Finite Group Databasebeta

← C11×#10028 #14587221

Subgroups — C11×#10028 #14587221

Order 2816.

512 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3112C212yesmaximal, complemented
3C11×#1985C211yesmaximal, characteristic, complemented
4C11×#1530C212yesmaximal, complemented
5C11×#1290C211yesmaximal, characteristic, complemented
6C11×#532C2212yes—
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#480—22no—
9C11×#477—22no—
10C11×#474—22no—
11C11×#466—22no—
12C11×#460—22no—
13C11×#459—22no—
14C11×#448—22no—
15C11×#440—24no—
16C11×#432C2212yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#97C2211yescharacteristic
19C11×#336—22no—
20C11×#329—24no—
21C2×C11×#41—22no—
22C22×Q8×C11D411yescharacteristic
23C2×C11×SD16—24no—
24C2×C11×D8—22no—
25C22×C8×C11—21no—
26C22×C8×C11D412yes—
27C11×C4⋊Q8D412yes—
28C11×#127D412yes—
29C11×#124—22no—
30C11×#121—22no—
31C11×#121—22no—
32C4×Q8×C11—22no—
33C4×Q8×C11—22no—
34C4×D4×C11—22no—
35C4×D4×C11—22no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C11×#107—24no—
41C11×#107—22no—
42C11×C4⋊C8—22no—
43C11×C4⋊C8—22no—
44C11×#103—24no—
45C11×#102—24no—
46C11×#102—24no—
47C11×C22⋊C8—22no—
48C11×#97—22no—
49C11×#97D414yes—
50#10028C1111yesmaximal, characteristic, direct product factor, Sylow
51C11×#41—84no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—42no—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—42no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—42no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C11×SD16—48no—
66C11×D8—82no—
67C2×C8×C11—22no—
68C2×C8×C11—24no—
69C2×C8×C11—22no—
70C2×C8×C11—42no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—42no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C42×C11—41no—
80C42×C11—41no—
81C42×C11C2×D412yes—
82C42×C11C2×D412yes—
83#3245C2×C1111yescharacteristic
84#3112C2×C1112yescomplemented
85#1985C2×C1111yescharacteristic, complemented
86#1530C2×C1112yescomplemented
87#1290C2×C1111yescharacteristic, complemented
88C23×C11—42no—
89C23×C11#12111yescharacteristic
90Q8×C11—24no—
91Q8×C11—42no—
92Q8×C11—82no—
93D4×C11—44no—
94D4×C11—42no—
95D4×C11—42no—
96D4×C11—82no—
97D4×C11—84no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—84no—
109C2×C4×C11#12012yes—
110C2×C4×C11#12011yescharacteristic
111C2×C4×C11#12112yes—
112C2×C4×C11#12711yescharacteristic
113C8×C11—42no—
114C8×C11—44no—
115C8×C11—42no—
116#532C22×C1112yes—
117C2×C4×Q8C22×C1111yescharacteristic
118#480—22no—
119#477—22no—
120#474—22no—
121#466—22no—
122#460—22no—
123#459—22no—
124#448—22no—
125#440—24no—
126#432C22×C1112yes—
127C2×C4⋊C8C22×C1111yescharacteristic
128C2×#97C22×C1111yescharacteristic
129#336—22no—
130#329—24no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11—82no—
134C22×C11—82no—
135C22×C11—82no—
136C22×C11#39211yescharacteristic
137C22×C11#47212yes—
138C4×C11—21no—
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—42no—
142C4×C11—81no—
143C4×C11—82no—
144C4×C11#45511yescharacteristic
145C4×C11#45611yescharacteristic
146C2×#41—22no—
147C22×Q8D4×C1111yescharacteristic
148C2×SD16—24no—
149C2×D8—22no—
150C22×C8—21no—
151C22×C8D4×C1112yes—
152C4⋊Q8D4×C1112yes—
153#127D4×C1112yes—
154#124—22no—
155#121—22no—
156#121—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×D4—22no—
160C4×D4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4D4×C1111yescharacteristic
163C2×C42—21no—
164C2×C42C23×C1111yescharacteristic
165#107—24no—
166#107—22no—
167C4⋊C8—22no—
168C4⋊C8—22no—
169#103—24no—
170#102—24no—
171#102—24no—
172C22⋊C8—22no—
173#97—22no—
174#97D4×C1114yes—
175C2×C11—22no—
176C2×C11—162no—
177C2×C11#200711yescharacteristic
178C2×C11#201011yescharacteristic
179C2×C11#201811yescharacteristic
180#41—84no—
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—42no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—42no—
191C22×C4C2×D4×C1111yescharacteristic
192C22×C4C2×D4×C1111yescharacteristic
193C22×C4C11×#4111yescharacteristic
194SD16—48no—
195D8—82no—
196C2×C8—22no—
197C2×C8—24no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—42no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—41no—
209C42—41no—
210C42C2×D4×C1112yes—
211C42C2×D4×C1112yes—
212C11#1002811yescharacteristic, direct product factor, Sylow
213C23—42no—
214C23C11×#12111yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—82no—
218D4—44no—
219D4—42no—
220D4—42no—
221D4—82no—
222D4—84no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—84no—
234C2×C4C11×#12012yes—
235C2×C4C11×#12011yescharacteristic
236C2×C4C11×#12112yes—
237C2×C4C11×#12711yescharacteristic
238C8—42no—
239C8—44no—
240C8—42no—
241C22—21no—
242C22—21no—
243C22—82no—
244C22—82no—
245C22—82no—
246C22C11×#39211yescharacteristic
247C22C11×#47212yes—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—42no—
252C4—81no—
253C4—82no—
254C4C11×#45511yescharacteristic
255C4C11×#45611yescharacteristic
256C2—22no—
257C2—162no—
258C2C11×#200711yescharacteristic
259C2C11×#201011yescharacteristic
260C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
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×#3112C2semidirect
3. C11×#1985C2semidirect
4. C11×#1530C2semidirect
5. C11×#1290C2semidirect
50. #10028C11direct (N × H)
84. #3112C2×C11semidirect
85. #1985C2×C11semidirect
86. #1530C2×C11semidirect
87. #1290C2×C11semidirect
212. C11#10028direct (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×#31122
C11×#19852
C11×#15302
C11×#12902
#1002811