Finite Group Databasebeta

← C11×#9908 #14587101

Subgroups — C11×#9908 #14587101

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2857C211yesmaximal, characteristic
2C11×#1797C211yesmaximal, characteristic
3C4×C11×#95C211yesmaximal, characteristic
4C11×#1294C214yesmaximal
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C22×C42×C11—21no—
8C22×C42×C11C2211yescharacteristic
9C2×C11×C4⋊C8—21no—
10C2×C11×C22⋊C8C2212yes—
11C11×#391—21no—
12C11×#389—21no—
13C11×#389C412yescomplemented
14C11×#384C411yescharacteristic, complemented
15C11×#380—21no—
16C11×#380C2212yes—
17C2×C11×#95—21no—
18C2×C11×#95C2212yes—
19C11×#336—21no—
20C22×Q8×C11—21no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×C8×C11—22no—
26C11×C4⋊Q8—42no—
27C11×C22⋊Q8—44no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C22⋊C4—22no—
35C2×C42×C11—24no—
36C2×C42×C11—42no—
37C2×C42×C11—42no—
38C2×C42×C11—42no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C11×C4⋊C8—42no—
44C11×C22⋊C8—24no—
45C11×#95—24no—
46C11×#95—22no—
47C11×#95—22no—
48C11×#95—22no—
49C11×#95Q814yescomplemented
50#9908C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11C2×D411yescharacteristic
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—24no—
58C22×C4×C11—24no—
59C22×C4×C11—24no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11SD1612yes—
76C22×C4×C11Q1612yes—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×Q812yes—
80C22×C4×C11#4112yes—
81C2×C8×C11—42no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—44no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C22⋊C4—44no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11—48no—
96#2857C2×C1111yescharacteristic
97#1797C2×C1111yescharacteristic
98C4×#95C2×C1111yescharacteristic
99#1294C2×C1114yes—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11C2×C22⋊C411yescharacteristic
105C23×C11C22⋊Q812yes—
106C23×C11C2×SD1611yescharacteristic
107C23×C11C2×Q1611yescharacteristic
108C23×C11AGL(1,ℤ/8)12yes—
109Q8×C11—84no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—28no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11#9912yes—
140C2×C4×C11#10312yes—
141C2×C4×C11#10312yes—
142C2×C4×C11#10412yes—
143C2×C4×C11#10412yes—
144C2×C4×C11C4×Q812yes—
145C2×C4×C11#12411yescharacteristic
146C2×C4×C11C4⋊Q811yescharacteristic
147C8×C11—82no—
148C2×C4⋊Q8C4×C1111yescharacteristic, complemented
149C2×C22⋊Q8—21no—
150C22×C42—21no—
151C22×C42C22×C1111yescharacteristic
152C2×C4⋊C8—21no—
153C2×C22⋊C8C22×C1112yes—
154#391—21no—
155#389—21no—
156#389C4×C1112yescomplemented
157#384C4×C1111yescharacteristic, complemented
158#380—21no—
159#380C22×C1112yes—
160C2×#95—21no—
161C2×#95C22×C1112yes—
162#336—21no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11#39111yescharacteristic
172C22×C11C2×#9911yescharacteristic
173C22×C11#41011yescharacteristic
174C22×C11C2×#10311yescharacteristic
175C22×C11#41811yescharacteristic
176C22×C11C2×#10411yescharacteristic
177C22×C11C2×#10411yescharacteristic
178C22×C11#47612yes—
179C22×C11#47712yes—
180C4×C11—22no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—22no—
184C4×C11—22no—
185C4×C11—48no—
186C4×C11—41no—
187C4×C11—82no—
188C4×C11—82no—
189C4×C11#32814yes—
190C22×Q8—21no—
191C23×C4—22no—
192C23×C4D4×C1111yescharacteristic
193C23×C4D4×C1111yescharacteristic
