Finite Group Databasebeta

← #25097685

Subgroups — #25097685

Order 11008.

1502 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147796C211yesmaximal, characteristic
2C2×#14582872C211yesmaximal, characteristic
3#19137083C211yesmaximal, characteristic
4#19137079C211yesmaximal, characteristic, complemented
5#19137077C211yesmaximal, characteristic, complemented
6#19134877C218yesmaximal, complemented
7#19134327C211yesmaximal, characteristic, complemented
8C43×#1740C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583380—22no—
11#14583379—22no—
12#14583376—21no—
13#14583373—21no—
14#14583372C2214yes—
15C4×#10621898—22no—
16#14583367—22no—
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19#117×D43—22no—
20C22×C4×Dic43C2211yescharacteristic
21#14582872C418yescomplemented
22C2×#13063239C2214yes—
23#14582804—21no—
24#14582800—21no—
25#14582798—22no—
26#14582795—22no—
27#14582776C2214yes—
28#14582774C2214yes—
29#14582771C2214yes—
30C4×Dic43⋊C4—22no—
31C4×C4⋊Dic43—22no—
32C4×(C2×D43)⋊C4—22no—
33#14582665C2214yes—
34C2×#117×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic
36C2×#117×C43C2211yescharacteristic
37C43×#342C2214yes—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898C2×C414yes—
45C2×#10621898Q814yes—
46C22×Dic86D411yescharacteristic
47C22×D172D411yescharacteristic
48C22×C22⋊D43C2312yes—
49C23×Dic43C2312yes—
50C22×C4×D43D412yes—
51C4×Dic86—24no—
52#13063290—24no—
53C4×D172—24no—
54#13063287—24no—
55C4×C22⋊D43—28no—
56(C22⋊D43)⋊C4—28no—
57#13063284—21no—
58#13063284—21no—
59#13063284—21no—
60#13063284—21no—
61#13063284—22no—
62#13063284C2×C414yescomplemented
63#13063283—24no—
64#13063282—24no—
65#13063281—24no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—24no—
68C2×C4⋊Dic43D412yes—
69C2×Dic43⋊C4—24no—
70C4⋊C4×D43—24no—
71C2×C22⋊Dic43C2312yes—
72C2×C22⋊Dic43C2312yes—
73C2×(C2×D43)⋊C4—24no—
74C22⋊C4×D43—24no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43D412yes—
83C42×D43—24no—
84#13063239C2×C4116yescomplemented
85C43⋊#95—24no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C23×C4×C43C2311yescharacteristic
89#117×C43—21no—
90#117×C43—21no—
91#117×C43—21no—
92#117×C43—21no—
93#117×C43—22no—
94#117×C43—22no—
95#117×C43—22no—
96#117×C43C2×C414yescomplemented
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43D412yes—
100C2×C22⋊C4×C43C2312yes—
101C2×C22⋊C4×C43C2312yes—
102C2×C22⋊C4×C43C2312yes—
103C2×C42×C43—21no—
104C2×C42×C43—21no—
105C2×C42×C43D412yes—
106C24×C43C2411yescharacteristic
107C23×D43C2×D412yes—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43C22×C412yes—
111C22×C4×C43C2×D414yes—
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×Q812yes—
119C22×C4×C43#4112yes—
120C22×C4×C43#4112yes—
121C2×C22⋊D43—22no—
122C2×C22⋊D43—22no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43—22no—
125C2×C22⋊D43C22×C414yes—
126C2×C22⋊D43C2×Q814yes—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—44no—
132C22×Dic43C2×D412yes—
133C22×Dic43C2×D414yes—
134#10621898—24no—
135#10621898—24no—
136#10621898—24no—
137#10621898—24no—
138#10621898—24no—
139#10621898—24no—
140#10621898—24no—
141#10621898—24no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—22no—
145C2×D172C4⋊C414yescomplemented
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—24no—
149C2×C4×D43—28no—
150C2×C4×D43C4⋊C418yescomplemented
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—22no—
154C2×Dic86C4⋊C414yescomplemented
155C4⋊C4×C43—24no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—42no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43C22×C414yes—
165C42×C43—24no—
166C42×C43—22no—
167C42×C43—22no—
168C42×C43—42no—
169C22⋊Dic43—22no—
170C22⋊Dic43—22no—
171C22⋊Dic43—22no—
172C22⋊Dic43C22×C414yes—
173(C2×D43)⋊C4—28no—
174(C2×D43)⋊C4—48no—
175C4⋊Dic43—24no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43—48no—
179Dic43⋊C4—28no—
180Dic43⋊C4—48no—
181C4×Dic43—28no—
182C4×Dic43—24no—
183C4×Dic43—22no—
184C4×Dic43—22no—
185C4×Dic43—41no—
186C4×Dic43—41no—
