Finite Group Databasebeta

← C2×C11×#2083 #14600846

Subgroups — C2×C11×#2083 #14600846

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#107C212yesmaximal
2C2×C11×#389C211yesmaximal, characteristic
3C2×C11×#384C211yesmaximal, characteristic
4C11×#2083C218yesmaximal, direct product factor
5C2×C11×#340C212yesmaximal
6C2×C11×#336C211yesmaximal, characteristic
7C23×C8×C11C2212yes—
8C22×C11×C4⋊C4—21no—
9C22×C11×C4⋊C4—21no—
10C22×C11×C4⋊C4—21no—
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×C11×#107—28no—
16C2×C11×#107C2218yes—
17C11×#389—22no—
18C11×#389C2214yes—
19C11×#384—22no—
20C11×#384C2214yes—
21C2×C11×#95—21no—
22C11×#340C2218yes—
23C11×#336C2214yes—
24C23×C4×C11—21no—
25C23×C4×C11—21no—
26C23×C4×C11—22no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C22×C8×C11—24no—
31C22×C8×C11—24no—
32C22×C8×C11Q818yes—
33C22×C8×C11C2314yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—24no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—44no—
45C2×C11×C4⋊C4—44no—
46C2×C11×C4⋊C4—44no—
47C2×C11×C4⋊C4D414yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2314yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11—24no—
52C2×C42×C11D412yes—
53C2×C42×C11C2312yes—
54C11×#107—216no—
55C11×#95—24no—
56C2×#2083C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11C2×D411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—24no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—44no—
69C22×C4×C11—42no—
70C22×C4×C11—44no—
71C22×C4×C11—42no—
72C22×C4×C11—44no—
73C22×C4×C11—42no—
74C22×C4×C11D814yes—
75C22×C4×C11Q1614yes—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×Q814yes—
81C22×C4×C11#4112yes—
82C22×C4×C11#4114yes—
83C22×C4×C11C2411yescharacteristic
84C2×C8×C11—216no—
85C2×C8×C11—24no—
86C2×C8×C11—24no—
87C2×C8×C11C2×Q818yes—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—48no—
94C11×C4⋊C4—44no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—48no—
97C11×C4⋊C4—48no—
98C11×C4⋊C4C2×D414yes—
99C42×C11—24no—
100C42×C11—24no—
101C22×#107C2×C1112yes—
102C2×#389C2×C1111yescharacteristic
103C2×#384C2×C1111yescharacteristic
104#2083C2×C1118yesdirect product factor
105C2×#340C2×C1112yes—
106C2×#336C2×C1111yescharacteristic
107C23×C11#12112yes—
108C23×C11#12312yes—
109C23×C11C4⋊Q812yes—
110C23×C11C2×D812yes—
111C23×C11C2×Q1612yes—
112C23×C11AGL(1,ℤ/8)12yes—
113C23×C11#13712yes—
114C23×C11C22×D411yescharacteristic
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—28no—
120C2×C4×C11—28no—
121C2×C4×C11—24no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—48no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—42no—
131C2×C4×C11—88no—
132C2×C4×C11—84no—
133C2×C4×C11#12112yes—
134C2×C4×C11C22⋊Q818yes—
135C2×C4×C11#12312yes—
136C2×C4×C11#12518yes—
137C2×C4×C11C4⋊Q812yes—
138C2×C4×C11C2×D814yes—
139C2×C4×C11C2×Q1614yes—
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C22×Q812yes—
142C2×C4×C11C2×#4112yes—
143C2×C4×C11C2×#4111yescharacteristic
144C8×C11—28no—
145C23×C8C22×C1112yes—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4C22×C1112yes—
150C22×C4⋊C4C22×C1111yescharacteristic
151C22×C4⋊C4C22×C1111yescharacteristic
152C22×C42C22×C1111yescharacteristic
153C2×#107—28no—
154C2×#107C22×C1118yes—
155#389—22no—
156#389C22×C1114yes—
157#384—22no—
158#384C22×C1114yes—
159C2×#95—21no—
160#340C22×C1118yes—
161#336C22×C1114yes—
162C22×C11#39814yes—
163C22×C11#45914yes—
164C22×C11#46214yes—
165C22×C11#48014yes—
166C22×C11#48414yes—
167C22×C11#50014yes—
168C22×C11#50114yes—
169C22×C11C2×#12111yescharacteristic
170C22×C11C2×#12311yescharacteristic
171C22×C11C2×C4⋊Q811yescharacteristic
172C22×C11C22×D811yescharacteristic
173C22×C11C22×Q1611yescharacteristic
174C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
