Finite Group Databasebeta

← C2×C11×#2134 #14610560

Subgroups — C2×C11×#2134 #14610560

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#413C212yesmaximal, complemented
3C11×#2134C218yesmaximal, direct product factor
4C2×C11×#355C214yesmaximal, complemented
5C22×C11×#41C2211yescharacteristic
6C23×D4×C11C411yescharacteristic
7C22×C11×M16—22no—
8C11×#535—24no—
9C11×#535C414yes—
10C11×#535C2214yes—
11C2×C11×#127C412yes—
12C2×C11×#124C2212yes—
13C2×C11×#121—22no—
14C2×C11×#120—22no—
15C2×C11×#117C411yescharacteristic
16C11×#413—24no—
17C11×#413C2218yescomplemented
18C2×C11×#101C2214yescomplemented
19C2×C11×#100—22no—
20C11×#355C22116yescomplemented
21C25×C11—21no—
22C2×C11×#41—42no—
23C2×C11×#41—42no—
24C2×C11×#41C2×C412yes—
25C2×C11×#41D414yes—
26C2×C11×#41C2312yes—
27C22×Q8×C11C2311yescharacteristic
28C22×D4×C11—24no—
29C22×D4×C11—22no—
30C22×D4×C11—21no—
31C22×D4×C11—42no—
32C22×D4×C11—42no—
33C22×D4×C11C2×C412yes—
34C22×D4×C11C2×C414yes—
35C22×D4×C11C2×C411yescharacteristic
36C22×D4×C11D412yes—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11D412yes—
39C2×C11×M16—24no—
40C2×C11×M16—28no—
41C2×C11×M16—42no—
42C2×C11×M16—44no—
43C22×C8×C11—42no—
44C11×#127—24no—
45C11×#127C2×C418yes—
46C11×#124—24no—
47C11×#124C2×C414yes—
48C11×#124C2314yes—
49C11×#121—28no—
50C11×#121—28no—
51C11×#120—28no—
52C11×#120—28no—
53C11×#117—22no—
54C11×#117C2×C414yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—24no—
58C2×C42×C11C2×C412yes—
59C11×#101—24no—
60C11×#101C2318yescomplemented
61C11×#100—28no—
62C2×#2134C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11—22no—
64C24×C11—24no—
65C24×C11—42no—
66C24×C11—42no—
67C24×C11—84no—
68C24×C11C22⋊C411yescharacteristic
69C24×C11C22⋊C412yes—
70C11×#41—44no—
71C11×#41—44no—
72C11×#41—44no—
73C11×#41—44no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11C22×C411yescharacteristic
77C2×Q8×C11C2×D412yes—
78C2×Q8×C11C2411yescharacteristic
79C2×D4×C11—216no—
80C2×D4×C11—24no—
81C2×D4×C11—22no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—48no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—48no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—88no—
93C2×D4×C11C22⋊C414yes—
94C2×D4×C11C22⋊C412yes—
95C2×D4×C11C22×C414yes—
96C2×D4×C11C22×C412yes—
97C2×D4×C11C2×D414yes—
98C22×C4×C11—22no—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C22⋊C412yes—
105C22×C4×C11C22⋊C414yes—
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D414yes—
111C11×M16—28no—
112C11×M16—44no—
113C11×M16—48no—
114C2×C8×C11—44no—
115C2×C8×C11—48no—
116C11×C4⋊C4—24no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—28no—
120C42×C11—22no—
121C42×C11C22×C414yes—
122C2×#535C2×C1111yescharacteristic
123C2×#413C2×C1112yescomplemented
124#2134C2×C1118yesdirect product factor
125C2×#355C2×C1114yescomplemented
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—24no—
131C23×C11—42no—
132C23×C11—44no—
133C23×C11—48no—
134C23×C11—48no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—88no—
138C23×C11—88no—
139C23×C11—88no—
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11C2×C22⋊C412yes—
142C23×C11C2×C22⋊C414yes—
143Q8×C11—41no—
144Q8×C11—42no—
145Q8×C11—41no—
146D4×C11—42no—
147D4×C11—44no—
148D4×C11—42no—
149D4×C11—44no—
150D4×C11—44no—
151D4×C11—44no—
152D4×C11—48no—
153D4×C11—816no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—44no—
166C2×C4×C11#9912yes—
167C2×C4×C11#9912yes—
168C2×C4×C11C2×C22⋊C411yescharacteristic
169C2×C4×C11C2×C22⋊C412yes—
170C2×C4×C11C2×C22⋊C412yes—
171C2×C4×C11C23×C411yescharacteristic
172C2×C4×C11C22×D412yes—
173C8×C11—48no—
174C22×#41C22×C1111yescharacteristic
175C23×D4C4×C1111yescharacteristic
176C22×M16—22no—
177#535—24no—
178#535C4×C1114yes—
179#535C22×C1114yes—
180C2×#127C4×C1112yes—
181C2×#124C22×C1112yes—
182C2×#121—22no—
183C2×#120—22no—
184C2×#117C4×C1111yescharacteristic
185#413—24no—
186#413C22×C1118yescomplemented
187C2×#101C22×C1114yescomplemented
188C2×#100—22no—
189#355C22×C11116yescomplemented
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—24no—
193C22×C11—44no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—48no—
197C22×C11—44no—
198C22×C11—42no—
199C22×C11—44no—
200C22×C11—82no—
201C22×C11—84no—
