Finite Group Databasebeta

← C11×#9138 #14586331

Subgroups — C11×#9138 #14586331

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#432C211yesmaximal, 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×#432—24no—
10C2×C11×C4⋊C8C2212yes—
11C2×C11×C4⋊C8C2212yes—
12C2×C11×C22⋊C8—21no—
13C2×C11×C22⋊C8—21no—
14C2×C11×#97—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—44no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C412yes—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C11×C22⋊C4—22no—
39C2×C42×C11—22no—
40C2×C42×C11—22no—
41C2×C42×C11C2×C411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C11×C4⋊C8—22no—
46C11×C4⋊C8—22no—
47C11×C4⋊C8—22no—
48C11×C4⋊C8D414yes—
49C11×C22⋊C8—24no—
50C11×C22⋊C8—42no—
51C11×#97—24no—
52C11×#95—22no—
53C11×#95—22no—
54#9138C1111yesmaximal, characteristic, direct product factor, Sylow
55C24×C11C22⋊C411yescharacteristic
56C2×Q8×C11—42no—
57C2×Q8×C11—42no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—41no—
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C8×C11—24no—
80C2×C8×C11—42no—
81C2×C8×C11—42no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C2×C8×C11—42no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—44no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C11×C22⋊C4—44no—
93C42×C11—22no—
94C42×C11—21no—
95C42×C11—22no—
96C42×C11—21no—
97C42×C11C2×D412yes—
98C42×C11#4112yes—
99C2×#432C2×C1111yescharacteristic
100#2857C2×C1111yescharacteristic
101#1797C2×C1111yescharacteristic
102C2×#332C2×C1112yescomplemented
103#1296C2×C1112yescomplemented
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11#10112yes—
111C23×C11C2×C22⋊C411yescharacteristic
112Q8×C11—82no—
113Q8×C11—82no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
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—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
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×C11C4×D412yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12112yes—
139C2×C4×C11#12311yescharacteristic
140C2×C4×C11#13512yes—
141C2×C4×C11AGL(1,ℤ/8)12yes—
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13712yes—
144C2×C4×C11#13711yescharacteristic
145C8×C11—44no—
146C8×C11—82no—
147C2×C4⋊Q8C22×C1111yescharacteristic
148C2×C22⋊Q8—21no—
149C22×C42C22×C1111yescharacteristic
150#432—24no—
151C2×C4⋊C8C22×C1112yes—
152C2×C4⋊C8C22×C1112yes—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×#97—21no—
156#391—21no—
157#389—21no—
158#389C4×C1112yes—
159#384C22×C1111yescharacteristic
160#380—21no—
161#380C4×C1112yes—
162#336—21no—
163#332—24no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11#38611yescharacteristic
172C22×C11C2×#10111yescharacteristic
173C22×C11#41311yescharacteristic
174C22×C11#41611yescharacteristic
175C22×C11#41711yescharacteristic
176C22×C11#41811yescharacteristic
177C22×C11#41911yescharacteristic
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—82no—
183C4×C11—82no—
184C4×C11#45212yes—
185C4×C11#46812yes—
186C4×C11#46912yes—
187C4×C11#48512yes—
188C22×Q8—21no—
189C23×C4C2×C4×C1111yescharacteristic
190C23×C4D4×C1111yescharacteristic
191C23×C4D4×C1111yescharacteristic
192C22×C8—22no—
193C22×C8—22no—
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C22⋊Q8—44no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C1112yes—
202C2×C4⋊C4C2×C4×C1112yes—
203C2×C22⋊C4—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C2×C4×C1111yescharacteristic
207C2×C42D4×C1111yescharacteristic
208C2×C42D4×C1111yescharacteristic
209C2×C42C23×C1111yescharacteristic
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8D4×C1114yes—
214C22⋊C8—24no—
215C22⋊C8—42no—
216#97—24no—
217#95—22no—
218#95—22no—
219C2×C11—42no—
220C2×C11#155211yescharacteristic
221C2×C11#155311yescharacteristic
222C2×C11#155611yescharacteristic
223C2×C11#155911yescharacteristic
224C2×C11#187311yescharacteristic
225C2×C11#189511yescharacteristic
226C2×C11#190111yescharacteristic
227C24C11×C22⋊C411yescharacteristic
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—41no—
245C22×C4C11×C22⋊C411yescharacteristic
246C22×C4C11×C22⋊C411yescharacteristic
247C22×C4C11×C22⋊C411yescharacteristic
248C22×C4C22×C4×C1111yescharacteristic
249C22×C4C2×D4×C1111yescharacteristic
250C22×C4C2×D4×C1111yescharacteristic
251C2×C8—24no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C4⋊C4—24no—
258C4⋊C4—42no—
259C4⋊C4—44no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C22⋊C4—44no—
265C42—22no—
266C42—21no—
267C42—22no—
268C42—21no—
269C42C2×D4×C1112yes—
270C42C11×#4112yes—
271C11#913811yescharacteristic, direct product factor, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C11×#10112yes—
279C23C2×C11×C22⋊C411yescharacteristic
280Q8—82no—
281Q8—82no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4C4×D4×C1112yes—
305C2×C4C11×#12011yescharacteristic
306C2×C4C11×#12112yes—
307C2×C4C11×#12311yescharacteristic
308C2×C4C11×#13512yes—
309C2×C4C11×AGL(1,ℤ/8)12yes—
310C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
311C2×C4C11×#13712yes—
312C2×C4C11×#13711yescharacteristic
313C8—44no—
314C8—82no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22C11×#38611yescharacteristic
323C22C2×C11×#10111yescharacteristic
324C22C11×#41311yescharacteristic
325C22C11×#41611yescharacteristic
326C22C11×#41711yescharacteristic
327C22C11×#41811yescharacteristic
328C22C11×#41911yescharacteristic
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4—82no—
335C4C11×#45212yes—
336C4C11×#46812yes—
337C4C11×#46912yes—
338C4C11×#48512yes—
339C2—42no—
340C2C11×#155211yescharacteristic
341C2C11×#155311yescharacteristic
342C2C11×#155611yescharacteristic
343C2C11×#155911yescharacteristic
344C2C11×#187311yescharacteristic
345C2C11×#189511yescharacteristic
346C2C11×#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
54. #9138C11direct (N × H)
102. C2×#332C2×C11semidirect
103. #1296C2×C11semidirect
271. C11#9138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4322
C11×#28572
C11×#17972
C2×C11×#3322
C11×#12962
#913811