Finite Group Databasebeta

← #14667053

Subgroups — #14667053

Order 2816.

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

normal subgroups only

This group has 354 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#13070799C212yesmaximal, complemented
2#13070109C211yesmaximal, characteristic, complemented
3#13066625C212yesmaximal, complemented
4#13066556C211yesmaximal, characteristic, complemented
5C11×#3245C211yesmaximal, characteristic
6C11×#532—21no—
7C11×#474—22no—
8C11×#466—21no—
9C11×#466C2212yes—
10C11×#459—22no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×#66882C2211yescharacteristic
13#10622541—21no—
14#10622200—22no—
15#10622189—21no—
16#10622189C2211yescharacteristic
17C22⋊(C11⋊C16)C2212yes—
18#10622128—22no—
19C2×C11×#41—41no—
20C2×C11×D8—21no—
21C2×C11×D8D412yes—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11C2311yescharacteristic
24C11×C4⋊Q8—21no—
25C11×#127—21no—
26C11×#124—41no—
27C11×#121—22no—
28C11×#121—41no—
29C4×D4×C11—22no—
30C4×D4×C11—41no—
31C2×C42×C11D411yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—41no—
35C11×#107—21no—
36C11×#107D412yes—
37C11×C4⋊C8—22no—
38C11×#102—22no—
39C11×#102—22no—
40C11⋊#95—41no—
41#66882—22no—
42C2×C11⋊C16—22no—
43#12291—111nomaximal, Sylow
44C11×#41—82no—
45C11×#41—82no—
46C2×Q8×C11—41no—
47C2×D4×C11—22no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11—42no—
51C22×C4×C11—42no—
52C22×C4×C11D811yescharacteristic
53C22×C4×C11D811yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×Dic11—41no—
56C22×Dic11—41no—
57C11×D8—42no—
58C11×D8—81no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D412yes—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—41no—
65C11×C22⋊C4—42no—
66C11×C22⋊C4—42no—
67C42×C11—21no—
68C42×C11—21no—
69C4⋊Dic11—22no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73Dic11⋊C4—82no—
74C11⋊C16—42no—
75#3245D1111yescharacteristic
76#2233—112no—
77#2087—111no—
78#1347—112no—
79#1322—111no—
80C23×C11—42no—
81C23×C11C2×D811yescharacteristic
82Q8×C11—82no—
83D4×C11—42no—
84D4×C11—42no—
85D4×C11—82no—
86D4×C11—82no—
87D4×C11—82no—
88D4×C11—82no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—84no—
97C2×C4×C11SD3212yes—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—42no—
101C2×Dic11—81no—
102C2×Dic11—81no—
103C2×Dic11—81no—
104C2×Dic11—81no—
105C2×Dic11—81no—
106C8×C11—22no—
107C8×C11—41no—
108#532—21no—
109#474—22no—
110#466—21no—
111#466C2×D1112yes—
112#459—22no—
113C2×#107—111no—
114C2×C4⋊C8C2×D1111yescharacteristic
115#389—221no—
116#367—222no—
117#357—222no—
118C22⋊C16—112no—
119#340—111no—
120#340—221no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—82no—
124C22×C11—82no—
125C22×C11—82no—
126C22×C11#44711yescharacteristic
127C22×C11C2×SD3211yescharacteristic
128C22×C11#50911yescharacteristic
129C4×C11—21no—
130C4×C11—22no—
131C4×C11—41no—
132C4×C11—82no—
133C4×C11#45611yescharacteristic
134C4×C11#45811yescharacteristic
135Dic11—82no—
136Dic11—161no—
137C2×#41—41no—
138C2×D8—21no—
139C2×D8C22⋊D1112yes—
140C22×C8C22⋊D1111yescharacteristic
141C22×C8C22×D1111yescharacteristic
142C4⋊Q8—21no—
143#127—21no—
144#124—41no—
145#121—22no—
146#121—41no—
147C4×D4—22no—
148C4×D4—41no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—441no—
152C2×C42C22⋊D1111yescharacteristic
153C2×C16—222no—
154#107—21no—
155#107—222no—
156#107C22⋊D1112yes—
157C4⋊C8—22no—
158#102—22no—
159#102—22no—
160#95—441no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11—162no—
164C2×C11#161011yescharacteristic
165C2×C11#218711yescharacteristic
166C2×C11#219011yescharacteristic
167#41—82no—
168#41—82no—
169C2×Q8—41no—
170C2×D4—22no—
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—42no—
174C22×C4—42no—
175C22×C4—441no—
176C22×C4—441no—
177C22×C4#432311yescharacteristic
178C22×C4#432311yescharacteristic
179C22×C4C2×C22⋊D1111yescharacteristic
180D8—42no—
181D8—81no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8C2×C22⋊D1112yes—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—222no—
189C4⋊C4—441no—
190C4⋊C4—441no—
191C4⋊C4—441no—
192C4⋊C4—882no—
193C22⋊C4—42no—
194C22⋊C4—42no—
195C42—21no—
196C42—21no—
197C16—442no—
198C11#1229111yescharacteristic, complemented, Sylow
199C23—42no—
200C23C2×#432311yescharacteristic
201Q8—82no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—82no—
207D4—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—84no—
216C2×C4—442no—
217C2×C4—881no—
218C2×C4—881no—
219C2×C4—881no—
220C2×C4—881no—
221C2×C4—881no—
222C2×C4#6689112yes—
223C2×C4#6698511yescharacteristic
224C2×C4#6700611yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—82no—
230C22—82no—
231C22—82no—
232C22#1062276011yescharacteristic
233C22C2×#6689111yescharacteristic
234C22#1062283011yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—82no—
239C4—882no—
240C4—1761no—
241C4#1062285611yescharacteristic
242C4#1062285911yescharacteristic
243C2—21no—
244C2—21no—
245C2—162no—
246C2#1306761911yescharacteristic
247C2#1307054511yescharacteristic
248C2#1307056211yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
Fitting, prime radicalC11×#3245C2
socleC22×C11#447
hypercenter#3245D11
hypocenterC11#12291
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13070799C2semidirect
2. #13070109C2semidirect
3. #13066625C2semidirect
4. #13066556C2semidirect
198. C11#12291semidirect

Maximal subgroups

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

subgroupindex
#130707992
#130701092
#130666252
#130665562
C11×#32452
#1229111