Finite Group Databasebeta

← C11×#18905 #14596098

Subgroups — C11×#18905 #14596098

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#3230C211yesmaximal, characteristic, complemented
3C11×#3209C211yesmaximal, characteristic, complemented
4C2×C11×#474C211yesmaximal, characteristic
5C11×#1649C214yesmaximal, complemented
6C11×#1644C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic
10C11×#554—21no—
11C11×#554—22no—
12C11×#554—22no—
13C11×#554C2212yes—
14D4×Q8×C11—21no—
15D4×Q8×C11C2212yes—
16C11×#544—21no—
17C11×#543—22no—
18C11×#533C2211yescharacteristic
19C11×#533C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8—22no—
22C11×#518—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#500C2212yescomplemented
25C11×#494—21no—
26C11×#487—21no—
27C11×#487C2212yescomplemented
28C11×#484—22no—
29C11×#477—22no—
30C11×#474—22no—
31C11×#474C2214yes—
32C11×#462C2214yescomplemented
33C11×#451—22no—
34C11×#431C2211yescharacteristic
35C11×#431C2211yescharacteristic
36C2×C11×#107—21no—
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#333C2212yescomplemented
40C11×#332C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yes—
43C22×Q8×C11—22no—
44C22×Q8×C11—21no—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×C11×Q16—24no—
48C22×C8×C11—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8C2312yes—
57C11×C4⋊Q8C2311yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×#125—22no—
60C11×#125—22no—
61C11×#125—21no—
62C11×#125—21no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8D412yes—
74C11×C22⋊Q8D412yes—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D412yes—
78C4×Q8×C11C2312yes—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11D412yes—
86C4×D4×C11C2312yes—
87C11×#117—21no—
88C11×#117—21no—
89C2×C11×C4⋊C4—24no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—21no—
96C2×C42×C11C2311yescharacteristic
97C11×#107—24no—
98C11×#107—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#18905C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C2×Q8×C11—24no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11—82no—
118C2×Q8×C11—84no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11C2×D412yes—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11Q1614yescomplemented
124C2×D4×C11C2×D412yes—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—41no—
131C22×C4×C11—82no—
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—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
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—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173#3501C2×C1111yescharacteristic
174#3230C2×C1111yescharacteristic, complemented
175#3209C2×C1111yescharacteristic, complemented
176C2×#474C2×C1111yescharacteristic
177#1649C2×C1114yescomplemented
178#1644C2×C1114yescomplemented
179#1542C2×C1111yescharacteristic, complemented
180#1481C2×C1111yescharacteristic, complemented
181#1478C2×C1111yescharacteristic
182C23×C11—22no—
183C23×C11—24no—
184C23×C11—81no—
185C23×C11—81no—
186C23×C11#12011yescharacteristic
187Q8×C11—24no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—44no—
191Q8×C11—81no—
192Q8×C11—82no—
193Q8×C11—84no—
194D4×C11—22no—
195D4×C11—24no—
196D4×C11C2×Q1614yes—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—44no—
205C2×C4×C11—42no—
206C2×C4×C11—82no—
207C2×C4×C11—81no—
208C2×C4×C11—84no—
209C2×C4×C11—84no—
210C2×C4×C11—82no—
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11C2×Q1612yes—
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#554—21no—
223#554—22no—
224#554—22no—
225#554C22×C1112yes—
226D4×Q8—21no—
227D4×Q8C22×C1112yes—
228#544—21no—
229#543—22no—
230#533C22×C1111yescharacteristic
231#533C22×C1111yescharacteristic
232C2×C4⋊Q8C22×C1111yescharacteristic
233C2×C22⋊Q8—22no—
234#518—21no—
235C2×C4×D4C22×C1111yescharacteristic
236#500C22×C1112yescomplemented
237#494—21no—
238#487—21no—
239#487C22×C1112yescomplemented
240#484—22no—
241#477—22no—
242#474—22no—
243#474C22×C1114yes—
244#462C22×C1114yescomplemented
245#451—22no—
246#431C22×C1111yescharacteristic
247#431C22×C1111yescharacteristic
248C2×#107—21no—
249C2×C4⋊C8C22×C1111yescharacteristic
250C2×#102—21no—
251#333C22×C1112yescomplemented
252#332C22×C1112yescomplemented
253Q8⋊C8C22×C1114yescomplemented
254D4⋊C8C22×C1114yes—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—24no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—84no—
