Finite Group Databasebeta

← C11×#34938 #14612131

Subgroups — C11×#34938 #14612131

Order 2816.

2290 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C212yesmaximal
2C11×#2552C212yesmaximal, complemented
3C11×#2551C212yesmaximal, complemented
4C11×#2550C214yesmaximal, complemented
5C11×#2549C214yesmaximal
6C11×#2440C214yesmaximal
7C11×#2399C214yesmaximal, complemented
8C4×C11×C4⋊Q8C214yesmaximal, complemented
9C11×#2296C212yesmaximal
10C11×#2285C211yesmaximal, characteristic
11C4×C11×#117C211yesmaximal, characteristic
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
13C11×#533—216no—
14C2×C11×C4⋊Q8C2214yes—
15C2×C11×C4⋊Q8C2214yes—
16C2×C11×#125C2214yes—
17C2×C11×C22⋊Q8C2218yes—
18C2×C4×Q8×C11C2218yes—
19C2×C11×#117C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
23C22×C42×C11C2212yes—
24C22×C42×C11C2211yescharacteristic
25C11×#398C2218yes—
26C11×#398C2218yes—
27C11×#395C2218yes—
28C11×#395C2218yes—
29C11×#391C2218yes—
30C11×#389C2214yes—
31C11×#389C2214yes—
32C11×#389C2218yes—
33C11×#389C2214yes—
34C11×#389C2214yes—
35C11×#385C2218yes—
36C11×#384C2214yes—
37C11×#384C2212yes—
38C11×#382C2212yes—
39C11×#380C2212yes—
40C11×#380C2212yes—
41C4×C11×C4⋊C4C2212yes—
42C4×C11×C4⋊C4C2212yes—
43C4×C11×C4⋊C4C2218yes—
44C4×C11×C4⋊C4C2212yes—
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2212yes—
48C4×C11×C4⋊C4C2212yes—
49C4×C11×C4⋊C4C2212yes—
50C4×C11×C4⋊C4C2212yes—
51C4×C11×C22⋊C4C2212yes—
52C4×C11×C22⋊C4C2212yes—
53C11×#376C2212yes—
54C2×C11×#95C2212yes—
55C43×C11C2212yes—
56C22×Q8×C11C2318yes—
57C23×C4×C11C2314yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C11×C4⋊Q8—216no—
62C11×C4⋊Q8—216no—
63C11×#125—216no—
64C11×C22⋊Q8—232no—
65C4×Q8×C11—232no—
66C11×#117—28no—
67C11×#117D418yes—
68C11×#117Q818yescomplemented
69C2×C11×C4⋊C4—28no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2318yes—
75C2×C11×C4⋊C4C2318yes—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2318yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2312yes—
85C2×C11×C22⋊C4C2312yes—
86C2×C42×C11—28no—
87C2×C42×C11Q818yescomplemented
88C2×C42×C11C2312yes—
89C2×C42×C11C2312yes—
90C2×C42×C11C2314yes—
91C2×C42×C11C2314yes—
92C2×C42×C11C2314yes—
93C2×C42×C11C2314yes—
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2312yes—
100C11×#95C2314yes—
101C11×#95C2312yes—
102C11×#95C2312yes—
103C11×#95C2314yes—
104C11×#95C2314yes—
105C11×#95C2314yes—
106C11×#95C2314yes—
107C11×#95C2318yes—
108C11×#95C2318yes—
109#34938C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11C2411yescharacteristic
111C2×Q8×C11—216no—
112C2×Q8×C11—216no—
113C2×Q8×C11—48no—
114C22×C4×C11—24no—
115C22×C4×C11—28no—
116C22×C4×C11—28no—
117C22×C4×C11—42no—
118C22×C4×C11—44no—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×Q814yes—
