Finite Group Databasebeta

← #25064539

Subgroups — #25064539

Order 11008.

1070 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#19147892C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3C2×#97×D43C211yesmaximal, characteristic, complemented
4#19133214C214yesmaximal, complemented
5#19133210C211yesmaximal, characteristic, complemented
6#19133207C211yesmaximal, characteristic, complemented
7#19133205C211yesmaximal, characteristic, complemented
8#19133182C214yesmaximal, complemented
9C43×#1531C211yesmaximal, characteristic, complemented
10C22×C8×D43—21no—
11#14583454C411yescharacteristic
12#14583454C411yescharacteristic
13#14583450C411yescharacteristic
14#14583450C411yescharacteristic
15#14583449C2211yescharacteristic
16#14583436—21no—
17#14583436—21no—
18#14583435—21no—
19#14583435—21no—
20#14583434C2212yes—
21#14583434C2212yes—
22#14583412—21no—
23#14583412—21no—
24#14583411C412yes—
25C4×#10621902—21no—
26C4×#10621902—21no—
27#14583367C412yes—
28C2×C42×D43C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582954C2212yes—
31#14582951—21no—
32#14582949—21no—
33#14582921—21no—
34#14582861—21no—
35#14582851C2212yes—
36C2×#13063236C2211yescharacteristic
37C2×#13063235—21no—
38#97×D43—21no—
39#97×D43—21no—
40#97×D43C2212yes—
41#97×D43C2212yes—
42#14582641C2214yescomplemented
43#14582638C2214yescomplemented
44#14582638C2214yescomplemented
45C43×#533C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C2×#97×C43C2211yescharacteristic
48C43×#330C2214yescomplemented
49C2×#10621902—21no—
50C2×#10621902—21no—
51C2×#10621898C2×C412yes—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C2×#10621872—22no—
56C22×C43⋊C8—21no—
57C2×C8×D43—28no—
58C2×C8×D43—22no—
59C2×C8×D43—22no—
60#13063325C2×C411yescharacteristic
61#13063322C2×C411yescharacteristic
62#13063320—22no—
63#13063320—22no—
64#13063316—21no—
65#13063316—21no—
66#13063314—21no—
67#13063314—21no—
68#13063313C2312yes—
69#13063310—22no—
70#13063310—22no—
71#13063309—22no—
72#13063305C2×C412yes—
73#13063305C2×C412yes—
74#13063301—21no—
75#13063301—21no—
76#13063300—21no—
77#13063300—21no—
78#13063300C2×C412yes—
79#13063300C2×C412yes—
80#13063299—21no—
81#13063299—21no—
82#13063295—22no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85#13063290C2×C412yes—
86#13063290C2×C412yes—
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—21no—
90C4×D172—21no—
91#13063287—22no—
92#13063287—22no—
93#13063287—21no—
94#13063287—21no—
95#13063287C2×C412yes—
96#13063287C2×C412yes—
97(C22⋊D43)⋊C4—22no—
98(C22⋊D43)⋊C4—22no—
99#13063283—21no—
100#13063283—21no—
101#13063283—22no—
102#13063283—22no—
103#13063282—22no—
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C42×D43—22no—
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43C2311yescharacteristic
115C42×D43C2311yescharacteristic
116C4⋊(C43⋊C8)—21no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120#13063236—21no—
121#13063236C2312yes—
122#13063236C2312yes—
123#13063235—22no—
124#13063235—22no—
125C8×Dic43—22no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128C4⋊Q8×C43C2×C411yescharacteristic
129#125×C43C2312yes—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43C2×C412yes—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43C2312yes—
140#97×C43C2312yes—
141C23×D43C22⋊C411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×C22⋊D43—22no—
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150C22×Dic43C22⋊C411yescharacteristic
151#10621902—44no—
152#10621902—44no—
153#10621898—44no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172C22×C412yes—
159C2×C4×D43—24no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C22×C411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×Dic86C22×C412yes—
178C2×C8×C43—24no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43C22×C412yes—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C42×C43—22no—
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2411yescharacteristic
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C2×C43⋊C8—24no—
222C2×C43⋊C8—22no—
223C2×C43⋊C8—22no—
224#10621872—44no—
225C8×D43—28no—
226C8×D43—28no—
227C23×C43C2×C22⋊C411yescharacteristic
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
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—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C22⋊D43—44no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—41no—
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258D172—42no—
259D172—42no—
260D172—44no—
261D172—44no—
262D172—42no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—44no—
275C4×D43—44no—
276C4×D43—44no—
277C4×D43#10414yes—
278Dic86—42no—
279C8×C43—24no—
280C8×C43—42no—
281C43⋊C8—24no—
282C43⋊C8—42no—
283#17646—431nomaximal, Sylow
284C22×C43—21no—
285C22×C43—21no—
286C22×C43#41312yes—
287C22×C43C22×C22⋊C411yescharacteristic
288C2×D43—28no—
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43C2×#10412yes—
297C2×D43#42112yes—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—42no—
304C4×C43—42no—
305C4×C43C2×#10412yes—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—42no—
312Dic43C2×#10412yes—
313#3444—431no—
314#2920—431no—
315C22×#97—431no—
316#1532—434no—
317#1531—431no—
318#1531D4311yescharacteristic, complemented
319#1530—431no—
320#1530—431no—
321#1524—434no—
322C2×C43—22no—
323C2×C43C2×#41311yescharacteristic
