Finite Group Databasebeta

← #25063298

Subgroups — #25063298

Order 11008.

1026 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic
3#423×D43C211yesmaximal, characteristic
4#19133048C214yesmaximal, complemented
5#19133025C211yesmaximal, characteristic, complemented
6#19133024C211yesmaximal, characteristic, complemented
7#19133023C211yesmaximal, characteristic, complemented
8#19132996C214yesmaximal, complemented
9C43×#1487C211yesmaximal, characteristic, complemented
10C2×M16×D43—21no—
11#14583453—21no—
12#14583453—21no—
13#14583453—21no—
14#14583453—21no—
15#14583453C412yes—
16#14583453C412yes—
17#14583453C2212yes—
18#14583453C2212yes—
19C2×#13063324C411yescharacteristic
20C2×#13063323C411yescharacteristic
21C2×#13063315—21no—
22C2×#13063305C411yescharacteristic
23C2×#13063303—21no—
24C2×#13063301C411yescharacteristic
25C2×C4×Dic86—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×#13063282—21no—
28C2×C42×D43C2211yescharacteristic
29#14582952C2211yescharacteristic
30#14582951—21no—
31#14582950C2212yes—
32#14582949—21no—
33#14582923C2211yescharacteristic
34#14582922—21no—
35#14582921—21no—
36#14582921C2212yes—
37C4⋊C8×D43—21no—
38C4⋊C8×D43—21no—
39C4⋊C8×D43C2212yes—
40C22⋊C8×D43—21no—
41C4×C8×D43C2212yes—
42#14582631C2214yescomplemented
43Q8⋊(C43⋊C8)C2214yescomplemented
44#14582629C2214yescomplemented
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#423C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C22×Dic86—21no—
50C22×Dic86C2×C411yescharacteristic
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621872—22no—
56M16×D43—44no—
57C2×C8×D43—22no—
58C2×C8×D43—22no—
59#13063324—21no—
60#13063324—21no—
61#13063324C2×C412yes—
62#13063324C2×C412yes—
63#13063323—21no—
64#13063323—21no—
65#13063323C2×C412yes—
66#13063323C2×C412yes—
67#13063315—22no—
68#13063315—22no—
69#13063315—22no—
70#13063315—22no—
71#13063305—21no—
72#13063305—21no—
73#13063305C2×C412yes—
74#13063305C2×C412yes—
75#13063303—22no—
76#13063303—22no—
77#13063303—22no—
78#13063303—22no—
79#13063301—21no—
80#13063301—21no—
81#13063301C2×C412yes—
82#13063301C2×C412yes—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86C2×C412yes—
90C4×Dic86C2312yes—
91#13063282—22no—
92#13063282—22no—
93#13063282—22no—
94#13063282—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
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×Q8×C43C2×C411yescharacteristic
127C2×M16×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2×C412yes—
131C4×Q8×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C42×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×C43—42no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43SD1614yes—
164C2×C4×D43Q1614yes—
165C2×C4×D43C22×C411yescharacteristic
166C2×C4×D43C22×C411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—42no—
175C2×Dic86—44no—
176C2×Dic86C22×C412yes—
177M16×C43—42no—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43C22×C412yes—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2411yescharacteristic
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
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—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222#10621877—42no—
223C2×C43⋊C8—22no—
224C2×C43⋊C8—22no—
225#10621872—44no—
226C8×D43—44no—
227C8×D43—44no—
228C23×C43C2×C22⋊C411yescharacteristic
229C22×D43—41no—
230C22×D43—41no—
231C22×D43#10314yes—
232C22×D43C2×C22⋊C411yescharacteristic
233C22×D43C2×C22⋊C411yescharacteristic
234Q8×C43—24no—
235Q8×C43—42no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×SD1612yes—
246C2×C4×C43C2×Q1612yes—
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43#10314yes—
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43#10314yes—
272C4×D43#10314yes—
273C4×D43C2×SD1612yes—
274C4×D43C2×SD1612yes—
275C4×D43C2×Q1612yes—
276C4×D43C2×Q1612yes—
277Dic86—24no—
278Dic86—44no—
279Dic86—42no—
280Dic86—44no—
281C8×C43—42no—
282C8×C43—42no—
283C43⋊C8—42no—
284C43⋊C8—42no—
285#17486—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43C2×#10312yes—
289C22×C43C22×C22⋊C411yescharacteristic
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—44no—
295C2×D43C2×#10312yes—
296C2×D43C2×#10312yes—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—42no—
301C4×C43—42no—
302C4×C43C2×#10312yes—
303C4×C43#56812yes—
304C4×C43C22×SD1611yescharacteristic
305C4×C43C22×Q1611yescharacteristic
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—42no—
310Dic43—42no—
311Dic43C2×#10312yes—
312Dic43C2×#10312yes—
313Dic43#42112yes—
314C2×#533—431no—
315C2×#431—431no—
316C2×#423—431no—
317#1493—434no—
318#1487—431no—
319#1487—431no—
320#1487—431no—
321#1487D4311yescharacteristic, complemented
322#1481—434no—
323C2×C43—22no—
324C2×C43#287911yescharacteristic
325C2×C43C22×#10311yescharacteristic
326C2×C43C2×#42111yescharacteristic
327D43—22no—
328D43—22no—
329C22×M16—861no—
330#533—432no—
331#533—432no—
332#533—432no—
333#533—432no—
