Finite Group Databasebeta

← #14911240

Subgroups — #14911240

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081009C211yesmaximal, characteristic
2#13080985C211yesmaximal, characteristic
3#13070902C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070819C211yesmaximal, characteristic, complemented
6#13070814C211yesmaximal, characteristic, complemented
7#13070814C211yesmaximal, characteristic, complemented
8#13070781C211yesmaximal, characteristic, complemented
9#13070759C211yesmaximal, characteristic, complemented
10#13070724C211yesmaximal, characteristic, complemented
11#13070707C211yesmaximal, characteristic, complemented
12#13070488C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14C2×#10622143C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic
16#10623074—21no—
17#10623072—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622729C2211yescharacteristic
22#10622729C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622719C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic88C2211yescharacteristic
30#10622463—21no—
31#10622442—21no—
32#10622336—21no—
33#10622335—21no—
34#10622335—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#10622143C2211yescharacteristic
49#10622143C2211yescharacteristic
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#66988—41no—
63D4×Dic11—41no—
64#66979—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68#66977—21no—
69#66977—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44C2311yescharacteristic
73C2×Dic44C2311yescharacteristic
74#66943—41no—
75#66942—41no—
76#66932—41no—
77#66931—41no—
78#66931—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#66882—21no—
97#66882—21no—
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
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#33911—111nomaximal, Sylow
114C2×D4×C11D811yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22—41no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4D811yescharacteristic
132C11×C22⋊C4D811yescharacteristic
133C11×C22⋊C4D811yescharacteristic
134C42×C11C2×D411yescharacteristic
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—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—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#3338—111no—
170#3336—111no—
171#2255—111no—
172#2237—111no—
173#2236—111no—
174#2235—111no—
175#2235—111no—
176#2229—111no—
177#2225—111no—
178#2219—111no—
179#2216—111no—
180#2176—111no—
181#2168D1111yescharacteristic
182#2159—111no—
183C2×#367—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186D4×C11—22no—
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—
205C2×Dic11—161no—
206C2×Dic11—161no—
207Dic22—41no—
208Dic22—41no—
209Dic22—41no—
210Dic22—41no—
211Dic22—161no—
212C8×C11—21no—
213C8×C11—21no—
214C8×C11—21no—
215C8×C11C2×#4111yescharacteristic
216C8×C112−1+411yescharacteristic
217#554—221no—
218#552—221no—
219C2×Q32—111no—
220C2×M32C2×D1111yescharacteristic
221C22×C16C2×D1111yescharacteristic
222#500—111no—
223#499—111no—
224#485—221no—
225#484—221no—
226#484—221no—
227#483—221no—
228#479—221no—
229#477—221no—
230#467—111no—
231#467—111no—
232#467—111no—
233#467—111no—
234C4×Q16—111no—
235C4×Q16—111no—
236C8×D4C2×D1111yescharacteristic
237#427—111no—
238C2×#107—111no—
239C2×#107—111no—
240C2×#107—111no—
241#367—111no—
242#367—111no—
243#367—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248#366—111no—
249#366—111no—
250C4⋊C16C2×D1111yescharacteristic
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257C22⋊C16C2×D1111yescharacteristic
258C22⋊C16C2×D1111yescharacteristic
259#346C2×D1111yescharacteristic
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11#51012yes—
266C22×C11C22×D811yescharacteristic
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11#54711yescharacteristic
272C4×C11#57811yescharacteristic
273Dic11—81no—
274Dic11—81no—
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280Dic11—81no—
281C2×Q16—111no—
282C2×Q16—111no—
283C22×C8C22×D1111yescharacteristic
284C22×C8C22×D1111yescharacteristic
285C4⋊Q8—221no—
286#126—441no—
287#125—221no—
288#125—441no—
289#125—441no—
290#123—441no—
291C22⋊Q8—221no—
292C22⋊Q8—221no—
293C22⋊Q8—221no—
294C22⋊Q8—221no—
295C22⋊Q8—441no—
296C22⋊Q8—441no—
297C4×Q8—221no—
298C4×Q8—221no—
299C4×D4—441no—
300C4×D4D4411yescharacteristic
301#117—221no—
302#117—441no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306Q32—222no—
307M32—22no—
308C2×C16—22no—
309C2×C16C22×D1111yescharacteristic
310C2×C16C22×D1111yescharacteristic
311C2×C16C22×D1111yescharacteristic
312C2×C16C22×D1111yescharacteristic
313#107—111no—
314#107—111no—
315#107—111no—
316#107—111no—
317#107—111no—
318#107—111no—
319#107—221no—
320#107—221no—
321#107—221no—
322#107—221no—
323#106—221no—
324#106—221no—
325C4⋊C8D4411yescharacteristic
326#103—221no—
327#103—221no—
328#103—221no—
329#103—221no—
330#103—221no—
331#103—221no—
332C22⋊C8D4411yescharacteristic
333C22⋊C8D4411yescharacteristic
334C4×C8C22×D1111yescharacteristic
335C2×C11—22no—
336C2×C11—41no—
337C2×C11#333411yescharacteristic
338C2×C11C2×#51011yescharacteristic
339C2×C11#341611yescharacteristic
340C2×Q8—221no—
341C2×Q8—221no—
342C2×Q8—441no—
343C2×D4D8811yescharacteristic
344C22×C4—441no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4C2×D4411yescharacteristic
348C22×C4C2×D4411yescharacteristic
349Q16—221no—
350Q16—221no—
351Q16—221no—
352Q16—221no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8C2×D4411yescharacteristic
358C2×C8C2×D4411yescharacteristic
359C2×C8C2×D4411yescharacteristic
360C2×C8C23×D1111yescharacteristic
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4D8811yescharacteristic
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4D8811yescharacteristic
386C22⋊C4D8811yescharacteristic
387C42—441no—
388C42—441no—
389C42—441no—
390C42C2×D4411yescharacteristic
391C16—21no—
392C16—21no—
393C16—21no—
394C16#434112yes—
395C11#3391111yescharacteristic, complemented, Sylow
396C23C2×D8811yescharacteristic
397C23C2×D8811yescharacteristic
398Q8—441no—
399Q8—441no—
400Q8—441no—
401Q8—441no—
402Q8—1761no—
403D4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—882no—
417C2×C4—1761no—
418C2×C4—1761no—
419C2×C4C2×D8811yescharacteristic
420C2×C4C2×D8811yescharacteristic
421C2×C4C2×D8811yescharacteristic
422C2×C4C2×D8811yescharacteristic
423C2×C4C22×D4411yescharacteristic
424C8—21no—
425C8—21no—
426C8—21no—
427C8C2×#434111yescharacteristic
428C8#6704311yescharacteristic
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22#1062252212yes—
435C22C22×D8811yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4—881no—
444C4—881no—
445C4—881no—
446C4—881no—
447C4—881no—
448C4#1062308611yescharacteristic
449C4#1062328411yescharacteristic
450C2—22no—
451C2—41no—
452C2#1308096411yescharacteristic
453C2C2×#1062252211yescharacteristic
454C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenter#2168D11
hypocenterC11#33911
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. #13070819C2semidirect
6. #13070814C2semidirect
7. #13070814C2semidirect
8. #13070781C2semidirect
9. #13070759C2semidirect
10. #13070724C2semidirect
11. #13070707C2semidirect
12. #13070488C2semidirect
13. #13070404C2semidirect
14. C2×#10622143C2semidirect
395. C11#33911semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130809852
#130709022
#130708252
#130708192
#130708142
#130707812
#130707592
#130707242
#130707072
#130704882
#130704042
C2×#106221432
C11×#21682
#3391111