Finite Group Databasebeta

← #25066732

Subgroups — #25066732

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144601C211yesmaximal, characteristic
2#19143686C211yesmaximal, characteristic, complemented
3#19143616C211yesmaximal, characteristic
4#19133455C211yesmaximal, characteristic, complemented
5#19133449C211yesmaximal, characteristic, complemented
6#19133432C211yesmaximal, characteristic, complemented
7#19133430C211yesmaximal, characteristic, complemented
8#19133407C211yesmaximal, characteristic, complemented
9#19133405C211yesmaximal, characteristic, complemented
10C8×#10621873C211yesmaximal, characteristic, complemented
11#19133372C211yesmaximal, characteristic, complemented
12#19133036C211yesmaximal, characteristic
13#19133014C211yesmaximal, characteristic, complemented
14#19132889C211yesmaximal, characteristic, complemented
15C8×SD16×C43C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17C4×D4×D43C2211yescharacteristic
18#14583231C411yescharacteristic
19#14583228C411yescharacteristic
20#14583188C411yescharacteristic
21#14583187C411yescharacteristic
22#14583103C411yescharacteristic
23#14583102C411yescharacteristic
24#14583051C411yescharacteristic
25#14583048C411yescharacteristic
26#14583030C2211yescharacteristic, complemented
27#14583029—21no—
28#14583028—21no—
29#14583026C2211yescharacteristic, complemented
30C8×Dic86C2211yescharacteristic, complemented
31C4×#10621873C2211yescharacteristic
32C4×#10621884C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34C8×D172C2211yescharacteristic
35D4×C43⋊C8C2211yescharacteristic
36#14582964C2211yescharacteristic
37C8×C22⋊D43—21no—
38(C22⋊D43)⋊C8—21no—
39#14582959—21no—
40#14582958—21no—
41#14582955C2211yescharacteristic
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582950C2211yescharacteristic
45C2×(C2×D43)⋊C8—21no—
46C22⋊C8×D43—21no—
47C4×#10621872C2211yescharacteristic
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
59#14582620C2211yescharacteristic, 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×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—
76#13063324C2×C411yescharacteristic
77#13063323C2×C411yescharacteristic
78#13063315—21no—
79#13063305C2×C411yescharacteristic
80#13063303—21no—
81#13063301C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84C4×D172C2311yescharacteristic
85D4×Dic43C2×C411yescharacteristic
86#13063287C2×C411yescharacteristic
87C4×C22⋊D43—21no—
88(C22⋊D43)⋊C4—21no—
89#13063282—21no—
90C4⋊C4×D43C2×C411yescharacteristic
91C22⋊C4×D43—21no—
92C42×D43C2311yescharacteristic
93#13063257C2×C411yescharacteristic
94#13063256C2×C411yescharacteristic
95#13063256C2×C411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8C2×C411yescharacteristic
102Dic43⋊C8C2×C411yescharacteristic
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063250C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063248C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8C2×C411yescharacteristic
117(C2×D43)⋊C8C2×C411yescharacteristic
118(C2×D43)⋊C8D411yescharacteristic
119(C2×D43)⋊C8D411yescharacteristic
120#13063236—21no—
121#13063235—21no—
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43C2×C411yescharacteristic
130C22×C8×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C23×D43—21no—
145C2×Q8×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150D4×D43—22no—
151D4×D43—22no—
152C2×D172C22×C411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—81no—
157C2×C4×D43—81no—
158C2×C4×D43C22×C411yescharacteristic
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43#4111yescharacteristic
161C2×Dic86—21no—
162C2×Dic86C22×C411yescharacteristic
163SD16×C43—22no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C22⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179#10621884—22no—
