Finite Group Databasebeta

← #13069267

Subgroups — #13069267

Order 1408.

224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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×C11×#104C211yesmaximal, characteristic
2#10622847C211yesmaximal, characteristic
3#10622846C211yesmaximal, characteristic
4C2×#66886C211yesmaximal, characteristic, complemented
5#10622735C211yesmaximal, characteristic, complemented
6#10622162C211yesmaximal, characteristic, complemented
7#10622161C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C2×C11×M16C2211yescharacteristic
10C2×C42×C11C2211yescharacteristic
11#66979C2211yescharacteristic
12C2×#4318C2211yescharacteristic
13C22×C11⋊C8C2211yescharacteristic
14C22×C11⋊C8C2211yescharacteristic
15C11×#104—22no—
16#66899C411yescharacteristic, complemented
17#66899C411yescharacteristic, complemented
18#66896C411yescharacteristic, complemented
19#66896C411yescharacteristic, complemented
20C22⋊(C11⋊C8)—21no—
21C22⋊(C11⋊C8)—21no—
22#66886—22no—
23#66879—21no—
24C8×Dic11—21no—
25C11×#41—21no—
26C11×#41—21no—
27C11×#41—21no—
28C11×#41—21no—
29C2×Q8×C11C2×C411yescharacteristic
30C2×D4×C11—21no—
31C2×D4×C11C2×C411yescharacteristic
32C22×C4×C11—21no—
33C22×C4×C11—21no—
34C22×C4×C11C2311yescharacteristic
35C11×M16—21no—
36C11×M16D412yes—
37C2×C8×C11—21no—
38C42×C11—21no—
39C42×C11—21no—
40C22⋊Dic11—21no—
41C4⋊Dic11C2×C411yescharacteristic
42C4⋊Dic11C2×C411yescharacteristic
43C4×Dic11—21no—
44#4318—21no—
45#4318—21no—
46C2×C11⋊C8—21no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8C2×C411yescharacteristic
52C2×C11⋊C8C2×C411yescharacteristic
53C2×C11⋊C8D411yescharacteristic
54C2×C11⋊C8D411yescharacteristic
55#1929—111nomaximal, Sylow
56C23×C11—21no—
57C23×C11#4111yescharacteristic
58Q8×C11—21no—
59Q8×C11—21no—
60D4×C11—21no—
61D4×C11—21no—
62D4×C11—41no—
63D4×C11—41no—
64C2×C4×C11—22no—
65C2×C4×C11—21no—
66C2×C4×C11—41no—
67C2×C4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11C22×C411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11#4111yescharacteristic
74C2×C4×C11#4111yescharacteristic
75C2×C4×C11#4111yescharacteristic
76C2×Dic11—21no—
77C2×Dic11—21no—
78C8×C11—22no—
79C11⋊C8—21no—
80C11⋊C8—21no—
81C11⋊C8—21no—
82C11⋊C8—21no—
83C11⋊C8—41no—
84C2×#108—111no—
85C2×#104D1111yescharacteristic
86#416—111no—
87#408—111no—
88#405—111no—
89#339—111no—
90#336—111no—
91C22×C11—21no—
92C22×C11—21no—
93C22×C11—41no—
94C22×C11—41no—
95C22×C11—41no—
96C22×C11C4×D411yescharacteristic
97C22×C11#12411yescharacteristic
98C22×C11#12611yescharacteristic
99C4×C11—42no—
100C4×C11—41no—
101C4×C11#11711yescharacteristic
102C4×C11C4×D411yescharacteristic
103C4×C11#12111yescharacteristic
104C4×C11#12311yescharacteristic
105Dic11—41no—
106Dic11—41no—
107C2×#41C2×D1111yescharacteristic
108C2×M16—111no—
109C2×M16C2×D1111yescharacteristic
110C22×C8—111no—
111C22×C8—111no—
112#117—111no—
113C2×C42C2×D1111yescharacteristic
114#108—222no—
115#104—22no—
116#103—111no—
117#103—111no—
118#102—111no—
119#102—111no—
120C22⋊C8—221no—
121C22⋊C8—221no—
122#97—221no—
123C4×C8—221no—
124C2×C11—21no—
125C2×C11—21no—
126C2×C11—81no—
127C2×C11#38811yescharacteristic
128C2×C11#44311yescharacteristic
129C2×C11#44411yescharacteristic
130#41—21no—
131#41—21no—
132#41—21no—
133#41—21no—
134C2×Q8C4×D1111yescharacteristic
135C2×D4—21no—
136C2×D4C4×D1111yescharacteristic
137C22×C4—21no—
138C22×C4—21no—
139C22×C4C22×D1111yescharacteristic
140M16—21no—
141M16—221no—
142M16—221no—
143M16C22⋊D1112yes—
144C2×C8—21no—
145C2×C8—111no—
146C2×C8—111no—
147C2×C8—111no—
148C2×C8—111no—
149C2×C8—221no—
150C2×C8—221no—
151C2×C8—221no—
152C2×C8—221no—
153C2×C8—221no—
154C4⋊C4—111no—
155C4⋊C4—111no—
156C22⋊C4—221no—
157C42—21no—
158C42—21no—
159C42—221no—
160C11#192911yescharacteristic, complemented, Sylow
161C23—21no—
162C23#434111yescharacteristic
163Q8—21no—
164Q8—21no—
165D4—21no—
166D4—21no—
167D4—41no—
168D4—41no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—221no—
176C2×C4—221no—
177C2×C4C2×C4×D1111yescharacteristic
178C2×C4#433911yescharacteristic
179C2×C4D4×D1111yescharacteristic
180C2×C4#434111yescharacteristic
181C2×C4#434111yescharacteristic
182C2×C4C2×C22⋊D1111yescharacteristic
183C8—22no—
184C8—221no—
185C8—221no—
186C8—221no—
187C8—221no—
188C8—441no—
189C22—21no—
190C22—21no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22#6693211yescharacteristic
195C22(C22⋊D11)⋊C411yescharacteristic
196C22#6698911yescharacteristic
197C4—42no—
198C4—41no—
199C4—441no—
200C4—441no—
201C4#6693011yescharacteristic
202C4#6693611yescharacteristic
203C4C4×C22⋊D1111yescharacteristic
204C4#6699211yescharacteristic
205C2—21no—
206C2—21no—
207C2—81no—
208C2#1062243611yescharacteristic
209C2#1062243711yescharacteristic
210C2#1062255811yescharacteristic
subgroupG/H
centerC2×C4D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×#104C2
socleC22×C11C4×D4
prime radicalC2×C11×#41C22
cosocleC22×C4×C11C23
hypercenterC2×#104D11
hypocenterC11#1929
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
4. C2×#66886C2semidirect
5. #10622735C2semidirect
6. #10622162C2semidirect
7. #10622161C2semidirect
16. #66899C4semidirect
17. #66899C4semidirect
18. #66896C4semidirect
19. #66896C4semidirect
160. C11#1929semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1042
#106228472
#106228462
C2×#668862
#106227352
#106221622
#106221612
#192911