Finite Group Databasebeta

← #25063705

Subgroups — #25063705

Order 11008.

1128 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic, complemented
3C4×#13063283C211yesmaximal, characteristic, complemented
4#19133095C211yesmaximal, characteristic, complemented
5#19133093C211yesmaximal, characteristic, complemented
6#19133090C211yesmaximal, characteristic, complemented
7#19133083C214yesmaximal, complemented
8#19133078C214yesmaximal, complemented
9C43×#1502C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583454C411yescharacteristic, complemented
12#14583454C411yescharacteristic, complemented
13#14583447C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583431—21no—
16#14583431C412yescomplemented
17#14583430—21no—
18#14583430C2212yes—
19#14583428—21no—
20#14583428—21no—
21#14583409—21no—
22#14583409C2212yes—
23#14583406—21no—
24#41×Dic43—21no—
25C4×#10621900—21no—
26C4×#10621900C412yescomplemented
27C2×#13063283—21no—
28C2×C42×D43C2211yescharacteristic
29#14582952C2211yescharacteristic
30#14582951—21no—
31#14582950—21no—
32#14582949C2212yes—
33C4⋊C8×D43—21no—
34C22⋊C8×D43C2212yes—
35C4×C8×D43—21no—
36C4⋊C4×Dic43—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38C4×(C2×D43)⋊C4—21no—
39#14582746C2212yes—
40#14582744C2212yes—
41C42×Dic43—21no—
42#14582637C2214yes—
43#14582635C2214yes—
44#14582633C2214yes—
45C43×#532C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#327C2214yes—
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×C8×D43—22no—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063318—22no—
58#13063318—22no—
59#13063317—21no—
60#13063316—21no—
61#13063316C2×C412yes—
62#13063312—21no—
63#13063312C2×C412yes—
64#13063307—22no—
65#13063307—22no—
66#13063306—22no—
67#13063305—21no—
68#13063305C2×C412yes—
69#13063304—21no—
70#13063304C2312yes—
71#13063301—21no—
72#13063301—21no—
73#13063296—21no—
74#13063296—21no—
75#13063296—21no—
76#13063296C2×C412yes—
77#13063293—22no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86C2×C412yes—
82#13063290—21no—
83#13063290C2×C412yes—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43C2×C412yes—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92(C22⋊D43)⋊C4—22no—
93(C22⋊D43)⋊C4—22no—
94#13063284—21no—
95#13063284—22no—
96#13063283—28no—
97#13063283—21no—
98#13063283C2×C412yes—
99#13063281—22no—
100#13063281—22no—
101C2×C4⋊Dic43—21no—
102C2×(C2×D43)⋊C4—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—22no—
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
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—
122C4×C43⋊C8—21no—
123C8×Dic43—22no—
124C43⋊#95—22no—
125C43⋊#95C2312yes—
126C2×#41×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128#127×C43C2×C411yescharacteristic
129#124×C43—21no—
130#121×C43—21no—
131#121×C43C2312yes—
132C4×D4×C43—21no—
133C4×D4×C43C2×C412yes—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139C4×C8×C43—21no—
140#95×C43C2312yes—
141C23×D43C2×D411yescharacteristic
142#41×C43—42no—
143#41×C43—42no—
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—22no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162#10621900—44no—
163#10621900—44no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—24no—
167C2×C4×D43—42no—
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22×C411yescharacteristic
177C2×C4×D43C22×C411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×C4×D43C2×D411yescharacteristic
180C2×Dic86—21no—
181C2×Dic86C22×C412yes—
182C2×C8×C43—22no—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C42×C43—42no—
189C42×C43C22×C411yescharacteristic
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198(C2×D43)⋊C4—28no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201C4⋊Dic43—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—22no—
206C4⋊Dic43—22no—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212C4×Dic43—28no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—44no—