180#10621883—22no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C4×Dic43C22×C411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206#10621873—22no—
207#10621872—42no—
208C8×D43—81no—
209C8×D43—81no—
210C23×C43—21no—
211C22×D43—21no—
212C22×D43—24no—
213C22×D43—81no—
214C22×D43—81no—
215C22×D43C4×D411yescharacteristic
216Q8×C43—21no—
217Q8×C43—21no—
218D4×C43—21no—
219D4×C43#13112yes—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—24no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—81no—
233C2×Dic43C4×D411yescharacteristic
234C2×Dic43C4×D411yescharacteristic
235C2×Dic43C4×D411yescharacteristic
236D172—21no—
237D172#13112yes—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—81no—
246C4×D43—81no—
247Dic86—21no—
248Dic86—21no—
249Dic86—81no—
250C8×C43—22no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#17924—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43C2×C4×D411yescharacteristic
269C2×D43—21no—
270C2×D43—22no—
271C2×D43—21no—
272C2×D43—21no—
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—84no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43C2×#13111yescharacteristic
281C4×C43C2×#13111yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—21no—
285Dic43—21no—
286Dic43—21no—
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290#3101—431no—
291#2985—431no—
292#2972—431no—
293#1585—431no—
294#1585—431no—
295#1582—431no—
296#1582—431no—
297SD16⋊C8—431no—
298SD16⋊C8—431no—
299C8×SD16—431no—
300C8×SD16D4311yescharacteristic, complemented
301#1572—431no—
302#1490—431no—
303#1485—431no—
304#1453—431no—
305C2×C43—42no—
306C2×C43#292911yescharacteristic
307C2×C43#294911yescharacteristic
308C2×C43#295611yescharacteristic
309D43—41no—
310D43—42no—
311#533—431no—
312C2×C4×D4—431no—
313#483—431no—
314#483—431no—
315#476—431no—
316#476—431no—
317#461—431no—
318#461—431no—
319#450—431no—
320#450—431no—
321#446—431no—
322#446—431no—
323#446—861no—
324#446—861no—
325C8×Q8—431no—
326C8×Q8C2×D4311yescharacteristic, complemented
327C4×SD16—431no—
328C4×SD16—431no—
329C4×SD16—431no—
330C4×SD16C2×D4311yescharacteristic
331C8×D4—431no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336C8×D4C2×D4311yescharacteristic
337#433—861no—
338#433—861no—
339#432—431no—
340#431—431no—
341#431—431no—
342#431—431no—
343C2×C22⋊C8—861no—
344C2×C22⋊C8—861no—
345C4×M16—431no—
346#335—431no—
347#335—431no—
348#334—431no—
349#334C2×D4311yescharacteristic, complemented
350Q8⋊C8—431no—
351Q8⋊C8—431no—
352Q8⋊C8—431no—
353Q8⋊C8C2×D4311yescharacteristic, complemented
354D4⋊C8—431no—
355D4⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8C2×D4311yescharacteristic
358#322—431no—
359#322—431no—
360#322—431no—
361C82C2×D4311yescharacteristic, complemented
362C43#1792411yescharacteristic, complemented, Sylow
363C22×D4—431no—
364C23×C4—861no—
365C2×SD16—431no—
366C2×SD16—431no—
367C2×SD16—431no—
368C2×SD16C4×D4311yescharacteristic
369C2×M16—861no—
370C22×C8—21no—
371C22×C8—861no—
372C22×C8—861no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376#125—861no—
377C22⋊Q8—431no—
378C22⋊Q8—431no—
379C22⋊Q8—861no—
380C4×Q8—431no—
381C4×Q8—861no—
382C4×Q8C22×D4311yescharacteristic
383C4×D4—431no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—861no—
387C4×D4—861no—
388C4×D4C22×D4311yescharacteristic
389#117—861no—
390C2×C4⋊C4—431no—
391C2×C22⋊C4—861no—
392C2×C42—431no—
393#106—431no—
394#106—431no—
395#106—431no—
396#106C4×D4311yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409#103—431no—
410#103—431no—
411#103—431no—
412#103C4×D4311yescharacteristic
413#102—431no—
414#102—431no—
415#102—431no—
416#102C4×D4311yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—431no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C22⋊C8—431no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427#97—861no—
