Finite Group Databasebeta

← #14911368

Subgroups — #14911368

Order 2816.

502 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081047C211yesmaximal, characteristic, complemented
2#13080964C211yesmaximal, characteristic
3#13070891C211yesmaximal, characteristic, complemented
4#13070819C212yesmaximal, complemented
5#13070808C212yesmaximal, complemented
6#13070759C211yesmaximal, characteristic, complemented
7#13070754C211yesmaximal, characteristic, complemented
8#13070729C212yesmaximal, complemented
9C4×#66864C211yesmaximal, characteristic, complemented
10#13070404C212yesmaximal, complemented
11C11×#2169C211yesmaximal, characteristic, complemented
12#10623086—21no—
13#10623073—21no—
14C2×C11×M32C2212yes—
15C8×D4×C11C2211yescharacteristic
16#10622729C2212yes—
17#10622728C2212yes—
18#10622719C2212yes—
19C2×#66882C2212yes—
20C2×#66864C2211yescharacteristic
21#10622464—21no—
22#10622459—21no—
23#10622349—22no—
24#10622336—22no—
25C4×Dic44C2211yescharacteristic
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C22⋊C16C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622147C2211yescharacteristic
33#10622147C2212yes—
34#10622143C2211yescharacteristic
35#10622143C2212yes—
36#10622142C2212yes—
37#10622142C2212yes—
38#10622142C2212yes—
39#10622141C2211yescharacteristic
40#10622141C2212yes—
41C2×#4341—41no—
42C22×C8×C11C2312yes—
43C4×D4×C11D411yescharacteristic
44#66989—41no—
45#66983—22no—
46#66979—22no—
47C2×C4⋊Dic11—22no—
48#66977—22no—
49C2×Dic44C2311yescharacteristic
50C2×D88C2311yescharacteristic
51#66950—41no—
52#66940—41no—
53#66939—42no—
54#66932—42no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58C4×Dic22—21no—
59C11×M32—24no—
60C2×C11×C16C2312yes—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×C22⋊C8D412yes—
65C4×C8×C11C2311yescharacteristic
66#66885—22no—
67#66885—21no—
68#66882—21no—
69#66882—21no—
70#66882—22no—
71#66882C2312yes—
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66882C2311yescharacteristic
75#66881—22no—
76#66880—22no—
77#66880—21no—
78#66864—22no—
79#33920—111nomaximal, Sylow
80C2×D4×C11D811yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×C22⋊D11—42no—
83C22×Dic11—42no—
84#4341—84no—
85C2×D44—21no—
86C2×C4×D11—41no—
87C2×Dic22—21no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11C2×D412yes—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C11×C4⋊C4D811yescharacteristic
96C11×C22⋊C4D812yes—
97C42×C11C2×D411yescharacteristic
98C22⋊Dic11—42no—
99C22⋊Dic11—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—21no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—42no—
109Dic11⋊C4—41no—
110Dic11⋊C4—42no—
111C4×Dic11—41no—
112C4×Dic11—42no—
113Dic44—21no—
114Dic44—21no—
115D88—21no—
116D88—21no—
117C11×C16—22no—
118C11×C16—21no—
119C11×C16#4112yescomplemented
120#3342—111no—
121#3334—111no—
122#2252—111no—
123#2236—112no—
124#2234—112no—
125#2225—111no—
126#2224—111no—
127#2220—112no—
128C4×SD32—111no—
129#2169D1111yescharacteristic, complemented
130#2159—112no—
131C23×C11C2×D812yes—
132C22×D11—41no—
133D4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11C2×D812yes—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C22⋊D11—84no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—84no—
147D44—41no—
148D44—41no—
149C4×D11—82no—
150Dic22—41no—
151Dic22—41no—
152Dic22—82no—
153Dic22—82no—
154C8×C11—22no—
155C8×C11—21no—
156C8×C11C2×#4111yescharacteristic
157C8×C112−1+411yescharacteristic
158#556—221no—
159#547—221no—
160C2×SD32—111no—
161C2×M32C2×D1112yes—
162#500—111no—
163#500—111no—
164#485—222no—
165#480—222no—
166#475—221no—
167#474—221no—
168#467—112no—
169#466—112no—
170C4×Q16—111no—
171C4×D8—111no—
172C8×D4C2×D1111yescharacteristic
173#427—112no—
174C2×#107—112no—
175#367—111no—
