Finite Group Databasebeta

← C11×#9130 #14586323

Subgroups — C11×#9130 #14586323

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#431C211yesmaximal, characteristic
2C11×#2857C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic
4C2×C11×#332C212yesmaximal, complemented
5C11×#1296C212yesmaximal, complemented
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C11×C22⋊Q8—21no—
8C22×C42×C11C2211yescharacteristic
9C11×#431—24no—
10C2×C11×C4⋊C8C2212yes—
11C2×C11×C4⋊C8C2212yes—
12C2×C11×C22⋊C8—21no—
13C2×C11×C22⋊C8—21no—
14C2×C4×C8×C11—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
27C22×C8×C11—22no—
28C22×C8×C11—22no—
29C11×C4⋊Q8—22no—
30C11×C4⋊Q8—22no—
31C11×C22⋊Q8—42no—
32C11×C22⋊Q8—42no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C4⋊C4C2×C412yes—
39C2×C11×C22⋊C4—22no—
40C2×C42×C11—22no—
41C2×C42×C11—22no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C11×C4⋊C8—22no—
47C11×C4⋊C8—22no—
48C11×C4⋊C8—22no—
49C11×C4⋊C8D414yes—
50C11×C22⋊C8—24no—
51C11×C22⋊C8—42no—
52C4×C8×C11—24no—
53C11×#95—22no—
54C11×#95—22no—
55#9130C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11C22⋊C411yescharacteristic
57C2×Q8×C11—42no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—42no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11D812yes—
76C22×C4×C11SD1612yes—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×C8×C11—24no—
81C2×C8×C11—42no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C2×C8×C11—42no—
85C2×C8×C11—42no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—44no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—42no—
94C11×C22⋊C4—44no—
95C42×C11—22no—
96C42×C11—21no—
97C42×C11—22no—
98C42×C11—21no—
99C42×C11C2×D412yes—
100C42×C11#4112yes—
101C2×#431C2×C1111yescharacteristic
102#2857C2×C1111yescharacteristic
103#1797C2×C1111yescharacteristic
104C2×#332C2×C1112yescomplemented
105#1296C2×C1112yescomplemented
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11#10212yes—
113C23×C11C2×C22⋊C411yescharacteristic
114Q8×C11—82no—
115Q8×C11—82no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—24no—
123C2×C4×C11—24no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—44no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11#10112yes—
137C2×C4×C11#10212yes—
138C2×C4×C11C4×D412yes—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12112yes—
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13512yes—
145C2×C4×C11#13512yes—
146C2×C4×C11#13712yes—
147C8×C11—44no—
148C8×C11—82no—
149C2×C4⋊Q8C22×C1111yescharacteristic
150C2×C22⋊Q8—21no—
151C22×C42C22×C1111yescharacteristic
152#431—24no—
153C2×C4⋊C8C22×C1112yes—
154C2×C4⋊C8C22×C1112yes—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157C2×C4×C8—21no—
158#391—21no—
159#389—21no—
160#389C4×C1112yes—
161#384C22×C1111yescharacteristic
162#380—21no—
163#380C4×C1112yes—
164#336—21no—
165#332—24no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11#38611yescharacteristic
174C22×C11C2×#10111yescharacteristic
175C22×C11#41311yescharacteristic
176C22×C11C2×#10211yescharacteristic
177C22×C11#41611yescharacteristic
178C22×C11#41611yescharacteristic
179C22×C11#41911yescharacteristic
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—41no—
184C4×C11—82no—
185C4×C11—82no—
186C4×C11#45212yes—
187C4×C11#46512yes—
188C4×C11#46612yes—
189C4×C11#48512yes—
190C22×Q8—21no—
191C23×C4C2×C4×C1111yescharacteristic
192C23×C4D4×C1111yescharacteristic
193C23×C4D4×C1111yescharacteristic
194C22×C8—22no—
195C22×C8—22no—
196C4⋊Q8—22no—
197C4⋊Q8—22no—
198C22⋊Q8—42no—
199C22⋊Q8—42no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×C4×C1112yes—
205C2×C4⋊C4C2×C4×C1112yes—
206C2×C22⋊C4—22no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42C2×C4×C1111yescharacteristic
210C2×C42D4×C1111yescharacteristic
211C2×C42D4×C1111yescharacteristic
212C2×C42C23×C1111yescharacteristic
213C4⋊C8—22no—
214C4⋊C8—22no—
215C4⋊C8—22no—
216C4⋊C8D4×C1114yes—
217C22⋊C8—24no—
218C22⋊C8—42no—
219C4×C8—24no—
220#95—22no—
221#95—22no—
222C2×C11—42no—
223C2×C11#154011yescharacteristic
224C2×C11#154411yescharacteristic
225C2×C11#154611yescharacteristic
226C2×C11#155411yescharacteristic
227C2×C11#187311yescharacteristic
228C2×C11#189311yescharacteristic
229C2×C11#190111yescharacteristic
230C24C11×C22⋊C411yescharacteristic
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—42no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4C11×C22⋊C411yescharacteristic
247C22×C4C11×C22⋊C411yescharacteristic
248C22×C4C11×C22⋊C411yescharacteristic
249C22×C4C11×D812yes—
250C22×C4C11×SD1612yes—
251C22×C4C22×C4×C1111yescharacteristic
252C22×C4C2×D4×C1111yescharacteristic
253C22×C4C2×D4×C1111yescharacteristic
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C4⋊C4—24no—
261C4⋊C4—42no—
262C4⋊C4—44no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C22⋊C4—44no—
269C42—22no—
270C42—21no—
271C42—22no—
272C42—21no—
273C42C2×D4×C1112yes—
274C42C11×#4112yes—
275C11#913011yescharacteristic, direct product factor, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23C11×#10212yes—
283C23C2×C11×C22⋊C411yescharacteristic
284Q8—82no—
285Q8—82no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4C11×#10112yes—
307C2×C4C11×#10212yes—
308C2×C4C4×D4×C1112yes—
309C2×C4C11×#12011yescharacteristic
310C2×C4C11×#12112yes—
311C2×C4C11×#12311yescharacteristic
312C2×C4C2×C11×D811yescharacteristic
313C2×C4C2×C11×SD1611yescharacteristic
314C2×C4C11×#13512yes—
315C2×C4C11×#13512yes—
316C2×C4C11×#13712yes—
317C8—44no—
318C8—82no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22C11×#38611yescharacteristic
327C22C2×C11×#10111yescharacteristic
328C22C11×#41311yescharacteristic
329C22C2×C11×#10211yescharacteristic
330C22C11×#41611yescharacteristic
331C22C11×#41611yescharacteristic
332C22C11×#41911yescharacteristic
333C4—22no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—82no—
338C4—82no—
339C4C11×#45212yes—
340C4C11×#46512yes—
341C4C11×#46612yes—
342C4C11×#48512yes—
343C2—42no—
344C2C11×#154011yescharacteristic
345C2C11×#154411yescharacteristic
346C2C11×#154611yescharacteristic
347C2C11×#155411yescharacteristic
348C2C11×#187311yescharacteristic
349C2C11×#189311yescharacteristic
350C2C11×#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
55. #9130C11direct (N × H)
104. C2×#332C2×C11semidirect
105. #1296C2×C11semidirect
275. C11#9130direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4312
C11×#28572
C11×#17972
C2×C11×#3322
C11×#12962
#913011