Finite Group Databasebeta

← #25106444

Subgroups — #25106444

Order 11008.

1076 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583428C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3#423×D43C211yesmaximal, characteristic, complemented
4#19135588C211yesmaximal, characteristic, complemented
5#19135587C211yesmaximal, characteristic, complemented
6#19135445C211yesmaximal, characteristic, complemented
7#19135060C212yesmaximal, complemented
8#19135055C212yesmaximal
9#19134589C212yesmaximal, complemented
10#19134585C212yesmaximal, complemented
11C43×#1967C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583428—21no—
14#14583428—21no—
15#14583428—21no—
16#14583428—21no—
17#14583428—21no—
18#14583428—21no—
19#14583428—21no—
20#14583428—21no—
21C2×#13063318C412yes—
22C2×#13063317C2211yescharacteristic
23C2×#13063307C412yes—
24C2×#13063301C2211yescharacteristic
25C2×#13063296C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×(C22⋊D43)⋊C4C412yes—
29C2×#13063281C412yes—
30C2×C42×D43C2211yescharacteristic
31#14582954—21no—
32#14582954—21no—
33#14582950—21no—
34#14582950—21no—
35#14582923C2211yescharacteristic
36#14582922C2212yes—
37#14582922C2212yes—
38#14582921—21no—
39#14582921—21no—
40C4⋊C8×D43—21no—
41C4⋊C8×D43—21no—
42C2×#13063244C2212yes—
43C2×#13063242C2212yes—
44#14582862C2212yes—
45C4×#10621877C2211yescharacteristic
46#14582667C2212yes—
47#14582667C2212yes—
48#14582667C2212yes—
49#14582667C2212yes—
50C2×#124×C43C2211yescharacteristic
51C43×#423C2211yescharacteristic
52C2×#101×C43C2212yes—
53C2×#100×C43C2212yes—
54C4×M16×C43C2211yescharacteristic
55C22×C22⋊D43C2×C412yes—
56C23×Dic43C2×C412yes—
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C2×#10621877C2312yes—
61C2×#10621877C2312yes—
62C2×#10621872—22no—
63M16×D43—42no—
64M16×D43—42no—
65C2×C8×D43—22no—
66#13063318—22no—
67#13063318—22no—
68#13063318—22no—
69#13063318—22no—
70#13063317—21no—
71#13063317—21no—
72#13063317—21no—
73#13063317—21no—
74#13063307—22no—
75#13063307—22no—
76#13063307—22no—
77#13063307—22no—
78#13063301—21no—
79#13063301—21no—
80#13063301—21no—
81#13063301—21no—
82#13063296—21no—
83#13063296—21no—
84#13063296—21no—
85#13063296—21no—
86Q8×Dic43—21no—
87Q8×Dic43—21no—
88Q8×Dic43—21no—
89Q8×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43—21no—
93D4×Dic43—21no—
94(C22⋊D43)⋊C4—22no—
95(C22⋊D43)⋊C4—22no—
96(C22⋊D43)⋊C4—22no—
97(C22⋊D43)⋊C4—22no—
98#13063281—22no—
99#13063281—22no—
100#13063281—22no—
101#13063281—22no—
102C2×C4⋊Dic43C2×C412yes—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4C2×C412yes—
106C2×Dic43⋊C4C2×C412yes—
107C2×Dic43⋊C4C2×C412yes—
108C2×C22⋊Dic43C2×C412yes—
109C2×C22⋊Dic43C2×C412yes—
110C2×(C2×D43)⋊C4C2×C412yes—
111C2×C4×Dic43C2×C412yes—
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119C42×D43D411yescharacteristic
120C42×D43D411yescharacteristic
121C42×D43D411yescharacteristic
122C42×D43D411yescharacteristic
123C4⋊(C43⋊C8)—21no—
124C4⋊(C43⋊C8)—21no—
125Dic43⋊C8—22no—
126Dic43⋊C8—22no—
127Dic43⋊C8—22no—
128Dic43⋊C8—22no—
129#13063244—42no—
130#13063242—42no—
131(C2×D43)⋊C8—22no—
132(C2×D43)⋊C8—22no—
133#13063236—21no—
134C4×C43⋊C8—21no—
135C22×Q8×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C2×M16×C43C2312yes—
138C2×M16×C43C2312yes—
139#124×C43—21no—
140#124×C43—21no—
141#124×C43—21no—
142#124×C43—21no—
143C2×C22⋊C4×C43C2×C412yes—
144C2×C22⋊C4×C43C2×C412yes—
145C2×C42×C43C2311yescharacteristic
146C4⋊C8×C43—21no—
147C4⋊C8×C43—21no—
148#101×C43—42no—
149#100×C43—42no—
