Finite Group Databasebeta

← C2×C11×#2028 #14600653

Subgroups — C2×C11×#2028 #14600653

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic
2C2×C11×#419C212yesmaximal
3C2×C11×#391C211yesmaximal, characteristic
4C11×#2028C218yesmaximal, direct product factor
5C2×C11×#343C211yesmaximal, characteristic
6C2×C11×#339C212yesmaximal
7C23×Q8×C11C2211yescharacteristic
8C22×C11×M16C2212yes—
9C11×#544—24no—
10C11×#544—22no—
11C11×#544C2214yes—
12C2×C11×C4⋊Q8—22no—
13C2×C11×#125—22no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×#117C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#419—24no—
19C11×#419C2218yes—
20C2×C11×#103—22no—
21C2×C11×#103—22no—
22C11×#391—22no—
23C11×#391C2214yes—
24C2×C11×#95—22no—
25C11×#343C2214yes—
26C11×#339C2218yes—
27C22×Q8×C11—22no—
28C22×Q8×C11—21no—
29C22×Q8×C11—22no—
30C22×Q8×C11—22no—
31C22×Q8×C11—22no—
32C22×Q8×C11—24no—
33C22×Q8×C11Q814yescomplemented
34C22×Q8×C11C2312yes—
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D412yes—
38C23×C4×C11C2311yescharacteristic
39C2×C11×M16—22no—
40C2×C11×M16—24no—
41C2×C11×M16—24no—
42C2×C11×M16C2314yes—
43C22×C8×C11—22no—
44C11×C4⋊Q8—28no—
45C11×C4⋊Q8—28no—
46C11×#125—28no—
47C11×#125—28no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8—28no—
50C11×#117—22no—
51C11×#117—22no—
52C11×#117D414yes—
53C11×#117C2314yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4D412yes—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—22no—
64C2×C42×C11—24no—
65C2×C42×C11—21no—
66C2×C42×C11C2312yes—
67C11×#103—28no—
68C11×#103—28no—
69C11×#95—28no—
70C2×#2028C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—28no—
73C2×Q8×C11—24no—
74C2×Q8×C11—22no—
75C2×Q8×C11—28no—
76C2×Q8×C11—28no—
77C2×Q8×C11—24no—
78C2×Q8×C11—24no—
79C2×Q8×C11—42no—
80C2×Q8×C11—42no—
81C2×Q8×C11—44no—
82C2×Q8×C11—44no—
83C2×Q8×C11—84no—
84C2×Q8×C11C2×Q814yescomplemented
85C22×C4×C11—24no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—42no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—44no—
99C22×C4×C11C2×D414yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11#4114yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C11×M16—24no—
108C11×M16—24no—
109C11×M16—44no—
110C2×C8×C11—24no—
111C2×C8×C11—44no—
112C11×C4⋊C4—28no—
113C11×C4⋊C4—216no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4C2×D414yes—
119C11×C4⋊C4C2×D414yes—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C42×C11—24no—
123C42×C11—24no—
124C42×C11—24no—
125C42×C11—42no—
126C2×#544C2×C1111yescharacteristic
127C2×#419C2×C1112yes—
128C2×#391C2×C1111yescharacteristic
129#2028C2×C1118yesdirect product factor
130C2×#343C2×C1111yescharacteristic
131C2×#339C2×C1112yes—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11#12011yescharacteristic
135C23×C11#12011yescharacteristic
136C23×C11C22⋊Q812yes—
137C23×C11#12412yes—
138C23×C11C22×D411yescharacteristic
139Q8×C11—28no—
140Q8×C11—44no—
141Q8×C11—48no—
142Q8×C11—88no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—42no—
149C2×C4×C11—48no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—44no—
159C2×C4×C11—82no—
160C2×C4×C11#12012yes—
161C2×C4×C11C22⋊Q814yes—
162C2×C4×C11C22⋊Q814yes—
163C2×C4×C11C22⋊Q812yes—
164C2×C4×C11#12414yes—
165C2×C4×C11#12414yes—
166C2×C4×C11#12412yes—
167C2×C4×C11C22×D412yes—
168C2×C4×C11C22×Q811yescharacteristic
169C2×C4×C11C2×#4112yes—
170C2×C4×C11C2×#4111yescharacteristic
171C8×C11—44no—
172C23×Q8C22×C1111yescharacteristic
173C22×M16C22×C1112yes—
174#544—24no—
175#544—22no—
176#544C22×C1114yes—
177C2×C4⋊Q8—22no—
178C2×#125—22no—
179C2×C22⋊Q8—22no—
180C2×#117C22×C1112yes—
181C22×C4⋊C4C22×C1111yescharacteristic
182C22×C42C22×C1111yescharacteristic
183#419—24no—
184#419C22×C1118yes—
185C2×#103—22no—
186C2×#103—22no—
187#391—22no—
188#391C22×C1114yes—
189C2×#95—22no—
190#343C22×C1114yes—
191#339C22×C1118yes—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—24no—
197C22×C11—24no—
198C22×C11#39312yes—
199C22×C11#39312yes—
