Finite Group Databasebeta

← C11×#18293 #14595486

Subgroups — C11×#18293 #14595486

Order 2816.

1220 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C11×#3187C212yesmaximal, complemented
3C11×#2627C211yesmaximal, characteristic, complemented
4C11×#1616C214yesmaximal, complemented
5C11×#1604C214yesmaximal, complemented
6C11×#1519C212yesmaximal, complemented
7C2×C11×#324C211yesmaximal, characteristic, complemented
8C22×C11×#41—21no—
9C11×#537—24no—
10C11×#537—22no—
11C11×#537C2214yes—
12C2×C11×C22⋊Q8—22no—
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#121—22no—
15C2×C11×#121—21no—
16C2×C11×#121C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C11×#483—22no—
19C11×#481C2214yescomplemented
20C11×#465—24no—
21C11×#450—22no—
22C11×#448C2214yescomplemented
23C2×C11×C22⋊C8C2212yes—
24C11×#400C2212yescomplemented
25C11×#398—22no—
26C11×#395C2212yescomplemented
27C11×#385—21no—
28C11×#381—21no—
29C11×#380C2211yescharacteristic
30C11×#327C2218yescomplemented
31C11×#324C2214yescomplemented
32C2×C11×#41—24no—
33C2×C11×#41—24no—
34C2×C11×#41—44no—
35C2×C11×#41—44no—
36C22×Q8×C11—21no—
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11—21no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11D412yes—
42C23×C4×C11—22no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C2×C11×SD16—24no—
47C22×C8×C11—22no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×#121—24no—
53C11×#121—28no—
54C11×#121—28no—
55C11×#121—24no—
56C11×#121—22no—
57C11×#121—22no—
58C11×#121D414yes—
59C11×#121C2314yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C11×#106—24no—
75C11×#103—24no—
76C11×#102—24no—
77C11×C22⋊C8—22no—
78C11×C22⋊C8C2314yes—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95C2312yes—
83#18293C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—22no—
85C24×C11C2×D411yescharacteristic
86C11×#41—48no—
87C11×#41—416no—
88C11×#41—48no—
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—44no—
92C2×Q8×C11—81no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—22no—
98C2×D4×C11—44no—
99C2×D4×C11—44no—
100C2×D4×C11—44no—
101C2×D4×C11—82no—
102C2×D4×C11—82no—
103C2×D4×C11C2×D414yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—28no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—48no—
115C22×C4×C11—81no—
116C22×C4×C11—81no—
117C22×C4×C11SD1614yescomplemented
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C11×SD16—84no—
125C2×C8×C11—24no—
126C2×C8×C11—82no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—81no—
134C11×C4⋊C4—82no—
135C11×C4⋊C4C2×D414yes—
136C11×C22⋊C4—28no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—42no—
142C2×#537C2×C1111yescharacteristic
143#3187C2×C1112yescomplemented
144#2627C2×C1111yescharacteristic, complemented
145#1616C2×C1114yescomplemented
146#1604C2×C1114yescomplemented
147#1519C2×C1112yescomplemented
148C2×#324C2×C1111yescharacteristic, complemented
149C23×C11—24no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—44no—
153C23×C11—44no—
154C23×C11—44no—
155C23×C11#12011yescharacteristic
156C23×C11#12011yescharacteristic
157C23×C11C2×SD1612yes—
158C23×C11AGL(1,ℤ/8)12yes—
159C23×C11C22×D411yescharacteristic
160Q8×C11—48no—
161Q8×C11—44no—
162D4×C11—44no—
163D4×C11—48no—
164D4×C11—44no—
165D4×C11—44no—
166D4×C11—48no—
167D4×C11—82no—
168D4×C11—84no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—416no—
180C2×C4×C11—42no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—81no—
191C2×C4×C11#12012yes—
192C2×C4×C11C2×SD1614yes—
193C2×C4×C11C22×D412yes—
194C8×C11—44no—
195C22×#41—21no—
196#537—24no—
197#537—22no—
198#537C22×C1114yes—
199C2×C22⋊Q8—22no—
200C2×C22⋊Q8C22×C1111yescharacteristic
201C2×#121—22no—
202C2×#121—21no—
203C2×#121C22×C1112yes—
204C22×C4⋊C4C22×C1111yescharacteristic
205#483—22no—
206#481C22×C1114yescomplemented
207#465—24no—
208#450—22no—
209#448C22×C1114yescomplemented
210C2×C22⋊C8C22×C1112yes—
211#400C22×C1112yescomplemented
212#398—22no—
213#395C22×C1112yescomplemented
214#385—21no—
215#381—21no—
216#380C22×C1111yescharacteristic
217#327C22×C1118yescomplemented
218#324C22×C1114yescomplemented
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—44no—
228C22×C11—44no—
229C22×C11—44no—
230C22×C11—88no—
231C22×C11#45012yes—
232C22×C11#45012yes—
233C22×C11C2×#12011yescharacteristic
234C22×C11C22×SD1611yescharacteristic
