Finite Group Databasebeta

← #25067719

Subgroups — #25067719

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144671C211yesmaximal, characteristic
2M16×Dic86C211yesmaximal, characteristic, complemented
3#19133502C211yesmaximal, characteristic, complemented
4#19133483C211yesmaximal, characteristic, complemented
5#19133464C211yesmaximal, characteristic, complemented
6#19133452C211yesmaximal, characteristic, complemented
7#19133445C211yesmaximal, characteristic, complemented
8#19133436C211yesmaximal, characteristic, complemented
9#19133407C211yesmaximal, characteristic, complemented
10C8×#10621885C211yesmaximal, characteristic, complemented
11#19133383C211yesmaximal, characteristic, complemented
12#19133060C211yesmaximal, characteristic
13#19132989C211yesmaximal, characteristic, complemented
14#19132892C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic
16C2×C4×Dic86C2211yescharacteristic
17#14583227C411yescharacteristic
18#14583210C411yescharacteristic
19#14583203C411yescharacteristic
20#14583203C411yescharacteristic
21#14583118C411yescharacteristic
22#14583118C411yescharacteristic
23#14583054C411yescharacteristic
24#14583037C411yescharacteristic
25#14583029C2211yescharacteristic
26#14583029C2211yescharacteristic
27#14583027—21no—
28#14583027—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C4×#10621885C2211yescharacteristic
32C4×#10621885C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34C4×#10621883C2211yescharacteristic
35#14582952C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582923C2211yescharacteristic
38#14582922—21no—
39M16×Dic43—21no—
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46#14582629C2211yescharacteristic
47#14582629C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50D4⋊(C43⋊C8)C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582620C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621877—21no—
73C4×Dic86—21no—
74C4×Dic86—21no—
75C4×Dic86C2×C411yescharacteristic
76C4×Dic86C2×C411yescharacteristic
77C4×Dic86C2311yescharacteristic
78C4×Dic86C2311yescharacteristic
79C2×C4⋊Dic43C2×C411yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×C4×Dic43—21no—
82#13063258C2×C411yescharacteristic
83#13063258C2×C411yescharacteristic
84#13063256C2×C411yescharacteristic
85#13063256C2×C411yescharacteristic
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)C2×C411yescharacteristic
89C4⋊(C43⋊C8)C2×C411yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94Dic43⋊C8—21no—
95Dic43⋊C8—21no—
96#13063249C2×C411yescharacteristic
97#13063249C2×C411yescharacteristic
98#13063248C2×C411yescharacteristic
99#13063248C2×C411yescharacteristic
100#13063248C2×C411yescharacteristic
101#13063248C2×C411yescharacteristic
102#13063246C2×C411yescharacteristic
103#13063246C2×C411yescharacteristic
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106C22⋊(C43⋊C8)C2×C411yescharacteristic
107#13063235—21no—
108#13063235—21no—
109C4×C43⋊C8C2311yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C8×Dic43—21no—
114C8×Dic43—21no—
115C2×M16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
119#126×C43—21no—
120#125×C43C2×C411yescharacteristic
121#124×C43C2×C411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43C2×C411yescharacteristic
124#121×C43C2×C411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C2×Dic86—22no—
154C2×Dic86—21no—
155C2×Dic86—41no—
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158M16×C43—22no—
159M16×C43—41no—
160M16×C43—42no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—42no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C42×C43—21no—
180C42×C43C22×C411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184#10621885—22no—
185#10621885—41no—
186#10621883—22no—
187#10621883—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C23×C43—21no—
209C23×C43C4×D411yescharacteristic
210Q8×C43—21no—
211Q8×C43—21no—
212D4×C43—21no—
213D4×C43—21no—
214D4×C43—81no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—42no—
236C2×Dic43—81no—
237Dic86—21no—
238Dic86—21no—
239Dic86—21no—
240Dic86—42no—
241Dic86#13112yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43#13712yes—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#18012—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43C2×C4×D411yescharacteristic
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43C2×#13111yescharacteristic
272C4×C43#56811yescharacteristic
273C4×C43C2×#13711yescharacteristic
274C4×C43#57511yescharacteristic
275Dic43—22no—
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279#3108—431no—
280#2969D4311yescharacteristic
281Q8×M16—431no—
282#1593—431no—
283#1590—431no—
284#1587—431no—
285#1585—431no—
286#1584—431no—
287#1583—431no—
288SD16⋊C8—431no—
289C8×Q16—431no—
