Finite Group Databasebeta

← C11×#18907 #14596100

Subgroups — C11×#18907 #14596100

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#3227C211yesmaximal, characteristic
3C11×#3209C211yesmaximal, characteristic, complemented
4C2×C11×#475C211yesmaximal, characteristic, complemented
5C11×#1653C214yesmaximal, complemented
6C11×#1640C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C11×#559C2212yes—
11C11×#557C2212yes—
12C11×#556—21no—
13C11×#556—22no—
14C11×#554—21no—
15C11×#552—22no—
16C11×#539—22no—
17C11×#536—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C11×#529—22no—
22C11×#520—21no—
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#498C2212yes—
25C11×#494—21no—
26C11×#487—21no—
27C11×#486C2212yes—
28C11×#481—22no—
29C11×#476—22no—
30C11×#475—22no—
31C11×#475C2214yes—
32C11×#462C2214yes—
33C11×#451—22no—
34C11×#431C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C2×C11×#106—21no—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#332C2212yes—
40C11×#331C2212yes—
41C11×Q8⋊C8C2214yes—
42C11×Q8⋊C8C2214yes—
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11D411yescharacteristic
46C2×C11×Q16—24no—
47C22×C8×C11—21no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#126—24no—
58C11×#126—24no—
59C11×#125—22no—
60C11×#125—24no—
61C11×#125—21no—
62C11×#124—22no—
63C11×#124—22no—
64C11×#124—21no—
65C11×#123—24no—
66C11×#123—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8D412yes—
72C11×#121—21no—
73C11×#121D412yes—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11D412yes—
80C4×Q8×C11C2312yes—
81C4×Q8×C11C2312yes—
82C4×D4×C11—24no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C11×#117—22no—
88C11×#117—24no—
89C11×#117—21no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C11×#106—24no—
98C11×#106—24no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2312yes—
102C11×C4⋊C8C2312yes—
103C11×#103—24no—
104C11×#103—24no—
105C11×#102—24no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2312yes—
110#18907C1111yesmaximal, characteristic, direct product factor, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—41no—
120C2×Q8×C11—82no—
121C2×Q8×C11C2×D412yes—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—22no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C11×Q16—84no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—42no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
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—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4C2×D412yes—
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×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173#3507C2×C1111yescharacteristic
174#3227C2×C1111yescharacteristic
175#3209C2×C1111yescharacteristic, complemented
176C2×#475C2×C1111yescharacteristic, complemented
177#1653C2×C1114yescomplemented
178#1640C2×C1114yescomplemented
179#1540C2×C1111yescharacteristic
180#1481C2×C1111yescharacteristic, complemented
181#1479C2×C1111yescharacteristic, complemented
182C23×C11—22no—
183C23×C11#12011yescharacteristic
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—24no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—42no—
190Q8×C11—44no—
191Q8×C11—81no—
192Q8×C11—82no—
193D4×C11—42no—
194D4×C11—44no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—42no—
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—41no—
205C2×C4×C11—42no—
206C2×C4×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11—81no—
209C2×C4×C11—84no—
210C2×C4×C11—82no—
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#13512yes—
215C2×C4×C11#13712yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C8×C11—42no—
220C8×C11—42no—
221C8×C11—42no—
222#559C22×C1112yes—
223#557C22×C1112yes—
224#556—21no—
225#556—22no—
226#554—21no—
227#552—22no—
228#539—22no—
229#536—21no—
230#533C22×C1111yescharacteristic
231#532C22×C1111yescharacteristic
232C2×C4⋊Q8C22×C1111yescharacteristic
233#529—22no—
234#520—21no—
235C2×C4×Q8C22×C1111yescharacteristic
236#498C22×C1112yes—
237#494—21no—
238#487—21no—
239#486C22×C1112yes—
240#481—22no—
241#476—22no—
242#475—22no—
243#475C22×C1114yes—
244#462C22×C1114yes—
245#451—22no—
246#431C22×C1111yescharacteristic
