Finite Group Databasebeta

← #14906809

Subgroups — #14906809

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×M32C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic
3D11×#427C211yesmaximal, characteristic
4#13070405C211yesmaximal, characteristic, complemented
5#13070404C211yesmaximal, characteristic, complemented
6#13070403C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070401C212yesmaximal, complemented
9#13070399C212yesmaximal, complemented
10#13070397C212yesmaximal, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13D11×#117—21no—
14C2×#66945—21no—
15C2×C11×M32C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622719C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622611—21no—
22C2×#66872—21no—
23D11×M32C418yescomplemented
24C2×#66862C2212yes—
25C2×C16×D11C2212yes—
26#10622493—21no—
27#10622493—21no—
28#10622493C2211yescharacteristic
29#10622493C2212yes—
30#10622493C2211yescharacteristic
31#10622493C2212yes—
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622473—21no—
35D11×#106—21no—
36C11×#367C2212yescomplemented
37C11×#366C2212yescomplemented
38#10622143C2212yescomplemented
39#10622142C2212yescomplemented
40#10622128C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43#10622127C2212yescomplemented
44C22×C4×D11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×(C2×D11)⋊C4—41no—
49#66979—21no—
50C2×C4⋊Dic11—21no—
51C2×C4×Dic11—41no—
52C22×C11⋊C8D411yescharacteristic
53C2×C8×D11C2×C414yes—
54C2×C8×D11D411yescharacteristic
55C2×C8×D11D411yescharacteristic
56C2×C8×D11Q814yes—
57C2×C8×D11C2311yescharacteristic
58C2×C8×D11C2311yescharacteristic
59#66945—21no—
60#66945—21no—
61#66945—22no—
62#66945—22no—
63#66945—41no—
64#66945—41no—
65C4⋊C4×D11—21no—
66C4⋊C4×D11—21no—
67C22⋊C4×D11—41no—
68#66930—41no—
69#66925—41no—
70C42×D11—41no—
71C11×M32C2×C414yescomplemented
72C2×C11×C16C2312yes—
73C11×#107—21no—
74C11×#107C2311yescharacteristic
75C11×#107C2311yescharacteristic
76C11×#107C2312yes—
77C11×#106—21no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2311yescharacteristic
81#66882C2312yes—
82#66881—21no—
83#66876C2×C414yescomplemented
84C2×C11⋊C16C2312yes—
85#66872—21no—
86#66872—21no—
87#66872—22no—
88#66872—22no—
89#66871—21no—
90#66871—21no—
91#66862C2×C418yescomplemented
92C16×D11C2×C418yescomplemented
93#33409—111nomaximal, Sylow
94C23×D11D811yescharacteristic
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—41no—
98C22×Dic11D811yescharacteristic
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11C4⋊C414yes—
102C2×C4×D11D811yescharacteristic
103C2×C4×D11D811yescharacteristic
104C2×C4×D11Q1614yes—
105C2×C4×D11C2×D411yescharacteristic
106C2×C4×D11C2×D411yescharacteristic
107C2×C8×C11C22×C412yes—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×Q812yes—
110C2×C8×C11C2411yescharacteristic
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11—41no—
117C22⋊Dic11—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—42no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130C4×Dic11—42no—
131C4×Dic11—42no—
132C4×Dic11—41no—
133C2×C11⋊C8C4⋊C414yes—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136C8×D11C4⋊C414yes—
