Finite Group Databasebeta

← C11×#2005 #13064843

Subgroups — C11×#2005 #13064843

Order 1408.

362 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×C11×#137C211yesmaximal, characteristic
2C11×#536C211yesmaximal, characteristic
3C2×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
4C2×C11×#104C211yesmaximal, characteristic
5C11×#419C211yesmaximal, characteristic, complemented
6C2×C11×#101C211yesmaximal, characteristic, complemented
7C11×#339C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×Q8×C11C2211yescharacteristic
10C22×Q8×C11C2211yescharacteristic
11C11×#137—22no—
12C11×#137—22no—
13C2×C11×Q16—21no—
14C2×C11×SD16—21no—
15C2×C11×M16C2211yescharacteristic
16C2×C11×M16C2211yescharacteristic
17C11×C4⋊Q8—22no—
18C11×C4⋊Q8—21no—
19C11×C4⋊Q8—22no—
20C11×#124—21no—
21C11×#123—22no—
22C11×C22⋊Q8—22no—
23C11×#117C2211yescharacteristic
24C2×C11×C4⋊C4—22no—
25C2×C42×C11C2211yescharacteristic
26C11×#104—22no—
27C11×#103—22no—
28C11×#101—22no—
29C11×#41—21no—
30C11×#41—21no—
31C11×#41—21no—
32C11×#41—21no—
33C2×Q8×C11—21no—
34C2×Q8×C11—21no—
35C2×Q8×C11—21no—
36C2×Q8×C11—21no—
37C2×Q8×C11—21no—
38C2×Q8×C11—21no—
39C2×Q8×C11—21no—
40C2×Q8×C11—21no—
41C2×Q8×C11—21no—
42C2×Q8×C11—21no—
43C2×Q8×C11—21no—
44C2×Q8×C11D411yescharacteristic
45C2×Q8×C11D412yes—
46C2×D4×C11—21no—
47C2×D4×C11D411yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11D412yes—
52C22×C4×C11C2311yescharacteristic
53C11×Q16—24no—
54C11×SD16—24no—
55C11×M16—21no—
56C11×M16—21no—
57C11×M16—21no—
58C11×M16D412yes—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C11×C4⋊C4—28no—
62C11×C4⋊C4—24no—
63C11×C4⋊C4D412yes—
64C11×C22⋊C4—24no—
65C11×C22⋊C4—21no—
66C42×C11—21no—
67C42×C11—21no—
68C42×C11D412yes—
69#2005C1111yesmaximal, characteristic, direct product factor, Sylow
70C23×C11—21no—
71C23×C11C2×D411yescharacteristic
72Q8×C11—22no—
73Q8×C11—21no—
74Q8×C11—22no—
75Q8×C11—21no—
76Q8×C11—41no—
77Q8×C11—41no—
78Q8×C11—41no—
79Q8×C11—41no—
80Q8×C11—41no—
81Q8×C11—41no—
82D4×C11—21no—
83D4×C11—21no—
84D4×C11—41no—
85D4×C11—41no—
86C2×C4×C11—24no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2×D411yescharacteristic
101C2×C4×C11C2×D411yescharacteristic
102C2×C4×C11C2×D411yescharacteristic
103C2×C4×C11#4111yescharacteristic
104C8×C11—22no—
105C8×C11—41no—
106C2×#137C2×C1111yescharacteristic
107#536C2×C1111yescharacteristic
108C2×C4⋊Q8C2×C1111yescharacteristic, complemented
109C2×#104C2×C1111yescharacteristic
110#419C2×C1111yescharacteristic, complemented
111C2×#101C2×C1111yescharacteristic, complemented
112#339C2×C1111yescharacteristic, complemented
113C22×C11—22no—
114C22×C11—41no—
115C22×C11—42no—
116C22×C11#12011yescharacteristic
117C22×C11#12011yescharacteristic
118C22×C11#12111yescharacteristic
