Finite Group Databasebeta

← #25066670

Subgroups — #25066670

Order 11008.

596 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#19144677C211yesmaximal, characteristic
2#19143740C211yesmaximal, characteristic
3#19143675C211yesmaximal, characteristic, complemented
4#19133472C211yesmaximal, characteristic, complemented
5#19133465C211yesmaximal, characteristic, complemented
6#19133444C211yesmaximal, characteristic, complemented
7#19133437C211yesmaximal, characteristic, complemented
8#19133413C211yesmaximal, characteristic, complemented
9#19133406C211yesmaximal, characteristic, complemented
10#19133401C211yesmaximal, characteristic, complemented
11#19133394C211yesmaximal, characteristic, complemented
12#19133023C211yesmaximal, characteristic, complemented
13#19133001C211yesmaximal, characteristic
14#19132895C211yesmaximal, characteristic, complemented
15C43×#1574C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583230C411yescharacteristic
19#14583213C411yescharacteristic
20#14583207C411yescharacteristic
21#14583207C411yescharacteristic
22#14583122C411yescharacteristic
23#14583122C411yescharacteristic
24#14583057C411yescharacteristic
25#14583040C411yescharacteristic
26#14583026C2211yescharacteristic
27C8×Dic86—21no—
28C8×Dic86—21no—
29#14583023C2211yescharacteristic
30#14583023C2211yescharacteristic
31#14583023C2211yescharacteristic
32#14583023C2211yescharacteristic
33#14583023C2211yescharacteristic
34C4×Dic172C2211yescharacteristic
35C4×Dic172C2211yescharacteristic
36C4×#10621873C2211yescharacteristic
37C4×#10621873C2211yescharacteristic
38#14582976C2211yescharacteristic
39#14582975—21no—
40#14582968—21no—
41#14582964C2211yescharacteristic
42#14582959—21no—
43#14582952C2211yescharacteristic
44#14582952C2211yescharacteristic
45#14582949—21no—
46#14582949—21no—
47#14582924—21no—
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582629C2211yescharacteristic
51#14582629C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×Dic172C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621872—21no—
73C2×C8×D43—21no—
74#13063319—21no—
75#13063317C2×C411yescharacteristic
76#13063313C2×C411yescharacteristic
77#13063308—21no—
78#13063304C2×C411yescharacteristic
79#13063299C2×C411yescharacteristic
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172C2311yescharacteristic
88C4×C22⋊D43—21no—
89#13063282—21no—
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×C4×Dic43—21no—
93#13063259C2×C411yescharacteristic
94#13063259C2×C411yescharacteristic
95#13063257C2×C411yescharacteristic
96#13063257C2×C411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)D411yescharacteristic
99C4⋊(C43⋊C8)D411yescharacteristic
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106#13063250C2×C411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063250C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)D411yescharacteristic
116C22⋊(C43⋊C8)D411yescharacteristic
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119#13063235—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×M16×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2×C411yescharacteristic
133C4⋊C8×C43C2×C411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43C2×C411yescharacteristic
140C22⋊C8×C43C2×C411yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172C22×C411yescharacteristic
151C2×C4×D43—21no—
152C2×Dic86—21no—
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158M16×C43—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C22×C411yescharacteristic
166C2×C8×C43C22×C411yescharacteristic
167C42×C43C22×C411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43#4111yescharacteristic
170C42×C43C2411yescharacteristic
171C22⋊Dic43—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43C22×C411yescharacteristic
178C4⋊Dic43C22×C411yescharacteristic
179C4⋊Dic43C22×C411yescharacteristic
180C4⋊Dic43C22×C411yescharacteristic
181Dic43⋊C4—21no—
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C2×D411yescharacteristic
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200Dic172—22no—
201Dic172—22no—
202#10621873—22no—
203#10621873—22no—
204#10621872—81no—
205C8×D43—81no—
206C23×C43C4×D411yescharacteristic
207C22×D43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C23×C411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C22⋊D43—81no—
220C2×Dic43—24no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—81no—
229D172—21no—
230D172—21no—
231C4×D43—41no—
232C4×D43—41no—
233Dic86—24no—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86#13112yes—
239Dic86#13112yes—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#17919—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43C2×C4×D411yescharacteristic
259C2×D43—41no—
260C2×D43—41no—
261C2×D43—41no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43C2×#13111yescharacteristic
267C4×C43C2×#13111yescharacteristic
268C4×C43#57711yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—22no—
