Finite Group Databasebeta

← C2×C11×#2027 #14600652

Subgroups — C2×C11×#2027 #14600652

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C2×C11×#418C212yesmaximal
3C2×C11×#390C211yesmaximal, characteristic
4C11×#2027C218yesmaximal, direct product factor
5C2×C11×#343C211yesmaximal, characteristic, complemented
6C2×C11×#339C212yesmaximal, complemented
7C23×D4×C11C2211yescharacteristic
8C22×C11×M16C2212yes—
9C11×#544—24no—
10C11×#544—22no—
11C11×#544C2214yescomplemented
12C2×C11×C4⋊Q8—22no—
13C2×C11×#125—22no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×#117C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4—22no—
18C22×C42×C11C2211yescharacteristic
19C11×#418—24no—
20C11×#418C2218yes—
21C2×C11×#102—22no—
22C2×C11×#102—22no—
23C11×#390—22no—
24C11×#390C2214yes—
25C11×#343C2214yescomplemented
26C11×#339C2218yescomplemented
27C25×C11—21no—
28C22×Q8×C11—22no—
29C22×D4×C11—22no—
30C22×D4×C11—22no—
31C22×D4×C11—21no—
32C22×D4×C11—24no—
33C22×D4×C11—22no—
34C22×D4×C11Q814yescomplemented
35C22×D4×C11C2312yes—
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×C11×C22⋊C4—28no—
64C2×C11×C22⋊C4—48no—
65C2×C42×C11—22no—
66C2×C42×C11—24no—
67C2×C42×C11—21no—
68C2×C42×C11C2312yes—
69C11×#102—28no—
70C11×#102—28no—
71C2×#2027C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—24no—
73C24×C11—22no—
74C24×C11—44no—
75C24×C11—44no—
76C24×C11—41no—
77C24×C11—41no—
78C24×C11—42no—
79C24×C11C2×D411yescharacteristic
80C2×Q8×C11—28no—
81C2×Q8×C11—84no—
82C2×D4×C11—28no—
83C2×D4×C11—28no—
84C2×D4×C11—24no—
85C2×D4×C11—24no—
86C2×D4×C11—24no—
87C2×D4×C11—22no—
88C2×D4×C11—42no—
89C2×D4×C11—44no—
90C2×D4×C11—44no—
91C2×D4×C11—42no—
92C2×D4×C11C2×Q814yescomplemented
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—44no—
102C22×C4×C11C2×D414yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4114yes—
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C11×M16—24no—
111C11×M16—24no—
112C11×M16—44no—
113C2×C8×C11—24no—
114C2×C8×C11—44no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—216no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4C2×D414yes—
122C11×C4⋊C4C2×D414yes—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—416no—
126C42×C11—24no—
127C42×C11—24no—
128C42×C11—24no—
129C42×C11—42no—
130C2×#544C2×C1111yescharacteristic, complemented
131C2×#418C2×C1112yes—
132C2×#390C2×C1111yescharacteristic
133#2027C2×C1118yesdirect product factor
134C2×#343C2×C1111yescharacteristic, complemented
135C2×#339C2×C1112yescomplemented
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—24no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—416no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—44no—
145C23×C11—44no—
146C23×C11—82no—
147C23×C11—82no—
148C23×C11—88no—
149C23×C11—82no—
150C23×C11—82no—
151C23×C11#12011yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11C22⋊Q812yes—
154C23×C11#12412yes—
155C23×C11C22×D411yescharacteristic
156Q8×C11—88no—
157D4×C11—28no—
158D4×C11—44no—
159D4×C11—48no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—42no—
165C2×C4×C11—48no—
166C2×C4×C11—42no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—44no—
170C2×C4×C11—44no—
171C2×C4×C11—82no—
172C2×C4×C11#12012yes—
173C2×C4×C11C22⋊Q814yes—
174C2×C4×C11C22⋊Q814yes—
175C2×C4×C11C22⋊Q812yes—
176C2×C4×C11#12414yes—
177C2×C4×C11#12414yes—
178C2×C4×C11#12412yes—
179C2×C4×C11C22×D412yes—
180C2×C4×C11C22×Q811yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×C4×C11C2×#4111yescharacteristic
183C8×C11—44no—
184C23×D4C22×C1111yescharacteristic
185C22×M16C22×C1112yes—
186#544—24no—
187#544—22no—
188#544C22×C1114yescomplemented
189C2×C4⋊Q8—22no—
190C2×#125—22no—
191C2×C22⋊Q8—22no—
192C2×#117C22×C1112yes—
193C22×C4⋊C4C22×C1111yescharacteristic
194C22×C22⋊C4—22no—
195C22×C42C22×C1111yescharacteristic
196#418—24no—
197#418C22×C1118yes—
198C2×#102—22no—
199C2×#102—22no—
200#390—22no—
201#390C22×C1114yes—
202#343C22×C1114yescomplemented
203#339C22×C1118yescomplemented
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—24no—
209C22×C11—24no—
210C22×C11—48no—
211C22×C11—44no—
212C22×C11—84no—
213C22×C11—88no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—88no—
217C22×C11#39312yes—
218C22×C11#39312yes—
219C22×C11#45312yes—
220C22×C11#45412yes—
221C22×C11C2×#12011yescharacteristic
222C22×C11C2×C22⋊Q811yescharacteristic
223C22×C11C2×#12411yescharacteristic
224C4×C11—44no—
225C4×C11—44no—
226C4×C11—44no—
227C4×C11—44no—
228C4×C11#39314yes—
