Finite Group Databasebeta

← C11×#23660 #14600853

Subgroups — C11×#23660 #14600853

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic
2C22×C11×#107C211yesmaximal, characteristic
3C11×#2317C211yesmaximal, characteristic
4C11×#2316C211yesmaximal, characteristic
5C11×#2085C214yesmaximal, complemented
6C11×#2083C214yesmaximal, complemented
7C11×#1736C211yesmaximal, characteristic
8C11×#1735C211yesmaximal, characteristic
9C11×#1729C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C11×#428—24no—
18C2×C11×#107—24no—
19C2×C11×#107C2214yes—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C11×#389—22no—
23C11×#389—22no—
24C11×#389C2214yes—
25C11×#385—22no—
26C11×#384C2212yes—
27C11×#382C2212yes—
28C11×#380—22no—
29C11×#340C2212yes—
30C11×#340C2212yes—
31C11×#340C2214yes—
32C11×#336C2214yes—
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11C2311yescharacteristic
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16Q814yes—
39C22×C8×C11—22no—
40C22×C8×C11—22no—
41C22×C8×C11Q814yes—
42C22×C8×C11C2312yes—
43C22×C8×C11C2312yes—
44C11×#117—22no—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4D414yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11C2312yes—
70C11×#107—28no—
71C11×#107—24no—
72C11×#106—24no—
73C11×#95—24no—
74C11×#95—24no—
75#23660C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—24no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—42no—
84C22×C4×C11—82no—
85C22×C4×C11—82no—
86C22×C4×C11C2×D414yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×Q812yes—
90C22×C4×C11C2×Q812yes—
91C22×C4×C11#4112yes—
92C22×C4×C11#4112yes—
93C22×C4×C11#4112yes—
94C22×C4×C11C2411yescharacteristic
95C11×M16—28no—
96C2×C8×C11—28no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11C2×Q814yes—
102C2×C8×C11C2×Q814yes—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—24no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—84no—
116C11×C4⋊C4—84no—
117C11×C4⋊C4C2×D414yes—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—42no—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11—42no—
124C42×C11—42no—
125C2×#428C2×C1111yescharacteristic
126C22×#107C2×C1111yescharacteristic
127#2317C2×C1111yescharacteristic
128#2316C2×C1111yescharacteristic
129#2085C2×C1114yescomplemented
130#2083C2×C1114yescomplemented
131#1736C2×C1111yescharacteristic
132#1735C2×C1111yescharacteristic
133#1729C2×C1111yescharacteristic
134C23×C11—22no—
135C23×C11—22no—
136C23×C11#12112yes—
137C23×C11#12312yes—
138C23×C11C4⋊Q812yes—
139C23×C11C22×D411yescharacteristic
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—44no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—84no—
155C2×C4×C11—84no—
156C2×C4×C11#12112yes—
157C2×C4×C11C22⋊Q814yes—
158C2×C4×C11C22⋊Q814yes—
159C2×C4×C11#12312yes—
160C2×C4×C11#12514yes—
161C2×C4×C11#12514yes—
162C2×C4×C11C4⋊Q812yes—
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C22×Q811yescharacteristic
165C2×C4×C11C22×Q811yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C8×C11—24no—
170C8×C11—24no—
171C22×M16C22×C1111yescharacteristic
172C23×C8C22×C1111yescharacteristic
173C2×#117C22×C1111yescharacteristic
174C2×#117C22×C1111yescharacteristic
175C2×#117C22×C1111yescharacteristic
176C22×C4⋊C4C22×C1111yescharacteristic
177C22×C4⋊C4C22×C1111yescharacteristic
178#428—24no—
179C2×#107—24no—
180C2×#107C22×C1112yes—
181C2×#107C22×C1114yes—
182C2×#106C22×C1112yes—
183#389—22no—
184#389—22no—
185#389C22×C1114yes—
186#385—22no—
187#384C22×C1112yes—
188#382C22×C1112yes—
189#380—22no—
190#340C22×C1112yes—
191#340C22×C1114yes—
192#340C22×C1112yes—
193#336C22×C1114yes—
194C22×C11—24no—
195C22×C11—24no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11#39814yes—
199C22×C11C2×#12111yescharacteristic
