Finite Group Databasebeta

← C11×#21066 #14598259

Subgroups — C11×#21066 #14598259

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#427C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic
3C22×C11×#103C211yesmaximal, characteristic
4C11×#2310C211yesmaximal, characteristic
5C11×#2274C211yesmaximal, characteristic
6C11×#1928C214yesmaximal, complemented
7C11×#1927C214yesmaximal, complemented
8C11×#1736C211yesmaximal, characteristic
9C11×#1729C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#427—24no—
18C2×C11×#107C2212yes—
19C2×C11×#106C2212yes—
20C11×#419—24no—
21C2×C11×#103C418yescomplemented
22C2×C11×#103C2214yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C11×#391—22no—
26C11×#391C2214yes—
27C11×#381—22no—
28C4×C11×C4⋊C4—22no—
29C4×C11×C4⋊C4C2214yes—
30C4×C11×C22⋊C4—22no—
31C11×#340C2214yes—
32C11×#336C2212yes—
33C11×#336C2212yes—
34C22×Q8×C11—21no—
35C22×Q8×C11—22no—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11C2×C414yes—
41C22×Q8×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C2×C11×M16—22no—
46C2×C11×M16—22no—
47C2×C11×M16—22no—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11C2×C414yes—
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#117—22no—
55C11×#117—22no—
56C11×#117—22no—
57C11×#117—22no—
58C11×#117—22no—
59C11×#117D414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2×C414yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11—24no—
73C2×C42×C11C2312yes—
74C11×#107—24no—
75C11×#106—24no—
76C11×#103—28no—
77C11×#103C2×C418yes—
78C11×#103C2×C418yes—
79C11×#95—24no—
80C11×#95—28no—
81#21066C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—28no—
86C2×Q8×C11—28no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—44no—
94C2×Q8×C11—44no—
95C2×Q8×C11C22×C414yes—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—82no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D414yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×C4×C11C2411yescharacteristic
114C11×M16—44no—
115C2×C8×C11—28no—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C22×C412yes—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4C22×C414yes—
132C11×C4⋊C4C2×D414yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—42no—
136C42×C11—24no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—42no—
140C42×C11—84no—
141C2×#427C2×C1111yescharacteristic
142C2×#419C2×C1111yescharacteristic
143C22×#103C2×C1111yescharacteristic
144#2310C2×C1111yescharacteristic
145#2274C2×C1111yescharacteristic
146#1928C2×C1114yescomplemented
147#1927C2×C1114yescomplemented
148#1736C2×C1111yescharacteristic
149#1729C2×C1111yescharacteristic
150C23×C11—22no—
151C23×C11—22no—
152C23×C11C4×D412yes—
153C23×C11#12112yes—
154C23×C11#12312yes—
155C23×C11C22×D411yescharacteristic
156Q8×C11—24no—
157Q8×C11—24no—
158Q8×C11—42no—
159Q8×C11—42no—
160Q8×C11—48no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11—48no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—84no—
177C2×C4×C11#11714yes—
178C2×C4×C11C4×D414yes—
179C2×C4×C11C4×D412yes—
180C2×C4×C11#12112yes—
181C2×C4×C11#12312yes—
182C2×C4×C11#12414yes—
183C2×C4×C11#12614yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C8×C11—22no—
191C8×C11—22no—
192C8×C11—42no—
193C23×Q8C22×C1111yescharacteristic
194C22×M16C22×C1111yescharacteristic
195C23×C8C22×C1111yescharacteristic
196C2×#117C22×C1111yescharacteristic
197C2×#117C22×C1111yescharacteristic
198C2×#117C22×C1111yescharacteristic
199C22×C4⋊C4C22×C1111yescharacteristic
200#427—24no—
201C2×#107C22×C1112yes—
202C2×#106C22×C1112yes—
203#419—24no—
204C2×#103C4×C1118yescomplemented
205C2×#103C22×C1114yes—
206C2×#103C22×C1112yes—
207C2×#103C22×C1112yes—
208#391—22no—
209#391C22×C1114yes—
210#381—22no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4C22×C1114yes—
213C4×C22⋊C4—22no—
214#340C22×C1114yes—
215#336C22×C1112yes—
216#336C22×C1112yes—
217C22×C11—24no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—24no—
221C22×C11#38814yes—
222C22×C11C2×C4×D411yescharacteristic
223C22×C11C2×#12111yescharacteristic
224C22×C11C2×#12311yescharacteristic
225C22×C11#57712yes—
226C22×C11#57812yes—
