Finite Group Databasebeta

← #14667213

Subgroups — #14667213

Order 2816.

384 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D4×Dic44C211yesmaximal, characteristic, complemented
2#13070872C211yesmaximal, characteristic, complemented
3#13070657C211yesmaximal, characteristic, complemented
4#13067971C211yesmaximal, characteristic
5#13066666C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×D4⋊C16C211yesmaximal, characteristic, complemented
8C22×Dic44—21no—
9D4×Dic22—21no—
10C8×D4×C11C2211yescharacteristic
11#10622729—21no—
12#10622628—21no—
13C2×#66864—22no—
14C2×#66864—21no—
15#10622462—21no—
16#10622352—22no—
17#10622312C2211yescharacteristic
18C4×Dic44C2211yescharacteristic
19#10622308C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C4×C11×C16C2211yescharacteristic
22#10622147—21no—
23#10622123—21no—
24#10622096C2211yescharacteristic
25C22×Dic22—22no—
26C22×C8×C11—21no—
27C4×D4×C11D411yescharacteristic
28D4×Dic11—41no—
29C2×#4323—41no—
30#66977—22no—
31C2×Dic44—22no—
32C2×Dic44—21no—
33C2×Dic44—42no—
34C2×Dic44—42no—
35C2×Dic44D411yescharacteristic
36C2×Dic44D412yes—
37C2×D88—21no—
38C2×D88—21no—
39#66941—41no—
40#66931—42no—
41#66927—21no—
42#66922—21no—
43C4×Dic22—21no—
44C2×C11×C16—21no—
45C2×C11×C16—21no—
46C11×C4⋊C8D411yescharacteristic
47C11×C22⋊C8—21no—
48C4×C8×C11C2311yescharacteristic
49#66882D411yescharacteristic
50#66880—22no—
51#66880—21no—
52#66873—41no—
53C4⋊(C11⋊C8)—21no—
54#66864—44no—
55#66864—42no—
56#12318—111nomaximal, Sylow
57C2×D4×C11D811yescharacteristic
58C22×C4×C11—21no—
59C22×Dic11—42no—
60C2×D44—41no—
61C2×D44—41no—
62C2×D44—41no—
63C2×Dic22—21no—
64C2×Dic22—22no—
65C2×Dic22—42no—
66C2×Dic22—44no—
67C2×Dic22—82no—
68C2×C8×C11—21no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11C2×D411yescharacteristic
72C2×C8×C11C2×D411yescharacteristic
73C11×C4⋊C4D811yescharacteristic
74C11×C22⋊C4—21no—
75C42×C11C2×D411yescharacteristic
76C22⋊Dic11—42no—
77#4323—82no—
78C4⋊Dic11—21no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81Dic11⋊C4—42no—
82Dic11⋊C4—41no—
83C4×Dic11—41no—
84C2×C11⋊C8—41no—
85Dic44—21no—
86Dic44—42no—
87Dic44—44no—
88Dic44—41no—
89Dic44—41no—
90Dic44D812yescomplemented
91D88—42no—
92D88—41no—
93D88—41no—
94C11×C16—22no—
95C11×C16—41no—
96D4×Q16—111no—
97#2248—111no—
98#2207—111no—
99#1667—111no—
100#1362—111no—
101#1332—111no—
102D4⋊C16D1111yescharacteristic, complemented
103C23×C11—21no—
104C22×D11—81no—
105D4×C11—21no—
106D4×C11SD3212yescomplemented
107C2×C4×C11—21no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—42no—
116C2×Dic11—84no—
117D44—81no—
118D44—81no—
119D44—81no—
120D44—81no—
121D44—161no—
122Dic22—22no—
123Dic22—41no—
124Dic22—42no—
125Dic22—42no—
126Dic22—84no—
127C8×C11—21no—
128C8×C11—41no—
129C8×C11C2×D811yescharacteristic
130C8×C11AGL(1,ℤ/8)11yescharacteristic
131C11⋊C8—81no—
132C22×Q16—221no—
133D4×Q8—221no—
134C2×SD32—221no—
135C2×SD32—222no—
136#494—111no—
137#493—111no—
138#467—221no—
139#462—221no—
140#459—221no—
141#451—222no—
142C4×Q16—111no—
143C8×D4C2×D1111yescharacteristic
144C4⋊C16C2×D1111yescharacteristic
145#357—221no—
146C4×C16C2×D1111yescharacteristic
147#335—111no—
148#331—221no—
149C22×C11—22no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11#44711yescharacteristic
