Finite Group Databasebeta

← #25096624

Subgroups — #25096624

Order 11008.

1358 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621902C211yesmaximal, characteristic
2C2×#14582951C211yesmaximal, characteristic, complemented
3#19136988C211yesmaximal, characteristic, complemented
4#19134688C212yesmaximal, complemented
5#19134610C211yesmaximal, characteristic, complemented
6#19134606C211yesmaximal, characteristic, complemented
7#19134602C211yesmaximal, characteristic, complemented
8#19134534C212yesmaximal
9#103×Dic43C212yesmaximal, complemented
10#19134409C212yesmaximal, complemented
11C43×#1805C211yesmaximal, characteristic, complemented
12C22×#10621902C2211yescharacteristic
13C4×#10621902—24no—
14C4×#10621902C418yescomplemented
15C2×Q8×Dic43C2211yescharacteristic
16C2×C4×D172—21no—
17C2×C4×D172C2211yescharacteristic
18C2×#13063287—21no—
19C2×#13063287C2211yescharacteristic
20C2×#13063283—21no—
21C2×#13063283C2211yescharacteristic
22C2×C42×D43—21no—
23C2×C42×D43C2211yescharacteristic
24#14582951—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2212yes—
27C2×#13063247C2212yes—
28C2×#13063245C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30C2×C8×Dic43C2212yes—
31#14582766—21no—
32#14582765C2211yescharacteristic
33#14582761—21no—
34#14582756C2212yes—
35C4⋊C4×Dic43C2212yes—
36#14582746—21no—
37#14582744—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×Q8×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#103×C43C2212yes—
44C43×#382C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621902—22no—
47C2×#10621902—22no—
48C2×#10621902—22no—
49C2×#10621902—22no—
50C2×#10621902—22no—
51C2×#10621902C2×C414yes—
52C22×D172—21no—
53C22×D172C2311yescharacteristic
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—21no—
57C22×C4×D43D411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8C2312yes—
61Q8×Dic43—22no—
62Q8×Dic43C2×C414yes—
63C4×D172—28no—
64C4×D172—22no—
65C4×D172C2×C414yes—
66#13063287—28no—
67#13063287—22no—
68#13063287C2×C414yes—
69#13063283—22no—
70#13063283—28no—
71#13063283C2×C414yes—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—22no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85C42×D43—28no—
86C42×D43C2×C414yes—
87C42×D43D414yes—
88C4⋊(C43⋊C8)—22no—
89#13063249—24no—
90#13063247—24no—
91#13063245—24no—
92(C2×D43)⋊C8—24no—
93C8×Dic43—24no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×Q8×C43C2311yescharacteristic
99C22×C8×C43C2312yes—
100C4×Q8×C43—22no—
101C4×Q8×C43C2×C414yes—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—22no—
108#103×C43—24no—
109#95×C43—21no—
110#95×C43—21no—
111C23×D43—21no—
112C23×D43C2×D411yescharacteristic
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43C22×C412yes—
117C2×Q8×C43#4112yes—
118C2×Q8×C43#4112yes—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2411yescharacteristic
125C22×Dic43—21no—
126C22×Dic43—22no—
127C22×Dic43C2×D411yescharacteristic
128C22×Dic43C2×D411yescharacteristic
129C22×Dic43C2×D411yescharacteristic
130#10621902—28no—
131#10621902—28no—
132#10621902—28no—
133#10621902—28no—
134C2×D172—24no—
135C2×D172—24no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—24no—
140C2×D172C22×C412yes—
141C2×D172#4112yes—
142C2×D172#4112yes—
143C2×C4×D43—24no—
144C2×C4×D43—24no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—24no—
150C2×C4×D43—24no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—42no—
154C2×C4×D43—44no—
155C2×C4×D43—44no—
156C2×C4×D43C22⋊C414yes—
157C2×C4×D43C22⋊C414yes—
158C2×C4×D43C22×C412yes—
159C2×C4×D43C2×D412yes—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43C22×C412yes—
168C42×C43—24no—
169C42×C43C22×C412yes—
170C42×C43C2×D412yes—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—44no—
175C4⋊Dic43—21no—
