Finite Group Databasebeta

← #25066698

Subgroups — #25066698

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144660C211yesmaximal, characteristic
2#19143703C211yesmaximal, characteristic
3#19133464C211yesmaximal, characteristic, complemented
4#19133450C211yesmaximal, characteristic, complemented
5#19133443C211yesmaximal, characteristic, complemented
6#19133429C211yesmaximal, characteristic, complemented
7#19133412C211yesmaximal, characteristic, complemented
8#19133405C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10C8×#10621884C211yesmaximal, characteristic, complemented
11#19133381C211yesmaximal, characteristic, complemented
12#19133027C211yesmaximal, characteristic
13#19132998C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#2985C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237C411yescharacteristic
18#14583237C411yescharacteristic
19#14583181C411yescharacteristic
20#14583176C411yescharacteristic
21#14583106C411yescharacteristic
22#14583101C411yescharacteristic
23#14583059C411yescharacteristic
24#14583059C411yescharacteristic
25C8×Dic86C2211yescharacteristic
26C8×Dic86C2211yescharacteristic
27C4×#10621885C2211yescharacteristic
28C4×#10621885C2211yescharacteristic
29C4×#10621884C2211yescharacteristic
30C4×#10621884C2211yescharacteristic
31C8×D172C2211yescharacteristic
32C8×D172C2211yescharacteristic
33(C22⋊D43)⋊C8—21no—
34(C22⋊D43)⋊C8—21no—
35#14582952C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582951—21no—
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39C4⋊C8×D43—21no—
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46Q8⋊(C43⋊C8)C2211yescharacteristic
47Q8⋊(C43⋊C8)C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582620C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#446—21no—
58C43×#446—21no—
59C43×#446C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C8×Q8×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#433—21no—
65C43×#432C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621898C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621884C2×C411yescharacteristic
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C4×Dic86C2×C411yescharacteristic
76C4×Dic86C2311yescharacteristic
77C4×D172C2×C411yescharacteristic
78C4×D172C2311yescharacteristic
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81#13063284C2×C411yescharacteristic
82#13063282—21no—
83C42×D43—21no—
84#13063258C2×C411yescharacteristic
85#13063258C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2×C411yescharacteristic
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95Dic43⋊C8—21no—
96#13063249C2×C411yescharacteristic
97#13063249C2×C411yescharacteristic
98#13063249C2×C411yescharacteristic
99#13063249C2×C411yescharacteristic
100#13063248C2×C411yescharacteristic
101#13063248C2×C411yescharacteristic
102#13063245C2×C411yescharacteristic
103#13063245C2×C411yescharacteristic
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106C22⋊(C43⋊C8)C2×C411yescharacteristic
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109C4×C43⋊C8C2311yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C8×Dic43—21no—
114C8×Dic43—21no—
115C4⋊Q8×C43C2×C411yescharacteristic
116C4⋊Q8×C43C2×C411yescharacteristic
117#125×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43C2×C411yescharacteristic
120C22⋊Q8×C43C2×C411yescharacteristic
121C4×Q8×C43—21no—
122C4×Q8×C43C2311yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124#117×C43—21no—
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—21no—
127C4⋊C8×C43—21no—
128C4⋊C8×C43—21no—
129C4⋊C8×C43—21no—
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43D411yescharacteristic
136C22⋊C8×C43D411yescharacteristic
137#97×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C22×C411yescharacteristic
146C2×Q8×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43#4111yescharacteristic
150C2×C22⋊D43—21no—
151#10621898—22no—
152#10621898—22no—
153C2×D172C22×C411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×Dic86C22×C411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C22×C411yescharacteristic
172C4⋊C4×C43C22×C411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43C22×C411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182#10621885—22no—
183#10621885—22no—
184#10621884—22no—
185#10621884—22no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C8×D43—81no—
205C8×D43—81no—
206C23×C43C4×D411yescharacteristic
207C22×D43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—81no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
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—41no—
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—24no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232D172—21no—
233D172#13112yes—
234C4×D43—24no—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—81no—
238Dic86—21no—
239Dic86#13112yes—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#17921—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43C2×C4×D411yescharacteristic
259C2×D43—22no—
260C2×D43—41no—
261C2×D43—41no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43C2×#13111yescharacteristic
271C4×C43C2×#13111yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—22no—
275Dic43—41no—
276Dic43—41no—
277#3107—431no—
278#2988—431no—
