Finite Group Databasebeta

← C11×#11224 #14588417

Subgroups — C11×#11224 #14588417

Order 2816.

706 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×#2317C211yesmaximal, characteristic
2C11×#2316C211yesmaximal, characteristic
3C2×C11×#343C211yesmaximal, characteristic
4C11×#1733C212yesmaximal
5C2×C11×H(3,ℤ/4)C212yesmaximal
6C22×C11×M16C2212yes—
7C2×C11×#117C2211yescharacteristic
8C2×C11×#117C2211yescharacteristic
9C2×C11×#117C2212yes—
10C22×C11×C4⋊C4C2211yescharacteristic
11C11×#389—22no—
12C11×#389—24no—
13C11×#385—22no—
14C11×#384C412yescomplemented
15C11×#382C412yescomplemented
16C11×#380—22no—
17C11×#343—22no—
18C11×#339—24no—
19C11×H(3,ℤ/4)—24no—
20C23×C4×C11D412yes—
21C23×C4×C11C2311yescharacteristic
22C2×C11×M16—22no—
23C2×C11×M16—22no—
24C2×C11×M16—22no—
25C2×C11×M16—22no—
26C2×C11×M16—22no—
27C2×C11×M16Q814yes—
28C22×C8×C11—22no—
29C11×#117—21no—
30C11×#117—21no—
31C11×#117—22no—
32C11×#117—22no—
33C11×#117—22no—
34C11×#117—22no—
35C11×#117—22no—
36C11×#117—22no—
37C11×#117D412yes—
38C11×#117Q812yes—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4D412yes—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2×C412yes—
54C2×C42×C11D414yes—
55C11×#95—24no—
56C11×#95—24no—
57#11224C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11C2×D411yescharacteristic
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—24no—
65C22×C4×C11—82no—
66C22×C4×C11C22⋊C414yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×Q811yescharacteristic
72C22×C4×C11C2×Q812yes—
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4112yes—
76C22×C4×C11#4112yes—
77C11×M16—24no—
78C11×M16—24no—
79C11×M16—42no—
80C11×M16—42no—
81C2×C8×C11—24no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—84no—
93C11×C4⋊C4—84no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—42no—
100C42×C11—22no—
101C42×C11—24no—
102C42×C11—24no—
103C42×C11—42no—
104C42×C11C4⋊C414yescomplemented
105#2317C2×C1111yescharacteristic
106#2316C2×C1111yescharacteristic
107C2×#343C2×C1111yescharacteristic
108#1733C2×C1112yes—
109C2×H(3,ℤ/4)C2×C1112yes—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11#12011yescharacteristic
114C23×C11#12111yescharacteristic
115C23×C11C22⋊Q811yescharacteristic
116C23×C11#12311yescharacteristic
117C23×C11#12411yescharacteristic
118C23×C11C4⋊Q811yescharacteristic
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11—42no—
122C2×C4×C11—44no—
123C2×C4×C11—42no—
124C2×C4×C11—44no—
125C2×C4×C11—44no—
126C2×C4×C11—42no—
127C2×C4×C11—44no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—44no—
132C2×C4×C11—82no—
133C2×C4×C11C2×C4⋊C411yescharacteristic
134C2×C4×C11#11711yescharacteristic
135C2×C4×C11C4×D412yes—
136C2×C4×C11C4×Q812yes—
137C2×C4×C11#12112yes—
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12112yes—
140C2×C4×C11C22⋊Q812yes—
141C2×C4×C11C22⋊Q812yes—
142C2×C4×C11C22⋊Q812yes—
143C2×C4×C11C22⋊Q811yescharacteristic
144C2×C4×C11#12312yes—
145C2×C4×C11#12512yes—
146C2×C4×C11#12512yes—
147C2×C4×C11#12612yes—
148C2×C4×C11C4⋊Q812yes—
149C8×C11—44no—
150C22×M16C22×C1112yes—
151C2×#117C22×C1111yescharacteristic
152C2×#117C22×C1111yescharacteristic
153C2×#117C22×C1112yes—
154C22×C4⋊C4C22×C1111yescharacteristic
155#389—22no—
156#389—24no—
157#385—22no—
158#384C4×C1112yescomplemented
159#382C4×C1112yescomplemented
160#380—22no—
161#343—22no—
162#339—24no—
163H(3,ℤ/4)—24no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11#38011yescharacteristic
175C22×C11#38611yescharacteristic
176C22×C11#39111yescharacteristic
177C22×C11#39411yescharacteristic
178C22×C11#39511yescharacteristic
179C22×C11#39811yescharacteristic
