Finite Group Databasebeta

← #25067996

Subgroups — #25067996

Order 11008.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144632C211yesmaximal, characteristic
2#19143693C211yesmaximal, characteristic
3#19143681C211yesmaximal, characteristic
4#19133501C211yesmaximal, characteristic, complemented
5#19133464C211yesmaximal, characteristic, complemented
6#19133464C211yesmaximal, characteristic, complemented
7#19133446C211yesmaximal, characteristic, complemented
8#19133444C211yesmaximal, characteristic, complemented
9#19133411C211yesmaximal, characteristic, complemented
10C8×Dic172C211yesmaximal, characteristic, complemented
11#19133374C211yesmaximal, characteristic
12#19133066C211yesmaximal, characteristic
13#19132988C211yesmaximal, characteristic
14#19132894C211yesmaximal, 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#14583028—21no—
28#14583027—21no—
29#14583027—21no—
30#14583026C2211yescharacteristic
31Q8×C43⋊C8C2211yescharacteristic
32C8×Dic86C2211yescharacteristic
33C8×Dic86C2211yescharacteristic
34#14583023—21no—
35#14583023C2211yescharacteristic
36C4×Dic172C2211yescharacteristic
37C4×#10621885C2211yescharacteristic
38C4×#10621885C2211yescharacteristic
39#14582961—21no—
40#14582959—21no—
41#14582955C2211yescharacteristic
42#14582954—21no—
43#14582951—21no—
44#14582951C2211yescharacteristic
45#14582950C2211yescharacteristic
46#14582950C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54Q8⋊(C43⋊C8)C2211yescharacteristic
55#14582629C2211yescharacteristic
56#14582629C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582621C2211yescharacteristic
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
71#13063324C2×C411yescharacteristic
72#13063323C2×C411yescharacteristic
73#13063315—21no—
74#13063305C2×C411yescharacteristic
75#13063303—21no—
76#13063301C2×C411yescharacteristic
77Q8×Dic43C2×C411yescharacteristic
78C4×Dic86—21no—
79C4×Dic86—21no—
80C4×Dic86C2311yescharacteristic
81C4×Dic86C2311yescharacteristic
82#13063290—21no—
83#13063290C2×C411yescharacteristic
84#13063282—21no—
85C4⋊C4×D43—21no—
86C4⋊C4×D43C2×C411yescharacteristic
87C42×D43—21no—
88C42×D43C2311yescharacteristic
89#13063259C2×C411yescharacteristic
90#13063258C2×C411yescharacteristic
91#13063258C2×C411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8C2×C411yescharacteristic
102Dic43⋊C8C2×C411yescharacteristic
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063250C2×C411yescharacteristic
106#13063250C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063248C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8C2×C411yescharacteristic
115(C2×D43)⋊C8C2×C411yescharacteristic
116(C2×D43)⋊C8D411yescharacteristic
117(C2×D43)⋊C8D411yescharacteristic
118#13063236—21no—
119#13063235—21no—
120#13063235—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
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—22no—
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—22no—
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—22no—
203C22×D43C4×D411yescharacteristic
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43C23×C411yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C2×#4111yescharacteristic
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43C4×D411yescharacteristic
220C2×Dic43C4×D411yescharacteristic
221C2×Dic43C4×D411yescharacteristic
222C4×D43—21no—
223C4×D43—21no—
224C4×D43—21no—
225C4×D43—21no—
226C4×D43—41no—
227C4×D43—42no—
228C4×D43—42no—
229Dic86—21no—
230Dic86—21no—
231Dic86—21no—
232Dic86—42no—
233Dic86—42no—
234Dic86#13112yes—
235C8×C43—21no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#18032—431nomaximal, Sylow
250C22×C43C2×C4×D411yescharacteristic
251C2×D43—21no—
252C2×D43—21no—
253C2×D43—21no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43C2×#13111yescharacteristic
260C4×C43#56811yescharacteristic
261C4×C43#57811yescharacteristic
262C4×C43#57811yescharacteristic
263Dic43—22no—
264Dic43—21no—
265Dic43—21no—
266Dic43—21no—
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270#3104—431no—
271#2986—431no—
272#2984—431no—
273#1593—431no—
274#1591D4311yescharacteristic, complemented
275#1587—431no—
276#1587—431no—
277#1584—431no—
278#1584—431no—
279#1579—431no—
280C8×Q16—431no—
281#1572—431no—
282#1497—431no—
283#1479—431no—
284#1454—431no—
285C2×C43#293311yescharacteristic
286C2×C43#295011yescharacteristic
287C2×C43#295511yescharacteristic
288D43—41no—
289#533—431no—
290C2×C4×Q8—431no—
291#484—431no—
292#484—431no—
293#477—431no—
294#477—431no—
295#462—431no—
296#462—431no—
297#451—431no—
298#451—431no—
299#446—431no—
300#446—431no—
301#446—861no—
302#446—861no—
303#446—861no—
304#446C2×D4311yescharacteristic
305#446C2×D4311yescharacteristic
306C8×Q8—431no—