187C4×Dic43—41no—
188C4×Dic43—41no—
189C23×C43—42no—
190C23×C43C23×C411yescharacteristic
191C23×C43C22×D411yescharacteristic
192C23×C43C22×D411yescharacteristic
193C23×C43C22×D411yescharacteristic
194C23×C43C22×Q811yescharacteristic
195C23×C43C2×#4111yescharacteristic
196C23×C43C2×#4111yescharacteristic
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—44no—
200C22×D43C2×C4⋊C414yes—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—44no—
204C2×C4×C43—44no—
205C2×C4×C43—44no—
206C2×C4×C43—42no—
207C2×C4×C43C2×C4⋊C412yes—
208C2×C4×C43C2×C4⋊C412yes—
209C2×C4×C43C4×D412yes—
210C2×C4×C43C4×D412yes—
211C2×C4×C43C4×D412yes—
212C2×C4×C43C4×D412yes—
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43C22⋊Q812yes—
218C2×C4×C43C22⋊Q812yes—
219C2×C4×C43C22⋊Q812yes—
220C2×C4×C43C22⋊Q812yes—
221C2×C4×C43#12312yes—
222C2×C4×C43#12312yes—
223C22⋊D43—24no—
224C22⋊D43—24no—
225C22⋊D43—24no—
226C22⋊D43—24no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—24no—
234C2×Dic43—44no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—44no—
240C2×Dic43C2×C4⋊C414yes—
241D172—24no—
242D172—24no—
243C4×D43—28no—
244C4×D43—28no—
245C4×D43—88no—
246Dic86—24no—
247Dic86—24no—
248#20888—431nomaximal, Sylow
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43C22×C4⋊C411yescharacteristic
257C22×C43C2×C4×D411yescharacteristic
258C22×C43C2×C4×D411yescharacteristic
259C22×C43C2×#12011yescharacteristic
260C22×C43C2×C22⋊Q811yescharacteristic
261C22×C43C2×C22⋊Q811yescharacteristic
262C22×C43C2×#12311yescharacteristic
263C2×D43—24no—
264C2×D43—44no—
265C2×D43—44no—
266C2×D43—82no—
267C4×C43—44no—
268C4×C43—44no—
269C4×C43—82no—
270C4×C43#38512yes—
271C4×C43#38512yes—
272C4×C43#38512yes—
273C4×C43#38512yes—
274Dic43—24no—
275Dic43—44no—
276Dic43—44no—
277Dic43—44no—
278#3428—431no—
279C2×#410—431no—
280#2297—431no—
281#2296—431no—
282#2296—431no—
283#1867—438no—
284#1740—431no—
285#1740D4311yescharacteristic, complemented
286C2×C43—21no—
287C2×C43—21no—
288C2×C43—21no—
289C2×C43—21no—
290C2×C43—21no—
291C2×C43—21no—
292C2×C43C2×#38511yescharacteristic
293C2×C43#302512yes—
294D43—44no—
295C22×#41—431no—
296#520—862no—
297#520—862no—
298#519—861no—
299#518—434no—
300#518—861no—
301C4×#41—862no—
302C4×#41—862no—
303C2×#117—431no—
304C2×#117—431no—
305C2×#117—862no—
306C2×#117C2×D4311yescharacteristic
307C2×#117C2×D4311yescharacteristic
308C2×#117C2×D4311yescharacteristic
309C22×C42—431no—
310#410—438no—
311C2×#99—434no—
312#391—861no—
313#390—861no—
314#389—862no—
315#389—862no—
316#386—434no—
317#385—434no—
318#385—434no—
319C4×C4⋊C4—862no—
320C4×C4⋊C4—862no—
321C4×C22⋊C4—862no—
322#342—434no—
323#342C2×D4314yes—
324C43#2088811yescharacteristic, complemented, Sylow
325C2×#41—434no—
326C2×#41—434no—
327C2×#41—861no—
328C2×#41—861no—
329C2×#41—862no—
330C2×#41—861no—
331C2×#41—861no—
332C2×#41—862no—
333C22×Q8—431no—
334C22×D4—432no—
335C22×D4—431no—
336C23×C4—432no—
337C23×C4—432no—
338C23×C4C22×D4311yescharacteristic
339C4×Q8—864no—
340C4×Q8—864no—
341C4×D4—864no—
342C4×D4—868no—
343C4×D4—864no—
344C4×D4—868no—
345#117—21no—
346#117—21no—
347#117—21no—
348#117—21no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—434no—
353#117—864no—
354#117—864no—
355#117—864no—
356#117—861no—
357#117—861no—
358#117—862no—
359#117—861no—
360#117—861no—
361#117C4×D4314yescomplemented
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—432no—
365C2×C4⋊C4—864no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—864no—
368C2×C4⋊C4—864no—
369C2×C4⋊C4D17212yes—
370C2×C22⋊C4—432no—
371C2×C22⋊C4—432no—
372C2×C22⋊C4—864no—
373C2×C22⋊C4—864no—
374C2×C22⋊C4C22×D4312yes—
375C2×C22⋊C4C22×D4312yes—
376C2×C22⋊C4C22×D4312yes—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—432no—
380C2×C42—864no—
381C2×C42—861no—
382C2×C42—861no—
383C2×C42—861no—
384C2×C42—861no—
385C2×C42—861no—
386C2×C42—861no—
387C2×C42—861no—
388C2×C42D17212yes—
389#99—4316no—
390#95—864no—
391#95—864no—
392#95—864no—
393C24—432no—
394C24C23×D4311yescharacteristic
