Finite Group Databasebeta

← #14667302

Subgroups — #14667302

Order 2816.

328 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070873C211yesmaximal, characteristic, complemented
2#13070651C211yesmaximal, characteristic
3#13067976C211yesmaximal, characteristic, complemented
4#13066665C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic, complemented
7C11×#3393C211yesmaximal, characteristic, complemented
8C11×#556—21no—
9C11×#495—21no—
10C11×#494C2211yescharacteristic
11C11×#464—22no—
12C11×#461—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×D8C2211yescharacteristic
16C2×#66892—22no—
17C2×#66890—21no—
18#10622640—21no—
19#10622308C2211yescharacteristic
20#10622129—21no—
21#10622123—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C2×C11×SD16—22no—
28C2×C11×D8D411yescharacteristic
29C11×C4⋊Q8—21no—
30C11×#126—42no—
31C11×#124—22no—
32C11×C22⋊Q8—41no—
33C4×Q8×C11—22no—
34C4×Q8×C11D411yescharacteristic
35C4×D4×C11—21no—
36C11×#117—41no—
37C2×#4325—41no—
38C2×D88—21no—
39C2×D88—21no—
40#66927—21no—
41C11×#107D411yescharacteristic
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#103—22no—
45C11×#102—21no—
46C4×C8×C11—21no—
47C4×C8×C11C2311yescharacteristic
48#66892—44no—
49#66890—42no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#66873—41no—
53C4⋊(C11⋊C8)—21no—
54#12331—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×Q8×C11D811yescharacteristic
57C2×D4×C11—21no—
58C22×C4×C11—41no—
59C2×D44—41no—
60C2×D44—41no—
61C2×D44—41no—
62C11×Q16—41no—
63C11×Q16—41no—
64C11×Q16—42no—
65C11×SD16—82no—
66C11×D8—21no—
67C11×D8—21no—
68C2×C8×C11—21no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4D811yescharacteristic
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—41no—
80C42×C11—21no—
81C42×C11—42no—
82C42×C11C2×D411yescharacteristic
83#4325—82no—
84C2×C11⋊C8—41no—
85D88—42no—
86D88—41no—
87D88—41no—
88C11⋊C16—22no—
89C11⋊C16—41no—
90#3393D1111yescharacteristic, complemented
91#2248—111no—
92#2206—111no—
93#1668—111no—
94#1362—111no—
95Q8⋊C16—111no—
96#1331—111no—
97C23×C11—41no—
98C22×D11—81no—
99Q8×C11—21no—
100Q8×C11—21no—
101Q8×C11—42no—
102Q8×C11—42no—
103D4×C11—41no—
104D4×C11—41no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11#12011yescharacteristic
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
114D44—81no—
115D44—81no—
116D44—81no—
117D44—81no—
118D44—161no—
119C8×C11—21no—
120C8×C11—41no—
121C8×C11#13511yescharacteristic
122C8×C11AGL(1,ℤ/8)11yescharacteristic
123C11⋊C8—81no—
124#556—21no—
125C2×SD32—222no—
126C2×D16—221no—
127#495—21no—
128#494C2×D1111yescharacteristic
129#493—111no—
130#464—22no—
131#461—21no—
132#460—221no—
133C8×Q8C2×D1111yescharacteristic
134C4×Q16—21no—
135C4×D8C2×D1111yescharacteristic
136C4⋊C16—111no—
137#357—221no—
138C4×C16—111no—
139#335—111no—
140#331—221no—
141C22×C11—81no—
142C22×C11—81no—
143C22×C11—81no—
144C22×C11#44711yescharacteristic
145C2×D11—161no—
146C2×D11—161no—
147C2×D11—161no—
148C4×C11—21no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11—82no—
152C4×C11—81no—
153C4×C11#44911yescharacteristic
154C4×C11#45311yescharacteristic
155C4×C11#50811yescharacteristic
156C4×C11#50911yescharacteristic
157C2×Q16—21no—
158C2×Q16C22⋊D1112yes—
159C2×SD16—22no—
160C2×SD16—441no—
161C2×D8—221no—
162C2×D8—221no—
163C2×D8C22⋊D1111yescharacteristic
164C4⋊Q8—21no—
165#127—221no—
166#126—42no—
167#124—22no—
168C22⋊Q8—41no—
169C4×Q8—22no—
170C4×Q8C22⋊D1111yescharacteristic
171C4×D4—21no—
172#117—41no—
173SD32—444no—
174D16—442no—
175C2×C16—221no—
176C2×C16—221no—
177#107C22⋊D1111yescharacteristic
178C4⋊C8—21no—
179C4⋊C8—221no—
180C4⋊C8C22⋊D1111yescharacteristic
181#103—22no—
182#102—21no—
183#102—441no—
184C4×C8—21no—
185C4×C8C22×D1111yescharacteristic
186C2×C11—161no—
187C2×C11#162111yescharacteristic
188C2×C11#218611yescharacteristic
189C2×C11#219311yescharacteristic
190D11—321no—
191C2×Q8—22no—
192C2×Q8#432311yescharacteristic
193C2×D4—21no—
194C2×D4—441no—
195C2×D4—441no—
196C2×D4—441no—
197C22×C4—41no—
198Q16—42no—
199Q16—41no—
200Q16—41no—
201SD16—82no—
202SD16—882no—
203D8—21no—
204D8—21no—
205D8—442no—
206D8—441no—
207D8—441no—
208C2×C8—21no—
209C2×C8—441no—
210C2×C8C2×C22⋊D1111yescharacteristic
211C2×C8C2×C22⋊D1111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4#432311yescharacteristic
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—41no—
221C42—21no—
222C42—42no—
223C42C2×C22⋊D1111yescharacteristic
224C16—222no—
225C16—441no—
226C11#1233111yescharacteristic, complemented, Sylow
227C23—41no—
228C23—881no—
229Q8—21no—
230Q8—21no—
231Q8—42no—
232Q8—42no—
233D4—41no—
234D4—41no—
235D4—881no—
236D4—881no—
237D4—881no—
238D4—881no—
239D4—1761no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C2×#432311yescharacteristic
247C2×C4#6698511yescharacteristic
248C2×C4#6700611yescharacteristic
249C8—21no—
250C8—41no—
251C8—881no—
252C8#6700211yescharacteristic
253C8#6700311yescharacteristic
254C22—81no—
255C22—81no—
256C22—81no—
257C22—1761no—
258C22—1761no—
259C22—1761no—
260C22#1062283011yescharacteristic
261C4—21no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4—81no—
266C4#1062280611yescharacteristic
267C4#1062280711yescharacteristic
268C4#1062285111yescharacteristic
269C4#1062285411yescharacteristic
270C2—161no—
271C2—3521no—
272C2#1306768111yescharacteristic
273C2#1307053911yescharacteristic
274C2#1307058011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3393C2
socleC22×C11#447
prime radical#13070651C2
hypercenter#3393D11
hypocenterC11#12331
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #13070873C2semidirect
3. #13067976C2semidirect
4. #13066665C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066577C2semidirect
7. C11×#3393C2semidirect
90. #3393D11semidirect
226. C11#12331semidirect

Maximal subgroups

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

subgroupindex
#130708732
#130706512
#130679762
#130666652
Q8⋊(C11⋊C16)2
#130665772
C11×#33932
#1233111