Finite Group Databasebeta

← C11×#13341 #14590534

Subgroups — C11×#13341 #14590534

Order 2816.

594 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 122 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×#509C212yesmaximal, complemented
2C11×#3150C211yesmaximal, characteristic, complemented
3C2×C11×#360C212yesmaximal, complemented
4C11×#1972C211yesmaximal, characteristic, complemented
5C11×#1377C211yesmaximal, characteristic, complemented
6C2×C11×#135—21no—
7C2×C11×#135C2212yes—
8C22×C11×D8C2211yescharacteristic
9C11×#532—21no—
10C11×#509—24no—
11C11×#509—24no—
12C2×C11×SD32—22no—
13C2×C11×D16—22no—
14C2×C11×M32C2212yes—
15C11×#497—22no—
16C11×#496—22no—
17C2×C11×#106C2211yescharacteristic
18C2×C11×#102—21no—
19C2×C11×#97C2211yescharacteristic
20C11×#390—21no—
21C11×#360—24no—
22C2×C11×#41—22no—
23C22×D4×C11—21no—
24C11×#135—22no—
25C11×#135—22no—
26C11×#135—22no—
27C11×#135—22no—
28C11×#135—42no—
29C11×#135—42no—
30C2×C11×Q16—21no—
31C2×C11×Q16D412yes—
32C2×C11×SD16—22no—
33C2×C11×SD16—22no—
34C2×C11×D8—21no—
35C2×C11×D8—22no—
36C2×C11×D8—22no—
37C2×C11×D8—21no—
38C2×C11×D8D412yes—
39C2×C11×D8D412yescomplemented
40C22×C8×C11D411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C11×C4⋊Q8—21no—
43C11×#127—21no—
44C11×#124—22no—
45C11×#121—42no—
46C4×D4×C11—42no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C22⋊C4—42no—
49C2×C42×C11D411yescharacteristic
50C11×SD32—28no—
51C11×D16—28no—
52C11×M32—22no—
53C11×M32D414yescomplemented
54C2×C11×C16—22no—
55C11×#106—22no—
56C11×#102—42no—
57C11×#97—22no—
58#13341C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11—41no—
60C11×#41—42no—
61C11×#41—42no—
62C11×#41—42no—
63C11×#41—42no—
64C2×Q8×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C22×C4×C11—42no—
75C22×C4×C11—41no—
76C22×C4×C11D812yes—
77C22×C4×C11C2×D411yescharacteristic
78C11×Q16—22no—
79C11×Q16—22no—
80C11×Q16—42no—
81C11×SD16—44no—
82C11×SD16—42no—
83C11×SD16—42no—
84C11×D8—22no—
85C11×D8—24no—
86C11×D8—22no—
87C11×D8—42no—
88C11×D8—42no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11D812yes—
92C2×C8×C11C2×D412yes—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D412yes—
95C2×C8×C11#4111yescharacteristic
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—44no—
100C11×C22⋊C4—84no—
101C42×C11—21no—
102C42×C11—21no—
103C11×C16—24no—
104C2×#509C2×C1112yescomplemented
105#3150C2×C1111yescharacteristic, complemented
106C2×#360C2×C1112yescomplemented
107#1972C2×C1111yescharacteristic, complemented
108#1377C2×C1111yescharacteristic, complemented
109C23×C11—42no—
110C23×C11—42no—
111C23×C11—82no—
112C23×C11—82no—
113C23×C11—81no—
114C23×C11—81no—
115C23×C11C2×D811yescharacteristic
116Q8×C11—42no—
117Q8×C11—42no—
118D4×C11—42no—
119D4×C11—42no—
120D4×C11—42no—
121D4×C11—42no—
122D4×C11—84no—
123D4×C11—82no—
124D4×C11—82no—
125D4×C11—81no—
126D4×C11—81no—
127C2×C4×C11—22no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11—82no—
133C2×C4×C11—81no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12711yescharacteristic
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C8×C11—22no—
141C8×C11#12012yes—
142C8×C11#12112yes—
143C2×#135—21no—
144C2×#135C22×C1112yes—
145C22×D8C22×C1111yescharacteristic
146#532—21no—
147#509—24no—
148#509—24no—
149C2×SD32—22no—
150C2×D16—22no—
151C2×M32C22×C1112yes—
152#497—22no—
153#496—22no—
154C2×#106C22×C1111yescharacteristic
155C2×#102—21no—
156C2×#97C22×C1111yescharacteristic
157#390—21no—
158#360—24no—
159C22×C11—22no—
160C22×C11—84no—
161C22×C11—84no—
