Finite Group Databasebeta

← C11×#23807 #14601000

Subgroups — C11×#23807 #14601000

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#441C212yesmaximal, complemented
2C2×C11×#440C212yesmaximal
3C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
4C4×C11×#124C211yesmaximal, characteristic
5C11×#2097C212yesmaximal, complemented
6C11×#2095C211yesmaximal, characteristic, complemented
7C11×#2094C211yesmaximal, characteristic
8C11×#2016C211yesmaximal, characteristic, complemented
9C11×#2015C212yesmaximal
10C11×#2013C211yesmaximal, characteristic
11C11×#1745C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C4×Q8×C11C2212yes—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#441—28no—
20C11×#440—28no—
21C2×C11×#107C2212yes—
22C2×C11×#106C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#97C2212yes—
28C11×#391C2212yes—
29C11×#391C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#389—22no—
32C11×#388—22no—
33C11×#384C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C4×C11×C4⋊C4—22no—
36C4×C11×C22⋊C4—22no—
37C43×C11C2211yescharacteristic
38C11×#336C2211yescharacteristic
39C11×#336C2212yes—
40C11×#336C2211yescharacteristic
41C22×Q8×C11C2311yescharacteristic
42C22×Q8×C11C2312yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C2×C11×Q16—24no—
46C2×C11×Q16—24no—
47C2×C11×Q16—24no—
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16—24no—
51C22×C8×C11C2312yes—
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—24no—
54C11×#124—22no—
55C11×#124—22no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×D4×C11—24no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11—22no—
72C2×C42×C11D412yes—
73C2×C42×C11D412yes—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C11×#107—24no—
78C11×#106—24no—
79C11×#103—24no—
80C11×#103—24no—
81C11×#103—24no—
82C11×#102—24no—
83C11×#97D418yes—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—24no—
87#23807C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11#4112yes—
98C2×Q8×C11#4114yes—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—44no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2411yescharacteristic
115C11×Q16—216no—
116C11×SD16—216no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D414yes—
122C2×C8×C11C2×D414yes—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—44no—
131C11×C22⋊C4—28no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—44no—
134C42×C11—24no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11—22no—
138C42×C11—42no—
139C42×C11—44no—
140C42×C11—42no—
141C42×C11C2×D414yes—
142C2×#441C2×C1112yescomplemented
143C2×#440C2×C1112yes—
144C4×C4⋊Q8C2×C1111yescharacteristic, complemented
145C4×#124C2×C1111yescharacteristic
146#2097C2×C1112yescomplemented
147#2095C2×C1111yescharacteristic, complemented
148#2094C2×C1111yescharacteristic
149#2016C2×C1111yescharacteristic, complemented
150#2015C2×C1112yes—
151#2013C2×C1111yescharacteristic
152#1745C2×C1111yescharacteristic, complemented
153C23×C11—22no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11C22×D411yescharacteristic
159Q8×C11—24no—
160Q8×C11—24no—
161Q8×C11—24no—
162Q8×C11—42no—
163Q8×C11—42no—
164Q8×C11—42no—
165D4×C11—24no—
166D4×C11—42no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—84no—
187C2×C4×C11#12712yes—
188C2×C4×C11#12712yes—
189C2×C4×C11#13714yes—
190C2×C4×C11C22×D412yes—
191C2×C4×C11C2×#4112yes—
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C8×C11—24no—
195C8×C11—24no—
196C22×Q16C22×C1112yes—
197C22×SD16C22×C1112yes—
198C2×C4⋊Q8C22×C1111yescharacteristic
199C2×#124C22×C1111yescharacteristic
200C2×C4×Q8C22×C1112yes—
201C2×C4×Q8C22×C1111yescharacteristic
202C2×C4×D4C22×C1111yescharacteristic
203#441—28no—
204#440—28no—
205C2×#107C22×C1112yes—
206C2×#106C22×C1112yes—
207C2×#103C22×C1112yes—
208C2×#103C22×C1112yes—
209C2×#103C22×C1112yes—
210C2×#102C22×C1112yes—
211C2×#97C22×C1112yes—
212#391C22×C1112yes—
213#391C22×C1111yescharacteristic
214#390C22×C1111yescharacteristic
215#389—22no—
216#388—22no—
217#384C22×C1111yescharacteristic
218#382C22×C1111yescharacteristic
