Finite Group Databasebeta

← #25063530

Subgroups — #25063530

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148173C211yesmaximal, characteristic
2#19143556C211yesmaximal, characteristic
3#19143260C211yesmaximal, characteristic
4#19133066C212yesmaximal, complemented
5#19133050C211yesmaximal, characteristic, complemented
6#19133040C212yesmaximal, complemented
7#19133025C211yesmaximal, characteristic, complemented
8#19133014C212yesmaximal, complemented
9#19132988C212yesmaximal, complemented
10C2×#14582629C211yesmaximal, characteristic, complemented
11C43×#1481C211yesmaximal, characteristic, complemented
12#14583629C411yescharacteristic
13#14583626—21no—
14#14583624C411yescharacteristic
15#14583610C411yescharacteristic
16#14583607C412yes—
17#14583605—21no—
18#14583603—22no—
19#14583564C411yescharacteristic
20#14583562C412yes—
21#14583453—22no—
22#14583453C2212yes—
23#14583452—21no—
24C4×#10621898C2211yescharacteristic
25#14583367—21no—
26C2×C4×Dic86C2211yescharacteristic
27C4×Q8×D43C2212yes—
28#14583026—21no—
29#14582976—21no—
30#14582967—22no—
31#14582959—22no—
32#14582955C2212yes—
33#14582951C2212yes—
34#14582950C2212yes—
35#14582923C2211yescharacteristic
36#14582865—21no—
37#14582854—21no—
38C4×#10621872C2212yes—
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582631C2212yes—
41#14582631C2212yes—
42Q8⋊(C43⋊C8)C2212yes—
43Q8⋊(C43⋊C8)C2212yes—
44#14582629C2211yescharacteristic
45#14582629C2211yescharacteristic
46#14582629C2211yescharacteristic
47#14582629C2211yescharacteristic
48C43×#533C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C2×C4⋊C8×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yes—
52C43×Q8⋊C8C2212yes—
53C2×#10621898D411yescharacteristic
54C22×Dic86C2×C411yescharacteristic
55C2×Q8×D43C2×C412yes—
56C2×#10621877—21no—
57C2×#10621872—22no—
58C22×C43⋊C8—21no—
59#13063324—21no—
60#13063324—21no—
61#13063324—22no—
62#13063324C2×C412yes—
63#13063323—22no—
64#13063323C2×C412yes—
65#13063316—21no—
66#13063316—21no—
67#13063315—22no—
68#13063315—22no—
69#13063315—22no—
70#13063305—22no—
71#13063305C2×C412yes—
72#13063303—22no—
73#13063303—22no—
74#13063303—22no—
75#13063302—22no—
76#13063302—22no—
77#13063301—22no—
78#13063301C2×C412yes—
79Q8×Dic43C2×C412yes—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—22no—
83C4×Dic86—22no—
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2×C411yescharacteristic
87C4×Dic86D411yescharacteristic
88C4×Dic86C2311yescharacteristic
89C4×Dic86C2311yescharacteristic
90#13063290—21no—
91#13063290—21no—
92#13063290—22no—
93#13063290C2×C412yes—
94C4×D172C2×C411yescharacteristic
95C4×D172D411yescharacteristic
96#13063287—21no—
97#13063287—21no—
98C4×C22⋊D43C2×C412yes—
99C4×C22⋊D43D412yes—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102#13063284D411yescharacteristic
103#13063282—22no—
104#13063282D412yes—
105C2×C4⋊Dic43C2×C411yescharacteristic
106C2×Dic43⋊C4—21no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43C2×C412yes—
109C2×C4×Dic43—21no—
110C42×D43—22no—
111C42×D43C2312yes—
112C4⋊(C43⋊C8)—21no—
113C4⋊(C43⋊C8)C2312yes—
114Dic43⋊C8—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063235—22no—
119#13063235—22no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—22no—
124C22×C8×C43—21no—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2×C412yes—
130C4×Q8×C43—21no—
131C4×Q8×C43C2312yes—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C4×C8×C43C2312yes—
140C2×Q8×C43—21no—
141C2×Q8×C43C22×C412yes—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43C22⋊C412yes—
146C22×Dic43—21no—
147C22×Dic43—21no—
148Q8×D43—24no—
149Q8×D43—42no—
150#10621898—22no—
151#10621898—22no—
152C2×D172C22⋊C411yescharacteristic
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43C22×C412yes—
156C2×C4×D43C2×D412yes—
157C2×C4×D43C2×D412yes—
158C2×Dic86—22no—
159C2×Dic86—21no—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—41no—
163C2×Dic86C22⋊C411yescharacteristic
164C2×Dic86C22×C411yescharacteristic
