Finite Group Databasebeta

← C11×#24315 #14601508

Subgroups — C11×#24315 #14601508

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic
2C11×#3078C212yesmaximal
3C4×C11×C4⋊Q8C211yesmaximal, characteristic
4C11×#2060C212yesmaximal
5C11×#2028C212yesmaximal
6C11×#1994C212yesmaximal
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×#389—22no—
31C11×#384C2211yescharacteristic
32C4×C11×C4⋊C4—22no—
33C43×C11C2211yescharacteristic
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—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11D412yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C11×#107—24no—
81C11×#106—24no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—22no—
84C11×#103—24no—
85C11×#103—24no—
86C11×#101—24no—
87C11×#95—22no—
88C11×#95—22no—
89#24315C1111yesmaximal, 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×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
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—44no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4C2×D414yes—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—24no—
130C42×C11—24no—
131C42×C11—28no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—24no—
135C42×C11—21no—
136C42×C11—22no—
137C42×C11—42no—
138C42×C11—41no—
139C42×C11—41no—
140C42×C11C2×D412yes—
141C42×C11C2×D412yes—
142C42×C11C2×Q812yes—
143#3502C2×C1111yescharacteristic
144#3078C2×C1112yes—
145C4×C4⋊Q8C2×C1111yescharacteristic
146#2060C2×C1112yes—
147#2028C2×C1112yes—
148#1994C2×C1112yes—
149#1886C2×C1112yes—
150#1857C2×C1112yes—
151#1801C2×C1111yescharacteristic
152C23×C11C22×D411yescharacteristic
153Q8×C11—24no—
154Q8×C11—24no—
155Q8×C11—24no—
156Q8×C11—42no—
157Q8×C11—44no—
158Q8×C11—82no—
159Q8×C11—84no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12012yes—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11C22⋊Q814yes—
183C2×C4×C11C22×D412yes—
184C2×C4×C11C22×Q811yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C112−1+412yes—
187C8×C11—44no—
188Q82—22no—
189#557—22no—
190#557—24no—
191#544—22no—
192#544C22×C1112yes—
193#533—22no—
194#533C22×C1112yes—
195C2×C4⋊Q8C22×C1111yescharacteristic
196#519C22×C1112yes—
197C2×C4×Q8C22×C1111yescharacteristic
198C2×C4×Q8C22×C1111yescharacteristic
199#479—24no—
200#477—22no—
201#475—22no—
202#428C22×C1114yes—
203#423C22×C1112yes—
204#419C22×C1114yes—
205C2×#101C22×C1112yes—
206#391C22×C1111yescharacteristic
207#391C22×C1111yescharacteristic
208#389—22no—
209#384C22×C1111yescharacteristic
210C4×C4⋊C4—22no—
211C43C22×C1111yescharacteristic
212#343C22×C1112yes—
213#339C22×C1114yes—
214#339C22×C1114yes—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11C2×#12011yescharacteristic
218C22×C11C2×C22⋊Q811yescharacteristic
219C22×C11#53611yescharacteristic
220C4×C11—24no—
221C4×C11—24no—
222C4×C11—21no—
223C4×C11—22no—
224C4×C11—42no—
225C4×C11—42no—
226C4×C11—44no—
227C4×C11—42no—
228C4×C11—44no—
229C4×C11—81no—
230C4×C11#45612yes—
231C4×C11#54812yes—
232C4×C11D4×Q812yes—
233C22×Q8C23×C1111yescharacteristic
234C22×Q8C23×C1111yescharacteristic
235C2×M16C23×C1114yes—
236C4⋊Q8—22no—
237C4⋊Q8—22no—
238C4⋊Q8—28no—
239C4⋊Q8—22no—
240C4⋊Q8—24no—
241C4⋊Q8D4×C1112yes—
242C4⋊Q8D4×C1112yes—
243C4⋊Q8Q8×C1114yescomplemented
244#125—24no—
245#125—28no—
246#125—24no—
247#125D4×C1114yes—
248C22⋊Q8—22no—
249C22⋊Q8—24no—
250C22⋊Q8—22no—
251C4×Q8—24no—
252C4×Q8—24no—
253C4×Q8—24no—
254C4×Q8—24no—
255C4×Q8—22no—
256C4×Q8—22no—
257C4×Q8—22no—
258C4×Q8—22no—
259C4×Q8—22no—
260C4×Q8—22no—
261#117—24no—
262#117C23×C1114yes—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4D4×C1112yes—
267C2×C4⋊C4C23×C1111yescharacteristic
268C2×C4⋊C4C23×C1111yescharacteristic
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42D4×C1112yes—
273C2×C42C23×C1111yescharacteristic
274C2×C42C23×C1111yescharacteristic
275C2×C42C23×C1111yescharacteristic
276#107—24no—
277#106—24no—
278C4⋊C8—22no—
279C4⋊C8—22no—
280#103—24no—
281#103—24no—
282#101—24no—
283#95—22no—
284#95—22no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11#240911yescharacteristic
288C2×C11C2×#45611yescharacteristic
289C2×C11#301811yescharacteristic
290C2×Q8—24no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8C2×Q8×C1112yes—
299C2×Q8C2×Q8×C1112yes—
300C2×Q8C11×#4112yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1112yes—
307C22×C4C2×D4×C1112yes—
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C24×C1111yescharacteristic
310M16—24no—
311M16—24no—
312C2×C8—24no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—28no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—24no—
322C4⋊C4—28no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—44no—
326C4⋊C4—42no—
327C4⋊C4C2×D4×C1114yes—
328C4⋊C4C2×D4×C1114yes—
329C22⋊C4—24no—
330C42—24no—
331C42—28no—
332C42—22no—
333C42—22no—
334C42—24no—
335C42—21no—
336C42—22no—
337C42—42no—
338C42—41no—
339C42—41no—
340C42C2×D4×C1112yes—
341C42C2×D4×C1112yes—
342C42C2×Q8×C1112yes—
343C11#2431511yescharacteristic, direct product factor, Sylow
344C23C22×D4×C1111yescharacteristic
345Q8—24no—
346Q8—24no—
347Q8—24no—
348Q8—42no—
349Q8—44no—
350Q8—82no—
351Q8—84no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4C11×#12011yescharacteristic
372C2×C4C11×#12012yes—
373C2×C4C11×#12011yescharacteristic
374C2×C4C11×C22⋊Q814yes—
375C2×C4C22×D4×C1112yes—
376C2×C4C22×Q8×C1111yescharacteristic
377C2×C4C2×C11×#4111yescharacteristic
378C2×C4C11×2−1+412yes—
379C8—44no—
380C22—21no—
381C22—21no—
382C22C2×C11×#12011yescharacteristic
383C22C2×C11×C22⋊Q811yescharacteristic
384C22C11×#53611yescharacteristic
385C4—24no—
386C4—24no—
387C4—21no—
388C4—22no—
389C4—42no—
390C4—42no—
391C4—44no—
392C4—42no—
393C4—44no—
394C4—81no—
395C4C11×#45612yes—
396C4C11×#54812yes—
397C4D4×Q8×C1112yes—
398C2—21no—
399C2—21no—
400C2C11×#240911yescharacteristic
401C2C2×C11×#45611yescharacteristic
402C2C11×#301811yescharacteristic
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. #24315C11direct (N × H)
243. C4⋊Q8Q8×C11semidirect
343. C11#24315direct (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
C4×C11×C4⋊Q82
C11×#20602
C11×#20282
C11×#19942
C11×#18862
C11×#18572
C11×#18012
#2431511