Finite Group Databasebeta

← C11×#9141 #14586334

Subgroups — C11×#9141 #14586334

Order 2816.

752 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#423C211yesmaximal, characteristic, complemented
2C11×#2856C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic, complemented
4C2×C11×#331C212yesmaximal, complemented
5C11×#1296C212yesmaximal, complemented
6C22×C11×M16—21no—
7C2×C11×#127C2211yescharacteristic
8C2×C11×#121—21no—
9C2×C11×#121—21no—
10C2×C11×#121C412yes—
11C22×C42×C11C2211yescharacteristic
12C11×#423—24no—
13C2×C11×C4⋊C8—21no—
14C2×C11×C4⋊C8C2212yes—
15C2×C11×C4⋊C8C2212yes—
16C2×C11×C22⋊C8—21no—
17C11×#390—21no—
18C11×#390—21no—
19C11×#390C412yes—
20C11×#384C2211yescharacteristic
21C11×#336—21no—
22C11×#331—24no—
23C22×D4×C11—22no—
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C412yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×M16—24no—
31C2×C11×M16—42no—
32C2×C11×M16—42no—
33C22×C8×C11—22no—
34C22×C8×C11—22no—
35C11×#127—22no—
36C11×#127—22no—
37C11×#121—44no—
38C11×#121—42no—
39C11×#121—42no—
40C11×#121—44no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4C2×C412yes—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C11×C4⋊C8—24no—
54C11×C4⋊C8—22no—
55C11×C4⋊C8—22no—
56C11×C4⋊C8—22no—
57C11×C4⋊C8D414yescomplemented
58C11×C22⋊C8—42no—
59#9141C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11—22no—
61C24×C11C22⋊C411yescharacteristic
62C2×D4×C11—24no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—44no—
66C2×D4×C11—44no—
67C2×D4×C11—44no—
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—41no—
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11D812yes—
94C22×C4×C11SD1612yes—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C11×M16—48no—
99C2×C8×C11—24no—
100C2×C8×C11—42no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C2×C8×C11—42no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—42no—
109C11×C22⋊C4—44no—
110C11×C22⋊C4—44no—
111C11×C22⋊C4—44no—
112C42×C11—22no—
113C42×C11—21no—
114C42×C11—22no—
115C42×C11—21no—
116C42×C11C2×D412yes—
117C42×C11#4112yes—
118C2×#423C2×C1111yescharacteristic, complemented
119#2856C2×C1111yescharacteristic
120#1797C2×C1111yescharacteristic, complemented
121C2×#331C2×C1112yescomplemented
122#1296C2×C1112yescomplemented
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11#10212yes—
137C23×C11C2×C22⋊C411yescharacteristic
138D4×C11—84no—
139D4×C11—88no—
140D4×C11—81no—
141D4×C11—81no—
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—81no—
145D4×C11—81no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11#10012yes—
166C2×C4×C11#10212yes—
167C2×C4×C11C4×D412yes—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12112yes—
170C2×C4×C11#12311yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×SD1611yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C8×C11—44no—
179C8×C11—82no—
180C22×M16—21no—
181C2×#127C22×C1111yescharacteristic
182C2×#121—21no—
183C2×#121—21no—
184C2×#121C4×C1112yes—
185C22×C42C22×C1111yescharacteristic
186#423—24no—
187C2×C4⋊C8—21no—
188C2×C4⋊C8C22×C1112yes—
189C2×C4⋊C8C22×C1112yes—
190C2×C22⋊C8—21no—
191#390—21no—
192#390—21no—
193#390C4×C1112yes—
194#384C22×C1111yescharacteristic
195#336—21no—
196#331—24no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11#38611yescharacteristic
212C22×C11C2×#10011yescharacteristic
213C22×C11#41311yescharacteristic
214C22×C11C2×#10211yescharacteristic
215C22×C11#41711yescharacteristic
216C22×C11#41711yescharacteristic
217C22×C11#41811yescharacteristic
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—41no—
222C4×C11—82no—
223C4×C11#44711yescharacteristic
224C4×C11#44811yescharacteristic
225C4×C11#46812yes—
226C4×C11#46912yes—
227C4×C11#48011yescharacteristic
228C4×C11#48111yescharacteristic
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4C2×C4×C1112yes—
