Finite Group Databasebeta

← C11×#24986 #14602179

Subgroups — C11×#24986 #14602179

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3067C211yesmaximal, characteristic
2C11×#2943C211yesmaximal, characteristic, complemented
3C11×#2080C212yesmaximal, complemented
4C11×#2053C212yesmaximal, complemented
5C11×#1976C211yesmaximal, characteristic, complemented
6C11×#1946C211yesmaximal, characteristic, complemented
7C11×#1906C212yesmaximal, complemented
8C11×#1833C211yesmaximal, characteristic, complemented
9C11×#1827C212yesmaximal, complemented
10C11×#1812C211yesmaximal, characteristic, complemented
11C11×#1765C211yesmaximal, characteristic, complemented
12C11×#575C2212yes—
13C2×C11×#135C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15C4×C11×#41C2212yes—
16C11×#473—21no—
17C11×#472—21no—
18C11×#471—22no—
19C11×#442—21no—
20C11×#441—21no—
21C11×#440—22no—
22C2×C11×#108C2211yescharacteristic
23C11×#427C2211yescharacteristic
24C11×#427C2211yescharacteristic
25C11×#424C2212yes—
26C11×#421C2212yes—
27C2×C11×#104C2211yescharacteristic
28C11×#416C2212yes—
29C11×#416C2211yescharacteristic
30C11×#413C2212yes—
31C11×#410C2212yes—
32C11×#410C2212yes—
33C11×#405C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C11×#344C2212yes—
36C11×#341C2211yescharacteristic
37C11×#339C2212yes—
38C11×#339C2211yescharacteristic
39C11×H(3,ℤ/4)C2212yes—
40C11×H(3,ℤ/4)C2212yes—
41C2×C11×#41C2312yes—
42C2×C11×#41C2311yescharacteristic
43C11×#137—22no—
44C11×#137—22no—
45C11×AGL(1,ℤ/8)—22no—
46C11×AGL(1,ℤ/8)—22no—
47C11×#135—21no—
48C11×#135—21no—
49C11×#135—21no—
50C11×#135—21no—
51C11×#135—42no—
52C2×C11×Q16D411yescharacteristic
53C2×C11×SD16D412yes—
54C2×C11×D8D411yescharacteristic
55C11×#131—21no—
56C11×#131—21no—
57C11×#131—21no—
58C11×#131—21no—
59C2×C11×M16—21no—
60C2×C11×M16C2311yescharacteristic
61C2×C11×M16C2312yes—
62C2×C11×M16C2311yescharacteristic
63C22×C8×C11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—42no—
69C11×#117—22no—
70C11×#117C2311yescharacteristic
71C11×#117C2312yes—
72C11×#117C2312yes—
73C2×C42×C11—22no—
74C2×C42×C11C2311yescharacteristic
75C11×#108—21no—
76C11×#108—21no—
77C11×#107—21no—
78C11×#107—21no—
79C11×#106—21no—
80C11×#106—21no—
81C11×C4⋊C8—42no—
82C11×#104—22no—
83C11×#104—42no—
84C11×#103—22no—
85C11×#103—21no—
86C11×#102—22no—
87C11×#102—21no—
88C11×#101—22no—
89C11×#100—22no—
90C11×#99—42no—
91C11×#99—42no—
92C11×#97—21no—
93C11×#97—21no—
94C11×#97—21no—
95C4×C8×C11—21no—
96#24986C1111yesmaximal, characteristic, direct product factor, Sylow
97C11×#41—21no—
98C11×#41—21no—
99C11×#41—21no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—21no—
105C2×Q8×C11C2×D412yes—
106C2×Q8×C11#4111yescharacteristic
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11C2×D412yes—
110C2×D4×C11#4111yescharacteristic
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11C2411yescharacteristic
116C11×Q16—21no—
117C11×Q16—21no—
118C11×Q16—42no—
119C11×SD16—22no—
120C11×SD16—22no—
121C11×SD16—42no—
122C11×SD16—42no—
123C11×D8—21no—
124C11×D8—21no—
125C11×D8—42no—
126C11×M16—21no—
127C11×M16—22no—
128C11×M16—21no—
129C11×M16—21no—
130C11×M16—22no—
131C11×M16—21no—
132C11×M16—41no—
133C11×M16—41no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—41no—
141C2×C8×C11—41no—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11#4111yescharacteristic
145C2×C8×C11#4111yescharacteristic
146C2×C8×C11#4111yescharacteristic
