Finite Group Databasebeta

← #25063776

Subgroups — #25063776

Order 11008.

1084 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic
3C4×#13063281C211yesmaximal, characteristic
4#19133116C211yesmaximal, characteristic
5#19133115C211yesmaximal, characteristic
6#19133114C211yesmaximal, characteristic
7#19133105C214yesmaximal, complemented
8#19133092C214yesmaximal, complemented
9C43×#1508C211yesmaximal, characteristic
10#14583451—21no—
11#14583451—21no—
12#14583451—21no—
13#14583451—21no—
14#14583451C412yescomplemented
15#14583451C412yescomplemented
16#14583451C2212yes—
17#14583451C2212yes—
18C2×#13063324C411yescharacteristic, complemented
19C2×#13063323C411yescharacteristic, complemented
20C2×#13063315—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063302—21no—
23C2×Q8×Dic43C411yescharacteristic, complemented
24C2×#13063290—21no—
25C2×#13063290C411yescharacteristic, complemented
26C2×#13063281—21no—
27C2×#13063281—21no—
28C22×C4×Dic43C2211yescharacteristic
29#14582953—21no—
30#14582953C2212yes—
31#14582949—21no—
32#14582949C2212yes—
33#14582922—21no—
34#14582863C2211yescharacteristic
35M16×Dic43—21no—
36C4×Dic43⋊C4—21no—
37#14582750C2212yes—
38C22⋊C4×Dic43—21no—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582744C2212yes—
41C42×Dic43—21no—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C2×C22⋊Q8×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#328C2214yes—
49C22×Dic86—21no—
50C22×Dic86C2×C411yescharacteristic
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C2×#10621877—21no—
54#13063324—21no—
55#13063324—21no—
56#13063324C2×C412yes—
57#13063324C2×C412yes—
58#13063323—21no—
59#13063323—21no—
60#13063323C2×C412yes—
61#13063323C2×C412yes—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063315—22no—
66#13063304—21no—
67#13063304—21no—
68#13063304C2×C412yes—
69#13063304C2312yes—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73#13063302—22no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76Q8×Dic43C2×C412yes—
77Q8×Dic43C2×C412yes—
78#13063290—22no—
79#13063290—22no—
80#13063290—21no—
81#13063290—21no—
82#13063290—22no—
83#13063290—22no—
84#13063290C2×C412yes—
85#13063290C2×C412yes—
86#13063281—28no—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90#13063281—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—22no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43C2×C411yescharacteristic
109C2×C4×Dic43C2×C411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43D411yescharacteristic
113C2×C4×Dic43D411yescharacteristic
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)C2312yes—
122#13063235—22no—
123C8×Dic43—22no—
124C43⋊#95—22no—
125C43⋊#95C2312yes—
126C22×Q8×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C2×M16×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43C2×C412yes—
132C22⋊Q8×C43C2312yes—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C42×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43C2312yes—
140#95×C43C2312yes—
141C24×C43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—42no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—42no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—24no—
156C22×Dic43—24no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—22no—
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C22×Dic43C22⋊C411yescharacteristic
163C22×Dic43C22⋊C411yescharacteristic
164C22×Dic43C22⋊C411yescharacteristic
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C2×Dic86—21no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—44no—
176C2×Dic86—42no—
177C2×Dic86C22×C412yes—
178M16×C43—42no—
179C2×C8×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C42×C43—42no—
188C22⋊Dic43—24no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C4⋊Dic43—21no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—28no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
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—28no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—42no—
212C4×Dic43—44no—
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C22×C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229#10621877—42no—
230C2×C43⋊C8—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43C2×C22⋊C411yescharacteristic
235C23×C43C2×C22⋊C411yescharacteristic
236C23×C43C22×D411yescharacteristic
237Q8×C43—42no—
238Q8×C43—42no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—24no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—24no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43#10414yes—
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43#13714yes—
283Dic86—42no—
284Dic86—44no—
285Dic86—44no—
286Dic86—42no—
287C8×C43—42no—
288C43⋊C8—42no—
289#17545—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—44no—
298C22×C43C2×#10412yes—
299C22×C43C22×C22⋊C411yescharacteristic
300C22×C43C2×#13712yes—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—44no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43#41012yes—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—44no—
313Dic43—42no—
314Dic43—42no—
315Dic43#41912yes—
316Dic43#41912yes—
317Dic43C2×#10412yes—
318Dic43C2×#10412yes—
