Finite Group Databasebeta

← C2×C11×#2132 #14610558

Subgroups — C2×C11×#2132 #14610558

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#413C212yesmaximal, complemented
3C11×#2132C218yesmaximal, direct product factor
4C2×C11×#356C212yesmaximal, complemented
5C2×C11×#355C212yesmaximal, complemented
6C22×C11×#41C411yescharacteristic
7C22×C11×#41C2211yescharacteristic
8C22×C11×M16—22no—
9C11×#532—24no—
10C11×#532C414yes—
11C11×#532C2214yes—
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C411yescharacteristic
14C2×C11×#124C411yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C11×#121—22no—
17C2×C4×D4×C11—22no—
18C22×C42×C11C411yescharacteristic
19C11×#413—24no—
20C11×#413C2218yescomplemented
21C2×C11×#101C2214yes—
22C2×C11×#100—22no—
23C11×#356C2218yescomplemented
24C11×#355C2218yescomplemented
25C2×C11×#41—22no—
26C2×C11×#41—41no—
27C2×C11×#41—42no—
28C2×C11×#41—41no—
29C2×C11×#41—42no—
30C2×C11×#41—41no—
31C2×C11×#41—41no—
32C2×C11×#41C2×C414yes—
33C2×C11×#41C2×C412yes—
34C2×C11×#41D414yes—
35C2×C11×#41C2312yes—
36C22×Q8×C11C2×C411yescharacteristic
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11—22no—
39C22×D4×C11—21no—
40C22×D4×C11C2×C411yescharacteristic
41C22×D4×C11C2×C411yescharacteristic
42C22×D4×C11D412yes—
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11D412yes—
47C2×C11×M16—24no—
48C2×C11×M16—28no—
49C2×C11×M16—42no—
50C2×C11×M16—44no—
51C22×C8×C11—42no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C412yes—
54C11×C4⋊Q8C2312yes—
55C11×#127—22no—
56C11×#127C2×C414yes—
57C11×#124—22no—
58C11×#124—22no—
59C11×#124C2×C414yes—
60C11×#124C2×C412yes—
61C11×#124C2312yes—
62C11×#121—28no—
63C11×#121—28no—
64C4×D4×C11—28no—
65C4×D4×C11—28no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C42×C11—22no—
70C2×C42×C11—21no—
71C2×C42×C11C2×C411yescharacteristic
72C2×C42×C11C2×C411yescharacteristic
73C2×C42×C11C2×C414yes—
74C11×#101—24no—
75C11×#101C2318yes—
76C11×#100—28no—
77C2×#2132C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C24×C11C22⋊C412yes—
80C24×C11C22⋊C411yescharacteristic
81C11×#41—42no—
82C11×#41—42no—
83C11×#41—44no—
84C11×#41—44no—
85C11×#41—42no—
86C11×#41—42no—
87C11×#41—44no—
88C11×#41—44no—
89C11×#41—44no—
90C11×#41—44no—
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11C22×C412yes—
97C2×Q8×C11C22×C411yescharacteristic
98C2×Q8×C11C2×D412yes—
99C2×Q8×C11C2411yescharacteristic
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11—48no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11C22⋊C414yes—
113C2×D4×C11C22⋊C412yes—
114C2×D4×C11C22×C412yes—
115C2×D4×C11C22×C412yes—
116C2×D4×C11C2×D414yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—24no—
126C22×C4×C11—21no—
127C22×C4×C11—24no—
128C22×C4×C11—44no—
129C22×C4×C11—42no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11C22⋊C412yes—
133C22×C4×C11C22⋊C414yes—
134C22×C4×C11C22⋊C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D414yes—
139C11×M16—28no—
140C11×M16—44no—
141C11×M16—48no—
142C2×C8×C11—44no—
143C2×C8×C11—48no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C22⋊C4—28no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—24no—
149C42×C11—24no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11C22×C412yes—
153C42×C11C22×C412yes—
154C2×#532C2×C1111yescharacteristic