324C2×C43C22×#10411yescharacteristic
325C2×C43C2×#42111yescharacteristic
326D43—22no—
327D43—22no—
328D43—82no—
329C23×C8—861no—
330#533—431no—
331#533—431no—
332#533C2×D4311yescharacteristic
333#532—431no—
334#532—431no—
335#532—431no—
336#529—432no—
337#529—432no—
338#529—861no—
339#529—861no—
340#529—861no—
341#529—861no—
342#525—432no—
343#525—861no—
344#525—861no—
345C4×#41—432no—
346C4×#41—861no—
347C4×#41—861no—
348C22×C42—431no—
349#432—431no—
350#432—432no—
351#432C2×D4311yescharacteristic
352#431—861no—
353#431—861no—
354#423—861no—
355#407—861no—
356C4×M16—432no—
357C2×#97—431no—
358C2×#97—432no—
359C2×#97—432no—
360C2×#97—861no—
361C2×#97—861no—
362C2×#97—861no—
363C2×#97C2×D4311yescharacteristic
364#330—434no—
365#330C2×D4314yescomplemented
366#329—434no—
367#329—434no—
368C43#1764611yescharacteristic, complemented, Sylow
369C2×#41—432no—
370C2×#41—861no—
371C2×#41—861no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C2×M16—862no—
376C22×C8—21no—
377C22×C8—862no—
378C22×C8—862no—
379C22×C8—868no—
380C22×C8—861no—
381C4⋊Q8—431no—
382C4⋊Q8C4×D4311yescharacteristic
383C4⋊Q8C4×D4311yescharacteristic
384#127—431no—
385#126—862no—
386#126—862no—
387#125—861no—
388#125—861no—
389#125C22×D4312yes—
390#124—432no—
391#124—861no—
392#124—861no—
393#123—862no—
394#123—862no—
395#123—862no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—432no—
399C22⋊Q8—432no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402#121—432no—
403#121—432no—
404#121—861no—
405#121—861no—
406#121—861no—
407#121—861no—
408#120—862no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—432no—
412C4×Q8—432no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×D4—432no—
416C4×D4—432no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—861no—
420C4×D4—861no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—861no—
426C4×D4—861no—
427#117—862no—
428#117—862no—
429#117—862no—
430#117—861no—
431#117—861no—
432#117C4×D4312yes—
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—862no—
445C2×C42C22×D4311yescharacteristic
446C4⋊C8—21no—
447C4⋊C8—862no—
448C4⋊C8—861no—
449C22⋊C8—21no—
450C22⋊C8—862no—
451C22⋊C8—861no—
452#97—21no—
453#97—432no—
454#97—432no—
455#97—862no—
456#97—862no—
457#97—861no—
458#97C22×D4312yes—
459#97C22×D4312yes—
460C4×C8—862no—
461C24—431no—
462#41—1724no—
463#41—1724no—
464#41—1724no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—432no—
468C2×D4—432no—
469C2×D4—862no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—861no—
473C2×D4—861no—
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—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—864no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4C2×C4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498M16—1724no—
499C2×C8—24no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—868no—
503C2×C8—868no—
504C2×C8—864no—
505C2×C8—862no—
506C2×C8—862no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4C2×C4×D4312yes—
518C4⋊C4C2×C4×D4312yes—
519C22⋊C4—22no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C42—22no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—862no—
542C42—862no—
543C42C2×C4×D4311yescharacteristic
544C42D4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42C23×D4311yescharacteristic
547C23—431no—
548C23—431no—
549C23—862no—
550C23—862no—
551C23—862no—
552C23—862no—
553C23C22⋊C4×D4311yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—1722no—
557D4—1722no—
558D4—1722no—
559D4—1724no—
560D4—1724no—
561D4—1724no—
562D4—1722no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—431no—
569C2×C4—434no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1724no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1721no—
593C2×C4C22⋊C4×D4311yescharacteristic
594C2×C4C22⋊C4×D4311yescharacteristic
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22×C4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4C2×D4×D4311yescharacteristic
599C8—24no—
600C8—42no—
601C8—864no—
602C8—1722no—
603C22—21no—
604C22—21no—
605C22—432no—
606C22—432no—
607C22—868no—
608C22—861no—
609C22—861no—
610C22—861no—
611C22—861no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22#1458288212yes—
616C22C2×C22⋊C4×D4311yescharacteristic
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—432no—
625C4—861no—
626C4—861no—
627C4—861no—
628C4—861no—
629C4—861no—
630C4—1722no—
631C4#104×D4312yes—
632C2—22no—
633C2—862no—
634C2—862no—
635C2—3442no—
636C2C2×#1458288211yescharacteristic
637C2C2×#104×D4311yescharacteristic
638C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1531C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC42×C43C24
hypercenter#1531D43
hypocenterC43#17646
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1531

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. C2×#97×D43C2semidirect
4. #19133214C2semidirect
5. #19133210C2semidirect
6. #19133207C2semidirect
7. #19133205C2semidirect
8. #19133182C2semidirect
9. C43×#1531C2semidirect
42. #14582641C22semidirect
43. #14582638C22semidirect
44. #14582638C22semidirect
48. C43×#330C22semidirect
318. #1531D43semidirect
365. #330C2×D43semidirect
368. C43#17646semidirect

Maximal subgroups

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

subgroupindex
#191478922
#191432252
C2×#97×D432
#191332142
#191332102
#191332072
#191332052
#191331822
C43×#15312
#1764643