Finite Group Databasebeta

← C11×#18398 #14595591

Subgroups — C11×#18398 #14595591

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 486 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
4C11×#2546C211yesmaximal, characteristic, complemented
5C11×#1609C218yesmaximal, complemented
6C11×#1503C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic
8C11×#1461C211yesmaximal, characteristic, complemented
9C11×#559—21no—
10C11×#557—21no—
11C11×#556—21no—
12C11×#556—22no—
13C11×#554—21no—
14C11×#552—22no—
15C11×#539C2214yes—
16C11×#536—21no—
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×C11×C4⋊Q8—21no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C11×#529—22no—
22C11×#520—21no—
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#500—21no—
25C11×#498—21no—
26C11×#487—21no—
27C11×#486—21no—
28C11×#483C2214yes—
29C11×#480C2214yes—
30C11×#475—22no—
31C11×#474—22no—
32C11×#431C2211yescharacteristic
33C11×#431C2211yescharacteristic
34C11×#398C2214yes—
35C11×#391—21no—
36C11×#389—22no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#328C2214yes—
39C11×#327C2214yes—
40C11×#324C2214yes—
41C2×C11×#41—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11D411yescharacteristic
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—44no—
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8D411yescharacteristic
52C11×C4⋊Q8D411yescharacteristic
53C11×#127D411yescharacteristic
54C11×#126—24no—
55C11×#126—24no—
56C11×#125—22no—
57C11×#125—24no—
58C11×#125—21no—
59C11×#124—22no—
60C11×#124—22no—
61C11×#124—21no—
62C11×#123—24no—
63C11×#123—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8C2312yes—
69C11×#121—21no—
70C11×#121C2312yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D412yes—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—24no—
82C4×D4×C11—21no—
83C4×D4×C11D412yes—
84C11×#117—22no—
85C11×#117—24no—
86C11×#117—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C42×C11—21no—
95C2×C42×C11D412yes—
96C2×C42×C11C2311yescharacteristic
97C11×#107—24no—
98C11×#106—24no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×#103—24no—
102C11×#102—24no—
103C11×C22⋊C8C2312yes—
104C11×C22⋊C8C2312yes—
105C4×C8×C11—21no—
106C4×C8×C11—21no—
107C11×#95—24no—
108C11×#95C2312yes—
109#18398C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—42no—
111C11×#41—42no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—22no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—48no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C42×C11—24no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—42no—
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174#3507C2×C1111yescharacteristic
175#3229C2×C1111yescharacteristic, complemented
176#3226C2×C1111yescharacteristic
177#2546C2×C1111yescharacteristic, complemented
178#1609C2×C1118yescomplemented
179#1503C2×C1111yescharacteristic, complemented
180#1502C2×C1111yescharacteristic
181#1461C2×C1111yescharacteristic, complemented
182C23×C11—22no—
183C23×C11C22×D411yescharacteristic
184Q8×C11—42no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—82no—
190Q8×C11—82no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
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—44no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—84no—
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#13512yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C8×C11—42no—
223C8×C11—42no—
224#559—21no—
225#557—21no—
226#556—21no—
227#556—22no—
228#554—21no—
229#552—22no—
230#539C22×C1114yes—
231#536—21no—
232#533C22×C1111yescharacteristic
233#532C22×C1111yescharacteristic
234C2×C4⋊Q8—21no—
235C2×C4⋊Q8C22×C1111yescharacteristic
236#529—22no—
237#520—21no—
238C2×C4×Q8C22×C1111yescharacteristic
239#500—21no—
240#498—21no—
241#487—21no—
242#486—21no—
243#483C22×C1114yes—
244#480C22×C1114yes—
245#475—22no—
246#474—22no—
247#431C22×C1111yescharacteristic
248#431C22×C1111yescharacteristic
249#398C22×C1114yes—
250#391—21no—
251#389—22no—
