Finite Group Databasebeta

← #14911470

Subgroups — #14911470

Order 2816.

472 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081605C211yesmaximal, characteristic
2#13081508C211yesmaximal, characteristic, complemented
3#13070848C212yesmaximal
4#13070844C211yesmaximal, characteristic, complemented
5#13070781C212yesmaximal, complemented
6#13070754C211yesmaximal, characteristic
7#13070679C212yesmaximal
8#13070667C211yesmaximal, characteristic, complemented
9C4×Dic88C212yesmaximal, complemented
10C4×#66864C211yesmaximal, characteristic
11Q8×C11×C16C211yesmaximal, characteristic, complemented
12#10623115—21no—
13#10623098—21no—
14C8×Q8×C11C2211yescharacteristic
15C2×Dic88C2212yes—
16C2×#66864C2211yescharacteristic
17#10622464—21no—
18#10622458—22no—
19#10622454—21no—
20#10622442—22no—
21#10622312C2211yescharacteristic
22C4×Dic44C2212yes—
23C4×Dic44C2211yescharacteristic
24C4×Dic44C2212yes—
25#10622309C2212yes—
26C4×D88C2211yescharacteristic
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×C4⋊C16C2212yes—
31C4×C11×C16C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622147C2211yescharacteristic
34#10622147C2212yes—
35#10622143C2211yescharacteristic
36#10622142C2212yes—
37#10622141C2212yes—
38#10622141C2212yes—
39#10622141C2212yes—
40#10622141C2211yescharacteristic
41C4×Q8×C11D411yescharacteristic
42#66999—41no—
43#66997—41no—
44C2×Dic44—21no—
45C2×Dic44C2312yes—
46C2×Dic44C2311yescharacteristic
47C2×D88C2311yescharacteristic
48C2×#4314—22no—
49#66951—42no—
50#66945—41no—
51#66942—42no—
52#66940—41no—
53#66928—22no—
54C4×D44—21no—
55#66923—22no—
56#66922—21no—
57#66922—21no—
58C4×Dic22—21no—
59C4×Dic22—22no—
60C4×Dic22—22no—
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C2×C11×C16C2312yes—
64C11×C4⋊C8D411yescharacteristic
65C11×C4⋊C8D412yes—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66885—21no—
69#66882—21no—
70#66882C2312yes—
71#66882C2311yescharacteristic
72#66882C2311yescharacteristic
73#66881—22no—
74#66880—22no—
75#66880—21no—
76#66880—22no—
77Dic88—24no—
78#66864—22no—
79#33931—111nomaximal, Sylow
80C2×Q8×C11D811yescharacteristic
81C2×D44—21no—
82C2×C4×D11—41no—
83C2×Dic22—21no—
84C2×Dic22—22no—
85C2×Dic22—41no—
86C2×C8×C11C2×D412yes—
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2411yescharacteristic
89C11×C4⋊C4D811yescharacteristic
90C11×C4⋊C4D812yes—
91C42×C11C2×D412yes—
92C42×C11C2×D411yescharacteristic
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—22no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107C4×Dic11—42no—
108C4×Dic11—41no—
109C4×Dic11—42no—
110Dic44—22no—
111Dic44—21no—
112Dic44—22no—
113Dic44—81no—
114Dic44#4112yes—
115D88—21no—
116D88—21no—
117#4314—82no—
118C11×C16—21no—
119C11×C16—22no—
120C11×C16—21no—
121#3393—111no—
122#3383—111no—
123#2242—112no—
124#2241—111no—
125#2229—112no—
126#2224—111no—
127#2211—112no—
128#2209—111no—
129Q8×C16D1111yescharacteristic, complemented
130C4×Q32—112no—
131C4×SD32—111no—
132C22×D11—41no—
133Q8×C11—22no—
134C2×C4×C11C2×D812yes—
135C2×C4×C11C2×D812yes—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144D44—41no—
145D44—41no—
146C4×D11—82no—
147Dic22—22no—
148Dic22—41no—
149Dic22—42no—
150Dic22—42no—
151Dic22—82no—
152C8×C11—22no—
153C8×C11—21no—
154C8×C11C2×#4111yescharacteristic
155C8×C112−1+411yescharacteristic
156#557—221no—
157#556—221no—
158C2×Q32—112no—
159C2×SD32—111no—
160#500—111no—
161#499—112no—
162#495—112no—
163#494—111no—
164#479—222no—
165#475—221no—
166#464—222no—
167#461—221no—
168C8×Q8C2×D1111yescharacteristic
169C4×Q16—111no—
170C4×Q16—112no—
171C4×Q16—112no—
172C4×D8—111no—
