Finite Group Databasebeta

← #14667241

Subgroups — #14667241

Order 2816.

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

normal subgroups only

This group has 368 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
2#13070869C211yesmaximal, characteristic, complemented
3#13070667C211yesmaximal, characteristic, complemented
4#13067981C211yesmaximal, characteristic
5#13066666C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×D4⋊C16C211yesmaximal, characteristic
8C22×Dic44—21no—
9D4×Dic22—21no—
10C8×D4×C11C2211yescharacteristic
11#10622729—21no—
12#10622620—21no—
13C2×Dic88—22no—
14C2×Dic88—21no—
15#10622462—21no—
16#10622352—22no—
17#10622312C2211yescharacteristic
18#10622312C2211yescharacteristic
19C4×Dic44C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C4×C11×C16C2211yescharacteristic
22#10622141—21no—
23#10622120—21no—
24#10622096C2211yescharacteristic
25C22×Dic22—22no—
26C22×C8×C11—21no—
27C4×D4×C11D411yescharacteristic
28D4×Dic11—41no—
29#66977—22no—
30C2×Dic44—22no—
31C2×Dic44—21no—
32C2×Dic44—21no—
33C2×Dic44—21no—
34C2×Dic44—42no—
35C2×Dic44—42no—
36C2×Dic44D411yescharacteristic
37C2×Dic44D412yes—
38#66941—41no—
39#66931—42no—
40#66922—21no—
41#66922—21no—
42C4×Dic22—21no—
43C2×C11×C16—21no—
44C2×C11×C16—21no—
45C11×C4⋊C8D411yescharacteristic
46C11×C22⋊C8—21no—
47C4×C8×C11C2311yescharacteristic
48#66896—41no—
49#66882D411yescharacteristic
50#66880—22no—
51#66880—21no—
52#66871—41no—
53C4⋊(C11⋊C8)—21no—
54Dic88—44no—
55Dic88—42no—
56#12322—111nomaximal, Sylow
57C2×D4×C11D811yescharacteristic
58C22×C4×C11—21no—
59C22×Dic11—42no—
60C2×Dic22—21no—
61C2×Dic22—22no—
62C2×Dic22—42no—
63C2×Dic22—44no—
64C2×Dic22—41no—
65C2×Dic22—82no—
66C2×C8×C11—21no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4D811yescharacteristic
72C11×C22⋊C4—21no—
73C42×C11C2×D411yescharacteristic
74C22⋊Dic11—42no—
75C4⋊Dic11—21no—
76C4⋊Dic11—41no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—42no—
81Dic11⋊C4—41no—
82C4×Dic11—41no—
83C2×C11⋊C8—41no—
84Dic44—21no—
85Dic44—42no—
86Dic44—42no—
87Dic44—44no—
88Dic44—41no—
89Dic44—41no—
90Dic44—41no—
91Dic44—41no—
92Dic44D812yes—
93C11×C16—22no—
94C11×C16—41no—
95D4×Q16—111no—
96#2247—111no—
97#2209—111no—
98#1669—111no—
99#1362—111no—
100#1332—111no—
101D4⋊C16D1111yescharacteristic
102C23×C11—21no—
103D4×C11—21no—
104D4×C11Q3212yescomplemented
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—42no—
114C2×Dic11—84no—
115C2×Dic11—81no—
116Dic22—22no—
117Dic22—41no—
118Dic22—42no—
119Dic22—42no—
120Dic22—84no—
121Dic22—81no—
122Dic22—81no—
123C8×C11—21no—
124C8×C11—41no—
125C8×C11C2×D811yescharacteristic
126C8×C11AGL(1,ℤ/8)11yescharacteristic
127C11⋊C8—81no—
128C22×Q16—221no—
129D4×Q8—221no—
130C2×Q32—221no—
131C2×Q32—222no—
132#494—111no—
133#494—111no—
134#474—221no—
135#467—221no—
136#462—221no—
137#451—222no—
138C4×Q16—111no—
139C8×D4C2×D1111yescharacteristic
140C4⋊C16C2×D1111yescharacteristic
141#358—221no—
142C4×C16C2×D1111yescharacteristic
143#335—111no—
144#332—221no—
145C22×C11—22no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11#44711yescharacteristic