176#367—112no—
177#366—112no—
178#366—112no—
179#366—112no—
180C4⋊C16C2×D1111yescharacteristic
181#358—111no—
182#358—112no—
183#357—111no—
184#357—112no—
185C22⋊C16C2×D1112yes—
186C4×C16C2×D1111yescharacteristic
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11C22×D811yescharacteristic
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C4×C11—22no—
195C4×C11—21no—
196C4×C11#50912yes—
197C4×C11#54711yescharacteristic
198C4×C11#57811yescharacteristic
199Dic11—81no—
200Dic11—82no—
201Dic11—82no—
202Dic11—81no—
203Dic11—81no—
204C2×#41—441no—
205C2×Q16—111no—
206C2×D8—111no—
207C22×C8C22×D1112yes—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210#126—442no—
211#124—441no—
212#123—442no—
213C22⋊Q8—222no—
214C22⋊Q8—441no—
215#121—222no—
216C4×Q8—221no—
217C4×Q8—441no—
218C4×D4—221no—
219C4×D4D4411yescharacteristic
220#117—222no—
221C2×C4⋊C4—222no—
222SD32—222no—
223M32—24no—
224C2×C16C22×D1111yescharacteristic
225C2×C16C22×D1112yes—
226C2×C16C22×D1111yescharacteristic
227#107—112no—
228#107—111no—
229#107—111no—
230#107—112no—
231#107—222no—
232#107—221no—
233#107—221no—
234#106—222no—
235C4⋊C8D4411yescharacteristic
236#103—221no—
237#103—222no—
238#102—221no—
239#102—222no—
240C22⋊C8D4412yes—
241C4×C8C22×D1111yescharacteristic
242C2×C11—42no—
243C2×C11#333411yescharacteristic
244C2×C11C2×#50911yescharacteristic
245C2×C11#341711yescharacteristic
246D11—161no—
247#41—884no—
248C2×Q8—221no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×D4—221no—
252C2×D4—442no—
253C2×D4D8811yescharacteristic
254C22×C4—442no—
255C22×C4—441no—
256C22×C4C2×D4412yes—
257Q16—221no—
258Q16—221no—
259D8—221no—
260D8—221no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8C2×D4411yescharacteristic
264C2×C8C2×D4412yes—
265C2×C8C23×D1111yescharacteristic
266C4⋊C4—221no—
267C4⋊C4—222no—
268C4⋊C4—221no—
269C4⋊C4—222no—
270C4⋊C4—442no—
271C4⋊C4—441no—
272C4⋊C4—442no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4D8811yescharacteristic
276C22⋊C4—442no—
277C22⋊C4—442no—
278C22⋊C4—441no—
279C22⋊C4—442no—
280C22⋊C4D8812yes—
281C42—442no—
282C42—441no—
283C42C2×D4411yescharacteristic
284C16—22no—
285C16—21no—
286C16#434112yescomplemented
287C11#3392011yescharacteristic, complemented, Sylow
288C23—441no—
289C23C2×D8812yes—
290Q8—441no—
291Q8—441no—
292Q8—882no—
293Q8—882no—
294D4—22no—
295D4—441no—
296D4—441no—
297D4—884no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—884no—
306C2×C4—882no—
307C2×C4C2×D8812yes—
308C2×C4C2×D8811yescharacteristic
309C2×C4C2×D8811yescharacteristic
310C2×C4C22×D4411yescharacteristic
311C8—21no—
312C8—22no—
313C8C2×#434111yescharacteristic
314C8#6704311yescharacteristic
315C22—22no—
316C22—22no—
317C22—22no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22C22×D8811yescharacteristic
322C4—22no—
323C4—21no—
324C4—881no—
325C4—881no—
326C4—882no—
327C4—882no—
328C4—881no—
329C4#1062252112yes—
330C4#1062308611yescharacteristic
331C4#1062328411yescharacteristic
332C2—42no—
333C2—1761no—
334C2#1308096411yescharacteristic
335C2C2×#1062252111yescharacteristic
336C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2169C2
socleC22×C11C22×D8
prime radical#13080964C2
hypercenter#2169D11
hypocenterC11#33920
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
3. #13070891C2semidirect
4. #13070819C2semidirect
5. #13070808C2semidirect
6. #13070759C2semidirect
7. #13070754C2semidirect
8. #13070729C2semidirect
9. C4×#66864C2semidirect
10. #13070404C2semidirect
11. C11×#2169C2semidirect
119. C11×C16#41semidirect
129. #2169D11semidirect
286. C16#4341semidirect
287. C11#33920semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130809642
#130708912
#130708192
#130708082
#130707592
#130707542
#130707292
C4×#668642
#130704042
C11×#21692
#3392011