Finite Group Databasebeta

← C11×#9137 #14586330

Subgroups — C11×#9137 #14586330

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#423C211yesmaximal, characteristic
2C11×#2857C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic
4C2×C11×#332C212yesmaximal, complemented
5C11×#1296C212yesmaximal, complemented
6C22×C11×M16—21no—
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×C11×C22⋊Q8—21no—
9C22×C42×C11C2211yescharacteristic
10C11×#423—24no—
11C2×C11×C4⋊C8—21no—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×C4⋊C8C2212yes—
14C2×C11×C22⋊C8—21no—
15C11×#391—21no—
16C11×#389—21no—
17C11×#389C412yes—
18C11×#384C2211yescharacteristic
19C11×#380—21no—
20C11×#380C412yes—
21C11×#336—21no—
22C11×#332—24no—
23C22×Q8×C11—21no—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C2×C11×M16—24no—
28C2×C11×M16—42no—
29C2×C11×M16—42no—
30C22×C8×C11—22no—
31C22×C8×C11—22no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8—22no—
34C11×C22⋊Q8—44no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C412yes—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C11×C22⋊C4—22no—
42C2×C42×C11—22no—
43C2×C42×C11—22no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C11×C4⋊C8—24no—
49C11×C4⋊C8—22no—
50C11×C4⋊C8—22no—
51C11×C4⋊C8—22no—
52C11×C4⋊C8D414yes—
53C11×C22⋊C8—42no—
54C11×#95—22no—
55C11×#95—22no—
56#9137C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11C22⋊C411yescharacteristic
58C2×Q8×C11—42no—
59C2×Q8×C11—42no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—41no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11SD1612yes—
79C22×C4×C11Q1612yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C11×M16—48no—
84C2×C8×C11—24no—
85C2×C8×C11—42no—
86C2×C8×C11—42no—
87C2×C8×C11—42no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—44no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—44no—
99C42×C11—22no—
100C42×C11—21no—
101C42×C11—22no—
102C42×C11—21no—
103C42×C11C2×D412yes—
104C42×C11#4112yes—
105C2×#423C2×C1111yescharacteristic
106#2857C2×C1111yescharacteristic
107#1797C2×C1111yescharacteristic
108C2×#332C2×C1112yescomplemented
109#1296C2×C1112yescomplemented
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11#10312yes—
117C23×C11C2×C22⋊C411yescharacteristic
118Q8×C11—82no—
119Q8×C11—82no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11#10112yes—
143C2×C4×C11#10312yes—
144C2×C4×C11C4×D412yes—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12112yes—
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11C2×Q1611yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)12yes—
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C8×C11—44no—
156C8×C11—82no—
157C22×M16—21no—
158C2×C4⋊Q8C22×C1111yescharacteristic
159C2×C22⋊Q8—21no—
160C22×C42C22×C1111yescharacteristic
161#423—24no—
162C2×C4⋊C8—21no—
163C2×C4⋊C8C22×C1112yes—
164C2×C4⋊C8C22×C1112yes—
165C2×C22⋊C8—21no—
166#391—21no—
167#389—21no—
168#389C4×C1112yes—
169#384C22×C1111yescharacteristic
170#380—21no—
171#380C4×C1112yes—
172#336—21no—
173#332—24no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11#38611yescharacteristic
182C22×C11C2×#10111yescharacteristic
183C22×C11#41311yescharacteristic
184C22×C11C2×#10311yescharacteristic
185C22×C11#41711yescharacteristic
186C22×C11#41711yescharacteristic
187C22×C11#41811yescharacteristic
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—41no—
192C4×C11—82no—
193C4×C11—82no—
194C4×C11#45011yescharacteristic
195C4×C11#45111yescharacteristic
196C4×C11#46812yes—
197C4×C11#46912yes—
198C4×C11#48311yescharacteristic