290#1574—431no—
291#1495—431no—
292#1479—431no—
293#1453—431no—
294C2×C43—41no—
295C2×C43—81no—
296C2×C43#293311yescharacteristic
297C2×C43C4×#13711yescharacteristic
298C2×C43#295711yescharacteristic
299#529C2×D4311yescharacteristic
300C2×C4×Q8—431no—
301#483—431no—
302#480—431no—
303#479—431no—
304#479—431no—
305#464—431no—
306#464—431no—
307#451—431no—
308#448—431no—
309#446—431no—
310#446—431no—
311#446—861no—
312#446—861no—
313#446C2×D4311yescharacteristic
314C8×Q8—431no—
315C8×Q8—431no—
316C8×Q8C2×D4311yescharacteristic
317C4×Q16—431no—
318C4×Q16—431no—
319C4×SD16—431no—
320C4×SD16—431no—
321#436—21no—
322#436C2×D4311yescharacteristic
323#435—21no—
324C8×D4C2×D4311yescharacteristic
325#433—21no—
326#431—431no—
327#431—431no—
328#431C2×D4311yescharacteristic
329#423—431no—
330#423—861no—
331#405—21no—
332C4×M16—861no—
333C4×M16C2×D4311yescharacteristic
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344D4⋊C8—431no—
345D4⋊C8—431no—
346#322—431no—
347#322—431no—
348#322—431no—
349C82—431no—
350C43#1801211yescharacteristic, complemented, Sylow
351C22×Q8—431no—
352C2×Q16—431no—
353C2×Q16—431no—
354C2×SD16—431no—
355C2×SD16—431no—
356C2×M16—21no—
357C2×M16—861no—
358C2×M16C22⋊D4311yescharacteristic
359C2×M16C22⋊D4311yescharacteristic
360C22×C8—21no—
361#126—21no—
362#125C4×D4311yescharacteristic
363#124C4×D4311yescharacteristic
364#123—21no—
365C22⋊Q8C4×D4311yescharacteristic
366#121C4×D4311yescharacteristic
367C4×Q8—431no—
368C4×Q8—431no—
369C4×Q8—431no—
370C4×Q8—431no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381#107—431no—
382#107—431no—
383#106—431no—
384#106—431no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#103—431no—
405#102—431no—
406#102—431no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—431no—
411C22⋊C8—431no—
412C22⋊C8—861no—
413#97—21no—
414#97—861no—
415#97—861no—
416#97C22⋊D4311yescharacteristic
417#97C22⋊D4311yescharacteristic
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428C2×Q8—431no—
429C2×Q8—431no—
430C2×Q8—862no—
431C2×Q8—861no—
432C2×Q8—1721no—
433C2×Q8C2×C4×D4311yescharacteristic
434C2×D4—21no—
435C2×D4C2×C4×D4311yescharacteristic
436C22×C4—21no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4C2×C4×D4311yescharacteristic
440C22×C4#1062189811yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442Q16—862no—
443Q16—1721no—
444SD16—862no—
445SD16—1721no—
446M16—22no—
447M16—41no—
448M16—42no—
449M16—1722no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8C2×C22⋊D4311yescharacteristic
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C2×C8C2×C22⋊D4311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—431no—
470C4⋊C4—431no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4C2×C4×D4311yescharacteristic
477C4⋊C4C2×C4×D4311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C42—21no—
484C42—861no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42C2×C4×D4311yescharacteristic
489C42#1062189811yescharacteristic
490C42C2×C22⋊D4311yescharacteristic
491C42C23×D4311yescharacteristic
492C23—21no—
493C23C4×C22⋊D4311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—432no—
497Q8—861no—
498Q8—861no—
499Q8—861no—
500Q8—1722no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—3441no—
519C2×C4—1722no—
520C2×C4C4×C22⋊D4311yescharacteristic
521C2×C4C4×C22⋊D4311yescharacteristic
522C2×C4C4×C22⋊D4311yescharacteristic
523C2×C4C22×C4×D4311yescharacteristic
524C2×C4C22×C22⋊D4311yescharacteristic
525C2×C4C2×#1062189811yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C8#1306335512yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×C22⋊D4311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—862no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4#131×D4311yescharacteristic
559C4#1458366411yescharacteristic
560C4C2×#1306335511yescharacteristic
561C4#1458369711yescharacteristic
562C2—41no—
563C2—81no—
564C2#1914331711yescharacteristic
565C2C4×#1306335511yescharacteristic
566C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×C4×D4
prime radical#121×C43C2×C4
cosocleC42×C43C24
hypercenter#2969D43
hypocenterC43#18012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
3. #19133502C2semidirect
4. #19133483C2semidirect
5. #19133464C2semidirect
6. #19133452C2semidirect
7. #19133445C2semidirect
8. #19133436C2semidirect
9. #19133407C2semidirect
10. C8×#10621885C2semidirect
11. #19133383C2semidirect
13. #19132989C2semidirect
14. #19132892C2semidirect
350. C43#18012semidirect

Maximal subgroups

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

subgroupindex
#191446712
M16×Dic862
#191335022
#191334832
#191334642
#191334522
#191334452
#191334362
#191334072
C8×#106218852
#191333832
#191330602
#191329892
#191328922
C43×#29692
#1801243