Finite Group Databasebeta

← C11×#10512 #14587705

Subgroups — C11×#10512 #14587705

Order 2816.

408 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C11×#3245C211yesmaximal, characteristic
2C11×#1843C211yesmaximal, characteristic, complemented
3C11×#1551C212yesmaximal, complemented
4C11×#1505C212yesmaximal, complemented
5C11×#1290C211yesmaximal, characteristic, complemented
6C11×#532C2212yes—
7C11×#474—22no—
8C11×#466—22no—
9C11×#459—22no—
10C11×#432C2212yes—
11C2×C11×C4⋊C8—22no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C11×#376C2211yescharacteristic
15C11×#333—22no—
16C11×#331—22no—
17C11×#327—24no—
18C2×C11×#41—22no—
19C2×C11×D8—22no—
20C22×C8×C11—21no—
21C22×C8×C11D412yes—
22C11×C4⋊Q8D412yes—
23C11×#127D412yes—
24C11×#124—22no—
25C11×#121—22no—
26C11×#121—22no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C11×#107—22no—
32C11×C4⋊C8—22no—
33C11×C4⋊C8—22no—
34C11×C4⋊C8—22no—
35C11×C4⋊C8—44no—
36C11×#102—24no—
37C11×C22⋊C8—22no—
38C11×#97—22no—
39C11×#95—21no—
40C11×#95D412yes—
41#10512C1111yesmaximal, characteristic, direct product factor, Sylow
42C11×#41—84no—
43C2×Q8×C11—22no—
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—22no—
47C2×D4×C11—42no—
48C22×C4×C11—22no—
49C22×C4×C11—42no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C11×D8—82no—
54C2×C8×C11—22no—
55C2×C8×C11—42no—
56C2×C8×C11—42no—
57C2×C8×C11—41no—
58C2×C8×C11—42no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—22no—
61C11×C22⋊C4—42no—
62C11×C22⋊C4—42no—
63C42×C11—22no—
64C42×C11—22no—
65C42×C11C2×D412yes—
66C42×C11#4112yes—
67#3245C2×C1111yescharacteristic
68#1843C2×C1111yescharacteristic, complemented
69#1551C2×C1112yescomplemented
70#1505C2×C1112yescomplemented
71#1290C2×C1111yescharacteristic, complemented
72C23×C11—42no—
73C23×C11#12111yescharacteristic
74Q8×C11—82no—
75D4×C11—42no—
76D4×C11—42no—
77D4×C11—82no—
78D4×C11—82no—
79D4×C11—84no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—24no—
84C2×C4×C11—41no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—84no—
89C2×C4×C11#12011yescharacteristic
90C2×C4×C11#12112yes—
91C2×C4×C11#12312yes—
92C2×C4×C11#12411yescharacteristic
93C8×C11—42no—
94C8×C11—82no—
95C8×C11—81no—
96#532C22×C1112yes—
97#474—22no—
98#466—22no—
99#459—22no—
100#432C22×C1112yes—
101C2×C4⋊C8—22no—
102C2×C4⋊C8C22×C1111yescharacteristic
103C2×C4⋊C8C22×C1111yescharacteristic
104#376C22×C1111yescharacteristic
105#333—22no—
106#331—22no—
107#327—24no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—82no—
111C22×C11—82no—
112C22×C11—82no—
113C22×C11#39411yescharacteristic
114C22×C11#47212yes—
115C4×C11—22no—
116C4×C11—21no—
117C4×C11—22no—
118C4×C11—44no—
119C4×C11—82no—
120C4×C11#45311yescharacteristic
121C4×C11#45611yescharacteristic
122C2×#41—22no—
123C2×D8—22no—
124C22×C8—21no—
125C22×C8D4×C1112yes—
126C4⋊Q8D4×C1112yes—
127#127D4×C1112yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42—21no—
134C2×C42C23×C1111yescharacteristic
135#107—22no—
136C4⋊C8—22no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—44no—
140#102—24no—
141C22⋊C8—22no—
142#97—22no—
143#95—21no—
144#95D4×C1112yes—
145C2×C11—22no—
146C2×C11—162no—
147C2×C11#203911yescharacteristic
148C2×C11#204511yescharacteristic
149C2×C11#205311yescharacteristic
150#41—84no—
151C2×Q8—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—42no—
156C22×C4—22no—
157C22×C4—42no—
158C22×C4C2×D4×C1111yescharacteristic
159C22×C4C2×D4×C1111yescharacteristic
160C22×C4C11×#4111yescharacteristic
161D8—82no—
162C2×C8—22no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—41no—
166C2×C8—42no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—22no—
172C42—22no—
173C42C2×D4×C1112yes—
174C42C11×#4112yes—
175C11#1051211yescharacteristic, direct product factor, Sylow
176C23—42no—
177C23C11×#12111yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—82no—
182D4—82no—
183D4—84no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—84no—
193C2×C4C11×#12011yescharacteristic
194C2×C4C11×#12112yes—
195C2×C4C11×#12312yes—
196C2×C4C11×#12411yescharacteristic
197C8—42no—
198C8—82no—
199C8—81no—
200C22—21no—
201C22—21no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22C11×#39411yescharacteristic
206C22C11×#47212yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—44no—
211C4—82no—
212C4C11×#45311yescharacteristic
213C4C11×#45611yescharacteristic
214C2—22no—
215C2—162no—
216C2C11×#203911yescharacteristic
217C2C11×#204511yescharacteristic
218C2C11×#205311yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3245C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1843C2semidirect
3. C11×#1551C2semidirect
4. C11×#1505C2semidirect
5. C11×#1290C2semidirect
41. #10512C11direct (N × H)
68. #1843C2×C11semidirect
69. #1551C2×C11semidirect
70. #1505C2×C11semidirect
71. #1290C2×C11semidirect
175. C11#10512direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32452
C11×#18432
C11×#15512
C11×#15052
C11×#12902
#1051211