Finite Group Databasebeta

← #25066511

Subgroups — #25066511

Order 11008.

698 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144601C211yesmaximal, characteristic
2#19143524C211yesmaximal, characteristic, complemented
3C8×D4×D43C211yesmaximal, characteristic
4#19133455C211yesmaximal, characteristic, complemented
5#19133453C211yesmaximal, characteristic, complemented
6#19133451C211yesmaximal, characteristic, complemented
7#19133449C211yesmaximal, characteristic, complemented
8#19133409C211yesmaximal, characteristic, complemented
9#19133407C211yesmaximal, characteristic, complemented
10#19133405C211yesmaximal, characteristic, complemented
11#19133368C211yesmaximal, characteristic, complemented
12#19133018C211yesmaximal, characteristic
13#19132996C211yesmaximal, characteristic, complemented
14#19132886C211yesmaximal, characteristic, complemented
15C43×SD16⋊C8C211yesmaximal, characteristic, complemented
16C22×C8×D43—21no—
17#14583453C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583231C411yescharacteristic
20#14583228C411yescharacteristic
21#14583188C411yescharacteristic
22#14583187C411yescharacteristic
23#14583103C411yescharacteristic
24#14583102C411yescharacteristic
25#14583051C411yescharacteristic
26#14583048C411yescharacteristic
27#14583030C2211yescharacteristic, complemented
28#14583028—21no—
29#14583026C2211yescharacteristic, complemented
30C8×Dic86—21no—
31C8×Dic86C2211yescharacteristic, complemented
32C4×#10621873C2211yescharacteristic
33C4×#10621884C2211yescharacteristic
34C4×#10621883C2211yescharacteristic
35C8×D172C2211yescharacteristic
36D4×C43⋊C8C2211yescharacteristic
37#14582964C2211yescharacteristic
38C8×C22⋊D43—21no—
39(C22⋊D43)⋊C8—21no—
40#14582950C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582924—21no—
43#14582921C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45C22⋊C8×D43—21no—
46#14582853—21no—
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582651C2211yescharacteristic, 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
59#14582620C2211yescharacteristic, complemented
60C8×Q8×C43C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×D4×D43C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621884C2×C411yescharacteristic
72C2×#10621872—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—44no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80#13063324C2×C411yescharacteristic
81#13063323C2×C411yescharacteristic
82#13063315—21no—
83#13063305C2×C411yescharacteristic
84#13063303—21no—
85#13063301C2×C411yescharacteristic
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88C4×D172C2311yescharacteristic
89D4×Dic43C2×C411yescharacteristic
90#13063287C2×C411yescharacteristic
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063282—21no—
94C4⋊C4×D43C2×C411yescharacteristic
95C22⋊C4×D43—21no—
96C42×D43C2311yescharacteristic
97#13063257C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99#13063256C2×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⋊C8C2×C411yescharacteristic
109Dic43⋊C8C2×C411yescharacteristic
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)⋊C8C2×C411yescharacteristic
121(C2×D43)⋊C8C2×C411yescharacteristic
122#13063236—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
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—
151D4×D43—22no—
152D4×D43—22no—
153C2×D172C22×C411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43C22×C411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86C22×C411yescharacteristic
164SD16×C43—22no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—42no—
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#10621884—22no—
181#10621883—22no—
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—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—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—42no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621873—22no—
208#10621872—42no—
209C8×D43—22no—
210C8×D43—22no—
211C8×D43—42no—
212C8×D43—42no—
213C8×D43—42no—
214C23×C43—21no—
215C22×D43—24no—
216C22×D43—21no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43C4×D411yescharacteristic
220Q8×C43—21no—
221Q8×C43—21no—
222D4×C43—21no—
223D4×C43#13112yes—
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—42no—
237C2×Dic43C4×D411yescharacteristic
238C2×Dic43C4×D411yescharacteristic
239C2×Dic43C4×D411yescharacteristic
240D172—21no—
241D172#13112yes—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—41no—
245C4×D43—42no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—42no—
249C4×D43AGL(1,ℤ/8)12yes—
250C4×D43#13712yes—
251Dic86—21no—
252Dic86—21no—
253Dic86—42no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17905—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C2×C4×D411yescharacteristic
273C2×D43—21no—
274C2×D43—21no—
275C2×D43—22no—
276C2×D43—48no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43#44012yes—
280C4×C43—21no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43C2×#13111yescharacteristic
285C4×C43C2×#13111yescharacteristic
286C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C43C2×#13711yescharacteristic
288Dic43—21no—
289Dic43—21no—
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43#44012yes—
294#3101—431no—
295#2960—431no—
296C2×C8×D4—431no—
297#1585—431no—
298#1585—431no—
299#1585—431no—
300#1585—431no—
301SD16⋊C8—431no—
302SD16⋊C8—431no—
303SD16⋊C8—431no—
304SD16⋊C8D4311yescharacteristic, complemented
305#1571—431no—
306#1486—431no—
307#1481—431no—
308#1452—431no—
309C2×C43—42no—
310C2×C43#292911yescharacteristic
311C2×C43C2×#44011yescharacteristic
312C2×C43#295511yescharacteristic
