Finite Group Databasebeta

← C11×#24319 #14601512

Subgroups — C11×#24319 #14601512

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3078C212yesmaximal
3C11×#2327C211yesmaximal, characteristic
4C11×#2061C212yesmaximal
5C11×#2028C212yesmaximal
6C11×#1995C212yesmaximal
7C11×#1886C212yesmaximal
8C11×#1857C212yesmaximal
9C11×#1801C211yesmaximal, characteristic
10Q82×C11—22no—
11C11×#557—22no—
12C11×#557—24no—
13C11×#544—22no—
14C11×#544C2212yes—
15C11×#533—22no—
16C11×#533C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C11×#519C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C11×#479—24no—
22C11×#477—22no—
23C11×#475—22no—
24C11×#428C2214yes—
25C11×#423C2212yes—
26C11×#419C2214yes—
27C2×C11×#101C2212yes—
28C11×#391C2211yescharacteristic
29C11×#391C2211yescharacteristic
30C11×#387—22no—
31C11×#387—22no—
32C11×#382C2211yescharacteristic
33C11×#376C2211yescharacteristic
34C11×#343C2212yes—
35C11×#339C2214yes—
36C11×#339C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×Q8×C11C2311yescharacteristic
39C2×C11×M16C2314yes—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8—28no—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8D412yes—
46C11×C4⋊Q8D412yes—
47C11×C4⋊Q8Q814yescomplemented
48C11×#125—24no—
49C11×#125—28no—
50C11×#125—24no—
51C11×#125D414yes—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—22no—
55C4×Q8×C11—24no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C11×#117—24no—
66C11×#117C2314yes—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11D412yes—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#107—24no—
78C11×#106—24no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—22no—
81C11×#103—24no—
82C11×#103—24no—
83C11×#101—24no—
84C11×#95—21no—
85C11×#95—21no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89#24319C1111yesmaximal, characteristic, direct product factor, Sylow
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C2×Q812yes—
99C2×Q8×C11C2×Q812yes—
100C2×Q8×C11#4112yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C11×M16—24no—
111C11×M16—24no—
112C2×C8×C11—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—28no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4C2×D414yes—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—24no—
130C42×C11—28no—
131C42×C11—22no—
132C42×C11—22no—
133C42×C11—24no—
134C42×C11—21no—
135C42×C11—22no—
136C42×C11—42no—
137C42×C11C2×D412yes—
138C42×C11C2×D412yes—
139C42×C11C2×Q812yes—
140#3502C2×C1111yescharacteristic
141#3078C2×C1112yes—
142#2327C2×C1111yescharacteristic
143#2061C2×C1112yes—
144#2028C2×C1112yes—
145#1995C2×C1112yes—
146#1886C2×C1112yes—
147#1857C2×C1112yes—
148#1801C2×C1111yescharacteristic
149C23×C11C22×D411yescharacteristic
150Q8×C11—24no—
151Q8×C11—24no—
152Q8×C11—24no—
153Q8×C11—44no—
154Q8×C11—42no—
155Q8×C11—82no—
156Q8×C11—84no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12012yes—
179C2×C4×C11C22⋊Q814yes—
180C2×C4×C11C22×D412yes—
181C2×C4×C11C22×Q811yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C112−1+412yes—
184C8×C11—44no—
185Q82—22no—
186#557—22no—
187#557—24no—
188#544—22no—
189#544C22×C1112yes—
190#533—22no—
191#533C22×C1112yes—
192C2×C4⋊Q8C22×C1111yescharacteristic
193#519C22×C1112yes—
194C2×C4×Q8C22×C1111yescharacteristic
195C2×C4×Q8C22×C1111yescharacteristic
196#479—24no—
197#477—22no—
198#475—22no—
199#428C22×C1114yes—
200#423C22×C1112yes—
201#419C22×C1114yes—
202C2×#101C22×C1112yes—
203#391C22×C1111yescharacteristic
204#391C22×C1111yescharacteristic
205#387—22no—
206#387—22no—
207#382C22×C1111yescharacteristic
208#376C22×C1111yescharacteristic
209#343C22×C1112yes—
210#339C22×C1114yes—