334#533—861no—
335#533—861no—
336#533—861no—
337#533—861no—
338C2×C4⋊Q8—431no—
339C2×C4⋊Q8—431no—
340C2×#125—861no—
341C2×C22⋊Q8—431no—
342C2×C22⋊Q8—431no—
343C2×C22⋊Q8—861no—
344C2×C4×Q8—431no—
345C2×C4×Q8—861no—
346C2×C4×Q8C2×D4311yescharacteristic
347C2×#117—861no—
348C22×C42—431no—
349#431—431no—
350#431—432no—
351#431—861no—
352#431—861no—
353#431C2×D4311yescharacteristic
354#423—431no—
355#423—432no—
356#423—861no—
357#423—861no—
358#423C2×D4311yescharacteristic
359C2×C4⋊C8—432no—
360C2×C4⋊C8—861no—
361C2×C4⋊C8—861no—
362C2×C22⋊C8—861no—
363C2×C4×C8—432no—
364Q8⋊C8—434no—
365Q8⋊C8—434no—
366Q8⋊C8—434no—
367Q8⋊C8C2×D4314yescomplemented
368C43#1748611yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×Q8—861no—
371C22×Q8C4×D4311yescharacteristic
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C2×M16—21no—
376C2×M16—862no—
377C2×M16—861no—
378C2×M16—1724no—
379C22×C8—862no—
380C22×C8—862no—
381C4⋊Q8—432no—
382C4⋊Q8—432no—
383C4⋊Q8—432no—
384C4⋊Q8—432no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389#125—862no—
390#125—862no—
391#125—862no—
392#125—862no—
393C22⋊Q8—432no—
394C22⋊Q8—432no—
395C22⋊Q8—432no—
396C22⋊Q8—432no—
397C22⋊Q8—861no—
398C22⋊Q8—861no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—432no—
408C4×Q8—432no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—862no—
412C4×Q8—862no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8C4×D4312yes—
416C4×Q8C22×D4312yes—
417#117—862no—
418#117—862no—
419#117—862no—
420#117—862no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4C4×D4311yescharacteristic
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—21no—
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—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42C22×D4311yescharacteristic
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—432no—
449C4⋊C8—862no—
450C4⋊C8—862no—
451C4⋊C8—862no—
452C4⋊C8—861no—
453C4⋊C8—861no—
454C4⋊C8C22×D4312yes—
455C22⋊C8—21no—
456C22⋊C8—862no—
457C22⋊C8—861no—
458C4×C8—432no—
459C4×C8—862no—
460C4×C8C22×D4312yes—
461C24—431no—
462C2×Q8—21no—
463C2×Q8—42no—
464C2×Q8—432no—
465C2×Q8—862no—
466C2×Q8—862no—
467C2×Q8—861no—
468C2×Q8—1722no—
469C2×Q8—1724no—
470C2×Q8C2×C4×D4312yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—434no—
477C22×C4—434no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4C2×C4×D4311yescharacteristic
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497M16—42no—
498M16—1724no—
499M16—1722no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—862no—
503C2×C8—862no—
504C2×C8—1724no—
505C2×C8—1724no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—432no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C42—22no—
529C42—22no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—862no—
543C42—862no—
544C42C2×C4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42C23×D4311yescharacteristic
548C23—431no—
549C23—431no—
550C23—434no—
551C23—1721no—
552C23—1721no—
553C23C22⋊C4×D4311yescharacteristic
554Q8—24no—
555Q8—42no—
556Q8—864no—
557Q8—1722no—
558Q8—1724no—
559Q8—1724no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—431no—
567C2×C4—431no—
568C2×C4—431no—
569C2×C4—434no—
570C2×C4—434no—
571C2×C4—434no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—432no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1722no—
592C2×C4—1722no—
593C2×C4C22⋊C4×D4311yescharacteristic
594C2×C4C22⋊C4×D4311yescharacteristic
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4SD16×D4312yes—
597C2×C4Q16×D4312yes—
598C2×C4C22×C4×D4311yescharacteristic
599C2×C4C2×D4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C8—42no—
602C8—42no—
603C8—1722no—
604C8—1722no—
605C22—21no—
606C22—21no—
607C22—432no—
608C22—432no—
609C22—861no—
610C22—861no—
611C22—861no—
612C22—861no—
613C22—1724no—
614C22#103×D4312yes—
615C22C2×C22⋊C4×D4311yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—42no—
621C4—432no—
622C4—432no—
623C4—432no—
624C4—861no—
625C4—861no—
626C4—861no—
627C4—1722no—
628C4—1722no—
629C4#103×D4312yes—
630C4#1458366512yes—
631C4C2×SD16×D4311yescharacteristic
632C4C2×Q16×D4311yescharacteristic
633C2—22no—
634C2—862no—
635C2—862no—
636C2#1914303811yescharacteristic
637C2C2×#103×D4311yescharacteristic
638C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1487C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1487D43
hypocenterC43#17486
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #19133048C2semidirect
5. #19133025C2semidirect
6. #19133024C2semidirect
7. #19133023C2semidirect
8. #19132996C2semidirect
9. C43×#1487C2semidirect
42. #14582631C22semidirect
43. Q8⋊(C43⋊C8)C22semidirect
44. #14582629C22semidirect
48. C43×Q8⋊C8C22semidirect
321. #1487D43semidirect
367. Q8⋊C8C2×D43semidirect
368. C43#17486semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
#431×D432
#423×D432
#191330482
#191330252
#191330242
#191330232
#191329962
C43×#14872
#1748643