Finite Group Databasebeta

← C11×#21530 #14598723

Subgroups — C11×#21530 #14598723

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic, complemented
3C2×C11×#405C211yesmaximal, characteristic
4C11×#2323C212yesmaximal
5C11×#1971C211yesmaximal, characteristic, complemented
6C11×#1943C211yesmaximal, characteristic, complemented
7C11×#1933C212yesmaximal, complemented
8C11×#1894C212yesmaximal
9C11×#1807C211yesmaximal, characteristic
10C11×#1776C211yesmaximal, characteristic, complemented
11C4×C11×#103C212yesmaximal, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C4×Q8×C11C2212yes—
17C2×C11×#117C2211yescharacteristic
18C11×#467C418yescomplemented
19C11×#441—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C11×#405—24no—
27C2×C11×#97C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C11×#391C2212yes—
32C11×#389—22no—
33C11×#389C2212yes—
34C11×#388—22no—
35C11×#388—22no—
36C11×#387—22no—
37C11×#380C2212yes—
38C4×C11×C4⋊C4C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11C2×C414yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8C2×C418yes—
59C4×Q8×C11—24no—
60C4×Q8×C11—24no—
61C11×#117—22no—
62C11×#117—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D412yes—
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#107C2×C414yes—
78C11×#106—22no—
79C11×#106—22no—
80C11×#103—24no—
81C11×#103—24no—
82C11×#103C2×C418yes—
83C11×#97—22no—
84C11×#97D414yes—
85C4×C8×C11—22no—
86C4×C8×C11—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95—22no—
92#21530C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C414yes—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11#4112yes—
113C22×C4×C11C2411yescharacteristic
114C11×Q16—28no—
115C11×M16—28no—
116C2×C8×C11—28no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C22×C412yes—
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D412yes—
127C2×C8×C11#4112yes—
128C2×C8×C11#4112yes—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4C22×C414yes—
139C11×C22⋊C4—28no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—82no—
142C42×C11—21no—
143C42×C11—21no—
144C42×C11—44no—
145C42×C11—82no—
146C42×C11C2×D412yes—
147C42×C11#4112yes—
148C2×#467C2×C1111yescharacteristic
149C2×#441C2×C1111yescharacteristic, complemented
150C2×#405C2×C1111yescharacteristic
151#2323C2×C1112yes—
152#1971C2×C1111yescharacteristic, complemented
153#1943C2×C1111yescharacteristic, complemented
154#1933C2×C1112yescomplemented
155#1894C2×C1112yes—
156#1807C2×C1111yescharacteristic
157#1776C2×C1111yescharacteristic, complemented
158C4×#103C2×C1112yescomplemented
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11C4×D412yes—
164C23×C11C22×D411yescharacteristic
165Q8×C11—24no—
166Q8×C11—24no—
167Q8×C11—42no—
168Q8×C11—42no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11C4×D412yes—
193C2×C4×C11#12114yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C8×C11—22no—
201C8×C11—22no—
202C8×C11—22no—
203C8×C11C4×D414yes—
204C22×Q16C22×C1111yescharacteristic
205C22×M16C22×C1111yescharacteristic
206C23×C8C22×C1111yescharacteristic
207C2×C22⋊Q8C22×C1112yes—
208C2×C4×Q8C22×C1112yes—
209C2×#117C22×C1111yescharacteristic
210#467C4×C1118yescomplemented
211#441—24no—
212C2×#107C22×C1111yescharacteristic
213C2×#106C22×C1111yescharacteristic
214C2×#106C22×C1111yescharacteristic
215C2×#103C22×C1112yes—
216C2×#103C22×C1112yes—
217C2×#103C22×C1112yes—
218#405—24no—
219C2×#97C22×C1111yescharacteristic
220C2×#97C22×C1111yescharacteristic
221C2×C4×C8C22×C1111yescharacteristic
222C2×C4×C8C22×C1111yescharacteristic
223#391C22×C1112yes—
224#389—22no—
225#389C22×C1112yes—
226#388—22no—
227#388—22no—
228#387—22no—
229#380C22×C1112yes—
230C4×C4⋊C4C22×C1112yes—
231#340C22×C1112yes—
232#340C22×C1112yes—
233#340C22×C1112yes—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11C2×C4×D411yescharacteristic
240C22×C11C2×#12111yescharacteristic
241C22×C11#53211yescharacteristic
242C22×C11#57712yes—
243C22×C11#57812yes—
244C4×C11—24no—
245C4×C11—22no—
246C4×C11—44no—
247C4×C11—42no—
248C4×C11—44no—
249C4×C11—82no—