217C4×Dic43—42no—
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C22×C411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230C2×C43⋊C8—22no—
231C8×D43—44no—
232C23×C43—22no—
233C23×C43C22×D411yescharacteristic
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—22no—
237C22×D43—41no—
238C22×D43C2×C22⋊C411yescharacteristic
239C22×D43C2×C22⋊C411yescharacteristic
240Q8×C43—42no—
241D4×C43—42no—
242D4×C43—42no—
243D4×C43—42no—
244D4×C43—42no—
245D4×C43—42no—
246C2×C4×C43—22no—
247C2×C4×C43—24no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—44no—
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43#13512yes—
258C2×C4×C43#13512yes—
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C22⋊D43—44no—
262C22⋊D43—44no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—24no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—44no—
273C2×Dic43—44no—
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—41no—
290C4×D43—41no—
291C4×D43#10414yes—
292Dic86—42no—
293Dic86—42no—
294C8×C43—42no—
295C43⋊C8—42no—
296#17533—431nomaximal, Sylow
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—42no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43C22×C22⋊C411yescharacteristic
303C22×C43C2×#13511yescharacteristic
304C22×C43C2×#13511yescharacteristic
305C2×D43—21no—
306C2×D43—21no—
307C2×D43—21no—
308C2×D43—21no—
309C2×D43—21no—
310C2×D43—42no—
311C2×D43—42no—
312C2×D43C2×#10412yes—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—44no—
317C4×C43—42no—
318C4×C43#41612yes—
319C4×C43#41612yes—
320C4×C43C2×#10412yes—
321Dic43—21no—
322Dic43—21no—
323Dic43—21no—
324Dic43—21no—
325Dic43—44no—
326Dic43—42no—
327Dic43—42no—
328Dic43#41012yes—
329Dic43C2×#10412yes—
330#3444—431no—
331C2×#431—431no—
332C4×#117—431no—
333#1503—431no—
334#1503—431no—
335#1502—431no—
336#1502D4311yescharacteristic, complemented
337#1501—434no—
338#1500—434no—
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—82no—
342C2×C43C2×#41011yescharacteristic
343C2×C43C2×#41611yescharacteristic
344C2×C43C22×#10411yescharacteristic
345D43—22no—
346D43—41no—
347#533—431no—
348#533—431no—
349#533—431no—
350#532—431no—
351#532—431no—
352#532C2×D4311yescharacteristic
353#529—432no—
354#529—432no—
355#529—861no—
356#529—861no—
357#529—861no—
358#529—861no—
359#525—432no—
360#525—861no—
361#525—861no—
362C4×#41—432no—
363C4×#41—861no—
364C4×#41—861no—
365C2×#117—861no—
366C22×C42—431no—
367#431—431no—
368#431—432no—
369#431—861no—
370#431—861no—
371#431C2×D4311yescharacteristic
372C2×C4⋊C8—861no—
373C2×C22⋊C8—432no—
374C2×C4×C8—861no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—861no—
377C4×C4⋊C4C2×D4311yescharacteristic
378C4×C22⋊C4—432no—
379C4×C22⋊C4—861no—
380#376—432no—
381C43—861no—
382#328—434no—
383#328—434no—
384#327—434no—
385#327C2×D4314yes—
386C43#1753311yescharacteristic, complemented, Sylow
387C2×#41—21no—
388C2×#41—432no—
389C2×#41—861no—
390C23×C4—431no—
391C23×C4—431no—
392C23×C4—431no—
393C22×C8—862no—
394C4⋊Q8—431no—
395C4⋊Q8—431no—
396C4⋊Q8C4×D4311yescharacteristic
397#127C4×D4311yescharacteristic
398#126—862no—
399#126—862no—
400#125—432no—
401#125—861no—
402#125—861no—
403#124—21no—
404#124—432no—
405#124—861no—
406#123—862no—
407#123—862no—
408#123—862no—
409C22⋊Q8—432no—
410C22⋊Q8—432no—
411C22⋊Q8—861no—
412C22⋊Q8—861no—
413C22⋊Q8—861no—
414C22⋊Q8—861no—
415#121—21no—
416#121—432no—
417#121—861no—
418#121—861no—
419#121—861no—
420#121C22×D4312yes—
421#120—862no—
422C4×Q8—432no—
423C4×Q8—432no—
424C4×Q8—861no—
425C4×Q8—861no—
426C4×Q8—861no—
427C4×Q8—861no—
428C4×D4—21no—
429C4×D4—432no—
430C4×D4—861no—
431C4×D4—861no—
432C4×D4—861no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—862no—
438C4×D4—862no—
439C4×D4C4×D4312yes—
440#117—432no—
441#117—862no—
442#117—862no—
443#117—862no—
444#117—861no—
445#117—868no—
446#117—861no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—861no—
