Finite Group Databasebeta

← #14911309

Subgroups — #14911309

Order 2816.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081044C211yesmaximal, characteristic
2#13080984C211yesmaximal, characteristic
3#13070901C211yesmaximal, characteristic, complemented
4#13070826C211yesmaximal, characteristic, complemented
5#13070824C211yesmaximal, characteristic, complemented
6#13070824C211yesmaximal, characteristic, complemented
7#13070820C211yesmaximal, characteristic, complemented
8#13070779C211yesmaximal, characteristic, complemented
9#13070767C211yesmaximal, characteristic, complemented
10#13070725C211yesmaximal, characteristic, complemented
11#13070707C211yesmaximal, characteristic, complemented
12#13070486C211yesmaximal, characteristic, complemented
13#13070441C211yesmaximal, characteristic
14#13070403C211yesmaximal, characteristic, complemented
15C11×#2158C211yesmaximal, characteristic, complemented
16#10623064—21no—
17#10623060—21no—
18C22×C11×C16C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C11×#427C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622729C2211yescharacteristic
23C8×C22⋊D11C2211yescharacteristic
24#10622609—21no—
25#10622609—21no—
26C2×Dic88C2211yescharacteristic
27C2×#66862C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622500C2211yescharacteristic
30#10622493C2211yescharacteristic
31D11×#107C2211yescharacteristic
32#10622491C2211yescharacteristic
33#10622487C2211yescharacteristic
34#10622486C2211yescharacteristic
35#10622486C2211yescharacteristic
36#10622480—21no—
37#10622475—21no—
38#10622470—21no—
39#10622467—21no—
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45(C2×D11)⋊C16C2211yescharacteristic
46#10622142C2211yescharacteristic
47#10622141C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622140C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#117—21no—
61C11×#117—21no—
62C4×C22⋊D11D411yescharacteristic
63#66977—21no—
64#66977—21no—
65C2×Dic44C2311yescharacteristic
66C2×Dic44C2311yescharacteristic
67C2×C8×D11C2311yescharacteristic
68#66950—21no—
69#66950—21no—
70#66945—21no—
71C4⋊C4×D11—21no—
72#66943—21no—
73#66941—21no—
74#66940—21no—
75#66940—21no—
76#66938—41no—
77#66936—41no—
78#66932—41no—
79#66932—41no—
80#66929—41no—
81#66925—41no—
82#66923—41no—
83C4×Dic22—41no—
84C2×C11×C16—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#106—21no—
92C11×#106—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94(C2×D11)⋊C8D411yescharacteristic
95#66882C2311yescharacteristic
96#66882C2311yescharacteristic
97#66880—21no—
98#66880—21no—
99Dic11⋊C8D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103#66874—21no—
104#66874—21no—
105#66874—21no—
106#66874—21no—
107#66872—21no—
108#66872—21no—
109#66871—21no—
110#66871—21no—
111Dic88—22no—
112#66862—22no—
113#33916—111nomaximal, Sylow
114C22×C4×C11C2×D411yescharacteristic
115C2×C22⋊D11D811yescharacteristic
116C2×C4×D11—41no—
117C2×C4×D11C2×D411yescharacteristic
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—41no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2411yescharacteristic
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11D811yescharacteristic
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4D811yescharacteristic
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—41no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145Dic11⋊C4—41no—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4D811yescharacteristic
153C4×Dic11—41no—
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159Dic44—21no—
160Dic44—21no—
161Dic44—21no—
162Dic44—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3342—111no—
170#3336—111no—
171#2255—111no—
172#2237—111no—
173#2237—111no—
174#2237—111no—
175#2236—111no—
176#2229—111no—
177#2227—111no—
178#2219—111no—
179#2216—111no—
180#2176—111no—
181#2168—111no—
182#2159—111no—
183#2158D1111yescharacteristic, complemented
184C23×C11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C22⋊D11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11C2×D811yescharacteristic
200C2×Dic11C2×D811yescharacteristic
201C2×Dic11C2×D811yescharacteristic
202C4×D11—21no—
203C4×D11—21no—
204C4×D11—82no—
205Dic22—41no—
206Dic22—41no—
207Dic22—41no—
208Dic22—41no—
209Dic22—82no—
210C8×C11—21no—
211C8×C11C2×#4111yescharacteristic
212C8×C112−1+411yescharacteristic
213C11⋊C8—21no—
214C11⋊C8—21no—
215#556—221no—
216#552—221no—
217C2×Q32—111no—
218C2×M32—111no—
219C22×C16C2×D1111yescharacteristic
220#500—111no—
221#499—111no—
222#485—221no—
223#485—221no—
224#485—221no—
225#483—221no—
226#479—221no—
227#475—221no—
