Finite Group Databasebeta

← C11×#12288 #14589481

Subgroups — C11×#12288 #14589481

Order 2816.

354 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2232C212yesmaximal, complemented
3C11×#2086C211yesmaximal, characteristic, complemented
4C11×#1347C212yesmaximal, complemented
5C11×#1322C211yesmaximal, characteristic, complemented
6C11×#532—21no—
7C11×#474—22no—
8C11×#466—21no—
9C11×#466C2212yes—
10C11×#459—22no—
11C2×C11×#107C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#389—21no—
14C11×#366—22no—
15C11×#357—22no—
16C11×C22⋊C16C2212yes—
17C11×#340—21no—
18C11×#340C2211yescharacteristic
19C2×C11×#41—41no—
20C2×C11×D8—21no—
21C2×C11×D8D412yes—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11C2311yescharacteristic
24C11×C4⋊Q8—21no—
25C11×#127—21no—
26C11×#124—41no—
27C11×#121—22no—
28C11×#121—41no—
29C4×D4×C11—22no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—41no—
34C2×C42×C11D411yescharacteristic
35C2×C11×C16—22no—
36C11×#107—21no—
37C11×#107—22no—
38C11×#107D412yes—
39C11×C4⋊C8—22no—
40C11×#102—22no—
41C11×#102—22no—
42C11×#95—41no—
43#12288C1111yesmaximal, characteristic, direct product factor, Sylow
44C11×#41—82no—
45C11×#41—82no—
46C2×Q8×C11—41no—
47C2×D4×C11—22no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11—42no—
51C22×C4×C11—42no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11D811yescharacteristic
55C22×C4×C11D811yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C11×D8—42no—
58C11×D8—81no—
59C2×C8×C11—21no—
60C2×C8×C11—41no—
61C2×C8×C11—41no—
62C2×C8×C11C2×D412yes—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—22no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—82no—
70C11×C22⋊C4—42no—
71C11×C22⋊C4—42no—
72C42×C11—21no—
73C42×C11—21no—
74C11×C16—42no—
75#3245C2×C1111yescharacteristic
76#2232C2×C1112yescomplemented
77#2086C2×C1111yescharacteristic, complemented
78#1347C2×C1112yescomplemented
79#1322C2×C1111yescharacteristic, complemented
80C23×C11—42no—
81C23×C11C2×D811yescharacteristic
82Q8×C11—82no—
83D4×C11—42no—
84D4×C11—42no—
85D4×C11—82no—
86D4×C11—82no—
87D4×C11—82no—
88D4×C11—82no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—41no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—84no—
98C2×C4×C11—81no—
99C2×C4×C11—81no—
100C2×C4×C11—81no—
101C2×C4×C11—81no—
102C2×C4×C11—81no—
103C2×C4×C11D1612yes—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C8×C11—22no—
107C8×C11—41no—
108#532—21no—
109#474—22no—
110#466—21no—
111#466C22×C1112yes—
112#459—22no—
113C2×#107C22×C1111yescharacteristic
114C2×C4⋊C8C22×C1111yescharacteristic
115#389—21no—
116#366—22no—
117#357—22no—
118C22⋊C16C22×C1112yes—
119#340—21no—
120#340C22×C1111yescharacteristic
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—82no—
124C22×C11—82no—
125C22×C11—82no—
126C22×C11#44711yescharacteristic
127C22×C11C2×D1611yescharacteristic
128C22×C11#50911yescharacteristic
129C4×C11—21no—
130C4×C11—22no—
131C4×C11—41no—
132C4×C11—82no—
133C4×C11—82no—
134C4×C11—161no—
135C4×C11#45611yescharacteristic
136C4×C11#45811yescharacteristic
137C2×#41—41no—
138C2×D8—21no—
139C2×D8D4×C1112yes—
140C22×C8D4×C1111yescharacteristic
141C22×C8C23×C1111yescharacteristic
142C4⋊Q8—21no—
143#127—21no—
144#124—41no—
145#121—22no—
146#121—41no—
147C4×D4—22no—
148C4×D4—41no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—41no—
152C2×C42D4×C1111yescharacteristic
153C2×C16—22no—
154#107—21no—
155#107—22no—
156#107D4×C1112yes—
157C4⋊C8—22no—
158#102—22no—
159#102—22no—
160#95—41no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11—162no—
164C2×C11#161011yescharacteristic
165C2×C11#218411yescharacteristic
166C2×C11#219111yescharacteristic
167#41—82no—
168#41—82no—
169C2×Q8—41no—
170C2×D4—22no—
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—42no—
174C22×C4—42no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4C11×D811yescharacteristic
178C22×C4C11×D811yescharacteristic
179C22×C4C2×D4×C1111yescharacteristic
180D8—42no—
181D8—81no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8C2×D4×C1112yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—82no—
193C22⋊C4—42no—
194C22⋊C4—42no—
195C42—21no—
196C42—21no—
197C16—42no—
198C11#1228811yescharacteristic, direct product factor, Sylow
199C23—42no—
200C23C2×C11×D811yescharacteristic
201Q8—82no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—82no—
207D4—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—84no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4C11×D1612yes—
223C2×C4C11×#12011yescharacteristic
224C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—82no—
230C22—82no—
231C22—82no—
232C22C11×#44711yescharacteristic
233C22C2×C11×D1611yescharacteristic
234C22C11×#50911yescharacteristic
235C4—21no—
236C4—22no—
237C4—41no—
238C4—82no—
239C4—82no—
240C4—161no—
241C4C11×#45611yescharacteristic
242C4C11×#45811yescharacteristic
243C2—21no—
244C2—21no—
245C2—162no—
246C2C11×#161011yescharacteristic
247C2C11×#218411yescharacteristic
248C2C11×#219111yescharacteristic
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC11×#3245C2
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2232C2semidirect
3. C11×#2086C2semidirect
4. C11×#1347C2semidirect
5. C11×#1322C2semidirect
43. #12288C11direct (N × H)
76. #2232C2×C11semidirect
77. #2086C2×C11semidirect
78. #1347C2×C11semidirect
79. #1322C2×C11semidirect
198. C11#12288direct (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×#22322
C11×#20862
C11×#13472
C11×#13222
#1228811