Finite Group Databasebeta

← #25063297

Subgroups — #25063297

Order 11008.

1026 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic
3C2×#14582921C211yesmaximal, characteristic
4#19133048C214yesmaximal, complemented
5#19133022C214yesmaximal, complemented
6#19132999C211yesmaximal, characteristic, complemented
7#19132998C211yesmaximal, characteristic, complemented
8#19132997C211yesmaximal, characteristic, complemented
9C43×#1481C211yesmaximal, characteristic, complemented
10C22×#10621872—21no—
11#14583456C2211yescharacteristic
12#14583455—21no—
13#14583454C411yescharacteristic
14#14583454C411yescharacteristic
15#14583453—21no—
16#14583453C2212yes—
17#14583452—21no—
18#14583451—21no—
19#14583451C412yes—
20C4⋊Q8×D43C411yescharacteristic
21C4⋊Q8×D43C411yescharacteristic
22#125×D43—21no—
23C22⋊Q8×D43—21no—
24C22⋊Q8×D43C412yes—
25C4×Q8×D43—21no—
26C4×Q8×D43C2212yes—
27#117×D43—21no—
28C2×C42×D43C2211yescharacteristic
29#14582952C2211yescharacteristic
30#14582951—21no—
31#14582950C2212yes—
32#14582949—21no—
33#14582921—21no—
34#14582921—21no—
35#14582921C2212yes—
36#14582921C2212yes—
37C2×C4⋊(C43⋊C8)C2211yescharacteristic
38C2×Dic43⋊C8—21no—
39C4⋊C8×D43—21no—
40C22⋊C8×D43—21no—
41C4×C8×D43C2212yes—
42#14582631C2214yescomplemented
43Q8⋊(C43⋊C8)C2214yescomplemented
44#14582629C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C2×C4⋊C8×C43C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621872—22no—
55C2×#10621872—22no—
56C2×#10621872—44no—
57C22×C43⋊C8—21no—
58C2×C8×D43—22no—
59#13063325C2×C411yescharacteristic
60#13063325C2×C411yescharacteristic
61#13063324—21no—
62#13063324—21no—
63#13063324—21no—
64#13063324C2×C412yes—
65#13063323—21no—
66#13063323C2×C412yes—
67#13063317—21no—
68#13063316—21no—
69#13063316—21no—
70#13063315—22no—
71#13063315—22no—
72#13063305—21no—
73#13063305C2×C412yes—
74#13063304—21no—
75#13063304C2×C412yes—
76#13063303—22no—
77#13063303—22no—
78#13063302—22no—
79#13063302—22no—
80#13063301—21no—
81#13063301C2×C412yes—
82Q8×Dic43—21no—
83Q8×Dic43C2×C412yes—
84C4×Dic86—21no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86C2312yes—
88#13063290—21no—
89#13063290—22no—
90#13063290—22no—
91#13063290C2×C412yes—
92#13063284—21no—
93#13063283—21no—
94#13063283—21no—
95#13063282—22no—
96#13063281—22no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C4⋊C4×D43C2×C412yes—
103C22⋊C4×D43—22no—
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C42×D43—22no—
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43C2311yescharacteristic
115C42×D43C2311yescharacteristic
116C4⋊(C43⋊C8)—21no—
117C4⋊(C43⋊C8)—21no—
118C4⋊(C43⋊C8)C2312yes—
119Dic43⋊C8—22no—
120Dic43⋊C8—22no—
121Dic43⋊C8—22no—
122C22⋊(C43⋊C8)—21no—
123(C2×D43)⋊C8—22no—
124C4×C43⋊C8C2312yes—
125C8×Dic43—22no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128C4⋊Q8×C43C2×C411yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43C2×C412yes—
132C4×Q8×C43—21no—
133C4×Q8×C43C2312yes—
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2312yes—
139C22⋊C8×C43—21no—
140C4×C8×C43C2312yes—
141C23×D43C22⋊C411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150Q8×D43—44no—
151Q8×D43—44no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43C22⋊C411yescharacteristic
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43SD1614yes—
163C2×C4×D43Q1614yes—
164C2×C4×D43C22×C411yescharacteristic
165C2×C4×D43C22×C411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×Dic86—21no—
171C2×Dic86—22no—
172C2×Dic86—22no—
173C2×Dic86C22×C412yes—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C2×C8×C43—42no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43C22×C412yes—