247#431C22×C1111yescharacteristic
248C2×#106—21no—
249C2×C4⋊C8C22×C1111yescharacteristic
250C2×#103—21no—
251#332C22×C1112yes—
252#331C22×C1112yes—
253Q8⋊C8C22×C1114yes—
254Q8⋊C8C22×C1114yes—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11#45212yes—
261C22×C11C2×#12011yescharacteristic
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—82no—
271C4×C11#45212yes—
272C4×C11C2×#13511yescharacteristic
273C4×C11C2×#13711yescharacteristic
274C4×C11#57712yes—
275C2×#41—21no—
276C22×Q8—21no—
277C22×Q8D4×C1111yescharacteristic
278C2×Q16—24no—
279C22×C8—21no—
280C4⋊Q8—22no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8D4×C1111yescharacteristic
285C4⋊Q8D4×C1111yescharacteristic
286C4⋊Q8C23×C1112yes—
287C4⋊Q8C23×C1111yescharacteristic
288#127C23×C1111yescharacteristic
289#126—24no—
290#126—24no—
291#125—22no—
292#125—24no—
293#125—21no—
294#124—22no—
295#124—22no—
296#124—21no—
297#123—24no—
298#123—24no—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301C22⋊Q8—24no—
302C22⋊Q8—21no—
303C22⋊Q8D4×C1112yes—
304#121—21no—
305#121D4×C1112yes—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×Q8D4×C1112yes—
312C4×Q8C23×C1112yes—
313C4×Q8C23×C1112yes—
314C4×D4—24no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—21no—
318C4×D4D4×C1112yes—
319#117—22no—
320#117—24no—
321#117—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4D4×C1111yescharacteristic
327C2×C42—21no—
328C2×C42C23×C1111yescharacteristic
329#106—24no—
330#106—24no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8C23×C1112yes—
334C4⋊C8C23×C1112yes—
335#103—24no—
336#103—24no—
337#102—24no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C4×C8—21no—
341C4×C8C23×C1112yes—
342C2×C11—22no—
343C2×C11—82no—
344C2×C11C2×#45211yescharacteristic
345C2×C11#301011yescharacteristic
346C2×C11#302211yescharacteristic
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—41no—
356C2×Q8—82no—
357C2×Q8C2×D4×C1112yes—
358C2×Q8C2×D4×C1112yes—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C2×D4×C1112yes—
363C22×C4—21no—
364C22×C4—24no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371Q16—84no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—42no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4C2×D4×C1112yes—
393C4⋊C4C2×D4×C1112yes—
394C4⋊C4C2×D4×C1112yes—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C42—24no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42C2×D4×C1111yescharacteristic
406C42C2×D4×C1111yescharacteristic
407C42C2×D4×C1111yescharacteristic
408C42C24×C1111yescharacteristic
409C11#1890711yescharacteristic, direct product factor, Sylow
410C23—22no—
411C23C11×#12011yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—24no—
415Q8—41no—
416Q8—41no—
417Q8—42no—
418Q8—44no—
419Q8—81no—
420Q8—82no—
421D4—42no—
422D4—44no—
423D4—41no—
424D4—41no—
425D4—42no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—84no—
438C2×C4—82no—
439C2×C4C11×#12011yescharacteristic
440C2×C4C11×#12011yescharacteristic
441C2×C4C11×#12011yescharacteristic
442C2×C4C11×#13512yes—
443C2×C4C11×#13712yes—
444C2×C4C22×D4×C1111yescharacteristic
445C2×C4C22×D4×C1111yescharacteristic
446C2×C4C22×D4×C1111yescharacteristic
447C8—42no—
448C8—42no—
449C8—42no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22C11×#45212yes—
456C22C2×C11×#12011yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—82no—
466C4C11×#45212yes—
467C4C2×C11×#13511yescharacteristic
468C4C2×C11×#13711yescharacteristic
469C4C11×#57712yes—
470C2—22no—
471C2—82no—
472C2C2×C11×#45211yescharacteristic
473C2C11×#301011yescharacteristic
474C2C11×#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
3. C11×#3209C2semidirect
4. C2×C11×#475C2semidirect
5. C11×#1653C2semidirect
6. C11×#1640C2semidirect
8. C11×#1481C2semidirect
9. C11×#1479C2semidirect
110. #18907C11direct (N × H)
175. #3209C2×C11semidirect
176. C2×#475C2×C11semidirect
177. #1653C2×C11semidirect
178. #1640C2×C11semidirect
180. #1481C2×C11semidirect
181. #1479C2×C11semidirect
409. C11#18907direct (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×#32272
C11×#32092
C2×C11×#4752
C11×#16532
C11×#16402
C11×#15402
C11×#14812
C11×#14792
#1890711