Finite Group Databasebeta

← C11×#22220 #14599413

Subgroups — C11×#22220 #14599413

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C4×C11×#127C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1957C211yesmaximal, characteristic
6C11×#1925C214yesmaximal, complemented
7C11×#1862C214yesmaximal, complemented
8C11×#1845C211yesmaximal, characteristic, complemented
9C11×#1744C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×Q8×C11—21no—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2212yes—
16C11×#486C418yescomplemented
17C2×C11×#107C2214yes—
18C2×C11×#102C2214yes—
19C2×C11×#102C2214yes—
20C2×C4×C8×C11C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C11×#391—21no—
23C11×#390—21no—
24C11×#390—21no—
25C11×#390C2212yes—
26C11×#389—21no—
27C11×#389C2212yes—
28C11×#384C2211yescharacteristic
29C11×#384C2211yescharacteristic
30C4×C11×C4⋊C4—21no—
31C4×C11×C4⋊C4C2212yes—
32C43×C11C2211yescharacteristic
33C11×#340C2214yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×Q8×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11C2312yes—
40C23×C4×C11—22no—
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8C2×C414yescomplemented
45C11×#127—22no—
46C11×#127C2×C414yes—
47C4×Q8×C11—44no—
48C4×D4×C11—44no—
49C4×D4×C11—44no—
50C4×D4×C11—44no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11—22no—
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D411yescharacteristic
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C11×#107—44no—
72C11×#102—44no—
73C11×#102C2×C4116yescomplemented
74C4×C8×C11—22no—
75C4×C8×C11C2×C414yescomplemented
76C11×#95—22no—
77C11×#95—22no—
78#22220C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—22no—
80C2×Q8×C11—24no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C2×D4×C11—24no—
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—42no—
89C2×D4×C11—42no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11C22×C414yes—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—44no—
97C22×C4×C11—44no—
98C22×C4×C11—44no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11C22×C414yes—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—44no—
118C11×C4⋊C4—42no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4C22×C414yes—
122C11×C22⋊C4—44no—
123C11×C22⋊C4—44no—
124C11×C22⋊C4—44no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—44no—
131C42×C11D814yes—
132C42×C11C22×C412yes—
133C42×C11#4112yes—
134C2×#486C2×C1111yescharacteristic
135C4×C4⋊Q8C2×C1111yescharacteristic, complemented
136C4×#127C2×C1111yescharacteristic
137#1990C2×C1111yescharacteristic, complemented
138#1957C2×C1111yescharacteristic
139#1925C2×C1114yescomplemented
140#1862C2×C1114yescomplemented
141#1845C2×C1111yescharacteristic, complemented
142#1744C2×C1111yescharacteristic, complemented
143C23×C11—24no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11C22×D411yescharacteristic
151Q8×C11—48no—
152D4×C11—28no—
153D4×C11—44no—
154D4×C11—48no—
155D4×C11—48no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—24no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—88no—
176C2×C4×C11C4×D412yes—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C2×D812yes—
179C2×C4×C11C2×D812yes—
180C2×C4×C11C2×D812yes—
181C2×C4×C11#13512yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11#13712yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11H(5,𝔽2)12yes—
187C2×C4×C112−1+412yes—
188C8×C11—24no—
189C8×C11—42no—
190C2×C4⋊Q8C22×C1111yescharacteristic
191C2×#127C22×C1111yescharacteristic
192C2×C4×Q8—21no—
193C2×C4×D4—21no—
194C2×C4×D4—21no—
195C2×C4×D4C22×C1112yes—
196#486C4×C1118yescomplemented
197C2×#107C22×C1114yes—
198C2×#102C22×C1114yes—
199C2×#102C22×C1114yes—
200C2×C4×C8C22×C1111yescharacteristic
201C2×C4×C8C22×C1111yescharacteristic
202#391—21no—
203#390—21no—
204#390—21no—
205#390C22×C1112yes—
206#389—21no—
207#389C22×C1112yes—
208#384C22×C1111yescharacteristic
209#384C22×C1111yescharacteristic
210C4×C4⋊C4—21no—
211C4×C4⋊C4C22×C1112yes—
212C43C22×C1111yescharacteristic
213#340C22×C1114yes—
214#336C22×C1112yes—
215#336C22×C1112yes—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—44no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11C2×C4×D411yescharacteristic
224C22×C11#53511yescharacteristic
225C22×C11#53611yescharacteristic
226C22×C11C22×D811yescharacteristic
227C22×C11C2×#13511yescharacteristic
228C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C22×C11C2×#13711yescharacteristic