183C22⋊C4×C43—22no—
184C42×C43—22no—
185C42×C43C22×C411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2411yescharacteristic
189C22⋊Dic43—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4⋊Dic43C22×C412yes—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C2×C43⋊C8—22no—
222C2×C43⋊C8—22no—
223C2×C43⋊C8—42no—
224#10621872—44no—
225#10621872—44no—
226C8×D43—44no—
227C23×C43C2×C22⋊C411yescharacteristic
228C22×D43—41no—
229C22×D43—41no—
230C22×D43#10314yes—
231C22×D43C2×C22⋊C411yescharacteristic
232C22×D43C2×C22⋊C411yescharacteristic
233Q8×C43—24no—
234Q8×C43—42no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×SD1612yes—
243C2×C4×C43C2×Q1612yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—41no—
251C2×Dic43#10314yes—
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—44no—
267C4×D43—44no—
268C4×D43#10314yes—
269C4×D43#10314yes—
270C4×D43C2×SD1612yes—
271C4×D43C2×SD1612yes—
272C4×D43C2×Q1612yes—
273C4×D43C2×Q1612yes—
274Dic86—24no—
275Dic86—44no—
276Dic86—42no—
277Dic86—44no—
278C8×C43—42no—
279C8×C43—42no—
280C43⋊C8—42no—
281C43⋊C8—42no—
282#17486—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43C2×#10312yes—
286C22×C43C22×C22⋊C411yescharacteristic
287C2×D43—21no—
288C2×D43—21no—
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—44no—
292C2×D43C2×#10312yes—
293C2×D43C2×#10312yes—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43C2×#10312yes—
300C4×C43#56812yes—
301C4×C43C22×SD1611yescharacteristic
302C4×C43C22×Q1611yescharacteristic
303Dic43—21no—
304Dic43—21no—
305Dic43—21no—
306Dic43—42no—
307Dic43—42no—
308Dic43C2×#10312yes—
309Dic43C2×#10312yes—
310Dic43#42112yes—
311C2×#533—431no—
312C2×#431—431no—
313C2×#423—431no—
314#1493—434no—
315#1487—434no—
316#1481—431no—
317#1481—431no—
318#1481—431no—
319#1481D4311yescharacteristic, complemented
320C2×C43—22no—
321C2×C43#287911yescharacteristic
322C2×C43C22×#10311yescharacteristic
323C2×C43C2×#42111yescharacteristic
324D43—22no—
325D43—22no—
326C22×M16—861no—
327#533—431no—
328#533—431no—
329#533—432no—
330#533—432no—
331#533—431no—
332#533—861no—
333#533—861no—
334#533—861no—
335#533—861no—
336#533C2×D4311yescharacteristic
337C2×C4⋊Q8—431no—
338C2×C4⋊Q8—431no—
339C2×#125—861no—
340C2×C22⋊Q8—432no—
341C2×C22⋊Q8—861no—
342C2×C4×Q8—432no—
343C2×C4×Q8—861no—
344C2×#117—861no—
345C22×C42—431no—
346#431—431no—
347#431—432no—
348#431—861no—
349#431—861no—
350#431C2×D4311yescharacteristic
351#423—432no—
352#423—432no—
353#423—861no—
354#423—861no—
355C2×C4⋊C8—431no—
356C2×C4⋊C8—861no—
357C2×C4⋊C8—861no—
358C2×C4⋊C8C2×D4311yescharacteristic
359C2×C22⋊C8—861no—
360C2×C4×C8—432no—
361Q8⋊C8—434no—
362Q8⋊C8—434no—
363Q8⋊C8—434no—
364Q8⋊C8C2×D4314yescomplemented
365C43#1748611yescharacteristic, complemented, Sylow
366C22×Q8—432no—
367C22×Q8—861no—
368C23×C4—431no—
369C23×C4—431no—
370C23×C4—431no—
371C2×M16—862no—
372C2×M16—862no—
373C2×M16—1724no—
374C22×C8—21no—
375C22×C8—862no—
376C22×C8—861no—
377C4⋊Q8—432no—
378C4⋊Q8—432no—
379C4⋊Q8—431no—
380C4⋊Q8—431no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8C4×D4311yescharacteristic
386C4⋊Q8C4×D4311yescharacteristic
387#125—21no—
388#125—862no—
389#125—862no—
390#125—861no—
391#125—861no—
392#125—861no—
393C22⋊Q8—21no—
394C22⋊Q8—432no—
395C22⋊Q8—432no—
396C22⋊Q8—432no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404C22⋊Q8C4×D4312yes—
405C4×Q8—21no—
406C4×Q8—432no—
407C4×Q8—432no—
408C4×Q8—432no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—861no—
413C4×Q8—862no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8C22×D4312yes—