202C22×C11—816no—
203C22×C11—84no—
204C22×C11C2×#9911yescharacteristic
205C22×C11C2×#9911yescharacteristic
206C22×C11C22×C22⋊C411yescharacteristic
207C4×C11—21no—
208C4×C11—22no—
209C4×C11—21no—
210C4×C11—22no—
211C4×C11—44no—
212C4×C11C2×#9914yes—
213C25—21no—
214C2×#41—42no—
215C2×#41—42no—
216C2×#41C2×C4×C1112yes—
217C2×#41D4×C1114yes—
218C2×#41C23×C1112yes—
219C22×Q8C23×C1111yescharacteristic
220C22×D4—24no—
221C22×D4—21no—
222C22×D4—22no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4C2×C4×C1112yes—
226C22×D4C2×C4×C1114yes—
227C22×D4C2×C4×C1111yescharacteristic
228C22×D4D4×C1112yes—
229C23×C4C2×C4×C1111yescharacteristic
230C23×C4D4×C1112yes—
231C2×M16—24no—
232C2×M16—28no—
233C2×M16—42no—
234C2×M16—44no—
235C22×C8—42no—
236#127—24no—
237#127C2×C4×C1118yes—
238#124—24no—
239#124C2×C4×C1114yes—
240#124C23×C1114yes—
241#121—28no—
242#121—28no—
243#120—28no—
244#120—28no—
245#117—22no—
246#117C2×C4×C1114yes—
247C2×C4⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—24no—
250C2×C42C2×C4×C1112yes—
251#101—24no—
252#101C23×C1118yescomplemented
253#100—28no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11—42no—
257C2×C11—44no—
258C2×C11—84no—
259C2×C11#213412yesdirect product factor
260C2×C11C22×#9911yescharacteristic
261C24—22no—
262C24—24no—
263C24—42no—
264C24—42no—
265C24—84no—
266C24C11×C22⋊C411yescharacteristic
267C24C11×C22⋊C412yes—
268#41—44no—
269#41—44no—
270#41—44no—
271#41—44no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8C22×C4×C1111yescharacteristic
275C2×Q8C2×D4×C1112yes—
276C2×Q8C24×C1111yescharacteristic
277C2×D4—216no—
278C2×D4—24no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—48no—
287C2×D4—48no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—88no—
291C2×D4C11×C22⋊C414yes—
292C2×D4C11×C22⋊C412yes—
293C2×D4C22×C4×C1114yes—
294C2×D4C22×C4×C1112yes—
295C2×D4C2×D4×C1114yes—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4C11×C22⋊C412yes—
303C22×C4C11×C22⋊C414yes—
304C22×C4C11×C22⋊C411yescharacteristic
305C22×C4C22×C4×C1111yescharacteristic
306C22×C4C22×C4×C1112yes—
307C22×C4C2×D4×C1112yes—
308C22×C4C2×D4×C1114yes—
309M16—28no—
310M16—44no—
311M16—48no—
312C2×C8—44no—
313C2×C8—48no—
314C4⋊C4—24no—
315C22⋊C4—24no—
316C22⋊C4—28no—
317C22⋊C4—28no—
318C42—22no—
319C42C22×C4×C1114yes—
320C11C2×#213411yescharacteristic, direct product factor, Sylow
321C23—21no—
322C23—21no—
323C23—22no—
324C23—22no—
325C23—24no—
326C23—42no—
327C23—44no—
328C23—48no—
329C23—48no—
330C23—42no—
331C23—42no—
332C23—88no—
333C23—88no—
334C23—88no—
335C23C2×C11×C22⋊C411yescharacteristic
336C23C2×C11×C22⋊C412yes—
337C23C2×C11×C22⋊C414yes—
338Q8—41no—
339Q8—42no—
340Q8—41no—
341D4—42no—
342D4—44no—
343D4—42no—
344D4—44no—
345D4—44no—
346D4—44no—
347D4—48no—
348D4—816no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—44no—
361C2×C4C11×#9912yes—
362C2×C4C11×#9912yes—
363C2×C4C2×C11×C22⋊C411yescharacteristic
364C2×C4C2×C11×C22⋊C412yes—
365C2×C4C2×C11×C22⋊C412yes—
366C2×C4C23×C4×C1111yescharacteristic
367C2×C4C22×D4×C1112yes—
368C8—48no—
369C22—22no—
370C22—22no—
371C22—24no—
372C22—44no—
373C22—42no—
374C22—42no—
375C22—48no—
376C22—42no—
377C22—44no—
378C22—44no—
379C22—82no—
380C22—84no—
381C22—816no—
382C22—84no—
383C22C2×C11×#9911yescharacteristic
384C22C2×C11×#9911yescharacteristic
385C22C22×C11×C22⋊C411yescharacteristic
386C4—22no—
387C4—21no—
388C4—22no—
389C4—21no—
390C4—44no—
391C4C2×C11×#9914yes—
392C2—21no—
393C2—21no—
394C2—42no—
395C2—44no—
396C2—84no—
397C2C11×#213412yesdirect product factor
398C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×Q8C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#413C2semidirect
3. C11×#2134C2direct (N × H)
4. C2×C11×#355C2semidirect
17. C11×#413C22semidirect
18. C2×C11×#101C22semidirect
20. C11×#355C22semidirect
60. C11×#101C23semidirect
62. C2×#2134C11direct (N × H)
123. C2×#413C2×C11semidirect
124. #2134C2×C11direct (N × H)
125. C2×#355C2×C11semidirect
186. #413C22×C11semidirect
187. C2×#101C22×C11semidirect
189. #355C22×C11semidirect
252. #101C23×C11semidirect
259. C2×C11#2134direct (N × H)
320. C11C2×#2134direct (N × H)
397. C2C11×#2134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4132
C11×#21342
C2×C11×#3552
C2×#213411