Finite Group Databasebeta

← #14666034

Subgroups — #14666034

Order 2816.

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

normal subgroups only

This group has 398 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#13076604C211yesmaximal, characteristic, complemented
2#13067653C212yesmaximal
3#13066642C212yesmaximal, complemented
4#13066550C211yesmaximal, characteristic, complemented
5C11×#2007C211yesmaximal, characteristic
6C2×C11×#137—21no—
7C11×#537C2211yescharacteristic
8C2×C11×#104—21no—
9C11×#391C2211yescharacteristic
10#10622843—21no—
11#10622647—22no—
12#10622599C2212yes—
13#10622541—21no—
14#10622274—22no—
15#10622268—22no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×Q8×C11D411yescharacteristic
21C11×#137—42no—
22C11×#137—42no—
23C2×C11×Q16—41no—
24C2×C11×SD16—41no—
25C2×C11×M16—21no—
26C11×C22⋊Q8—41no—
27C11×#121—22no—
28C11×#121—41no—
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11D412yes—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37C11×#104—42no—
38C11×#95—22no—
39#66896—42no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95D412yes—
44C22⋊(C11⋊C8)—22no—
45#66872—42no—
46#12131—111nomaximal, Sylow
47C11×#41—41no—
48C11×#41—41no—
49C11×#41—41no—
50C11×#41—41no—
51C2×Q8×C11—21no—
52C2×Q8×C11—21no—
53C2×Q8×C11—41no—
54C2×Q8×C11—41no—
55C2×Q8×C11SD1612yes—
56C2×D4×C11—21no—
57C2×D4×C11—22no—
58C2×D4×C11—41no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C11×Q16—44no—
67C11×SD16—44no—
68C11×M16—22no—
69C11×M16—41no—
70C2×C8×C11—41no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—42no—
74C42×C11—41no—
75C4⋊Dic11—42no—
76C4⋊Dic11—42no—
77C4⋊Dic11—81no—
78C4⋊Dic11—81no—
79Dic11⋊C4—44no—
80C4×Dic11—81no—
81C2×C11⋊C8—42no—
82#2809—111no—
83#2007D1111yescharacteristic
84#1616—112no—
85#1353—112no—
86#1319—111no—
87C23×C11—41no—
88C23×C11#12011yescharacteristic
89Q8×C11—42no—
90Q8×C11—41no—
91Q8×C11—41no—
92Q8×C11—81no—
93D4×C11—41no—
94D4×C11—41no—
95D4×C11—82no—
96D4×C11—81no—
97D4×C11—81no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11—81no—
110C2×C4×C11—81no—
111C2×C4×C11C2×SD1611yescharacteristic
112C2×C4×C11#13711yescharacteristic
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C8×C11—42no—
120C11⋊C8—82no—
121C2×#137—21no—
122#537C2×D1111yescharacteristic
123#481—222no—
124C2×#104—21no—
125#400—112no—
126#398—222no—
127#391—221no—
128#391C2×D1111yescharacteristic
129#389—221no—
130#387—222no—
131#343C2×D1111yescharacteristic
132#327—222no—
133#324—112no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—81no—
137C22×C11—81no—
138C22×C11—81no—
139C22×C11#44811yescharacteristic
140C22×C11#45311yescharacteristic
141C22×C11B(4,𝔽2)11yescharacteristic
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—42no—
145C4×C11—42no—
146C4×C11—42no—
147C4×C11—81no—
148Dic11—82no—
149Dic11—82no—
150C2×#41—21no—
151C22×Q8C22⋊D1111yescharacteristic
152#137—42no—
153#137—42no—
154C2×Q16—41no—
155C2×SD16—41no—
156C2×M16—21no—
157C22⋊Q8—41no—
158#121—22no—
159#121—41no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—222no—
162C2×C4⋊C4—221no—
163C2×C4⋊C4—221no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4C22×D1111yescharacteristic
166C2×C42—221no—
167C2×C42C22⋊D1111yescharacteristic
168#106—442no—
169#104—42no—
170#102—442no—
171C22⋊C8—222no—
172#95—22no—
173#95—112no—
174#95—222no—
175#95—222no—
176#95—222no—
177C2×C11—21no—
178C2×C11—21no—
179C2×C11—161no—
180C2×C11#159611yescharacteristic
181C2×C11#220111yescharacteristic
182C2×C11#220411yescharacteristic
183#41—41no—
184#41—41no—
185#41—41no—
186#41—41no—
187C2×Q8—21no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#432412yes—
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—41no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—41no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4D4×D1112yes—
201C22×C4C2×C22⋊D1111yescharacteristic
202Q16—44no—
203SD16—44no—
204M16—22no—
205M16—41no—
206C2×C8—41no—
207C2×C8—442no—
208C4⋊C4—22no—
209C4⋊C4—41no—
210C4⋊C4—442no—
211C4⋊C4—444no—
212C4⋊C4—442no—
213C4⋊C4—881no—
214C4⋊C4—881no—
215C22⋊C4—42no—
216C42—41no—
217C42—881no—
218C11#1213111yescharacteristic, complemented, Sylow
219C23—41no—
220C23#6699011yescharacteristic
221Q8—42no—
222Q8—41no—
223Q8—41no—
224Q8—81no—
225D4—41no—
226D4—41no—
227D4—82no—
228D4—81no—
229D4—81no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4C2×#432411yescharacteristic
250C2×C4#6700411yescharacteristic
251C8—42no—
252C8—882no—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22#1062264511yescharacteristic
259C22#1062265311yescharacteristic
260C22#1062269011yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—42no—
266C4—81no—
267C4—882no—
268C4—882no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2#1306753811yescharacteristic
273C2#1307062811yescharacteristic
274C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2007C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#2007D11
hypocenterC11#12131
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2007

Complements

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

NH ≅ G/Ntype
1. #13076604C2semidirect
3. #13066642C2semidirect
4. #13066550C2semidirect
218. C11#12131semidirect

Maximal subgroups

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

subgroupindex
#130766042
#130676532
#130666422
#130665502
C11×#20072
#1213111