Finite Group Databasebeta

← #25066813

Subgroups — #25066813

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144632C211yesmaximal, characteristic
2#19143526C211yesmaximal, characteristic
3#446×D43C211yesmaximal, characteristic
4#19133493C211yesmaximal, characteristic, complemented
5#19133490C211yesmaximal, characteristic, complemented
6#19133490C211yesmaximal, characteristic, complemented
7#19133448C211yesmaximal, characteristic, complemented
8#19133446C211yesmaximal, characteristic, complemented
9#19133444C211yesmaximal, characteristic, complemented
10#19133442C211yesmaximal, characteristic, complemented
11#19133368C211yesmaximal, characteristic
12#19133022C211yesmaximal, characteristic
13#19132996C211yesmaximal, characteristic
14#19132877C211yesmaximal, characteristic
15C43×#1591C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18#14583236C411yescharacteristic
19#14583233C411yescharacteristic
20#14583193C411yescharacteristic
21#14583192C411yescharacteristic
22#14583108C411yescharacteristic
23#14583107C411yescharacteristic
24#14583056C411yescharacteristic
25#14583053C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583029C2211yescharacteristic
28#14583029C2211yescharacteristic
29#14583028—21no—
30#14583027—21no—
31#14583027—21no—
32#14583026C2211yescharacteristic
33Q8×C43⋊C8C2211yescharacteristic
34#14583023—21no—
35#14583023C2211yescharacteristic
36C4×Dic172C2211yescharacteristic
37C4×#10621885C2211yescharacteristic
38C4×#10621885C2211yescharacteristic
39#14582950C2211yescharacteristic
40#14582950C2211yescharacteristic
41#14582924—21no—
42#14582921C2211yescharacteristic
43C4⋊C8×D43—21no—
44C4⋊C8×D43C2211yescharacteristic
45#14582856—21no—
46#97×D43—21no—
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582651C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54Q8⋊(C43⋊C8)C2211yescharacteristic
55#14582629C2211yescharacteristic
56#14582629C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C43×#446C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×Q8×D43C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621885C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×C8×D43—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063324C2×C411yescharacteristic
76#13063323C2×C411yescharacteristic
77#13063315—21no—
78#13063305C2×C411yescharacteristic
79#13063303—21no—
80#13063301C2×C411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86C2311yescharacteristic
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87#13063290C2×C411yescharacteristic
88#13063282—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43C2×C411yescharacteristic
91C42×D43—21no—
92C42×D43C2311yescharacteristic
93#13063259C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8C2×C411yescharacteristic
108Dic43⋊C8C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063249C2×C411yescharacteristic
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8C2×C411yescharacteristic
117(C2×D43)⋊C8C2×C411yescharacteristic
118#13063236—21no—
119#13063235—21no—
120#13063235—21no—
121#13063235—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×Q16×C43C2×C411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43C2×C411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#103×C43C2×C411yescharacteristic
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146Q8×D43—41no—
147Q8×D43—41no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43C22×C411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43#4111yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157Q16×C43—41no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C22×C411yescharacteristic
168C4⋊C4×C43C22×C411yescharacteristic
169C42×C43—21no—
170C42×C43—21no—
171C42×C43C2411yescharacteristic
172#10621885—41no—
173#10621885—41no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43C22×C411yescharacteristic
179C4⋊Dic43C22×C411yescharacteristic
180Dic43⋊C4—21no—
181Dic43⋊C4—21no—
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43C22×C411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202Dic172—41no—
203#10621872—42no—
204C8×D43—22no—
205C8×D43—42no—
206C8×D43Q1614yescomplemented
207C22×D43C4×D411yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43C23×C411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43C4×D411yescharacteristic
224C2×Dic43C4×D411yescharacteristic
225C2×Dic43C4×D411yescharacteristic
226C4×D43—21no—
227C4×D43—21no—
228C4×D43—41no—
229C4×D43—42no—
230C4×D43—42no—
231C4×D43C2×Q1612yes—
232C4×D43#13512yes—
233Dic86—21no—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—42no—
238Dic86—42no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43C2×Q1612yes—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8C2×Q1612yes—
253#17931—431nomaximal, Sylow
254C22×C43C2×C4×D411yescharacteristic
255C2×D43—21no—
256C2×D43—21no—
257C2×D43C4×Q1612yes—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43#56811yescharacteristic
264C4×C43#56811yescharacteristic
265C4×C43C22×Q1611yescharacteristic
266C4×C43C2×#13511yescharacteristic
267Dic43—21no—
268Dic43—21no—
269Dic43—41no—
270Dic43—41no—
271Dic43—41no—
272Dic43—41no—
273Dic43C4×Q1612yes—
274#3104—431no—
275#2960—431no—
276C2×#446—431no—
277#1591—431no—
278#1591—431no—
279#1591—431no—
280#1591D4311yescharacteristic, complemented
281#1584—431no—
282#1584—431no—
283#1584—431no—
284#1584—431no—
