Finite Group Databasebeta

← C11×#2088 #13064926

Subgroups — C11×#2088 #13064926

Order 1408.

224 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 104 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×#106C211yesmaximal, characteristic
2C2×C11×C4⋊C8C211yesmaximal, characteristic
3C11×#389C211yesmaximal, characteristic
4C11×#389C211yesmaximal, characteristic
5C11×#340C211yesmaximal, characteristic
6C11×#340C211yesmaximal, characteristic
7C11×#340C211yesmaximal, characteristic
8C22×C8×C11C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4—21no—
11C2×C11×C4⋊C4—21no—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C42×C11C2211yescharacteristic
17C11×#106—22no—
18C11×C4⋊C8—22no—
19C11×#95—21no—
20C11×#95—21no—
21C22×C4×C11—21no—
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11—21no—
25C22×C4×C11D411yescharacteristic
26C22×C4×C11D411yescharacteristic
27C22×C4×C11C2311yescharacteristic
28C2×C8×C11—21no—
29C2×C8×C11—21no—
30C2×C8×C11—21no—
31C2×C8×C11—21no—
32C2×C8×C11—21no—
33C2×C8×C11D412yes—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—42no—
41C11×C4⋊C4—42no—
42C11×C4⋊C4Q812yes—
43C11×C4⋊C4Q812yes—
44C42×C11—21no—
45C42×C11—21no—
46#2088C1111yesmaximal, characteristic, direct product factor, Sylow
47C23×C11C2×D411yescharacteristic
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—21no—
51C2×C4×C11—22no—
52C2×C4×C11—22no—
53C2×C4×C11—21no—
54C2×C4×C11—21no—
55C2×C4×C11—41no—
56C2×C4×C11—41no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11SD1612yes—
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×Q811yescharacteristic
68C2×C4×C11C2×Q811yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×C4×C11#4111yescharacteristic
71C2×C4×C11#4111yescharacteristic
72C8×C11—22no—
73C8×C11—41no—
74C2×#106C2×C1111yescharacteristic
75C2×C4⋊C8C2×C1111yescharacteristic
76#389C2×C1111yescharacteristic
77#389C2×C1111yescharacteristic
78#340C2×C1111yescharacteristic
79#340C2×C1111yescharacteristic
80#340C2×C1111yescharacteristic
81C22×C11#12111yescharacteristic
82C22×C11C22⋊Q811yescharacteristic
83C22×C11C22⋊Q811yescharacteristic
84C22×C11C2×SD1611yescharacteristic
85C22×C11#13511yescharacteristic
86C22×C11AGL(1,ℤ/8)11yescharacteristic
87C22×C11#13711yescharacteristic
88C4×C11—22no—
89C4×C11—41no—
90C4×C11—42no—
91C4×C11—42no—
92C4×C11—81no—
93C4×C11—81no—
94C4×C11#12311yescharacteristic
95C4×C11#12511yescharacteristic
96C4×C11#12511yescharacteristic
97C4×C11C4⋊Q811yescharacteristic
98C22×C8C22×C1111yescharacteristic
99C22×C8C22×C1111yescharacteristic
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4C22×C1111yescharacteristic
103C2×C4⋊C4C22×C1111yescharacteristic
104C2×C4⋊C4C22×C1111yescharacteristic
105C2×C4⋊C4C22×C1111yescharacteristic
106C2×C42C22×C1111yescharacteristic
107#106—22no—
108C4⋊C8—22no—
109#95—21no—
110#95—21no—
111C2×C11#39811yescharacteristic
112C2×C11#46511yescharacteristic
113C2×C11#46811yescharacteristic
114C2×C11#47511yescharacteristic
115C2×C11#47611yescharacteristic
116C2×C11#47811yescharacteristic
117C2×C11#47911yescharacteristic
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4D4×C1111yescharacteristic
123C22×C4D4×C1111yescharacteristic
124C22×C4C23×C1111yescharacteristic
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8D4×C1112yes—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—42no—
138C4⋊C4—42no—
139C4⋊C4Q8×C1112yes—
140C4⋊C4Q8×C1112yes—
141C42—21no—
142C42—21no—
143C11#208811yescharacteristic, direct product factor, Sylow
144C23C2×D4×C1111yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4C11×SD1612yes—
163C2×C4C2×D4×C1111yescharacteristic
164C2×C4C2×Q8×C1111yescharacteristic
165C2×C4C2×Q8×C1111yescharacteristic
166C2×C4C11×#4111yescharacteristic
167C2×C4C11×#4111yescharacteristic
168C2×C4C11×#4111yescharacteristic
169C8—22no—
170C8—41no—
171C22C11×#12111yescharacteristic
172C22C11×C22⋊Q811yescharacteristic
173C22C11×C22⋊Q811yescharacteristic
174C22C2×C11×SD1611yescharacteristic
175C22C11×#13511yescharacteristic
176C22C11×AGL(1,ℤ/8)11yescharacteristic
177C22C11×#13711yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—42no—
182C4—81no—
183C4—81no—
184C4C11×#12311yescharacteristic
185C4C11×#12511yescharacteristic
186C4C11×#12511yescharacteristic
187C4C11×C4⋊Q811yescharacteristic
188C2C11×#39811yescharacteristic
189C2C11×#46511yescharacteristic
190C2C11×#46811yescharacteristic
191C2C11×#47511yescharacteristic
192C2C11×#47611yescharacteristic
193C2C11×#47811yescharacteristic
194C2C11×#47911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C2×D4
commutator, Frattini, cosocleC22×C4C23×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
46. #2088C11direct (N × H)
143. C11#2088direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1062
C2×C11×C4⋊C82
C11×#3892
C11×#3402
#208811