252C4×C4⋊C4C22×C1111yescharacteristic
253#328C22×C1114yes—
254#327C22×C1114yes—
255#324C22×C1114yes—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C2×#12011yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—44no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—82no—
274C4×C11#44912yes—
275C4×C11#44912yes—
276C4×C11#45612yes—
277C2×#41—21no—
278C22×Q8—21no—
279C22×Q8D4×C1111yescharacteristic
280C4⋊Q8—22no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—44no—
286C4⋊Q8D4×C1111yescharacteristic
287C4⋊Q8D4×C1111yescharacteristic
288C4⋊Q8D4×C1111yescharacteristic
289#127D4×C1111yescharacteristic
290#126—24no—
291#126—24no—
292#125—22no—
293#125—24no—
294#125—21no—
295#124—22no—
296#124—22no—
297#124—21no—
298#123—24no—
299#123—24no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302C22⋊Q8—24no—
303C22⋊Q8—21no—
304C22⋊Q8C23×C1112yes—
305#121—21no—
306#121C23×C1112yes—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C1112yes—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—24no—
318C4×D4—21no—
319C4×D4D4×C1112yes—
320#117—22no—
321#117—24no—
322#117—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4D4×C1111yescharacteristic
328C2×C4⋊C4C23×C1112yes—
329C2×C4⋊C4C23×C1112yes—
330C2×C42—21no—
331C2×C42D4×C1112yes—
332C2×C42C23×C1111yescharacteristic
333#107—24no—
334#106—24no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337#103—24no—
338#102—24no—
339C22⋊C8C23×C1112yes—
340C22⋊C8C23×C1112yes—
341C4×C8—21no—
342C4×C8—21no—
343#95—24no—
344#95C23×C1112yes—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—82no—
348C2×C11C2×#44911yescharacteristic
349C2×C11C2×#45611yescharacteristic
350C2×C11#302811yescharacteristic
351#41—42no—
352#41—42no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—42no—
362C2×Q8—42no—
363C2×Q8C2×D4×C1112yes—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C2×D4×C1112yes—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4C2×D4×C1112yes—
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1112yes—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C24×C1111yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—48no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C1112yes—
399C4⋊C4C2×D4×C1112yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C42—24no—
407C42—22no—
408C42—22no—
409C42—22no—
410C42—42no—
411C42C2×D4×C1111yescharacteristic
412C42C2×D4×C1111yescharacteristic
413C42C2×D4×C1111yescharacteristic
414C42C2×D4×C1111yescharacteristic
415C11#1839811yescharacteristic, direct product factor, Sylow
416C23—22no—
417C23C22×D4×C1111yescharacteristic
418Q8—42no—
419Q8—42no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—82no—
424Q8—82no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—84no—
448C2×C4C11×#12011yescharacteristic
449C2×C4C11×#12011yescharacteristic
450C2×C4C11×#12011yescharacteristic
451C2×C4C11×#12011yescharacteristic
452C2×C4C11×#13512yes—
453C2×C4C11×AGL(1,ℤ/8)12yes—
454C2×C4C22×D4×C1111yescharacteristic
455C2×C4C22×D4×C1111yescharacteristic
456C8—42no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22C2×C11×#12011yescharacteristic
464C22C2×C11×#13511yescharacteristic
465C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—44no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4C11×#44912yes—
477C4C11×#44912yes—
478C4C11×#45612yes—
479C2—21no—
480C2—21no—
481C2—82no—
482C2C2×C11×#44911yescharacteristic
483C2C2×C11×#45611yescharacteristic
484C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#532C22
LCSG ▷ C22×C4 ▷ 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. C11×#2546C2semidirect
5. C11×#1609C2semidirect
6. C11×#1503C2semidirect
8. C11×#1461C2semidirect
109. #18398C11direct (N × H)
175. #3229C2×C11semidirect
177. #2546C2×C11semidirect
178. #1609C2×C11semidirect
179. #1503C2×C11semidirect
181. #1461C2×C11semidirect
415. C11#18398direct (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
C11×#25462
C11×#16092
C11×#15032
C11×#15022
C11×#14612
#1839811