313D43—22no—
314D43—42no—
315C23×C8—861no—
316#533—431no—
317C2×C4×D4—431no—
318#483—431no—
319#483—431no—
320#476—431no—
321#476—431no—
322#461—431no—
323#461—431no—
324#450—431no—
325#450—431no—
326#446—431no—
327#446—431no—
328#446—861no—
329C8×Q8—431no—
330C8×Q8—861no—
331C8×Q8C2×D4311yescharacteristic, complemented
332C4×SD16—431no—
333C4×SD16—431no—
334C4×SD16—431no—
335C4×SD16C2×D4311yescharacteristic
336C8×D4—431no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—861no—
340C8×D4—861no—
341C8×D4C2×D4311yescharacteristic
342#431—431no—
343#431—431no—
344#424—861no—
345#423—431no—
346C2×C4⋊C8—431no—
347C2×C22⋊C8—861no—
348#405—861no—
349C2×C4×C8—431no—
350#335—431no—
351#335—431no—
352#335—431no—
353#335C2×D4311yescharacteristic, complemented
354Q8⋊C8—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357Q8⋊C8C2×D4311yescharacteristic, complemented
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8C2×D4311yescharacteristic
362#322—431no—
363#322—431no—
364#322—431no—
365#322C2×D4311yescharacteristic, complemented
366C43#1790511yescharacteristic, complemented, Sylow
367C22×D4—431no—
368C23×C4—861no—
369C2×SD16—431no—
370C2×SD16—431no—
371C2×SD16—431no—
372C2×SD16C4×D4311yescharacteristic
373C2×M16—861no—
374C22×C8—21no—
375C22×C8—431no—
376C22×C8—431no—
377C22×C8—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—1724no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384#125—861no—
385C22⋊Q8—431no—
386C22⋊Q8—431no—
387C22⋊Q8—861no—
388C4×Q8—431no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×D4—431no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397#117—861no—
398C2×C4⋊C4—431no—
399C2×C22⋊C4—861no—
400C2×C42—431no—
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⋊C8—861no—
415C4⋊C8—861no—
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418#103—431no—
419#103—431no—
420#103—431no—
421#103C4×D4311yescharacteristic
422#102—431no—
423#102—431no—
424#102—431no—
425#102C4×D4311yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—861no—
434#97—861no—
435C4×C8—21no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—861no—
442C4×C8C22×D4311yescharacteristic
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445C24—861no—
446C2×Q8—431no—
447C2×Q8—861no—
448C2×Q8C2×C4×D4311yescharacteristic
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4C2×C4×D4311yescharacteristic
454C22×C4—21no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—1722no—
463C22×C4—1722no—
464SD16—22no—
465SD16—862no—
466SD16—862no—
467SD16—862no—
468M16—1722no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—862no—
478C2×C8—862no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—1722no—
483C2×C8—1722no—
484C2×C8—1722no—
485C2×C8—1722no—
486C2×C8C2×C4×D4311yescharacteristic
487C2×C8C2×C4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C2×C8D4×D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—431no—
492C4⋊C4—431no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4C2×C4×D4311yescharacteristic
501C4⋊C4C2×C4×D4311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C42—21no—
509C42—431no—
510C42—431no—
511C42—431no—
512C42—861no—
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—431no—
516C23—864no—
517C23—861no—
518C23—1722no—
519C23—1722no—
520Q8—21no—
521Q8—21no—
522Q8—861no—
523Q8—861no—
524Q8—1722no—
525D4—21no—
526D4—432no—
527D4—864no—
528D4—861no—
529D4#1306333112yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—431no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—431no—
539C2×C4—431no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—1721no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—861no—
565C8—1721no—
566C8—1721no—
567C8—1721no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—432no—
572C22—861no—
573C22—861no—
574C22—862no—
575C22—1728no—
576C22—1721no—
577C22—1721no—
578C22C4×D4×D4311yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—432no—
584C4—861no—
585C4—861no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4#131×D4311yescharacteristic
590C4C2×#1306333111yescharacteristic
591C4AGL(1,ℤ/8)×D4311yescharacteristic
592C4#137×D4311yescharacteristic
593C2—42no—
594C2—862no—
595C2—1722no—
596C2#1914328411yescharacteristic
597C2#440×D4311yescharacteristic
598C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×SD16⋊C8C2
socleC22×C43C2×C4×D4
prime radicalC2×D4×D43C2×C4
cosocleC42×C43C24
hypercenterSD16⋊C8D43
hypocenterC43#17905
LCSG ▷ C2×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
2. #19143524C2semidirect
4. #19133455C2semidirect
5. #19133453C2semidirect
6. #19133451C2semidirect
7. #19133449C2semidirect
8. #19133409C2semidirect
9. #19133407C2semidirect
10. #19133405C2semidirect
11. #19133368C2semidirect
13. #19132996C2semidirect
14. #19132886C2semidirect
15. C43×SD16⋊C8C2semidirect
27. #14583030C22semidirect
29. #14583026C22semidirect
31. C8×Dic86C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582651C22semidirect
51. #14582631C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
53. #14582629C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582620C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#335C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
304. SD16⋊C8D43semidirect
331. C8×Q8C2×D43semidirect
353. #335C2×D43semidirect
357. Q8⋊C8C2×D43semidirect
365. #322C2×D43semidirect
366. C43#17905semidirect

Maximal subgroups

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

subgroupindex
#191446012
#191435242
C8×D4×D432
#191334552
#191334532
#191334512
#191334492
#191334092
#191334072
#191334052
#191333682
#191330182
#191329962
#191328862
C43×SD16⋊C82
#1790543