Finite Group Databasebeta

← #14667055

Subgroups — #14667055

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#13070802C212yesmaximal, complemented
3#13070109C211yesmaximal, characteristic, complemented
4#13066626C212yesmaximal, complemented
5C11×#1322C211yesmaximal, characteristic, complemented
6#10623008—21no—
7C2×C11×C4⋊C8C2211yescharacteristic
8#10622728—21no—
9#10622728C2212yes—
10C2×#66882C2211yescharacteristic
11#10622541—21no—
12#10622459—22no—
13#10622456—22no—
14C11×C22⋊C16C2212yes—
15#10622189—21no—
16#10622189C2211yescharacteristic
17#10622147—22no—
18#10622143—22no—
19C2×#4339—41no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66983—22no—
24#66983—41no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×Dic11⋊C4—41no—
28C2×D88—21no—
29C2×D88D412yes—
30#66928—41no—
31#66927—21no—
32C4×D44—22no—
33C4×D44—41no—
34#66922—21no—
35C2×C11×C16—22no—
36C11×C4⋊C8—22no—
37C11⋊#95—41no—
38#66885—22no—
39#66885—22no—
40#66882—21no—
41#66882—22no—
42#66882D412yes—
43#12291—111nomaximal, Sylow
44C22×C4×C11D811yescharacteristic
45C22×C4×C11D811yescharacteristic
46C22×C4×C11C2×D411yescharacteristic
47C2×C22⋊D11—42no—
48C22×Dic11—41no—
49C22×Dic11—41no—
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—
61C42×C11—21no—
62C42×C11—21no—
63(C2×D11)⋊C4—42no—
64(C2×D11)⋊C4—42no—
65C4⋊Dic11—22no—
66C4⋊Dic11—22no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71Dic11⋊C4—82no—
72D88—42no—
73D88—81no—
74C11×C16—42no—
75#3245—111no—
76#2233—112no—
77#2087—111no—
78#1347—112no—
79#1322D1111yescharacteristic, complemented
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×C11SD3212yes—
89C2×C4×C11#12011yescharacteristic
90C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
91C22⋊D11—82no—
92C22⋊D11—82no—
93C2×Dic11—42no—
94C2×Dic11—42no—
95C2×Dic11—81no—
96C2×Dic11—81no—
97C2×Dic11—81no—
98C2×Dic11—81no—
99C2×Dic11—81no—
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×#107—111no—
114C2×C4⋊C8C2×D1111yescharacteristic
115#389—221no—
116#367—222no—
117#357—222no—
118C22⋊C16C2×D1112yes—
119#340—111no—
120#340—221no—
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#45611yescharacteristic
133C4×C11#45811yescharacteristic
134Dic11—82no—
135Dic11—82no—
136Dic11—161no—
137C2×#41—441no—
138C2×D8—112no—
139C2×D8—221no—
140C22×C8D4411yescharacteristic
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—221no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—441no—
152C2×C42D4411yescharacteristic
153C2×C16—22no—
154#107—112no—
155#107—221no—
156#107—222no—
157C4⋊C8—22no—
158#102—222no—
159#102—222no—
160#95—441no—
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—442no—
175C22×C4—441no—
176C22×C4—441no—
177C22×C4D8811yescharacteristic
178C22×C4D8811yescharacteristic
179C22×C4C2×D4411yescharacteristic
180D8—442no—
181D8—881no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8D4×D1112yes—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—441no—
189C4⋊C4—441no—
190C4⋊C4—441no—
191C4⋊C4—441no—
192C4⋊C4—882no—
193C22⋊C4—442no—
194C22⋊C4—442no—
195C42—21no—
196C42—21no—
197C16—42no—
198C11#1229111yescharacteristic, complemented, Sylow
199C23—442no—
200C23C2×D8811yescharacteristic
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—442no—
215C2×C4—442no—
216C2×C4—884no—
217C2×C4—881no—
218C2×C4—881no—
219C2×C4—881no—
220C2×C4—881no—
221C2×C4—881no—
222C2×C4#6686412yes—
223C2×C4#6693511yescharacteristic
224C2×C4#6696111yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—882no—
230C22—882no—
231C22—882no—
232C22#1062234511yescharacteristic
233C22C2×#6686411yescharacteristic
234C22#1062252111yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—882no—
239C4—882no—
240C4—1761no—
241C4#1062235511yescharacteristic
242C4#1062236511yescharacteristic
243C2—21no—
244C2—21no—
245C2—1762no—
246C2#1306762111yescharacteristic
247C2#1307054711yescharacteristic
248C2#1307056411yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1322C2
socleC22×C11#447
prime radical#13079926C2
hypercenter#1322D11
hypocenterC11#12291
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #13070802C2semidirect
3. #13070109C2semidirect
4. #13066626C2semidirect
5. C11×#1322C2semidirect
79. #1322D11semidirect
198. C11#12291semidirect

Maximal subgroups

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

subgroupindex
#130799262
#130708022
#130701092
#130666262
C11×#13222
#1229111