Finite Group Databasebeta

← C11×#24070 #14601263

Subgroups — C11×#24070 #14601263

Order 2816.

1130 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×#540C211yesmaximal, characteristic
2C2×C11×#482C212yesmaximal, complemented
3C11×#2316C211yesmaximal, characteristic, complemented
4C11×#2059C212yesmaximal, complemented
5C11×#2041C212yesmaximal, complemented
6C11×#1874C212yesmaximal, complemented
7C11×#1864C212yesmaximal, complemented
8C11×#1862C212yesmaximal, complemented
9C11×#1818C211yesmaximal, characteristic, complemented
10C11×#540—28no—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#125C2211yescharacteristic
13C2×C11×#123—22no—
14C2×C11×#121—22no—
15C2×C11×#121C2212yes—
16C2×C4×D4×C11C2212yes—
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C11×#482—28no—
21C2×C11×#107C2212yes—
22C2×C11×#106C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C11×#389—22no—
29C11×#389C2212yes—
30C11×#389C2212yes—
31C11×#380—22no—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2211yescharacteristic
36C11×#336C2211yescharacteristic
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2312yes—
40C23×C4×C11—21no—
41C23×C4×C11—22no—
42C23×C4×C11C2311yescharacteristic
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C11×#127—24no—
46C11×#125—24no—
47C11×#123—216no—
48C11×#121—216no—
49C11×#121—24no—
50C11×#121D418yes—
51C4×D4×C11—24no—
52C4×D4×C11—24no—
53C11×#117—24no—
54C11×#117—24no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C11×#107—24no—
72C11×#106—24no—
73C11×#102—24no—
74C11×#102—24no—
75C11×#102—24no—
76C11×#102—24no—
77C11×C22⋊C8—24no—
78C11×#95—22no—
79C11×#95—22no—
80#24070C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—22no—
82C24×C11C2×D411yescharacteristic
83C2×D4×C11—28no—
84C2×D4×C11—28no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—82no—
91C2×D4×C11—82no—
92C2×D4×C11—82no—
93C2×D4×C11—82no—
94C2×D4×C11C2×D414yes—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—28no—
102C22×C4×C11—22no—
103C22×C4×C11—82no—
104C22×C4×C11—82no—
105C22×C4×C11—82no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D414yes—
110C22×C4×C11C2411yescharacteristic
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—28no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—82no—
125C11×C4⋊C4—82no—
126C11×C4⋊C4C2×D414yes—
127C11×C4⋊C4#4114yes—
128C11×C22⋊C4—28no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—42no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—42no—
135C2×#540C2×C1111yescharacteristic
136C2×#482C2×C1112yescomplemented
137#2316C2×C1111yescharacteristic, complemented
138#2059C2×C1112yescomplemented
139#2041C2×C1112yescomplemented
140#1874C2×C1112yescomplemented
141#1864C2×C1112yescomplemented
142#1862C2×C1112yescomplemented
143#1818C2×C1111yescharacteristic, complemented
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—24no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11#12012yes—
156C23×C11C22×D411yescharacteristic
157D4×C11—24no—
158D4×C11—24no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—88no—
162D4×C11—88no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—84no—
183C2×C4×C11—88no—
184C2×C4×C11#12012yes—
185C2×C4×C11C22×D412yes—
186C2×C4×C11C2×#4112yes—
187C2×C4×C112−1+411yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C8×C11—42no—
190C8×C11—42no—
191#540—28no—
192C2×#127C22×C1111yescharacteristic
193C2×#125C22×C1111yescharacteristic
194C2×#123—22no—
195C2×#121—22no—
196C2×#121C22×C1112yes—
197C2×C4×D4C22×C1112yes—
198C2×#117C22×C1111yescharacteristic
199C2×#117C22×C1111yescharacteristic
200C22×C4⋊C4C22×C1111yescharacteristic
201#482—28no—
202C2×#107C22×C1112yes—
203C2×#106C22×C1112yes—
204C2×#102C22×C1112yes—
205C2×#102C22×C1112yes—
206C2×#102C22×C1112yes—
207C2×#102C22×C1112yes—
208C2×C22⋊C8C22×C1112yes—
209#389—22no—
210#389C22×C1112yes—
211#389C22×C1112yes—
212#380—22no—
213#340C22×C1112yes—
214#340C22×C1112yes—
215#336C22×C1112yes—
216#336C22×C1111yescharacteristic
217#336C22×C1111yescharacteristic
218C22×C11—22no—
