Finite Group Databasebeta

← C11×#22278 #14599471

Subgroups — C11×#22278 #14599471

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#497C211yesmaximal, characteristic
2C11×#2327C211yesmaximal, characteristic, complemented
3C11×#2326C211yesmaximal, characteristic
4C11×#1958C211yesmaximal, characteristic
5C11×#1956C211yesmaximal, characteristic, complemented
6C11×#1880C212yesmaximal
7C11×#1878C212yesmaximal, complemented
8C11×#1878C212yesmaximal, complemented
9C11×#1877C212yesmaximal
10C11×#1836C211yesmaximal, characteristic, complemented
11C11×#1746C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C11×#497C418yescomplemented
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#391C2212yes—
27C11×#391C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#388—22no—
30C11×#387—22no—
31C11×#387—22no—
32C11×#385—22no—
33C11×#384C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C11×#376C2211yescharacteristic
36C11×#340C2212yes—
37C11×#340C2212yes—
38C11×#336C2212yes—
39C11×#336C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×Q8×C11C2312yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C2×C11×Q16—42no—
45C2×C11×Q16—42no—
46C2×C11×Q16C2×C418yescomplemented
47C2×C11×SD16—42no—
48C2×C11×SD16—42no—
49C2×C11×SD16C2×C418yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2×C414yescomplemented
54C11×#124—22no—
55C11×#124C2×C414yes—
56C4×Q8×C11—42no—
57C4×Q8×C11—42no—
58C4×Q8×C11—42no—
59C4×D4×C11—42no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11—22no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C11×#103—42no—
76C11×#103—42no—
77C11×#103—42no—
78C11×#102—42no—
79C11×#97C2×C414yescomplemented
80C4×C8×C11—22no—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95D412yes—
86C11×#95D412yes—
87#22278C1111yesmaximal, 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×C11C22×C412yes—
98C2×Q8×C11C22×C414yes—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11C22×C412yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—82no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2411yescharacteristic
115C11×Q16—48no—
116C11×SD16—48no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11C22×C414yes—
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—82no—
131C11×C22⋊C4—28no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—82no—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11—42no—
137C42×C11—44no—
138C42×C11C22×C412yes—
139C42×C11#4112yes—
140C2×#497C2×C1111yescharacteristic
141#2327C2×C1111yescharacteristic, complemented
142#2326C2×C1111yescharacteristic
143#1958C2×C1111yescharacteristic
144#1956C2×C1111yescharacteristic, complemented
145#1880C2×C1112yes—
146#1878C2×C1112yescomplemented
147#1878C2×C1112yescomplemented
148#1877C2×C1112yes—
149#1836C2×C1111yescharacteristic, complemented
150#1746C2×C1111yescharacteristic, complemented
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11C22×D411yescharacteristic
157Q8×C11—24no—
158Q8×C11—24no—
159Q8×C11—24no—
160Q8×C11—42no—
161Q8×C11—42no—
162Q8×C11—42no—
163D4×C11—24no—
164D4×C11—42no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—21no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—84no—
188C2×C4×C11C4×D414yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11H(5,𝔽2)12yes—
192C2×C4×C11H(5,𝔽2)12yes—
193C8×C11—24no—
194C8×C11—42no—
195C22×Q16C22×C1112yes—
196C22×SD16C22×C1112yes—
197C2×C4⋊Q8C22×C1111yescharacteristic
198C2×#124C22×C1111yescharacteristic
199C2×C4×Q8C22×C1111yescharacteristic
200C2×C4×Q8C22×C1112yes—
201C2×C4×D4C22×C1111yescharacteristic
202#497C4×C1118yescomplemented
203C2×#103C22×C1112yes—
204C2×#103C22×C1112yes—
205C2×#103C22×C1112yes—
206C2×#102C22×C1112yes—
207C2×#97C22×C1111yescharacteristic
208C2×C4×C8C22×C1111yescharacteristic
209#391C22×C1111yescharacteristic
210#391C22×C1112yes—
211#390C22×C1111yescharacteristic
212#388—22no—
213#387—22no—
214#387—22no—
215#385—22no—
216#384C22×C1111yescharacteristic
217#382C22×C1111yescharacteristic
218#376C22×C1111yescharacteristic
219#340C22×C1112yes—
220#340C22×C1112yes—
221#336C22×C1112yes—
222#336C22×C1112yes—
223C22×C11—42no—