449C2×C22⋊C4—862no—
450C2×C42—21no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—862no—
463C2×C42—862no—
464C2×C42—862no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—862no—
469C4⋊C8—861no—
470C22⋊C8—432no—
471C22⋊C8—862no—
472C22⋊C8C22×D4312yes—
473C4×C8—21no—
474C4×C8—862no—
475C4×C8—861no—
476#95—432no—
477#95—862no—
478#95C22×D4312yes—
479C24—431no—
480#41—42no—
481#41—42no—
482#41—1724no—
483#41—1724no—
484C2×Q8—21no—
485C2×Q8—432no—
486C2×Q8—861no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—862no—
491C2×D4—862no—
492C2×D4C2×C4×D4312yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—864no—
511C22×C4—862no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—1722no—
517C22×C4D4×D4311yescharacteristic
518C22×C4D4×D4311yescharacteristic
519C22×C4C23×D4311yescharacteristic
520C2×C8—22no—
521C2×C8—862no—
522C2×C8—1724no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—432no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—864no—
531C4⋊C4—862no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—862no—
536C4⋊C4C2×C4×D4312yes—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—868no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C42—42no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—862no—
561C42—862no—
562C42—868no—
563C42—862no—
564C42—1724no—
565C42—1722no—
566C42C2×C4×D4311yescharacteristic
567C42C2×C4×D4311yescharacteristic
568C42D4×D4311yescharacteristic
569C42D4×D4311yescharacteristic
570C23—22no—
571C23—431no—
572C23—431no—
573C23—862no—
574C23—861no—
575C23—861no—
576C23—1721no—
577C23C2×D4×D4311yescharacteristic
578Q8—42no—
579Q8—1722no—
580Q8—1722no—
581D4—42no—
582D4—42no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—1724no—
587D4—1724no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—431no—
596C2×C4—431no—
597C2×C4—434no—
598C2×C4—431no—
599C2×C4—431no—
600C2×C4—431no—
601C2×C4—431no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—864no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1724no—
621C2×C4—1724no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4C22⋊C4×D4311yescharacteristic
625C2×C4C22⋊C4×D4311yescharacteristic
626C2×C4C22⋊C4×D4311yescharacteristic
627C2×C4C22⋊C4×D4311yescharacteristic
628C2×C4#1306334412yes—
629C2×C4#1306334612yes—
630C2×C4C22×C4×D4311yescharacteristic
631C2×C4C2×D4×D4311yescharacteristic
632C8—42no—
633C8—1722no—
634C22—21no—
635C22—21no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—432no—
640C22—861no—
641C22—861no—
642C22—861no—
643C22—861no—
644C22—861no—
645C22—1722no—
646C22—1722no—
647C22C2×C22⋊C4×D4311yescharacteristic
648C22C2×#1306334411yescharacteristic
649C22C2×#1306334611yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—44no—
654C4—42no—
655C4—432no—
656C4—432no—
657C4—861no—
658C4—861no—
659C4—861no—
660C4—861no—
661C4—1724no—
662C4—1722no—
663C4—1722no—
664C4#1458289212yes—
665C4#1458289212yes—
666C4#104×D4312yes—
667C2—21no—
668C2—21no—
669C2—82no—
670C2—862no—
671C2—1721no—
672C2#410×D4311yescharacteristic
673C2C2×#1458289211yescharacteristic
674C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1502C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1502D43
hypocenterC43#17533
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #431×D43C2semidirect
3. C4×#13063283C2semidirect
4. #19133095C2semidirect
5. #19133093C2semidirect
6. #19133090C2semidirect
7. #19133083C2semidirect
8. #19133078C2semidirect
9. C43×#1502C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583447C4semidirect
14. #14583447C4semidirect
16. #14583431C4semidirect
26. C4×#10621900C4semidirect
336. #1502D43semidirect
386. C43#17533semidirect

Maximal subgroups

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

subgroupindex
#191478902
#431×D432
C4×#130632832
#191330952
#191330932
#191330902
#191330832
#191330782
C43×#15022
#1753343