119C4×C11—24no—
120C4×C11—42no—
121C4×C11—41no—
122C4×C11—42no—
123C4×C11—42no—
124C4×C11#12011yescharacteristic
125C4×C11#12111yescharacteristic
126C4×C11#12111yescharacteristic
127C4×C11#12711yescharacteristic
128C2×#41C22×C1111yescharacteristic
129C22×Q8C22×C1111yescharacteristic
130C22×Q8C22×C1111yescharacteristic
131#137—22no—
132#137—22no—
133C2×Q16—21no—
134C2×SD16—21no—
135C2×M16C22×C1111yescharacteristic
136C2×M16C22×C1111yescharacteristic
137C4⋊Q8—22no—
138C4⋊Q8—21no—
139C4⋊Q8—22no—
140#124—21no—
141#123—22no—
142C22⋊Q8—22no—
143#117C22×C1111yescharacteristic
144C2×C4⋊C4—22no—
145C2×C42C22×C1111yescharacteristic
146#104—22no—
147#103—22no—
148#101—22no—
149C2×C11—21no—
150C2×C11—21no—
151C2×C11—81no—
152C2×C11#39211yescharacteristic
153C2×C11#45612yes—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8D4×C1111yescharacteristic
170C2×Q8D4×C1112yes—
171C2×D4—21no—
172C2×D4D4×C1111yescharacteristic
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4D4×C1112yes—
177C22×C4C23×C1111yescharacteristic
178Q16—24no—
179SD16—24no—
180M16—21no—
181M16—21no—
182M16—21no—
183M16D4×C1112yes—
184C2×C8—21no—
185C2×C8—21no—
186C4⋊C4—28no—
187C4⋊C4—24no—
188C4⋊C4D4×C1112yes—
189C22⋊C4—24no—
190C22⋊C4—21no—
191C42—21no—
192C42—21no—
193C42D4×C1112yes—
194C11#200511yescharacteristic, direct product factor, Sylow
195C23—21no—
196C23C2×D4×C1111yescharacteristic
197Q8—22no—
198Q8—21no—
199Q8—22no—
200Q8—21no—
201Q8—41no—
202Q8—41no—
203Q8—41no—
204Q8—41no—
205Q8—41no—
206Q8—41no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4C2×D4×C1111yescharacteristic
224C2×C4C2×D4×C1111yescharacteristic
225C2×C4C2×D4×C1111yescharacteristic
226C2×C4C2×D4×C1111yescharacteristic
227C2×C4C2×D4×C1111yescharacteristic
228C2×C4C11×#4111yescharacteristic
229C8—22no—
230C8—41no—
231C22—22no—
232C22—41no—
233C22—42no—
234C22C11×#12011yescharacteristic
235C22C11×#12011yescharacteristic
236C22C11×#12111yescharacteristic
237C4—24no—
238C4—42no—
239C4—41no—
240C4—42no—
241C4—42no—
242C4C11×#12011yescharacteristic
243C4C11×#12111yescharacteristic
244C4C11×#12111yescharacteristic
245C4C11×#12711yescharacteristic
246C2—21no—
247C2—21no—
248C2—81no—
249C2C11×#39211yescharacteristic
250C2C11×#45612yes—
subgroupG/H
center, socleC22×C11#120
commutator, Frattini, cosocleC22×C4C23×C11
prime radicalC2×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×C4⋊Q8C2semidirect
5. C11×#419C2semidirect
6. C2×C11×#101C2semidirect
7. C11×#339C2semidirect
69. #2005C11direct (N × H)
108. C2×C4⋊Q8C2×C11semidirect
110. #419C2×C11semidirect
111. C2×#101C2×C11semidirect
112. #339C2×C11semidirect
194. C11#2005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1372
C11×#5362
C2×C11×C4⋊Q82
C2×C11×#1042
C11×#4192
C2×C11×#1012
C11×#3392
#200511