Finite Group Databasebeta

← C2×C11×#2043 #14600696

Subgroups — C2×C11×#2043 #14600696

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C22×C11×#103C212yesmaximal
3C22×C11×#103C212yesmaximal
4C2×C11×#389C211yesmaximal, characteristic
5C11×#2043C218yesmaximal, direct product factor
6C2×C11×#336C211yesmaximal, characteristic
7C23×Q8×C11C2212yes—
8C23×C8×C11C2212yes—
9C2×C11×C4⋊Q8—28no—
10C2×C11×C4⋊Q8—22no—
11C2×C11×C4⋊Q8C2214yes—
12C22×C11×C4⋊C4—21no—
13C22×C11×C4⋊C4—21no—
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C2×C11×#103—28no—
19C2×C11×#103—28no—
20C2×C11×#103C2218yes—
21C2×C11×#103C2218yes—
22C11×#389—22no—
23C11×#389C2214yes—
24C2×C11×#95—21no—
25C11×#336C2214yes—
26C22×Q8×C11—24no—
27C22×Q8×C11—22no—
28C22×Q8×C11—24no—
29C22×Q8×C11—24no—
30C22×Q8×C11—24no—
31C22×Q8×C11—24no—
32C22×Q8×C11D418yes—
33C22×Q8×C11C2314yes—
34C23×C4×C11—21no—
35C23×C4×C11—22no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C8×C11—24no—
41C22×C8×C11—24no—
42C22×C8×C11—24no—
43C22×C8×C11C2314yes—
44C11×C4⋊Q8—216no—
45C11×C4⋊Q8—216no—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4—28no—
48C2×C11×C4⋊C4—24no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—44no—
56C2×C11×C4⋊C4D414yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11—24no—
60C2×C42×C11D412yes—
61C2×C42×C11C2312yes—
62C11×#103—216no—
63C11×#103—216no—
64C11×#95—24no—
65C2×#2043C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11C2×D411yescharacteristic
67C2×Q8×C11—28no—
68C2×Q8×C11—24no—
69C2×Q8×C11—216no—
70C2×Q8×C11—216no—
71C2×Q8×C11—24no—
72C2×Q8×C11—24no—
73C2×Q8×C11—24no—
74C2×Q8×C11—24no—
75C2×Q8×C11—44no—
76C2×Q8×C11—48no—
77C2×Q8×C11—48no—
78C2×Q8×C11—44no—
79C2×Q8×C11C2×D418yes—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—28no—
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—24no—
88C22×C4×C11—22no—
89C22×C4×C11—44no—
90C22×C4×C11—44no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11SD1614yes—
97C22×C4×C11Q1614yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D414yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11#4114yes—
104C22×C4×C11#4112yes—
105C22×C4×C11C2411yescharacteristic
106C2×C8×C11—24no—
107C2×C8×C11—24no—
108C2×C8×C11—24no—
109C2×C8×C11—48no—
110C11×C4⋊C4—216no—
111C11×C4⋊C4—216no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—48no—
117C11×C4⋊C4C2×D414yes—
118C42×C11—24no—
119C42×C11—24no—
120C22×C4⋊Q8C2×C1111yescharacteristic
121C22×#103C2×C1112yes—
122C22×#103C2×C1112yes—
123C2×#389C2×C1111yescharacteristic
124#2043C2×C1118yesdirect product factor
125C2×#336C2×C1111yescharacteristic
126C23×C11#12012yes—
127C23×C11#12112yes—
128C23×C11#12412yes—
129C23×C11C2×SD1612yes—
130C23×C11C2×Q1612yes—
131C23×C11#13712yes—
132C23×C11#13712yes—
133C23×C11C22×D411yescharacteristic
134Q8×C11—28no—
135Q8×C11—28no—
136Q8×C11—44no—
137Q8×C11—44no—
138Q8×C11—416no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—28no—
144C2×C4×C11—28no—
145C2×C4×C11—28no—
146C2×C4×C11—24no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—416no—
152C2×C4×C11—48no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—84no—
157C2×C4×C11#12012yes—
158C2×C4×C11#12118yes—
159C2×C4×C11#12112yes—
160C2×C4×C11#12318yes—
161C2×C4×C11#12412yes—
162C2×C4×C11C2×SD1614yes—
163C2×C4×C11C2×Q1614yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D412yes—
166C2×C4×C11C2×#4112yes—
167C2×C4×C11C2×#4111yescharacteristic
168C8×C11—44no—
169C23×Q8C22×C1112yes—
170C23×C8C22×C1112yes—
171C2×C4⋊Q8—28no—
172C2×C4⋊Q8—22no—
173C2×C4⋊Q8C22×C1114yes—
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4—21no—
177C22×C4⋊C4C22×C1111yescharacteristic
178C22×C4⋊C4C22×C1111yescharacteristic
179C22×C42C22×C1111yescharacteristic
180C2×#103—28no—
181C2×#103—28no—
182C2×#103C22×C1118yes—
183C2×#103C22×C1118yes—
184#389—22no—
185#389C22×C1114yes—
186C2×#95—21no—
187#336C22×C1114yes—
188C22×C11#39414yes—
189C22×C11#44814yes—
190C22×C11#45114yes—
191C22×C11#46114yes—
192C22×C11#46214yes—
193C22×C11#48714yes—
194C22×C11#49114yes—
195C22×C11C2×#12011yescharacteristic
196C22×C11C2×#12111yescharacteristic
197C22×C11C2×#12411yescharacteristic
