Finite Group Databasebeta

← #14667326

Subgroups — #14667326

Order 2816.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081621C211yesmaximal, characteristic
2#13070869C211yesmaximal, characteristic
3#13070666C211yesmaximal, characteristic
4#13067987C211yesmaximal, characteristic
5#13066664C211yesmaximal, characteristic
6#13066596C211yesmaximal, characteristic
7C11×#1332C211yesmaximal, characteristic
8#10623098—21no—
9C4×C11×Q16C2211yescharacteristic
10#10622794—21no—
11C2×#66893—21no—
12#10622644—21no—
13C2×Dic88—22no—
14#10622486—21no—
15#10622464—21no—
16#10622406—22no—
17#10622312C2211yescharacteristic
18#10622312C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21C11×#335C2211yescharacteristic
22#10622130—21no—
23#10622124—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C4×Q8×C11—21no—
27#66997—22no—
28C2×#4326—22no—
29C2×Dic44—21no—
30C2×Dic44—21no—
31C2×Dic44—21no—
32C2×Dic44D412yes—
33#66942—42no—
34#66940—22no—
35#66923—41no—
36#66922—21no—
37#66922—21no—
38C4×Dic22—41no—
39C4×Dic22D411yescharacteristic
40C2×C11×C16—21no—
41C11×#107D411yescharacteristic
42C11×C4⋊C8—21no—
43C11×#103—21no—
44C4×C8×C11C2311yescharacteristic
45#66893—42no—
46#66881—41no—
47#66880—41no—
48Dic11⋊C8—21no—
49C8×Dic11—21no—
50C2×C11⋊C16—21no—
51#66874—22no—
52C4⋊(C11⋊C8)D411yescharacteristic
53Dic88—44no—
54#12334—111nomaximal, Sylow
55C2×Q8×C11—21no—
56C2×Dic22—22no—
57C2×Dic22—41no—
58C2×Dic22D811yescharacteristic
59C11×Q16—21no—
60C11×Q16—21no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4—21no—
65C11×C4⋊C4—41no—
66C42×C11—41no—
67C42×C11C2×D411yescharacteristic
68#4326—82no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11D811yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—42no—
76Dic11⋊C4—42no—
77Dic11⋊C4—42no—
78C4×Dic11—21no—
79C4×Dic11—42no—
80C2×C11⋊C8—21no—
81Dic44—42no—
82Dic44—42no—
83Dic44—41no—
84Dic44—41no—
85Dic44—41no—
86Dic44—41no—
87C11×C16—22no—
88C11⋊C16—41no—
89#3395—111no—
90#2247—111no—
91#2209—111no—
92#1670—111no—
93#1362—111no—
94Q8⋊C16—111no—
95#1332D1111yescharacteristic
96Q8×C11—41no—
97Q8×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—42no—
106C2×Dic11—81no—
107Dic22—21no—
108Dic22—42no—
109Dic22—42no—
110Dic22—81no—
111Dic22—81no—
112Dic22Q3212yescomplemented
113C8×C11—21no—
114C8×C11—81no—
115C8×C11#13511yescharacteristic
116C8×C11AGL(1,ℤ/8)11yescharacteristic
117C11⋊C8—41no—
118#557—221no—
119C2×Q32—222no—
120C2×Q32—221no—
121#494—111no—
122#494—111no—
123#494—221no—
124#475—221no—
125#462—222no—
126#462—221no—
127C8×Q8—111no—
128C4×Q16—221no—
129C4×Q16C2×D1111yescharacteristic
130C4⋊C16—111no—
131#358—221no—
132C4×C16C2×D1111yescharacteristic
133#335C2×D1111yescharacteristic
134#332—221no—
135C22×C11#44711yescharacteristic
136C4×C11—21no—
137C4×C11—81no—
138C4×C11—81no—
139C4×C11#44911yescharacteristic
140C4×C11#45311yescharacteristic
141C4×C11C2×Q3211yescharacteristic
142C4×C11#51011yescharacteristic
143Dic11—22no—
144Dic11—41no—
145Dic11—82no—
146Dic11—161no—
147C2×Q16—112no—
148C2×Q16—222no—
149C2×Q16—221no—
150C2×Q16—221no—
151C2×Q16—221no—
152C2×Q16D4411yescharacteristic
153C4⋊Q8—222no—
154C4⋊Q8—221no—
155C4⋊Q8—221no—
156#125—441no—
157#125—442no—
158C4×Q8—21no—
159C4×Q8—111no—
160C4×Q8—222no—
161C4×Q8—441no—
162Q32—444no—
163Q32—442no—
164C2×C16—21no—
165C2×C16—221no—
166#107D4411yescharacteristic
167#106—441no—
168C4⋊C8—21no—
169C4⋊C8—111no—
170C4⋊C8—221no—
171#103—21no—
172#103—222no—
173#103—441no—
174C4×C8—221no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162111yescharacteristic
177C2×C11#218811yescharacteristic
178C2×C11#219511yescharacteristic
179C2×Q8—21no—
180C2×Q8—111no—
181C2×Q8—222no—
182C2×Q8—441no—
183Q16—21no—
184Q16—21no—
185Q16—442no—
186Q16—442no—
187Q16—441no—
188Q16—441no—
189Q16—441no—
190Q16—441no—
191Q16—882no—
192C2×C8—41no—
193C2×C8—221no—
194C2×C8C2×D4411yescharacteristic
195C2×C8D4×D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—41no—
198C4⋊C4—111no—
199C4⋊C4—221no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C4⋊C4—441no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C4⋊C4—441no—
207C42—41no—
208C42—221no—
209C42—442no—
210C42D4×D1111yescharacteristic
211C16—22no—
212C16—441no—
213C11#1233411yescharacteristic, complemented, Sylow
214Q8—41no—
215Q8—41no—
216Q8—112no—
217Q8—221no—
218Q8—442no—
219Q8—442no—
220Q8—881no—
221Q8—881no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—221no—
225C2×C4—221no—
226C2×C4—442no—
227C2×C4—881no—
228C2×C4#6693511yescharacteristic
229C2×C4D8×D1111yescharacteristic
230C2×C4#6696711yescharacteristic
231C8—21no—
232C8—81no—
233C8—441no—
234C8#6695711yescharacteristic
235C8#6696111yescharacteristic
236C22#1062238611yescharacteristic
237C4—21no—
238C4—81no—
239C4—81no—
240C4—222no—
241C4—441no—
242C4—882no—
243C4—1761no—
244C4#1062234711yescharacteristic
245C4#1062243511yescharacteristic
246C4#1062252811yescharacteristic
247C4D11×Q3211yescharacteristic
248C2#1306768411yescharacteristic
249C2#1307055111yescharacteristic
250C2#1307059511yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socle, prime radicalC22×C11#447
hypercenter#1332D11
hypocenterC11#12334
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
112. Dic22Q32semidirect
213. C11#12334semidirect

Maximal subgroups

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

subgroupindex
#130816212
#130708692
#130706662
#130679872
#130666642
#130665962
C11×#13322
#1233411