200C22×C11#45512yes—
201C22×C11#45612yes—
202C22×C11C2×#12011yescharacteristic
203C22×C11C2×C22⋊Q811yescharacteristic
204C22×C11C2×#12411yescharacteristic
205C4×C11—44no—
206C4×C11—44no—
207C4×C11—44no—
208C4×C11—44no—
209C4×C11—44no—
210C4×C11#39314yes—
211C4×C11C2×C22⋊Q812yes—
212C4×C11C2×#12412yes—
213C22×Q8—22no—
214C22×Q8—21no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—24no—
219C22×Q8Q8×C1114yescomplemented
220C22×Q8C23×C1112yes—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4D4×C1112yes—
224C23×C4C23×C1111yescharacteristic
225C2×M16—22no—
226C2×M16—24no—
227C2×M16—24no—
228C2×M16C23×C1114yes—
229C22×C8—22no—
230C4⋊Q8—28no—
231C4⋊Q8—28no—
232#125—28no—
233#125—28no—
234C22⋊Q8—28no—
235C22⋊Q8—28no—
236#117—22no—
237#117—22no—
238#117D4×C1114yes—
239#117C23×C1114yes—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4D4×C1112yes—
245C2×C4⋊C4D4×C1112yes—
246C2×C4⋊C4D4×C1112yes—
247C2×C4⋊C4C23×C1112yes—
248C2×C22⋊C4—22no—
249C2×C42—22no—
250C2×C42—24no—
251C2×C42—21no—
252C2×C42C23×C1112yes—
253#103—28no—
254#103—28no—
255#95—28no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—22no—
259C2×C11#202814yesdirect product factor
260C2×C11C2×#39311yescharacteristic
261C2×C11C2×#45511yescharacteristic
262C2×C11C2×#45611yescharacteristic
263C24C2×D4×C1111yescharacteristic
264C2×Q8—28no—
265C2×Q8—24no—
266C2×Q8—22no—
267C2×Q8—28no—
268C2×Q8—28no—
269C2×Q8—24no—
270C2×Q8—24no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—44no—
274C2×Q8—44no—
275C2×Q8—84no—
276C2×Q8C2×Q8×C1114yescomplemented
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—44no—
291C22×C4C2×D4×C1114yes—
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1112yes—
294C22×C4C2×D4×C1112yes—
295C22×C4C2×Q8×C1112yes—
296C22×C4C11×#4114yes—
297C22×C4C11×#4112yes—
298C22×C4C24×C1111yescharacteristic
299M16—24no—
300M16—24no—
301M16—44no—
302C2×C8—24no—
303C2×C8—44no—
304C4⋊C4—28no—
305C4⋊C4—216no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—24no—
310C4⋊C4C2×D4×C1114yes—
311C4⋊C4C2×D4×C1114yes—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C42—24no—
315C42—24no—
316C42—24no—
317C42—42no—
318C11C2×#202811yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—22no—
321C23C11×#12011yescharacteristic
322C23C11×#12011yescharacteristic
323C23C11×C22⋊Q812yes—
324C23C11×#12412yes—
325C23C22×D4×C1111yescharacteristic
326Q8—28no—
327Q8—44no—
328Q8—48no—
329Q8—88no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—42no—
336C2×C4—48no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—82no—
347C2×C4C11×#12012yes—
348C2×C4C11×C22⋊Q814yes—
349C2×C4C11×C22⋊Q814yes—
350C2×C4C11×C22⋊Q812yes—
351C2×C4C11×#12414yes—
352C2×C4C11×#12414yes—
353C2×C4C11×#12412yes—
354C2×C4C22×D4×C1112yes—
355C2×C4C22×Q8×C1111yescharacteristic
356C2×C4C2×C11×#4112yes—
357C2×C4C2×C11×#4111yescharacteristic
358C8—44no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—24no—
365C22C11×#39312yes—
366C22C11×#39312yes—
367C22C11×#45512yes—
368C22C11×#45612yes—
369C22C2×C11×#12011yescharacteristic
370C22C2×C11×C22⋊Q811yescharacteristic
371C22C2×C11×#12411yescharacteristic
372C4—44no—
373C4—44no—
374C4—44no—
375C4—44no—
376C4—44no—
377C4C11×#39314yes—
378C4C2×C11×C22⋊Q812yes—
379C4C2×C11×#12412yes—
380C2—21no—
381C2—21no—
382C2—22no—
383C2C11×#202814yesdirect product factor
384C2C2×C11×#39311yescharacteristic
385C2C2×C11×#45511yescharacteristic
386C2C2×C11×#45611yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
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
4. C11×#2028C2direct (N × H)
33. C22×Q8×C11Q8semidirect
70. C2×#2028C11direct (N × H)
84. C2×Q8×C11C2×Q8semidirect
129. #2028C2×C11direct (N × H)
219. C22×Q8Q8×C11semidirect
259. C2×C11#2028direct (N × H)
276. C2×Q8C2×Q8×C11semidirect
318. C11C2×#2028direct (N × H)
383. C2C11×#2028direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#4192
C2×C11×#3912
C11×#20282
C2×C11×#3432
C2×C11×#3392
C2×#202811