229C4×C11C2×C22⋊Q812yes—
230C4×C11C2×#12412yes—
231C25—21no—
232C22×Q8—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—21no—
236C22×D4—24no—
237C22×D4—22no—
238C22×D4Q8×C1114yescomplemented
239C22×D4C23×C1112yes—
240C23×C4—21no—
241C23×C4D4×C1112yes—
242C23×C4C23×C1111yescharacteristic
243C2×M16—22no—
244C2×M16—24no—
245C2×M16—24no—
246C2×M16C23×C1114yes—
247C22×C8—22no—
248C4⋊Q8—28no—
249C4⋊Q8—28no—
250#125—28no—
251#125—28no—
252C22⋊Q8—28no—
253C22⋊Q8—28no—
254#117—22no—
255#117—22no—
256#117D4×C1114yes—
257#117C23×C1114yes—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4D4×C1112yes—
263C2×C4⋊C4D4×C1112yes—
264C2×C4⋊C4D4×C1112yes—
265C2×C4⋊C4C23×C1112yes—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—28no—
268C2×C22⋊C4—48no—
269C2×C42—22no—
270C2×C42—24no—
271C2×C42—21no—
272C2×C42C23×C1112yes—
273#102—28no—
274#102—28no—
275C2×C11—21no—
276C2×C11—21no—
277C2×C11—22no—
278C2×C11—84no—
279C2×C11#202714yesdirect product factor
280C2×C11C2×#39311yescharacteristic
281C2×C11C2×#45311yescharacteristic
282C2×C11C2×#45411yescharacteristic
283C24—24no—
284C24—22no—
285C24—44no—
286C24—44no—
287C24—41no—
288C24—41no—
289C24—42no—
290C24C2×D4×C1111yescharacteristic
291C2×Q8—28no—
292C2×Q8—84no—
293C2×D4—28no—
294C2×D4—28no—
295C2×D4—24no—
296C2×D4—24no—
297C2×D4—24no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—44no—
301C2×D4—44no—
302C2×D4—42no—
303C2×D4C2×Q8×C1114yescomplemented
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—44no—
313C22×C4C2×D4×C1114yes—
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×D4×C1112yes—
316C22×C4C2×D4×C1112yes—
317C22×C4C2×Q8×C1112yes—
318C22×C4C11×#4114yes—
319C22×C4C11×#4112yes—
320C22×C4C24×C1111yescharacteristic
321M16—24no—
322M16—24no—
323M16—44no—
324C2×C8—24no—
325C2×C8—44no—
326C4⋊C4—28no—
327C4⋊C4—216no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4C2×D4×C1114yes—
333C4⋊C4C2×D4×C1114yes—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—416no—
337C42—24no—
338C42—24no—
339C42—24no—
340C42—42no—
341C11C2×#202711yescharacteristic, direct product factor, Sylow
342C23—22no—
343C23—22no—
344C23—24no—
345C23—44no—
346C23—44no—
347C23—416no—
348C23—42no—
349C23—42no—
350C23—44no—
351C23—44no—
352C23—82no—
353C23—82no—
354C23—88no—
355C23—82no—
356C23—82no—
357C23C11×#12011yescharacteristic
358C23C11×#12011yescharacteristic
359C23C11×C22⋊Q812yes—
360C23C11×#12412yes—
361C23C22×D4×C1111yescharacteristic
362Q8—88no—
363D4—28no—
364D4—44no—
365D4—48no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—48no—
372C2×C4—42no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—82no—
378C2×C4C11×#12012yes—
379C2×C4C11×C22⋊Q814yes—
380C2×C4C11×C22⋊Q814yes—
381C2×C4C11×C22⋊Q812yes—
382C2×C4C11×#12414yes—
383C2×C4C11×#12414yes—
384C2×C4C11×#12412yes—
385C2×C4C22×D4×C1112yes—
386C2×C4C22×Q8×C1111yescharacteristic
387C2×C4C2×C11×#4112yes—
388C2×C4C2×C11×#4111yescharacteristic
389C8—44no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—24no—
395C22—24no—
396C22—48no—
397C22—44no—
398C22—84no—
399C22—88no—
400C22—82no—
401C22—82no—
402C22—88no—
403C22C11×#39312yes—
404C22C11×#39312yes—
405C22C11×#45312yes—
406C22C11×#45412yes—
407C22C2×C11×#12011yescharacteristic
408C22C2×C11×C22⋊Q811yescharacteristic
409C22C2×C11×#12411yescharacteristic
410C4—44no—
411C4—44no—
412C4—44no—
413C4—44no—
414C4C11×#39314yes—
415C4C2×C11×C22⋊Q812yes—
416C4C2×C11×#12412yes—
417C2—21no—
418C2—21no—
419C2—22no—
420C2—84no—
421C2C11×#202714yesdirect product factor
422C2C2×C11×#39311yescharacteristic
423C2C2×C11×#45311yescharacteristic
424C2C2×C11×#45411yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
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
1. C2×C11×#544C2semidirect
4. C11×#2027C2direct (N × H)
5. C2×C11×#343C2semidirect
6. C2×C11×#339C2semidirect
11. C11×#544C22semidirect
25. C11×#343C22semidirect
26. C11×#339C22semidirect
34. C22×D4×C11Q8semidirect
71. C2×#2027C11direct (N × H)
92. C2×D4×C11C2×Q8semidirect
130. C2×#544C2×C11semidirect
133. #2027C2×C11direct (N × H)
134. C2×#343C2×C11semidirect
135. C2×#339C2×C11semidirect
188. #544C22×C11semidirect
202. #343C22×C11semidirect
203. #339C22×C11semidirect
238. C22×D4Q8×C11semidirect
279. C2×C11#2027direct (N × H)
303. C2×D4C2×Q8×C11semidirect
341. C11C2×#2027direct (N × H)
421. C2C11×#2027direct (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×#4182
C2×C11×#3902
C11×#20272
C2×C11×#3432
C2×C11×#3392
C2×#202711