Finite Group Databasebeta

← #14666348

Subgroups — #14666348

Order 2816.

372 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 59 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#13073858C211yesmaximal, characteristic, complemented
2#13067653C212yesmaximal
3#13066642C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic
6C11×#537C2211yescharacteristic
7C2×C11×#104—21no—
8C11×#417—21no—
9C11×#384C2211yescharacteristic
10#10622647—22no—
11#10622599—21no—
12#10622599C2212yes—
13#10622598—22no—
14#10622590—22no—
15C4×C4⋊Dic11—21no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C2×C11×M16—21no—
21C11×C22⋊Q8—41no—
22C11×#121—22no—
23C11×#121—41no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C11×C4⋊C4C2311yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11D412yes—
32C2×C4×Dic11—22no—
33C11×#104—42no—
34C11×#103—41no—
35C11×#102—41no—
36#66896—42no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95—22no—
41C11⋊#95D412yes—
42C22⋊(C11⋊C8)—22no—
43#66872—42no—
44#12181—111nomaximal, Sylow
45C11×#41—41no—
46C11×#41—41no—
47C11×#41—41no—
48C11×#41—41no—
49C2×Q8×C11—21no—
50C2×D4×C11—21no—
51C2×D4×C11—22no—
52C2×D4×C11—41no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—41no—
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D412yes—
58C22×Dic11—22no—
59C22×Dic11—22no—
60C11×M16—41no—
61C11×M16—41no—
62C2×C8×C11—41no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—44no—
66C11×C4⋊C4—41no—
67C11×C22⋊C4—42no—
68C42×C11—21no—
69C42×C11SD1612yes—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73C4⋊Dic11—81no—
74C4×Dic11—44no—
75C2×C11⋊C8—42no—
76#2571—111no—
77#2039D1111yescharacteristic
78#1616—112no—
79#1353—112no—
80#1325—111no—
81C23×C11—41no—
82C23×C11#12011yescharacteristic
83Q8×C11—41no—
84Q8×C11—41no—
85D4×C11—41no—
86D4×C11—41no—
87D4×C11—82no—
88D4×C11—81no—
89D4×C11—81no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—81no—
101C2×C4×C11—81no—
102C2×C4×C11C2×SD1611yescharacteristic
103C2×C4×C11#13711yescharacteristic
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C8×C11—81no—
111C11⋊C8—82no—
112#537C2×D1111yescharacteristic
113#481—222no—
114C2×#104—21no—
115#417—21no—
116#400—112no—
117#400—221no—
118#389—222no—
119#384C2×D1111yescharacteristic
120#382—222no—
121C4×C4⋊C4—221no—
122#343C2×D1111yescharacteristic
123#327—222no—
124#324—112no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—81no—
128C22×C11—81no—
129C22×C11—81no—
130C22×C11#44811yescharacteristic
131C22×C11#45411yescharacteristic
132C22×C11B(4,𝔽2)11yescharacteristic
133C4×C11—24no—
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—42no—
137C4×C11—81no—
138C4×C11—81no—
139Dic11—82no—
140Dic11—82no—
141C2×#41—21no—
142C2×M16—21no—
143C22⋊Q8—41no—
144#121—22no—
145#121—41no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4C22⋊D1111yescharacteristic
152C2×C4⋊C4C22×D1111yescharacteristic
153C2×C42—222no—
154C2×C42C22⋊D1111yescharacteristic
155#106—442no—
156#104—42no—
157#103—41no—
158#102—41no—
159#102—442no—
160C22⋊C8—222no—
161#95—112no—
162#95—221no—
163#95—222no—
164#95—222no—
165#95—222no—
166C2×C11—21no—
167C2×C11—21no—
168C2×C11—161no—
169C2×C11#159911yescharacteristic
170C2×C11#219811yescharacteristic
171C2×C11#220411yescharacteristic
172#41—41no—
173#41—41no—
174#41—41no—
175#41—41no—
176C2×Q8—21no—
177C2×D4—21no—
178C2×D4—22no—
179C2×D4—41no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—41no—
183C22×C4—222no—
184C22×C4—222no—
185C22×C4D4×D1112yes—
186C22×C4C2×C22⋊D1111yescharacteristic
187M16—41no—
188M16—41no—
189C2×C8—41no—
190C2×C8—442no—
191C4⋊C4—22no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—44no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C4⋊C4—442no—
198C4⋊C4—881no—
199C22⋊C4—42no—
200C42—21no—
201C42—444no—
202C42#432412yes—
203C11#1218111yescharacteristic, complemented, Sylow
204C23—41no—
205C23#6699011yescharacteristic
206Q8—41no—
207Q8—41no—
208D4—41no—
209D4—41no—
210D4—82no—
211D4—81no—
212D4—81no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4C2×#432411yescharacteristic
232C2×C4#6700411yescharacteristic
233C8—81no—
234C8—882no—
235C22—21no—
236C22—21no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22#1062264511yescharacteristic
241C22#1062265311yescharacteristic
242C22#1062267511yescharacteristic
243C4—24no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—81no—
248C4—81no—
249C4—882no—
250C4—882no—
251C2—21no—
252C2—21no—
253C2—161no—
254C2#1306755511yescharacteristic
255C2#1307061111yescharacteristic
256C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2039C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#2039D11
hypocenterC11#12181
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13073858C2semidirect
3. #13066642C2semidirect
4. #13066562C2semidirect
203. C11#12181semidirect

Maximal subgroups

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

subgroupindex
#130738582
#130676532
#130666422
#130665622
C11×#20392
#1218111