2×D4311yescharacteristic
369#322—431no—
370#322C2×D4311yescharacteristic, complemented
371C82—431no—
372C82—431no—
373C43M16×SD1611yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×D4—431no—
376C23×C4—861no—
377C2×SD16—431no—
378C2×SD16—431no—
379C2×SD16—431no—
380C2×SD16—864no—
381C2×SD16C4×D4311yescharacteristic
382C2×M16—21no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—1724no—
389C22×C8—431no—
390C22×C8—431no—
391C22×C8—861no—
392C22×C8—861no—
393C4×Q8—431no—
394C4×Q8—431no—
395C4×Q8—431no—
396C4×Q8—861no—
397C4×Q8—861no—
398C4×Q8C22×D4311yescharacteristic
399C4×D4—431no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404C4×D4C22×D4311yescharacteristic
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410C2×C42—861no—
411#106—431no—
412#106—431no—
413#106—431no—
414#106C4×D4311yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8—861no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8C22×D4311yescharacteristic
425C4⋊C8C22×D4311yescharacteristic
426#103—431no—
427#103—431no—
428#103—431no—
429#103C4×D4311yescharacteristic
430#102—431no—
431#102—431no—
432#102—431no—
433#102C4×D4311yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439#97—431no—
440#97—431no—
441#97—861no—
442#97—861no—
443C4×C8—21no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—861no—
450C4×C8C22×D4311yescharacteristic
451C4×C8C22×D4311yescharacteristic
452C4×C8C22×D4311yescharacteristic
453C24—861no—
454C2×Q8—431no—
455C2×Q8—861no—
456C2×Q8—862no—
457C2×Q8—1721no—
458C2×Q8C2×C4×D4311yescharacteristic
459C2×D4—431no—
460C2×D4—861no—
461C2×D4—862no—
462C2×D4—1721no—
463C2×D4C2×C4×D4311yescharacteristic
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—1722no—
475C22×C4—1722no—
476SD16—22no—
477SD16—434no—
478SD16—862no—
479SD16—862no—
480M16—42no—
481M16—434no—
482M16—862no—
483M16—1722no—
484M16—1722no—
485M16—1722no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—431no—
492C2×C8—431no—
493C2×C8—862no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—1721no—
498C2×C8—1722no—
499C2×C8—1722no—
500C2×C8C2×C4×D4311yescharacteristic
501C2×C8C2×C4×D4311yescharacteristic
502C2×C8D4×D4311yescharacteristic
503C2×C8D4×D4311yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—431no—
506C4⋊C4—431no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4C2×C4×D4311yescharacteristic
513C4⋊C4C2×C4×D4311yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—861no—
516C22⋊C4—861no—
517C22⋊C4—861no—
518C42—21no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42C23×D4311yescharacteristic
526C23—21no—
527C23—431no—
528C23—861no—
529C23—3441no—
530C23—1722no—
531C23—1722no—
532Q8—21no—
533Q8—861no—
534Q8—861no—
535Q8—1722no—
536Q8M16×D4312yescomplemented
537D4—21no—
538D4—21no—
539D4—432no—
540D4—861no—
541D4—1722no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—431no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—431no—
551C2×C4—431no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—3441no—
558C2×C4—1721no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4C22×C4×D4311yescharacteristic
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—432no—
575C8—432no—
576C8—861no—
577C8—861no—
578C8—1721no—
579C8—1721no—
580C8—1721no—
581C8SD16×D4312yescomplemented
582C22—41no—
583C22—41no—
584C22—41no—
585C22—432no—
586C22—861no—
587C22—861no—
588C22—862no—
589C22—3444no—
590C22—1721no—
591C22—1721no—
592C22C4×D4×D4311yescharacteristic
593C4—21no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—432no—
598C4—861no—
599C4—861no—
600C4—1721no—
601C4—1721no—
602C4—1721no—
603C4C2×M16×D4311yescharacteristic
604C4#1458366411yescharacteristic
605C4C2×SD16×D4311yescharacteristic
606C4#135×D4311yescharacteristic
607C2—81no—
608C2—862no—
609C2—1722no—
610C2#1914332811yescharacteristic
611C2C4×SD16×D4311yescharacteristic
612C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1583C2
socleC22×C43C2×C4×D4
prime radicalC2×D4×D43C2×C4
cosocleC42×C43C24
hypercenter#1583D43
hypocenterC43M16×SD16
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
1. Q8×#10621872C2semidirect
4. #19133488C2semidirect
5. #19133483C2semidirect
6. #19133439C2semidirect
7. #19133433C2semidirect
8. #19133430C2semidirect
9. C8×#10621884C2semidirect
10. #19133392C2semidirect
11. #19133349C2semidirect
12. #19133022C2semidirect
14. #19132874C2semidirect
15. C43×#1583C2semidirect
21. #14583029C22semidirect
23. #14583026C22semidirect
24. Q8×C43⋊C8C22semidirect
48. #14582650C22semidirect
49. #14582649C22semidirect
50. #14582649C22semidirect
51. #14582631C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
53. #14582629C22semidirect
57. #14582621C22semidirect
58. C8×C43⋊C8C22semidirect
59. C8×C43⋊C8C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#334C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
185. #10621884M16semidirect
214. #10621872SD16semidirect
226. Q8×C43C2×M16semidirect
267. C8×C43C2×SD16semidirect
273. C43⋊C8C2×M16semidirect
274. C43⋊C8C2×SD16semidirect
307. #1583D43semidirect
331. C8×Q8C2×D43semidirect
360. #334C2×D43semidirect
364. Q8⋊C8C2×D43semidirect
370. #322C2×D43semidirect
373. C43M16×SD16semidirect
536. Q8M16×D43semidirect
581. C8SD16×D43semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218722
C4×SD16×D432
#191433312
#191334882
#191334832
#191334392
#191334332
#191334302
C8×#106218842
#191333922
#191333492
#191330222
#191330182
#191328742
C43×#15832
M16×SD1643