279#2985D4311yescharacteristic, complemented
280#1587—431no—
281#1585—431no—
282#1584—431no—
283#1582—431no—
284#1579—431no—
285SD16⋊C8—431no—
286C8×Q16—431no—
287C8×SD16—431no—
288#1573—431no—
289#1488—431no—
290#1481—431no—
291#1454—431no—
292C2×C43—41no—
293C2×C43#292911yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43#295711yescharacteristic
296D43—42no—
297#533C2×D4311yescharacteristic
298C4×#41—431no—
299#485—431no—
300#485—431no—
301#475—431no—
302#474—431no—
303#462—431no—
304#461—431no—
305#452—431no—
306#452—431no—
307#446—21no—
308#446—21no—
309#446C2×D4311yescharacteristic
310#446C2×D4311yescharacteristic
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8C2×D4311yescharacteristic
314C8×Q8C2×D4311yescharacteristic
315C4×Q16—431no—
316C4×Q16—431no—
317C4×SD16—431no—
318C4×SD16—431no—
319C8×D4—431no—
320C8×D4—431no—
321C8×D4—861no—
322C8×D4—861no—
323#433—21no—
324#433—21no—
325#432C2×D4311yescharacteristic
326#431—431no—
327#431—431no—
328#431—861no—
329#431C2×D4311yescharacteristic
330C2×C4⋊C8—431no—
331C2×C4⋊C8—861no—
332#335—431no—
333#335—431no—
334#334—431no—
335#334—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342D4⋊C8—431no—
343D4⋊C8—431no—
344#322—431no—
345#322—431no—
346#322—431no—
347C82—431no—
348C43#1792111yescharacteristic, complemented, Sylow
349C2×#41—431no—
350C2×Q16—431no—
351C2×Q16—431no—
352C2×SD16—431no—
353C2×SD16—431no—
354C22×C8—861no—
355C22×C8—861no—
356C22×C8—861no—
357C4⋊Q8C4×D4311yescharacteristic
358C4⋊Q8C4×D4311yescharacteristic
359#125—21no—
360C22⋊Q8—21no—
361C22⋊Q8C4×D4311yescharacteristic
362C22⋊Q8C4×D4311yescharacteristic
363C4×Q8—21no—
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8C22×D4311yescharacteristic
367C4×Q8C22×D4311yescharacteristic
368C4×D4—431no—
369C4×D4—431no—
370C4×D4—861no—
371C4×D4—861no—
372#117—21no—
373#117—431no—
374#117—861no—
375C2×C42—861no—
376C2×C42C22×D4311yescharacteristic
377#107—431no—
378#107—431no—
379#106—431no—
380#106—431no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8C22⋊D4311yescharacteristic
394C4⋊C8C22⋊D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#102—431no—
404#102—431no—
405C22⋊C8—21no—
406C22⋊C8—431no—
407C22⋊C8—431no—
408C22⋊C8—861no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8C22⋊D4311yescharacteristic
412C22⋊C8C22⋊D4311yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426#41—862no—
427#41—862no—
428C2×Q8—21no—
429C2×Q8—431no—
430C2×Q8C2×C4×D4311yescharacteristic
431C2×Q8C2×C4×D4311yescharacteristic
432C2×D4—431no—
433C2×D4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4C2×C4×D4311yescharacteristic
438C22×C4#1062189811yescharacteristic
439C22×C4C2×C22⋊D4311yescharacteristic
440Q16—862no—
441Q16—862no—
442SD16—862no—
443SD16—862no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—3441no—
455C2×C8—3441no—
456C2×C8—3441no—
457C2×C8C2×C22⋊D4311yescharacteristic
458C2×C8C2×C22⋊D4311yescharacteristic
459C2×C8C2×C22⋊D4311yescharacteristic
460C2×C8C2×C22⋊D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—431no—
469C4⋊C4—431no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4C2×C4×D4311yescharacteristic
473C4⋊C4C2×C4×D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C42—21no—
480C42—21no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42#1062189811yescharacteristic
486C42C2×C22⋊D4311yescharacteristic
487C42C23×D4311yescharacteristic
488C23—861no—
489C23C4×C22⋊D4311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—432no—
496Q8—861no—
497D4—432no—
498D4—864no—
499D4—861no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—864no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—3441no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4C4×C22⋊D4311yescharacteristic
517C2×C4C4×C22⋊D4311yescharacteristic
518C2×C4C4×C22⋊D4311yescharacteristic
519C2×C4C22×C4×D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4C2×#1062189811yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—861no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—862no—
540C22—1721no—
541C22—1721no—
542C22C2×C4×C22⋊D4311yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—862no—
552C4—1721no—
553C4—1721no—
554C4#131×D4311yescharacteristic
555C4#131×D4311yescharacteristic
556C4#1458370711yescharacteristic
557C4#1458371411yescharacteristic
558C2—41no—
559C2—1722no—
560C2#1914328711yescharacteristic
561C2#1914343811yescharacteristic
562C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2985C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C2×C4
cosocleC42×C43C24
hypercenter#2985D43
hypocenterC43#17921
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #19133464C2semidirect
4. #19133450C2semidirect
5. #19133443C2semidirect
6. #19133429C2semidirect
7. #19133412C2semidirect
8. #19133405C2semidirect
9. C8×#10621885C2semidirect
10. C8×#10621884C2semidirect
11. #19133381C2semidirect
13. #19132998C2semidirect
14. #19132895C2semidirect
15. C43×#2985C2semidirect
279. #2985D43semidirect
348. C43#17921semidirect

Maximal subgroups

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

subgroupindex
#191446602
#191437032
#191334642
#191334502
#191334432
#191334292
#191334122
#191334052
C8×#106218852
C8×#106218842
#191333812
#191330272
#191329982
#191328952
C43×#29852
#1792143