149C4×C11—21no—
150C4×C11—41no—
151C4×C11#44711yescharacteristic
152C4×C11#45311yescharacteristic
153C4×C11C2×Q3211yescharacteristic
154C4×C11#51011yescharacteristic
155Dic11—42no—
156Dic11—82no—
157Dic11—81no—
158Dic11—161no—
159C22×Q8—222no—
160C2×Q16—111no—
161C2×Q16—112no—
162C2×Q16—222no—
163C2×Q16—221no—
164C2×Q16—221no—
165C2×Q16—221no—
166C2×Q16—442no—
167C2×Q16—442no—
168C22×C8—21no—
169C4⋊Q8—221no—
170C4⋊Q8—221no—
171C4⋊Q8—441no—
172C22⋊Q8—222no—
173C22⋊Q8—442no—
174C4×Q8—221no—
175C4×D4—441no—
176C4×D4D4411yescharacteristic
177Q32—444no—
178Q32—442no—
179C2×C16—21no—
180C2×C16—21no—
181#107—111no—
182#107—441no—
183C4⋊C8—221no—
184C4⋊C8D4411yescharacteristic
185#103—222no—
186#103—221no—
187#102—441no—
188C22⋊C8—21no—
189C4×C8C22×D1111yescharacteristic
190C2×C11—42no—
191C2×C11#161911yescharacteristic
192C2×C11#218811yescharacteristic
193C2×C11#219511yescharacteristic
194C2×Q8—221no—
195C2×Q8—222no—
196C2×Q8—442no—
197C2×Q8—444no—
198C2×Q8—441no—
199C2×Q8—882no—
200C2×D4D8811yescharacteristic
201C22×C4—21no—
202C22×C4—442no—
203Q16—112no—
204Q16—221no—
205Q16—442no—
206Q16—442no—
207Q16—444no—
208Q16—441no—
209Q16—441no—
210Q16—441no—
211Q16—441no—
212C2×C8—21no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—441no—
216C2×C8D4×D1111yescharacteristic
217C2×C8D4×D1111yescharacteristic
218C4⋊C4—221no—
219C4⋊C4—442no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4D8811yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—442no—
228C42—441no—
229C42C2×D4411yescharacteristic
230C16—22no—
231C16—41no—
232C11#1232211yescharacteristic, complemented, Sylow
233C23—21no—
234Q8—222no—
235Q8—441no—
236Q8—442no—
237Q8—442no—
238Q8—884no—
239Q8—881no—
240Q8—881no—
241D4—21no—
242D4Dic8812yescomplemented
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—441no—
247C2×C4—441no—
248C2×C4—442no—
249C2×C4—884no—
250C2×C4—881no—
251C2×C4#6693511yescharacteristic
252C2×C4C2×D8811yescharacteristic
253C2×C4#6696111yescharacteristic
254C8—21no—
255C8—41no—
256C8—881no—
257C8D8×D1111yescharacteristic
258C8#6696711yescharacteristic
259C22—22no—
260C22—41no—
261C22—41no—
262C22#1062234511yescharacteristic
263C4—21no—
264C4—41no—
265C4—442no—
266C4—881no—
267C4—882no—
268C4—1761no—
269C4#1062238611yescharacteristic
270C4#1062243511yescharacteristic
271C4C2×Dic8811yescharacteristic
272C4#1062252211yescharacteristic
273C2—42no—
274C2#1306767211yescharacteristic
275C2#1307055211yescharacteristic
276C2#1307059611yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×D4⋊C16C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenterD4⋊C16D11
hypocenterC11#12322
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
2. #13070869C2semidirect
3. #13070667C2semidirect
5. #13066666C2semidirect
6. #13066581C2semidirect
104. D4×C11Q32semidirect
232. C11#12322semidirect
242. D4Dic88semidirect

Maximal subgroups

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

subgroupindex
D4×Dic442
#130708692
#130706672
#130679812
#130666662
#130665812
C11×D4⋊C162
#1232211