Finite Group Databasebeta

← C11×#18218 #14595411

Subgroups — C11×#18218 #14595411

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic, complemented
2C11×#3100C212yesmaximal, complemented
3C11×#2536C211yesmaximal, characteristic, complemented
4C11×#1610C214yesmaximal, complemented
5C11×#1598C214yesmaximal, complemented
6C11×#1517C212yesmaximal, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C2×C11×2−1+4—21no—
9C11×#550—22no—
10D4×Q8×C11—22no—
11C11×#548—24no—
12C11×#537—21no—
13C11×#537C2214yes—
14C11×#532—22no—
15C11×#532C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#480C2214yes—
20C11×#474—22no—
21C11×#459—22no—
22C11×#447C2214yes—
23C4×C11×D8—24no—
24C11×#431C2212yes—
25C11×#398C2212yes—
26C11×#394C2212yes—
27C11×#388—22no—
28C11×#382C2211yescharacteristic
29C11×#380—21no—
30C11×#327C2218yes—
31C11×#324C2214yes—
32C11×2−1+4—44no—
33C11×2−1+4—44no—
34C2×C11×#41—24no—
35C2×C11×#41—24no—
36C2×C11×#41—22no—
37C22×Q8×C11—24no—
38C22×Q8×C11D411yescharacteristic
39C22×D4×C11C2311yescharacteristic
40C23×C4×C11—21no—
41C2×C11×D8—24no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8D412yes—
44C11×#127—22no—
45C11×#127D412yes—
46C11×#124—24no—
47C11×#124—22no—
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—44no—
51C11×#121—24no—
52C11×#121—28no—
53C11×#121—22no—
54C11×#121—24no—
55C11×#121C2314yes—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—24no—
59C4×D4×C11—24no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11D414yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11D412yes—
73C2×C42×C11C2311yescharacteristic
74C11×#107—24no—
75C11×C4⋊C8—22no—
76C11×#102—24no—
77C11×#102—24no—
78C11×C22⋊C8C2314yes—
79C4×C8×C11—22no—
80C11×#95—22no—
81C11×#95—21no—
82C11×#95C2312yes—
83#18218C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—21no—
85C11×#41—48no—
86C11×#41—416no—
87C11×#41—48no—
88C11×#41—44no—
89C11×#41—44no—
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—416no—
95C2×Q8×C11D814yescomplemented
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—42no—
103C2×D4×C11C2×D414yes—
104C22×C4×C11—28no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C11×D8—48no—
117C2×C8×C11—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4C2×D414yes—
126C11×C22⋊C4—28no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—44no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—44no—
133C42×C11—22no—
134C42×C11—22no—
135C42×C11C2×D412yes—
136C42×C11C2×D412yes—
137#3497C2×C1111yescharacteristic, complemented
138#3100C2×C1112yescomplemented
139#2536C2×C1111yescharacteristic, complemented
140#1610C2×C1114yescomplemented
141#1598C2×C1114yescomplemented
142#1517C2×C1112yescomplemented
143#1461C2×C1111yescharacteristic, complemented
144C23×C11—22no—
145C23×C11—24no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11C22×D411yescharacteristic
153Q8×C11—28no—
154Q8×C11—48no—
155Q8×C11—44no—
156D4×C11—24no—
157D4×C11—44no—
158D4×C11—44no—
159D4×C11—42no—
160D4×C11—48no—
161D4×C11—44no—
162D4×C11—44no—
163D4×C11—44no—
164D4×C11—84no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—416no—
172C2×C4×C11—48no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—84no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12012yes—
184C2×C4×C11C2×D814yes—
185C2×C4×C11C2×D812yes—
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11C22×D412yes—
188C8×C11—44no—
189C2×2−1+4—21no—
190#550—22no—
191D4×Q8—22no—
192#548—24no—
193#537—21no—
194#537C22×C1114yes—
195#532—22no—
196#532C22×C1112yes—
197C2×C22⋊Q8—21no—
198C2×C4×Q8C22×C1111yescharacteristic
199C2×C4×D4C22×C1111yescharacteristic
200#480C22×C1114yes—
201#474—22no—
202#459—22no—
203#447C22×C1114yes—
204C4×D8—24no—
205#431C22×C1112yes—
206#398C22×C1112yes—
207#394C22×C1112yes—
208#388—22no—
209#382C22×C1111yescharacteristic
210#380—21no—
211#327C22×C1118yes—
212#324C22×C1114yes—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—44no—
218C22×C11—44no—
219C22×C11—42no—
220C22×C11—44no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11C2×#12011yescharacteristic
226C22×C11C22×D811yescharacteristic