199C4×C11#48411yescharacteristic
200C22×Q8—21no—
201C23×C4C2×C4×C1111yescharacteristic
202C23×C4D4×C1111yescharacteristic
203C23×C4D4×C1111yescharacteristic
204C2×M16—24no—
205C2×M16—42no—
206C2×M16—42no—
207C22×C8—22no—
208C22×C8—22no—
209C4⋊Q8—22no—
210C4⋊Q8—22no—
211C22⋊Q8—44no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C2×C4×C1112yes—
217C2×C4⋊C4C2×C4×C1112yes—
218C2×C22⋊C4—22no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42C2×C4×C1111yescharacteristic
222C2×C42D4×C1111yescharacteristic
223C2×C42D4×C1111yescharacteristic
224C2×C42C23×C1111yescharacteristic
225C4⋊C8—24no—
226C4⋊C8—22no—
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8D4×C1114yes—
230C22⋊C8—42no—
231#95—22no—
232#95—22no—
233C2×C11—42no—
234C2×C11#154911yescharacteristic
235C2×C11#155011yescharacteristic
236C2×C11#155711yescharacteristic
237C2×C11#156111yescharacteristic
238C2×C11#187211yescharacteristic
239C2×C11#189511yescharacteristic
240C2×C11#190111yescharacteristic
241C24C11×C22⋊C411yescharacteristic
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—41no—
245C2×Q8—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4C11×C22⋊C411yescharacteristic
260C22×C4C11×C22⋊C411yescharacteristic
261C22×C4C11×C22⋊C411yescharacteristic
262C22×C4C11×SD1612yes—
263C22×C4C11×Q1612yes—
264C22×C4C22×C4×C1111yescharacteristic
265C22×C4C2×D4×C1111yescharacteristic
266C22×C4C2×D4×C1111yescharacteristic
267M16—48no—
268C2×C8—24no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C4⋊C4—24no—
275C4⋊C4—42no—
276C4⋊C4—44no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—44no—
283C42—22no—
284C42—21no—
285C42—22no—
286C42—21no—
287C42C2×D4×C1112yes—
288C42C11×#4112yes—
289C11#913711yescharacteristic, direct product factor, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23C11×#10312yes—
297C23C2×C11×C22⋊C411yescharacteristic
298Q8—82no—
299Q8—82no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4C11×#10112yes—
323C2×C4C11×#10312yes—
324C2×C4C4×D4×C1112yes—
325C2×C4C11×#12011yescharacteristic
326C2×C4C11×#12112yes—
327C2×C4C11×#12311yescharacteristic
328C2×C4C2×C11×SD1611yescharacteristic
329C2×C4C2×C11×Q1611yescharacteristic
330C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
331C2×C4C11×AGL(1,ℤ/8)12yes—
332C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
333C2×C4C11×#13711yescharacteristic
334C2×C4C11×#13711yescharacteristic
335C8—44no—
336C8—82no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C11×#38611yescharacteristic
345C22C2×C11×#10111yescharacteristic
346C22C11×#41311yescharacteristic
347C22C2×C11×#10311yescharacteristic
348C22C11×#41711yescharacteristic
349C22C11×#41711yescharacteristic
350C22C11×#41811yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—82no—
356C4—82no—
357C4C11×#45011yescharacteristic
358C4C11×#45111yescharacteristic
359C4C11×#46812yes—
360C4C11×#46912yes—
361C4C11×#48311yescharacteristic
362C4C11×#48411yescharacteristic
363C2—42no—
364C2C11×#154911yescharacteristic
365C2C11×#155011yescharacteristic
366C2C11×#155711yescharacteristic
367C2C11×#156111yescharacteristic
368C2C11×#187211yescharacteristic
369C2C11×#189511yescharacteristic
370C2C11×#190111yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC24×C11C22⋊C4
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
4. C2×C11×#332C2semidirect
5. C11×#1296C2semidirect
56. #9137C11direct (N × H)
108. C2×#332C2×C11semidirect
109. #1296C2×C11semidirect
289. C11#9137direct (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×#28572
C11×#17972
C2×C11×#3322
C11×#12962
#913711