147C2×C8×C11#4111yescharacteristic
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—42no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—42no—
161C42×C11#4112yes—
162#3067C2×C1111yescharacteristic
163#2943C2×C1111yescharacteristic, complemented
164#2080C2×C1112yescomplemented
165#2053C2×C1112yescomplemented
166#1976C2×C1111yescharacteristic, complemented
167#1946C2×C1111yescharacteristic, complemented
168#1906C2×C1112yescomplemented
169#1833C2×C1111yescharacteristic, complemented
170#1827C2×C1112yescomplemented
171#1812C2×C1111yescharacteristic, complemented
172#1765C2×C1111yescharacteristic, complemented
173C23×C11—22no—
174C23×C11—21no—
175C23×C11H(5,𝔽2)11yescharacteristic
176Q8×C11—22no—
177Q8×C11—21no—
178Q8×C11—21no—
179Q8×C11—22no—
180D4×C11—22no—
181D4×C11—21no—
182D4×C11—21no—
183D4×C11—22no—
184D4×C11—41no—
185D4×C11—42no—
186D4×C11—41no—
187D4×C11—42no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—81no—
199C2×C4×C11—84no—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C8×C11—41no—
207C8×C11—41no—
208C8×C11—42no—
209C8×C11—41no—
210C8×C11#12311yescharacteristic
211C8×C11#12311yescharacteristic
212C8×C11#12311yescharacteristic
213C8×C11#12311yescharacteristic
214#575C22×C1112yes—
215C2×#135C22×C1111yescharacteristic
216C2×#131C22×C1111yescharacteristic
217C4×#41C22×C1112yes—
218#473—21no—
219#472—21no—
220#471—22no—
221#442—21no—
222#441—21no—
223#440—22no—
224C2×#108C22×C1111yescharacteristic
225#427C22×C1111yescharacteristic
226#427C22×C1111yescharacteristic
227#424C22×C1112yes—
228#421C22×C1112yes—
229C2×#104C22×C1111yescharacteristic
230#416C22×C1111yescharacteristic
231#416C22×C1112yes—
232#413C22×C1112yes—
233#410C22×C1112yes—
234#410C22×C1112yes—
235#405C22×C1111yescharacteristic
236C2×#97C22×C1111yescharacteristic
237#344C22×C1112yes—
238#341C22×C1111yescharacteristic
239#339C22×C1111yescharacteristic
240#339C22×C1112yes—
241H(3,ℤ/4)C22×C1112yes—
242H(3,ℤ/4)C22×C1112yes—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—42no—
246C22×C11—82no—
247C22×C11—81no—
248C22×C11#54011yescharacteristic
249C22×C11#54611yescharacteristic
250C22×C11#55311yescharacteristic
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—41no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11—82no—
257C4×C11C2×#12311yescharacteristic
258C4×C11#52911yescharacteristic
259C4×C11#54611yescharacteristic
260C4×C11#55511yescharacteristic
261C2×#41C23×C1112yes—
262C2×#41C23×C1111yescharacteristic
263#137—22no—
264#137—22no—
265AGL(1,ℤ/8)—22no—
266AGL(1,ℤ/8)—22no—
267#135—21no—
268#135—21no—
269#135—21no—
270#135—21no—
271#135—42no—
272C2×Q16D4×C1111yescharacteristic
273C2×SD16D4×C1112yes—
274C2×D8D4×C1111yescharacteristic
275#131—21no—
276#131—21no—
277#131—21no—
278#131—21no—
279C2×M16—21no—
280C2×M16C23×C1111yescharacteristic
281C2×M16C23×C1112yes—
282C2×M16C23×C1111yescharacteristic
283C22×C8—21no—
284C22×C8C23×C1111yescharacteristic
285C22×C8C23×C1111yescharacteristic
286C4×Q8—22no—
287C4×D4—22no—
288C4×D4—42no—
289#117—22no—
290#117C23×C1112yes—
291#117C23×C1111yescharacteristic
292#117C23×C1112yes—
293C2×C42—22no—
294C2×C42C23×C1111yescharacteristic
295#108—21no—
296#108—21no—
297#107—21no—
298#107—21no—
299#106—21no—
300#106—21no—
301C4⋊C8—42no—
302#104—22no—
303#104—42no—
304#103—22no—
305#103—21no—
306#102—22no—
307#102—21no—
308#101—22no—
309#100—22no—
310#99—42no—
311#99—42no—