162C22×C11—82no—
163C22×C11—82no—
164C22×C11—161no—
165C22×C11—161no—
166C22×C11—162no—
167C22×C11#44711yescharacteristic
168C22×C11#45911yescharacteristic
169C22×C11#49311yescharacteristic
170C4×C11—42no—
171C4×C11—82no—
172C4×C11—161no—
173C4×C11#39211yescharacteristic
174C4×C11#44711yescharacteristic
175C4×C11#45911yescharacteristic
176C4×C11#49611yescharacteristic
177C2×#41—22no—
178C22×D4—21no—
179#135—22no—
180#135—22no—
181#135—22no—
182#135—22no—
183#135—42no—
184#135—42no—
185C2×Q16—21no—
186C2×Q16D4×C1112yes—
187C2×SD16—22no—
188C2×SD16—22no—
189C2×D8—21no—
190C2×D8—22no—
191C2×D8—22no—
192C2×D8—21no—
193C2×D8D4×C1112yes—
194C2×D8D4×C1112yescomplemented
195C22×C8D4×C1111yescharacteristic
196C22×C8C23×C1111yescharacteristic
197C4⋊Q8—21no—
198#127—21no—
199#124—22no—
200#121—42no—
201C4×D4—42no—
202C2×C4⋊C4—21no—
203C2×C22⋊C4—42no—
204C2×C42D4×C1111yescharacteristic
205SD32—28no—
206D16—28no—
207M32—22no—
208M32D4×C1114yescomplemented
209C2×C16—22no—
210#106—22no—
211#102—42no—
212#97—22no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—162no—
216C2×C11—162no—
217C2×C11#201111yescharacteristic
218C2×C11#219012yes—
219C24—41no—
220#41—42no—
221#41—42no—
222#41—42no—
223#41—42no—
224C2×Q8—22no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4C11×D812yes—
237C22×C4C2×D4×C1111yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—42no—
241SD16—44no—
242SD16—42no—
243SD16—42no—
244D8—22no—
245D8—24no—
246D8—22no—
247D8—42no—
248D8—42no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8C11×D812yes—
252C2×C8C2×D4×C1111yescharacteristic
253C2×C8C2×D4×C1112yes—
254C2×C8C2×D4×C1112yes—
255C2×C8C11×#4111yescharacteristic
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C22⋊C4—44no—
260C22⋊C4—84no—
261C42—21no—
262C42—21no—
263C16—24no—
264C11#1334111yescharacteristic, direct product factor, Sylow
265C23—42no—
266C23—42no—
267C23—82no—
268C23—82no—
269C23—81no—
270C23—81no—
271C23C2×C11×D811yescharacteristic
272Q8—42no—
273Q8—42no—
274D4—42no—
275D4—42no—
276D4—42no—
277D4—42no—
278D4—84no—
279D4—82no—
280D4—82no—
281D4—81no—
282D4—81no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—81no—
290C2×C4C11×#12011yescharacteristic
291C2×C4C11×#12111yescharacteristic
292C2×C4C11×#12711yescharacteristic
293C2×C4C2×C11×D811yescharacteristic
294C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
295C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
296C8—22no—
297C8C11×#12012yes—
298C8C11×#12112yes—
299C22—22no—
300C22—84no—
301C22—84no—
302C22—82no—
303C22—82no—
304C22—161no—
305C22—161no—
306C22—162no—
307C22C11×#44711yescharacteristic
308C22C11×#45911yescharacteristic
309C22C11×#49311yescharacteristic
310C4—42no—
311C4—82no—
312C4—161no—
313C4C11×#39211yescharacteristic
314C4C11×#44711yescharacteristic
315C4C11×#45911yescharacteristic
316C4C11×#49611yescharacteristic
317C2—21no—
318C2—21no—
319C2—162no—
320C2—162no—
321C2C11×#201111yescharacteristic
322C2C11×#219012yes—
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#509C2semidirect
2. C11×#3150C2semidirect
3. C2×C11×#360C2semidirect
4. C11×#1972C2semidirect
5. C11×#1377C2semidirect
39. C2×C11×D8D4semidirect
53. C11×M32D4semidirect
58. #13341C11direct (N × H)
104. C2×#509C2×C11semidirect
105. #3150C2×C11semidirect
106. C2×#360C2×C11semidirect
107. #1972C2×C11semidirect
108. #1377C2×C11semidirect
194. C2×D8D4×C11semidirect
208. M32D4×C11semidirect
264. C11#13341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5092
C11×#31502
C2×C11×#3602
C11×#19722
C11×#13772
#1334111