Finite Group Databasebeta

← #14910635

Subgroups — #14910635

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13080303C211yesmaximal, characteristic, complemented
3#13070848C211yesmaximal, characteristic, complemented
4#13070819C211yesmaximal, characteristic, complemented
5#13070808C211yesmaximal, characteristic, complemented
6#13070774C211yesmaximal, characteristic, complemented
7#13070712C211yesmaximal, characteristic, complemented
8#13070702C211yesmaximal, characteristic, complemented
9#13070672C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic, complemented
11#13070530C211yesmaximal, characteristic, complemented
12C4×D176C211yesmaximal, characteristic, complemented
13#13070324C211yesmaximal, characteristic, complemented
14C2×#10622147C211yesmaximal, characteristic, complemented
15D4×C11×C16C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C22×D88C2211yescharacteristic
18#10623096—21no—
19#10623081—21no—
20C22×C11×C16C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic, complemented
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622728C2211yescharacteristic, complemented
27#10622719C2211yescharacteristic, complemented
28C2×#66882C2211yescharacteristic
29C2×#66864C2211yescharacteristic, complemented
30C2×D176C2211yescharacteristic
31C2×D176C2211yescharacteristic
32#10622460—21no—
33#10622457—21no—
34#10622350—21no—
35#10622348—21no—
36#10622347—21no—
37#10622344—21no—
38#10622309C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic, complemented
41#10622296C2211yescharacteristic, complemented
42C11×C4⋊C16C2211yescharacteristic, complemented
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic, complemented
45C4×C11×C16C2211yescharacteristic, complemented
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic, complemented
53#10622143C2211yescharacteristic, complemented
54#10622142C2211yescharacteristic, complemented
55#10622142C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59C2×#4339—21no—
60C22×D44—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D411yescharacteristic
64#66992—41no—
65#66990—41no—
66#66983—21no—
67#66983—21no—
68#66983—21no—
69#66979—21no—
70C2×C4⋊Dic11—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73#66957—22no—
74#66957—41no—
75C2×D88—22no—
76C2×D88—21no—
77C2×D88—41no—
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66951—41no—
84#66947—41no—
85#66937—41no—
86#66936—41no—
87(C22⋊D11)⋊C4—41no—
88C22⋊C4×D11—41no—
89#66928—21no—
90C4×D44—21no—
91C4×D44—21no—
92#66923—21no—
93C2×C11×C16—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66885—21no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66885—21no—
108#66882—21no—
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66881—21no—
114#66881—21no—
115#66880—21no—
116#66864—41no—
117D176—22no—
118D176—41no—
119#33864—111nomaximal, Sylow
120C23×D11—41no—
121C2×D4×C11D811yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C22×Dic11—41no—
129#4339—42no—
130#4339—81no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—42no—
135C2×D44—41no—
136C2×D44—81no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×Dic22—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4D811yescharacteristic
150C11×C22⋊C4D811yescharacteristic
151C11×C22⋊C4D811yescharacteristic
152C42×C11C2×D411yescharacteristic
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170C4×Dic11—41no—
171Dic44—21no—
172Dic44—21no—
173D88—21no—
174D88—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—42no—
179D88#4112yes—
180#4314—42no—
181#4314—81no—
182C11×C16—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186#3339—111no—
187#3280—111no—
188#2242—111no—
189#2236—111no—
190#2234—111no—
191#2228—111no—
192#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2184—111no—
197C4×D16—111no—
198D4×C16D1111yescharacteristic, complemented
199#2138—111no—
200C2×#357—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—82no—
207C22×D11—82no—
208C22×D11—161no—
209D4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—82no—
220C22⋊D11—82no—
221C22⋊D11—161no—
222C22⋊D11—161no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—161no—
229D44—22no—
230D44—41no—
231D44—41no—
232D44—41no—
233D44—41no—
234D44—41no—
235D44—82no—
236C4×D11—82no—
237C4×D11—161no—
238C4×D11—161no—
239Dic22—41no—
240Dic22—41no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—21no—
244C8×C11C2×#4111yescharacteristic
245C8×C11H(5,𝔽2)11yescharacteristic
246C2×#135—111no—
247C22×D8—111no—
248#553—221no—
249#546—221no—
250C2×SD32—111no—
251C2×D16—111no—
252C2×D16—111no—
253C22×C16C2×D1111yescharacteristic
254C22×C16C2×D1111yescharacteristic, complemented
255#499—111no—
256#495—111no—
257#482—221no—
258#481—221no—
259#478—221no—
260#467—111no—
261#466—111no—
262#466—111no—
263#466—111no—
264#463—221no—
265#450—221no—
266#449—221no—
267C4×D8—111no—
268C4×D8—111no—
269C8×D4C2×D1111yescharacteristic
270#427—111no—
271C2×#107—111no—
272#367—111no—
273#366—111no—
274#366—111no—
275C4⋊C16C2×D1111yescharacteristic, complemented
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286C22⋊C16C2×D1111yescharacteristic
287C22⋊C16C2×D1111yescharacteristic, complemented
288C4×C16C2×D1111yescharacteristic, complemented