428#97—861no—
429#97—861no—
430#97—861no—
431C4×C8—21no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C4×C8C22×D4311yescharacteristic
439C4×C8C22×D4311yescharacteristic
440C24—861no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8C2×C4×D4311yescharacteristic
444C2×D4—431no—
445C2×D4—861no—
446C2×D4—862no—
447C2×D4—862no—
448C2×D4C2×C4×D4311yescharacteristic
449C22×C4—21no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—3441no—
458C22×C4—3441no—
459SD16—22no—
460SD16—862no—
461SD16—862no—
462SD16—862no—
463M16—1722no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
476C2×C8—3441no—
477C2×C8—3441no—
478C2×C8C2×C4×D4311yescharacteristic
479C2×C8C2×C4×D4311yescharacteristic
480C2×C8D4×D4311yescharacteristic
481C2×C8D4×D4311yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—431no—
484C4⋊C4—431no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4C2×C4×D4311yescharacteristic
493C4⋊C4C2×C4×D4311yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C42—21no—
501C42—431no—
502C42—431no—
503C42—431no—
504C42—861no—
505C42C23×D4311yescharacteristic
506C23—21no—
507C23—431no—
508C23—864no—
509C23—861no—
510C23—3441no—
511C23—3441no—
512Q8—21no—
513Q8—21no—
514Q8—861no—
515Q8—861no—
516Q8—3441no—
517D4—21no—
518D4—432no—
519D4—864no—
520D4—861no—
521D4#1306333112yes—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—431no—
528C2×C4—431no—
529C2×C4—431no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—3441no—
538C2×C4—3441no—
539C2×C4—3441no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4C22×C4×D4311yescharacteristic
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4#41×D4311yescharacteristic
546C8—22no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—861no—
554C8—861no—
555C8—861no—
556C8—861no—
557C8—1721no—
558C8—1721no—
559C8—1721no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—861no—
564C22—861no—
565C22—861no—
566C22—862no—
567C22—3444no—
568C22—1721no—
569C22—1721no—
570C22C4×D4×D4311yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—861no—
576C4—861no—
577C4—861no—
578C4—1721no—
579C4—1721no—
580C4—1721no—
581C4#131×D4311yescharacteristic
582C4C2×#1306333111yescharacteristic
583C4#1458370511yescharacteristic
584C4#1458370611yescharacteristic
585C2—42no—
586C2—1721no—
587C2—1722no—
588C2#1914328411yescharacteristic
589C2#1914344911yescharacteristic
590C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×SD16×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×D4×D43C2×C4
cosocleC42×C43C24
hypercenterC8×SD16D43
hypocenterC43#17924
LCSG ▷ C2×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
2. #19143686C2semidirect
4. #19133455C2semidirect
5. #19133449C2semidirect
6. #19133432C2semidirect
7. #19133430C2semidirect
8. #19133407C2semidirect
9. #19133405C2semidirect
10. C8×#10621873C2semidirect
11. #19133372C2semidirect
13. #19133014C2semidirect
14. #19132889C2semidirect
15. C8×SD16×C43C2semidirect
26. #14583030C22semidirect
29. #14583026C22semidirect
30. C8×Dic86C22semidirect
48. #14582651C22semidirect
49. #14582651C22semidirect
50. #14582650C22semidirect
51. #14582631C22semidirect
52. Q8⋊(C43⋊C8)C22semidirect
53. #14582629C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582620C22semidirect
60. C8×Q8×C43C22semidirect
63. C43×#334C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C82×C43C22semidirect
300. C8×SD16D43semidirect
326. C8×Q8C2×D43semidirect
349. #334C2×D43semidirect
353. Q8⋊C8C2×D43semidirect
361. C82C2×D43semidirect
362. C43#17924semidirect

Maximal subgroups

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

subgroupindex
#191446012
#191436862
#191436162
#191334552
#191334492
#191334322
#191334302
#191334072
#191334052
C8×#106218732
#191333722
#191330362
#191330142
#191328892
C8×SD16×C432
#1792443