Finite Group Databasebeta

← C2×C11×#2102 #14600943

Subgroups — C2×C11×#2102 #14600943

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic
2C2×C11×#423C211yesmaximal, characteristic
3C11×#2102C218yesmaximal, direct product factor
4C2×C11×#344C212yesmaximal
5C2×C11×#339C212yesmaximal
6C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic
7C22×C11×M16C2211yescharacteristic
8C22×C11×M16C2212yes—
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2212yes—
11C22×C42×C11C2211yescharacteristic
12C11×#430—22no—
13C11×#430C2214yes—
14C2×C11×#108—22no—
15C11×#423—22no—
16C11×#423C2214yes—
17C2×C11×C4⋊C8—22no—
18C11×#344C2218yes—
19C11×#339C2218yes—
20C11×H(3,ℤ/4)C2214yes—
21C23×C4×C11—21no—
22C23×C4×C11C2311yescharacteristic
23C2×C11×M16—22no—
24C2×C11×M16—22no—
25C2×C11×M16—21no—
26C2×C11×M16—22no—
27C2×C11×M16—22no—
28C2×C11×M16—22no—
29C2×C11×M16—22no—
30C2×C11×M16—22no—
31C2×C11×M16—22no—
32C2×C11×M16—22no—
33C2×C11×M16D412yes—
34C2×C11×M16C2314yes—
35C2×C11×M16C2312yes—
36C2×C11×M16C2312yes—
37C22×C8×C11—21no—
38C22×C8×C11—22no—
39C22×C8×C11D412yes—
40C11×#117—22no—
41C11×#117—22no—
42C11×#117—22no—
43C11×#117C2314yes—
44C2×C11×C4⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C42×C11—21no—
47C2×C42×C11—21no—
48C2×C42×C11—21no—
49C2×C42×C11—22no—
50C2×C42×C11Q811yescharacteristic
51C2×C42×C11Q812yes—
52C2×C42×C11Q811yescharacteristic
53C2×C42×C11C2312yes—
54C11×#108—28no—
55C11×C4⋊C8—28no—
56C2×#2102C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11#4111yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—44no—
63C22×C4×C11—42no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×Q811yescharacteristic
67C22×C4×C11C2×Q811yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×C4×C11#4112yes—
70C22×C4×C11#4112yes—
71C22×C4×C11#4112yes—
72C22×C4×C11#4112yes—
73C22×C4×C11C2411yescharacteristic
74C11×M16—24no—
75C11×M16—24no—
76C11×M16—24no—
77C11×M16—24no—
78C11×M16—24no—
79C11×M16—42no—
80C11×M16—42no—
81C11×M16—42no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11—24no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C2×C8×C11C2×D414yes—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—42no—
93C11×C22⋊C4—24no—
94C11×C22⋊C4—42no—
95C42×C11—21no—
96C42×C11—22no—
97C42×C11—21no—
98C42×C11—22no—
99C42×C11—24no—
100C42×C11—42no—
101C42×C11C2×Q812yes—
102C42×C11C2×Q812yes—
103C2×#430C2×C1111yescharacteristic
104C2×#423C2×C1111yescharacteristic
105#2102C2×C1118yesdirect product factor
106C2×#344C2×C1112yes—
107C2×#339C2×C1112yes—
108C2×H(3,ℤ/4)C2×C1111yescharacteristic
109C23×C11—42no—
110C23×C11C22⋊Q811yescharacteristic
111C23×C11C22⋊Q811yescharacteristic
112C23×C11#12612yes—
113C23×C11#12612yes—
114C23×C11C2×#4111yescharacteristic
115C2×C4×C11—24no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11—84no—
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11#12311yescharacteristic
126C2×C4×C11#12311yescharacteristic
127C2×C4×C11#12312yes—
128C2×C4×C11#12412yes—
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11#12411yescharacteristic
131C2×C4×C11#12512yes—
132C2×C4×C11#12512yes—
133C2×C4×C11#12512yes—
134C2×C4×C11#12512yes—
135C2×C4×C11#12612yes—
136C2×C4×C11#12612yes—
137C2×C4×C11C22×D411yescharacteristic
138C2×C4×C11C22×Q811yescharacteristic
139C2×C4×C11C2×#4112yes—
140C2×C4×C11C2×#4112yes—
141C8×C11—24no—
142C8×C11—42no—
143C8×C11—44no—
144C22×M16C22×C1111yescharacteristic
145C22×M16C22×C1112yes—
146C22×M16C22×C1111yescharacteristic
147C2×#117C22×C1112yes—
148C22×C42C22×C1111yescharacteristic
149#430—22no—
150#430C22×C1114yes—
151C2×#108—22no—
152#423—22no—
153#423C22×C1114yes—
154C2×C4⋊C8—22no—
155#344C22×C1118yes—
156#339C22×C1118yes—
157H(3,ℤ/4)C22×C1114yes—
158C22×C11—22no—
159C22×C11—24no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—42no—
163C22×C11#40011yescharacteristic
164C22×C11#40012yes—
165C22×C11#40011yescharacteristic
