Finite Group Databasebeta

← #25066702

Subgroups — #25066702

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#19144666C211yesmaximal, characteristic
2#19143689C211yesmaximal, characteristic, complemented
3#19133466C211yesmaximal, characteristic, complemented
4#19133452C211yesmaximal, characteristic, complemented
5#19133445C211yesmaximal, characteristic, complemented
6#19133431C211yesmaximal, characteristic, complemented
7#19133412C211yesmaximal, characteristic, complemented
8#19133407C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10C8×#10621883C211yesmaximal, characteristic, complemented
11#19133378C211yesmaximal, characteristic, complemented
12#19133029C211yesmaximal, characteristic
13#19132997C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#2988C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583240C411yescharacteristic
18#14583240C411yescharacteristic
19#14583184C411yescharacteristic
20#14583179C411yescharacteristic
21#14583109C411yescharacteristic
22#14583104C411yescharacteristic
23#14583061C411yescharacteristic
24#14583061C411yescharacteristic
25#14583029C2211yescharacteristic
26#14583029C2211yescharacteristic
27#14583028—21no—
28#14583028—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C4×#10621885C2211yescharacteristic
32C4×#10621885C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34C4×#10621883C2211yescharacteristic
35#14582957—21no—
36#14582957—21no—
37#14582956C2211yescharacteristic
38#14582952C2211yescharacteristic
39#14582952C2211yescharacteristic
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
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4⋊C8×C43—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71#13063325C2×C411yescharacteristic
72#13063325C2×C411yescharacteristic
73#13063317—21no—
74#13063304—21no—
75#13063304C2×C411yescharacteristic
76#13063304C2×C411yescharacteristic
77C4×Dic86—21no—
78C4×Dic86C2311yescharacteristic
79C4×Dic86C2311yescharacteristic
80#13063284—21no—
81#13063258C2×C411yescharacteristic
82#13063258C2×C411yescharacteristic
83#13063256C2×C411yescharacteristic
84#13063256C2×C411yescharacteristic
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)C2×C411yescharacteristic
87C4⋊(C43⋊C8)C2×C411yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89C4⋊(C43⋊C8)C2311yescharacteristic
90Dic43⋊C8—21no—
91Dic43⋊C8—21no—
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94#13063249C2×C411yescharacteristic
95#13063249C2×C411yescharacteristic
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063248C2×C411yescharacteristic
99#13063248C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)C2×C411yescharacteristic
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106#13063236—21no—
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×#41×C43C2×C411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C4×Q8×C43C2×C411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43C2×C411yescharacteristic
124C4×D4×C43C2311yescharacteristic
125#117×C43—21no—
126#117×C43C2×C411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—81no—
161C2×C8×C43—81no—
162C2×C8×C43—81no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43C22×C411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182C22⋊Dic43—21no—
183#10621885—22no—
184#10621885—22no—
185#10621883—22no—
186#10621883—22no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C411yescharacteristic
191C4⋊Dic43C22×C411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C23×C43—21no—
207C23×C43C4×D411yescharacteristic
208Q8×C43—21no—
209Q8×C43#13112yes—
210D4×C43—24no—
211D4×C43—21no—
212D4×C43#13112yes—
213C2×C4×C43—24no—
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×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—81no—
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—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—21no—
239Dic86—81no—
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—22no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43C2×C4×D411yescharacteristic
262C4×C43—21no—
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43C2×#13111yescharacteristic
270C4×C43C2×#13111yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277#3107—431no—
278#2988D4311yescharacteristic
279#2985—431no—
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—42no—
294C2×C43#292911yescharacteristic
295C2×C43#294711yescharacteristic
296C2×C43#295711yescharacteristic
297#533—431no—
298C4×#41C2×D4311yescharacteristic
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—431no—
308#446—431no—
309#446—861no—
310#446—861no—
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—21no—
320C8×D4—21no—
321C8×D4C2×D4311yescharacteristic
322C8×D4C2×D4311yescharacteristic
323#433—861no—
324#433—861no—
325#432—431no—
326#431—21no—
327#431—431no—
328#431—431no—
329#431C2×D4311yescharacteristic
330C2×C4⋊C8—21no—
331C2×C4⋊C8C2×D4311yescharacteristic
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×#41C4×D4311yescharacteristic
350C2×Q16—431no—
351C2×Q16—431no—
352C2×SD16—431no—
353C2×SD16—431no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359#125—861no—
360C22⋊Q8—431no—
361C22⋊Q8—431no—
362C22⋊Q8—861no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—861no—
366C4×Q8C4×D4311yescharacteristic
367C4×Q8C22×D4311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4C4×D4311yescharacteristic
371C4×D4C22×D4311yescharacteristic
372#117—21no—
373#117—861no—
374#117C4×D4311yescharacteristic
375C2×C42—21no—
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—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
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—21no—
407C22⋊C8—431no—
408C22⋊C8—431no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8C22⋊D4311yescharacteristic
412C22⋊C8C22⋊D4311yescharacteristic
413#97—861no—
414#97—861no—
415#97—861no—
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—22no—
427#41—22no—
428C2×Q8—431no—
429C2×Q8—431no—
430C2×Q8—861no—
431C2×Q8C2×C4×D4311yescharacteristic
432C2×D4—21no—
433C2×D4C2×C4×D4311yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
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—81no—
447C2×C8—81no—
448C2×C8—81no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8C2×C22⋊D4311yescharacteristic
458C2×C8C2×C22⋊D4311yescharacteristic
459C2×C8C2×C22⋊D4311yescharacteristic
460C2×C8C2×C22⋊D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
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⋊C4C2×C4×D4311yescharacteristic
473C4⋊C4C2×C4×D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—861no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42#1062189811yescharacteristic
486C42C2×C22⋊D4311yescharacteristic
487C42C23×D4311yescharacteristic
488C23—21no—
489C23C4×C22⋊D4311yescharacteristic
490Q8—21no—
491Q8—861no—
492Q8—861no—
493Q8—861no—
494Q8—861no—
495Q8—3441no—
496Q8#1306333112yes—
497D4—24no—
498D4—21no—
499D4#1306333112yes—
500C2×C4—24no—
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—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
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—22no—
540C22—41no—
541C22—41no—
542C22C2×C4×C22⋊D4311yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—1721no—
551C4—1721no—
552C4—1721no—
553C4—1721no—
554C4C2×#1306333111yescharacteristic
555C4C2×#1306333111yescharacteristic
556C4#1458371011yescharacteristic
557C4#1458371411yescharacteristic
558C2—41no—
559C2—42no—
560C2#1914328911yescharacteristic
561C2#1914343411yescharacteristic
562C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×C43C2×C4
cosocleC42×C43C24
hypercenter#2988D43
hypocenterC43#17921
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #19143689C2semidirect
3. #19133466C2semidirect
4. #19133452C2semidirect
5. #19133445C2semidirect
6. #19133431C2semidirect
7. #19133412C2semidirect
8. #19133407C2semidirect
9. C8×#10621885C2semidirect
10. C8×#10621883C2semidirect
11. #19133378C2semidirect
13. #19132997C2semidirect
14. #19132895C2semidirect
348. C43#17921semidirect

Maximal subgroups

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

subgroupindex
#191446662
#191436892
#191334662
#191334522
#191334452
#191334312
#191334122
#191334072
C8×#106218852
C8×#106218832
#191333782
#191330292
#191329972
#191328952
C43×#29882
#1792143