Finite Group Databasebeta

← C11×#2033 #13064871

Subgroups — C11×#2033 #13064871

Order 1408.

368 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 104 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×#121C211yesmaximal, characteristic
2C2×C11×#107C211yesmaximal, characteristic, complemented
3C2×C11×#102C211yesmaximal, characteristic, complemented
4C2×C11×#102C211yesmaximal, characteristic, complemented
5C2×C11×C22⋊C8C211yesmaximal, characteristic, complemented
6C11×#380C211yesmaximal, characteristic, complemented
7C11×#340C211yesmaximal, characteristic, complemented
8C22×D4×C11—21no—
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C22×C8×C11C2211yescharacteristic
12C22×C8×C11C2211yescharacteristic
13C11×#121—22no—
14C11×#121—22no—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4—21no—
19C2×C11×C22⋊C4—21no—
20C11×#107—22no—
21C11×#102—22no—
22C11×#102—22no—
23C11×C22⋊C8—22no—
24C11×#95—21no—
25C24×C11—21no—
26C24×C11D411yescharacteristic
27C2×D4×C11—24no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—21no—
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—42no—
34C2×D4×C11—42no—
35C2×D4×C11D412yes—
36C22×C4×C11—21no—
37C22×C4×C11—21no—
38C22×C4×C11—21no—
39C22×C4×C11—21no—
40C22×C4×C11—21no—
41C22×C4×C11—21no—
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11D411yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C2×C8×C11—21no—
48C2×C8×C11—21no—
49C2×C8×C11—21no—
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11D412yescomplemented
53C11×C4⋊C4—21no—
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4D412yes—
59C11×C22⋊C4—24no—
60C11×C22⋊C4—42no—
61#2033C1111yesmaximal, characteristic, direct product factor, Sylow
62C23×C11—21no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—21no—
66C23×C11—21no—
67C23×C11—21no—
68C23×C11—22no—
69C23×C11—41no—
70C23×C11—41no—
71C23×C11—41no—
72C23×C11—41no—
73C23×C11—41no—
74C23×C11—41no—
75C23×C11D812yes—
76C23×C11C2×D411yescharacteristic
77D4×C11—22no—
78D4×C11—22no—
79D4×C11—48no—
80D4×C11—41no—
81D4×C11—41no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
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×C11#4111yescharacteristic
102C2×C4×C11#4111yescharacteristic
103C2×C4×C11#4111yescharacteristic
104C8×C11—22no—
105C8×C11—41no—
106C2×#121C2×C1111yescharacteristic
107C2×#107C2×C1111yescharacteristic, complemented
108C2×#102C2×C1111yescharacteristic, complemented
109C2×#102C2×C1111yescharacteristic, complemented
110C2×C22⋊C8C2×C1111yescharacteristic, complemented
111#380C2×C1111yescharacteristic, complemented
112#340C2×C1111yescharacteristic, complemented
113C22×C11—22no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11—81no—
124C22×C11—81no—
125C22×C11—81no—
126C22×C11—81no—
127C22×C11#12011yescharacteristic
128C22×C11#12111yescharacteristic
129C22×C11#12311yescharacteristic
130C22×C11C2×D811yescharacteristic
131C22×C11#13511yescharacteristic
132C22×C11AGL(1,ℤ/8)11yescharacteristic
133C22×C11#13711yescharacteristic
134C4×C11—41no—
135C4×C11—42no—
136C4×C11—81no—
137C4×C11—81no—
138C4×C11#12111yescharacteristic
139C4×C11#12111yescharacteristic
140C4×C11#12311yescharacteristic
141C4×C11#12411yescharacteristic
142C22×D4—21no—
143C22×D4C22×C1111yescharacteristic
144C23×C4C22×C1111yescharacteristic
145C22×C8C22×C1111yescharacteristic
146C22×C8C22×C1111yescharacteristic
147#121—22no—
148#121—22no—
149C2×C4⋊C4C22×C1111yescharacteristic
150C2×C4⋊C4C22×C1111yescharacteristic
151C2×C4⋊C4C22×C1111yescharacteristic
152C2×C22⋊C4—21no—
153C2×C22⋊C4—21no—
154#107—22no—
155#102—22no—
156#102—22no—
157C22⋊C8—22no—
158#95—21no—
159C2×C11—42no—
160C2×C11—82no—
161C2×C11#39411yescharacteristic
162C2×C11#44711yescharacteristic
163C2×C11#45211yescharacteristic
164C2×C11#46611yescharacteristic
165C2×C11#46811yescharacteristic
166C2×C11#48011yescharacteristic
167C2×C11#48211yescharacteristic
168C24—21no—
169C24D4×C1111yescharacteristic
170C2×D4—24no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4D4×C1112yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4D4×C1111yescharacteristic
189C22×C4C23×C1111yescharacteristic
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8D4×C1112yescomplemented
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4D4×C1112yes—
202C22⋊C4—24no—
203C22⋊C4—42no—
204C11#203311yescharacteristic, direct product factor, Sylow
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—22no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23C11×D812yes—
219C23C2×D4×C1111yescharacteristic
220D4—22no—
221D4—22no—
222D4—48no—
223D4—41no—
224D4—41no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4C2×D4×C1111yescharacteristic
242C2×C4C2×D4×C1111yescharacteristic
243C2×C4C2×D4×C1111yescharacteristic
244C2×C4C11×#4111yescharacteristic
245C2×C4C11×#4111yescharacteristic
246C2×C4C11×#4111yescharacteristic
247C8—22no—
248C8—41no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22C11×#12011yescharacteristic
264C22C11×#12111yescharacteristic
265C22C11×#12311yescharacteristic
266C22C2×C11×D811yescharacteristic
267C22C11×#13511yescharacteristic
268C22C11×AGL(1,ℤ/8)11yescharacteristic
269C22C11×#13711yescharacteristic
270C4—41no—
271C4—42no—
272C4—81no—
273C4—81no—
274C4C11×#12111yescharacteristic
275C4C11×#12111yescharacteristic
276C4C11×#12311yescharacteristic
277C4C11×#12411yescharacteristic
278C2—42no—
279C2—82no—
280C2C11×#39411yescharacteristic
281C2C11×#44711yescharacteristic
282C2C11×#45211yescharacteristic
283C2C11×#46611yescharacteristic
284C2C11×#46811yescharacteristic
285C2C11×#48011yescharacteristic
286C2C11×#48211yescharacteristic
subgroupG/H
center, socleC23×C11C2×D4
commutator, Frattini, cosocleC22×C4C23×C11
prime radicalC2×C11×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#107C2semidirect
3. C2×C11×#102C2semidirect
4. C2×C11×#102C2semidirect
5. C2×C11×C22⋊C8C2semidirect
6. C11×#380C2semidirect
7. C11×#340C2semidirect
52. C2×C8×C11D4semidirect
61. #2033C11direct (N × H)
107. C2×#107C2×C11semidirect
108. C2×#102C2×C11semidirect
109. C2×#102C2×C11semidirect
110. C2×C22⋊C8C2×C11semidirect
111. #380C2×C11semidirect
112. #340C2×C11semidirect
195. C2×C8D4×C11semidirect
204. C11#2033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×C11×#1072
C2×C11×#1022
C2×C11×C22⋊C82
C11×#3802
C11×#3402
#203311