Finite Group Databasebeta

← #14667290

Subgroups — #14667290

Order 2816.

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

normal subgroups only

This group has 340 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#13081629C211yesmaximal, characteristic, complemented
2#13070866C211yesmaximal, characteristic
3#13070657C211yesmaximal, characteristic, complemented
4#13067976C211yesmaximal, characteristic, complemented
5#13066663C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×Q8⋊C16C211yesmaximal, characteristic, complemented
8#10623116—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622640—21no—
11C2×#66864—21no—
12C2×D176—22no—
13#10622461—21no—
14#10622457—22no—
15C4×Dic44C2211yescharacteristic
16#10622309—21no—
17#10622308C2211yescharacteristic
18#10622308C2211yescharacteristic
19C4×D88—21no—
20C11×C4⋊C16C2211yescharacteristic
21C4×C11×C16C2211yescharacteristic
22#10622147—21no—
23#10622123—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26#67000—41no—
27C2×#4325—41no—
28C2×Dic44D411yescharacteristic
29C2×D88—21no—
30C2×D88—21no—
31C2×D88—21no—
32C2×D88D412yes—
33C2×#4314—22no—
34#66947—42no—
35#66946—41no—
36#66928—22no—
37#66927—21no—
38#66927—21no—
39C4×D44—22no—
40C4×Dic22—21no—
41C2×C11×C16—21no—
42C2×C11×C16—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8D411yescharacteristic
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66885—22no—
48#66882D411yescharacteristic
49#66880—21no—
50#66873—41no—
51C4⋊(C11⋊C8)—21no—
52#66864—42no—
53D176—44no—
54#12329—111nomaximal, Sylow
55C2×Q8×C11D811yescharacteristic
56C2×D44—22no—
57C2×D44—41no—
58C2×D44—41no—
59C2×D44—41no—
60C2×D44—41no—
61C2×D44—41no—
62C2×C4×D11—42no—
63C2×Dic22—21no—
64C2×C8×C11—21no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4D811yescharacteristic
69C42×C11—21no—
70C42×C11C2×D411yescharacteristic
71#4325—82no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75C4⋊Dic11—21no—
76Dic11⋊C4—41no—
77C4×Dic11—41no—
78C2×C11⋊C8—41no—
79Dic44—21no—
80Dic44—21no—
81D88—42no—
82D88—42no—
83D88—41no—
84D88—41no—
85D88—41no—
86D88—41no—
87#4314—82no—
88C11×C16—22no—
89C11×C16—41no—
90#3396—111no—
91#2246—111no—
92#2207—111no—
93#1668—111no—
94#1361—111no—
95Q8⋊C16D1111yescharacteristic, complemented
96#1332—111no—
97C22×D11—42no—
98C22×D11—81no—
99Q8×C11—21no—
100Q8×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11#12011yescharacteristic
104C2×C4×C11C2×D811yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×Dic11—41no—
107C2×Dic11—41no—
108D44—42no—
109D44—42no—
110D44—81no—
111D44—81no—
112D44—81no—
113D44—81no—
114D44—81no—
115D44—81no—
116D44—161no—
117D44—161no—
118C4×D11—162no—
119Dic22—41no—
120Dic22—41no—
121C8×C11—21no—
122C8×C11—41no—
123C8×C11#13511yescharacteristic
124C8×C11AGL(1,ℤ/8)11yescharacteristic
125C11⋊C8—81no—
126#559—221no—
127C2×SD32—221no—
128C2×D16—222no—
129#495—221no—
130#493—111no—
131#493—111no—
132#463—222no—
133#460—221no—
134#460—221no—
135C8×Q8C2×D1111yescharacteristic
136C4×Q16—111no—
137C4×D8—221no—
138C4⋊C16C2×D1111yescharacteristic
139#357—221no—
140C4×C16C2×D1111yescharacteristic
141#335—111no—