137C8×D11C4⋊C414yes—
138C8×D11C22×C412yes—
139C8×D11C22×C412yes—
140C8×D11C2×Q812yes—
141C8×D11C2×Q812yes—
142C11×C16C22×C414yes—
143C11⋊C16C22×C414yes—
144C22×M32—111no—
145C2×#427—111no—
146C2×#427—111no—
147#2159—111no—
148#2159—111no—
149#2159—111no—
150#2159—112no—
151#2159—112no—
152#2159D1111yescharacteristic, complemented
153#2158—112no—
154#2158—112no—
155C23×C11C2×D811yescharacteristic
156C22×D11—41no—
157C22×D11—41no—
158C22×D11#10714yes—
159C22×D11C2×D811yescharacteristic
160C22×D11C2×D811yescharacteristic
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—82no—
165C2×C4×C11C2×C4⋊C412yes—
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×Q1612yes—
168C2×C4×C11C22×D411yescharacteristic
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—82no—
173C2×Dic11#10714yes—
174C2×Dic11C2×D811yescharacteristic
175C2×Dic11C2×D811yescharacteristic
176C4×D11—82no—
177C4×D11—82no—
178C4×D11#10714yes—
179C4×D11#10714yes—
180C4×D11C2×C4⋊C412yes—
181C4×D11C2×C4⋊C412yes—
182C4×D11C2×Q1612yes—
183C4×D11C2×Q1612yes—
184C8×C11C2×C4⋊C412yes—
185C8×C11C23×C411yescharacteristic
186C8×C11C22×Q811yescharacteristic
187C11⋊C8C2×C4⋊C412yes—
188C11⋊C8C2×C4⋊C412yes—
189C23×C8—111no—
190C2×#117—221no—
191C2×#117—221no—
192C2×M32—111no—
193C2×M32—118no—
194C2×M32—112no—
195C2×M32C2×D1111yescharacteristic
196C22×C16—112no—
197#427—111no—
198#427—111no—
199#427—112no—
200#427—111no—
201#427—112no—
202#427—221no—
203#427—221no—
204#427—221no—
205#427—221no—
206#427C2×D1111yescharacteristic
207C2×#107—111no—
208C2×#107—111no—
209C2×#107—111no—
210C2×#107C2×D1111yescharacteristic
211C2×#106—221no—
212C2×#106—221no—
213#367—112no—
214#367—112no—
215#367—112no—
216#367C2×D1112yescomplemented
217#366—112no—
218#366—112no—
219#366—112no—
220#366C2×D1112yescomplemented
221C22×C11—21no—
222C22×C11—21no—
223C22×C11C2×#10712yes—
224C22×C11C22×D811yescharacteristic
225C2×D11—21no—
226C2×D11—21no—
227C2×D11—21no—
228C2×D11—21no—
229C2×D11—44no—
230C2×D11C2×#10712yes—
231C2×D11C2×#10712yes—
232C4×C11—82no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11C2×#10712yes—
236C4×C11C22×C4⋊C411yescharacteristic
237C4×C11C22×Q1611yescharacteristic
238Dic11—81no—
239Dic11—81no—
240Dic11—82no—
241Dic11C2×#10712yes—
242Dic11C2×#10712yes—
243C23×C4—111no—
244C22×C8—111no—
245C22×C8—114no—
246C22×C8—111no—
247C22×C8—111no—
248C22×C8—114no—
249C22×C8—111no—
250C22×C8—111no—
251C22×C8C22×D1111yescharacteristic
252#117—21no—
253#117—221no—
254#117—221no—
255#117—222no—
256#117—222no—
257#117—221no—
258#117—441no—
259#117—441no—
260#117—441no—
261#117—441no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C22⋊C4—441no—
267C2×C22⋊C4—441no—
268C2×C42—441no—
269C2×C42—441no—
270M32—114no—
271M32—118no—
272M32C4×D1114yescomplemented
273C2×C16—112no—
274C2×C16—118no—
275C2×C16C22×D1112yes—
276#107—21no—
277#107—111no—
278#107—111no—
279#107—112no—
280#107—221no—
281#107—221no—
282#107—221no—
283#107C22×D1111yescharacteristic
284#107C22×D1112yes—
285#107C22×D1111yescharacteristic
286#106—21no—
287#106—221no—
288#106—221no—
289#106—222no—
290#106—222no—
291#106—221no—
292C2×C11—22no—
293C2×C11C22×#10711yescharacteristic