233C23×C4C2×C4×C1111yescharacteristic
234C23×C4D4×C1111yescharacteristic
235C23×C4D4×C1111yescharacteristic
236C2×M16—24no—
237C2×M16—42no—
238C2×M16—42no—
239C22×C8—22no—
240C22×C8—22no—
241#127—22no—
242#127—22no—
243#121—44no—
244#121—42no—
245#121—42no—
246#121—44no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4C2×C4×C1112yes—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C42—22no—
254C2×C42—22no—
255C2×C42C2×C4×C1111yescharacteristic
256C2×C42D4×C1111yescharacteristic
257C2×C42D4×C1111yescharacteristic
258C2×C42C23×C1111yescharacteristic
259C4⋊C8—24no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8D4×C1114yescomplemented
264C22⋊C8—42no—
265C2×C11—42no—
266C2×C11—162no—
267C2×C11#154511yescharacteristic
268C2×C11#154711yescharacteristic
269C2×C11#155711yescharacteristic
270C2×C11#156011yescharacteristic
271C2×C11#187411yescharacteristic
272C2×C11#189511yescharacteristic
273C2×C11#190011yescharacteristic
274C24—22no—
275C24C11×C22⋊C411yescharacteristic
276C2×D4—24no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—44no—
280C2×D4—44no—
281C2×D4—44no—
282C2×D4—41no—
283C2×D4—42no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—42no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4C11×C22⋊C411yescharacteristic
305C22×C4C11×C22⋊C411yescharacteristic
306C22×C4C11×C22⋊C411yescharacteristic
307C22×C4C11×D812yes—
308C22×C4C11×SD1612yes—
309C22×C4C22×C4×C1111yescharacteristic
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C2×D4×C1111yescharacteristic
312M16—48no—
313C2×C8—24no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—42no—
323C22⋊C4—44no—
324C22⋊C4—44no—
325C22⋊C4—44no—
326C42—22no—
327C42—21no—
328C42—22no—
329C42—21no—
330C42C2×D4×C1112yes—
331C42C11×#4112yes—
332C11#914111yescharacteristic, direct product factor, Sylow
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23C11×#10212yes—
347C23C2×C11×C22⋊C411yescharacteristic
348D4—84no—
349D4—88no—
350D4—81no—
351D4—81no—
352D4—82no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4C11×#10012yes—
376C2×C4C11×#10212yes—
377C2×C4C4×D4×C1112yes—
378C2×C4C11×#12011yescharacteristic
379C2×C4C11×#12112yes—
380C2×C4C11×#12311yescharacteristic
381C2×C4C2×C11×D811yescharacteristic
382C2×C4C2×C11×SD1611yescharacteristic
383C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C11×AGL(1,ℤ/8)12yes—
385C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
386C2×C4C11×#13711yescharacteristic
387C2×C4C11×#13711yescharacteristic
388C8—44no—
389C8—82no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—82no—
403C22—82no—
404C22C11×#38611yescharacteristic
405C22C2×C11×#10011yescharacteristic
406C22C11×#41311yescharacteristic
407C22C2×C11×#10211yescharacteristic
408C22C11×#41711yescharacteristic
409C22C11×#41711yescharacteristic
410C22C11×#41811yescharacteristic
411C4—22no—
412C4—22no—
413C4—22no—
414C4—41no—
415C4—82no—
416C4C11×#44711yescharacteristic
417C4C11×#44811yescharacteristic
418C4C11×#46812yes—
419C4C11×#46912yes—
420C4C11×#48011yescharacteristic
421C4C11×#48111yescharacteristic
422C2—42no—
423C2—162no—
424C2C11×#154511yescharacteristic
425C2C11×#154711yescharacteristic
426C2C11×#155711yescharacteristic
427C2C11×#156011yescharacteristic
428C2C11×#187411yescharacteristic
429C2C11×#189511yescharacteristic
430C2C11×#190011yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2856C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#423C2semidirect
3. C11×#1797C2semidirect
4. C2×C11×#331C2semidirect
5. C11×#1296C2semidirect
57. C11×C4⋊C8D4semidirect
59. #9141C11direct (N × H)
118. C2×#423C2×C11semidirect
120. #1797C2×C11semidirect
121. C2×#331C2×C11semidirect
122. #1296C2×C11semidirect
263. C4⋊C8D4×C11semidirect
332. C11#9141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4232
C11×#28562
C11×#17972
C2×C11×#3312
C11×#12962
#914111