Finite Group Databasebeta

← #25063778

Subgroups — #25063778

Order 11008.

1084 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
1#533×D43C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic
3#19136934C211yesmaximal, characteristic
4#19133113C214yesmaximal
5#19133108C211yesmaximal, characteristic, complemented
6#19133107C211yesmaximal, characteristic, complemented
7#19133106C211yesmaximal, characteristic, complemented
8#19133092C214yesmaximal, complemented
9C43×#1506C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583455—21no—
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583453—21no—
15#14583453C412yescomplemented
16#14583452—21no—
17#14583451—21no—
18#14583451C2212yes—
19C4⋊Q8×D43C411yescharacteristic, complemented
20C4⋊Q8×D43C411yescharacteristic, complemented
21#125×D43—21no—
22C22⋊Q8×D43—21no—
23C22⋊Q8×D43C2212yes—
24C4×Q8×D43—21no—
25C4×Q8×D43C412yescomplemented
26C2×#13063282—21no—
27#117×D43—21no—
28C2×C42×D43C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582954—21no—
31#14582951—21no—
32#14582949C2212yes—
33#14582921—21no—
34#14582861C2212yes—
35#14582851—21no—
36#14582750—21no—
37#14582750C2212yes—
38#14582746—21no—
39#14582746C2212yes—
40#14582745C2211yescharacteristic
41C42×Dic43—21no—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C43×#533C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#376C2211yescharacteristic
48C43×#328C2214yes—
49C2×Q8×D43—21no—
50C2×Q8×D43C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621872—22no—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063324—21no—
58#13063324—21no—
59#13063324—21no—
60#13063324C2×C412yes—
61#13063323—21no—
62#13063323C2×C412yes—
63#13063317—21no—
64#13063316—21no—
65#13063316—21no—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305C2×C412yes—
70#13063304—21no—
71#13063304C2312yes—
72#13063303—22no—
73#13063303—22no—
74#13063302—22no—
75#13063302—22no—
76#13063301—21no—
77#13063301C2×C412yes—
78Q8×Dic43—21no—
79Q8×Dic43C2×C412yes—
80C4×Dic86—21no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86C2×C412yes—
84#13063290—21no—
85#13063290—22no—
86#13063290—22no—
87#13063290C2×C412yes—
88#13063284—21no—
89#13063283—21no—
90#13063283—21no—
91#13063282—28no—
92#13063282—22no—
93#13063281—22no—
94C2×Dic43⋊C4—22no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43—22no—
100C4⋊C4×D43C2×C412yes—
101C2×(C2×D43)⋊C4—22no—
102C22⋊C4×D43—22no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—22no—
110C42×D43C2×C411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C4⋊(C43⋊C8)—21no—
119Dic43⋊C8—22no—
120C22⋊(C43⋊C8)C2312yes—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123C8×Dic43—22no—
124C43⋊#95—21no—
125C43⋊#95C2312yes—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2312yes—
131C4×Q8×C43—21no—
132C4×Q8×C43C2×C412yes—
133#117×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138#97×C43—21no—
139#95×C43—21no—
140#95×C43C2312yes—
141C23×D43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—22no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—22no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152Q8×D43—44no—
153Q8×D43—44no—
154C2×C4×D43—24no—
155C2×C4×D43—24no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—42no—
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22×C411yescharacteristic
168C2×C4×D43C22×C411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86C22×C412yes—
175C2×C8×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43C22×C412yes—
182C22⋊C4×C43—22no—
183C42×C43—24no—
184C42×C43—22no—
185C42×C43C22×C411yescharacteristic
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C22⋊Dic43—22no—
190(C2×D43)⋊C4—28no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198C4⋊Dic43C22×C412yes—
199Dic43⋊C4—28no—
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—24no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—44no—
213C4×Dic43—44no—
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×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C2×C43⋊C8—22no—
227#10621872—44no—
228C23×C43C22×D411yescharacteristic
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—41no—
232C22×D43C2×C22⋊C411yescharacteristic
233C22×D43C2×C22⋊C411yescharacteristic
234Q8×C43—42no—
235Q8×C43—42no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—24no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—41no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43#13714yes—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—44no—
276C4×D43—44no—
277C4×D43#10414yes—
278Dic86—42no—
279Dic86—44no—
280Dic86—44no—
281Dic86—42no—
282C8×C43—42no—
283C43⋊C8—42no—
284#17545—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43C22×C22⋊C411yescharacteristic
288C22×C43C2×#13712yes—
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—44no—
295C2×D43C2×#10412yes—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—44no—
302C4×C43—42no—
303C4×C43—42no—
304C4×C43C2×#10412yes—
305Dic43—21no—
306Dic43—21no—
307Dic43—44no—
308Dic43—42no—
309Dic43—42no—
310Dic43#41012yes—
311Dic43#41912yes—
312Dic43#41912yes—
313Dic43C2×#10412yes—
314C2×#533—431no—
315#2920—431no—
316C4×#117—431no—
317#1508—434no—
318#1506—431no—
319#1506—431no—
320#1506—431no—
321#1506D4311yescharacteristic, complemented
