Finite Group Databasebeta

← C11×#18204 #14595397

Subgroups — C11×#18204 #14595397

Order 2816.

1002 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
1C11×#3501C211yesmaximal, characteristic
2C2×C11×#483C212yesmaximal, complemented
3C11×#2486C211yesmaximal, characteristic
4C11×#1611C214yesmaximal, complemented
5C11×#1608C214yesmaximal, complemented
6C11×#1520C212yesmaximal, complemented
7C11×#1459C211yesmaximal, characteristic
8C11×#554—24no—
9C11×#554—22no—
10D4×Q8×C11—22no—
11C11×#544C2212yes—
12C11×#543—21no—
13C11×#543C2212yes—
14C11×#533—21no—
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8C2212yes—
18C11×#518—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C11×#483—24no—
22C11×#483C2218yes—
23C2×C11×#106—22no—
24C2×C11×#103—22no—
25C2×C11×C22⋊C8C2212yes—
26C11×#398C2212yes—
27C11×#397C2212yes—
28C11×#389—21no—
29C11×#381—21no—
30C11×#380—21no—
31C11×#380C2211yescharacteristic
32C11×#328C2218yes—
33C11×#324C2212yes—
34C11×#323C2212yes—
35C22×Q8×C11—21no—
36C22×Q8×C11D412yes—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C8×C11—22no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—24no—
45C11×#125—22no—
46C11×#125—24no—
47C11×#123—44no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8D414yes—
59C11×C22⋊Q8C2314yes—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4C2311yescharacteristic
84C2×C42×C11D411yescharacteristic
85C11×#106—28no—
86C11×#103—28no—
87C11×C22⋊C8—22no—
88C11×C22⋊C8C2314yes—
89C11×#95—22no—
90C11×#95—22no—
91C11×#95C2312yes—
92#18204C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C2×D411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—44no—
99C2×Q8×C11—82no—
100C2×Q8×C11C2×D414yes—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11SD1614yes—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C2×C8×C11—24no—
125C2×C8×C11—44no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—44no—
141C11×C4⋊C4C2×D414yes—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—44no—
149C42×C11—24no—
150C42×C11—21no—
151C42×C11—21no—
152#3501C2×C1111yescharacteristic
153C2×#483C2×C1112yescomplemented
154#2486C2×C1111yescharacteristic
155#1611C2×C1114yescomplemented
156#1608C2×C1114yescomplemented
157#1520C2×C1112yescomplemented
158#1459C2×C1111yescharacteristic
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12012yes—
166C23×C11C2×SD1612yes—
167C23×C11C2×SD1612yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170Q8×C11—44no—
171Q8×C11—44no—
172Q8×C11—82no—
173Q8×C11—82no—
174D4×C11—28no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—21no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—21no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—81no—
195C2×C4×C11—82no—
196C2×C4×C11—82no—
197C2×C4×C11—82no—
198C2×C4×C11—82no—
199C2×C4×C11—84no—
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11C22×D412yes—
204C8×C11—44no—
205#554—24no—
206#554—22no—
207D4×Q8—22no—
208#544C22×C1112yes—
209#543—21no—
210#543C22×C1112yes—
211#533—21no—
212C2×#123—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8C22×C1112yes—
215#518—21no—
216C2×C4×D4C22×C1111yescharacteristic
217C22×C4⋊C4C22×C1111yescharacteristic
218#483—24no—
219#483C22×C1118yes—
220C2×#106—22no—
221C2×#103—22no—
222C2×C22⋊C8C22×C1112yes—
223#398C22×C1112yes—
224#397C22×C1112yes—
225#389—21no—
226#381—21no—
227#380—21no—
228#380C22×C1111yescharacteristic
229#328C22×C1118yes—
230#324C22×C1112yes—
231#323C22×C1112yes—
232C22×C11—21no—
233C22×C11—22no—
234C22×C11—21no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—81no—
243C22×C11#44814yes—
244C22×C11C2×#12011yescharacteristic
245C22×C11C22×SD1611yescharacteristic