121C22×C4×C11C2×Q814yes—
122C22×C4×C11C2×Q814yes—
123C22×C4×C11C2×Q814yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2418yes—
126C22×C4×C11C2414yes—
127C22×C4×C11C2411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×C4×C11C2414yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C11×C4⋊C4—28no—
136C11×C4⋊C4—216no—
137C11×C4⋊C4—216no—
138C11×C4⋊C4—216no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—216no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—48no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4C2×D418yes—
146C11×C4⋊C4C2×Q818yes—
147C11×C4⋊C4#4118yes—
148C11×C22⋊C4—28no—
149C11×C22⋊C4C2×D418yes—
150C11×C22⋊C4C2×Q818yes—
151C42×C11—28no—
152C42×C11—24no—
153C42×C11—24no—
154C42×C11—28no—
155C42×C11—28no—
156C42×C11—44no—
157C42×C11C2×D418yes—
158C42×C11C2×Q814yes—
159C42×C11C2×Q814yes—
160C42×C11C2×Q814yes—
161C42×C11C2×Q814yes—
162C42×C11C2×Q818yes—
163C2×#533C2×C1112yes—
164#2552C2×C1112yescomplemented
165#2551C2×C1112yescomplemented
166#2550C2×C1114yescomplemented
167#2549C2×C1114yes—
168#2440C2×C1114yes—
169#2399C2×C1114yescomplemented
170C4×C4⋊Q8C2×C1114yescomplemented
171#2296C2×C1112yes—
172#2285C2×C1111yescharacteristic
173C4×#117C2×C1111yescharacteristic
174C2×C4×C4⋊C4C2×C1111yescharacteristic
175C23×C11—22no—
176C23×C11—22no—
177C23×C11C22×D412yes—
178C23×C11C22×Q812yes—
179C23×C11C22×Q812yes—
180C23×C11C2511yescharacteristic
181Q8×C11—432no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—28no—
192C2×C4×C11—24no—
193C2×C4×C11—28no—
194C2×C4×C11—24no—
195C2×C4×C11—28no—
196C2×C4×C11—24no—
197C2×C4×C11—28no—
198C2×C4×C11—44no—
199C2×C4×C11—416no—
200C2×C4×C11C4⋊Q8116yescomplemented
201C2×C4×C11C22×D418yes—
202C2×C4×C11C22×D412yes—
203C2×C4×C11C22×D412yes—
204C2×C4×C11C22×Q812yes—
205C2×C4×C11C22×Q812yes—
206C2×C4×C11C22×Q812yes—
207C2×C4×C11C22×Q818yes—
208C2×C4×C11C22×Q812yes—
209C2×C4×C11C22×Q812yes—
210C2×C4×C11C22×Q812yes—
211C2×C4×C11C22×Q812yes—
212C2×C4×C11C22×Q812yes—
213C2×C4×C11C2×#4118yes—
214C2×C4×C11C2×#4114yes—
215#533—216no—
216C2×C4⋊Q8C22×C1114yes—
217C2×C4⋊Q8C22×C1114yes—
218C2×#125C22×C1114yes—
219C2×C22⋊Q8C22×C1118yes—
220C2×C4×Q8C22×C1118yes—
221C2×#117C22×C1112yes—
222C2×#117C22×C1111yescharacteristic
223C2×#117C22×C1111yescharacteristic
224C22×C4⋊C4C22×C1112yes—
225C22×C42C22×C1112yes—
226C22×C42C22×C1111yescharacteristic
227#398C22×C1118yes—
228#398C22×C1118yes—
229#395C22×C1118yes—
230#395C22×C1118yes—
231#391C22×C1118yes—
232#389C22×C1114yes—
233#389C22×C1114yes—
234#389C22×C1118yes—
235#389C22×C1114yes—
236#389C22×C1114yes—
237#385C22×C1118yes—
238#384C22×C1114yes—
239#384C22×C1112yes—
240#382C22×C1112yes—
241#380C22×C1112yes—
242#380C22×C1112yes—
243C4×C4⋊C4C22×C1112yes—
244C4×C4⋊C4C22×C1112yes—
245C4×C4⋊C4C22×C1118yes—