322#1503—434no—
323C2×C43—22no—
324C2×C43C2×#41011yescharacteristic
325C2×C43C2×#41911yescharacteristic
326C2×C43C22×#10411yescharacteristic
327D43—22no—
328D43—41no—
329#533—431no—
330#533—431no—
331#533—432no—
332#533—432no—
333#533—431no—
334#533—861no—
335#533—861no—
336#533—861no—
337#533—861no—
338#533C2×D4311yescharacteristic
339C2×C4⋊Q8—431no—
340C2×C4⋊Q8—431no—
341C2×#125—861no—
342C2×C22⋊Q8—432no—
343C2×C22⋊Q8—861no—
344C2×C4×Q8—432no—
345C2×C4×Q8—861no—
346C2×#117—861no—
347C2×#117—861no—
348C22×C42—431no—
349#432—431no—
350#432—861no—
351#432C2×D4311yescharacteristic
352#431—432no—
353#431—861no—
354#423—861no—
355#407—432no—
356C4×M16—861no—
357C4×C4⋊C4—432no—
358C4×C4⋊C4—861no—
359C4×C22⋊C4—432no—
360C4×C22⋊C4—861no—
361#376—431no—
362#376C2×D4311yescharacteristic
363C43—861no—
364#328—434no—
365#328—434no—
366#328—434no—
367#328C2×D4314yes—
368C43#1754511yescharacteristic, complemented, Sylow
369C22×Q8—432no—
370C22×Q8—861no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—431no—
374C2×M16—862no—
375C4⋊Q8—432no—
376C4⋊Q8—432no—
377C4⋊Q8—431no—
378C4⋊Q8—431no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8C4×D4311yescharacteristic
384C4⋊Q8C4×D4311yescharacteristic
385#125—21no—
386#125—862no—
387#125—862no—
388#125—861no—
389#125—861no—
390#125—861no—
391C22⋊Q8—21no—
392C22⋊Q8—432no—
393C22⋊Q8—432no—
394C22⋊Q8—432no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402C22⋊Q8C22×D4312yes—
403C4×Q8—21no—
404C4×Q8—432no—
405C4×Q8—432no—
406C4×Q8—432no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×Q8—861no—
411C4×Q8—862no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8C4×D4312yes—
415#117—21no—
416#117—862no—
417#117—868no—
418#117—862no—
419#117—861no—
420#117—861no—
421#117—861no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—862no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—862no—
431C2×C42—21no—
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—431no—
442C2×C42—431no—
443C2×C42—862no—
444C2×C42—861no—
445C2×C42—862no—
446C2×C42—862no—
447C2×C42C22×D4311yescharacteristic
448C4⋊C8—21no—
449C4⋊C8—862no—
450C4⋊C8—861no—
451C22⋊C8—432no—
452C22⋊C8—862no—
453C22⋊C8C22×D4312yes—
454#97—21no—
455#97—861no—
456C4×C8—862no—
457#95—21no—
458#95—432no—
459#95—861no—
460#95C22×D4312yes—
461C24—431no—
462C2×Q8—21no—
463C2×Q8—432no—
464C2×Q8—862no—
465C2×Q8—862no—
466C2×Q8—861no—
467C2×Q8—1724no—
468C2×Q8—1724no—
469C2×Q8C2×C4×D4312yes—
470C22×C4—22no—
471C22×C4—431no—
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—431no—
485C22×C4—431no—
486C22×C4—864no—
487C22×C4—864no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—1722no—
492C22×C4D4×D4311yescharacteristic
493C22×C4D4×D4311yescharacteristic
494C22×C4C23×D4311yescharacteristic
495M16—1724no—
496C2×C8—22no—
497C2×C8—862no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—432no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—868no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—862no—
516C4⋊C4—861no—
517C4⋊C4—862no—
518C4⋊C4C2×C4×D4312yes—
519C22⋊C4—22no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—868no—
523C22⋊C4—862no—
524C42—24no—
525C42—22no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—862no—
539C42—862no—
540C42—864no—
541C42—862no—
542C42—1724no—
543C42—1724no—
544C42C2×C4×D4311yescharacteristic
545C42C2×C4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42D4×D4311yescharacteristic
548C23—431no—
549C23—431no—
550C23—862no—
551C23—862no—
552C23—1721no—
553C23C2×D4×D4311yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—1722no—
557Q8—1724no—
558Q8—1724no—
559Q8—1722no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—431no—
569C2×C4—431no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—434no—
573C2×C4—434no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—864no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1724no—
593C2×C4—1724no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4C22⋊C4×D4311yescharacteristic
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C8—42no—
603C8—1722no—
604C22—21no—
605C22—21no—
606C22—432no—
607C22—861no—
608C22—861no—
609C22—861no—
610C22—861no—
611C22—861no—
612C22—1724no—
613C22C2×C22⋊C4×D4311yescharacteristic
614C22#137×D4312yes—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—44no—
621C4—42no—
622C4—42no—
623C4—432no—
624C4—432no—
625C4—432no—
626C4—432no—
627C4—861no—
628C4—861no—
629C4—1724no—
630C4—1722no—
631C4—1722no—
632C4#104×D4312yes—
633C2—22no—
634C2—862no—
635C2—1721no—
636C2#410×D4311yescharacteristic
637C2#419×D4311yescharacteristic
638C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1506C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1506D43
hypocenterC43#17545
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
5. #19133108C2semidirect
6. #19133107C2semidirect
7. #19133106C2semidirect
8. #19133092C2semidirect
9. C43×#1506C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
15. #14583453C4semidirect
19. C4⋊Q8×D43C4semidirect
20. C4⋊Q8×D43C4semidirect
25. C4×Q8×D43C4semidirect
321. #1506D43semidirect
368. C43#17545semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191432252
#191369342
#191331132
#191331082
#191331072
#191331062
#191330922
C43×#15062
#1754543