198C22×C11C22×SD1611yescharacteristic
199C22×C11C22×Q1611yescharacteristic
200C22×C11C2×#13711yescharacteristic
201C22×C11C2×#13711yescharacteristic
202C4×C11—24no—
203C4×C11—24no—
204C4×C11—48no—
205C4×C11—44no—
206C4×C11—82no—
207C4×C11#39414yes—
208C4×C11C2×#12112yes—
209C4×C11C2×#12312yes—
210C22×Q8—24no—
211C22×Q8—22no—
212C22×Q8—24no—
213C22×Q8—24no—
214C22×Q8—24no—
215C22×Q8—24no—
216C22×Q8D4×C1118yes—
217C22×Q8C23×C1114yes—
218C23×C4—22no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4D4×C1111yescharacteristic
222C23×C4D4×C1111yescharacteristic
223C23×C4C23×C1111yescharacteristic
224C22×C8—24no—
225C22×C8—24no—
226C22×C8—24no—
227C22×C8C23×C1114yes—
228C4⋊Q8—216no—
229C4⋊Q8—216no—
230C2×C4⋊C4—28no—
231C2×C4⋊C4—28no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—44no—
240C2×C4⋊C4D4×C1114yes—
241C2×C4⋊C4C23×C1112yes—
242C2×C4⋊C4C23×C1112yes—
243C2×C42—24no—
244C2×C42D4×C1112yes—
245C2×C42C23×C1112yes—
246#103—216no—
247#103—216no—
248#95—24no—
249C2×C11#204318yesdirect product factor
250C2×C11C2×#39411yescharacteristic
251C2×C11C2×#44811yescharacteristic
252C2×C11C2×#45111yescharacteristic
253C2×C11C2×#46111yescharacteristic
254C2×C11C2×#46211yescharacteristic
255C2×C11C2×#48711yescharacteristic
256C2×C11C2×#49111yescharacteristic
257C24C2×D4×C1111yescharacteristic
258C2×Q8—28no—
259C2×Q8—24no—
260C2×Q8—216no—
261C2×Q8—216no—
262C2×Q8—24no—
263C2×Q8—24no—
264C2×Q8—24no—
265C2×Q8—24no—
266C2×Q8—44no—
267C2×Q8—48no—
268C2×Q8—48no—
269C2×Q8—44no—
270C2×Q8C2×D4×C1118yes—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—44no—
281C22×C4—44no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4C11×SD1614yes—
288C22×C4C11×Q1614yes—
289C22×C4C2×D4×C1112yes—
290C22×C4C2×D4×C1112yes—
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C2×D4×C1114yes—
293C22×C4C2×D4×C1112yes—
294C22×C4C11×#4114yes—
295C22×C4C11×#4112yes—
296C22×C4C24×C1111yescharacteristic
297C2×C8—24no—
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—48no—
301C4⋊C4—216no—
302C4⋊C4—216no—
303C4⋊C4—24no—
304C4⋊C4—22no—
305C4⋊C4—24no—
306C4⋊C4—42no—
307C4⋊C4—48no—
308C4⋊C4C2×D4×C1114yes—
309C42—24no—
310C42—24no—
311C11C2×#204311yescharacteristic, direct product factor, Sylow
312C23C11×#12012yes—
313C23C11×#12112yes—
314C23C11×#12412yes—
315C23C2×C11×SD1612yes—
316C23C2×C11×Q1612yes—
317C23C11×#13712yes—
318C23C11×#13712yes—
319C23C22×D4×C1111yescharacteristic
320Q8—28no—
321Q8—28no—
322Q8—44no—
323Q8—44no—
324Q8—416no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—416no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—48no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—84no—
343C2×C4C11×#12012yes—
344C2×C4C11×#12118yes—
345C2×C4C11×#12112yes—
346C2×C4C11×#12318yes—
347C2×C4C11×#12412yes—
348C2×C4C2×C11×SD1614yes—
349C2×C4C2×C11×Q1614yes—
350C2×C4C22×D4×C1111yescharacteristic
351C2×C4C22×D4×C1112yes—
352C2×C4C2×C11×#4112yes—
353C2×C4C2×C11×#4111yescharacteristic
354C8—44no—
355C22C11×#39414yes—
356C22C11×#44814yes—
357C22C11×#45114yes—
358C22C11×#46114yes—
359C22C11×#46214yes—
360C22C11×#48714yes—
361C22C11×#49114yes—
362C22C2×C11×#12011yescharacteristic
363C22C2×C11×#12111yescharacteristic
364C22C2×C11×#12411yescharacteristic
365C22C22×C11×SD1611yescharacteristic
366C22C22×C11×Q1611yescharacteristic
367C22C2×C11×#13711yescharacteristic
368C22C2×C11×#13711yescharacteristic
369C4—24no—
370C4—24no—
371C4—48no—
372C4—44no—
373C4—82no—
374C4C11×#39414yes—
375C4C2×C11×#12112yes—
376C4C2×C11×#12312yes—
377C2C11×#204318yesdirect product factor
378C2C2×C11×#39411yescharacteristic
379C2C2×C11×#44811yescharacteristic
380C2C2×C11×#45111yescharacteristic
381C2C2×C11×#46111yescharacteristic
382C2C2×C11×#46211yescharacteristic
383C2C2×C11×#48711yescharacteristic
384C2C2×C11×#49111yescharacteristic
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
5. C11×#2043C2direct (N × H)
65. C2×#2043C11direct (N × H)
124. #2043C2×C11direct (N × H)
249. C2×C11#2043direct (N × H)
311. C11C2×#2043direct (N × H)
377. C2C11×#2043direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C22×C11×#1032
C2×C11×#3892
C11×#20432
C2×C11×#3362
C2×#204311