235C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
236C4×C11—24no—
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—44no—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11—81no—
243C4×C11—81no—
244C2×#41—24no—
245C2×#41—24no—
246C2×#41—44no—
247C2×#41—44no—
248C22×Q8—21no—
249C22×Q8C23×C1111yescharacteristic
250C22×D4—21no—
251C22×D4—22no—
252C22×D4—21no—
253C22×D4D4×C1112yes—
254C23×C4—22no—
255C23×C4D4×C1111yescharacteristic
256C23×C4D4×C1111yescharacteristic
257C23×C4C23×C1111yescharacteristic
258C2×SD16—24no—
259C22×C8—22no—
260C22⋊Q8—28no—
261C22⋊Q8—28no—
262C22⋊Q8—22no—
263C22⋊Q8—22no—
264#121—24no—
265#121—28no—
266#121—28no—
267#121—24no—
268#121—22no—
269#121—22no—
270#121D4×C1114yes—
271#121C23×C1114yes—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4D4×C1112yes—
279C2×C4⋊C4D4×C1112yes—
280C2×C4⋊C4C23×C1111yescharacteristic
281C2×C4⋊C4C23×C1112yes—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286#106—24no—
287#103—24no—
288#102—24no—
289C22⋊C8—22no—
290C22⋊C8C23×C1114yes—
291#95—22no—
292#95—22no—
293#95—22no—
294#95C23×C1112yes—
295C2×C11—21no—
296C2×C11—22no—
297C2×C11—21no—
298C2×C11—22no—
299C2×C11—84no—
300C2×C11C2×#45011yescharacteristic
301C2×C11#302011yescharacteristic
302C2×C11#302611yescharacteristic
303C24—22no—
304C24C2×D4×C1111yescharacteristic
305#41—48no—
306#41—416no—
307#41—48no—
308C2×Q8—24no—
309C2×Q8—22no—
310C2×Q8—44no—
311C2×Q8—81no—
312C2×D4—24no—
313C2×D4—24no—
314C2×D4—24no—
315C2×D4—24no—
316C2×D4—22no—
317C2×D4—44no—
318C2×D4—44no—
319C2×D4—44no—
320C2×D4—82no—
321C2×D4—82no—
322C2×D4C2×D4×C1114yes—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—28no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—48no—
334C22×C4—81no—
335C22×C4—81no—
336C22×C4C11×SD1614yescomplemented
337C22×C4C2×D4×C1112yes—
338C22×C4C2×D4×C1112yes—
339C22×C4C2×D4×C1111yescharacteristic
340C22×C4C2×D4×C1112yes—
341C22×C4C2×D4×C1112yes—
342C22×C4C24×C1111yescharacteristic
343SD16—84no—
344C2×C8—24no—
345C2×C8—82no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—22no—
349C4⋊C4—24no—
350C4⋊C4—22no—
351C4⋊C4—42no—
352C4⋊C4—81no—
353C4⋊C4—82no—
354C4⋊C4C2×D4×C1114yes—
355C22⋊C4—28no—
356C22⋊C4—24no—
357C22⋊C4—24no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—42no—
361C11#1829311yescharacteristic, direct product factor, Sylow
362C23—24no—
363C23—41no—
364C23—41no—
365C23—44no—
366C23—44no—
367C23—44no—
368C23C11×#12011yescharacteristic
369C23C11×#12011yescharacteristic
370C23C2×C11×SD1612yes—
371C23C11×AGL(1,ℤ/8)12yes—
372C23C22×D4×C1111yescharacteristic
373Q8—48no—
374Q8—44no—
375D4—44no—
376D4—48no—
377D4—44no—
378D4—44no—
379D4—48no—
380D4—82no—
381D4—84no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—416no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—81no—
404C2×C4C11×#12012yes—
405C2×C4C2×C11×SD1614yes—
406C2×C4C22×D4×C1112yes—
407C8—44no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—44no—
418C22—44no—
419C22—88no—
420C22C11×#45012yes—
421C22C11×#45012yes—
422C22C2×C11×#12011yescharacteristic
423C22C22×C11×SD1611yescharacteristic
424C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
425C4—24no—
426C4—22no—
427C4—22no—
428C4—44no—
429C4—42no—
430C4—82no—
431C4—81no—
432C4—81no—
433C2—21no—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—84no—
438C2C2×C11×#45011yescharacteristic
439C2C11×#302011yescharacteristic
440C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
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. C11×#3187C2semidirect
3. C11×#2627C2semidirect
4. C11×#1616C2semidirect
5. C11×#1604C2semidirect
6. C11×#1519C2semidirect
7. C2×C11×#324C2semidirect
19. C11×#481C22semidirect
22. C11×#448C22semidirect
24. C11×#400C22semidirect
26. C11×#395C22semidirect
30. C11×#327C22semidirect
31. C11×#324C22semidirect
83. #18293C11direct (N × H)
117. C22×C4×C11SD16semidirect
143. #3187C2×C11semidirect
144. #2627C2×C11semidirect
145. #1616C2×C11semidirect
146. #1604C2×C11semidirect
147. #1519C2×C11semidirect
148. C2×#324C2×C11semidirect
206. #481C22×C11semidirect
209. #448C22×C11semidirect
211. #400C22×C11semidirect
213. #395C22×C11semidirect
217. #327C22×C11semidirect
218. #324C22×C11semidirect
336. C22×C4C11×SD16semidirect
361. C11#18293direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C11×#31872
C11×#26272
C11×#16162
C11×#16042
C11×#15192
C2×C11×#3242
#1829311