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—44no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—82no—
236C4×C11—82no—
237C4×C11C4×D814yes—
238C4×C11#44014yes—
239C4×C11#52012yes—
240C4×C11#54212yes—
241C22×Q8—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4C23×C1112yes—
245C23×C4—22no—
246C22×C8C23×C1112yes—
247C22×C8C23×C1112yes—
248C4⋊Q8—22no—
249C4⋊Q8C2×C4×C1114yescomplemented
250#127—22no—
251#127C2×C4×C1114yes—
252C4×Q8—44no—
253C4×D4—44no—
254C4×D4—44no—
255C4×D4—44no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C23×C1112yes—
263C2×C4⋊C4C23×C1112yes—
264C2×C4⋊C4C23×C1112yes—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C42—22no—
269C2×C42D4×C1111yescharacteristic
270C2×C42D4×C1111yescharacteristic
271C2×C42D4×C1111yescharacteristic
272C2×C42D4×C1111yescharacteristic
273C2×C42C23×C1111yescharacteristic
274C2×C42C23×C1111yescharacteristic
275C2×C42C23×C1111yescharacteristic
276#107—44no—
277#102—44no—
278#102C2×C4×C11116yescomplemented
279C4×C8—22no—
280C4×C8C2×C4×C1114yescomplemented
281#95—22no—
282#95—22no—
283C2×C11—84no—
284C2×C11#232611yescharacteristic
285C2×C11C2×C4×D811yescharacteristic
286C2×C11C2×#44011yescharacteristic
287C2×C11#320511yescharacteristic
288C2×C11#321011yescharacteristic
289C2×C11#322611yescharacteristic
290C2×C11#322811yescharacteristic
291C24—22no—
292C2×Q8—24no—
293C2×Q8—42no—
294C2×Q8—42no—
295C2×D4—24no—
296C2×D4—24no—
297C2×D4—22no—
298C2×D4—24no—
299C2×D4—24no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4C22×C4×C1114yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—44no—
309C22×C4—44no—
310C22×C4—44no—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1111yescharacteristic
313C22×C4C2×D4×C1111yescharacteristic
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C2×D4×C1111yescharacteristic
317C22×C4C24×C1111yescharacteristic
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8C22×C4×C1114yes—
324C4⋊C4—24no—
325C4⋊C4—22no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—42no—
329C4⋊C4—44no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4C22×C4×C1114yes—
334C22⋊C4—44no—
335C22⋊C4—44no—
336C22⋊C4—44no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42—44no—
343C42C11×D814yes—
344C42C22×C4×C1112yes—
345C42C11×#4112yes—
346C11#2222011yescharacteristic, direct product factor, Sylow
347C23—24no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23C22×D4×C1111yescharacteristic
355Q8—48no—
356D4—28no—
357D4—44no—
358D4—48no—
359D4—48no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—24no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—88no—
380C2×C4C4×D4×C1112yes—
381C2×C4C4×D4×C1112yes—
382C2×C4C2×C11×D812yes—
383C2×C4C2×C11×D812yes—
384C2×C4C2×C11×D812yes—
385C2×C4C11×#13512yes—
386C2×C4C11×AGL(1,ℤ/8)12yes—
387C2×C4C11×#13712yes—
388C2×C4C23×C4×C1111yescharacteristic
389C2×C4C2×C11×#4111yescharacteristic
390C2×C4C11×H(5,𝔽2)12yes—
391C2×C4C11×2−1+412yes—
392C8—24no—
393C8—42no—
394C22—44no—
395C22—44no—
396C22—44no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22C2×C4×D4×C1111yescharacteristic
402C22C11×#53511yescharacteristic
403C22C11×#53611yescharacteristic
404C22C22×C11×D811yescharacteristic
405C22C2×C11×#13511yescharacteristic
406C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
407C22C2×C11×#13711yescharacteristic
408C4—22no—
409C4—22no—
410C4—44no—
411C4—41no—
412C4—41no—
413C4—82no—
414C4—82no—
415C4C4×C11×D814yes—
416C4C11×#44014yes—
417C4C11×#52012yes—
418C4C11×#54212yes—
419C2—84no—
420C2C11×#232611yescharacteristic
421C2C2×C4×C11×D811yescharacteristic
422C2C2×C11×#44011yescharacteristic
423C2C11×#320511yescharacteristic
424C2C11×#321011yescharacteristic
425C2C11×#322611yescharacteristic
426C2C11×#322811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×C4⋊Q8C2semidirect
4. C11×#1990C2semidirect
6. C11×#1925C2semidirect
7. C11×#1862C2semidirect
8. C11×#1845C2semidirect
9. C11×#1744C2semidirect
16. C11×#486C4semidirect
44. C11×C4⋊Q8C2×C4semidirect
73. C11×#102C2×C4semidirect
75. C4×C8×C11C2×C4semidirect
78. #22220C11direct (N × H)
135. C4×C4⋊Q8C2×C11semidirect
137. #1990C2×C11semidirect
139. #1925C2×C11semidirect
140. #1862C2×C11semidirect
141. #1845C2×C11semidirect
142. #1744C2×C11semidirect
196. #486C4×C11semidirect
249. C4⋊Q8C2×C4×C11semidirect
278. #102C2×C4×C11semidirect
280. C4×C8C2×C4×C11semidirect
346. C11#22220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C4×C11×C4⋊Q82
C4×C11×#1272
C11×#19902
C11×#19572
C11×#19252
C11×#18622
C11×#18452
C11×#17442
#2222011