Finite Group Databasebeta

← #14910685

Subgroups — #14910685

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13070847C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070799C211yesmaximal, characteristic, complemented
5#13070780C211yesmaximal, characteristic, complemented
6#13070714C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070668C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070533C211yesmaximal, characteristic, complemented
11C4×#66892C211yesmaximal, characteristic, complemented
12D4×C11⋊C16C211yesmaximal, characteristic, complemented
13#13070323C211yesmaximal, characteristic, complemented
14C2×#10622202C211yesmaximal, characteristic, complemented
15C11×#3285C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C11×#548—21no—
19#10623096—21no—
20C11×#495C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#464—21no—
24C11×#452—21no—
25C11×#448—21no—
26C4×C11×Q16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622728C2211yescharacteristic
32#10622728C2211yescharacteristic
33#10622719C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622460—21no—
38#10622350—21no—
39#10622348—21no—
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×#41—21no—
60C22×Q8×C11—21no—
61C11×#135—22no—
62C11×#135—41no—
63C2×C11×Q16—22no—
64C2×C11×Q16—21no—
65C2×C11×Q16—41no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×Q16C2311yescharacteristic
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×D8C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#124—21no—
74C11×#124—41no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—41no—
77C11×#121—21no—
78C11×#121—41no—
79C4×Q8×C11—21no—
80C4×D4×C11—41no—
81C4×D4×C11D411yescharacteristic
82#66992—41no—
83#66983—21no—
84#66983—21no—
85#66979—21no—
86C2×C4⋊Dic11—21no—
87C2×D88C2311yescharacteristic
88#66951—41no—
89#66936—41no—
90(C22⋊D11)⋊C4—41no—
91C4×D44—21no—
92#66923—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#103—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66892—22no—
102#66892—41no—
103#66890—41no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66881—21no—
112#66881—21no—
113C2×C11⋊C16—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33868—111nomaximal, Sylow
120C11×#41—42no—
121C11×#41—81no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—42no—
125C2×Q8×C11—41no—
126C2×Q8×C11—81no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11D811yescharacteristic
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C22×Dic11—41no—
138C2×D44—21no—
139C2×C4×D11—41no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×Q16—21no—
143C11×Q16—42no—
144C11×Q16#4112yes—
145C11×SD16—42no—
146C11×SD16—81no—
147C11×D8—21no—
148C11×D8—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2411yescharacteristic
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4D811yescharacteristic
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4D811yescharacteristic
166C11×C22⋊C4D811yescharacteristic
167C42×C11—41no—
168C42×C11C2×D411yescharacteristic
169C22⋊Dic11—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180D88—21no—
181D88—21no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3285D1111yescharacteristic, complemented
188#2242—111no—
189#2237—111no—
190#2233—111no—
191#2229—111no—
192#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2185—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#358—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205Q8×C11—22no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—82no—
210D4×C11—22no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—82no—
214D4×C11—82no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—82no—
223C2×C4×C11—82no—
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C22⋊D11—82no—
230C22⋊D11—161no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—161no—
235D44—41no—
236D44—41no—
237C4×D11—161no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135C2×D1111yescharacteristic
244C22×Q16C2×D1111yescharacteristic
245#553—221no—
246#548—21no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16—111no—
250C22×C16—111no—
251C22×C16—111no—
252#499—111no—
253#495C2×D1111yescharacteristic
254#482—221no—
255#481—221no—
256#478—221no—
257#467C2×D1111yescharacteristic
258#466—111no—
259#466—111no—
260#466C2×D1111yescharacteristic
261#464—21no—
262#452—21no—
