Finite Group Databasebeta

← #13069857

Subgroups — #13069857

Order 1408.

318 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#66928C211yesmaximal, characteristic
2C11×#389C211yesmaximal, characteristic, complemented
3C2×#66874C211yesmaximal, characteristic, complemented
4C2×#66874C211yesmaximal, characteristic, complemented
5C2×#66873C211yesmaximal, characteristic
6C2×#66873C211yesmaximal, characteristic
7#10622162C211yesmaximal, characteristic, complemented
8C22×D44C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C2×C11×C4⋊C4—21no—
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×(C2×D11)⋊C4—21no—
15C2×(C2×D11)⋊C4—21no—
16C22×C11⋊C8C2211yescharacteristic
17C22×C11⋊C8C2211yescharacteristic
18#66928—22no—
19#66928—22no—
20C11×#95—21no—
21#66874—22no—
22#66874—22no—
23#66873—22no—
24#66873—22no—
25C23×D11—21no—
26C22×C4×C11—21no—
27C22×C4×C11—21no—
28C22×C4×C11D411yescharacteristic
29C22×C4×C11D411yescharacteristic
30C22×C4×C11C2311yescharacteristic
31C22×Dic11—21no—
32C2×D44—21no—
33C2×D44—21no—
34C2×D44—21no—
35C2×D44—21no—
36C2×D44—21no—
37C2×D44D412yes—
38C2×Dic22—21no—
39C2×Dic22—21no—
40C2×Dic22—21no—
41C2×Dic22—21no—
42C2×Dic22—21no—
43C2×Dic22D412yes—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C11×C4⋊C4—21no—
47C11×C4⋊C4—42no—
48C11×C4⋊C4D412yes—
49C42×C11—21no—
50C42×C11—21no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—24no—
53C2×C11⋊C8—21no—
54C2×C11⋊C8—21no—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8—21no—
59#2042—111nomaximal, Sylow
60C23×C11C2×D411yescharacteristic
61C22×D11—22no—
62C22×D11—41no—
63C22×D11—41no—
64C22×D11—41no—
65C22×D11—41no—
66C22×D11—41no—
67C22×D11—41no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—21no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—41no—
76C2×C4×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11#4111yescharacteristic
84C2×C4×C11#4111yescharacteristic
85C2×C4×C11#4111yescharacteristic
86C2×Dic11—22no—
87C2×Dic11—41no—
88C2×Dic11—41no—
89D44—22no—
90D44—22no—
91D44—41no—
92D44—41no—
93Dic22—22no—
94Dic22—22no—
95Dic22—41no—
96Dic22—41no—
97C11⋊C8—41no—
98C11⋊C8—41no—
99C2×#124—111no—
100C2×#103—111no—
101C2×#103—111no—
102C2×#102—111no—
103C2×#102—111no—
104#389D1111yescharacteristic, complemented
105#336—111no—
106C22×C11#12011yescharacteristic
107C22×C11#12111yescharacteristic
108C22×C11#12411yescharacteristic
109C22×C11#13511yescharacteristic
110C22×C11#13511yescharacteristic
111C22×C11AGL(1,ℤ/8)11yescharacteristic
112C22×C11#13711yescharacteristic
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C2×D11—81no—
117C2×D11—81no—
118C2×D11—81no—
119C2×D11—81no—
120C4×C11—41no—
121C4×C11—41no—
122C4×C11—42no—
123C4×C11—81no—
124C4×C11#12111yescharacteristic
125C4×C11#12111yescharacteristic
126C4×C11#12311yescharacteristic
127C4×C11#12311yescharacteristic
128Dic11—42no—
129C22×Q8—111no—
130C22×D4—111no—
131C22×C8—111no—
132C22×C8—111no—
133#124—222no—
134#124—222no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4C2×D1111yescharacteristic
137C2×C4⋊C4C2×D1111yescharacteristic
138C2×C22⋊C4—221no—
139C2×C22⋊C4—221no—
140C2×C42C2×D1111yescharacteristic
141#103—222no—
142#103—222no—
143#102—222no—
144#102—222no—
145#95—21no—
146C2×C11#39411yescharacteristic
147C2×C11#44911yescharacteristic
148C2×C11#45211yescharacteristic
149C2×C11#46311yescharacteristic
150C2×C11#46411yescharacteristic
151C2×C11#48811yescharacteristic
152C2×C11#48911yescharacteristic
153D11—82no—
154C24—221no—
155C2×Q8—112no—
156C2×Q8—221no—
157C2×Q8—221no—
158C2×Q8—221no—
159C2×Q8—221no—
160C2×Q8—221no—
161C2×D4—112no—
162C2×D4—221no—
163C2×D4—221no—
164C2×D4—221no—
165C2×D4—221no—
166C2×D4—221no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—221no—
170C22×C4C22⋊D1111yescharacteristic
171C22×C4C22⋊D1111yescharacteristic
172C22×C4C22×D1111yescharacteristic
173C2×C8—221no—
174C2×C8—221no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8—221no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—42no—
183C4⋊C4D4412yes—
184C22⋊C4—224no—
185C22⋊C4—224no—
186C42—21no—
187C42—21no—
188C11#204211yescharacteristic, complemented, Sylow
189C23—222no—
190C23—441no—
191C23—441no—
192C23—441no—
193C23—441no—
194C23—441no—
195C23—441no—
196C23C2×C22⋊D1111yescharacteristic
197Q8—222no—
198Q8—222no—
199Q8—441no—
200Q8—441no—
201D4—222no—
202D4—222no—
203D4—441no—
204D4—441no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—222no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4C2×D4411yescharacteristic
221C2×C4#433911yescharacteristic
222C2×C4D4×D1111yescharacteristic
223C2×C4D4×D1111yescharacteristic
224C2×C4#434311yescharacteristic
225C2×C4#434311yescharacteristic
226C8—441no—
227C8—441no—
228C22—442no—
229C22—442no—
230C22—442no—
231C22—881no—
232C22—881no—
233C22—881no—
234C22—881no—
235C22#6698311yescharacteristic
236C22#6698511yescharacteristic
237C22#6699011yescharacteristic
238C22#6699511yescharacteristic
239C22#6700011yescharacteristic
240C22#6700311yescharacteristic
241C22#6700311yescharacteristic
242C4—42no—
243C4—41no—
244C4—41no—
245C4—81no—
246C4—442no—
247C4#6694711yescharacteristic
248C4#6694711yescharacteristic
249C4#6694811yescharacteristic
250C4#6694811yescharacteristic
251C2—882no—
252C2#1062260411yescharacteristic
253C2#1062262911yescharacteristic
254C2#1062264111yescharacteristic
255C2#1062265011yescharacteristic
256C2#1062266011yescharacteristic
257C2#1062268111yescharacteristic
258C2#1062270211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#389C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenter#389D11
hypocenterC11#2042
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C11×#389C2semidirect
3. C2×#66874C2semidirect
4. C2×#66874C2semidirect
7. #10622162C2semidirect
104. #389D11semidirect
188. C11#2042semidirect

Maximal subgroups

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

subgroupindex
C2×#669282
C11×#3892
C2×#668742
C2×#668732
#106221622
#204211