Finite Group Databasebeta

← C11×#21897 #14599090

Subgroups — C11×#21897 #14599090

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#540C211yesmaximal, characteristic
2C2×C11×#424C211yesmaximal, characteristic, complemented
3C11×#2314C211yesmaximal, characteristic, complemented
4C11×#1989C212yesmaximal, complemented
5C11×#1982C212yesmaximal, complemented
6C11×#1895C212yesmaximal, complemented
7C11×#1893C212yesmaximal, complemented
8C11×#1804C212yesmaximal, complemented
9C11×#1802C212yesmaximal, complemented
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C11×#540—24no—
13C11×#540C418yescomplemented
14C2×C11×#127C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×#121—22no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C11×#424—24no—
22C2×C11×C4⋊C8C2212yes—
23C2×C11×C4⋊C8C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C11×#388—22no—
29C11×#387—22no—
30C11×#384C2211yescharacteristic
31C11×#382C2211yescharacteristic
32C11×#380C2212yes—
33C4×C11×C4⋊C4C2212yes—
34C11×#340C2212yes—
35C11×#340C2212yes—
36C11×#340C2212yes—
37C11×#340C2212yes—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11C2312yes—
41C23×C4×C11—22no—
42C23×C4×C11C2311yescharacteristic
43C2×C11×M16—22no—
44C2×C11×M16—41no—
45C2×C11×M16—41no—
46C22×C8×C11—22no—
47C22×C8×C11—41no—
48C22×C8×C11—41no—
49C22×C8×C11C2312yes—
50C22×C8×C11C2312yes—
51C11×#127—22no—
52C11×#127C2×C414yes—
53C11×#125—22no—
54C11×#125C2×C414yes—
55C11×#123—216no—
56C11×#121—24no—
57C11×#121—216no—
58C11×#121C2×C418yes—
59C4×D4×C11—24no—
60C4×D4×C11C2×C418yes—
61C11×#117C2×C414yes—
62C11×#117D414yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D412yes—
73C2×C42×C11—22no—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C11×C4⋊C8—24no—
77C11×C4⋊C8—24no—
78C11×#102—42no—
79C11×#102—42no—
80C11×#102—42no—
81C11×#102—42no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—22no—
85#21897C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11—22no—
87C24×C11C2×D411yescharacteristic
88C2×D4×C11—28no—
89C2×D4×C11—28no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—82no—
96C2×D4×C11—82no—
97C2×D4×C11—82no—
98C2×D4×C11—82no—
99C2×D4×C11C22×C414yes—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—28no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—82no—
109C22×C4×C11—82no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2411yescharacteristic
116C11×M16—44no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—44no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—82no—
131C11×C4⋊C4C22⋊C418yes—
132C11×C4⋊C4C22×C414yes—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—28no—
135C11×C22⋊C4—82no—
136C11×C22⋊C4C22⋊C418yes—
137C42×C11—82no—
138C42×C11C22×C412yes—
139C42×C11C22×C412yes—
140C42×C11C2×D412yes—
141C42×C11C2×D412yes—
142C2×#540C2×C1111yescharacteristic
143C2×#424C2×C1111yescharacteristic, complemented
144#2314C2×C1111yescharacteristic, complemented
145#1989C2×C1112yescomplemented
146#1982C2×C1112yescomplemented
147#1895C2×C1112yescomplemented
148#1893C2×C1112yescomplemented
149#1804C2×C1112yescomplemented
150#1802C2×C1112yescomplemented
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—24no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11C2×C22⋊C412yes—
163C23×C11C22×D411yescharacteristic
164D4×C11—24no—
165D4×C11—24no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—88no—
169D4×C11—88no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—88no—
190C2×C4×C11C2×C22⋊C414yes—
191C2×C4×C11C2×C22⋊C414yes—
192C2×C4×C11C2×C22⋊C412yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C8×C11—42no—
200C8×C11—42no—
201C22×M16C22×C1111yescharacteristic
202C23×C8C22×C1111yescharacteristic
203#540—24no—
204#540C4×C1118yescomplemented
205C2×#127C22×C1111yescharacteristic
206C2×#125C22×C1111yescharacteristic
207C2×#123—22no—
208C2×#121—22no—
209C2×#121C22×C1112yes—
210C2×C4×D4C22×C1112yes—
211C2×#117C22×C1111yescharacteristic
212#424—24no—
213C2×C4⋊C8C22×C1112yes—
214C2×C4⋊C8C22×C1112yes—
215C2×#102C22×C1112yes—
216C2×#102C22×C1112yes—
217C2×#102C22×C1112yes—
218C2×#102C22×C1112yes—
219#388—22no—
220#387—22no—
221#384C22×C1111yescharacteristic
222#382C22×C1111yescharacteristic
223#380C22×C1112yes—
224C4×C4⋊C4C22×C1112yes—
225#340C22×C1112yes—
226#340C22×C1112yes—
227#340C22×C1112yes—
228#340C22×C1112yes—
229C22×C11—22no—
230C22×C11—24no—
231C22×C11—42no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11C22×C22⋊C411yescharacteristic
242C22×C11#53711yescharacteristic
