Finite Group Databasebeta

← C11×#18908 #14596101

Subgroups — C11×#18908 #14596101

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#3229C211yesmaximal, characteristic, complemented
3C11×#3226C211yesmaximal, characteristic
4C2×C11×#462C211yesmaximal, characteristic, complemented
5C11×#1652C214yesmaximal, complemented
6C11×#1644C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic
9C11×#1479C211yesmaximal, characteristic, complemented
10C22×C11×Q16—21no—
11C11×#559—21no—
12C11×#557—21no—
13C11×#556—22no—
14C11×#556C2212yes—
15C11×#554C2212yes—
16C11×#552—22no—
17C11×#539—22no—
18C11×#536—21no—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#529—22no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#500—21no—
26C11×#498C2212yes—
27C11×#487C2212yes—
28C11×#486—21no—
29C11×#483—22no—
30C11×#480—22no—
31C11×#475—22no—
32C11×#474C2214yes—
33C11×#462—22no—
34C11×#462C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#333C2212yes—
40C11×#332C2212yes—
41C11×Q8⋊C8C2214yes—
42C11×D4⋊C8C2214yes—
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11D411yescharacteristic
46C2×C11×Q16—24no—
47C2×C11×Q16—44no—
48C22×C8×C11—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127D411yescharacteristic
58C11×#126—24no—
59C11×#126—24no—
60C11×#125—24no—
61C11×#125—22no—
62C11×#125—21no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#124—21no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8D412yes—
73C11×#121—21no—
74C11×#121D412yes—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×Q8×C11D412yes—
82C4×Q8×C11C2312yes—
83C4×D4×C11—24no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—21no—
87C4×D4×C11C2312yes—
88C11×#117—24no—
89C11×#117—21no—
90C11×#117—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C11×#107—24no—
99C11×#106—24no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#103—24no—
105C11×#103—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18908C1111yesmaximal, characteristic, direct product factor, Sylow
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—41no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11C2×D412yes—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C11×Q16—48no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—42no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11—24no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175#3507C2×C1111yescharacteristic
176#3229C2×C1111yescharacteristic, complemented
177#3226C2×C1111yescharacteristic
178C2×#462C2×C1111yescharacteristic, complemented
179#1652C2×C1114yescomplemented
180#1644C2×C1114yescomplemented
181#1542C2×C1111yescharacteristic, complemented
182#1480C2×C1111yescharacteristic
183#1479C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11#12011yescharacteristic
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—82no—
195D4×C11—24no—
196D4×C11—44no—
197D4×C11—42no—
198D4×C11—81no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—81no—
211C2×C4×C11—84no—
212C2×C4×C11—82no—
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#13512yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C8×C11—42no—
222C8×C11—42no—
223C8×C11—42no—
224C22×Q16—21no—
225#559—21no—
226#557—21no—
227#556—22no—
228#556C22×C1112yes—
229#554C22×C1112yes—
230#552—22no—
231#539—22no—
232#536—21no—
233#533C22×C1111yescharacteristic
234#532C22×C1111yescharacteristic
235C2×C4⋊Q8C22×C1111yescharacteristic
236#529—22no—
237#520—21no—
238C2×C4×Q8C22×C1111yescharacteristic
239#500—21no—
240#498C22×C1112yes—
241#487C22×C1112yes—
242#486—21no—
243#483—22no—
244#480—22no—
245#475—22no—
246#474C22×C1114yes—
247#462—22no—
248#462C22×C1114yes—
249#431C22×C1111yescharacteristic
250#431C22×C1111yescharacteristic
251C2×C4⋊C8C22×C1111yescharacteristic
252C2×#103—21no—
253#333C22×C1112yes—
254#332C22×C1112yes—
255Q8⋊C8C22×C1114yes—
256D4⋊C8C22×C1114yes—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11#44912yes—
263C22×C11C2×#12011yescharacteristic