150#97×C43—21no—
151C4×C8×C43—21no—
152C24×C43C22×C412yes—
153C23×D43C22×C411yescharacteristic
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—22no—
157C2×Q8×C43—22no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C22×C4×C43C22×C412yes—
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C22×C411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—44no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—44no—
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C412yes—
175C22×Dic43C22×C412yes—
176C22×Dic43C22×C411yescharacteristic
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43C22⋊C411yescharacteristic
182C2×C4×D43C22⋊C411yescharacteristic
183C2×C4×D43C22⋊C411yescharacteristic
184C2×C4×D43C22⋊C411yescharacteristic
185C2×C4×D43C22⋊C411yescharacteristic
186C2×C4×D43C22⋊C411yescharacteristic
187C2×C4×D43C22⋊C411yescharacteristic
188C2×C4×D43C22⋊C411yescharacteristic
189C2×C4×D43C2×D411yescharacteristic
190C2×C4×D43C2×D411yescharacteristic
191C2×C4×D43C2×D411yescharacteristic
192C2×C4×D43C2×D411yescharacteristic
193M16×C43—22no—
194M16×C43—22no—
195M16×C43—22no—
196M16×C43—22no—
197C2×C8×C43—22no—
198C2×C8×C43—22no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C42×C43C2×D411yescharacteristic
204C42×C43C2×D411yescharacteristic
205C42×C43C2×D411yescharacteristic
206C42×C43C2×D411yescharacteristic
207C22⋊Dic43—22no—
208C22⋊Dic43—22no—
209C22⋊Dic43—22no—
210C22⋊Dic43—22no—
211(C2×D43)⋊C4—22no—
212(C2×D43)⋊C4—22no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—22no—
218C4⋊Dic43—22no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221Dic43⋊C4—22no—
222Dic43⋊C4—22no—
223Dic43⋊C4—22no—
224Dic43⋊C4—22no—
225C4×Dic43—22no—
226C4×Dic43—22no—
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22⋊C411yescharacteristic
234C4×Dic43C22⋊C411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237C4×Dic43C2×D411yescharacteristic
238C4×Dic43C2×D411yescharacteristic
239#10621877—22no—
240#10621877—22no—
241#10621877—22no—
242#10621877—22no—
243C2×C43⋊C8—22no—
244C2×C43⋊C8—22no—
245#10621872—44no—
246C8×D43—44no—
247C23×C43—22no—
248C23×C43—24no—
249C23×C43—42no—
250C23×C43—42no—
251C23×C43C23×C411yescharacteristic
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—41no—
255C22×D43C2×C22⋊C411yescharacteristic
256C22×D43C2×C22⋊C411yescharacteristic
257Q8×C43—41no—
258Q8×C43—41no—
259Q8×C43—42no—
260D4×C43—41no—
261D4×C43—41no—
262D4×C43—42no—
263C2×C4×C43—22no—
264C2×C4×C43—24no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43C2×C22⋊C411yescharacteristic
268C2×C4×C43C2×C22⋊C411yescharacteristic
269C2×C4×C43C2×C22⋊C411yescharacteristic
270C2×C4×C43C2×C22⋊C411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43H(5,𝔽2)12yes—
274C2×C4×C432−1+412yes—
275C22⋊D43—44no—
276C22⋊D43—44no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—41no—
282C2×Dic43—44no—
283C2×Dic43—44no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43C2×C22⋊C411yescharacteristic
287C2×Dic43C2×C22⋊C411yescharacteristic
288C2×Dic43C2×C22⋊C411yescharacteristic
289C2×Dic43C2×C22⋊C411yescharacteristic
290C2×Dic43C2×C22⋊C411yescharacteristic
291C2×Dic43C2×C22⋊C411yescharacteristic
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—21no—
295C4×D43—21no—
296C4×D43—21no—
297C4×D43—21no—
298C4×D43—22no—
299C4×D43—22no—
300C4×D43—22no—
301C4×D43—22no—
302C4×D43—41no—
303C4×D43—41no—
304C4×D43—41no—
305C4×D43—41no—
306C8×C43—42no—
307C8×C43—42no—
308C43⋊C8—42no—
309C43⋊C8—42no—
310#21880—431nomaximal, Sylow