294C2×C11#341411yescharacteristic
295C2×C11#341411yescharacteristic
296D11—22no—
297D11—22no—
298C24—111no—
299C22×C4—41no—
300C22×C4—111no—
301C22×C4—114no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—114no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4D4×D1111yescharacteristic
311C2×C8—114no—
312C2×C8—111no—
313C2×C8—111no—
314C2×C8—114no—
315C2×C8—114no—
316C2×C8—112no—
317C2×C8—112no—
318C2×C8—112no—
319C2×C8—112no—
320C2×C8C2×C4×D1112yes—
321C2×C8D4×D1111yescharacteristic
322C2×C8Q8×D1112yes—
323C2×C8C23×D1111yescharacteristic
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—222no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C22⋊C4—41no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—442no—
338C22⋊C4—442no—
339C22⋊C4—441no—
340C42—41no—
341C42—441no—
342C42—441no—
343C42—442no—
344C42—442no—
345C42—441no—
346C16—114no—
347C16C2×C4×D1114yes—
348C11#3340911yescharacteristic, complemented, Sylow
349C23—111no—
350C23—111no—
351C23—114no—
352C23—441no—
353C23—441no—
354C23D8×D1111yescharacteristic
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—114no—
360C2×C4—111no—
361C2×C4—111no—
362C2×C4—114no—
363C2×C4—114no—
364C2×C4—112no—
365C2×C4—112no—
366C2×C4—112no—
367C2×C4—112no—
368C2×C4—441no—
369C2×C4—442no—
370C2×C4—441no—
371C2×C4—882no—
372C2×C4—882no—
373C2×C4—882no—
374C2×C4C4⋊C4×D1112yes—
375C2×C4D8×D1111yescharacteristic
376C2×C4Q16×D1112yes—
377C2×C4C2×D4×D1111yescharacteristic
378C8—112no—
379C8—112no—
380C8C4⋊C4×D1112yes—
381C8C22×C4×D1111yescharacteristic
382C8C2×Q8×D1111yescharacteristic
383C22—21no—
384C22—21no—
385C22—112no—
386C22—112no—
387C22—221no—
388C22—221no—
389C22—221no—
390C22—221no—
391C22—444no—
392C22D11×#10712yes—
393C22C2×D8×D1111yescharacteristic
394C4—82no—
395C4—81no—
396C4—81no—
397C4—112no—
398C4—112no—
399C4—881no—
400C4—881no—
401C4—882no—
402C4D11×#10712yes—
403C4C2×C4⋊C4×D1111yescharacteristic
404C4C2×Q16×D1111yescharacteristic
405C2—22no—
406C2—222no—
407C2—222no—
408C2C2×D11×#10711yescharacteristic
409C2#1308174811yescharacteristic
410C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC23×D11D8
cosocleC2×C8×C11C24
hypercenter#2159D11
hypocenterC11#33409
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
4. #13070405C2semidirect
5. #13070404C2semidirect
6. #13070403C2semidirect
7. #13070402C2semidirect
8. #13070401C2semidirect
9. #13070399C2semidirect
10. #13070397C2semidirect
11. C11×#2159C2semidirect
23. D11×M32C4semidirect
36. C11×#367C22semidirect
37. C11×#366C22semidirect
38. #10622143C22semidirect
39. #10622142C22semidirect
40. #10622128C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
43. #10622127C22semidirect
71. C11×M32C2×C4semidirect
83. #66876C2×C4semidirect
91. #66862C2×C4semidirect
92. C16×D11C2×C4semidirect
152. #2159D11semidirect
216. #367C2×D11semidirect
220. #366C2×D11semidirect
272. M32C4×D11semidirect
348. C11#33409semidirect

Maximal subgroups

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

subgroupindex
C2×D11×M322
C2×#106224932
D11×#4272
#130704052
#130704042
#130704032
#130704022
#130704012
#130703992
#130703972
C11×#21592
#3340911