Finite Group Databasebeta

← C11×#12307 #14589500

Subgroups — C11×#12307 #14589500

Order 2816.

318 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 70 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×#3253C211yesmaximal, characteristic
2C11×#2238C212yesmaximal, complemented
3C11×#2102C211yesmaximal, characteristic, complemented
4C11×#1339C212yesmaximal, complemented
5C11×#1327C211yesmaximal, characteristic, complemented
6C11×#532—21no—
7C11×#476—22no—
8C11×#469—21no—
9C11×#469C2212yes—
10C11×#459—22no—
11C11×#430C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C11×#365—22no—
14C11×#361—22no—
15C11×#349C2212yes—
16C11×#344—21no—
17C11×#339—21no—
18C11×H(3,ℤ/4)C2211yescharacteristic
19C2×C11×#41—41no—
20C2×C11×D8—21no—
21C2×C11×D8D412yes—
22C2×C11×M16—21no—
23C2×C11×M16D411yescharacteristic
24C2×C11×M16C2311yescharacteristic
25C11×C4⋊Q8—21no—
26C11×#127—21no—
27C11×#124—41no—
28C11×#121—22no—
29C11×#121—41no—
30C4×D4×C11—22no—
31C4×D4×C11—41no—
32C11×#117—21no—
33C2×C42×C11D411yescharacteristic
34C11×M32—22no—
35C11×#108—22no—
36C11×#106—21no—
37C11×#106D412yes—
38C11×C4⋊C8—22no—
39C11×#102—22no—
40C11×#102—22no—
41#12307C1111yesmaximal, characteristic, direct product factor, Sylow
42C11×#41—84no—
43C2×Q8×C11—41no—
44C2×D4×C11—22no—
45C2×D4×C11—41no—
46C2×D4×C11—41no—
47C2×D4×C11—42no—
48C22×C4×C11—21no—
49C22×C4×C11—42no—
50C22×C4×C11C2×D411yescharacteristic
51C11×D8—42no—
52C11×D8—81no—
53C11×M16—41no—
54C11×M16—41no—
55C11×M16—41no—
56C11×M16—41no—
57C2×C8×C11—21no—
58C2×C8×C11—41no—
59C2×C8×C11C2×D412yes—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C11×C22⋊C4—42no—
64C11×C22⋊C4—42no—
65C11×C22⋊C4—41no—
66C42×C11—21no—
67C42×C11—41no—
68C42×C11SD1611yescharacteristic
69C42×C11SD1611yescharacteristic
70C11×C16—42no—
71#3253C2×C1111yescharacteristic
72#2238C2×C1112yescomplemented
73#2102C2×C1111yescharacteristic, complemented
74#1339C2×C1112yescomplemented
75#1327C2×C1111yescharacteristic, complemented
76C23×C11—42no—
77C23×C11AGL(1,ℤ/8)11yescharacteristic
78Q8×C11—82no—
79D4×C11—42no—
80D4×C11—42no—
81D4×C11—82no—
82D4×C11—82no—
83D4×C11—84no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—84no—
91C2×C4×C11—81no—
92C2×C4×C11#12011yescharacteristic
93C2×C4×C11C2×SD1611yescharacteristic
94C8×C11—22no—
95C8×C11—41no—
96C8×C11—81no—
97#532—21no—
98#476—22no—
99#469—21no—
100#469C22×C1112yes—
101#459—22no—
102#430C22×C1111yescharacteristic
103#423C22×C1111yescharacteristic
104#365—22no—
105#361—22no—
106#349C22×C1112yes—
107#344—21no—
108#339—21no—
109H(3,ℤ/4)C22×C1111yescharacteristic
110C22×C11—21no—
111C22×C11—41no—
112C22×C11—82no—
113C22×C11—82no—
114C22×C11—82no—
115C22×C11#45011yescharacteristic
116C4×C11—22no—
117C4×C11—21no—
118C4×C11—41no—
119C4×C11—82no—
120C4×C11—161no—
121C4×C11#45411yescharacteristic
122C4×C11#45811yescharacteristic
123C2×#41—41no—
124C2×D8—21no—
125C2×D8D4×C1112yes—
126C2×M16—21no—
127C2×M16D4×C1111yescharacteristic
128C2×M16C23×C1111yescharacteristic
129C4⋊Q8—21no—
130#127—21no—
131#124—41no—
132#121—22no—
133#121—41no—
134C4×D4—22no—
135C4×D4—41no—
136#117—21no—
137C2×C42D4×C1111yescharacteristic
138M32—22no—
139#108—22no—
140#106—21no—
141#106D4×C1112yes—
142C4⋊C8—22no—
143#102—22no—
144#102—22no—
145C2×C11—21no—
146C2×C11—41no—
147C2×C11—162no—
148C2×C11#161611yescharacteristic
149#41—84no—
150C2×Q8—41no—
151C2×D4—22no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—42no—
155C22×C4—21no—
156C22×C4—42no—
157C22×C4C2×D4×C1111yescharacteristic
158D8—42no—
159D8—81no—
160M16—41no—
161M16—41no—
162M16—41no—
163M16—41no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8C2×D4×C1112yes—
167C4⋊C4—22no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—41no—
173C42—21no—
174C42—41no—
175C42C11×SD1611yescharacteristic
176C42C11×SD1611yescharacteristic
177C16—42no—
178C11#1230711yescharacteristic, direct product factor, Sylow
179C23—42no—
180C23C11×AGL(1,ℤ/8)11yescharacteristic
181Q8—82no—
182D4—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—84no—
194C2×C4—81no—
195C2×C4C11×#12011yescharacteristic
196C2×C4C2×C11×SD1611yescharacteristic
197C8—22no—
198C8—41no—
199C8—81no—
200C22—21no—
201C22—41no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22C11×#45011yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—82no—
210C4—161no—
211C4C11×#45411yescharacteristic
212C4C11×#45811yescharacteristic
213C2—21no—
214C2—41no—
215C2—162no—
216C2C11×#161611yescharacteristic
subgroupG/H
center, socleC2×C11#1616
commutator, Frattini, cosocleC2×M16C23×C11
prime radicalC11×#3253C2
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2238C2semidirect
3. C11×#2102C2semidirect
4. C11×#1339C2semidirect
5. C11×#1327C2semidirect
41. #12307C11direct (N × H)
72. #2238C2×C11semidirect
73. #2102C2×C11semidirect
74. #1339C2×C11semidirect
75. #1327C2×C11semidirect
178. C11#12307direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32532
C11×#22382
C11×#21022
C11×#13392
C11×#13272
#1230711