Finite Group Databasebeta

← #13069935

Subgroups — #13069935

Order 1408.

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

normal subgroups only

This group has 324 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
1C22×#4314C211yesmaximal, characteristic
2C2×Dic11⋊C8C211yesmaximal, characteristic, complemented
3#10622601C211yesmaximal, characteristic
4#10622587C211yesmaximal, characteristic, complemented
5C2×#66874C211yesmaximal, characteristic, complemented
6C2×#66873C211yesmaximal, characteristic
7C11×#340C211yesmaximal, characteristic, complemented
8C22×D44C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C4—21no—
14C2×(C2×D11)⋊C4—21no—
15C2×C4×Dic11C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C2×#4314—22no—
18C2×#4314—22no—
19C2×#4314—22no—
20C11⋊#95—21no—
21C11⋊#95—21no—
22Dic11⋊C8—22no—
23#66874—22no—
24#66873—22no—
25C23×D11—21no—
26C22×C4×C11—21no—
27C22×C4×C11—21no—
28C22×C4×C11C2311yescharacteristic
29C22×Dic11—21no—
30C22×Dic11D411yescharacteristic
31C22×Dic11D411yescharacteristic
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—
44C2×C8×C11—21no—
45C2×C8×C11—21no—
46C2×C8×C11D412yes—
47C11×C4⋊C4—21no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51(C2×D11)⋊C4—42no—
52(C2×D11)⋊C4—42no—
53C4×Dic11—21no—
54C4×Dic11—21no—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58#4314—28no—
59#2055—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—41no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11—41no—
72C2×C4×C11—41no—
73C2×C4×C11—41no—
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11#4111yescharacteristic
78C2×C4×C11#4111yescharacteristic
79C2×C4×C11#4111yescharacteristic
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—22no—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—41no—
87C2×Dic11—41no—
88C2×Dic11SD1612yescomplemented
89D44—22no—
90D44—22no—
91D44—41no—
92D44—41no—
93Dic22—22no—
94Dic22—22no—
95Dic22—41no—
96Dic22—41no—
97C8×C11—22no—
98C11⋊C8—41no—
99C22×SD16—111no—
100C2×C4⋊C8—111no—
101C2×#103—111no—
102C2×#102—111no—
103#391—111no—
104#390—111no—
105#340D1111yescharacteristic, complemented
106C22×C11#12111yescharacteristic
107C22×C11#12111yescharacteristic
108C22×C11#12111yescharacteristic
109C22×C11C2×SD1611yescharacteristic
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—81no—
121C4×C11—81no—
122C4×C11#12011yescharacteristic
123C4×C11#12311yescharacteristic
124C4×C11#12311yescharacteristic
125C4×C11#12411yescharacteristic
126Dic11—22no—
127Dic11—42no—
128Dic11—41no—
129C22×Q8—111no—
130C22×D4—111no—
131C2×SD16—222no—
132C2×SD16—222no—
133C2×SD16—222no—
134C22×C8—111no—
135C22×C8C2×D1111yescharacteristic
136C2×C4⋊C4C2×D1111yescharacteristic
137C2×C4⋊C4C2×D1111yescharacteristic
138C2×C22⋊C4—221no—
139C2×C22⋊C4—221no—
140C2×C42—111no—
141C4⋊C8—222no—
142#103—222no—
143#102—222no—
144#95—221no—
145#95—221no—
146C2×C11#39411yescharacteristic
147C2×C11#46011yescharacteristic
148C2×C11#46111yescharacteristic
149C2×C11#46311yescharacteristic
150C2×C11#46411yescharacteristic
151C2×C11#46511yescharacteristic
152C2×C11#46811yescharacteristic
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—111no—
170C22×C4—111no—
171C22×C4—221no—
172C22×C4C22×D1111yescharacteristic
173SD16—228no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8—221no—
179C2×C8D4412yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C22⋊C4—442no—
185C22⋊C4—442no—
186C42—221no—
187C42—221no—
188C11#205511yescharacteristic, complemented, Sylow
189C23—222no—
190C23—441no—
191C23—441no—
192C23—441no—
193C23—441no—
194C23—441no—
195C23—441no—
196C23D4×D1111yescharacteristic
197Q8—222no—
198Q8—222no—
199Q8—441no—
200Q8—441no—
201D4—222no—
202D4—222no—
203D4—441no—
204D4—441no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—112no—
212C2×C4—221no—
213C2×C4—221no—
214C2×C4—222no—
215C2×C4—221no—
216C2×C4—221no—
217C2×C4—221no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4C2×D4411yescharacteristic
221C2×C4#433911yescharacteristic
222C2×C4#433911yescharacteristic
223C2×C4D4×D1111yescharacteristic
224C2×C4D4×D1111yescharacteristic
225C2×C4#434311yescharacteristic
226C8—22no—
227C8—441no—
228C22—442no—
229C22—442no—
230C22—442no—
231C22—881no—
232C22—881no—
233C22—881no—
234C22—881no—
235C22#6693711yescharacteristic
236C22#6693711yescharacteristic
237C22#6694811yescharacteristic
238C22#6696411yescharacteristic
239C22SD16×D1111yescharacteristic
240C22#6696911yescharacteristic
241C22#6697111yescharacteristic
242C4—81no—
243C4—81no—
244C4—222no—
245C4—441no—
246C4—442no—
247C4#6692811yescharacteristic
248C4#6693511yescharacteristic
249C4#6694711yescharacteristic
250C4#6694711yescharacteristic
251C2—882no—
252C2#1062228511yescharacteristic
253C2#1062237511yescharacteristic
254C2#1062240011yescharacteristic
255C2#1062241111yescharacteristic
256C2#1062243111yescharacteristic
257C2#1062247711yescharacteristic
258C2#1062249911yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenter#340D11
hypocenterC11#2055
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×Dic11⋊C8C2semidirect
4. #10622587C2semidirect
5. C2×#66874C2semidirect
7. C11×#340C2semidirect
88. C2×Dic11SD16semidirect
105. #340D11semidirect
188. C11#2055semidirect

Maximal subgroups

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

subgroupindex
C22×#43142
C2×Dic11⋊C82
#106226012
#106225872
C2×#668742
C2×#668732
C11×#3402
#205511