Finite Group Databasebeta

← C11×#20992 #14598185

Subgroups — C11×#20992 #14598185

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C211yesmaximal, characteristic, complemented
2C2×C11×#537C211yesmaximal, characteristic
3C2×C11×#413C212yesmaximal, complemented
4C11×#2879C211yesmaximal, characteristic, complemented
5C11×#1901C214yesmaximal, complemented
6C11×#1900C214yesmaximal, complemented
7C2×C11×#343C212yesmaximal, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×#41C2211yescharacteristic
10C11×#568—28no—
11C2×C11×#131—24no—
12C22×C11×M16C2214yes—
13C22×C11×M16C2212yes—
14C22×C11×M16C2212yes—
15C11×#537—24no—
16C11×#537—24no—
17C2×C11×C22⋊Q8C412yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121C412yes—
20C2×C11×#121C414yes—
21C2×C11×#121C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#413—28no—
24C2×C11×#101C2214yes—
25C2×C11×#100C2214yes—
26C11×#408—24no—
27C11×#407C2214yes—
28C11×#343C2218yes—
29C2×C11×#41—24no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—24no—
33C2×C11×#41—24no—
34C2×C11×#41—24no—
35C2×C11×#41D414yes—
36C2×C11×#41D414yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11C2×C412yes—
40C22×D4×C11C2×C412yes—
41C22×D4×C11C2×C411yescharacteristic
42C22×D4×C11C2×C414yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11C2×C412yes—
45C23×C4×C11C2×C412yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C11×#131—232no—
49C2×C11×M16—24no—
50C2×C11×M16—22no—
51C2×C11×M16—24no—
52C2×C11×M16—216no—
53C2×C11×M16—22no—
54C2×C11×M16—24no—
55C2×C11×M16—24no—
56C2×C11×M16D418yescomplemented
57C2×C11×M16C2314yes—
58C2×C11×M16C2314yes—
59C22×C8×C11—24no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×#121—28no—
66C11×#121—216no—
67C11×#121—24no—
68C11×#121—24no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2×C412yes—
72C2×C11×C4⋊C4C2×C414yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4C2×C414yes—
75C2×C11×C22⋊C4C2×C414yes—
76C11×#101—28no—
77C11×#100—28no—
78C11×C22⋊C8—28no—
79#20992C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11C22×C412yes—
81C24×C11C22×C412yes—
82C24×C11C22×C411yescharacteristic
83C11×#41—28no—
84C11×#41—28no—
85C11×#41—28no—
86C11×#41—28no—
87C11×#41—44no—
88C11×#41—44no—
89C11×#41—44no—
90C11×#41—44no—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11C22⋊C414yes—
97C2×D4×C11—28no—
98C2×D4×C11—24no—
99C2×D4×C11—28no—
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—22no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—84no—
107C2×D4×C11C22⋊C418yes—
108C2×D4×C11C22⋊C414yes—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—28no—
114C22×C4×C11—82no—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D414yes—
124C22×C4×C11#4114yes—
125C22×C4×C11C2411yescharacteristic
126C11×M16—216no—
127C11×M16—28no—
128C11×M16—24no—
129C11×M16—24no—
130C11×M16—24no—
131C11×M16—44no—
132C11×M16C2×D418yes—
133C2×C8×C11—216no—
134C2×C8×C11—28no—
135C2×C8×C11—24no—
136C2×C8×C11—24no—
137C2×C8×C11—44no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—28no—
144C2×#568C2×C1111yescharacteristic, complemented
145C2×#537C2×C1111yescharacteristic
146C2×#413C2×C1112yescomplemented
