Finite Group Databasebeta

← #14910791

Subgroups — #14910791

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13080376C211yesmaximal, characteristic, complemented
3#13070858C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070719C211yesmaximal, characteristic, complemented
8#13070702C211yesmaximal, characteristic, complemented
9#13070652C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic, complemented
11#13070541C211yesmaximal, characteristic, complemented
12#13070482C211yesmaximal, characteristic, complemented
13#13070329C211yesmaximal, characteristic, complemented
14#13070324C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic, complemented
16C2×#66957C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18#10623096—21no—
19#10623084—21no—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622728C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622728C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66864C2211yescharacteristic
30C2×D176C2211yescharacteristic
31C2×D176C2211yescharacteristic
32#10622461—21no—
33#10622460—21no—
34#10622350—21no—
35#10622348—21no—
36#10622347—21no—
37#10622347—21no—
38C4×Dic44C2211yescharacteristic
39#10622308C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×#346C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic
53#10622143C2211yescharacteristic
54#10622142C2211yescharacteristic
55#10622142C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4339—21no—
60C2×#4339—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D411yescharacteristic
64#66993—41no—
65#66992—41no—
66#66983—21no—
67#66983—21no—
68#66983—21no—
69#66983—21no—
70#66979—21no—
71C2×C4⋊Dic11—21no—
72C2×Dic44C2311yescharacteristic
73#66957—22no—
74#66957—22no—
75#66957—41no—
76#66957—41no—
77C2×D88—21no—
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66951—41no—
84#66946—41no—
85#66937—41no—
86#66937—41no—
87#66936—41no—
88(C22⋊D11)⋊C4—41no—
89#66927—21no—
90C4×D44—21no—
91#66923—21no—
92C4×Dic22—21no—
93C11×M32—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—22no—
117D176—41no—
118D176—41no—
119#33876—111nomaximal, Sylow
120C2×D4×C11D811yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C22×Dic11—41no—
130#4339—42no—
131#4339—42no—
132#4339—81no—
133#4339—81no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—41no—
138C2×D44—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2411yescharacteristic
151C11×C4⋊C4D811yescharacteristic
152C11×C22⋊C4D811yescharacteristic
153C11×C22⋊C4D811yescharacteristic
154C42×C11C2×D411yescharacteristic
155C22⋊Dic11—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—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171Dic44—21no—
172Dic44#4112yes—
173D88—21no—
174D88—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—21no—
179D88—81no—
180#4314—42no—
181#4314—42no—
182C11×C16—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186#3339—111no—
187#3287—111no—
188#2244—111no—
189#2234—111no—
190#2232—111no—
191#2229—111no—
192#2218—111no—
193#2215—111no—
194#2206—111no—
195#2186—111no—
196#2186—111no—
197#2175—111no—
198#2168D1111yescharacteristic, complemented
199#2139—111no—
200#2138—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206D4×C11—41no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C22⋊D11—82no—
217C22⋊D11—82no—
218C22⋊D11—82no—
219C22⋊D11—161no—
220C22⋊D11—161no—
221C22⋊D11—161no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—161no—
228D44—41no—
229D44—41no—
230D44—41no—
231D44—41no—
232D44—41no—
233D44—41no—
234D44—82no—
235D44—161no—
236C4×D11—82no—
237C4×D11—82no—
238C4×D11—161no—
239Dic22—22no—
240Dic22—41no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—21no—
244C8×C11C2×#4111yescharacteristic
245C8×C11H(5,𝔽2)11yescharacteristic
246C2×#135—111no—
247C2×#135—111no—
248#553—221no—
249#550—221no—
250C2×SD32—111no—
251C2×D16—111no—
252C2×D16—111no—
253C2×M32C2×D1111yescharacteristic
254C22×C16C2×D1111yescharacteristic
255#499—111no—
256#493—111no—
257#482—221no—
258#481—221no—
259#478—221no—
260#466—111no—
261#466—111no—
262#466—111no—
263#466—111no—
264#460—221no—
265#449—221no—
266#449—221no—
267C4×Q16—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
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
288#346C2×D1111yescharacteristic
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11C22×D811yescharacteristic