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43—42no—
316C22×C43—84no—
317C22×C43C22×C22⋊C411yescharacteristic
318C22×C43#52012yes—
319C2×D43—21no—
320C2×D43—21no—
321C2×D43—21no—
322C2×D43—21no—
323C2×D43—21no—
324C2×D43—44no—
325C2×D43#41312yes—
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—21no—
330C4×C43—42no—
331C4×C43#53511yescharacteristic
332C4×C43#53611yescharacteristic
333C4×C43#53712yes—
334Dic43—21no—
335Dic43—21no—
336Dic43—21no—
337Dic43—21no—
338Dic43—21no—
339Dic43—42no—
340Dic43—42no—
341Dic43#41312yes—
342C2×#529—431no—
343#2920—431no—
344C2×#423—431no—
345#1998—431no—
346#1998—431no—
347#1967—431no—
348#1967D4311yescharacteristic, complemented
349#1901—432no—
350#1900—432no—
351#1801—432no—
352#1800—432no—
353C2×C43—22no—
354C2×C43—82no—
355C2×C43#231111yescharacteristic
356C2×C43C2×#41311yescharacteristic
357C2×C43C2×#41311yescharacteristic
358D43—22no—
359D43—41no—
360C22×M16—432no—
361#529—861no—
362#529—861no—
363#529—861no—
364#529—861no—
365#529—861no—
366#529—861no—
367#529—861no—
368#529—861no—
369C2×#126—432no—
370C2×#125—431no—
371C2×#124C2×D4311yescharacteristic
372C2×#123—432no—
373C2×C22⋊Q8—431no—
374C2×#121—431no—
375C2×C4×Q8—431no—
376C2×C4×D4—431no—
377C2×C4×D4—432no—
378C2×#117—432no—
379C22×C42—431no—
380#432—861no—
381#432—861no—
382#431—861no—
383#431—861no—
384#423—432no—
385#423—432no—
386#423—431no—
387#423—861no—
388#423—861no—
389#423C2×D4311yescharacteristic
390C2×C4⋊C8—861no—
391C2×C4⋊C8—861no—
392C2×#101—432no—
393C2×#101C2×D4312yes—
394C2×#100—432no—
395C2×#100C2×D4312yes—
396#407—432no—
397C4×M16—431no—
398C4×M16C2×D4311yescharacteristic
399#343—432no—
400#343—432no—
401#343—432no—
402#343—432no—
403C43#2188011yescharacteristic, complemented, Sylow
404C22×Q8C22×D4311yescharacteristic
405C22×D4—432no—
406C22×D4C22×D4311yescharacteristic
407C23×C4—431no—
408C23×C4—431no—
409C23×C4—431no—
410C23×C4—432no—
411C2×M16—432no—
412C2×M16—432no—
413C2×M16—862no—
414C2×M16—1722no—
415C2×M16—1722no—
416C2×M16C22×D4312yes—
417C2×M16C22×D4312yes—
418C22×C8—862no—
419#126—862no—
420#126—862no—
421#126—862no—
422#126—862no—
423#125—861no—
424#125—861no—
425#125—861no—
426#125—861no—
427#124—21no—
428#124—21no—
429#124—21no—
430#124—21no—
431#123—862no—
432#123—862no—
433#123—862no—
434#123—862no—
435C22⋊Q8—861no—
436C22⋊Q8—861no—
437C22⋊Q8—861no—
438C22⋊Q8—861no—
439#121—861no—
440#121—861no—
441#121—861no—
442#121—861no—
443C4×Q8—861no—
444C4×Q8—861no—
445C4×Q8—861no—
446C4×Q8—861no—
447C4×D4—861no—
448C4×D4—861no—
449C4×D4—861no—
450C4×D4—861no—
451C4×D4—862no—
452C4×D4—862no—
453C4×D4—862no—
454C4×D4—862no—
455#117—862no—
456#117—862no—
457#117—862no—
458#117—862no—
459C2×C4⋊C4—432no—
460C2×C4⋊C4—432no—
461C2×C4⋊C4—432no—
462C2×C4⋊C4—432no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C22⋊C4—432no—
466C2×C22⋊C4—432no—
467C2×C22⋊C4—432no—
468C2×C22⋊C4C4×D4312yes—
469C2×C22⋊C4C4×D4312yes—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—431no—
474C2×C42—431no—
475C2×C42—431no—
476C2×C42—431no—
477C2×C42—431no—
478C2×C42—431no—
479C2×C42—431no—
480C2×C42—431no—
481C2×C42—432no—
482C2×C42C22×D4311yescharacteristic
483C4⋊C8—21no—
484C4⋊C8—21no—
485C4⋊C8—862no—
486C4⋊C8—862no—
487C4⋊C8—862no—
488C4⋊C8—862no—
489C4⋊C8—861no—
490C4⋊C8—861no—
491#101—42no—
492#101—1722no—
493#100—42no—
494#100—1722no—
495C22⋊C8—862no—
496C22⋊C8—862no—
497#97—21no—
498#97—861no—
499C4×C8—21no—
500C4×C8—861no—
501C24—431no—
502C24C2×C4×D4312yes—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—862no—