246C4×C4⋊C4C22×C1112yes—
247C4×C4⋊C4C22×C1112yes—
248C4×C4⋊C4C22×C1112yes—
249C4×C4⋊C4C22×C1111yescharacteristic
250C4×C4⋊C4C22×C1111yescharacteristic
251C4×C4⋊C4C22×C1112yes—
252C4×C4⋊C4C22×C1112yes—
253C4×C22⋊C4C22×C1112yes—
254C4×C22⋊C4C22×C1112yes—
255#376C22×C1112yes—
256C2×#95C22×C1112yes—
257C43C22×C1112yes—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11C2×C4⋊Q814yes—
263C22×C11C23×D411yescharacteristic
264C22×C11C23×Q811yescharacteristic
265C22×C11C23×Q811yescharacteristic
266C22×C11C22×#4112yes—
267C22×C11#58512yes—
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—28no—
272C4×C11—28no—
273C4×C11—28no—
274C4×C11—44no—
275C4×C11—48no—
276C4×C11C2×C4⋊Q814yes—
277C4×C11C2×C4⋊Q814yes—
278C4×C11#53314yescomplemented
279C22×Q8C23×C1118yes—
280C23×C4C23×C1114yes—
281C23×C4C23×C1111yescharacteristic
282C23×C4C23×C1111yescharacteristic
283C23×C4C23×C1111yescharacteristic
284C4⋊Q8—216no—
285C4⋊Q8—216no—
286#125—216no—
287C22⋊Q8—232no—
288C4×Q8—232no—
289#117—28no—
290#117D4×C1118yes—
291#117Q8×C1118yescomplemented
292C2×C4⋊C4—28no—
293C2×C4⋊C4C23×C1112yes—
294C2×C4⋊C4C23×C1114yes—
295C2×C4⋊C4C23×C1114yes—
296C2×C4⋊C4C23×C1118yes—
297C2×C4⋊C4C23×C1118yes—
298C2×C4⋊C4C23×C1118yes—
299C2×C4⋊C4C23×C1114yes—
300C2×C4⋊C4C23×C1118yes—
301C2×C4⋊C4C23×C1114yes—
302C2×C4⋊C4C23×C1118yes—
303C2×C4⋊C4C23×C1112yes—
304C2×C4⋊C4C23×C1112yes—
305C2×C4⋊C4C23×C1112yes—
306C2×C22⋊C4C23×C1114yes—
307C2×C22⋊C4C23×C1112yes—
308C2×C22⋊C4C23×C1112yes—
309C2×C42—28no—
310C2×C42Q8×C1118yescomplemented
311C2×C42C23×C1114yes—
312C2×C42C23×C1114yes—
313C2×C42C23×C1112yes—
314C2×C42C23×C1112yes—
315C2×C42C23×C1114yes—
316C2×C42C23×C1114yes—
317C2×C42C23×C1112yes—
318C2×C42C23×C1112yes—
319C2×C42C23×C1111yescharacteristic
320C2×C42C23×C1111yescharacteristic
321C2×C42C23×C1111yescharacteristic
322C2×C42C23×C1111yescharacteristic
323#95C23×C1114yes—
324#95C23×C1112yes—
325#95C23×C1112yes—
326#95C23×C1114yes—
327#95C23×C1114yes—
328#95C23×C1114yes—
329#95C23×C1114yes—
330#95C23×C1118yes—
331#95C23×C1118yes—
332C2×C11—24no—
333C2×C11C22×C4⋊Q811yescharacteristic
334C2×C11C2×#53311yescharacteristic
335C2×C11#345811yescharacteristic
336C2×C11D4×#4112yes—
337C2×C11Q8×#4112yes—
338C24C24×C1111yescharacteristic
339C2×Q8—216no—
340C2×Q8—216no—
341C2×Q8—48no—
342C22×C4—24no—
343C22×C4—28no—
344C22×C4—28no—
345C22×C4—42no—
346C22×C4—44no—
347C22×C4C2×D4×C1114yes—
348C22×C4C2×Q8×C1114yes—
349C22×C4C2×Q8×C1114yes—
350C22×C4C2×Q8×C1114yes—
351C22×C4C2×Q8×C1114yes—
352C22×C4C24×C1114yes—
353C22×C4C24×C1118yes—
354C22×C4C24×C1114yes—
355C22×C4C24×C1111yescharacteristic
356C22×C4C24×C1111yescharacteristic
357C22×C4C24×C1111yescharacteristic
358C22×C4C24×C1114yes—
359C22×C4C24×C1114yes—
360C22×C4C24×C1111yescharacteristic
