Finite Group Databasebeta

← C11×#24317 #14601510

Subgroups — C11×#24317 #14601510

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3502C211yesmaximal, characteristic, complemented
2C11×#3077C212yesmaximal
3C11×#2326C211yesmaximal, characteristic
4C11×#2060C212yesmaximal, complemented
5C11×#2027C212yesmaximal
6C11×#1995C212yesmaximal, complemented
7C11×#1888C212yesmaximal
8C11×#1857C212yesmaximal, complemented
9C11×#1801C211yesmaximal, characteristic, complemented
10Q82×C11—22no—
11C11×#557—22no—
12C11×#557—24no—
13C11×#544—22no—
14C11×#544C2212yes—
15C11×#533—22no—
16C11×#533C2212yes—
17C2×C11×#124C2211yescharacteristic
18C11×#519C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C11×#478—24no—
22C11×#476—22no—
23C11×#474—22no—
24C11×#428C2214yes—
25C11×#423C2212yes—
26C11×#418C2214yes—
27C2×C11×#101C2212yes—
28C11×#391C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#388—22no—
31C11×#385—22no—
32C11×#384C2211yescharacteristic
33C11×#376C2211yescharacteristic
34C11×#343C2212yes—
35C11×#339C2214yes—
36C11×#339C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11—21no—
40C2×C11×M16C2314yes—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8—22no—
43C11×C4⋊Q8—28no—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8D412yes—
46C11×C4⋊Q8D412yes—
47C11×#125—24no—
48C11×#125—28no—
49C11×#125—24no—
50C11×#125D414yes—
51C11×#124—22no—
52C11×#124Q814yescomplemented
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—22no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117—24no—
67C11×#117C2314yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C42×C11D412yes—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C11×#107—24no—
80C11×#106—24no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—22no—
83C11×#102—24no—
84C11×#102—24no—
85C11×#101—24no—
86C11×#95—21no—
87C11×#95—21no—
88C11×#95—22no—
89#24317C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11—21no—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11C2×Q812yes—
97C2×Q8×C11#4112yes—
98C2×D4×C11—22no—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11C2×Q812yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C11×M16—24no—
113C11×M16—24no—
114C2×C8×C11—24no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—28no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—82no—
127C11×C4⋊C4C2×D414yes—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—82no—
134C42×C11—28no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—24no—
138C42×C11—21no—
139C42×C11—22no—
140C42×C11C2×D412yes—
141C42×C11C2×D412yes—
142C42×C11C2×Q812yes—
143#3502C2×C1111yescharacteristic, complemented
144#3077C2×C1112yes—
145#2326C2×C1111yescharacteristic
146#2060C2×C1112yescomplemented
147#2027C2×C1112yes—
148#1995C2×C1112yescomplemented
149#1888C2×C1112yes—
150#1857C2×C1112yescomplemented
151#1801C2×C1111yescharacteristic, complemented
152C23×C11—22no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11C22×D411yescharacteristic
158Q8×C11—24no—
159Q8×C11—24no—
160Q8×C11—44no—
161Q8×C11—82no—
162Q8×C11—84no—
163D4×C11—24no—
164D4×C11—42no—
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—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—84no—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12012yes—
185C2×C4×C11C22⋊Q814yes—
186C2×C4×C11C22×D412yes—
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C112−1+412yes—
190C8×C11—44no—
191Q82—22no—
192#557—22no—
193#557—24no—
194#544—22no—
195#544C22×C1112yes—
196#533—22no—
197#533C22×C1112yes—
198C2×#124C22×C1111yescharacteristic
199#519C22×C1112yes—
200C2×C4×Q8C22×C1111yescharacteristic
201C2×C4×D4C22×C1111yescharacteristic
202#478—24no—
203#476—22no—
204#474—22no—
205#428C22×C1114yes—
206#423C22×C1112yes—
207#418C22×C1114yes—
208C2×#101C22×C1112yes—
209#391C22×C1111yescharacteristic
210#390C22×C1111yescharacteristic
211#388—22no—
212#385—22no—
213#384C22×C1111yescharacteristic
214#376C22×C1111yescharacteristic
215#343C22×C1112yes—
216#339C22×C1114yes—