165C2×Dic86C22×C411yescharacteristic
166C2×C8×C43—22no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43C22×C412yes—
176C22⋊C4×C43—22no—
177C42×C43—22no—
178C42×C43C22×C411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43C22⋊C412yes—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185(C2×D43)⋊C4C22⋊C412yes—
186(C2×D43)⋊C4C22⋊C412yes—
187C4⋊Dic43—21no—
188C4⋊Dic43—22no—
189C4⋊Dic43—22no—
190C4⋊Dic43C22⋊C411yescharacteristic
191C4⋊Dic43C22⋊C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4C22⋊C412yes—
205Dic43⋊C4C22⋊C412yes—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43C22×C412yes—
213C4×Dic43C2×D412yes—
214C4×Dic43C2×D412yes—
215#10621877—42no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—42no—
220#10621872—44no—
221C23×C43C2×C22⋊C411yescharacteristic
222C22×D43C2×C22⋊C412yes—
223Q8×C43—22no—
224Q8×C43—22no—
225Q8×C43—81no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—41no—
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43C2×C22⋊C411yescharacteristic
234C2×C4×C43#13712yes—
235C2×C4×C43#13712yes—
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C22⋊D43—24no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—42no—
245C2×Dic43—81no—
246C2×Dic43C2×C22⋊C412yes—
247C2×Dic43C2×C22⋊C412yes—
248C2×Dic43C2×C22⋊C412yes—
249D172—22no—
250C4×D43—22no—
251C4×D43—22no—
252C4×D43—22no—
253C4×D43—22no—
254C4×D43—42no—
255C4×D43—44no—
256C4×D43—82no—
257Dic86—21no—
258Dic86—22no—
259Dic86—21no—
260Dic86—21no—
261Dic86—44no—
262Dic86—42no—
263Dic86—82no—
264Dic86#13112yes—
265C8×C43—42no—
266C8×C43—41no—
267C8×C43—41no—
268C43⋊C8—22no—
269C43⋊C8—41no—
270C43⋊C8—42no—
271#17514—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43#41912yes—
275C22×C43C22×C22⋊C411yescharacteristic
276C2×D43—22no—
277C2×D43—22no—
278C2×D43—22no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43#41912yes—
285C4×C43C2×#13111yescharacteristic
286C4×C43#56811yescharacteristic
287C4×C43C2×#13711yescharacteristic
288C4×C43C2×#13711yescharacteristic
289Dic43—22no—
290Dic43—22no—
291Dic43—22no—
292Dic43—22no—
293Dic43—41no—
294Dic43—41no—
295Dic43—41no—
296Q8×#41—431no—
297#2965—431no—
298#2925—431no—
299#1497—432no—
300#1493—431no—
301#1491—432no—
302#1487—431no—
303#1485—432no—
304#1481D4311yescharacteristic, complemented
305#1479—432no—
306C2×Q8⋊C8—431no—
307C2×C43—22no—
308C2×C43#288011yescharacteristic
309C2×C43C2×#41911yescharacteristic
310C2×C43#290111yescharacteristic
311D43—42no—
312Q82—431no—
313#557—431no—
314#557—861no—
315#554—431no—
316#554—432no—
317#554—862no—
318#554—861no—
319D4×Q8—431no—
320D4×Q8—432no—
321#533—432no—
322#533—861no—
323#533—862no—
324#533C2×D4311yescharacteristic
325C4×#41—431no—
326C4×#41—861no—
327C2×C4×Q8—432no—
328C2×C4×Q8—431no—
329#446—861no—
330#436—861no—
331#435—862no—
332#433—862no—
333#432—432no—
334#431—432no—
335#431—432no—
336#431C2×D4311yescharacteristic
337#423—431no—
338C2×C4⋊C8C2×D4311yescharacteristic
339#408—861no—
340#405—861no—
341C4×M16—432no—
342C2×C4×C8—431no—
343Q8⋊C8—432no—
344Q8⋊C8—432no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348Q8⋊C8—431no—
349Q8⋊C8—432no—
350Q8⋊C8—432no—
351Q8⋊C8C2×D4312yes—
352Q8⋊C8C2×D4312yes—
353C43#1751411yescharacteristic, complemented, Sylow
354C2×#41—431no—
355C22×Q8—432no—
356C22×Q8—431no—
357C2×M16—862no—
358C2×M16—861no—
359C22×C8—21no—
360C22×C8—861no—
361C4⋊Q8—432no—
362C4⋊Q8—432no—
363C4⋊Q8—862no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366C4⋊Q8—862no—
367C4⋊Q8C4×D4311yescharacteristic
368C4⋊Q8C4×D4311yescharacteristic
369#125—21no—
370#125—862no—
371#125—862no—
372#125—861no—
373#125—862no—
374#125—861no—
375C22⋊Q8—21no—
376C22⋊Q8—432no—
377C22⋊Q8—432no—
378C22⋊Q8—862no—
379C22⋊Q8—862no—
380C22⋊Q8—862no—
381C22⋊Q8—862no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—862no—
385C22⋊Q8C4×D4312yes—
386C4×Q8—21no—
387C4×Q8—431no—
388C4×Q8—431no—
389C4×Q8—432no—
390C4×Q8—432no—
391C4×Q8—431no—
392C4×Q8—431no—