250C4×C11—82no—
251C4×C11C2×C4×D411yescharacteristic
252C4×C11C4×#4111yescharacteristic
253C4×C11#52511yescharacteristic
254C4×C11#52911yescharacteristic
255C22×Q8C23×C1112yes—
256C23×C4C23×C1111yescharacteristic
257C2×Q16—22no—
258C2×Q16—22no—
259C2×Q16C2×C4×C1114yes—
260C2×M16—22no—
261C2×M16—22no—
262C2×M16—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8C2×C4×C1114yes—
266C22×C8C23×C1111yescharacteristic
267C22×C8C23×C1111yescharacteristic
268C22×C8C23×C1111yescharacteristic
269C22×C8C23×C1111yescharacteristic
270C22⋊Q8—24no—
271C22⋊Q8C2×C4×C1118yes—
272C4×Q8—24no—
273C4×Q8—24no—
274#117—22no—
275#117—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4D4×C1112yes—
280C2×C4⋊C4C23×C1112yes—
281C2×C4⋊C4C23×C1112yes—
282C2×C4⋊C4C23×C1112yes—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4D4×C1112yes—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42C23×C1111yescharacteristic
289C2×C42C23×C1111yescharacteristic
290#107C2×C4×C1114yes—
291#106—22no—
292#106—22no—
293#103—24no—
294#103—24no—
295#103C2×C4×C1118yes—
296#97—22no—
297#97D4×C1114yes—
298C4×C8—22no—
299C4×C8—22no—
300#95—22no—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—22no—
305C2×C11—42no—
306C2×C11C4×#12111yescharacteristic
307C2×C11#295011yescharacteristic
308C2×C11#295211yescharacteristic
309C2×C11#306312yes—
310C2×C11#317812yes—
311C24C2×D4×C1111yescharacteristic
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8C22×C4×C1114yes—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4C22×C4×C1112yes—
327C22×C4C2×D4×C1112yes—
328C22×C4C2×D4×C1111yescharacteristic
329C22×C4C2×D4×C1112yes—
330C22×C4C11×#4112yes—
331C22×C4C24×C1111yescharacteristic
332Q16—28no—
333M16—28no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—28no—
341C2×C8C22×C4×C1112yes—
342C2×C8C22×C4×C1112yes—
343C2×C8C2×D4×C1112yes—
344C2×C8C2×D4×C1112yes—
345C2×C8C11×#4112yes—
346C2×C8C11×#4112yes—
347C4⋊C4—28no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—44no—
355C4⋊C4—82no—
356C4⋊C4C22×C4×C1114yes—
357C22⋊C4—28no—
358C22⋊C4—24no—
359C22⋊C4—82no—
360C42—21no—
361C42—21no—
362C42—44no—
363C42—82no—
364C42C2×D4×C1112yes—
365C42C11×#4112yes—
366C11#2153011yescharacteristic, direct product factor, Sylow
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23C4×D4×C1112yes—
372C23C22×D4×C1111yescharacteristic
373Q8—24no—
374Q8—24no—
375Q8—42no—
376Q8—42no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4C4×D4×C1112yes—
401C2×C4C11×#12114yes—
402C2×C4C23×C4×C1111yescharacteristic
403C2×C4C22×D4×C1111yescharacteristic
404C2×C4C2×C11×#4111yescharacteristic
405C2×C4C2×C11×#4111yescharacteristic
406C2×C4C2×C11×#4111yescharacteristic
407C2×C4C2×C11×#4111yescharacteristic
408C8—22no—
409C8—22no—
410C8—22no—
411C8C4×D4×C1114yes—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—42no—
416C22—42no—
417C22C2×C4×D4×C1111yescharacteristic
418C22C2×C11×#12111yescharacteristic
419C22C11×#53211yescharacteristic
420C22C11×#57712yes—
421C22C11×#57812yes—
422C4—24no—
423C4—22no—
424C4—44no—
425C4—42no—
426C4—44no—
427C4—82no—
428C4—82no—
429C4C2×C4×D4×C1111yescharacteristic
430C4C4×C11×#4111yescharacteristic
431C4C11×#52511yescharacteristic
432C4C11×#52911yescharacteristic
433C2—42no—
434C2C4×C11×#12111yescharacteristic
435C2C11×#295011yescharacteristic
436C2C11×#295211yescharacteristic
437C2C11×#306312yes—
438C2C11×#317812yes—
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
2. C2×C11×#441C2semidirect
5. C11×#1971C2semidirect
6. C11×#1943C2semidirect
7. C11×#1933C2semidirect
10. C11×#1776C2semidirect
11. C4×C11×#103C2semidirect
18. C11×#467C4semidirect
92. #21530C11direct (N × H)
149. C2×#441C2×C11semidirect
152. #1971C2×C11semidirect
153. #1943C2×C11semidirect
154. #1933C2×C11semidirect
157. #1776C2×C11semidirect
158. C4×#103C2×C11semidirect
210. #467C4×C11semidirect
366. C11#21530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C11×#4412
C2×C11×#4052
C11×#23232
C11×#19712
C11×#19432
C11×#19332
C11×#18942
C11×#18072
C11×#17762
C4×C11×#1032
#2153011