312#97—21no—
313#97—21no—
314#97—21no—
315C4×C8—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—21no—
319C2×C11—82no—
320C2×C11—81no—
321C2×C11#242011yescharacteristic
322#41—21no—
323#41—21no—
324#41—21no—
325#41—22no—
326#41—22no—
327#41—22no—
328#41—22no—
329#41—21no—
330C2×Q8C2×D4×C1112yes—
331C2×Q8C11×#4111yescharacteristic
332C2×D4—21no—
333C2×D4—22no—
334C2×D4C2×D4×C1112yes—
335C2×D4C11×#4111yescharacteristic
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4C24×C1111yescharacteristic
341Q16—21no—
342Q16—21no—
343Q16—42no—
344SD16—22no—
345SD16—22no—
346SD16—42no—
347SD16—42no—
348D8—21no—
349D8—21no—
350D8—42no—
351M16—21no—
352M16—22no—
353M16—21no—
354M16—21no—
355M16—22no—
356M16—21no—
357M16—41no—
358M16—41no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—22no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8C2×D4×C1111yescharacteristic
368C2×C8C2×D4×C1111yescharacteristic
369C2×C8C11×#4111yescharacteristic
370C2×C8C11×#4111yescharacteristic
371C2×C8C11×#4111yescharacteristic
372C2×C8C11×#4111yescharacteristic
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—42no—
377C22⋊C4—22no—
378C22⋊C4—21no—
379C22⋊C4—22no—
380C22⋊C4—42no—
381C42—21no—
382C42—21no—
383C42—22no—
384C42—22no—
385C42—42no—
386C42C11×#4112yes—
387C11#2498611yescharacteristic, direct product factor, Sylow
388C23—22no—
389C23—21no—
390C23C11×H(5,𝔽2)11yescharacteristic
391Q8—22no—
392Q8—21no—
393Q8—21no—
394Q8—22no—
395D4—22no—
396D4—21no—
397D4—21no—
398D4—22no—
399D4—41no—
400D4—42no—
401D4—41no—
402D4—42no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—84no—
415C2×C4C22×D4×C1111yescharacteristic
416C2×C4C2×C11×#4111yescharacteristic
417C2×C4C2×C11×#4111yescharacteristic
418C2×C4C2×C11×#4111yescharacteristic
419C2×C4C2×C11×#4111yescharacteristic
420C2×C4C11×H(5,𝔽2)11yescharacteristic
421C8—41no—
422C8—41no—
423C8—42no—
424C8—41no—
425C8C11×#12311yescharacteristic
426C8C11×#12311yescharacteristic
427C8C11×#12311yescharacteristic
428C8C11×#12311yescharacteristic
429C22—41no—
430C22—41no—
431C22—42no—
432C22—82no—
433C22—81no—
434C22C11×#54011yescharacteristic
435C22C11×#54611yescharacteristic
436C22C11×#55311yescharacteristic
437C4—42no—
438C4—42no—
439C4—41no—
440C4—82no—
441C4—82no—
442C4—81no—
443C4C2×C11×#12311yescharacteristic
444C4C11×#52911yescharacteristic
445C4C11×#54611yescharacteristic
446C4C11×#55511yescharacteristic
447C2—21no—
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2C11×#242011yescharacteristic
subgroupG/H
centerC4×C11#555
commutator, Frattini, cosocleC22×C4C24×C11
socleC2×C11#2420
prime radicalC11×#3067C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2943C2semidirect
3. C11×#2080C2semidirect
4. C11×#2053C2semidirect
5. C11×#1976C2semidirect
6. C11×#1946C2semidirect
7. C11×#1906C2semidirect
8. C11×#1833C2semidirect
9. C11×#1827C2semidirect
10. C11×#1812C2semidirect
11. C11×#1765C2semidirect
96. #24986C11direct (N × H)
163. #2943C2×C11semidirect
164. #2080C2×C11semidirect
165. #2053C2×C11semidirect
166. #1976C2×C11semidirect
167. #1946C2×C11semidirect
168. #1906C2×C11semidirect
169. #1833C2×C11semidirect
170. #1827C2×C11semidirect
171. #1812C2×C11semidirect
172. #1765C2×C11semidirect
387. C11#24986direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30672
C11×#29432
C11×#20802
C11×#20532
C11×#19762
C11×#19462
C11×#19062
C11×#18332
C11×#18272
C11×#18122
C11×#17652
#2498611