176C4⋊Dic43—24no—
177C4⋊Dic43—22no—
178C4⋊Dic43—22no—
179C4⋊Dic43C22×C412yes—
180C4×Dic43—24no—
181C4×Dic43—24no—
182C4×Dic43—44no—
183C4×Dic43C22⋊C414yes—
184C4×Dic43C22⋊C414yes—
185C4×Dic43C22×C412yes—
186C4×Dic43C2×D412yes—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C23×C43C22×D411yescharacteristic
191C22×D43—22no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43C2×C22⋊C412yes—
201Q8×C43—22no—
202Q8×C43—22no—
203Q8×C43—22no—
204Q8×C43#11714yes—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43C2×C22⋊C412yes—
216C2×C4×C43C2×C22⋊C412yes—
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43C2×C22⋊C412yes—
232C2×Dic43C2×C22⋊C412yes—
233C2×Dic43C2×C22⋊C412yes—
234C2×Dic43#13514yes—
235D172—216no—
236D172—22no—
237D172—22no—
238D172—22no—
239D172#11714yes—
240C4×D43—216no—
241C4×D43—22no—
242C4×D43—22no—
243C4×D43—22no—
244C4×D43—22no—
245C4×D43—28no—
246C4×D43—44no—
247C4×D43—48no—
248C4×D43—48no—
249C8×C43—42no—
250C43⋊C8—42no—
251#20736—431nomaximal, Sylow
252C22×C43C22×C22⋊C411yescharacteristic
253C22×C43#52511yescharacteristic
254C22×C43#52511yescharacteristic
255C22×C43C2×#13512yes—
256C22×C43#57512yes—
257C2×D43—22no—
258C2×D43—22no—
259C2×D43—24no—
260C2×D43—22no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—44no—
264C2×D43—44no—
265C2×D43—42no—
266C2×D43—42no—
267C4×C43—22no—
268C4×C43—22no—
269C4×C43—24no—
270C4×C43—42no—
271C4×C43—82no—
272C4×C43C2×#11711yescharacteristic
273C4×C43C2×#11711yescharacteristic
274C4×C43#52511yescharacteristic
275C4×C43#52511yescharacteristic
276Dic43—22no—
277Dic43—22no—
278Dic43—42no—
279Dic43—82no—
280Dic43#41614yes—
281C2×C4×#41—431no—
282C2×#431—431no—
283#2283—431no—
284#1825—432no—
285#1805—431no—
286#1805D4311yescharacteristic, complemented
287#1804—431no—
288#1804—431no—
289#1788—432no—
290C4×#103—432no—
291C4×#102—432no—
292C2×C43#228011yescharacteristic
293C2×C43C2×#41611yescharacteristic
294C2×C43#289611yescharacteristic
295C2×C43#310212yes—
296C2×C43#310212yes—
297D43—42no—
298D43—44no—
299C22×#41—431no—
300C4×#41—438no—
301C4×#41—864no—
302C2×C4×Q8—431no—
303C2×C4×Q8C2×D4311yescharacteristic
304C2×C4×D4—431no—
305C2×C4×D4—431no—
306C2×C4×D4—861no—
307C2×C4×D4—861no—
308C2×#117—431no—
309C2×#117—861no—
310C22×C42—431no—
311C22×C42—861no—
312#431—864no—
313C2×C4⋊C8—431no—
314C2×C4⋊C8C2×D4311yescharacteristic
315C2×#103—432no—
316C2×#103C2×D4312yes—
317C2×#102—432no—
318C2×#102—432no—
319C2×C22⋊C8—432no—
320C2×C4×C8—432no—
321#383—861no—
322#382—431no—
323#382C2×D4311yescharacteristic
324#381—861no—
325#380—432no—
326C4×C4⋊C4—432no—
327C4×C22⋊C4—861no—
328#376—861no—
329#340—432no—
330#340—432no—
331#340—432no—
332#340C2×D4312yes—
333C43#2073611yescharacteristic, complemented, Sylow
334C2×#41—434no—
335C2×#41—862no—
336C2×#41—862no—
337C2×#41—862no—
338C2×#41—862no—
339C2×#41—862no—
340C22×Q8C22×D4311yescharacteristic
341C22×D4—431no—
342C22×D4—861no—
343C23×C4—431no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—861no—
347C23×C4—861no—
348C23×C4—861no—
349C22×C8—432no—
350C22×C8C22×D4312yes—
351C4×Q8—22no—
352C4×Q8—434no—
353C4×Q8—862no—
354C4×Q8C4×D4314yes—
355C4×D4—434no—
356C4×D4—434no—
357C4×D4—868no—
358C4×D4—862no—
359C4×D4—868no—
360C4×D4—862no—
361#117—434no—
362#117—868no—
363#117—862no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—432no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4C22×D4312yes—
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C22⋊C4—861no—
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—862no—
374C2×C42—21no—
375C2×C42—431no—
376C2×C42—431no—
377C2×C42—431no—
378C2×C42—434no—
379C2×C42—434no—
380C2×C42—868no—
381C2×C42—861no—
382C2×C42—861no—
383C2×C42—862no—
384C2×C42C22×D4311yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—862no—