200C22×C11C2×#12311yescharacteristic
201C22×C11C2×C4⋊Q811yescharacteristic
202C22×C11#57612yes—
203C22×C11#57812yes—
204C4×C11—44no—
205C4×C11—44no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11—82no—
209C4×C11—81no—
210C4×C11#39814yes—
211C4×C11C2×C22⋊Q811yescharacteristic
212C4×C11C2×C22⋊Q811yescharacteristic
213C4×C11C2×#12511yescharacteristic
214C4×C11C2×#12511yescharacteristic
215C23×C4—21no—
216C23×C4—21no—
217C23×C4C23×C1111yescharacteristic
218C2×M16—22no—
219C2×M16—22no—
220C2×M16Q8×C1114yes—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8Q8×C1114yes—
224C22×C8C23×C1112yes—
225C22×C8C23×C1112yes—
226#117—22no—
227#117—22no—
228#117—22no—
229#117—22no—
230#117—22no—
231#117—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4D4×C1112yes—
240C2×C4⋊C4D4×C1114yes—
241C2×C4⋊C4C23×C1112yes—
242C2×C4⋊C4C23×C1112yes—
243C2×C4⋊C4C23×C1111yescharacteristic
244C2×C4⋊C4C23×C1111yescharacteristic
245C2×C4⋊C4C23×C1112yes—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4D4×C1112yes—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42C23×C1112yes—
252#107—28no—
253#107—24no—
254#106—24no—
255#95—24no—
256#95—24no—
257C2×C11—24no—
258C2×C11C2×#39811yescharacteristic
259C2×C11#304111yescharacteristic
260C2×C11#304411yescharacteristic
261C2×C11#309812yes—
262C2×C11#316412yes—
263C24C2×D4×C1111yescharacteristic
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—82no—
272C22×C4—82no—
273C22×C4C2×D4×C1114yes—
274C22×C4C2×D4×C1111yescharacteristic
275C22×C4C2×D4×C1112yes—
276C22×C4C2×Q8×C1112yes—
277C22×C4C2×Q8×C1112yes—
278C22×C4C11×#4112yes—
279C22×C4C11×#4112yes—
280C22×C4C11×#4112yes—
281C22×C4C24×C1111yescharacteristic
282M16—28no—
283C2×C8—28no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8C2×Q8×C1114yes—
289C2×C8C2×Q8×C1114yes—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—42no—
302C4⋊C4—84no—
303C4⋊C4—84no—
304C4⋊C4C2×D4×C1114yes—
305C22⋊C4—24no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C42—22no—
309C42—22no—
310C42—42no—
311C42—42no—
312C11#2366011yescharacteristic, direct product factor, Sylow
313C23—22no—
314C23—22no—
315C23C11×#12112yes—
316C23C11×#12312yes—
317C23C11×C4⋊Q812yes—
318C23C22×D4×C1111yescharacteristic
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—44no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—84no—
334C2×C4—84no—
335C2×C4C11×#12112yes—
336C2×C4C11×C22⋊Q814yes—
337C2×C4C11×C22⋊Q814yes—
338C2×C4C11×#12312yes—
339C2×C4C11×#12514yes—
340C2×C4C11×#12514yes—
341C2×C4C11×C4⋊Q812yes—
342C2×C4C22×D4×C1111yescharacteristic
343C2×C4C22×Q8×C1111yescharacteristic
344C2×C4C22×Q8×C1111yescharacteristic
345C2×C4C2×C11×#4111yescharacteristic
346C2×C4C2×C11×#4111yescharacteristic
347C2×C4C2×C11×#4111yescharacteristic
348C8—24no—
349C8—24no—
350C22—24no—
351C22—22no—
352C22—22no—
353C22—24no—
354C22C11×#39814yes—
355C22C2×C11×#12111yescharacteristic
356C22C2×C11×#12311yescharacteristic
357C22C2×C11×C4⋊Q811yescharacteristic
358C22C11×#57612yes—
359C22C11×#57812yes—
360C4—44no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—82no—
366C4C11×#39814yes—
367C4C2×C11×C22⋊Q811yescharacteristic
368C4C2×C11×C22⋊Q811yescharacteristic
369C4C2×C11×#12511yescharacteristic
370C4C2×C11×#12511yescharacteristic
371C2—24no—
372C2C2×C11×#39811yescharacteristic
373C2C11×#304111yescharacteristic
374C2C11×#304411yescharacteristic
375C2C11×#309812yes—
376C2C11×#316412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2085C2semidirect
6. C11×#2083C2semidirect
75. #23660C11direct (N × H)
129. #2085C2×C11semidirect
130. #2083C2×C11semidirect
312. C11#23660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C22×C11×#1072
C11×#23172
C11×#23162
C11×#20852
C11×#20832
C11×#17362
C11×#17352
C11×#17292
#2366011