155C2×#413C2×C1112yescomplemented
156#2132C2×C1118yesdirect product factor
157C2×#356C2×C1112yescomplemented
158C2×#355C2×C1112yescomplemented
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—42no—
165C23×C11—44no—
166C23×C11—44no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11C2×C22⋊C414yes—
171C23×C11C2×C22⋊C412yes—
172Q8×C11—41no—
173Q8×C11—42no—
174Q8×C11—41no—
175Q8×C11—42no—
176Q8×C11—42no—
177D4×C11—42no—
178D4×C11—44no—
179D4×C11—42no—
180D4×C11—44no—
181D4×C11—42no—
182D4×C11—416no—
183D4×C11—42no—
184D4×C11—48no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—48no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11#9911yescharacteristic
208C2×C4×C11#9912yes—
209C2×C4×C11#9911yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D412yes—
215C8×C11—48no—
216C22×#41C4×C1111yescharacteristic
217C22×#41C22×C1111yescharacteristic
218C22×M16—22no—
219#532—24no—
220#532C4×C1114yes—
221#532C22×C1114yes—
222C2×C4⋊Q8C22×C1111yescharacteristic
223C2×#127C4×C1111yescharacteristic
224C2×#124C4×C1111yescharacteristic
225C2×#124C22×C1111yescharacteristic
226C2×#121—22no—
227C2×C4×D4—22no—
228C22×C42C4×C1111yescharacteristic
229#413—24no—
230#413C22×C1118yescomplemented
231C2×#101C22×C1114yes—
232C2×#100—22no—
233#356C22×C1118yescomplemented
234#355C22×C1118yescomplemented
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—24no—
238C22×C11—42no—
239C22×C11—44no—
240C22×C11—42no—
241C22×C11—44no—
242C22×C11—42no—
243C22×C11—44no—
244C22×C11—42no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11C2×#9911yescharacteristic
249C22×C11C2×#9911yescharacteristic
250C22×C11C22×C22⋊C411yescharacteristic
251C4×C11—24no—
252C4×C11—21no—
253C4×C11—22no—
254C4×C11—21no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11C2×#9912yes—
259C4×C11C2×#9912yes—
260C2×#41—22no—
261C2×#41—41no—
262C2×#41—41no—
263C2×#41—42no—
264C2×#41—42no—
265C2×#41—41no—
266C2×#41—41no—
267C2×#41C2×C4×C1114yes—
268C2×#41C2×C4×C1112yes—
269C2×#41D4×C1114yes—
270C2×#41C23×C1112yes—
271C22×Q8C2×C4×C1111yescharacteristic
272C22×Q8C23×C1111yescharacteristic
273C22×D4—22no—
274C22×D4—21no—
275C22×D4C2×C4×C1111yescharacteristic
276C22×D4C2×C4×C1111yescharacteristic
277C22×D4D4×C1112yes—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4C2×C4×C1111yescharacteristic
281C23×C4D4×C1112yes—
282C2×M16—24no—
283C2×M16—28no—
284C2×M16—42no—
285C2×M16—44no—
286C22×C8—42no—
287C4⋊Q8—22no—
288C4⋊Q8C2×C4×C1112yes—
289C4⋊Q8C23×C1112yes—
290#127—22no—
291#127C2×C4×C1114yes—
292#124—22no—
293#124—22no—
294#124C2×C4×C1114yes—
295#124C2×C4×C1112yes—
296#124C23×C1112yes—
297#121—28no—
298#121—28no—
299C4×D4—28no—
300C4×D4—28no—
301C2×C4⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C42—21no—
305C2×C42—22no—
306C2×C42C2×C4×C1111yescharacteristic
307C2×C42C2×C4×C1111yescharacteristic
308C2×C42C2×C4×C1114yes—
309#101—24no—
310#101C23×C1118yes—
311#100—28no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—42no—
315C2×C11—44no—
316C2×C11—82no—
317C2×C11#213212yesdirect product factor
318C2×C11C22×#9911yescharacteristic
319C24—21no—
320C24C11×C22⋊C412yes—
321C24C11×C22⋊C411yescharacteristic
322#41—42no—
323#41—42no—
324#41—44no—
325#41—44no—
326#41—42no—
327#41—42no—
328#41—44no—
329#41—44no—
330#41—44no—
331#41—44no—
