Finite Group Databasebeta

← C11×#24985 #14602178

Subgroups — C11×#24985 #14602178

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3067C211yesmaximal, characteristic
2C4×C11×#135C211yesmaximal, characteristic, complemented
3C11×#2080C212yesmaximal, complemented
4C11×#2053C212yesmaximal, complemented
5C11×#1976C211yesmaximal, characteristic, complemented
6C11×#1945C211yesmaximal, characteristic, complemented
7C11×#1906C212yesmaximal, complemented
8C11×#1833C211yesmaximal, characteristic, complemented
9C11×#1827C212yesmaximal, complemented
10C11×#1812C211yesmaximal, characteristic, complemented
11C11×#1764C211yesmaximal, characteristic, complemented
12C11×#575C2212yes—
13C2×C11×#135C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15C4×C11×#41C2212yes—
16C11×#473—21no—
17C11×#472—21no—
18C11×#471—22no—
19C4×C11×Q16—21no—
20C4×C11×SD16—22no—
21C4×C11×D8—21no—
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×C4×C8×C11C2211yescharacteristic
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—21no—
83C11×#104—21no—
84C11×#104—42no—
85C11×#103—22no—
86C11×#103—21no—
87C11×#102—22no—
88C11×#102—21no—
89C11×#101—22no—
90C11×#100—22no—
91C11×#99—42no—
92C11×#99—42no—
93C11×#97—21no—
94C4×C8×C11—21no—
95C4×C8×C11—21no—
96C4×C8×C11—21no—
97#24985C1111yesmaximal, characteristic, direct product factor, Sylow
98C11×#41—21no—
99C11×#41—21no—
100C11×#41—21no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—21no—
106C2×Q8×C11C2×D412yes—
107C2×Q8×C11#4111yescharacteristic
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11C2×D412yes—
111C2×D4×C11#4111yescharacteristic
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11C2411yescharacteristic
117C11×Q16—21no—
118C11×Q16—21no—
119C11×Q16—42no—
120C11×SD16—22no—
121C11×SD16—22no—
122C11×SD16—42no—
123C11×SD16—42no—
124C11×D8—21no—
125C11×D8—21no—
126C11×D8—42no—
127C11×M16—21no—
128C11×M16—22no—
129C11×M16—21no—
130C11×M16—21no—
131C11×M16—22no—
132C11×M16—21no—
133C11×M16—41no—
134C11×M16—41no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11—22no—
141C2×C8×C11—41no—
142C2×C8×C11—41no—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11#4111yescharacteristic
146C2×C8×C11#4111yescharacteristic
147C2×C8×C11#4111yescharacteristic
148C2×C8×C11#4111yescharacteristic
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—42no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—42no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—42no—
162C42×C11#4111yescharacteristic
163C42×C11#4111yescharacteristic
164#3067C2×C1111yescharacteristic
165C4×#135C2×C1111yescharacteristic, complemented
166#2080C2×C1112yescomplemented
167#2053C2×C1112yescomplemented
168#1976C2×C1111yescharacteristic, complemented
169#1945C2×C1111yescharacteristic, complemented
170#1906C2×C1112yescomplemented
171#1833C2×C1111yescharacteristic, complemented
172#1827C2×C1112yescomplemented
173#1812C2×C1111yescharacteristic, complemented
174#1764C2×C1111yescharacteristic, complemented
175C23×C11—22no—
176C23×C11—21no—
177C23×C11H(5,𝔽2)11yescharacteristic
178Q8×C11—22no—
179Q8×C11—21no—
180Q8×C11—21no—
181Q8×C11—22no—
182D4×C11—22no—
183D4×C11—21no—
184D4×C11—21no—
185D4×C11—22no—
186D4×C11—41no—
187D4×C11—42no—
188D4×C11—41no—
189D4×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—84no—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C8×C11—41no—
210C8×C11—41no—
211C8×C11—42no—
212C8×C11—41no—
213C8×C11#12311yescharacteristic
214C8×C11#12311yescharacteristic
215C8×C11#12311yescharacteristic
216C8×C11#12311yescharacteristic
217#575C22×C1112yes—
218C2×#135C22×C1111yescharacteristic
219C2×#131C22×C1111yescharacteristic
220C4×#41C22×C1112yes—
221#473—21no—
222#472—21no—
223#471—22no—
224C4×Q16—21no—
225C4×SD16—22no—
226C4×D8—21no—
227C2×#108C22×C1111yescharacteristic
228#427C22×C1111yescharacteristic
229#427C22×C1111yescharacteristic
230#424C22×C1112yes—
231#421C22×C1112yes—
232C2×#104C22×C1111yescharacteristic
233#416C22×C1111yescharacteristic
234#416C22×C1112yes—
235#413C22×C1112yes—
236#410C22×C1112yes—
237#410C22×C1112yes—
238#405C22×C1111yescharacteristic
239C2×C4×C8C22×C1111yescharacteristic
240#344C22×C1112yes—
241#341C22×C1111yescharacteristic
242#339C22×C1111yescharacteristic
243#339C22×C1112yes—
244H(3,ℤ/4)C22×C1112yes—
245H(3,ℤ/4)C22×C1112yes—
246C22×C11—41no—
247C22×C11—41no—
248C22×C11—42no—
249C22×C11—82no—
250C22×C11—81no—
251C22×C11#54011yescharacteristic
252C22×C11#54611yescharacteristic
253C22×C11#55311yescharacteristic