211#339C22×C1114yes—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11C2×#12011yescharacteristic
215C22×C11C2×C22⋊Q811yescharacteristic
216C22×C11#53611yescharacteristic
217C4×C11—24no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—22no—
221C4×C11—42no—
222C4×C11—42no—
223C4×C11—44no—
224C4×C11—42no—
225C4×C11—44no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11#54812yes—
229C4×C11D4×Q812yes—
230C22×Q8C23×C1111yescharacteristic
231C22×Q8C23×C1111yescharacteristic
232C2×M16C23×C1114yes—
233C4⋊Q8—22no—
234C4⋊Q8—22no—
235C4⋊Q8—28no—
236C4⋊Q8—22no—
237C4⋊Q8—24no—
238C4⋊Q8D4×C1112yes—
239C4⋊Q8D4×C1112yes—
240C4⋊Q8Q8×C1114yescomplemented
241#125—24no—
242#125—28no—
243#125—24no—
244#125D4×C1114yes—
245C22⋊Q8—22no—
246C22⋊Q8—24no—
247C22⋊Q8—22no—
248C4×Q8—24no—
249C4×Q8—24no—
250C4×Q8—24no—
251C4×Q8—24no—
252C4×Q8—22no—
253C4×Q8—22no—
254C4×Q8—22no—
255C4×Q8—22no—
256C4×Q8—22no—
257C4×Q8—22no—
258#117—24no—
259#117C23×C1114yes—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4D4×C1112yes—
263C2×C4⋊C4C23×C1111yescharacteristic
264C2×C4⋊C4C23×C1111yescharacteristic
265C2×C42—21no—
266C2×C42D4×C1112yes—
267C2×C42C23×C1111yescharacteristic
268C2×C42C23×C1111yescharacteristic
269C2×C42C23×C1111yescharacteristic
270#107—24no—
271#106—24no—
272C4⋊C8—22no—
273C4⋊C8—22no—
274#103—24no—
275#103—24no—
276#101—24no—
277#95—21no—
278#95—21no—
279#95—22no—
280#95—22no—
281#95—22no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11#240911yescharacteristic
285C2×C11#302011yescharacteristic
286C2×C11#302211yescharacteristic
287C2×Q8—24no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—21no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8C2×Q8×C1112yes—
296C2×Q8C2×Q8×C1112yes—
297C2×Q8C11×#4112yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4C2×D4×C1112yes—
303C22×C4C2×D4×C1112yes—
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C24×C1111yescharacteristic
307M16—24no—
308M16—24no—
309C2×C8—24no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—28no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—24no—
319C4⋊C4—28no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4C2×D4×C1114yes—
325C4⋊C4C2×D4×C1114yes—
326C22⋊C4—24no—
327C42—28no—
328C42—22no—
329C42—22no—
330C42—24no—
331C42—21no—
332C42—22no—
333C42—42no—
334C42C2×D4×C1112yes—
335C42C2×D4×C1112yes—
336C42C2×Q8×C1112yes—
337C11#2431911yescharacteristic, direct product factor, Sylow
338C23C22×D4×C1111yescharacteristic
339Q8—24no—
340Q8—24no—
341Q8—24no—
342Q8—44no—
343Q8—42no—
344Q8—82no—
345Q8—84no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4C11×#12011yescharacteristic
366C2×C4C11×#12011yescharacteristic
367C2×C4C11×#12012yes—
368C2×C4C11×C22⋊Q814yes—
369C2×C4C22×D4×C1112yes—
370C2×C4C22×Q8×C1111yescharacteristic
371C2×C4C2×C11×#4111yescharacteristic
372C2×C4C11×2−1+412yes—
373C8—44no—
374C22—21no—
375C22—21no—
376C22C2×C11×#12011yescharacteristic
377C22C2×C11×C22⋊Q811yescharacteristic
378C22C11×#53611yescharacteristic
379C4—24no—
380C4—21no—
381C4—21no—
382C4—22no—
383C4—42no—
384C4—42no—
385C4—44no—
386C4—42no—
387C4—44no—
388C4—81no—
389C4—81no—
390C4C11×#54812yes—
391C4D4×Q8×C1112yes—
392C2—21no—
393C2—21no—
394C2C11×#240911yescharacteristic
395C2C11×#302011yescharacteristic
396C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×C11C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
47. C11×C4⋊Q8Q8semidirect
89. #24319C11direct (N × H)
240. C4⋊Q8Q8×C11semidirect
337. C11#24319direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35022
C11×#30782
C11×#23272
C11×#20612
C11×#20282
C11×#19952
C11×#18862
C11×#18572
C11×#18012
#2431911