332C2×Q8—21no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8C22×C4×C1112yes—
338C2×Q8C22×C4×C1111yescharacteristic
339C2×Q8C2×D4×C1112yes—
340C2×Q8C24×C1111yescharacteristic
341C2×D4—28no—
342C2×D4—24no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—48no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4C11×C22⋊C414yes—
354C2×D4C11×C22⋊C412yes—
355C2×D4C22×C4×C1112yes—
356C2×D4C22×C4×C1112yes—
357C2×D4C2×D4×C1114yes—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—24no—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—44no—
370C22×C4—42no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4C11×C22⋊C412yes—
374C22×C4C11×C22⋊C414yes—
375C22×C4C11×C22⋊C411yescharacteristic
376C22×C4C22×C4×C1111yescharacteristic
377C22×C4C22×C4×C1112yes—
378C22×C4C2×D4×C1112yes—
379C22×C4C2×D4×C1114yes—
380M16—28no—
381M16—44no—
382M16—48no—
383C2×C8—44no—
384C2×C8—48no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C22⋊C4—28no—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C42—24no—
391C42—21no—
392C42—21no—
393C42C22×C4×C1112yes—
394C42C22×C4×C1112yes—
395C11C2×#213211yescharacteristic, direct product factor, Sylow
396C23—21no—
397C23—21no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—42no—
402C23—44no—
403C23—44no—
404C23—41no—
405C23—41no—
406C23C2×C11×C22⋊C411yescharacteristic
407C23C2×C11×C22⋊C414yes—
408C23C2×C11×C22⋊C412yes—
409Q8—41no—
410Q8—42no—
411Q8—41no—
412Q8—42no—
413Q8—42no—
414D4—42no—
415D4—44no—
416D4—42no—
417D4—44no—
418D4—42no—
419D4—416no—
420D4—42no—
421D4—48no—
422C2×C4—24no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—48no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4C11×#9912yes—
445C2×C4C11×#9911yescharacteristic
446C2×C4C11×#9911yescharacteristic
447C2×C4C2×C11×C22⋊C411yescharacteristic
448C2×C4C2×C11×C22⋊C412yes—
449C2×C4C2×C11×C22⋊C412yes—
450C2×C4C23×C4×C1111yescharacteristic
451C2×C4C22×D4×C1112yes—
452C8—48no—
453C22—22no—
454C22—22no—
455C22—24no—
456C22—42no—
457C22—44no—
458C22—42no—
459C22—44no—
460C22—42no—
461C22—44no—
462C22—42no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22C2×C11×#9911yescharacteristic
467C22C2×C11×#9911yescharacteristic
468C22C22×C11×C22⋊C411yescharacteristic
469C4—24no—
470C4—22no—
471C4—21no—
472C4—22no—
473C4—21no—
474C4—42no—
475C4—42no—
476C4C2×C11×#9912yes—
477C4C2×C11×#9912yes—
478C2—21no—
479C2—21no—
480C2—42no—
481C2—44no—
482C2—82no—
483C2C11×#213212yesdirect product factor
484C2C22×C11×#9911yescharacteristic
subgroupG/H
centerC2×C4×C11#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×Q8C24×C11
socleC22×C11C2×#99
prime radicalC2×C11×#532C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×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×#2132C2direct (N × H)
4. C2×C11×#356C2semidirect
5. C2×C11×#355C2semidirect
20. C11×#413C22semidirect
23. C11×#356C22semidirect
24. C11×#355C22semidirect
77. C2×#2132C11direct (N × H)
155. C2×#413C2×C11semidirect
156. #2132C2×C11direct (N × H)
157. C2×#356C2×C11semidirect
158. C2×#355C2×C11semidirect
230. #413C22×C11semidirect
233. #356C22×C11semidirect
234. #355C22×C11semidirect
317. C2×C11#2132direct (N × H)
395. C11C2×#2132direct (N × H)
483. C2C11×#2132direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4132
C11×#21322
C2×C11×#3562
C2×C11×#3552
C2×#213211