173#367—111no—
174#366—112no—
175C4⋊C16C2×D1111yescharacteristic
176C4⋊C16C2×D1112yes—
177#358—111no—
178#358—112no—
179#358—112no—
180#358—112no—
181#357—111no—
182#357—112no—
183C4×C16C2×D1111yescharacteristic
184C4×C16C2×D1112yes—
185C22×C11C22×D811yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—21no—
192C4×C11#50812yes—
193C4×C11#54811yescharacteristic
194C4×C11#57711yescharacteristic
195Dic11—42no—
196Dic11—82no—
197Dic11—82no—
198Dic11—81no—
199Dic11—81no—
200C2×Q16—111no—
201C2×Q16—112no—
202C2×Q16—221no—
203C2×SD16—222no—
204C2×D8—111no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8—441no—
208#126—442no—
209#125—222no—
210#125—442no—
211#124—222no—
212C22⋊Q8—441no—
213C4×Q8—222no—
214C4×Q8—221no—
215C4×Q8—222no—
216C4×Q8—441no—
217C4×Q8D4411yescharacteristic
218C4×D4—221no—
219#117—441no—
220Q32—224no—
221SD32—222no—
222C2×C16C22×D1111yescharacteristic
223C2×C16C22×D1112yes—
224C2×C16C22×D1111yescharacteristic
225#107—112no—
226#107—111no—
227#107—111no—
228#107—221no—
229#106—222no—
230C4⋊C8D4411yescharacteristic
231C4⋊C8D4412yes—
232#103—222no—
233#103—222no—
234#103—221no—
235#102—221no—
236C4×C8C22×D1111yescharacteristic
237C4×C8C22×D1112yes—
238C2×C11#335811yescharacteristic
239C2×C11C2×#50811yescharacteristic
240C2×C11#341711yescharacteristic
241D11—161no—
242C2×Q8—221no—
243C2×Q8—222no—
244C2×Q8—441no—
245C2×Q8D8811yescharacteristic
246C2×D4—221no—
247C22×C4—441no—
248Q16—112no—
249Q16—221no—
250Q16—222no—
251Q16—222no—
252Q16—881no—
253SD16—882no—
254D8—221no—
255D8—221no—
256C2×C8C2×D4411yescharacteristic
257C2×C8C2×D4412yes—
258C2×C8C23×D1111yescharacteristic
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—222no—
262C4⋊C4—441no—
263C4⋊C4—442no—
264C4⋊C4—441no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—442no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4D8811yescharacteristic
271C4⋊C4D8812yes—
272C22⋊C4—442no—
273C22⋊C4—441no—
274C22⋊C4—442no—
275C42—442no—
276C42—442no—
277C42—441no—
278C42C2×D4411yescharacteristic
279C42C2×D4412yes—
280C16—21no—
281C16—21no—
282C16—22no—
283C11#3393111yescharacteristic, complemented, Sylow
284C23—441no—
285Q8—22no—
286Q8—222no—
287Q8—441no—
288Q8—442no—
289Q8—442no—
290Q8—882no—
291D4—441no—
292D4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4—441no—
297C2×C4—442no—
298C2×C4—882no—
299C2×C4C2×D8812yes—
300C2×C4C2×D8811yescharacteristic
301C2×C4C2×D8812yes—
302C2×C4C2×D8811yescharacteristic
303C2×C4C22×D4411yescharacteristic
304C8—22no—
305C8—21no—
306C8#6704011yescharacteristic
307C8#41×D1111yescharacteristic
308C22—881no—
309C22—881no—
310C22—881no—
311C22C22×D8811yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—442no—
316C4—881no—
317C4—882no—
318C4—882no—
319C4—881no—
320C4#1062251712yes—
321C4#1062310711yescharacteristic
322C4#1062328211yescharacteristic
323C2—1761no—
324C2#1308125211yescharacteristic
325C2C2×#1062251711yescharacteristic
326C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingQ8×C11×C16C2
socleC22×C11C22×D8
prime radicalC2×D88C23
hypercenterQ8×C16D11
hypocenterC11#33931
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ Q8×C16

Complements

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

NH ≅ G/Ntype
2. #13081508C2semidirect
4. #13070844C2semidirect
5. #13070781C2semidirect
8. #13070667C2semidirect
9. C4×Dic88C2semidirect
11. Q8×C11×C16C2semidirect
129. Q8×C16D11semidirect
283. C11#33931semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130815082
#130708482
#130708442
#130707812
#130707542
#130706792
#130706672
C4×Dic882
C4×#668642
Q8×C11×C162
#3393111