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11#50812yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—42no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—164no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—21no—
310C4×C11#54611yescharacteristic
311C4×C11#57711yescharacteristic
312Dic11—81no—
313Dic11—81no—
314Dic11—81no—
315Dic11—81no—
316Dic11—81no—
317C2×#41—221no—
318C22×D4—221no—
319#135—222no—
320#135—441no—
321C2×Q16—111no—
322C2×SD16—221no—
323C2×SD16—221no—
324C2×D8—111no—
325C2×D8—111no—
326C2×D8—111no—
327C2×D8—222no—
328C2×D8—221no—
329C2×D8—441no—
330C22×C8C22×D1111yescharacteristic
331C22×C8C22×D1111yescharacteristic
332#126—441no—
333#125—221no—
334#124—221no—
335#123—441no—
336#123—441no—
337C22⋊Q8—221no—
338#121—221no—
339#121—221no—
340#121—221no—
341#121—441no—
342#121—441no—
343#120—441no—
344C4×D4—221no—
345C4×D4—221no—
346C4×D4—441no—
347C4×D4D4411yescharacteristic
348#117—221no—
349C2×C4⋊C4—221no—
350C2×C22⋊C4—441no—
351SD32—441no—
352D16—222no—
353D16—441no—
354C2×C16—41no—
355C2×C16—41no—
356C2×C16C22×D1111yescharacteristic
357C2×C16C22×D1111yescharacteristic
358C2×C16C22×D1111yescharacteristic
359C2×C16C22×D1111yescharacteristic
360#107—111no—
361#107—111no—
362#107—111no—
363#107—111no—
364#107—221no—
365#106—221no—
366#106—221no—
367C4⋊C8D4411yescharacteristic
368#103—221no—
369#102—221no—
370#102—221no—
371#102—221no—
372#102—221no—
373#102—221no—
374C22⋊C8D4411yescharacteristic
375C22⋊C8D4411yescharacteristic
376C4×C8C22×D1111yescharacteristic
377C2×C11—22no—
378C2×C11—41no—
379C2×C11#329411yescharacteristic
380C2×C11C2×#50811yescharacteristic
381C2×C11#341511yescharacteristic
382D11—82no—
383D11—161no—
384D11—161no—
385C24—441no—
386#41—442no—
387#41—881no—
388C2×Q8—221no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—442no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—881no—
399C2×D4D8811yescharacteristic
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4C2×D4411yescharacteristic
405C22×C4C2×D4411yescharacteristic
406Q16—221no—
407Q16—221no—
408SD16—442no—
409SD16—881no—
410D8—112no—
411D8—221no—
412D8—221no—
413D8—221no—
414D8—221no—
415D8—221no—
416D8—442no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8C2×D4411yescharacteristic
422C2×C8C2×D4411yescharacteristic
423C2×C8C2×D4411yescharacteristic
424C2×C8C23×D1111yescharacteristic
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4D8811yescharacteristic
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4—441no—
442C22⋊C4—441no—
443C22⋊C4D8811yescharacteristic
444C22⋊C4D8811yescharacteristic
445C42—441no—
446C42C2×D4411yescharacteristic
447C16—21no—
448C16—21no—
449C16—21no—
450C16—21no—
451C11#3386411yescharacteristic, complemented, Sylow
452C23—441no—
453C23—441no—
454C23—441no—
455C23—882no—
456C23—882no—
457C23—1761no—
458C23C2×D8811yescharacteristic
459C23C2×D8811yescharacteristic
460Q8—441no—
461Q8—441no—
462D4—22no—
463D4—222no—
464D4—441no—
465D4—441no—
466D4—441no—
467D4—441no—
468D4—441no—
469D4—882no—
470D4—882no—
471D4—882no—
472D4—1761no—
473D4—1761no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—882no—
484C2×C4—1761no—
485C2×C4—1761no—
486C2×C4—1761no—
487C2×C4C2×D8811yescharacteristic
488C2×C4C2×D8811yescharacteristic
489C2×C4C2×D8811yescharacteristic
490C2×C4C2×D8811yescharacteristic
491C2×C4C22×D4411yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8#6703711yescharacteristic
496C8#41×D1111yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—442no—
503C22—881no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22—881no—
511C22—1764no—
512C22#1062251712yes—
513C22C22×D8811yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—881no—
519C4—881no—
520C4—881no—
521C4—881no—
522C4—881no—
523C4#1062308511yescharacteristic
524C4#1062328211yescharacteristic
525C2—22no—
526C2—41no—
527C2—882no—
528C2—1761no—
529C2—1761no—
530C2#1308043011yescharacteristic
531C2C2×#1062251711yescharacteristic
532C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
hypercenterD4×C16D11
hypocenterC11#33864
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13080303C2semidirect
3. #13070848C2semidirect
4. #13070819C2semidirect
5. #13070808C2semidirect
6. #13070774C2semidirect
7. #13070712C2semidirect
8. #13070702C2semidirect
9. #13070672C2semidirect
10. #13070541C2semidirect
11. #13070530C2semidirect
12. C4×D176C2semidirect
13. #13070324C2semidirect
14. C2×#10622147C2semidirect
15. D4×C11×C16C2semidirect
21. C22×C11×C16C22semidirect
26. #10622728C22semidirect
27. #10622719C22semidirect
29. C2×#66864C22semidirect
40. C4×D88C22semidirect
41. #10622296C22semidirect
42. C11×C4⋊C16C22semidirect
44. C11×C22⋊C16C22semidirect
45. C4×C11×C16C22semidirect
52. #10622147C22semidirect
53. #10622143C22semidirect
54. #10622142C22semidirect
55. #10622142C22semidirect
56. #10622141C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
198. D4×C16D11semidirect
254. C22×C16C2×D11semidirect
275. C4⋊C16C2×D11semidirect
287. C22⋊C16C2×D11semidirect
288. C4×C16C2×D11semidirect
451. C11#33864semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130803032
#130708482
#130708192
#130708082
#130707742
#130707122
#130707022
#130706722
#130705412
#130705302
C4×D1762
#130703242
C2×#106221472
D4×C11×C162
#3386411