Finite Group Databasebeta

← #14911315

Subgroups — #14911315

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#13081047C211yesmaximal, characteristic
2#13080985C211yesmaximal, characteristic
3#13070902C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070825C211yesmaximal, characteristic, complemented
6#13070825C211yesmaximal, characteristic, complemented
7#13070819C211yesmaximal, characteristic, complemented
8#13070781C211yesmaximal, characteristic, complemented
9#13070769C211yesmaximal, characteristic, complemented
10#13070724C211yesmaximal, characteristic, complemented
11#13070707C211yesmaximal, characteristic, complemented
12#13070488C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14#13070400C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic
16#10623073—21no—
17#10623072—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622729C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622719C2211yescharacteristic
26#10622719C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic88C2211yescharacteristic
30#10622464—21no—
31#10622442—21no—
32#10622336—21no—
33#10622336—21no—
34#10622336—21no—
35#10622334—21no—
36C4×Dic44C2211yescharacteristic
37C4×Dic44C2211yescharacteristic
38#10622296C2211yescharacteristic
39#10622295C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×C22⋊C16C2211yescharacteristic
42C11×C22⋊C16C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622143C2211yescharacteristic
45#10622143C2211yescharacteristic
46#10622143C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622142C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C4×D4×C11D411yescharacteristic
62#66989—41no—
63#66988—41no—
64#66979—21no—
65#66979—21no—
66#66979—21no—
67C2×C4⋊Dic11—21no—
68#66977—21no—
69#66977—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73C2×Dic44C2311yescharacteristic
74#66942—41no—
75#66940—41no—
76#66932—41no—
77#66932—41no—
78#66932—41no—
79#66930—41no—
80#66923—21no—
81#66922—21no—
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×M32—22no—
85C2×C11×C16—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×C22⋊C8D411yescharacteristic
92C11×C22⋊C8D411yescharacteristic
93C4×C8×C11C2311yescharacteristic
94#66882—21no—
95#66882—21no—
96#66882C2311yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66881—21no—
103#66881—21no—
104#66881—21no—
105#66881—21no—
106#66880—21no—
107#66880—21no—
108#66880—21no—
109#66880—21no—
110#66880—21no—
111#66880—21no—
112Dic88—22no—
113#33916—111nomaximal, Sylow
114C2×D4×C11D811yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×Dic11—41no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—41no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4D811yescharacteristic
130C11×C22⋊C4D811yescharacteristic
131C11×C22⋊C4D811yescharacteristic
132C42×C11C2×D411yescharacteristic
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11—41no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148Dic11⋊C4—41no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161Dic44—21no—
162Dic44—21no—
163Dic44—21no—
164Dic44—21no—
165C11×C16—21no—
166C11×C16—21no—
167C11×C16—21no—
168C11×C16#4112yes—
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#2168D1111yescharacteristic
182#2159—111no—
183#2158—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186D4×C11—41no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—82no—
205Dic22—41no—
206Dic22—41no—
207Dic22—41no—
208Dic22—41no—
209Dic22—82no—
210C8×C11—21no—
211C8×C11—21no—
212C8×C11—21no—
213C8×C11C2×#4111yescharacteristic
214C8×C112−1+411yescharacteristic
215#556—221no—
216#552—221no—
217C2×Q32—111no—
218C2×M32C2×D1111yescharacteristic
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×D4C2×D1111yescharacteristic
235#427—111no—
236#427—111no—
237#427—111no—
238C2×#107—111no—
239#367—111no—
240#367—111no—
241#367—111no—
242#367—111no—
243#366—111no—
244#366—111no—
245#366—111no—
246#366—111no—