271Dic43—22no—
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277#3108—431no—
278#2993—431no—
279#2982—431no—
280#1588—431no—
281#1587—431no—
282#1584—431no—
283#1583—431no—
284#1579—431no—
285SD16⋊C8—431no—
286C8×Q16—431no—
287C8×SD16—431no—
288#1574D4311yescharacteristic, complemented
289#1487—431no—
290#1482—431no—
291#1454—431no—
292C2×C43—41no—
293C2×C43#292911yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43#295711yescharacteristic
296D43—81no—
297#529—431no—
298C2×C4×Q8—431no—
299#483—431no—
300#480—431no—
301#479—431no—
302#479—431no—
303#464—431no—
304#464—431no—
305#451—431no—
306#448—431no—
307#446—431no—
308C8×Q8—431no—
309C8×Q8—431no—
310C8×Q8—431no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—861no—
314C8×Q8—861no—
315C4×Q16—431no—
316C4×Q16—431no—
317C4×SD16—431no—
318C4×SD16—431no—
319#436—431no—
320#436—861no—
321#435—861no—
322C8×D4—431no—
323#433—861no—
324#431—431no—
325#431—431no—
326#431—861no—
327#431—861no—
328#431C2×D4311yescharacteristic
329#431C2×D4311yescharacteristic
330#424—861no—
331#423C2×D4311yescharacteristic
332#335C2×D4311yescharacteristic
333#335C2×D4311yescharacteristic
334#334C2×D4311yescharacteristic
335#334C2×D4311yescharacteristic
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#1791911yescharacteristic, complemented, Sylow
349C22×Q8—431no—
350C2×Q16—431no—
351C2×Q16—431no—
352C2×SD16—431no—
353C2×SD16—431no—
354C2×M16—21no—
355C2×M16—861no—
356C22×C8—861no—
357#126—861no—
358#125—431no—
359#124—431no—
360#123—861no—
361C22⋊Q8—431no—
362#121—431no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×D4—431no—
371C4×D4—861no—
372#117—861no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C42—861no—
376C2×C42C22×D4311yescharacteristic
377#107—431no—
378#107—431no—
379#106—431no—
380#106—431no—
381C4⋊C8—21no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—861no—
385C4⋊C8—861no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8C4×D4311yescharacteristic
392C4⋊C8C4×D4311yescharacteristic
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⋊C8C4×D4311yescharacteristic
412C22⋊C8C4×D4311yescharacteristic
413#97—861no—
414C4×C8—21no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C2×Q8—431no—
427C2×Q8—431no—
428C2×Q8—431no—
429C2×Q8—862no—
430C2×Q8—862no—
431C2×Q8—861no—
432C2×D4—431no—
433C2×D4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4C2×C4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4#1062190211yescharacteristic
440Q16—862no—
441Q16—862no—
442SD16—862no—
443SD16—862no—
444M16—81no—
445M16—3441no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—3441no—
457C2×C8C2×C4×D4311yescharacteristic
458C2×C8C2×C4×D4311yescharacteristic
459C2×C8C2×C4×D4311yescharacteristic
460C2×C8C2×C4×D4311yescharacteristic
461C4⋊C4—431no—
462C4⋊C4—431no—
463C4⋊C4—431no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C42—861no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42D4×D4311yescharacteristic
486C42#1062190211yescharacteristic
487C42C23×D4311yescharacteristic
488C23—861no—
489C23#1306328711yescharacteristic
490Q8—432no—
491Q8—432no—
492Q8—864no—
493Q8—861no—
494Q8—861no—
495Q8—861no—
496Q8—861no—
497D4—861no—
498D4—861no—
499D4—3441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—864no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—3441no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306328711yescharacteristic
517C2×C4#1306328711yescharacteristic
518C2×C4#1306328711yescharacteristic
519C2×C4C22×C4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C2×#1062190211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—861no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1721no—
540C22—1721no—
541C22—1721no—
542C22C2×#1306328711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—862no—
548C4—862no—
549C4—1721no—
550C4—1721no—
551C4—1721no—
552C4—1721no—
553C4—1721no—
554C4#131×D4311yescharacteristic
555C4#131×D4311yescharacteristic
556C4#1458370911yescharacteristic
557C4#1458371511yescharacteristic
558C2—41no—
559C2—3441no—
560C2#1914328811yescharacteristic
561C2#1914343611yescharacteristic
562C2#1914351111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1574C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenter#1574D43
hypocenterC43#17919
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #19143675C2semidirect
4. #19133472C2semidirect
5. #19133465C2semidirect
6. #19133444C2semidirect
7. #19133437C2semidirect
8. #19133413C2semidirect
9. #19133406C2semidirect
10. #19133401C2semidirect
11. #19133394C2semidirect
12. #19133023C2semidirect
14. #19132895C2semidirect
15. C43×#1574C2semidirect
288. #1574D43semidirect
348. C43#17919semidirect

Maximal subgroups

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

subgroupindex
#191446772
#191437402
#191436752
#191334722
#191334652
#191334442
#191334372
#191334132
#191334062
#191334012
#191333942
#191330232
#191330012
#191328952
C43×#15742
#1791943