395#41—864no—
396#41—864no—
397#41—864no—
398#41—864no—
399#41—864no—
400#41—864no—
401#41—864no—
402#41—864no—
403C2×Q8—434no—
404C2×Q8—861no—
405C2×Q8—861no—
406C2×Q8—862no—
407C2×D4—434no—
408C2×D4—434no—
409C2×D4—434no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—862no—
413C2×D4—862no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—862no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—432no—
420C22×C4—438no—
421C22×C4—434no—
422C22×C4—868no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—864no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—1724no—
431C22×C4C2×C4×D4312yes—
432C22×C4C2×D17214yes—
433C22×C4C2×D17211yescharacteristic
434C22×C4C2×D17211yescharacteristic
435C22×C4#1062189812yes—
436C22×C4D4×D4311yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4#1062190012yes—
441C22×C4Q8×D4312yes—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—42no—
446C4⋊C4—868no—
447C4⋊C4—864no—
448C4⋊C4—862no—
449C4⋊C4—862no—
450C4⋊C4—1728no—
451C4⋊C4—1728no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—434no—
458C22⋊C4—868no—
459C22⋊C4—862no—
460C22⋊C4—862no—
461C22⋊C4—862no—
462C22⋊C4—1728no—
463C22⋊C4C2×C4×D4314yes—
464C42—24no—
465C42—22no—
466C42—22no—
467C42—42no—
468C42—868no—
469C42—864no—
470C42—862no—
471C42—862no—
472C42—1721no—
473C42—1721no—
474C42—1721no—
475C42—1721no—
476C23—42no—
477C23—434no—
478C23—862no—
479C23—862no—
480C23—1724no—
481C23C22×C4×D4311yescharacteristic
482C23C2×D4×D4311yescharacteristic
483C23C2×D4×D4311yescharacteristic
484C23C22×D17211yescharacteristic
485C23C2×Q8×D4311yescharacteristic
486C23C2×#1062190011yescharacteristic
487C23C2×#1062189811yescharacteristic
488Q8—864no—
489Q8—864no—
490D4—864no—
491D4—864no—
492D4—864no—
493D4—864no—
494D4—864no—
495D4—864no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—434no—
503C2×C4—862no—
504C2×C4—862no—
505C2×C4—868no—
506C2×C4—868no—
507C2×C4—864no—
508C2×C4—864no—
509C2×C4—864no—
510C2×C4—864no—
511C2×C4—864no—
512C2×C4—3448no—
513C2×C4—1724no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1724no—
519C2×C4C4⋊C4×D4312yes—
520C2×C4C4⋊C4×D4312yes—
521C2×C4(C22⋊D43)⋊C412yes—
522C2×C4(C22⋊D43)⋊C412yes—
523C2×C4C4×D17212yes—
524C2×C4C4×D17212yes—
525C2×C4#1306329511yescharacteristic
526C2×C4#1306329511yescharacteristic
527C2×C4#1306329511yescharacteristic
528C2×C4#1306329511yescharacteristic
529C2×C4#1306330312yes—
530C2×C4#1306330312yes—
531C2×C4#1306330512yes—
532C2×C4#1306330512yes—
533C2×C4#1306330712yes—
534C2×C4#1306330712yes—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—864no—
543C22—3442no—
544C22—1724no—
545C22—1724no—
546C22C2×C4⋊C4×D4311yescharacteristic
547C22C2×(C22⋊D43)⋊C411yescharacteristic
548C22C2×C4×D17211yescharacteristic
549C22C2×#1306329511yescharacteristic
550C22C2×#1306330311yescharacteristic
551C22C2×#1306330511yescharacteristic
552C22C2×#1306330711yescharacteristic
553C4—44no—
554C4—44no—
555C4—82no—
556C4—864no—
557C4—1724no—
558C4—1724no—
559C4—1724no—
560C4#1458277312yes—
561C4#1458277312yes—
562C4#1458277312yes—
563C4#1458277312yes—
564C2—21no—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2—1724no—
571C2C2×#1458277311yescharacteristic
572C2#1914398912yes—
subgroupG/H
centerC2×C4#13063295
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1740C2
socleC22×C43C2×#120
prime radicalC22×#10621898C22
cosocleC24×C43C24
hypercenter#1740D43
hypocenterC43#20888
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
4. #19137079C2semidirect
5. #19137077C2semidirect
6. #19134877C2semidirect
7. #19134327C2semidirect
8. C43×#1740C2semidirect
21. #14582872C4semidirect
62. #13063284C2×C4semidirect
84. #13063239C2×C4semidirect
96. #117×C43C2×C4semidirect
145. C2×D172C4⋊C4semidirect
150. C2×C4×D43C4⋊C4semidirect
154. C2×Dic86C4⋊C4semidirect
285. #1740D43semidirect
324. C43#20888semidirect
361. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191477962
C2×#145828722
#191370832
#191370792
#191370772
#191348772
#191343272
C43×#17402
#2088843