243C22×C11#53711yescharacteristic
244C22×C11#57612yes—
245C22×C11#57712yes—
246C4×C11—22no—
247C4×C11—24no—
248C4×C11—24no—
249C4×C11—44no—
250C4×C11—82no—
251C4×C11—82no—
252C4×C11#52011yescharacteristic
253C4×C11#52011yescharacteristic
254C4×C11#53511yescharacteristic
255C4×C11#53611yescharacteristic
256C22×D4—22no—
257C22×D4—22no—
258C22×D4C23×C1112yes—
259C23×C4—22no—
260C23×C4C23×C1111yescharacteristic
261C2×M16—22no—
262C2×M16—41no—
263C2×M16—41no—
264C22×C8—22no—
265C22×C8—41no—
266C22×C8—41no—
267C22×C8C23×C1112yes—
268C22×C8C23×C1112yes—
269#127—22no—
270#127C2×C4×C1114yes—
271#125—22no—
272#125C2×C4×C1114yes—
273#123—216no—
274#121—24no—
275#121—216no—
276#121C2×C4×C1118yes—
277C4×D4—24no—
278C4×D4C2×C4×C1118yes—
279#117C2×C4×C1114yes—
280#117D4×C1114yes—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4D4×C1112yes—
284C2×C4⋊C4C23×C1112yes—
285C2×C4⋊C4C23×C1112yes—
286C2×C4⋊C4C23×C1112yes—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4D4×C1112yes—
291C2×C42—22no—
292C2×C42C23×C1111yescharacteristic
293C2×C42C23×C1111yescharacteristic
294C4⋊C8—24no—
295C4⋊C8—24no—
296#102—42no—
297#102—42no—
298#102—42no—
299#102—42no—
300#95—22no—
301#95—22no—
302#95—22no—
303C2×C11—42no—
304C2×C11—84no—
305C2×C11#231111yescharacteristic
306C2×C11#289712yes—
307C2×C11#325712yes—
308C2×C11#325911yescharacteristic
309C2×C11#326011yescharacteristic
310C24—22no—
311C24C2×D4×C1111yescharacteristic
312C2×D4—28no—
313C2×D4—28no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—82no—
320C2×D4—82no—
321C2×D4—82no—
322C2×D4—82no—
323C2×D4C22×C4×C1114yes—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—28no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—82no—
333C22×C4—82no—
334C22×C4C22×C4×C1112yes—
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C2×D4×C1112yes—
337C22×C4C2×D4×C1112yes—
338C22×C4C2×D4×C1112yes—
339C22×C4C24×C1111yescharacteristic
340M16—44no—
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—44no—
348C4⋊C4—28no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—82no—
355C4⋊C4C11×C22⋊C418yes—
356C4⋊C4C22×C4×C1114yes—
357C22⋊C4—28no—
358C22⋊C4—28no—
359C22⋊C4—82no—
360C22⋊C4C11×C22⋊C418yes—
361C42—82no—
362C42C22×C4×C1112yes—
363C42C22×C4×C1112yes—
364C42C2×D4×C1112yes—
365C42C2×D4×C1112yes—
366C11#2189711yescharacteristic, direct product factor, Sylow
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23—24no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23C2×C11×C22⋊C412yes—
379C23C22×D4×C1111yescharacteristic
380D4—24no—
381D4—24no—
382D4—42no—
383D4—42no—
384D4—88no—
385D4—88no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—88no—
406C2×C4C2×C11×C22⋊C414yes—
407C2×C4C2×C11×C22⋊C414yes—
408C2×C4C2×C11×C22⋊C412yes—
409C2×C4C23×C4×C1111yescharacteristic
410C2×C4C22×D4×C1111yescharacteristic
411C2×C4C11×H(5,𝔽2)11yescharacteristic
412C2×C4C11×H(5,𝔽2)11yescharacteristic
413C2×C4C11×2−1+411yescharacteristic
414C2×C4C11×2−1+411yescharacteristic
415C8—42no—
416C8—42no—
417C22—24no—
418C22—22no—
419C22—42no—
420C22—41no—
421C22—41no—
422C22—44no—
423C22—44no—
424C22—44no—
425C22—82no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22C22×C11×C22⋊C411yescharacteristic
430C22C11×#53711yescharacteristic
431C22C11×#53711yescharacteristic
432C22C11×#57612yes—
433C22C11×#57712yes—
434C4—24no—
435C4—24no—
436C4—22no—
437C4—44no—
438C4—82no—
439C4—82no—
440C4C11×#52011yescharacteristic
441C4C11×#52011yescharacteristic
442C4C11×#53511yescharacteristic
443C4C11×#53611yescharacteristic
444C2—42no—
445C2—84no—
446C2C11×#231111yescharacteristic
447C2C11×#289712yes—
448C2C11×#325712yes—
449C2C11×#325911yescharacteristic
450C2C11×#326011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#540C2
LCSG ▷ C2×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×#424C2semidirect
3. C11×#2314C2semidirect
4. C11×#1989C2semidirect
5. C11×#1982C2semidirect
6. C11×#1895C2semidirect
7. C11×#1893C2semidirect
8. C11×#1804C2semidirect
9. C11×#1802C2semidirect
13. C11×#540C4semidirect
85. #21897C11direct (N × H)
143. C2×#424C2×C11semidirect
144. #2314C2×C11semidirect
145. #1989C2×C11semidirect
146. #1982C2×C11semidirect
147. #1895C2×C11semidirect
148. #1893C2×C11semidirect
149. #1804C2×C11semidirect
150. #1802C2×C11semidirect
204. #540C4×C11semidirect
366. C11#21897direct (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×#4242
C11×#23142
C11×#19892
C11×#19822
C11×#18952
C11×#18932
C11×#18042
C11×#18022
#2189711