147#2879C2×C1111yescharacteristic, complemented
148#1901C2×C1114yescomplemented
149#1900C2×C1114yescomplemented
150C2×#343C2×C1112yescomplemented
151C23×C11—24no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11C2×C22⋊C414yes—
161C23×C11C2×C22⋊C412yes—
162C23×C11C4×D414yes—
163C23×C11C23×C411yescharacteristic
164Q8×C11—28no—
165Q8×C11—41no—
166Q8×C11—42no—
167Q8×C11—41no—
168D4×C11—216no—
169D4×C11—28no—
170D4×C11—48no—
171D4×C11—41no—
172D4×C11—42no—
173D4×C11—41no—
174D4×C11—88no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—28no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—48no—
183C2×C4×C11—44no—
184C2×C4×C11—84no—
185C2×C4×C11C2×C22⋊C414yes—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C4×D414yes—
188C2×C4×C11#12014yes—
189C2×C4×C11#12114yes—
190C2×C4×C11#12114yes—
191C2×C4×C11#12314yes—
192C2×C4×C11C22×D412yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4112yes—
196C8×C11—28no—
197C8×C11—44no—
198C22×#41C22×C1111yescharacteristic
199C22×#41C22×C1111yescharacteristic
200#568—28no—
201C2×#131—24no—
202C22×M16C22×C1112yes—
203C22×M16C22×C1114yes—
204C22×M16C22×C1112yes—
205#537—24no—
206#537—24no—
207C2×C22⋊Q8C4×C1112yes—
208C2×C22⋊Q8C22×C1112yes—
209C2×#121C4×C1112yes—
210C2×#121C4×C1114yes—
211C2×#121C22×C1112yes—
212C22×C4⋊C4C22×C1111yescharacteristic
213#413—28no—
214C2×#101C22×C1114yes—
215C2×#100C22×C1114yes—
216#408—24no—
217#407C22×C1114yes—
218#343C22×C1118yes—
219C22×C11—21no—
220C22×C11—22no—
221C22×C11—21no—
222C22×C11—22no—
223C22×C11—24no—
224C22×C11—24no—
225C22×C11—24no—
226C22×C11—44no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—84no—
231C22×C11—84no—
232C22×C11#38614yes—
233C22×C11C22×C22⋊C411yescharacteristic
234C22×C11C2×C4×D412yes—
235C4×C11—24no—
236C4×C11—44no—
237C4×C11—42no—
238C4×C11#38614yes—
239C4×C11C2×#12011yescharacteristic
240C4×C11C2×#12112yes—
241C4×C11C2×#12311yescharacteristic
242C2×#41—24no—
243C2×#41—22no—
244C2×#41—22no—
245C2×#41—24no—
246C2×#41—24no—
247C2×#41—24no—
248C2×#41D4×C1114yes—
249C2×#41D4×C1114yes—
250C22×Q8C2×C4×C1111yescharacteristic
251C22×Q8C23×C1111yescharacteristic
252C22×D4C2×C4×C1112yes—
253C22×D4C2×C4×C1112yes—
254C22×D4C2×C4×C1111yescharacteristic
255C22×D4C2×C4×C1114yes—
256C22×D4C23×C1111yescharacteristic
257C23×C4C2×C4×C1112yes—
258C23×C4C2×C4×C1112yes—
259C23×C4C23×C1112yes—
260C23×C4C23×C1111yescharacteristic
261#131—232no—
262C2×M16—24no—
263C2×M16—22no—
264C2×M16—24no—
265C2×M16—216no—
266C2×M16—22no—
267C2×M16—24no—
268C2×M16—24no—
269C2×M16D4×C1118yescomplemented
270C2×M16C23×C1114yes—
271C2×M16C23×C1114yes—
272C22×C8—24no—
273C22×C8—22no—
274C22×C8—22no—
275C22⋊Q8—28no—
276C22⋊Q8—24no—
277C22⋊Q8—24no—
278#121—28no—
279#121—216no—
280#121—24no—
281#121—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4C2×C4×C1112yes—
285C2×C4⋊C4C2×C4×C1114yes—
286C2×C4⋊C4C23×C1112yes—
287C2×C22⋊C4C2×C4×C1114yes—
288C2×C22⋊C4C2×C4×C1114yes—
289#101—28no—
290#100—28no—
291C22⋊C8—28no—
292C2×C11—22no—
293C2×C11—24no—
294C2×C11—44no—
295C2×C11—82no—
296C2×C11C2×#38611yescharacteristic
297C2×C11#288811yescharacteristic
298C2×C11#288911yescharacteristic