227C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C11—24no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—22no—
232C4×C11—44no—
233C4×C11—42no—
234C4×C11—82no—
235C4×C11—81no—
236C4×C11#44714yes—
2372−1+4—44no—
2382−1+4—44no—
239C2×#41—24no—
240C2×#41—24no—
241C2×#41—22no—
242C22×Q8—24no—
243C22×Q8D4×C1111yescharacteristic
244C22×D4C23×C1111yescharacteristic
245C23×C4—21no—
246C2×D8—24no—
247C4⋊Q8—22no—
248C4⋊Q8D4×C1112yes—
249#127—22no—
250#127D4×C1112yes—
251#124—24no—
252#124—22no—
253C22⋊Q8—24no—
254C22⋊Q8—28no—
255C22⋊Q8—44no—
256#121—24no—
257#121—28no—
258#121—22no—
259#121—24no—
260#121C23×C1114yes—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×D4—24no—
264C4×D4—24no—
265C4×D4—22no—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4D4×C1114yes—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4D4×C1111yescharacteristic
272C2×C4⋊C4C23×C1111yescharacteristic
273C2×C4⋊C4C23×C1112yes—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C42D4×C1112yes—
278C2×C42C23×C1111yescharacteristic
279#107—24no—
280C4⋊C8—22no—
281#102—24no—
282#102—24no—
283C22⋊C8C23×C1114yes—
284C4×C8—22no—
285#95—22no—
286#95—21no—
287#95C23×C1112yes—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—84no—
291C2×C11—82no—
292C2×C11C2×#44711yescharacteristic
293C2×C11#302011yescharacteristic
294C2×C11#302511yescharacteristic
295C24—21no—
296#41—48no—
297#41—416no—
298#41—48no—
299#41—44no—
300#41—44no—
301C2×Q8—24no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—416no—
306C2×Q8C11×D814yescomplemented
307C2×D4—24no—
308C2×D4—24no—
309C2×D4—24no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—42no—
314C2×D4C2×D4×C1114yes—
315C22×C4—28no—
316C22×C4—24no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4C2×D4×C1112yes—
323C22×C4C2×D4×C1112yes—
324C22×C4C2×D4×C1111yescharacteristic
325C22×C4C2×D4×C1111yescharacteristic
326C22×C4C24×C1111yescharacteristic
327D8—48no—
328C2×C8—24no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—42no—
335C4⋊C4—44no—
336C4⋊C4C2×D4×C1114yes—
337C22⋊C4—28no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—44no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—44no—
344C42—22no—
345C42—22no—
346C42C2×D4×C1112yes—
347C42C2×D4×C1112yes—
348C11#1821811yescharacteristic, direct product factor, Sylow
349C23—22no—
350C23—24no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C22×D4×C1111yescharacteristic
358Q8—28no—
359Q8—48no—
360Q8—44no—
361D4—24no—
362D4—44no—
363D4—44no—
364D4—42no—
365D4—48no—
366D4—44no—
367D4—44no—
368D4—44no—
369D4—84no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—416no—
377C2×C4—48no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—84no—
386C2×C4C11×#12011yescharacteristic
387C2×C4C11×#12011yescharacteristic
388C2×C4C11×#12012yes—
389C2×C4C2×C11×D814yes—
390C2×C4C2×C11×D812yes—
391C2×C4C11×AGL(1,ℤ/8)12yes—
392C2×C4C22×D4×C1112yes—
393C8—44no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—44no—
399C22—44no—
400C22—42no—
401C22—44no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22C2×C11×#12011yescharacteristic
407C22C22×C11×D811yescharacteristic
408C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
409C4—24no—
410C4—21no—
411C4—21no—
412C4—22no—
413C4—44no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4C11×#44714yes—
418C2—21no—
419C2—21no—
420C2—82no—
421C2—84no—
422C2C2×C11×#44711yescharacteristic
423C2C11×#302011yescharacteristic
424C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C11×#3497C2semidirect
2. C11×#3100C2semidirect
3. C11×#2536C2semidirect
4. C11×#1610C2semidirect
5. C11×#1598C2semidirect
6. C11×#1517C2semidirect
7. C11×#1461C2semidirect
83. #18218C11direct (N × H)
95. C2×Q8×C11D8semidirect
137. #3497C2×C11semidirect
138. #3100C2×C11semidirect
139. #2536C2×C11semidirect
140. #1610C2×C11semidirect
141. #1598C2×C11semidirect
142. #1517C2×C11semidirect
143. #1461C2×C11semidirect
306. C2×Q8C11×D8semidirect
348. C11#18218direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34972
C11×#31002
C11×#25362
C11×#16102
C11×#15982
C11×#15172
C11×#14612
#1821811