217#339C22×C1114yes—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—82no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11C2×#12011yescharacteristic
226C22×C11C2×C22⋊Q811yescharacteristic
227C22×C11#53611yescharacteristic
228C4×C11—24no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—22no—
232C4×C11—42no—
233C4×C11—44no—
234C4×C11—42no—
235C4×C11—44no—
236C4×C11—81no—
237C4×C11—81no—
238C4×C11#54812yes—
239C4×C11D4×Q812yes—
240C22×Q8C23×C1111yescharacteristic
241C22×D4C23×C1111yescharacteristic
242C23×C4—21no—
243C2×M16C23×C1114yes—
244C4⋊Q8—22no—
245C4⋊Q8—22no—
246C4⋊Q8—28no—
247C4⋊Q8—24no—
248C4⋊Q8D4×C1112yes—
249C4⋊Q8D4×C1112yes—
250#125—24no—
251#125—28no—
252#125—24no—
253#125D4×C1114yes—
254#124—22no—
255#124Q8×C1114yescomplemented
256C22⋊Q8—22no—
257C22⋊Q8—24no—
258C22⋊Q8—22no—
259C4×Q8—24no—
260C4×Q8—24no—
261C4×Q8—24no—
262C4×Q8—24no—
263C4×Q8—22no—
264C4×Q8—22no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×D4—22no—
268C4×D4—22no—
269#117—24no—
270#117C23×C1114yes—
271C2×C4⋊C4—22no—
272C2×C4⋊C4D4×C1112yes—
273C2×C4⋊C4C23×C1111yescharacteristic
274C2×C4⋊C4C23×C1111yescharacteristic
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C42D4×C1112yes—
279C2×C42C23×C1111yescharacteristic
280C2×C42C23×C1111yescharacteristic
281C2×C42C23×C1111yescharacteristic
282#107—24no—
283#106—24no—
284C4⋊C8—22no—
285C4⋊C8—22no—
286#102—24no—
287#102—24no—
288#101—24no—
289#95—21no—
290#95—21no—
291#95—22no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11#240911yescharacteristic
296C2×C11#302011yescharacteristic
297C2×C11#302111yescharacteristic
298C24—21no—
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8C2×Q8×C1112yes—
305C2×Q8C11×#4112yes—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—22no—
309C2×D4C2×Q8×C1112yes—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—82no—
315C22×C4C2×D4×C1112yes—
316C22×C4C2×D4×C1112yes—
317C22×C4C2×D4×C1111yescharacteristic
318C22×C4C2×D4×C1111yescharacteristic
319C22×C4C24×C1111yescharacteristic
320M16—24no—
321M16—24no—
322C2×C8—24no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—24no—
326C4⋊C4—28no—
327C4⋊C4—24no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—82no—
335C4⋊C4C2×D4×C1114yes—
336C4⋊C4C2×D4×C1114yes—
337C22⋊C4—24no—
338C22⋊C4—28no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—82no—
342C42—28no—
343C42—22no—
344C42—22no—
345C42—24no—
346C42—21no—
347C42—22no—
348C42C2×D4×C1112yes—
349C42C2×D4×C1112yes—
350C42C2×Q8×C1112yes—
351C11#2431711yescharacteristic, direct product factor, Sylow
352C23—22no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23C22×D4×C1111yescharacteristic
358Q8—24no—
359Q8—24no—
360Q8—44no—
361Q8—82no—
362Q8—84no—
363D4—24no—
364D4—42no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—84no—
382C2×C4C11×#12011yescharacteristic
383C2×C4C11×#12011yescharacteristic
384C2×C4C11×#12012yes—
385C2×C4C11×C22⋊Q814yes—
386C2×C4C22×D4×C1112yes—
387C2×C4C22×Q8×C1111yescharacteristic
388C2×C4C2×C11×#4111yescharacteristic
389C2×C4C11×2−1+412yes—
390C8—44no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—42no—
395C22—82no—
396C22—81no—
397C22—81no—
398C22C2×C11×#12011yescharacteristic
399C22C2×C11×C22⋊Q811yescharacteristic
400C22C11×#53611yescharacteristic
401C4—24no—
402C4—21no—
403C4—21no—
404C4—22no—
405C4—42no—
406C4—44no—
407C4—42no—
408C4—44no—
409C4—81no—
410C4—81no—
411C4C11×#54812yes—
412C4D4×Q8×C1112yes—
413C2—21no—
414C2—21no—
415C2—82no—
416C2C11×#240911yescharacteristic
417C2C11×#302011yescharacteristic
418C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
1. C11×#3502C2semidirect
4. C11×#2060C2semidirect
6. C11×#1995C2semidirect
8. C11×#1857C2semidirect
9. C11×#1801C2semidirect
52. C11×#124Q8semidirect
89. #24317C11direct (N × H)
143. #3502C2×C11semidirect
146. #2060C2×C11semidirect
148. #1995C2×C11semidirect
150. #1857C2×C11semidirect
151. #1801C2×C11semidirect
255. #124Q8×C11semidirect
351. C11#24317direct (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×#30772
C11×#23262
C11×#20602
C11×#20272
C11×#19952
C11×#18882
C11×#18572
C11×#18012
#2431711