299C24C22×C4×C1112yes—
300C24C22×C4×C1112yes—
301C24C22×C4×C1111yescharacteristic
302#41—28no—
303#41—28no—
304#41—28no—
305#41—28no—
306#41—44no—
307#41—44no—
308#41—44no—
309#41—44no—
310C2×Q8—24no—
311C2×Q8—22no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—22no—
315C2×Q8C11×C22⋊C414yes—
316C2×D4—28no—
317C2×D4—24no—
318C2×D4—28no—
319C2×D4—28no—
320C2×D4—24no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—84no—
326C2×D4C11×C22⋊C418yes—
327C2×D4C11×C22⋊C414yes—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—28no—
333C22×C4—82no—
334C22×C4C22×C4×C1112yes—
335C22×C4C22×C4×C1112yes—
336C22×C4C22×C4×C1114yes—
337C22×C4C22×C4×C1111yescharacteristic
338C22×C4C2×D4×C1114yes—
339C22×C4C2×D4×C1114yes—
340C22×C4C2×D4×C1112yes—
341C22×C4C2×D4×C1112yes—
342C22×C4C2×D4×C1114yes—
343C22×C4C11×#4114yes—
344C22×C4C24×C1111yescharacteristic
345M16—216no—
346M16—28no—
347M16—24no—
348M16—24no—
349M16—24no—
350M16—44no—
351M16C2×D4×C1118yes—
352C2×C8—216no—
353C2×C8—28no—
354C2×C8—24no—
355C2×C8—24no—
356C2×C8—44no—
357C4⋊C4—24no—
358C4⋊C4—28no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C22⋊C4—28no—
362C22⋊C4—28no—
363C11#2099211yescharacteristic, direct product factor, Sylow
364C23—24no—
365C23—22no—
366C23—24no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23C2×C11×C22⋊C414yes—
374C23C2×C11×C22⋊C412yes—
375C23C4×D4×C1114yes—
376C23C23×C4×C1111yescharacteristic
377Q8—28no—
378Q8—41no—
379Q8—42no—
380Q8—41no—
381D4—216no—
382D4—28no—
383D4—48no—
384D4—41no—
385D4—42no—
386D4—41no—
387D4—88no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—48no—
396C2×C4—44no—
397C2×C4—84no—
398C2×C4C2×C11×C22⋊C414yes—
399C2×C4C2×C11×C22⋊C412yes—
400C2×C4C4×D4×C1114yes—
401C2×C4C11×#12014yes—
402C2×C4C11×#12114yes—
403C2×C4C11×#12114yes—
404C2×C4C11×#12314yes—
405C2×C4C22×D4×C1112yes—
406C2×C4C22×D4×C1111yescharacteristic
407C2×C4C22×D4×C1111yescharacteristic
408C2×C4C2×C11×#4112yes—
409C8—28no—
410C8—44no—
411C22—21no—
412C22—22no—
413C22—21no—
414C22—22no—
415C22—24no—
416C22—24no—
417C22—24no—
418C22—44no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—84no—
423C22—84no—
424C22C11×#38614yes—
425C22C22×C11×C22⋊C411yescharacteristic
426C22C2×C4×D4×C1112yes—
427C4—24no—
428C4—42no—
429C4—44no—
430C4C11×#38614yes—
431C4C2×C11×#12011yescharacteristic
432C4C2×C11×#12112yes—
433C4C2×C11×#12311yescharacteristic
434C2—22no—
435C2—24no—
436C2—44no—
437C2—82no—
438C2C2×C11×#38611yescharacteristic
439C2C11×#288811yescharacteristic
440C2C11×#288911yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#568C2semidirect
3. C2×C11×#413C2semidirect
4. C11×#2879C2semidirect
5. C11×#1901C2semidirect
6. C11×#1900C2semidirect
7. C2×C11×#343C2semidirect
56. C2×C11×M16D4semidirect
79. #20992C11direct (N × H)
144. C2×#568C2×C11semidirect
146. C2×#413C2×C11semidirect
147. #2879C2×C11semidirect
148. #1901C2×C11semidirect
149. #1900C2×C11semidirect
150. C2×#343C2×C11semidirect
269. C2×M16D4×C11semidirect
363. C11#20992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5682
C2×C11×#5372
C2×C11×#4132
C11×#28792
C11×#19012
C11×#19002
C2×C11×#3432
#2099211