224C22×C11—44no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—82no—
228C22×C11C2×C4×D411yescharacteristic
229C22×C11#53511yescharacteristic
230C22×C11#53511yescharacteristic
231C22×C11#57712yes—
232C22×C11#57812yes—
233C4×C11—24no—
234C4×C11—42no—
235C4×C11—44no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—42no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11—82no—
242C4×C11#51812yes—
243C4×C11#54012yes—
244C22×Q8C23×C1111yescharacteristic
245C22×Q8C23×C1112yes—
246C22×D4C23×C1111yescharacteristic
247C23×C4—21no—
248C2×Q16—42no—
249C2×Q16—42no—
250C2×Q16C2×C4×C1118yescomplemented
251C2×SD16—42no—
252C2×SD16—42no—
253C2×SD16C2×C4×C1118yes—
254C22×C8C23×C1112yes—
255C22×C8C23×C1112yes—
256C4⋊Q8—22no—
257C4⋊Q8C2×C4×C1114yescomplemented
258#124—22no—
259#124C2×C4×C1114yes—
260C4×Q8—42no—
261C4×Q8—42no—
262C4×Q8—42no—
263C4×D4—42no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4C23×C1111yescharacteristic
269C2×C4⋊C4C23×C1112yes—
270C2×C4⋊C4C23×C1111yescharacteristic
271C2×C22⋊C4—22no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—22no—
274C2×C42—22no—
275C2×C42—21no—
276C2×C42C23×C1111yescharacteristic
277C2×C42C23×C1111yescharacteristic
278C2×C42C23×C1111yescharacteristic
279#103—42no—
280#103—42no—
281#103—42no—
282#102—42no—
283#97C2×C4×C1114yescomplemented
284C4×C8—22no—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—22no—
289#95D4×C1112yes—
290#95D4×C1112yes—
291C2×C11—82no—
292C2×C11#232811yescharacteristic
293C2×C11#294712yes—
294C2×C11#322211yescharacteristic
295C2×C11#322311yescharacteristic
296C2×C11#322512yes—
297C24—21no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8C22×C4×C1112yes—
307C2×Q8C22×C4×C1114yes—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4C22×C4×C1112yes—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—82no—
319C22×C4C2×D4×C1111yescharacteristic
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1112yes—
322C22×C4C2×D4×C1112yes—
323C22×C4C24×C1111yescharacteristic
324Q16—48no—
325SD16—48no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8C22×C4×C1114yes—
332C4⋊C4—28no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—44no—
338C4⋊C4—42no—
339C4⋊C4—82no—
340C22⋊C4—28no—
341C22⋊C4—42no—
342C22⋊C4—82no—
343C42—22no—
344C42—22no—
345C42—42no—
346C42—44no—
347C42C22×C4×C1112yes—
348C42C11×#4112yes—
349C11#2227811yescharacteristic, direct product factor, Sylow
350C23—22no—
351C23—41no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23C22×D4×C1111yescharacteristic
356Q8—24no—
357Q8—24no—
358Q8—24no—
359Q8—42no—
360Q8—42no—
361Q8—42no—
362D4—24no—
363D4—42no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—84no—
387C2×C4C4×D4×C1114yes—
388C2×C4C23×C4×C1111yescharacteristic
389C2×C4C2×C11×#4111yescharacteristic
390C2×C4C11×H(5,𝔽2)12yes—
391C2×C4C11×H(5,𝔽2)12yes—
392C8—24no—
393C8—42no—
394C22—44no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22—82no—
399C22C2×C4×D4×C1111yescharacteristic
400C22C11×#53511yescharacteristic
401C22C11×#53511yescharacteristic
402C22C11×#57712yes—
403C22C11×#57812yes—
404C4—24no—
405C4—41no—
406C4—41no—
407C4—42no—
408C4—42no—
409C4—44no—
410C4—81no—
411C4—81no—
412C4—82no—
413C4C11×#51812yes—
414C4C11×#54012yes—
415C2—82no—
416C2C11×#232811yescharacteristic
417C2C11×#294712yes—
418C2C11×#322211yescharacteristic
419C2C11×#322311yescharacteristic
420C2C11×#322512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2327C2semidirect
5. C11×#1956C2semidirect
7. C11×#1878C2semidirect
8. C11×#1878C2semidirect
10. C11×#1836C2semidirect
11. C11×#1746C2semidirect
19. C11×#497C4semidirect
46. C2×C11×Q16C2×C4semidirect
53. C11×C4⋊Q8C2×C4semidirect
79. C11×#97C2×C4semidirect
87. #22278C11direct (N × H)
141. #2327C2×C11semidirect
144. #1956C2×C11semidirect
146. #1878C2×C11semidirect
147. #1878C2×C11semidirect
149. #1836C2×C11semidirect
150. #1746C2×C11semidirect
202. #497C4×C11semidirect
250. C2×Q16C2×C4×C11semidirect
257. C4⋊Q8C2×C4×C11semidirect
283. #97C2×C4×C11semidirect
349. C11#22278direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4972
C11×#23272
C11×#23262
C11×#19582
C11×#19562
C11×#18802
C11×#18782
C11×#18772
C11×#18362
C11×#17462
#2227811