247#366—111no—
248C4⋊C16C2×D1111yescharacteristic
249#358—111no—
250#358—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255C22⋊C16C2×D1111yescharacteristic
256C22⋊C16C2×D1111yescharacteristic
257#346C2×D1111yescharacteristic
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11C22×D811yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11#54711yescharacteristic
270C4×C11#57811yescharacteristic
271Dic11—81no—
272Dic11—81no—
273Dic11—81no—
274Dic11—81no—
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279C2×Q16—111no—
280C2×Q16—111no—
281C22×C8C22×D1111yescharacteristic
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×D4D4411yescharacteristic
299#117—221no—
300#117—221no—
301#117—221no—
302#117—441no—
303C2×C4⋊C4—221no—
304Q32—222no—
305M32—22no—
306C2×C16—22no—
307C2×C16C22×D1111yescharacteristic
308C2×C16C22×D1111yescharacteristic
309C2×C16C22×D1111yescharacteristic
310C2×C16C22×D1111yescharacteristic
311#107—111no—
312#107—111no—
313#107—111no—
314#107—111no—
315#107—111no—
316#107—111no—
317#107—221no—
318#107—221no—
319#106—221no—
320#106—221no—
321#106—221no—
322#106—221no—
323C4⋊C8D4411yescharacteristic
324#103—221no—
325#103—221no—
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330C22⋊C8D4411yescharacteristic
331C22⋊C8D4411yescharacteristic
332C4×C8C22×D1111yescharacteristic
333C2×C11—41no—
334C2×C11—41no—
335C2×C11#333411yescharacteristic
336C2×C11#341411yescharacteristic
337C2×C11#341711yescharacteristic
338C2×Q8—221no—
339C2×Q8—221no—
340C2×Q8—441no—
341C2×D4D8811yescharacteristic
342C22×C4—441no—
343C22×C4C2×D4411yescharacteristic
344C22×C4C2×D4411yescharacteristic
345Q16—221no—
346Q16—221no—
347Q16—221no—
348Q16—221no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8C2×D4411yescharacteristic
354C2×C8C2×D4411yescharacteristic
355C2×C8C2×D4411yescharacteristic
356C2×C8C23×D1111yescharacteristic
357C4⋊C4—221no—
358C4⋊C4—221no—
359C4⋊C4—221no—
360C4⋊C4—221no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4—441no—
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⋊C4D8811yescharacteristic
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4D8811yescharacteristic
382C22⋊C4D8811yescharacteristic
383C42—441no—
384C42—441no—
385C42—441no—
386C42—441no—
387C42—441no—
388C42C2×D4411yescharacteristic
389C16—21no—
390C16—21no—
391C16—21no—
392C16#434112yes—
393C11#3391611yescharacteristic, complemented, Sylow
394C23C2×D8811yescharacteristic
395C23C2×D8811yescharacteristic
396Q8—441no—
397Q8—441no—
398Q8—441no—
399Q8—441no—
400Q8—882no—
401D4—41no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—882no—
415C2×C4C2×D8811yescharacteristic
416C2×C4C2×D8811yescharacteristic
417C2×C4C2×D8811yescharacteristic
418C2×C4C2×D8811yescharacteristic
419C2×C4C22×D4411yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8C2×#434111yescharacteristic
424C8#6704311yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22C22×D8811yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—881no—
437C4—881no—
438C4—881no—
439C4—881no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4—881no—
444C4#1062308611yescharacteristic
445C4#1062328411yescharacteristic
446C2—41no—
447C2—41no—
448C2#1308096411yescharacteristic
449C2#1308175211yescharacteristic
450C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenter#2168D11
hypocenterC11#33916
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
3. #13070902C2semidirect
4. #13070825C2semidirect
5. #13070825C2semidirect
6. #13070825C2semidirect
7. #13070819C2semidirect
8. #13070781C2semidirect
9. #13070769C2semidirect
10. #13070724C2semidirect
11. #13070707C2semidirect
12. #13070488C2semidirect
13. #13070404C2semidirect
14. #13070400C2semidirect
393. C11#33916semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130809852
#130709022
#130708252
#130708192
#130707812
#130707692
#130707242
#130707072
#130704882
#130704042
#130704002
C11×#21682
#3391611