175C22×C11C2×#13711yescharacteristic
176C4×C11—24no—
177C4×C11—24no—
178C4×C11—44no—
179C4×C11—82no—
180C4×C11—84no—
181C4×C11#39814yes—
182C4×C11C2×C22⋊Q812yes—
183C4×C11C2×#12512yes—
184C23×C4—21no—
185C23×C4—22no—
186C23×C4—21no—
187C23×C4D4×C1111yescharacteristic
188C23×C4D4×C1111yescharacteristic
189C23×C4C23×C1111yescharacteristic
190C22×C8—24no—
191C22×C8—24no—
192C22×C8Q8×C1118yes—
193C22×C8C23×C1114yes—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—44no—
205C2×C4⋊C4—44no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4D4×C1114yes—
208C2×C4⋊C4C23×C1112yes—
209C2×C4⋊C4C23×C1114yes—
210C2×C4⋊C4C23×C1112yes—
211C2×C42—24no—
212C2×C42D4×C1112yes—
213C2×C42C23×C1112yes—
214#107—216no—
215#95—24no—
216C2×C11#208318yesdirect product factor
217C2×C11C2×#39811yescharacteristic
218C2×C11C2×#45911yescharacteristic
219C2×C11C2×#46211yescharacteristic
220C2×C11C2×#48011yescharacteristic
221C2×C11C2×#48411yescharacteristic
222C2×C11C2×#50011yescharacteristic
223C2×C11C2×#50111yescharacteristic
224C24C2×D4×C1111yescharacteristic
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—44no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4—42no—
239C22×C4—44no—
240C22×C4—42no—
241C22×C4C11×D814yes—
242C22×C4C11×Q1614yes—
243C22×C4C2×D4×C1112yes—
244C22×C4C2×D4×C1112yes—
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C2×D4×C1112yes—
247C22×C4C2×Q8×C1114yes—
248C22×C4C11×#4112yes—
249C22×C4C11×#4114yes—
250C22×C4C24×C1111yescharacteristic
251C2×C8—216no—
252C2×C8—24no—
253C2×C8—24no—
254C2×C8C2×Q8×C1118yes—
255C4⋊C4—24no—
256C4⋊C4—22no—
257C4⋊C4—24no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—48no—
261C4⋊C4—44no—
262C4⋊C4—42no—
263C4⋊C4—48no—
264C4⋊C4—48no—
265C4⋊C4C2×D4×C1114yes—
266C42—24no—
267C42—24no—
268C11C2×#208311yescharacteristic, direct product factor, Sylow
269C23C11×#12112yes—
270C23C11×#12312yes—
271C23C11×C4⋊Q812yes—
272C23C2×C11×D812yes—
273C23C2×C11×Q1612yes—
274C23C11×AGL(1,ℤ/8)12yes—
275C23C11×#13712yes—
276C23C22×D4×C1111yescharacteristic
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—28no—
282C2×C4—28no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—48no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—88no—
294C2×C4—84no—
295C2×C4C11×#12112yes—
296C2×C4C11×C22⋊Q818yes—
297C2×C4C11×#12312yes—
298C2×C4C11×#12518yes—
299C2×C4C11×C4⋊Q812yes—
300C2×C4C2×C11×D814yes—
301C2×C4C2×C11×Q1614yes—
302C2×C4C22×D4×C1111yescharacteristic
303C2×C4C22×Q8×C1112yes—
304C2×C4C2×C11×#4112yes—
305C2×C4C2×C11×#4111yescharacteristic
306C8—28no—
307C22C11×#39814yes—
308C22C11×#45914yes—
309C22C11×#46214yes—
310C22C11×#48014yes—
311C22C11×#48414yes—
312C22C11×#50014yes—
313C22C11×#50114yes—
314C22C2×C11×#12111yescharacteristic
315C22C2×C11×#12311yescharacteristic
316C22C2×C11×C4⋊Q811yescharacteristic
317C22C22×C11×D811yescharacteristic
318C22C22×C11×Q1611yescharacteristic
319C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
320C22C2×C11×#13711yescharacteristic
321C4—24no—
322C4—24no—
323C4—44no—
324C4—84no—
325C4—82no—
326C4C11×#39814yes—
327C4C2×C11×C22⋊Q812yes—
328C4C2×C11×#12512yes—
329C2C11×#208318yesdirect product factor
330C2C2×C11×#39811yescharacteristic
331C2C2×C11×#45911yescharacteristic
332C2C2×C11×#46211yescharacteristic
333C2C2×C11×#48011yescharacteristic
334C2C2×C11×#48411yescharacteristic
335C2C2×C11×#50011yescharacteristic
336C2C2×C11×#50111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2083C2direct (N × H)
56. C2×#2083C11direct (N × H)
104. #2083C2×C11direct (N × H)
216. C2×C11#2083direct (N × H)
268. C11C2×#2083direct (N × H)
329. C2C11×#2083direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1072
C2×C11×#3892
C2×C11×#3842
C11×#20832
C2×C11×#3402
C2×C11×#3362
C2×#208311