261C22×C11#45112yes—
262C22×C11C2×#12011yescharacteristic
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—82no—
272C4×C11#45112yes—
273C4×C11C22×Q1611yescharacteristic
274C4×C11C2×#13711yescharacteristic
275C4×C11#57612yes—
276C22×Q8—22no—
277C22×Q8—21no—
278C22×D4D4×C1111yescharacteristic
279C23×C4—21no—
280C2×Q16—24no—
281C22×C8—21no—
282C4⋊Q8—22no—
283C4⋊Q8—22no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8D4×C1111yescharacteristic
288C4⋊Q8D4×C1111yescharacteristic
289C4⋊Q8C23×C1112yes—
290C4⋊Q8C23×C1111yescharacteristic
291C4⋊Q8C23×C1111yescharacteristic
292#125—22no—
293#125—22no—
294#125—21no—
295#125—21no—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—24no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306C22⋊Q8D4×C1112yes—
307C22⋊Q8D4×C1112yes—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8D4×C1112yes—
311C4×Q8C23×C1112yes—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4D4×C1112yes—
319C4×D4C23×C1112yes—
320#117—21no—
321#117—21no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4D4×C1111yescharacteristic
327C2×C22⋊C4—24no—
328C2×C22⋊C4—21no—
329C2×C42C23×C1111yescharacteristic
330#107—24no—
331#107—24no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8C23×C1112yes—
335C4⋊C8C23×C1112yes—
336#103—24no—
337#103—24no—
338#102—24no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C4×C8—21no—
342C4×C8C23×C1112yes—
343C2×C11—22no—
344C2×C11—44no—
345C2×C11C2×#45111yescharacteristic
346C2×C11#300811yescharacteristic
347C2×C11#302211yescharacteristic
348C24—21no—
349C2×Q8—24no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×Q8—84no—
356C2×Q8C2×D4×C1112yes—
357C2×Q8C2×D4×C1112yes—
358C2×D4—21no—
359C2×D4—22no—
360C2×D4C11×Q1614yescomplemented
361C2×D4C2×D4×C1112yes—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4—82no—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1111yescharacteristic
372Q16—84no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—42no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4C2×D4×C1112yes—
396C4⋊C4C2×D4×C1112yes—
397C4⋊C4C2×D4×C1112yes—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C42—22no—
405C42—22no—
406C42C2×D4×C1111yescharacteristic
407C42C2×D4×C1111yescharacteristic
408C42C2×D4×C1111yescharacteristic
409C42C24×C1111yescharacteristic
410C11#1890511yescharacteristic, direct product factor, Sylow
411C23—22no—
412C23—24no—
413C23—81no—
414C23—81no—
415C23C11×#12011yescharacteristic
416Q8—24no—
417Q8—42no—
418Q8—42no—
419Q8—44no—
420Q8—81no—
421Q8—82no—
422Q8—84no—
423D4—22no—
424D4—24no—
425D4C2×C11×Q1614yes—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—82no—
436C2×C4—81no—
437C2×C4—84no—
438C2×C4—84no—
439C2×C4—82no—
440C2×C4C11×#12011yescharacteristic
441C2×C4C11×#12011yescharacteristic
442C2×C4C11×#12011yescharacteristic
443C2×C4C2×C11×Q1612yes—
444C2×C4C11×#13712yes—
445C2×C4C22×D4×C1111yescharacteristic
446C2×C4C22×D4×C1111yescharacteristic
447C2×C4C22×D4×C1111yescharacteristic
448C8—42no—
449C8—42no—
450C8—42no—
451C22—21no—
452C22—21no—
453C22—24no—
454C22—42no—
455C22—42no—
456C22—84no—
457C22C11×#45112yes—
458C22C2×C11×#12011yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—82no—
468C4C11×#45112yes—
469C4C22×C11×Q1611yescharacteristic
470C4C2×C11×#13711yescharacteristic
471C4C11×#57612yes—
472C2—22no—
473C2—44no—
474C2C2×C11×#45111yescharacteristic
475C2C11×#300811yescharacteristic
476C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
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×#3230C2semidirect
3. C11×#3209C2semidirect
5. C11×#1649C2semidirect
6. C11×#1644C2semidirect
7. C11×#1542C2semidirect
8. C11×#1481C2semidirect
24. C11×#500C22semidirect
27. C11×#487C22semidirect
32. C11×#462C22semidirect
39. C11×#333C22semidirect
40. C11×#332C22semidirect
41. C11×Q8⋊C8C22semidirect
110. #18905C11direct (N × H)
123. C2×D4×C11Q16semidirect
174. #3230C2×C11semidirect
175. #3209C2×C11semidirect
177. #1649C2×C11semidirect
178. #1644C2×C11semidirect
179. #1542C2×C11semidirect
180. #1481C2×C11semidirect
236. #500C22×C11semidirect
239. #487C22×C11semidirect
244. #462C22×C11semidirect
251. #333C22×C11semidirect
252. #332C22×C11semidirect
253. Q8⋊C8C22×C11semidirect
360. C2×D4C11×Q16semidirect
410. C11#18905direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#32302
C11×#32092
C2×C11×#4742
C11×#16492
C11×#16442
C11×#15422
C11×#14812
C11×#14782
#1890511