361C22×C4C24×C1111yescharacteristic
362C22×C4C24×C1111yescharacteristic
363C4⋊C4—28no—
364C4⋊C4—216no—
365C4⋊C4—216no—
366C4⋊C4—216no—
367C4⋊C4—28no—
368C4⋊C4—24no—
369C4⋊C4—216no—
370C4⋊C4—28no—
371C4⋊C4—48no—
372C4⋊C4—44no—
373C4⋊C4C2×D4×C1118yes—
374C4⋊C4C2×Q8×C1118yes—
375C4⋊C4C11×#4118yes—
376C22⋊C4—28no—
377C22⋊C4C2×D4×C1118yes—
378C22⋊C4C2×Q8×C1118yes—
379C42—28no—
380C42—24no—
381C42—24no—
382C42—28no—
383C42—28no—
384C42—44no—
385C42C2×D4×C1118yes—
386C42C2×Q8×C1114yes—
387C42C2×Q8×C1114yes—
388C42C2×Q8×C1114yes—
389C42C2×Q8×C1114yes—
390C42C2×Q8×C1118yes—
391C11#3493811yescharacteristic, direct product factor, Sylow
392C23—22no—
393C23—22no—
394C23C22×D4×C1112yes—
395C23C22×Q8×C1112yes—
396C23C22×Q8×C1112yes—
397C23C25×C1111yescharacteristic
398Q8—432no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—28no—
409C2×C4—24no—
410C2×C4—28no—
411C2×C4—24no—
412C2×C4—28no—
413C2×C4—24no—
414C2×C4—28no—
415C2×C4—44no—
416C2×C4—416no—
417C2×C4C11×C4⋊Q8116yescomplemented
418C2×C4C22×D4×C1118yes—
419C2×C4C22×D4×C1112yes—
420C2×C4C22×D4×C1112yes—
421C2×C4C22×Q8×C1112yes—
422C2×C4C22×Q8×C1112yes—
423C2×C4C22×Q8×C1112yes—
424C2×C4C22×Q8×C1118yes—
425C2×C4C22×Q8×C1112yes—
426C2×C4C22×Q8×C1112yes—
427C2×C4C22×Q8×C1112yes—
428C2×C4C22×Q8×C1112yes—
429C2×C4C22×Q8×C1112yes—
430C2×C4C2×C11×#4118yes—
431C2×C4C2×C11×#4114yes—
432C22—22no—
433C22—22no—
434C22—24no—
435C22—24no—
436C22C2×C11×C4⋊Q814yes—
437C22C23×D4×C1111yescharacteristic
438C22C23×Q8×C1111yescharacteristic
439C22C23×Q8×C1111yescharacteristic
440C22C22×C11×#4112yes—
441C22C11×#58512yes—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—28no—
446C4—28no—
447C4—28no—
448C4—44no—
449C4—48no—
450C4C2×C11×C4⋊Q814yes—
451C4C2×C11×C4⋊Q814yes—
452C4C11×#53314yescomplemented
453C2—24no—
454C2C22×C11×C4⋊Q811yescharacteristic
455C2C2×C11×#53311yescharacteristic
456C2C11×#345811yescharacteristic
457C2D4×C11×#4112yes—
458C2Q8×C11×#4112yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC24×C11C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2552C2semidirect
3. C11×#2551C2semidirect
4. C11×#2550C2semidirect
7. C11×#2399C2semidirect
8. C4×C11×C4⋊Q8C2semidirect
68. C11×#117Q8semidirect
87. C2×C42×C11Q8semidirect
109. #34938C11direct (N × H)
164. #2552C2×C11semidirect
165. #2551C2×C11semidirect
166. #2550C2×C11semidirect
169. #2399C2×C11semidirect
170. C4×C4⋊Q8C2×C11semidirect
200. C2×C4×C11C4⋊Q8semidirect
278. C4×C11#533semidirect
291. #117Q8×C11semidirect
310. C2×C42Q8×C11semidirect
391. C11#34938direct (N × H)
417. C2×C4C11×C4⋊Q8semidirect
452. C4C11×#533semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C11×#25522
C11×#25512
C11×#25502
C11×#25492
C11×#24402
C11×#23992
C4×C11×C4⋊Q82
C11×#22962
C11×#22852
C4×C11×#1172
C2×C4×C11×C4⋊C42
#3493811