254C4×C11—22no—
255C4×C11—41no—
256C4×C11—42no—
257C4×C11—41no—
258C4×C11—82no—
259C4×C11—81no—
260C4×C11—82no—
261C4×C11C2×#12311yescharacteristic
262C4×C11#52911yescharacteristic
263C4×C11#54611yescharacteristic
264C4×C11#55511yescharacteristic
265C2×#41C23×C1112yes—
266C2×#41C23×C1111yescharacteristic
267#137—22no—
268#137—22no—
269AGL(1,ℤ/8)—22no—
270AGL(1,ℤ/8)—22no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—42no—
276C2×Q16D4×C1111yescharacteristic
277C2×SD16D4×C1112yes—
278C2×D8D4×C1111yescharacteristic
279#131—21no—
280#131—21no—
281#131—21no—
282#131—21no—
283C2×M16—21no—
284C2×M16C23×C1111yescharacteristic
285C2×M16C23×C1112yes—
286C2×M16C23×C1111yescharacteristic
287C22×C8—21no—
288C22×C8C23×C1111yescharacteristic
289C22×C8C23×C1111yescharacteristic
290C4×Q8—22no—
291C4×D4—22no—
292C4×D4—42no—
293#117—22no—
294#117C23×C1112yes—
295#117C23×C1111yescharacteristic
296#117C23×C1112yes—
297C2×C42—22no—
298C2×C42C23×C1111yescharacteristic
299#108—21no—
300#108—21no—
301#107—21no—
302#107—21no—
303#106—21no—
304#106—21no—
305C4⋊C8—42no—
306#104—21no—
307#104—21no—
308#104—42no—
309#103—22no—
310#103—21no—
311#102—22no—
312#102—21no—
313#101—22no—
314#100—22no—
315#99—42no—
316#99—42no—
317#97—21no—
318C4×C8—21no—
319C4×C8—21no—
320C4×C8—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—82no—
325C2×C11—81no—
326C2×C11#242011yescharacteristic
327#41—21no—
328#41—21no—
329#41—21no—
330#41—22no—
331#41—22no—
332#41—22no—
333#41—22no—
334#41—21no—
335C2×Q8C2×D4×C1112yes—
336C2×Q8C11×#4111yescharacteristic
337C2×D4—21no—
338C2×D4—22no—
339C2×D4C2×D4×C1112yes—
340C2×D4C11×#4111yescharacteristic
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4C24×C1111yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—42no—
349SD16—22no—
350SD16—22no—
351SD16—42no—
352SD16—42no—
353D8—21no—
354D8—21no—
355D8—42no—
356M16—21no—
357M16—22no—
358M16—21no—
359M16—21no—
360M16—22no—
361M16—21no—
362M16—41no—
363M16—41no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8C2×D4×C1111yescharacteristic
373C2×C8C2×D4×C1111yescharacteristic
374C2×C8C11×#4111yescharacteristic
375C2×C8C11×#4111yescharacteristic
376C2×C8C11×#4111yescharacteristic
377C2×C8C11×#4111yescharacteristic
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—42no—
382C22⋊C4—22no—
383C22⋊C4—21no—
384C22⋊C4—22no—
385C22⋊C4—42no—
386C42—21no—
387C42—21no—
388C42—22no—
389C42—22no—
390C42—42no—
391C42C11×#4111yescharacteristic
392C42C11×#4111yescharacteristic
393C11#2498511yescharacteristic, direct product factor, Sylow
394C23—22no—
395C23—21no—
396C23C11×H(5,𝔽2)11yescharacteristic
397Q8—22no—
398Q8—21no—
399Q8—21no—
400Q8—22no—
401D4—22no—
402D4—21no—
403D4—21no—
404D4—22no—
405D4—41no—
406D4—42no—
407D4—41no—
408D4—42no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—84no—
422C2×C4C22×D4×C1111yescharacteristic
423C2×C4C2×C11×#4111yescharacteristic
424C2×C4C2×C11×#4111yescharacteristic
425C2×C4C2×C11×#4111yescharacteristic
426C2×C4C2×C11×#4111yescharacteristic
427C2×C4C11×H(5,𝔽2)11yescharacteristic
428C8—41no—
429C8—41no—
430C8—42no—
431C8—41no—
432C8C11×#12311yescharacteristic
433C8C11×#12311yescharacteristic
434C8C11×#12311yescharacteristic
435C8C11×#12311yescharacteristic
436C22—41no—
437C22—41no—
438C22—42no—
439C22—82no—
440C22—81no—
441C22C11×#54011yescharacteristic
442C22C11×#54611yescharacteristic
443C22C11×#55311yescharacteristic
444C4—22no—
445C4—41no—
446C4—42no—
447C4—41no—
448C4—82no—
449C4—82no—
450C4—81no—
451C4C2×C11×#12311yescharacteristic
452C4C11×#52911yescharacteristic
453C4C11×#54611yescharacteristic
454C4C11×#55511yescharacteristic
455C2—21no—
456C2—21no—
457C2—21no—
458C2—82no—
459C2—81no—
460C2C11×#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. C4×C11×#135C2semidirect
3. C11×#2080C2semidirect
4. C11×#2053C2semidirect
5. C11×#1976C2semidirect
6. C11×#1945C2semidirect
7. C11×#1906C2semidirect
8. C11×#1833C2semidirect
9. C11×#1827C2semidirect
10. C11×#1812C2semidirect
11. C11×#1764C2semidirect
97. #24985C11direct (N × H)
165. C4×#135C2×C11semidirect
166. #2080C2×C11semidirect
167. #2053C2×C11semidirect
168. #1976C2×C11semidirect
169. #1945C2×C11semidirect
170. #1906C2×C11semidirect
171. #1833C2×C11semidirect
172. #1827C2×C11semidirect
173. #1812C2×C11semidirect
174. #1764C2×C11semidirect
393. C11#24985direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30672
C4×C11×#1352
C11×#20802
C11×#20532
C11×#19762
C11×#19452
C11×#19062
C11×#18332
C11×#18272
C11×#18122
C11×#17642
#2498511