180C22×C11#40011yescharacteristic
181C4×C11—44no—
182C4×C11—44no—
183C4×C11—84no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11#38712yes—
187C4×C11#38912yes—
188C4×C11#39612yes—
189C4×C11#39812yes—
190C23×C4D4×C1112yes—
191C23×C4C23×C1111yescharacteristic
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16Q8×C1114yes—
198C22×C8—22no—
199#117—21no—
200#117—21no—
201#117—22no—
202#117—22no—
203#117—22no—
204#117—22no—
205#117—22no—
206#117—22no—
207#117D4×C1112yes—
208#117Q8×C1112yes—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4C2×C4×C1111yescharacteristic
216C2×C4⋊C4C2×C4×C1111yescharacteristic
217C2×C4⋊C4C2×C4×C1112yes—
218C2×C4⋊C4D4×C1112yes—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—21no—
222C2×C42—21no—
223C2×C42C2×C4×C1112yes—
224C2×C42D4×C1114yes—
225#95—24no—
226#95—24no—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#144111yescharacteristic
234C2×C11#191111yescharacteristic
235C2×C11#191211yescharacteristic
236C24C2×D4×C1111yescharacteristic
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—24no—
243C22×C4—82no—
244C22×C4C11×C22⋊C414yes—
245C22×C4C22×C4×C1111yescharacteristic
246C22×C4C2×D4×C1111yescharacteristic
247C22×C4C2×D4×C1112yes—
248C22×C4C2×D4×C1111yescharacteristic
249C22×C4C2×Q8×C1111yescharacteristic
250C22×C4C2×Q8×C1112yes—
251C22×C4C11×#4111yescharacteristic
252C22×C4C11×#4111yescharacteristic
253C22×C4C11×#4112yes—
254C22×C4C11×#4112yes—
255M16—24no—
256M16—24no—
257M16—42no—
258M16—42no—
259C2×C8—24no—
260C2×C8—42no—
261C2×C8—42no—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—84no—
271C4⋊C4—84no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—41no—
277C22⋊C4—42no—
278C42—22no—
279C42—24no—
280C42—24no—
281C42—42no—
282C42C11×C4⋊C414yescomplemented
283C11#1122411yescharacteristic, direct product factor, Sylow
284C23—41no—
285C23—41no—
286C23C2×C11×C22⋊C411yescharacteristic
287C23C11×#12011yescharacteristic
288C23C11×#12111yescharacteristic
289C23C11×C22⋊Q811yescharacteristic
290C23C11×#12311yescharacteristic
291C23C11×#12411yescharacteristic
292C23C11×C4⋊Q811yescharacteristic
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—44no—
306C2×C4—82no—
307C2×C4C2×C11×C4⋊C411yescharacteristic
308C2×C4C11×#11711yescharacteristic
309C2×C4C4×D4×C1112yes—
310C2×C4C4×Q8×C1112yes—
311C2×C4C11×#12112yes—
312C2×C4C11×#12111yescharacteristic
313C2×C4C11×#12112yes—
314C2×C4C11×C22⋊Q812yes—
315C2×C4C11×C22⋊Q812yes—
316C2×C4C11×C22⋊Q812yes—
317C2×C4C11×C22⋊Q811yescharacteristic
318C2×C4C11×#12312yes—
319C2×C4C11×#12512yes—
320C2×C4C11×#12512yes—
321C2×C4C11×#12612yes—
322C2×C4C11×C4⋊Q812yes—
323C8—44no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C11×#38011yescharacteristic
335C22C11×#38611yescharacteristic
336C22C11×#39111yescharacteristic
337C22C11×#39411yescharacteristic
338C22C11×#39511yescharacteristic
339C22C11×#39811yescharacteristic
340C22C11×#40011yescharacteristic
341C4—44no—
342C4—44no—
343C4—84no—
344C4—81no—
345C4—81no—
346C4C11×#38712yes—
347C4C11×#38912yes—
348C4C11×#39612yes—
349C4C11×#39812yes—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2—21no—
355C2—21no—
356C2C11×#144111yescharacteristic
357C2C11×#191111yescharacteristic
358C2C11×#191211yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
14. C11×#384C4semidirect
15. C11×#382C4semidirect
57. #11224C11direct (N × H)
104. C42×C11C4⋊C4semidirect
158. #384C4×C11semidirect
159. #382C4×C11semidirect
282. C42C11×C4⋊C4semidirect
283. C11#11224direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23172
C11×#23162
C2×C11×#3432
C11×#17332
C2×C11×H(3,ℤ/4)2
#1122411