263#448—21no—
264C4×Q16C2×D1111yescharacteristic
265C4×D8—111no—
266C8×D4C2×D1111yescharacteristic
267#427—111no—
268C2×#107—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11#50812yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—42no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—21no—
312C22×Q8—21no—
313#135—22no—
314#135—41no—
315C2×Q16—22no—
316C2×Q16—21no—
317C2×Q16—41no—
318C2×Q16C22×D1111yescharacteristic
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—21no—
321C2×SD16—21no—
322C2×D8—111no—
323C2×D8C22×D1111yescharacteristic
324C22×C8C22×D1111yescharacteristic
325C22×C8C22×D1111yescharacteristic
326#126—441no—
327#125—221no—
328#124—21no—
329#124—41no—
330#123—441no—
331C22⋊Q8—21no—
332C22⋊Q8—41no—
333#121—21no—
334#121—41no—
335#121—221no—
336#121—221no—
337#121—441no—
338C4×Q8—21no—
339C4×D4—41no—
340C4×D4—221no—
341C4×D4—441no—
342C4×D4C22⋊D1111yescharacteristic
343#117—221no—
344C2×C4⋊C4—221no—
345SD32—222no—
346SD32—441no—
347D16—441no—
348C2×C16—111no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16—441no—
353C2×C16—441no—
354#107—111no—
355#107—111no—
356#107—111no—
357#107—221no—
358#107C22×D1111yescharacteristic
359#106—221no—
360#106—221no—
361C4⋊C8C22⋊D1111yescharacteristic
362#103—21no—
363#103—21no—
364#102—21no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8C22⋊D1111yescharacteristic
369C22⋊C8C22⋊D1111yescharacteristic
370C4×C8C22×D1111yescharacteristic
371C2×C11—22no—
372C2×C11—41no—
373C2×C11—161no—
374C2×C11#329411yescharacteristic
375C2×C11C2×#50811yescharacteristic
376C2×C11#341611yescharacteristic
377D11—161no—
378#41—42no—
379#41—81no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—42no—
383C2×Q8—41no—
384C2×Q8—81no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—221no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4#432311yescharacteristic
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—21no—
401Q16—42no—
402Q16#434112yes—
403SD16—42no—
404SD16—81no—
405D8—21no—
406D8—21no—
407D8—221no—
408D8—221no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×C22⋊D1111yescharacteristic
414C2×C8C2×C22⋊D1111yescharacteristic
415C2×C8C2×C22⋊D1111yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4#432311yescharacteristic
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4#432311yescharacteristic
436C22⋊C4#432311yescharacteristic
437C42—41no—
438C42—441no—
439C42C2×C22⋊D1111yescharacteristic
440C16—221no—
441C16—221no—
442C16—221no—
443C16—221no—
444C11#3386811yescharacteristic, complemented, Sylow
445C23—41no—
446C23—441no—
447C23C2×#432311yescharacteristic
448C23C2×#432311yescharacteristic
449Q8—22no—
450Q8—41no—
451Q8—41no—
452Q8—41no—
453Q8—82no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—82no—
458D4—82no—
459D4—441no—
460D4—441no—
461D4—882no—
462D4—1761no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—1761no—
476C2×C4—1761no—
477C2×C4C2×#432311yescharacteristic
478C2×C4C2×#432311yescharacteristic
479C2×C4C2×#432311yescharacteristic
480C2×C4C2×#432311yescharacteristic
481C2×C4C22×C22⋊D1111yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8C2×#434111yescharacteristic
486C8#6703711yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22#1062280712yes—
499C22C22×#432311yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4—881no—
508C4—881no—
509C4—881no—
510C4#1062333711yescharacteristic
511C4#1062336711yescharacteristic
512C2—22no—
513C2—41no—
514C2—161no—
515C2—1761no—
516C2#1308042911yescharacteristic
517C2C2×#1062280711yescharacteristic
518C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3285C2
socleC22×C11C22×D8
hypercenter#3285D11
hypocenterC11#33868
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13070847C2semidirect
3. #13070821C2semidirect
4. #13070799C2semidirect
5. #13070780C2semidirect
6. #13070714C2semidirect
7. #13070700C2semidirect
8. #13070668C2semidirect
9. #13070539C2semidirect
10. #13070533C2semidirect
11. C4×#66892C2semidirect
12. D4×C11⋊C16C2semidirect
13. #13070323C2semidirect
14. C2×#10622202C2semidirect
15. C11×#3285C2semidirect
187. #3285D11semidirect
444. C11#33868semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130708472
#130708212
#130707992
#130707802
#130707142
#130707002
#130706682
#130705392
#130705332
C4×#668922
D4×C11⋊C162
#130703232
C2×#106222022
C11×#32852
#3386811