166C22×C11C2×C22⋊Q811yescharacteristic
167C22×C11C2×#12612yes—
168C4×C11—24no—
169C4×C11—42no—
170C4×C11—84no—
171C4×C11#40011yescharacteristic
172C4×C11#40012yes—
173C4×C11#40011yescharacteristic
174C4×C11C2×#12311yescharacteristic
175C4×C11C2×#12411yescharacteristic
176C4×C11C2×#12512yes—
177C23×C4—21no—
178C23×C4C23×C1111yescharacteristic
179C2×M16—22no—
180C2×M16—22no—
181C2×M16—21no—
182C2×M16—22no—
183C2×M16—22no—
184C2×M16—22no—
185C2×M16—22no—
186C2×M16—22no—
187C2×M16—22no—
188C2×M16—22no—
189C2×M16D4×C1112yes—
190C2×M16C23×C1114yes—
191C2×M16C23×C1112yes—
192C2×M16C23×C1112yes—
193C22×C8—21no—
194C22×C8—22no—
195C22×C8D4×C1112yes—
196#117—22no—
197#117—22no—
198#117—22no—
199#117C23×C1114yes—
200C2×C4⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—22no—
206C2×C42Q8×C1111yescharacteristic
207C2×C42Q8×C1112yes—
208C2×C42Q8×C1111yescharacteristic
209C2×C42C23×C1112yes—
210#108—28no—
211C4⋊C8—28no—
212C2×C11—21no—
213C2×C11—22no—
214C2×C11—21no—
215C2×C11—22no—
216C2×C11#210212yesdirect product factor
217C2×C11C2×#40011yescharacteristic
218C24C11×#4111yescharacteristic
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—44no—
224C22×C4—42no—
225C22×C4C2×D4×C1111yescharacteristic
226C22×C4C2×D4×C1111yescharacteristic
227C22×C4C2×Q8×C1111yescharacteristic
228C22×C4C2×Q8×C1111yescharacteristic
229C22×C4C11×#4111yescharacteristic
230C22×C4C11×#4112yes—
231C22×C4C11×#4112yes—
232C22×C4C11×#4112yes—
233C22×C4C11×#4112yes—
234C22×C4C24×C1111yescharacteristic
235M16—24no—
236M16—24no—
237M16—24no—
238M16—24no—
239M16—24no—
240M16—42no—
241M16—42no—
242M16—42no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—24no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8C2×D4×C1114yes—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C22⋊C4—24no—
255C22⋊C4—42no—
256C42—21no—
257C42—22no—
258C42—21no—
259C42—22no—
260C42—24no—
261C42—42no—
262C42C2×Q8×C1112yes—
263C42C2×Q8×C1112yes—
264C11C2×#210211yescharacteristic, direct product factor, Sylow
265C23—42no—
266C23C11×C22⋊Q811yescharacteristic
267C23C11×C22⋊Q811yescharacteristic
268C23C11×#12612yes—
269C23C11×#12612yes—
270C23C2×C11×#4111yescharacteristic
271C2×C4—24no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—44no—
278C2×C4—84no—
279C2×C4C11×C22⋊Q811yescharacteristic
280C2×C4C11×C22⋊Q811yescharacteristic
281C2×C4C11×#12311yescharacteristic
282C2×C4C11×#12311yescharacteristic
283C2×C4C11×#12312yes—
284C2×C4C11×#12412yes—
285C2×C4C11×#12411yescharacteristic
286C2×C4C11×#12411yescharacteristic
287C2×C4C11×#12512yes—
288C2×C4C11×#12512yes—
289C2×C4C11×#12512yes—
290C2×C4C11×#12512yes—
291C2×C4C11×#12612yes—
292C2×C4C11×#12612yes—
293C2×C4C22×D4×C1111yescharacteristic
294C2×C4C22×Q8×C1111yescharacteristic
295C2×C4C2×C11×#4112yes—
296C2×C4C2×C11×#4112yes—
297C8—24no—
298C8—42no—
299C8—44no—
300C22—22no—
301C22—24no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22C11×#40011yescharacteristic
306C22C11×#40012yes—
307C22C11×#40011yescharacteristic
308C22C2×C11×C22⋊Q811yescharacteristic
309C22C2×C11×#12612yes—
310C4—24no—
311C4—42no—
312C4—84no—
313C4C11×#40011yescharacteristic
314C4C11×#40011yescharacteristic
315C4C11×#40012yes—
316C4C2×C11×#12311yescharacteristic
317C4C2×C11×#12411yescharacteristic
318C4C2×C11×#12512yes—
319C2—21no—
320C2—22no—
321C2—21no—
322C2—22no—
323C2C11×#210212yesdirect product factor
324C2C2×C11×#40011yescharacteristic
subgroupG/H
centerC2×C4×C11#124
commutator, Frattini, cosocleC22×C4C24×C11
socleC22×C11#400
prime radicalC24×C11#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2102C2direct (N × H)
56. C2×#2102C11direct (N × H)
105. #2102C2×C11direct (N × H)
216. C2×C11#2102direct (N × H)
264. C11C2×#2102direct (N × H)
323. C2C11×#2102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C2×C11×#4232
C11×#21022
C2×C11×#3442
C2×C11×#3392
C2×C11×H(3,ℤ/4)2
C2×#210211