Finite Group Databasebeta

← #13069099

Subgroups — #13069099

Order 1408.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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×#66985C211yesmaximal, characteristic
2#10623276C211yesmaximal, characteristic, complemented
3C2×C11×#100C211yesmaximal, characteristic, complemented
4#10622828C211yesmaximal, characteristic, complemented
5#10622752C211yesmaximal, characteristic, complemented
6C11⋊#338C211yesmaximal, characteristic, complemented
7#10622197C211yesmaximal, characteristic, complemented
8C22×D4×C11C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×M16C2211yescharacteristic
12C2×#4324C412yescomplemented
13#66985—22no—
14#66985—22no—
15C2×#4323C412yescomplemented
16#66979C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19#66960—22no—
20M16×D11—22no—
21#66954—22no—
22C11×#100—22no—
23#66896—22no—
24#66889—22no—
25C24×C11—21no—
26C2×D4×C11—21no—
27C2×D4×C11—21no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11C2×C412yes—
32C22×C4×C11C2311yescharacteristic
33C2×C22⋊D11—21no—
34#4339—21no—
35#4339—21no—
36#4339D412yes—
37#4339D412yes—
38C2×D44C2×C411yescharacteristic
39C2×C4×D11—21no—
40C2×Dic22C2×C411yescharacteristic
41C11×M16—21no—
42C11×M16—21no—
43C11×M16—21no—
44C11×M16D412yes—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C22⋊Dic11—21no—
48#4324—24no—
49#4323—24no—
50C4⋊Dic11—21no—
51C4×Dic11—21no—
52#4318—21no—
53#4318—21no—
54#4318—21no—
55#4318—21no—
56C2×C11⋊C8C2×C412yes—
57C2×C11⋊C8D412yes—
58#4313—24no—
59C8×D11—24no—
60#1903—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11—41no—
63C23×C11—41no—
64C23×C11—82no—
65C23×C11#4111yescharacteristic
66C22×D11—21no—
67D4×C11—22no—
68D4×C11—22no—
69D4×C11—41no—
70D4×C11—41no—
71C2×C4×C11C22×C411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11#4111yescharacteristic
77C22⋊D11—22no—
78C22⋊D11—22no—
79C2×Dic11—21no—
80C2×Dic11—41no—
81D44—21no—
82D44C22⋊C412yes—
83C4×D11—22no—
84C4×D11—22no—
85Dic22—21no—
86Dic22C22⋊C412yes—
87C8×C11—22no—
88C8×C11—41no—
89C11⋊C8—22no—
90C11⋊C8—22no—
91C2×AGL(1,ℤ/8)—111no—
92#568—111no—
93#421—111no—
94#418—111no—
95C2×#100D1111yescharacteristic, complemented
96#344—111no—
97#338—111no—
98C22×C11—41no—
99C22×C11—42no—
100C22×C11—82no—
101C22×C11—82no—
102C22×C11—82no—
103C22×C11C4×D411yescharacteristic
104C22×C11#12111yescharacteristic
105C22×C11#12311yescharacteristic
106C2×D11—22no—
107C2×D11—81no—
108C4×C11C2×C22⋊C411yescharacteristic
109C4×C11C4×D411yescharacteristic
110C4×C11#12011yescharacteristic
111C4×C11#12111yescharacteristic
112Dic11—22no—
113Dic11—81no—
114C2×#41—111no—
115C22×D4C2×D1111yescharacteristic
116AGL(1,ℤ/8)—222no—
117AGL(1,ℤ/8)—222no—
118C2×SD16—112no—
119C2×D8—112no—
120#131—222no—
121#131—222no—
122C2×M16—111no—
123C2×M16—111no—
124C2×M16—222no—
125C2×M16C2×D1111yescharacteristic
126C2×M16C2×D1111yescharacteristic
127#117—111no—
128#104—222no—
129#102—222no—
130#100—22no—
131C2×C11—21no—
132C2×C11—21no—
133C2×C11—21no—
134C2×C11—82no—
135C2×C11#38611yescharacteristic
136D11—42no—
137C24—21no—
138#41—112no—
139#41—112no—
140#41—221no—
141#41—221no—
142C2×Q8—111no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—111no—
149C2×D4—221no—
150C2×D4C4×D1112yes—
151C22×C4—221no—
152C22×C4C22×D1111yescharacteristic
153SD16—224no—
154D8—224no—
155M16—21no—
156M16—21no—
157M16—21no—
158M16—224no—
159M16—221no—
160M16—221no—
161M16—221no—
162M16—221no—
163M16C22⋊D1112yes—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—112no—
167C2×C8—112no—
168C2×C8—224no—
169C4⋊C4—221no—
170C22⋊C4—221no—
171C42—221no—
172C11#190311yescharacteristic, complemented, Sylow
173C23—22no—
174C23—41no—
175C23—41no—
176C23—82no—
177C23—221no—
178C23#433911yescharacteristic
179Q8—112no—
180Q8—221no—
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185D4—112no—
186D4—222no—
187D4—222no—
188D4—221no—
189C2×C4—221no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—441no—
193C2×C4C2×C4×D1111yescharacteristic
194C2×C4D4×D1111yescharacteristic
195C2×C4D4×D1111yescharacteristic
196C2×C4D4×D1111yescharacteristic
197C2×C4#434111yescharacteristic
198C2×C4C2×C22⋊D1111yescharacteristic
199C8—22no—
200C8—41no—
201C8—222no—
202C8—222no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—222no—
209C22—881no—
210C22#6693611yescharacteristic
211C22#6693711yescharacteristic
212C22C4×C22⋊D1111yescharacteristic
213C4—222no—
214C4—881no—
215C4C22⋊C4×D1111yescharacteristic
216C4(C22⋊D11)⋊C411yescharacteristic
217C4#6699011yescharacteristic
218C4#6699111yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—82no—
223C2—442no—
224C2#1062256911yescharacteristic
subgroupG/H
centerC2#10622569
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×#100C2
socleC2×C11#386
prime radicalC2×#66985C2
cosocleC22×C4×C11C23
hypercenterC2×#100D11
hypocenterC11#1903
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #10623276C2semidirect
3. C2×C11×#100C2semidirect
4. #10622828C2semidirect
5. #10622752C2semidirect
6. C11⋊#338C2semidirect
7. #10622197C2semidirect
12. C2×#4324C4semidirect
15. C2×#4323C4semidirect
95. C2×#100D11semidirect
172. C11#1903semidirect

Maximal subgroups

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

subgroupindex
C2×#669852
#106232762
C2×C11×#1002
#106228282
#106227522
C11⋊#3382
#106221972
#190311