219C4×C4⋊C4—22no—
220C4×C22⋊C4—22no—
221C43C22×C1111yescharacteristic
222#336C22×C1111yescharacteristic
223#336C22×C1111yescharacteristic
224#336C22×C1112yes—
225C22×C11—44no—
226C22×C11—42no—
227C22×C11—82no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#52511yescharacteristic
231C22×C11#52511yescharacteristic
232C22×C11C2×#12711yescharacteristic
233C22×C11C2×#13712yes—
234C22×C11#57512yes—
235C4×C11—24no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—44no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11#52512yes—
245C4×C11#52512yes—
246C22×Q8C23×C1111yescharacteristic
247C22×Q8C23×C1112yes—
248C22×D4C23×C1111yescharacteristic
249C23×C4—21no—
250C2×Q16—24no—
251C2×Q16—24no—
252C2×Q16—24no—
253C2×SD16—24no—
254C2×SD16—24no—
255C2×SD16—24no—
256C22×C8C23×C1112yes—
257C22×C8C23×C1112yes—
258C4⋊Q8—24no—
259#124—22no—
260#124—22no—
261C4×Q8—24no—
262C4×Q8—24no—
263C4×Q8—24no—
264C4×D4—24no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4C23×C1111yescharacteristic
270C2×C4⋊C4C23×C1111yescharacteristic
271C2×C4⋊C4C23×C1112yes—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—22no—
275C2×C42—21no—
276C2×C42—22no—
277C2×C42D4×C1112yes—
278C2×C42D4×C1112yes—
279C2×C42C23×C1111yescharacteristic
280C2×C42C23×C1111yescharacteristic
281C2×C42C23×C1111yescharacteristic
282#107—24no—
283#106—24no—
284#103—24no—
285#103—24no—
286#103—24no—
287#102—24no—
288#97D4×C1118yes—
289#95—22no—
290#95—22no—
291#95—24no—
292C2×C11—82no—
293C2×C11#239711yescharacteristic
294C2×C11#311612yes—
295C2×C11#311712yes—
296C2×C11#315211yescharacteristic
297C2×C11#315311yescharacteristic
298C24—21no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8C11×#4112yes—
308C2×Q8C11×#4114yes—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—21no—
312C2×D4C11×#4112yes—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—44no—
319C22×C4—42no—
320C22×C4C2×D4×C1112yes—
321C22×C4C2×D4×C1111yescharacteristic
322C22×C4C2×D4×C1111yescharacteristic
323C22×C4C2×D4×C1112yes—
324C22×C4C24×C1111yescharacteristic
325Q16—216no—
326SD16—216no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8C2×D4×C1114yes—
332C2×C8C2×D4×C1114yes—
333C4⋊C4—28no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—44no—
339C4⋊C4—42no—
340C4⋊C4—44no—
341C22⋊C4—28no—
342C22⋊C4—42no—
343C22⋊C4—44no—
344C42—24no—
345C42—21no—
346C42—21no—
347C42—22no—
348C42—42no—
349C42—44no—
350C42—42no—
351C42C2×D4×C1114yes—
352C11#2380711yescharacteristic, direct product factor, Sylow
353C23—22no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23C22×D4×C1111yescharacteristic
359Q8—24no—
360Q8—24no—
361Q8—24no—
362Q8—42no—
363Q8—42no—
364Q8—42no—
365D4—24no—
366D4—42no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—84no—
387C2×C4C11×#12712yes—
388C2×C4C11×#12712yes—
389C2×C4C11×#13714yes—
390C2×C4C22×D4×C1112yes—
391C2×C4C2×C11×#4112yes—
392C2×C4C2×C11×#4111yescharacteristic
393C2×C4C2×C11×#4111yescharacteristic
394C8—24no—
395C8—24no—
396C22—42no—
397C22—44no—
398C22—81no—
399C22—81no—
400C22—82no—
401C22C11×#52511yescharacteristic
402C22C11×#52511yescharacteristic
403C22C2×C11×#12711yescharacteristic
404C22C2×C11×#13712yes—
405C22C11×#57512yes—
406C4—22no—
407C4—22no—
408C4—24no—
409C4—42no—
410C4—44no—
411C4—42no—
412C4—81no—
413C4—81no—
414C4—82no—
415C4C11×#52512yes—
416C4C11×#52512yes—
417C2—82no—
418C2C11×#239711yescharacteristic
419C2C11×#311612yes—
420C2C11×#311712yes—
421C2C11×#315211yescharacteristic
422C2C11×#315311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#441C2semidirect
3. C4×C11×C4⋊Q8C2semidirect
5. C11×#2097C2semidirect
6. C11×#2095C2semidirect
8. C11×#2016C2semidirect
11. C11×#1745C2semidirect
87. #23807C11direct (N × H)
142. C2×#441C2×C11semidirect
144. C4×C4⋊Q8C2×C11semidirect
146. #2097C2×C11semidirect
147. #2095C2×C11semidirect
149. #2016C2×C11semidirect
152. #1745C2×C11semidirect
352. C11#23807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4412
C2×C11×#4402
C4×C11×C4⋊Q82
C4×C11×#1242
C11×#20972
C11×#20952
C11×#20942
C11×#20162
C11×#20152
C11×#20132
C11×#17452
#2380711