194C23×C4C23×C1111yescharacteristic
195C22×C8—22no—
196C4⋊Q8—42no—
197C22⋊Q8—44no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×C4×C1112yes—
203C2×C4⋊C4C2×C4×C1112yes—
204C2×C22⋊C4—22no—
205C2×C42—24no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42—42no—
209C2×C42C2×C4×C1111yescharacteristic
210C2×C42C2×C4×C1111yescharacteristic
211C2×C42D4×C1111yescharacteristic
212C2×C42D4×C1111yescharacteristic
213C4⋊C8—42no—
214C22⋊C8—24no—
215#95—24no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95Q8×C1114yescomplemented
220C2×C11—22no—
221C2×C11—22no—
222C2×C11C2×#32811yescharacteristic
223C2×C11#150311yescharacteristic
224C2×C11#150511yescharacteristic
225C2×C11#150711yescharacteristic
226C2×C11#198711yescharacteristic
227C2×C11#199411yescharacteristic
228C2×C11#199611yescharacteristic
229C24C2×D4×C1111yescharacteristic
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4C11×C22⋊C411yescharacteristic
250C22×C4C11×C22⋊C411yescharacteristic
251C22×C4C11×C22⋊C411yescharacteristic
252C22×C4C11×C22⋊C411yescharacteristic
253C22×C4C11×SD1612yes—
254C22×C4C11×Q1612yes—
255C22×C4C22×C4×C1111yescharacteristic
256C22×C4C2×D4×C1111yescharacteristic
257C22×C4C2×Q8×C1112yes—
258C22×C4C11×#4112yes—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—44no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C22⋊C4—44no—
269C42—22no—
270C42—22no—
271C42—41no—
272C42—41no—
273C42—48no—
274C11#990811yescharacteristic, direct product factor, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C11×C22⋊C411yescharacteristic
280C23C11×C22⋊Q812yes—
281C23C2×C11×SD1611yescharacteristic
282C23C2×C11×Q1611yescharacteristic
283C23C11×AGL(1,ℤ/8)12yes—
284Q8—84no—
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—24no—
294C2×C4—24no—
295C2×C4—28no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4C11×#9912yes—
315C2×C4C11×#10312yes—
316C2×C4C11×#10312yes—
317C2×C4C11×#10412yes—
318C2×C4C11×#10412yes—
319C2×C4C4×Q8×C1112yes—
320C2×C4C11×#12411yescharacteristic
321C2×C4C11×C4⋊Q811yescharacteristic
322C8—82no—
323C22—22no—
324C22—22no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—22no—
331C22C11×#39111yescharacteristic
332C22C2×C11×#9911yescharacteristic
333C22C11×#41011yescharacteristic
334C22C2×C11×#10311yescharacteristic
335C22C11×#41811yescharacteristic
336C22C2×C11×#10411yescharacteristic
337C22C2×C11×#10411yescharacteristic
338C22C11×#47612yes—
339C22C11×#47712yes—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—22no—
344C4—22no—
345C4—48no—
346C4—41no—
347C4—82no—
348C4—82no—
349C4C11×#32814yes—
350C2—22no—
351C2—22no—
352C2C2×C11×#32811yescharacteristic
353C2C11×#150311yescharacteristic
354C2C11×#150511yescharacteristic
355C2C11×#150711yescharacteristic
356C2C11×#198711yescharacteristic
357C2C11×#199411yescharacteristic
358C2C11×#199611yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
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
5. C2×C11×C4⋊Q8C4semidirect
13. C11×#389C4semidirect
14. C11×#384C4semidirect
49. C11×#95Q8semidirect
50. #9908C11direct (N × H)
148. C2×C4⋊Q8C4×C11semidirect
156. #389C4×C11semidirect
157. #384C4×C11semidirect
219. #95Q8×C11semidirect
274. C11#9908direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28572
C11×#17972
C4×C11×#952
C11×#12942
#990811