219C22×C11—24no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—42no—
223C22×C11—44no—
224C22×C11—44no—
225C22×C11—44no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11C2×#12011yescharacteristic
231C22×C11#52511yescharacteristic
232C22×C11#53611yescharacteristic
233C22×C11#57612yes—
234C22×C11#57712yes—
235C4×C11—22no—
236C4×C11—44no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—44no—
240C4×C11—82no—
241C4×C11#54712yes—
242C4×C11#54712yes—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4C23×C1112yes—
246C23×C4—21no—
247C23×C4—22no—
248C23×C4C23×C1111yescharacteristic
249C22×C8C23×C1112yes—
250C22×C8C23×C1112yes—
251#127—24no—
252#125—24no—
253#123—216no—
254#121—216no—
255#121—24no—
256#121D4×C1118yes—
257C4×D4—24no—
258C4×D4—24no—
259#117—24no—
260#117—24no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4D4×C1112yes—
267C2×C4⋊C4C23×C1112yes—
268C2×C4⋊C4C23×C1112yes—
269C2×C4⋊C4C23×C1112yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4D4×C1112yes—
274C2×C42—21no—
275C2×C42C23×C1111yescharacteristic
276C2×C42C23×C1111yescharacteristic
277#107—24no—
278#106—24no—
279#102—24no—
280#102—24no—
281#102—24no—
282#102—24no—
283C22⋊C8—24no—
284#95—22no—
285#95—22no—
286C2×C11—42no—
287C2×C11—84no—
288C2×C11#240611yescharacteristic
289C2×C11#301212yes—
290C2×C11#312211yescharacteristic
291C2×C11#312611yescharacteristic
292C2×C11#324112yes—
293C24—22no—
294C24C2×D4×C1111yescharacteristic
295C2×D4—28no—
296C2×D4—28no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—82no—
303C2×D4—82no—
304C2×D4—82no—
305C2×D4—82no—
306C2×D4C2×D4×C1114yes—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—28no—
314C22×C4—22no—
315C22×C4—82no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4C2×D4×C1112yes—
319C22×C4C2×D4×C1112yes—
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1114yes—
322C22×C4C24×C1111yescharacteristic
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C4⋊C4—24no—
330C4⋊C4—28no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—82no—
337C4⋊C4—82no—
338C4⋊C4C2×D4×C1114yes—
339C4⋊C4C11×#4114yes—
340C22⋊C4—28no—
341C22⋊C4—24no—
342C22⋊C4—28no—
343C22⋊C4—42no—
344C42—22no—
345C42—22no—
346C42—42no—
347C11#2407011yescharacteristic, direct product factor, Sylow
348C23—21no—
349C23—21no—
350C23—22no—
351C23—22no—
352C23—24no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23C11×#12012yes—
360C23C22×D4×C1111yescharacteristic
361D4—24no—
362D4—24no—
363D4—42no—
364D4—42no—
365D4—88no—
366D4—88no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—88no—
387C2×C4—84no—
388C2×C4C11×#12012yes—
389C2×C4C22×D4×C1112yes—
390C2×C4C2×C11×#4112yes—
391C2×C4C11×2−1+411yescharacteristic
392C2×C4C11×2−1+411yescharacteristic
393C8—42no—
394C8—42no—
395C22—22no—
396C22—24no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—44no—
401C22—44no—
402C22—44no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22—82no—
407C22C2×C11×#12011yescharacteristic
408C22C11×#52511yescharacteristic
409C22C11×#53611yescharacteristic
410C22C11×#57612yes—
411C22C11×#57712yes—
412C4—22no—
413C4—42no—
414C4—42no—
415C4—44no—
416C4—44no—
417C4—82no—
418C4C11×#54712yes—
419C4C11×#54712yes—
420C2—42no—
421C2—84no—
422C2C11×#240611yescharacteristic
423C2C11×#301212yes—
424C2C11×#312211yescharacteristic
425C2C11×#312611yescharacteristic
426C2C11×#324112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#482C2semidirect
3. C11×#2316C2semidirect
4. C11×#2059C2semidirect
5. C11×#2041C2semidirect
6. C11×#1874C2semidirect
7. C11×#1864C2semidirect
8. C11×#1862C2semidirect
9. C11×#1818C2semidirect
80. #24070C11direct (N × H)
136. C2×#482C2×C11semidirect
137. #2316C2×C11semidirect
138. #2059C2×C11semidirect
139. #2041C2×C11semidirect
140. #1874C2×C11semidirect
141. #1864C2×C11semidirect
142. #1862C2×C11semidirect
143. #1818C2×C11semidirect
347. C11#24070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5402
C2×C11×#4822
C11×#23162
C11×#20592
C11×#20412
C11×#18742
C11×#18642
C11×#18622
C11×#18182
#2407011