393C4×Q8—431no—
394C4×Q8—431no—
395C4×Q8—862no—
396C4×Q8—862no—
397C4×Q8—862no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8C22×D4312yes—
403C4×D4—432no—
404C4×D4—432no—
405C4×D4—431no—
406C4×D4—431no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—861no—
410C4×D4—861no—
411#117—21no—
412#117—431no—
413#117—432no—
414#117—862no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—861no—
419C2×C42—432no—
420C2×C42—862no—
421C2×C42—861no—
422C2×C42C22×D4311yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8—432no—
426C4⋊C8—862no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429C4⋊C8C22×D4311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—862no—
432C22⋊C8—862no—
433C22⋊C8—862no—
434#97—862no—
435#97—862no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—862no—
439C4×C8—861no—
440C4×C8C22×D4312yes—
441#41—862no—
442#41—862no—
443C2×Q8—21no—
444C2×Q8—431no—
445C2×Q8—431no—
446C2×Q8—431no—
447C2×Q8—862no—
448C2×Q8—862no—
449C2×Q8—862no—
450C2×Q8—861no—
451C2×Q8—864no—
452C2×Q8—1721no—
453C2×Q8—1722no—
454C2×Q8C2×C4×D4312yes—
455C2×D4—432no—
456C2×D4—431no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4C2×C4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467M16—1724no—
468M16—1722no—
469C2×C8—22no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—862no—
476C2×C8—1722no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—432no—
483C4⋊C4—432no—
484C4⋊C4—431no—
485C4⋊C4—431no—
486C4⋊C4—431no—
487C4⋊C4—431no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4—862no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4C2×C4×D4312yes—
502C22⋊C4—22no—
503C22⋊C4—432no—
504C22⋊C4—432no—
505C22⋊C4—432no—
506C22⋊C4—862no—
507C22⋊C4—862no—
508C42—22no—
509C42—432no—
510C42—432no—
511C42—432no—
512C42—862no—
513C42—862no—
514C42—861no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42C2×C4×D4311yescharacteristic
519C42D4×D4311yescharacteristic
520C42D4×D4311yescharacteristic
521C42C23×D4311yescharacteristic
522C23—432no—
523C23C22⋊C4×D4311yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—81no—
527Q8—432no—
528Q8—861no—
529Q8—862no—
530Q8—861no—
531Q8—861no—
532Q8—3442no—
533Q8—1722no—
534Q8—1724no—
535D4—864no—
536D4—862no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3442no—
554C2×C4—3441no—
555C2×C4—1722no—
556C2×C4—1724no—
557C2×C4—1722no—
558C2×C4C22⋊C4×D4311yescharacteristic
559C2×C4C22⋊C4×D4311yescharacteristic
560C2×C4C22⋊C4×D4311yescharacteristic
561C2×C4#1306335412yes—
562C2×C4#1306335712yes—
563C2×C4C22×C4×D4311yescharacteristic
564C2×C4C2×D4×D4311yescharacteristic
565C2×C4C2×D4×D4311yescharacteristic
566C8—42no—
567C8—41no—
568C8—41no—
569C8—862no—
570C8—1721no—
571C8—1722no—
572C22—21no—
573C22—21no—
574C22—862no—
575C22—862no—
576C22—862no—
577C22#1458290612yes—
578C22C2×C22⋊C4×D4311yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—42no—
583C4—42no—
584C4—862no—
585C4—862no—
586C4—862no—
587C4—862no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4#1458290612yes—
592C4#131×D4311yescharacteristic
593C4#1458366411yescharacteristic
594C4C2×#1306335411yescharacteristic
595C4C2×#1306335711yescharacteristic
596C2—22no—
597C2—1722no—
598C2#1914304311yescharacteristic
599C2C2×#1458290611yescharacteristic
600C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1481C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898D4
cosocleC42×C43C24
hypercenter#1481D43
hypocenterC43#17514
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #19133066C2semidirect
5. #19133050C2semidirect
6. #19133040C2semidirect
7. #19133025C2semidirect
8. #19133014C2semidirect
9. #19132988C2semidirect
10. C2×#14582629C2semidirect
11. C43×#1481C2semidirect
304. #1481D43semidirect
353. C43#17514semidirect

Maximal subgroups

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

subgroupindex
#191481732
#191435562
#191432602
#191330662
#191330502
#191330402
#191330252
#191330142
#191329882
C2×#145826292
C43×#14812
#1751443