227C4×C11—44no—
228C4×C11—44no—
229C4×C11—44no—
230C4×C11—44no—
231C4×C11—82no—
232C4×C11#38814yes—
233C4×C11C2×#11711yescharacteristic
234C4×C11C2×C4×D411yescharacteristic
235C4×C11C2×#12411yescharacteristic
236C4×C11C2×#12611yescharacteristic
237C22×Q8—21no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8C2×C4×C1114yes—
244C22×Q8C23×C1112yes—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4C23×C1111yescharacteristic
248C2×M16—22no—
249C2×M16—22no—
250C2×M16—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8C2×C4×C1114yes—
254C22×C8C23×C1112yes—
255C22×C8C23×C1111yescharacteristic
256C22×C8C23×C1111yescharacteristic
257#117—22no—
258#117—22no—
259#117—22no—
260#117—22no—
261#117—22no—
262#117D4×C1114yes—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4C2×C4×C1114yes—
266C2×C4⋊C4D4×C1112yes—
267C2×C4⋊C4C23×C1112yes—
268C2×C4⋊C4C23×C1112yes—
269C2×C4⋊C4C23×C1112yes—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4D4×C1112yes—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—24no—
276C2×C42C23×C1112yes—
277#107—24no—
278#106—24no—
279#103—28no—
280#103C2×C4×C1118yes—
281#103C2×C4×C1118yes—
282#95—24no—
283#95—28no—
284C2×C11—24no—
285C2×C11C2×#38811yescharacteristic
286C2×C11#294911yescharacteristic
287C2×C11#295011yescharacteristic
288C2×C11#304612yes—
289C2×C11#309712yes—
290C24C2×D4×C1111yescharacteristic
291C2×Q8—24no—
292C2×Q8—22no—
293C2×Q8—28no—
294C2×Q8—28no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—42no—
300C2×Q8—42no—
301C2×Q8—44no—
302C2×Q8—44no—
303C2×Q8C22×C4×C1114yes—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—22no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—82no—
313C22×C4C22×C4×C1112yes—
314C22×C4C2×D4×C1114yes—
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C2×D4×C1112yes—
317C22×C4C11×#4112yes—
318C22×C4C11×#4112yes—
319C22×C4C11×#4112yes—
320C22×C4C11×#4112yes—
321C22×C4C24×C1111yescharacteristic
322M16—44no—
323C2×C8—28no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8C22×C4×C1112yes—
332C2×C8C22×C4×C1112yes—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4C22×C4×C1114yes—
340C4⋊C4C2×D4×C1114yes—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—42no—
344C42—24no—
345C42—22no—
346C42—22no—
347C42—42no—
348C42—84no—
349C11#2106611yescharacteristic, direct product factor, Sylow
350C23—22no—
351C23—22no—
352C23C4×D4×C1112yes—
353C23C11×#12112yes—
354C23C11×#12312yes—
355C23C22×D4×C1111yescharacteristic
356Q8—24no—
357Q8—24no—
358Q8—48no—
359Q8—42no—
360Q8—42no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—48no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—84no—
377C2×C4C11×#11714yes—
378C2×C4C4×D4×C1114yes—
379C2×C4C4×D4×C1112yes—
380C2×C4C11×#12112yes—
381C2×C4C11×#12312yes—
382C2×C4C11×#12414yes—
383C2×C4C11×#12614yes—
384C2×C4C23×C4×C1111yescharacteristic
385C2×C4C22×D4×C1111yescharacteristic
386C2×C4C2×C11×#4111yescharacteristic
387C2×C4C2×C11×#4111yescharacteristic
388C2×C4C2×C11×#4111yescharacteristic
389C2×C4C2×C11×#4111yescharacteristic
390C8—22no—
391C8—22no—
392C8—42no—
393C22—22no—
394C22—22no—
395C22—24no—
396C22—24no—
397C22C11×#38814yes—
398C22C2×C4×D4×C1111yescharacteristic
399C22C2×C11×#12111yescharacteristic
400C22C2×C11×#12311yescharacteristic
401C22C11×#57712yes—
402C22C11×#57812yes—
403C4—44no—
404C4—44no—
405C4—44no—
406C4—44no—
407C4—82no—
408C4C11×#38814yes—
409C4C2×C11×#11711yescharacteristic
410C4C2×C4×D4×C1111yescharacteristic
411C4C2×C11×#12411yescharacteristic
412C4C2×C11×#12611yescharacteristic
413C2—24no—
414C2C2×C11×#38811yescharacteristic
415C2C11×#294911yescharacteristic
416C2C11×#295011yescharacteristic
417C2C11×#304612yes—
418C2C11×#309712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
6. C11×#1928C2semidirect
7. C11×#1927C2semidirect
21. C2×C11×#103C4semidirect
81. #21066C11direct (N × H)
146. #1928C2×C11semidirect
147. #1927C2×C11semidirect
204. C2×#103C4×C11semidirect
349. C11#21066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4272
C2×C11×#4192
C22×C11×#1032
C11×#23102
C11×#22742
C11×#19282
C11×#19272
C11×#17362
C11×#17292
#2106611