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—82no—
273C4×C11#44912yes—
274C4×C11C2×#13511yescharacteristic
275C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
276C4×C11#57812yes—
277C2×#41—21no—
278C22×Q8—21no—
279C22×Q8D4×C1111yescharacteristic
280C2×Q16—24no—
281C2×Q16—44no—
282C22×C8—21no—
283C4⋊Q8—22no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8D4×C1111yescharacteristic
288C4⋊Q8C23×C1112yes—
289C4⋊Q8C23×C1111yescharacteristic
290C4⋊Q8C23×C1111yescharacteristic
291#127D4×C1111yescharacteristic
292#126—24no—
293#126—24no—
294#125—24no—
295#125—22no—
296#125—21no—
297#124—22no—
298#124—22no—
299#124—21no—
300#123—24no—
301#123—24no—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C22⋊Q8—24no—
305C22⋊Q8—21no—
306C22⋊Q8D4×C1112yes—
307#121—21no—
308#121D4×C1112yes—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C1112yes—
315C4×Q8D4×C1112yes—
316C4×Q8C23×C1112yes—
317C4×D4—24no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—21no—
321C4×D4C23×C1112yes—
322#117—24no—
323#117—21no—
324#117—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4D4×C1111yescharacteristic
330C2×C42—21no—
331C2×C42C23×C1111yescharacteristic
332#107—24no—
333#106—24no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8C23×C1112yes—
337C4⋊C8C23×C1112yes—
338#103—24no—
339#103—24no—
340#102—24no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C4×C8—21no—
344C4×C8C23×C1112yes—
345C2×C11—22no—
346C2×C11—82no—
347C2×C11C2×#44911yescharacteristic
348C2×C11#301111yescharacteristic
349C2×C11#302211yescharacteristic
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8C2×D4×C1112yes—
362C2×Q8C2×D4×C1112yes—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4C2×D4×C1112yes—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—41no—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1111yescharacteristic
375Q16—48no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—42no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C1112yes—
397C4⋊C4C2×D4×C1112yes—
398C4⋊C4C2×D4×C1112yes—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C42—24no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42C2×D4×C1111yescharacteristic
410C42C2×D4×C1111yescharacteristic
411C42C2×D4×C1111yescharacteristic
412C42C24×C1111yescharacteristic
413C11#1890811yescharacteristic, direct product factor, Sylow
414C23—22no—
415C23C11×#12011yescharacteristic
416Q8—22no—
417Q8—22no—
418Q8—42no—
419Q8—42no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—42no—
424Q8—82no—
425D4—24no—
426D4—44no—
427D4—42no—
428D4—81no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—84no—
442C2×C4—82no—
443C2×C4C11×#12011yescharacteristic
444C2×C4C11×#12011yescharacteristic
445C2×C4C11×#12011yescharacteristic
446C2×C4C11×#13512yes—
447C2×C4C11×AGL(1,ℤ/8)12yes—
448C2×C4C22×D4×C1111yescharacteristic
449C2×C4C22×D4×C1111yescharacteristic
450C2×C4C22×D4×C1111yescharacteristic
451C8—42no—
452C8—42no—
453C8—42no—
454C22—21no—
455C22—21no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22C11×#44912yes—
460C22C2×C11×#12011yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4C11×#44912yes—
471C4C2×C11×#13511yescharacteristic
472C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
473C4C11×#57812yes—
474C2—22no—
475C2—82no—
476C2C2×C11×#44911yescharacteristic
477C2C11×#301111yescharacteristic
478C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3229C2semidirect
4. C2×C11×#462C2semidirect
5. C11×#1652C2semidirect
6. C11×#1644C2semidirect
7. C11×#1542C2semidirect
9. C11×#1479C2semidirect
111. #18908C11direct (N × H)
176. #3229C2×C11semidirect
178. C2×#462C2×C11semidirect
179. #1652C2×C11semidirect
180. #1644C2×C11semidirect
181. #1542C2×C11semidirect
183. #1479C2×C11semidirect
413. C11#18908direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#32292
C11×#32262
C2×C11×#4622
C11×#16522
C11×#16442
C11×#15422
C11×#14802
C11×#14792
#1890811