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11#54611yescharacteristic
310C4×C11#57711yescharacteristic
311Dic11—42no—
312Dic11—81no—
313Dic11—81no—
314Dic11—81no—
315Dic11—81no—
316C2×#41—221no—
317C2×#41—221no—
318#135—222no—
319#135—222no—
320#135—441no—
321#135—441no—
322C2×Q16—111no—
323C2×SD16—221no—
324C2×SD16—221no—
325C2×D8—111no—
326C2×D8—111no—
327C2×D8—111no—
328C2×D8—221no—
329C22×C8C22×D1111yescharacteristic
330C22×C8C22×D1111yescharacteristic
331#127—221no—
332#127—441no—
333#126—441no—
334#125—221no—
335#123—441no—
336#121—221no—
337#121—221no—
338#121—221no—
339#121—221no—
340#121—441no—
341#121—441no—
342#121—441no—
343C4×Q8—221no—
344C4×D4—221no—
345C4×D4—441no—
346C4×D4—441no—
347C4×D4D4411yescharacteristic
348#117—221no—
349C2×C4⋊C4—221no—
350SD32—222no—
351D16—441no—
352D16—441no—
353M32—41no—
354C2×C16—41no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357C2×C16C22×D1111yescharacteristic
358C2×C16C22×D1111yescharacteristic
359#107—111no—
360#107—111no—
361#107—111no—
362#107—111no—
363#107—221no—
364#106—221no—
365#106—221no—
366C4⋊C8D4411yescharacteristic
367#103—221no—
368#102—221no—
369#102—221no—
370#102—221no—
371#102—221no—
372#102—221no—
373C22⋊C8D4411yescharacteristic
374C22⋊C8D4411yescharacteristic
375C4×C8C22×D1111yescharacteristic
376C2×C11—41no—
377C2×C11—41no—
378C2×C11#329411yescharacteristic
379C2×C11#341411yescharacteristic
380C2×C11#341511yescharacteristic
381D11—161no—
382D11—161no—
383D11—161no—
384#41—442no—
385#41—442no—
386#41—881no—
387#41—881no—
388C2×Q8—221no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—441no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4—441no—
400C2×D4D8811yescharacteristic
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4C2×D4411yescharacteristic
406C22×C4C2×D4411yescharacteristic
407Q16—112no—
408Q16—221no—
409SD16—442no—
410SD16—442no—
411D8—221no—
412D8—221no—
413D8—221no—
414D8—221no—
415D8—221no—
416D8—221no—
417D8—881no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×D4411yescharacteristic
423C2×C8C2×D4411yescharacteristic
424C2×C8C2×D4411yescharacteristic
425C2×C8C23×D1111yescharacteristic
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4—441no—
434C4⋊C4D8811yescharacteristic
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4D8811yescharacteristic
442C22⋊C4D8811yescharacteristic
443C42—441no—
444C42—441no—
445C42C2×D4411yescharacteristic
446C16—21no—
447C16—21no—
448C16—21no—
449C16—21no—
450C11#3387611yescharacteristic, complemented, Sylow
451C23—441no—
452C23—441no—
453C23—441no—
454C23C2×D8811yescharacteristic
455C23C2×D8811yescharacteristic
456Q8—222no—
457Q8—441no—
458D4—41no—
459D4—441no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—441no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—882no—
468D4—882no—
469D4—1761no—
470D4—1761no—
471D4—1761no—
472D4—1761no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—882no—
483C2×C4—882no—
484C2×C4—1761no—
485C2×C4—1761no—
486C2×C4C2×D8811yescharacteristic
487C2×C4C2×D8811yescharacteristic
488C2×C4C2×D8811yescharacteristic
489C2×C4C2×D8811yescharacteristic
490C2×C4C22×D4411yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8#6703711yescharacteristic
495C8#41×D1111yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22—881no—
511C22C22×D8811yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—442no—
517C4—881no—
518C4—881no—
519C4—881no—
520C4—881no—
521C4#1062308511yescharacteristic
522C4#1062328211yescharacteristic
523C2—41no—
524C2—41no—
525C2—1761no—
526C2—1761no—
527C2—1761no—
528C2#1308043011yescharacteristic
529C2#1308175211yescharacteristic
530C2#1308175711yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
hypercenter#2168D11
hypocenterC11#33876
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13080376C2semidirect
3. #13070858C2semidirect
4. #13070808C2semidirect
5. #13070797C2semidirect
6. #13070781C2semidirect
7. #13070719C2semidirect
8. #13070702C2semidirect
9. #13070652C2semidirect
10. #13070541C2semidirect
11. #13070541C2semidirect
12. #13070482C2semidirect
13. #13070329C2semidirect
14. #13070324C2semidirect
15. C11×#2168C2semidirect
198. #2168D11semidirect
450. C11#33876semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130803762
#130708582
#130708082
#130707972
#130707812
#130707192
#130707022
#130706522
#130705412
#130704822
#130703292
#130703242
C11×#21682
#3387611