153C2×D11—161no—
154C2×D11—161no—
155C2×D11—161no—
156C4×C11—21no—
157C4×C11—41no—
158C4×C11#44711yescharacteristic
159C4×C11#45311yescharacteristic
160C4×C11C2×SD3211yescharacteristic
161C4×C11#51011yescharacteristic
162Dic11—42no—
163Dic11—82no—
164Dic11—81no—
165C22×Q8—222no—
166C2×Q16—111no—
167C2×Q16—112no—
168C2×Q16—222no—
169C2×Q16—221no—
170C2×Q16—442no—
171C2×Q16—442no—
172C2×D8—221no—
173C2×D8—221no—
174C2×D8—441no—
175C22×C8—21no—
176C4⋊Q8—221no—
177C4⋊Q8—441no—
178#127—221no—
179C22⋊Q8—222no—
180C22⋊Q8—442no—
181C4×Q8—221no—
182C4×D4—441no—
183C4×D4D4411yescharacteristic
184SD32—444no—
185SD32—442no—
186C2×C16—21no—
187C2×C16—21no—
188#107—111no—
189C4⋊C8—221no—
190C4⋊C8D4411yescharacteristic
191#103—222no—
192#103—221no—
193#102—441no—
194C22⋊C8—21no—
195C4×C8C22×D1111yescharacteristic
196C2×C11—42no—
197C2×C11#161911yescharacteristic
198C2×C11#218511yescharacteristic
199C2×C11#219311yescharacteristic
200D11—321no—
201C2×Q8—221no—
202C2×Q8—222no—
203C2×Q8—442no—
204C2×Q8—444no—
205C2×Q8—882no—
206C2×D4—441no—
207C2×D4—441no—
208C2×D4—441no—
209C2×D4D8811yescharacteristic
210C22×C4—21no—
211C22×C4—442no—
212Q16—112no—
213Q16—221no—
214Q16—442no—
215Q16—444no—
216Q16—441no—
217Q16—441no—
218D8—442no—
219D8—441no—
220D8—441no—
221D8—882no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—441no—
226C2×C8D4×D1111yescharacteristic
227C2×C8D4×D1111yescharacteristic
228C4⋊C4—221no—
229C4⋊C4—442no—
230C4⋊C4—441no—
231C4⋊C4—441no—
232C4⋊C4—441no—
233C4⋊C4D8811yescharacteristic
234C22⋊C4—21no—
235C22⋊C4—442no—
236C42—441no—
237C42C2×D4411yescharacteristic
238C16—22no—
239C16—41no—
240C11#1231811yescharacteristic, complemented, Sylow
241C23—21no—
242C23—881no—
243Q8—222no—
244Q8—441no—
245Q8—442no—
246Q8—442no—
247Q8—884no—
248D4—21no—
249D4—881no—
250D4—881no—
251D4—881no—
252D4—881no—
253D4—1761no—
254D4#6686412yescomplemented
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—442no—
261C2×C4—884no—
262C2×C4#6693511yescharacteristic
263C2×C4C2×D8811yescharacteristic
264C2×C4#6696111yescharacteristic
265C8—21no—
266C8—41no—
267C8—881no—
268C8D8×D1111yescharacteristic
269C8#6696711yescharacteristic
270C22—22no—
271C22—41no—
272C22—41no—
273C22—1761no—
274C22—1761no—
275C22—1761no—
276C22#1062234511yescharacteristic
277C4—21no—
278C4—41no—
279C4—442no—
280C4—882no—
281C4—881no—
282C4#1062238611yescharacteristic
283C4#1062243511yescharacteristic
284C4C2×#6686411yescharacteristic
285C4#1062252211yescharacteristic
286C2—42no—
287C2—3521no—
288C2#1306767211yescharacteristic
289C2#1307053511yescharacteristic
290C2#1307058211yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×D4⋊C16C2
socleC22×C11#447
prime radical#13067971C2
hypercenterD4⋊C16D11
hypocenterC11#12318
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
1. D4×Dic44C2semidirect
2. #13070872C2semidirect
3. #13070657C2semidirect
5. #13066666C2semidirect
6. #13066581C2semidirect
7. C11×D4⋊C16C2semidirect
90. Dic44D8semidirect
102. D4⋊C16D11semidirect
106. D4×C11SD32semidirect
240. C11#12318semidirect
254. D4#66864semidirect

Maximal subgroups

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

subgroupindex
D4×Dic442
#130708722
#130706572
#130679712
#130666662
#130665812
C11×D4⋊C162
#1231811