387#103—24no—
388#103—864no—
389#102—864no—
390#102—864no—
391C22⋊C8—864no—
392C4×C8—864no—
393#95—21no—
394#95—21no—
395#95—862no—
396#95—862no—
397#95—861no—
398#95—861no—
399C24—431no—
400C24—861no—
401#41—868no—
402#41—868no—
403#41—868no—
404#41—868no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×C4×D4312yes—
409C2×Q8#1062190012yes—
410C2×Q8#1062190212yes—
411C2×D4—432no—
412C2×D4—432no—
413C2×D4—432no—
414C2×D4—864no—
415C2×D4—864no—
416C2×D4—864no—
417C2×D4—861no—
418C2×D4—861no—
419C2×D4—861no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—434no—
427C22×C4—432no—
428C22×C4—432no—
429C22×C4—434no—
430C22×C4—864no—
431C22×C4—864no—
432C22×C4—864no—
433C22×C4—864no—
434C22×C4—864no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—864no—
441C22×C4—862no—
442C22×C4—1722no—
443C22×C4—1724no—
444C22×C4—1724no—
445C22×C4D4×D4311yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4C23×D4311yescharacteristic
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—862no—
452C2×C8—862no—
453C2×C8—862no—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—432no—
459C4⋊C4—864no—
460C4⋊C4—861no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4C2×C4×D4312yes—
464C22⋊C4—864no—
465C22⋊C4—864no—
466C22⋊C4—864no—
467C22⋊C4—1724no—
468C42—24no—
469C42—434no—
470C42—434no—
471C42—432no—
472C42—432no—
473C42—864no—
474C42—864no—
475C42—1724no—
476C42C2×C4×D4312yes—
477C42D4×D4312yes—
478C23—432no—
479C23—862no—
480C23—862no—
481C23—861no—
482C23—862no—
483C23—861no—
484C23—862no—
485C23—862no—
486C23—1722no—
487C23—1722no—
488C23C2×D4×D4311yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—22no—
492Q8#1306328314yes—
493D4—434no—
494D4—8616no—
495D4—862no—
496D4—862no—
497D4—862no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—432no—
509C2×C4—434no—
510C2×C4—432no—
511C2×C4—432no—
512C2×C4—868no—
513C2×C4—8616no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—1724no—
523C2×C4—1728no—
524C2×C4—1728no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4C22⋊C4×D4312yes—
530C2×C4C22⋊C4×D4312yes—
531C2×C4C22×C4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4#41×D4311yescharacteristic
534C2×C4#41×D4311yescharacteristic
535C2×C4C2×#1062190011yescharacteristic
536C2×C4C2×#1062190211yescharacteristic
537C8—42no—
538C8—1722no—
539C22—862no—
540C22—862no—
541C22—864no—
542C22—862no—
543C22—1722no—
544C22—1724no—
545C22—1722no—
546C22—1724no—
547C22—1722no—
548C22—1722no—
549C22C2×C22⋊C4×D4311yescharacteristic
550C22#1458340911yescharacteristic
551C22#1458341211yescharacteristic
552C22#135×D4312yes—
553C22#1458369812yes—
554C4—22no—
555C4—22no—
556C4—24no—
557C4—42no—
558C4—82no—
559C4—434no—
560C4—862no—
561C4—862no—
562C4—3442no—
563C4—1722no—
564C4#117×D4311yescharacteristic
565C4C2×#1306328311yescharacteristic
566C4#1458340911yescharacteristic
567C4#1458341211yescharacteristic
568C2—1722no—
569C2—1724no—
570C2#1913697711yescharacteristic
571C2#416×D4311yescharacteristic
572C2#1914311311yescharacteristic
573C2#1914461212yes—
574C2#1914462012yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1805C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenter#1805D43
hypocenterC43#20736
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. C2×#14582951C2semidirect
3. #19136988C2semidirect
4. #19134688C2semidirect
5. #19134610C2semidirect
6. #19134606C2semidirect
7. #19134602C2semidirect
9. #103×Dic43C2semidirect
10. #19134409C2semidirect
11. C43×#1805C2semidirect
14. C4×#10621902C4semidirect
286. #1805D43semidirect
333. C43#20736semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
C2×#145829512
#191369882
#191346882
#191346102
#191346062
#191346022
#191345342
#103×Dic432
#191344092
C43×#18052
#2073643