285#1571—431no—
286#1487—431no—
287#1481—431no—
288#1450—431no—
289C2×C43#293011yescharacteristic
290C2×C43C2×C4×Q1611yescharacteristic
291C2×C43#295511yescharacteristic
292D43—22no—
293#533—431no—
294C2×C4×Q8—431no—
295#484—431no—
296#484—431no—
297#477—431no—
298#477—431no—
299#462—431no—
300#462—431no—
301#451—431no—
302#451—431no—
303#446—431no—
304#446—431no—
305#446—431no—
306#446—431no—
307#446—861no—
308#446—861no—
309#446—861no—
310#446C2×D4311yescharacteristic
311#446C2×D4311yescharacteristic
312C8×Q8—431no—
313C8×Q8—431no—
314C8×Q8—861no—
315C4×Q16—431no—
316C4×Q16—431no—
317C4×Q16—431no—
318C4×Q16C2×D4311yescharacteristic
319#431—431no—
320#431—431no—
321#424—861no—
322#423—431no—
323C2×C4⋊C8—431no—
324C2×C4⋊C8—861no—
325#405—861no—
326C2×#97—861no—
327C2×C4×C8—431no—
328#335—431no—
329#335—431no—
330#335—431no—
331#335C2×D4311yescharacteristic
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8C2×D4311yescharacteristic
339Q8⋊C8C2×D4311yescharacteristic
340#322—431no—
341#322—431no—
342C82—431no—
343C82C2×D4311yescharacteristic
344C43#1793111yescharacteristic, complemented, Sylow
345C22×Q8—431no—
346C2×Q16—431no—
347C2×Q16—431no—
348C2×Q16—431no—
349C2×Q16C4×D4311yescharacteristic
350C2×M16—861no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356#125—861no—
357C22⋊Q8—431no—
358C22⋊Q8—431no—
359C22⋊Q8—861no—
360C4×Q8—431no—
361C4×Q8—431no—
362C4×Q8—431no—
363C4×Q8—431no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8C22×D4311yescharacteristic
368C4×Q8C22×D4311yescharacteristic
369#117—861no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—861no—
372C2×C42—431no—
373C2×C42—861no—
374#107—431no—
375#107—431no—
376#107—431no—
377#107C4×D4311yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—431no—
381C4⋊C8—431no—
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⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395#103—431no—
396#103—431no—
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103C4×D4311yescharacteristic
402#103C4×D4311yescharacteristic
403C22⋊C8—431no—
404C22⋊C8—431no—
405C22⋊C8—861no—
406#97—21no—
407#97—21no—
408#97—861no—
409#97—861no—
410#97—861no—
411#97—861no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—431no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—861no—
418C4×C8—861no—
419C4×C8C22×D4311yescharacteristic
420C4×C8C22×D4311yescharacteristic
421C4×C8C22×D4311yescharacteristic
422C2×Q8—431no—
423C2×Q8—431no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—1721no—
427C2×Q8—1721no—
428C2×Q8C2×C4×D4311yescharacteristic
429C2×Q8C2×C4×D4311yescharacteristic
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—861no—
434C22×C4—861no—
435Q16—41no—
436Q16—1721no—
437Q16—1721no—
438Q16—1721no—
439M16—1722no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—431no—
444C2×C8—434no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—862no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—1722no—
453C2×C8C2×C4×D4311yescharacteristic
454C2×C8C2×C4×D4311yescharacteristic
455C2×C8D4×D4311yescharacteristic
456C2×C8D4×D4311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—431no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4C2×C4×D4311yescharacteristic
472C4⋊C4C2×C4×D4311yescharacteristic
473C22⋊C4—861no—
474C22⋊C4—861no—
475C42—21no—
476C42—21no—
477C42—431no—
478C42—431no—
479C42—431no—
480C42—861no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42C23×D4311yescharacteristic
485C23—431no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—861no—
491Q8—861no—
492Q8—861no—
493Q8—861no—
494Q8—1722no—
495Q8—1722no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—431no—
501C2×C4—432no—
502C2×C4—432no—
503C2×C4—431no—
504C2×C4—431no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—1721no—
512C2×C4—1722no—
513C2×C4—1722no—
514C2×C4C22×C4×D4311yescharacteristic
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4#41×D4311yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—432no—
524C8—861no—
525C8—861no—
526C8—861no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C8Q16×D4312yes—
531C22—432no—
532C22—861no—
533C22—861no—
534C22C4×D4×D4311yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—432no—
541C4—861no—
542C4—861no—
543C4—1721no—
544C4—1721no—
545C4—1721no—
546C4—1721no—
547C4#1458366411yescharacteristic
548C4#1458366511yescharacteristic
549C4C2×Q16×D4311yescharacteristic
550C4#135×D4311yescharacteristic
551C2—862no—
552C2#1914329511yescharacteristic
553C2C4×Q16×D4311yescharacteristic
554C2#1914349311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1591C2
socleC22×C43C2×C4×D4
prime radicalC22×D43C4×D4
cosocleC42×C43C24
hypercenter#1591D43
hypocenterC43#17931
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1591

Complements

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

NH ≅ G/Ntype
4. #19133493C2semidirect
5. #19133490C2semidirect
6. #19133490C2semidirect
7. #19133448C2semidirect
8. #19133446C2semidirect
9. #19133444C2semidirect
10. #19133442C2semidirect
15. C43×#1591C2semidirect
206. C8×D43Q16semidirect
280. #1591D43semidirect
344. C43#17931semidirect

Maximal subgroups

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

subgroupindex
#191446322
#191435262
#446×D432
#191334932
#191334902
#191334482
#191334462
#191334442
#191334422
#191333682
#191330222
#191329962
#191328772
C43×#15912
#1793143