307C8×Q8—431no—
308C8×Q8—431no—
309C8×Q8—431no—
310C8×Q8—861no—
311C4×Q16—431no—
312C4×Q16—431no—
313C4×Q16—431no—
314C4×Q16C2×D4311yescharacteristic
315#433—861no—
316#433—861no—
317#432—431no—
318#432—861no—
319#431—431no—
320#431—431no—
321#431—431no—
322#431—431no—
323#431—861no—
324#335—431no—
325#335C2×D4311yescharacteristic
326#334—431no—
327#334—431no—
328Q8⋊C8—431no—
329Q8⋊C8—431no—
330Q8⋊C8—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334Q8⋊C8C2×D4311yescharacteristic
335Q8⋊C8C2×D4311yescharacteristic
336#322—431no—
337#322—431no—
338#322—431no—
339C82C2×D4311yescharacteristic
340C43#1803211yescharacteristic, complemented, Sylow
341C22×Q8—431no—
342C2×Q16—431no—
343C2×Q16—431no—
344C2×Q16—431no—
345C2×Q16C4×D4311yescharacteristic
346C4⋊Q8—431no—
347C4⋊Q8—431no—
348#125—861no—
349C22⋊Q8—431no—
350C22⋊Q8—431no—
351C22⋊Q8—861no—
352C4×Q8—431no—
353C4×Q8—431no—
354C4×Q8—431no—
355C4×Q8—431no—
356C4×Q8—861no—
357C4×Q8—861no—
358C4×Q8—861no—
359C4×Q8C22×D4311yescharacteristic
360C4×Q8C22×D4311yescharacteristic
361#117—861no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C42—431no—
365C2×C42—861no—
366#107—431no—
367#107—431no—
368#107—431no—
369#107C4×D4311yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—431no—
373C4⋊C8—431no—
374C4⋊C8—431no—
375C4⋊C8—431no—
376C4⋊C8—431no—
377C4⋊C8—431no—
378C4⋊C8—861no—
379C4⋊C8—861no—
380C4⋊C8—861no—
381C4⋊C8—861no—
382C4⋊C8—861no—
383C4⋊C8—861no—
384C4⋊C8—861no—
385C4⋊C8C22×D4311yescharacteristic
386C4⋊C8C22×D4311yescharacteristic
387#103—431no—
388#103—431no—
389#103—431no—
390#103—431no—
391#103—431no—
392#103—431no—
393#103C4×D4311yescharacteristic
394#103C4×D4311yescharacteristic
395C22⋊C8—431no—
396C22⋊C8—431no—
397C22⋊C8—431no—
398C22⋊C8—431no—
399C22⋊C8—861no—
400C22⋊C8—861no—
401C22⋊C8—861no—
402#97—21no—
403#97—21no—
404#97—861no—
405#97—861no—
406#97—861no—
407C4×C8—431no—
408C4×C8—431no—
409C4×C8—431no—
410C4×C8—861no—
411C4×C8—861no—
412C4×C8—861no—
413C4×C8—861no—
414C4×C8—861no—
415C4×C8C22×D4311yescharacteristic
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C2×Q8—431no—
419C2×Q8—431no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—862no—
423C2×Q8—1721no—
424C2×Q8C2×C4×D4311yescharacteristic
425C2×Q8C2×C4×D4311yescharacteristic
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—861no—
430C22×C4—861no—
431Q16—41no—
432Q16—862no—
433Q16—862no—
434Q16—1721no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—431no—
439C2×C8—431no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8C2×C4×D4311yescharacteristic
446C2×C8C2×C4×D4311yescharacteristic
447C2×C8D4×D4311yescharacteristic
448C2×C8D4×D4311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—431no—
452C4⋊C4—431no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4C2×C4×D4311yescharacteristic
464C4⋊C4C2×C4×D4311yescharacteristic
465C22⋊C4—861no—
466C22⋊C4—861no—
467C42—21no—
468C42—21no—
469C42—431no—
470C42—431no—
471C42—431no—
472C42—861no—
473C42—861no—
474C42—861no—
475C42—861no—
476C42C23×D4311yescharacteristic
477C23—431no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—432no—
483Q8—861no—
484Q8—861no—
485Q8—861no—
486Q8—1722no—
487Q8—1722no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—431no—
493C2×C4—431no—
494C2×C4—431no—
495C2×C4—861no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—1721no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4C22×C4×D4311yescharacteristic
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4#41×D4311yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—861no—
517C8—861no—
518C8—861no—
519C8—861no—
520C8—1721no—
521C8—1721no—
522C8—1721no—
523C22—861no—
524C22—861no—
525C22—861no—
526C22C4×D4×D4311yescharacteristic
527C4—21no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—861no—
533C4—861no—
534C4—861no—
535C4—862no—
536C4—1721no—
537C4—1721no—
538C4—1721no—
539C4#131×D4311yescharacteristic
540C4#1458366511yescharacteristic
541C4#1458371211yescharacteristic
542C4#1458371311yescharacteristic
543C2—1721no—
544C2#1914332411yescharacteristic
545C2#1914345811yescharacteristic
546C2#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#18032
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. #19133501C2semidirect
5. #19133464C2semidirect
6. #19133464C2semidirect
7. #19133446C2semidirect
8. #19133444C2semidirect
9. #19133411C2semidirect
10. C8×Dic172C2semidirect
15. C43×#1591C2semidirect
274. #1591D43semidirect
340. C43#18032semidirect

Maximal subgroups

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

subgroupindex
#191446322
#191436932
#191436812
#191335012
#191334642
#191334462
#191334442
#191334112
C8×Dic1722
#191333742
#191330662
#191329882
#191328942
C43×#15912
#1803243