512C2×D4—862no—
513C2×D4—1724no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—431no—
527C22×C4—431no—
528C22×C4—431no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—1722no—
536C22×C4—1722no—
537C22×C4—1724no—
538C22×C4C2×C4×D4312yes—
539C22×C4C2×C4×D4311yescharacteristic
540C22×C4C2×C4×D4311yescharacteristic
541C22×C4C23×D4311yescharacteristic
542M16—22no—
543M16—22no—
544M16—22no—
545M16—22no—
546M16—862no—
547M16—862no—
548M16—862no—
549M16—862no—
550M16—1724no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—862no—
554C2×C8—862no—
555C2×C8—1724no—
556C4⋊C4—862no—
557C4⋊C4—862no—
558C4⋊C4—862no—
559C4⋊C4—862no—
560C4⋊C4—862no—
561C4⋊C4—862no—
562C4⋊C4—862no—
563C4⋊C4—862no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—862no—
573C22⋊C4—862no—
574C22⋊C4—862no—
575C22⋊C4—862no—
576C22⋊C4—862no—
577C22⋊C4—862no—
578C42—431no—
579C42—431no—
580C42—431no—
581C42—431no—
582C42—431no—
583C42—431no—
584C42—431no—
585C42—431no—
586C42—431no—
587C42—431no—
588C42—431no—
589C42—431no—
590C42—862no—
591C42—862no—
592C42D4×D4311yescharacteristic
593C42D4×D4311yescharacteristic
594C42D4×D4311yescharacteristic
595C42D4×D4311yescharacteristic
596C23—22no—
597C23—24no—
598C23—42no—
599C23—42no—
600C23—431no—
601C23—431no—
602C23—862no—
603C23—862no—
604C23—1721no—
605C23C22×C4×D4311yescharacteristic
606Q8—41no—
607Q8—41no—
608Q8—42no—
609D4—41no—
610D4—41no—
611D4—42no—
612D4—1724no—
613D4—1724no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—431no—
619C2×C4—431no—
620C2×C4—431no—
621C2×C4—431no—
622C2×C4—431no—
623C2×C4—431no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—862no—
637C2×C4—862no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1724no—
643C2×C4—1721no—
644C2×C4—1724no—
645C2×C4—1722no—
646C2×C4—1722no—
647C2×C4C22⋊C4×D4311yescharacteristic
648C2×C4C22⋊C4×D4311yescharacteristic
649C2×C4C22⋊C4×D4311yescharacteristic
650C2×C4C22⋊C4×D4311yescharacteristic
651C2×C4C2×D4×D4311yescharacteristic
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4#1306337012yes—
654C2×C4#1306337212yes—
655C8—42no—
656C8—42no—
657C8—1722no—
658C8—1722no—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—84no—
665C22—432no—
666C22—861no—
667C22—861no—
668C22—861no—
669C22—861no—
670C22—861no—
671C22—1724no—
672C22C2×C22⋊C4×D4311yescharacteristic
673C22#1458337812yes—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—21no—
678C4—42no—
679C4—432no—
680C4—861no—
681C4—861no—
682C4—861no—
683C4—861no—
684C4—861no—
685C4—1722no—
686C4—1722no—
687C4#1458346211yescharacteristic
688C4#1458346911yescharacteristic
689C4#1458347812yes—
690C2—22no—
691C2—82no—
692C2—862no—
693C2—1721no—
694C2#1913718511yescharacteristic
695C2#413×D4311yescharacteristic
696C2#413×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1967C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1967D43
hypocenterC43#21880
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1967

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. #423×D43C2semidirect
4. #19135588C2semidirect
5. #19135587C2semidirect
6. #19135445C2semidirect
7. #19135060C2semidirect
9. #19134589C2semidirect
10. #19134585C2semidirect
11. C43×#1967C2semidirect
348. #1967D43semidirect
403. C43#21880semidirect

Maximal subgroups

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

subgroupindex
C2×#145834282
#191432262
#423×D432
#191355882
#191355872
#191354452
#191350602
#191350552
#191345892
#191345852
C43×#19672
#2188043