142#331—221no—
143C22×C11#44711yescharacteristic
144C2×D11—82no—
145C2×D11—82no—
146C2×D11—82no—
147C2×D11—161no—
148C2×D11—161no—
149C2×D11—161no—
150C4×C11—21no—
151C4×C11—41no—
152C4×C11—41no—
153C4×C11#44911yescharacteristic
154C4×C11#45311yescharacteristic
155C4×C11#50811yescharacteristic
156C4×C11#50911yescharacteristic
157Dic11—81no—
158Dic11—81no—
159C2×Q16—111no—
160C2×SD16—222no—
161C2×SD16—441no—
162C2×D8—112no—
163C2×D8—221no—
164C2×D8—221no—
165C2×D8—221no—
166#127—221no—
167#127—221no—
168#124—222no—
169#124—441no—
170#123—442no—
171C4×Q8—221no—
172C4×Q8D4411yescharacteristic
173C4×D4—222no—
174C4×D4—441no—
175SD32—442no—
176D16—444no—
177C2×C16—21no—
178C2×C16—21no—
179#107—111no—
180C4⋊C8—21no—
181C4⋊C8—221no—
182C4⋊C8D4411yescharacteristic
183#103—221no—
184#102—222no—
185#102—441no—
186C4×C8—21no—
187C4×C8C22×D1111yescharacteristic
188C2×C11#162111yescharacteristic
189C2×C11#218611yescharacteristic
190C2×C11#219211yescharacteristic
191D11—162no—
192D11—321no—
193C2×Q8—221no—
194C2×Q8D8811yescharacteristic
195C2×D4—222no—
196C2×D4—441no—
197C2×D4—441no—
198C2×D4—441no—
199C2×D4—441no—
200C2×D4—441no—
201C22×C4—442no—
202Q16—221no—
203Q16—221no—
204SD16—882no—
205SD16—882no—
206D8—442no—
207D8—442no—
208D8—441no—
209D8—441no—
210D8—441no—
211D8—441no—
212C2×C8—21no—
213C2×C8—441no—
214C2×C8D4×D1111yescharacteristic
215C2×C8D4×D1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—221no—
218C4⋊C4—441no—
219C4⋊C4D8811yescharacteristic
220C22⋊C4—442no—
221C22⋊C4—442no—
222C22⋊C4—442no—
223C42—21no—
224C42—441no—
225C42C2×D4411yescharacteristic
226C16—22no—
227C16—41no—
228C11#1232911yescharacteristic, complemented, Sylow
229C23—442no—
230C23—881no—
231Q8—21no—
232Q8—21no—
233Q8—441no—
234Q8—441no—
235D4—442no—
236D4—442no—
237D4—881no—
238D4—881no—
239D4—881no—
240D4—881no—
241D4—881no—
242D4—881no—
243D4—1761no—
244D4—1761no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—441no—
248C2×C4—441no—
249C2×C4—1762no—
250C2×C4#6693511yescharacteristic
251C2×C4C2×D8811yescharacteristic
252C2×C4#6696111yescharacteristic
253C8—21no—
254C8—41no—
255C8—881no—
256C8#6696711yescharacteristic
257C8#6697211yescharacteristic
258C22—882no—
259C22—882no—
260C22—882no—
261C22—1761no—
262C22—1761no—
263C22—1761no—
264C22#1062234511yescharacteristic
265C4—21no—
266C4—41no—
267C4—41no—
268C4—881no—
269C4—881no—
270C4#1062242411yescharacteristic
271C4#1062243511yescharacteristic
272C4#1062251711yescharacteristic
273C4#1062252111yescharacteristic
274C2—3521no—
275C2—1762no—
276C2#1306768311yescharacteristic
277C2#1307054111yescharacteristic
278C2#1307057511yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socleC22×C11#447
prime radical#13070866C2
hypercenterQ8⋊C16D11
hypocenterC11#12329
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
1. #13081629C2semidirect
3. #13070657C2semidirect
4. #13067976C2semidirect
5. #13066663C2semidirect
6. #13066581C2semidirect
7. C11×Q8⋊C16C2semidirect
95. Q8⋊C16D11semidirect
228. C11#12329semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130708662
#130706572
#130679762
#130666632
#130665812
C11×Q8⋊C162
#1232911