319C2×#533—431no—
320#2920—431no—
321C4×#117—431no—
322#1508—431no—
323#1508—431no—
324#1508—431no—
325#1508D4311yescharacteristic
326#1506—434no—
327#1503—434no—
328C2×C43—22no—
329C2×C43—22no—
330C2×C43—41no—
331C2×C43C2×#41011yescharacteristic
332C2×C43C2×#41911yescharacteristic
333C2×C43C22×#10411yescharacteristic
334#533—432no—
335#533—432no—
336#533—432no—
337#533—432no—
338#533—861no—
339#533—861no—
340#533—861no—
341#533—861no—
342C2×C4⋊Q8—431no—
343C2×C4⋊Q8—431no—
344C2×#125—861no—
345C2×C22⋊Q8—431no—
346C2×C22⋊Q8—861no—
347C2×C22⋊Q8C2×D4311yescharacteristic
348C2×C4×Q8—431no—
349C2×C4×Q8—431no—
350C2×C4×Q8—861no—
351C2×#117—861no—
352C2×#117—861no—
353C22×C42—431no—
354#432—432no—
355#432—861no—
356#431—432no—
357#431—861no—
358#423—861no—
359#407—431no—
360#407C2×D4311yescharacteristic
361C4×M16—861no—
362C4×C4⋊C4—432no—
363C4×C4⋊C4—861no—
364C4×C22⋊C4—431no—
365C4×C22⋊C4—861no—
366C4×C22⋊C4C2×D4311yescharacteristic
367#376—432no—
368C43—861no—
369#328—434no—
370#328—434no—
371#328—434no—
372#328C2×D4314yes—
373C43#1754511yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×Q8—861no—
376C22×Q8C4×D4311yescharacteristic
377C23×C4—431no—
378C23×C4—431no—
379C23×C4C22×D4311yescharacteristic
380C2×M16—21no—
381C2×M16—861no—
382C4⋊Q8—432no—
383C4⋊Q8—432no—
384C4⋊Q8—432no—
385C4⋊Q8—432no—
386C4⋊Q8—861no—
387C4⋊Q8—861no—
388C4⋊Q8—861no—
389C4⋊Q8—861no—
390#125—862no—
391#125—862no—
392#125—862no—
393#125—862no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—432no—
397C22⋊Q8—432no—
398C22⋊Q8—862no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404C22⋊Q8C4×D4312yes—
405C22⋊Q8C22×D4312yes—
406C4×Q8—432no—
407C4×Q8—432no—
408C4×Q8—432no—
409C4×Q8—432no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—861no—
417C4×Q8—861no—
418#117—862no—
419#117—862no—
420#117—862no—
421#117—862no—
422#117—868no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C4×D4311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—21no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42—862no—
453C2×C42—862no—
454C2×C42—861no—
455C4⋊C8—862no—
456C4⋊C8—862no—
457C22⋊C8—21no—
458C22⋊C8—432no—
459C22⋊C8—861no—
460C22⋊C8C22×D4312yes—
461#97—862no—
462C4×C8—862no—
463#95—432no—
464#95—862no—
465#95C22×D4312yes—
466C24D4×D4311yescharacteristic
467C2×Q8—21no—
468C2×Q8—42no—
469C2×Q8—432no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8—861no—
473C2×Q8—1722no—
474C2×Q8—1724no—
475C2×Q8C2×C4×D4312yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—42no—
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—431no—
491C22×C4—431no—
492C22×C4—864no—
493C22×C4—864no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—862no—
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4C2×C4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500C22×C4D4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4C23×D4311yescharacteristic
503M16—42no—
504M16—1722no—
505C2×C8—22no—
506C2×C8—862no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—432no—
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—862no—
521C4⋊C4—868no—
522C4⋊C4—861no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4C2×C4×D4312yes—
526C22⋊C4—24no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—864no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C42—42no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—862no—
550C42—862no—
551C42—862no—
552C42—862no—
553C42—868no—
554C42—1722no—
555C42—1724no—
556C23—22no—
557C23—22no—
558C23—41no—
559C23C22⋊C4×D4311yescharacteristic
560C23C22⋊C4×D4311yescharacteristic
561C23C2×D4×D4311yescharacteristic
562Q8—42no—
563Q8—42no—
564Q8—1722no—
565Q8—1724no—
566Q8—1724no—
567Q8—1722no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—431no—
585C2×C4—434no—
586C2×C4—434no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—864no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4C22⋊C4×D4311yescharacteristic
609C2×C4C22⋊C4×D4311yescharacteristic
610C2×C4C22×C4×D4311yescharacteristic
611C2×C4C2×D4×D4311yescharacteristic
612C8—42no—
613C8—1722no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—44no—
622C22#104×D4312yes—
623C22C2×C22⋊C4×D4311yescharacteristic
624C22#137×D4312yes—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—44no—
629C4—42no—
630C4—42no—
631C4—432no—
632C4—432no—
633C4—432no—
634C4—432no—
635C4—861no—
636C4—861no—
637C4—861no—
638C4—861no—
639C4—1724no—
640C4—1722no—
641C4—1722no—
642C4#1458287112yes—
643C2—22no—
644C2—22no—
645C2—41no—
646C2C2×#1458287111yescharacteristic
647C2#419×D4311yescharacteristic
648C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1508C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1508D43
hypocenterC43#17545
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
7. #19133105C2semidirect
8. #19133092C2semidirect
14. #14583451C4semidirect
15. #14583451C4semidirect
18. C2×#13063324C4semidirect
19. C2×#13063323C4semidirect
23. C2×Q8×Dic43C4semidirect
25. C2×#13063290C4semidirect
373. C43#17545semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
#191432242
C4×#130632812
#191331162
#191331152
#191331142
#191331052
#191330922
C43×#15082
#1754543