Finite Group Databasebeta

← C11×#12174 #14589367

Subgroups — C11×#12174 #14589367

Order 2816.

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

normal subgroups only

This group has 340 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×#3255C211yesmaximal, characteristic, complemented
2C11×#2191C212yesmaximal
3C11×#2050C211yesmaximal, characteristic
4C11×#1342C212yesmaximal, complemented
5C11×#1327C211yesmaximal, characteristic, complemented
6C11×#575C2211yescharacteristic
7C11×#533—21no—
8C11×#510—22no—
9C11×#475—22no—
10C11×#470—21no—
11C11×#470C2212yes—
12C11×#462—22no—
13C11×#423C2211yescharacteristic
14C2×C11×#104—21no—
15C11×#413—21no—
16C11×#360—22no—
17C11×#349C2212yes—
18C11×#338C2211yescharacteristic
19C2×C11×#41—21no—
20C11×#137—41no—
21C11×AGL(1,ℤ/8)—41no—
22C11×#135—22no—
23C2×C11×Q16—21no—
24C2×C11×Q16D412yes—
25C2×C11×M16—21no—
26C2×C11×M16D411yescharacteristic
27C2×C11×M16C2311yescharacteristic
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×#125—41no—
31C11×C22⋊Q8—22no—
32C11×C22⋊Q8—41no—
33C4×Q8×C11—22no—
34C4×Q8×C11—41no—
35C11×#117—41no—
36C2×C42×C11D411yescharacteristic
37C11×Q32—42no—
38C11×SD32—42no—
39C11×M32—22no—
40C11×#106—21no—
41C11×#106D412yes—
42C11×C4⋊C8—22no—
43C11×#104—41no—
44C11×#104—41no—
45C11×#103—22no—
46C11×#103—22no—
47C11×#101—41no—
48C11×#100—41no—
49#12174C1111yesmaximal, characteristic, direct product factor, Sylow
50C11×#41—41no—
51C11×#41—41no—
52C11×#41—41no—
53C11×#41—41no—
54C2×Q8×C11—21no—
55C2×Q8×C11—22no—
56C2×Q8×C11—41no—
57C2×D4×C11—21no—
58C2×D4×C11—41no—
59C22×C4×C11—21no—
60C22×C4×C11—41no—
61C22×C4×C11C2×D411yescharacteristic
62C11×Q16—22no—
63C11×Q16—42no—
64C11×Q16—81no—
65C11×SD16—42no—
66C11×D8—22no—
67C11×M16—41no—
68C11×M16—41no—
69C11×M16—41no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11—41no—
73C2×C8×C11C2×D412yes—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C22⋊C4—42no—
81C42×C11—21no—
82C42×C11—42no—
83C42×C11D811yescharacteristic
84C42×C11D811yescharacteristic
85C11×C16—42no—
86#3255C2×C1111yescharacteristic, complemented
87#2191C2×C1112yes—
88#2050C2×C1111yescharacteristic
89#1342C2×C1112yescomplemented
90#1327C2×C1111yescharacteristic, complemented
91C23×C11—41no—
92C23×C11AGL(1,ℤ/8)11yescharacteristic
93Q8×C11—41no—
94Q8×C11—42no—
95Q8×C11—41no—
96Q8×C11—42no—
97Q8×C11—82no—
98D4×C11—41no—
99D4×C11—41no—
100D4×C11—81no—
101D4×C11—81no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—42no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11C2×D811yescharacteristic
114C8×C11—22no—
115C8×C11—41no—
116C8×C11—81no—
117#575C22×C1111yescharacteristic
118#533—21no—
119#510—22no—
120#475—22no—
121#470—21no—
122#470C22×C1112yes—
123#462—22no—
124#423C22×C1111yescharacteristic
125C2×#104—21no—
126#413—21no—
127#360—22no—
128#349C22×C1112yes—
129#338C22×C1111yescharacteristic
130C22×C11—21no—
131C22×C11—41no—
132C22×C11—81no—
133C22×C11—161no—
134C22×C11#44711yescharacteristic
135C4×C11—22no—
136C4×C11—21no—
137C4×C11—41no—
138C4×C11—82no—
139C4×C11—81no—
140C4×C11—82no—
141C4×C11#45411yescharacteristic
142C4×C11B(4,𝔽2)11yescharacteristic
143C2×#41—21no—
144#137—41no—
145AGL(1,ℤ/8)—41no—
146#135—22no—
147C2×Q16—21no—
148C2×Q16D4×C1112yes—
149C2×M16—21no—
150C2×M16D4×C1111yescharacteristic
151C2×M16C23×C1111yescharacteristic
152C4⋊Q8—21no—
153C4⋊Q8—21no—
154#125—41no—
155C22⋊Q8—22no—
156C22⋊Q8—41no—
157C4×Q8—22no—
158C4×Q8—41no—
159#117—41no—
160C2×C42D4×C1111yescharacteristic
161Q32—42no—
162SD32—42no—
163M32—22no—
164#106—21no—
165#106D4×C1112yes—
166C4⋊C8—22no—
167#104—41no—
168#104—41no—
169#103—22no—
170#103—22no—
171#101—41no—
172#100—41no—
173C2×C11—21no—
174C2×C11—41no—
175C2×C11—161no—
176C2×C11#159811yescharacteristic
177#41—41no—
178#41—41no—
179#41—41no—
180#41—41no—
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—41no—
184C2×D4—21no—
185C2×D4—41no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4C2×D4×C1111yescharacteristic
189Q16—22no—
190Q16—42no—
191Q16—81no—
192SD16—42no—
193D8—22no—
194M16—41no—
195M16—41no—
196M16—41no—
197M16—41no—
198C2×C8—21no—
199C2×C8—41no—
200C2×C8C2×D4×C1112yes—
201C4⋊C4—22no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C22⋊C4—42no—
208C42—21no—
209C42—42no—
210C42C11×D811yescharacteristic
211C42C11×D811yescharacteristic
212C16—42no—
213C11#1217411yescharacteristic, direct product factor, Sylow
214C23—41no—
215C23C11×AGL(1,ℤ/8)11yescharacteristic
216Q8—41no—
217Q8—42no—
218Q8—41no—
219Q8—42no—
220Q8—82no—
221D4—41no—
222D4—41no—
223D4—81no—
224D4—81no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4C11×#12011yescharacteristic
236C2×C4C2×C11×D811yescharacteristic
237C8—22no—
238C8—41no—
239C8—81no—
240C22—21no—
241C22—41no—
242C22—81no—
243C22—161no—
244C22C11×#44711yescharacteristic
245C4—22no—
246C4—21no—
247C4—41no—
248C4—82no—
249C4—81no—
250C4—82no—
251C4C11×#45411yescharacteristic
252C4C11×B(4,𝔽2)11yescharacteristic
253C2—21no—
254C2—41no—
255C2—161no—
256C2C11×#159811yescharacteristic
subgroupG/H
center, socleC2×C11#1598
commutator, Frattini, cosocleC2×M16C23×C11
prime radicalC11×#575C22
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
1. C11×#3255C2semidirect
4. C11×#1342C2semidirect
5. C11×#1327C2semidirect
49. #12174C11direct (N × H)
86. #3255C2×C11semidirect
89. #1342C2×C11semidirect
90. #1327C2×C11semidirect
213. C11#12174direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32552
C11×#21912
C11×#20502
C11×#13422
C11×#13272
#1217411