Finite Group Databasebeta

← #14667052

Subgroups — #14667052

Order 2816.

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

normal subgroups only

This group has 354 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#13079926C211yesmaximal, characteristic
2#13070801C212yesmaximal, complemented
3#13066624C212yesmaximal, complemented
4#13066556C211yesmaximal, characteristic, complemented
5C11×#2087C211yesmaximal, characteristic, complemented
6#10623008—21no—
7C2×C11×#107C2211yescharacteristic
8C2×C11×C4⋊C8C2211yescharacteristic
9C11×#389—21no—
10#10622728—21no—
11#10622728C2212yes—
12#10622459—22no—
13#10622456—22no—
14C11×#340—21no—
15C11×#340C2211yescharacteristic
16C22⋊(C11⋊C16)C2212yes—
17#10622129—22no—
18#10622128—22no—
19C2×#4339—41no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11D411yescharacteristic
26#66983—22no—
27#66983—41no—
28C2×D88—21no—
29C2×D88D412yes—
30#66928—41no—
31#66927—21no—
32C4×D44—22no—
33C4×D44—41no—
34#66922—21no—
35C11×#107—22no—
36C11×C4⋊C8—22no—
37C11×#95—41no—
38#66885—22no—
39#66885—22no—
40#66882—21no—
41#66882D412yes—
42C2×C11⋊C16—22no—
43#12291—111nomaximal, Sylow
44C22×C4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11D811yescharacteristic
47C22×C4×C11D811yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C2×C22⋊D11—42no—
50#4339—82no—
51#4339—82no—
52C2×D44—22no—
53C2×D44—41no—
54C2×D44—41no—
55C2×C4×D11—42no—
56C2×Dic22—41no—
57C2×C8×C11—21no—
58C2×C8×C11—41no—
59C2×C8×C11—41no—
60C2×C8×C11C2×D412yes—
61C11×C4⋊C4—22no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—82no—
66C42×C11—21no—
67C42×C11—21no—
68(C2×D11)⋊C4—42no—
69(C2×D11)⋊C4—42no—
70C4⋊Dic11—22no—
71C4⋊Dic11—41no—
72D88—42no—
73D88—81no—
74C11⋊C16—42no—
75#3245—111no—
76#2233—112no—
77#2087D1111yescharacteristic, complemented
78#1347—112no—
79#1322—111no—
80C23×C11C2×D811yescharacteristic
81C22×D11—42no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11—42no—
89C2×C4×C11—81no—
90C2×C4×C11—81no—
91C2×C4×C11—81no—
92C2×C4×C11—81no—
93C2×C4×C11—81no—
94C2×C4×C11SD3212yes—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C22⋊D11—82no—
98C22⋊D11—82no—
99C2×Dic11—42no—
100D44—42no—
101D44—42no—
102D44—82no—
103D44—82no—
104C4×D11—84no—
105Dic22—82no—
106C8×C11—22no—
107C8×C11—41no—
108#532—221no—
109#474—222no—
110#466—112no—
111#466—221no—
112#459—222no—
113C2×#107C2×D1111yescharacteristic
114C2×C4⋊C8C2×D1111yescharacteristic
115#389—21no—
116#367—222no—
117#357—222no—
118C22⋊C16—112no—
119#340—21no—
120#340C2×D1111yescharacteristic
121C22×C11—21no—
122C22×C11—21no—
123C22×C11#44711yescharacteristic
124C22×C11C2×SD3211yescharacteristic
125C22×C11#50911yescharacteristic
126C2×D11—82no—
127C2×D11—82no—
128C2×D11—82no—
129C4×C11—21no—
130C4×C11—22no—
131C4×C11—41no—
132C4×C11—82no—
133C4×C11—161no—
134C4×C11#45611yescharacteristic
135C4×C11#45811yescharacteristic
136Dic11—82no—
137C2×#41—441no—
138C2×D8—112no—
139C2×D8—221no—
140C22×C8C22⋊D1111yescharacteristic
141C22×C8C22×D1111yescharacteristic
142C4⋊Q8—221no—
143#127—221no—
144#124—441no—
145#121—222no—
146#121—441no—
147C4×D4—222no—
148C4×D4—441no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—41no—
152C2×C42C22⋊D1111yescharacteristic
153C2×C16—222no—
154#107—22no—
155#107—112no—
156#107—221no—
157C4⋊C8—22no—
158#102—222no—
159#102—222no—
160#95—41no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11#161011yescharacteristic
164C2×C11#218711yescharacteristic
165C2×C11#219011yescharacteristic
166D11—162no—
167#41—882no—
168#41—882no—
169C2×Q8—441no—
170C2×D4—222no—
171C2×D4—441no—
172C2×D4—441no—
173C2×D4—442no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—442no—
177C22×C4#432311yescharacteristic
178C22×C4#432311yescharacteristic
179C22×C4C2×C22⋊D1111yescharacteristic
180D8—442no—
181D8—881no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8D4×D1112yes—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—82no—
191C4⋊C4—222no—
192C4⋊C4—441no—
193C22⋊C4—442no—
194C22⋊C4—442no—
195C42—21no—
196C42—21no—
197C16—442no—
198C11#1229111yescharacteristic, complemented, Sylow
199C23—442no—
200C23C2×#432311yescharacteristic
201Q8—882no—
202D4—442no—
203D4—442no—
204D4—882no—
205D4—882no—
206D4—882no—
207D4—882no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—442no—
221C2×C4—884no—
222C2×C4#6689212yes—
223C2×C4#6699011yescharacteristic
224C2×C4#6700211yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—882no—
230C22—882no—
231C22—882no—
232C22#1062264911yescharacteristic
233C22C2×#6689211yescharacteristic
234C22#1062280611yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—82no—
239C4—161no—
240C4—882no—
241C4#1062266611yescharacteristic
242C4#1062270811yescharacteristic
243C2—21no—
244C2—21no—
245C2—1762no—
246C2#1306761811yescharacteristic
247C2#1307054411yescharacteristic
248C2#1307056111yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2087C2
socleC22×C11#447
prime radical#13079926C2
hypercenter#2087D11
hypocenterC11#12291
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2087

Complements

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

NH ≅ G/Ntype
2. #13070801C2semidirect
3. #13066624C2semidirect
4. #13066556C2semidirect
5. C11×#2087C2semidirect
77. #2087D11semidirect
198. C11#12291semidirect

Maximal subgroups

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

subgroupindex
#130799262
#130708012
#130666242
#130665562
C11×#20872
#1229111