Finite Group Databasebeta

← #13069931

Subgroups — #13069931

Order 1408.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#4325C211yesmaximal, characteristic
2C11×#391C211yesmaximal, characteristic, complemented
3C2×#66899C211yesmaximal, characteristic, complemented
4C2×#66873C211yesmaximal, characteristic
5#10622552C211yesmaximal, characteristic
6C2×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12C2×#4325—22no—
13C2×#4325—22no—
14C2×#4325—22no—
15C2×(C2×D11)⋊C4—21no—
16C2×(C2×D11)⋊C4—21no—
17C2×C4⋊Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20C11×#95—21no—
21C11×#95—21no—
22#66899—22no—
23#66873—22no—
24C4⋊(C11⋊C8)—22no—
25C23×D11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11—21no—
30C2×Q8×C11—21no—
31C2×Q8×C11D412yes—
32C22×C4×C11—21no—
33C22×C4×C11—21no—
34C22×C4×C11D411yescharacteristic
35C22×C4×C11D411yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11—21no—
38C2×D44—21no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44D412yes—
44C11×C4⋊C4—21no—
45C11×C4⋊C4—21no—
46C42×C11—21no—
47C42×C11—21no—
48#4325—28no—
49(C2×D11)⋊C4—42no—
50(C2×D11)⋊C4—42no—
51C4⋊Dic11—21no—
52C4⋊Dic11—21no—
53C2×C11⋊C8—21no—
54C2×C11⋊C8—21no—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8D412yes—
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—
68Q8×C11—22no—
69Q8×C11—22no—
70Q8×C11—41no—
71Q8×C11—41no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11SD1612yescomplemented
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11#4111yescharacteristic
88C2×C4×C11#4111yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C2×Dic11—41no—
91C2×Dic11—41no—
92C2×Dic11—41no—
93D44—22no—
94D44—22no—
95D44—41no—
96D44—41no—
97C11⋊C8—22no—
98C11⋊C8—41no—
99C22×SD16—111no—
100C2×C4⋊C8—111no—
101C2×#103—111no—
102C2×#102—111no—
103#391D1111yescharacteristic, complemented
104#390—111no—
105#340—111no—
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—22no—
121C4×C11—42no—
122C4×C11—41no—
123C4×C11—81no—
124C4×C11#12011yescharacteristic
125C4×C11#12311yescharacteristic
126C4×C11#12311yescharacteristic
127C4×C11#12411yescharacteristic
128Dic11—81no—
129C22×Q8C2×D1111yescharacteristic
130C22×D4—111no—
131C2×SD16—222no—
132C2×SD16—222no—
133C2×SD16—222no—
134C22×C8—111no—
135C22×C8—111no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4C2×D1111yescharacteristic
138C2×C22⋊C4—221no—
139C2×C22⋊C4—221no—
140C2×C42C2×D1111yescharacteristic
141C4⋊C8—222no—
142#103—222no—
143#102—222no—
144#95—21no—
145#95—21no—
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—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8D4412yes—
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
173SD16—228no—
174C2×C8—112no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8—221no—
179C2×C8—221no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—221no—
183C4⋊C4—221no—
184C22⋊C4—442no—
185C22⋊C4—442no—
186C42—21no—
187C42—21no—
188C11#205511yescharacteristic, complemented, Sylow
189C23—222no—
190C23—441no—
191C23—441no—
192C23—441no—
193C23—441no—
194C23—441no—
195C23—441no—
196C23C2×C22⋊D1111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—222no—
202D4—222no—
203D4—441no—
204D4—441no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4#432512yescomplemented
220C2×C4C2×D4411yescharacteristic
221C2×C4#433911yescharacteristic
222C2×C4D4×D1111yescharacteristic
223C2×C4D4×D1111yescharacteristic
224C2×C4#434111yescharacteristic
225C2×C4#434111yescharacteristic
226C8—222no—
227C8—441no—
228C22—442no—
229C22—442no—
230C22—442no—
231C22—881no—
232C22—881no—
233C22—881no—
234C22—881no—
235C22#6698311yescharacteristic
236C22#6699111yescharacteristic
237C22#6699211yescharacteristic
238C22C2×#432511yescharacteristic
239C22#6699511yescharacteristic
240C22#6700211yescharacteristic
241C22#6700311yescharacteristic
242C4—22no—
243C4—42no—
244C4—41no—
245C4—81no—
246C4—881no—
247C4#6693511yescharacteristic
248C4#6693611yescharacteristic
249C4#6693811yescharacteristic
250C4#6693911yescharacteristic
251C2—882no—
252C2#1062257411yescharacteristic
253C2#1062264011yescharacteristic
254C2#1062264111yescharacteristic
255C2#1062266111yescharacteristic
256C2#1062266211yescharacteristic
257C2#1062267011yescharacteristic
258C2#1062269611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#391C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2055
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C11×#391C2semidirect
3. C2×#66899C2semidirect
6. C2×C4⋊(C11⋊C8)C2semidirect
7. #10622167C2semidirect
83. C2×C4×C11SD16semidirect
103. #391D11semidirect
188. C11#2055semidirect
219. C2×C4#4325semidirect

Maximal subgroups

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

subgroupindex
C22×#43252
C11×#3912
C2×#668992
C2×#668732
#106225522
C2×C4⋊(C11⋊C8)2
#106221672
#205511