246C22×C11C2×#13711yescharacteristic
247C4×C11—22no—
248C4×C11—21no—
249C4×C11—22no—
250C4×C11—41no—
251C4×C11—44no—
252C4×C11—41no—
253C4×C11—44no—
254C4×C11—82no—
255C4×C11—82no—
256C4×C11#45812yes—
257C22×Q8—21no—
258C22×Q8D4×C1112yes—
259C22×D4D4×C1111yescharacteristic
260C23×C4—21no—
261C23×C4D4×C1111yescharacteristic
262C23×C4C23×C1111yescharacteristic
263C22×C8—22no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—24no—
267#125—22no—
268#125—24no—
269#123—44no—
270C22⋊Q8—22no—
271C22⋊Q8—22no—
272C22⋊Q8—24no—
273C22⋊Q8—24no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—24no—
280C22⋊Q8D4×C1114yes—
281C22⋊Q8C23×C1114yes—
282C4×Q8—22no—
283C4×Q8—22no—
284C4×D4—24no—
285C4×D4—24no—
286C4×D4—22no—
287C4×D4—22no—
288#117—22no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4D4×C1112yes—
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1111yescharacteristic
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4D4×C1111yescharacteristic
305C2×C22⋊C4C23×C1111yescharacteristic
306C2×C42D4×C1111yescharacteristic
307#106—28no—
308#103—28no—
309C22⋊C8—22no—
310C22⋊C8C23×C1114yes—
311#95—22no—
312#95—22no—
313#95C23×C1112yes—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—24no—
317C2×C11—42no—
318C2×C11C2×#44811yescharacteristic
319C2×C11#302211yescharacteristic
320C2×C11C2×#45811yescharacteristic
321C24C2×D4×C1111yescharacteristic
322C24C2×D4×C1111yescharacteristic
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—44no—
327C2×Q8—82no—
328C2×Q8C2×D4×C1114yes—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4C11×SD1614yes—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C2×D4×C1112yes—
347C22×C4C2×D4×C1111yescharacteristic
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1112yes—
351C22×C4C24×C1111yescharacteristic
352C2×C8—24no—
353C2×C8—44no—
354C4⋊C4—22no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—42no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—44no—
369C4⋊C4C2×D4×C1114yes—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—22no—
373C22⋊C4—24no—
374C22⋊C4—22no—
375C22⋊C4—42no—
376C22⋊C4—44no—
377C42—24no—
378C42—21no—
379C42—21no—
380C11#1820411yescharacteristic, direct product factor, Sylow
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23C11×#12012yes—
388C23C2×C11×SD1612yes—
389C23C2×C11×SD1612yes—
390C23C11×#13712yes—
391C23C22×D4×C1111yescharacteristic
392Q8—44no—
393Q8—44no—
394Q8—82no—
395Q8—82no—
396D4—28no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—81no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—84no—
422C2×C4C11×#12011yescharacteristic
423C2×C4C11×#12011yescharacteristic
424C2×C4C2×C11×SD1612yes—
425C2×C4C22×D4×C1112yes—
426C8—44no—
427C22—21no—
428C22—22no—
429C22—21no—
430C22—22no—
431C22—22no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—41no—
436C22—41no—
437C22—81no—
438C22C11×#44814yes—
439C22C2×C11×#12011yescharacteristic
440C22C22×C11×SD1611yescharacteristic
441C22C2×C11×#13711yescharacteristic
442C4—22no—
443C4—22no—
444C4—21no—
445C4—41no—
446C4—44no—
447C4—41no—
448C4—44no—
449C4—82no—
450C4—82no—
451C4C11×#45812yes—
452C2—21no—
453C2—21no—
454C2—24no—
455C2—42no—
456C2C2×C11×#44811yescharacteristic
457C2C11×#302211yescharacteristic
458C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#483C2semidirect
4. C11×#1611C2semidirect
5. C11×#1608C2semidirect
6. C11×#1520C2semidirect
92. #18204C11direct (N × H)
153. C2×#483C2×C11semidirect
155. #1611C2×C11semidirect
156. #1608C2×C11semidirect
157. #1520C2×C11semidirect
380. C11#18204direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C2×C11×#4832
C11×#24862
C11×#16112
C11×#16082
C11×#15202
C11×#14592
#1820411