417#117—21no—
418#117—862no—
419#117—862no—
420#117—861no—
421#117—861no—
422#117—861no—
423C2×C4⋊C4—432no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—861no—
429C2×C22⋊C4—862no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—862no—
442C2×C42C22×D4311yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—432no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C4⋊C8—862no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8C22×D4312yes—
452C22⋊C8—21no—
453C22⋊C8—862no—
454C22⋊C8—861no—
455C4×C8—432no—
456C4×C8—862no—
457C4×C8C22×D4312yes—
458C24—431no—
459C2×Q8—21no—
460C2×Q8—432no—
461C2×Q8—862no—
462C2×Q8—862no—
463C2×Q8—861no—
464C2×Q8—1724no—
465C2×Q8—1724no—
466C2×Q8C2×C4×D4312yes—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—434no—
471C22×C4—434no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—1722no—
487C22×C4—1722no—
488C22×C4C2×C4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491M16—1724no—
492M16—1724no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—42no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—1724no—
499C2×C8—1722no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—432no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—862no—
517C4⋊C4—861no—
518C4⋊C4—862no—
519C4⋊C4C2×C4×D4312yes—
520C22⋊C4—22no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C42—22no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—862no—
538C42—862no—
539C42—862no—
540C42C2×C4×D4311yescharacteristic
541C42D4×D4311yescharacteristic
542C42D4×D4311yescharacteristic
543C42C23×D4311yescharacteristic
544C23—431no—
545C23—431no—
546C23—434no—
547C23—1721no—
548C23—1721no—
549C23C22⋊C4×D4311yescharacteristic
550Q8—24no—
551Q8—42no—
552Q8—864no—
553Q8—1722no—
554Q8—1724no—
555Q8—1724no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—431no—
561C2×C4—431no—
562C2×C4—431no—
563C2×C4—434no—
564C2×C4—434no—
565C2×C4—434no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1724no—
585C2×C4—1724no—
586C2×C4—1721no—
587C2×C4C22⋊C4×D4311yescharacteristic
588C2×C4C22⋊C4×D4311yescharacteristic
589C2×C4C22⋊C4×D4311yescharacteristic
590C2×C4SD16×D4312yes—
591C2×C4Q16×D4312yes—
592C2×C4C22×C4×D4311yescharacteristic
593C2×C4C2×D4×D4311yescharacteristic
594C2×C4C2×D4×D4311yescharacteristic
595C8—42no—
596C8—42no—
597C8—1722no—
598C8—1722no—
599C22—21no—
600C22—21no—
601C22—432no—
602C22—432no—
603C22—861no—
604C22—861no—
605C22—861no—
606C22—861no—
607C22—1724no—
608C22#103×D4312yes—
609C22C2×C22⋊C4×D4311yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—432no—
616C4—432no—
617C4—432no—
618C4—861no—
619C4—861no—
620C4—861no—
621C4—1722no—
622C4—1722no—
623C4#103×D4312yes—
624C4#1458366412yes—
625C4C2×SD16×D4311yescharacteristic
626C4C2×Q16×D4311yescharacteristic
627C2—22no—
628C2—862no—
629C2—862no—
630C2#1914303711yescharacteristic
631C2C2×#103×D4311yescharacteristic
632C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1481C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1481D43
hypocenterC43#17486
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. #19133048C2semidirect
5. #19133022C2semidirect
6. #19132999C2semidirect
7. #19132998C2semidirect
8. #19132997C2semidirect
9. C43×#1481C2semidirect
42. #14582631C22semidirect
43. Q8⋊(C43⋊C8)C22semidirect
44. #14582629C22semidirect
48. C43×Q8⋊C8C22semidirect
319. #1481D43semidirect
364. Q8⋊C8C2×D43semidirect
365. C43#17486semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#431×D432
C2×#145829212
#191330482
#191330222
#191329992
#191329982
#191329972
C43×#14812
#1748643