228#467—111no—
229#467—111no—
230#467—111no—
231#467—111no—
232C4×Q16—111no—
233C4×Q16—111no—
234C8×D4—111no—
235#427—111no—
236#427C2×D1111yescharacteristic
237#427C2×D1111yescharacteristic
238C2×#107—111no—
239#367—111no—
240#367—111no—
241#367C2×D1111yescharacteristic
242#367C2×D1111yescharacteristic
243#366—111no—
244#366—111no—
245#366—111no—
246#366C2×D1111yescharacteristic
247#366C2×D1111yescharacteristic
248C4⋊C16—111no—
249#358—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255C22⋊C16—111no—
256C22⋊C16—111no—
257#346—111no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11C22×D811yescharacteristic
262C2×D11—21no—
263C2×D11—21no—
264C2×D11—21no—
265C4×C11—21no—
266C4×C11—81no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11#54711yescharacteristic
271C4×C11#57811yescharacteristic
272Dic11—21no—
273Dic11—21no—
274Dic11—21no—
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279C2×Q16—111no—
280C2×Q16—111no—
281C22×C8—111no—
282C22×C8C22×D1111yescharacteristic
283C4⋊Q8—221no—
284#126—441no—
285#126—441no—
286#126—441no—
287#125—221no—
288#125—441no—
289#124—441no—
290#123—441no—
291C22⋊Q8—221no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C4×Q8—221no—
296C4×Q8—221no—
297C4×Q8—441no—
298C4×D4—111no—
299#117—21no—
300#117—21no—
301#117—221no—
302#117—441no—
303C2×C4⋊C4—221no—
304Q32—222no—
305M32—222no—
306C2×C16—22no—
307C2×C16—111no—
308C2×C16—111no—
309C2×C16C22×D1111yescharacteristic
310C2×C16C22×D1111yescharacteristic
311#107—111no—
312#107—111no—
313#107—221no—
314#107—221no—
315#107C22×D1111yescharacteristic
316#107C22×D1111yescharacteristic
317#107C22×D1111yescharacteristic
318#107C22×D1111yescharacteristic
319#106—21no—
320#106—21no—
321#106—221no—
322#106—221no—
323C4⋊C8—111no—
324#103—221no—
325#103—221no—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330C22⋊C8—111no—
331C22⋊C8—111no—
332C4×C8—111no—
333C2×C11—41no—
334C2×C11#333411yescharacteristic
335C2×C11#341411yescharacteristic
336C2×C11#341711yescharacteristic
337D11—41no—
338C2×Q8—221no—
339C2×Q8—221no—
340C2×Q8—441no—
341C2×D4—111no—
342C22×C4—111no—
343C22×C4—441no—
344C22×C4D4×D1111yescharacteristic
345Q16—221no—
346Q16—221no—
347Q16—221no—
348Q16—221no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8D4×D1111yescharacteristic
356C2×C8C23×D1111yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—111no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4—441no—
365C4⋊C4—441no—
366C4⋊C4—441no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—111no—
377C22⋊C4—111no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C42—41no—
384C42—41no—
385C42—111no—
386C42—441no—
387C42—441no—
388C42—441no—
389C16—21no—
390C16—221no—
391C16—221no—
392C16#433912yes—
393C11#3391611yescharacteristic, complemented, Sylow
394C23—111no—
395C23D8×D1111yescharacteristic
396Q8—441no—
397Q8—441no—
398Q8—441no—
399Q8—441no—
400Q8—882no—
401D4—441no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—111no—
409C2×C4—111no—
410C2×C4—111no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—882no—
418C2×C4D8×D1111yescharacteristic
419C2×C4C2×D4×D1111yescharacteristic
420C8—21no—
421C8—221no—
422C8—221no—
423C8C2×#433911yescharacteristic
424C8#6704011yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—221no—
429C22—221no—
430C22—221no—
431C22C2×D8×D1111yescharacteristic
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—221no—
438C4—221no—
439C4—221no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4—881no—
444C4#1062303811yescharacteristic
445C4#1062329711yescharacteristic
446C2—41no—
447C2—441no—
448C2#1308096111yescharacteristic
449C2#1308174911yescharacteristic
450C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2158C2
socleC22×C11C22×D8
prime radicalC2×C22⋊D11D8
hypercenter#2158D11
hypocenterC11#33916
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2158

Complements

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

NH ≅ G/Ntype
3. #13070901C2semidirect
4. #13070826C2semidirect
5. #13070824C2semidirect
6. #13070824C2semidirect
7. #13070820C2semidirect
8. #13070779C2semidirect
9. #13070767C2semidirect
10. #13070725C2semidirect
11. #13070707C2semidirect
12. #13070486C2semidirect
14. #13070403C2semidirect
15. C11×#2158C2semidirect
183. #2158D11semidirect
393. C11#33916semidirect

Maximal subgroups

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

subgroupindex
#130810442
#130809842
#130709012
#130708262
#130708242
#130708202
#130707792
#130707672
#130707252
#130707072
#130704862
#130704412
#130704032
C11×#21582
#3391611