Finite Group Databasebeta

← C2×C11×#1894 #14598161

Subgroups — C2×C11×#1894 #14598161

Order 2816.

1966 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
1C23×C11×M16C211yesmaximal, characteristic
2C22×C11×C22⋊Q8C211yesmaximal, characteristic
3C22×C11×#103C212yesmaximal, complemented
4C2×C11×#380C211yesmaximal, characteristic
5C11×#1894C218yesmaximal, direct product factor
6C2×C11×#340C212yesmaximal, complemented
7C23×Q8×C11C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C22×C11×M16—24no—
10C22×C11×M16—28no—
11C22×C11×M16C2214yes—
12C23×C8×C11C2212yes—
13C2×C11×C22⋊Q8—24no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×C22⋊Q8C418yescomplemented
16C2×C11×C22⋊Q8C2214yes—
17C22×C11×C4⋊C4—21no—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4—21no—
21C22×C11×C22⋊C4—21no—
22C2×C11×#103—28no—
23C2×C11×#103C2218yescomplemented
24C11×#380—22no—
25C11×#380C2214yes—
26C2×C11×#95—21no—
27C11×#340C2218yescomplemented
28C25×C11D411yescharacteristic
29C22×Q8×C11—22no—
30C22×Q8×C11—21no—
31C22×Q8×C11—24no—
32C22×Q8×C11—24no—
33C22×Q8×C11C2×C414yes—
34C22×Q8×C11C2312yes—
35C23×C4×C11—24no—
36C23×C4×C11—24no—
37C23×C4×C11—21no—
38C23×C4×C11—21no—
39C23×C4×C11—22no—
40C23×C4×C11C2×C414yes—
41C23×C4×C11D412yes—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—232no—
47C2×C11×M16—28no—
48C2×C11×M16—216no—
49C22×C8×C11—24no—
50C22×C8×C11—24no—
51C22×C8×C11D418yes—
52C22×C8×C11C2314yes—
53C11×C22⋊Q8—216no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8C2×C4116yescomplemented
56C2×C11×C4⋊C4—28no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—28no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—44no—
70C11×#103—216no—
71C11×#95—24no—
72C2×#1894C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—24no—
74C24×C11—22no—
75C24×C11—22no—
76C24×C11—24no—
77C24×C11C22⋊C414yes—
78C24×C11C2×D412yes—
79C24×C11C2×D411yescharacteristic
80C2×Q8×C11—24no—
81C2×Q8×C11—22no—
82C2×Q8×C11—216no—
83C2×Q8×C11—24no—
84C2×Q8×C11—24no—
85C2×Q8×C11—44no—
86C2×Q8×C11—44no—
87C2×Q8×C11—44no—
88C2×Q8×C11C22×C414yes—
89C22×C4×C11—24no—
90C22×C4×C11—216no—
91C22×C4×C11—28no—
92C22×C4×C11—28no—
93C22×C4×C11—28no—
94C22×C4×C11—24no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—44no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—44no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11C22⋊C414yes—
108C22×C4×C11C22⋊C418yes—
109C22×C4×C11C22×C414yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D414yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D414yes—
116C22×C4×C11#4114yes—
117C22×C4×C11C2411yescharacteristic
118C11×M16—232no—
119C2×C8×C11—216no—
120C2×C8×C11—24no—
121C2×C8×C11—24no—
122C2×C8×C11C2×D418yes—
123C11×C4⋊C4—216no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—44no—
129C11×C4⋊C4C22×C414yes—
130C11×C22⋊C4—216no—
131C11×C22⋊C4—48no—
132C23×M16C2×C1111yescharacteristic
133C22×C22⋊Q8C2×C1111yescharacteristic
134C22×#103C2×C1112yescomplemented
135C2×#380C2×C1111yescharacteristic
136#1894C2×C1118yesdirect product factor
137C2×#340C2×C1112yescomplemented
138C23×C11—24no—
139C23×C11—22no—
140C23×C11—24no—
141C23×C11—22no—
142C23×C11—28no—
143C23×C11—28no—
144C23×C11—28no—
145C23×C11—48no—
146C23×C11—48no—
147C23×C11C2×C22⋊C414yes—
148C23×C11C2×C22⋊C412yes—
149C23×C11#12114yes—
150C23×C11AGL(1,ℤ/8)12yes—
151C23×C11#13712yes—
152C23×C11#13714yes—
153C23×C11C22×D411yescharacteristic
154Q8×C11—28no—
155Q8×C11—42no—
156Q8×C11—42no—
157Q8×C11—48no—
158C2×C4×C11—24no—
159C2×C4×C11—28no—
160C2×C4×C11—28no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—216no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—44no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—48no—
170C2×C4×C11—48no—
171C2×C4×C11—44no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—88no—
175C2×C4×C11C2×C22⋊C414yes—
176C2×C4×C11C2×C22⋊C412yes—
177C2×C4×C11C4×D418yes—
178C2×C4×C11#12014yes—
179C2×C4×C11#12114yes—
180C2×C4×C11#12314yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C22×D412yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4112yes—
185C8×C11—28no—
186C23×Q8C22×C1111yescharacteristic
187C24×C4C22×C1111yescharacteristic
188C22×M16—24no—
189C22×M16—28no—
190C22×M16C22×C1114yes—
191C23×C8C22×C1112yes—
192C2×C22⋊Q8—24no—
193C2×C22⋊Q8—22no—
194C2×C22⋊Q8C4×C1118yescomplemented
195C2×C22⋊Q8C22×C1114yes—
196C22×C4⋊C4—21no—
197C22×C4⋊C4C22×C1112yes—
198C22×C4⋊C4C22×C1111yescharacteristic
199C22×C22⋊C4—21no—
200C22×C22⋊C4—21no—
201C2×#103—28no—
202C2×#103C22×C1118yescomplemented
203#380—22no—
204#380C22×C1114yes—
205C2×#95—21no—
206#340C22×C1118yescomplemented
207C22×C11—24no—
208C22×C11—24no—
209C22×C11—24no—
210C22×C11—416no—
211C22×C11—44no—
212C22×C11—44no—
213C22×C11#38614yes—
214C22×C11#41714yes—
215C22×C11#41914yes—
216C22×C11#46818yes—
217C22×C11#47018yes—
218C22×C11C22×C22⋊C411yescharacteristic
219C22×C11C2×#12112yes—
220C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C22×C11C2×#13712yes—
222C22×C11C2×#13711yescharacteristic
223C4×C11—24no—
224C4×C11—44no—
225C4×C11—44no—
226C4×C11—84no—
227C4×C11#38614yes—
228C4×C11C2×C4×D412yes—
229C4×C11C2×#12011yescharacteristic
230C4×C11C2×#12311yescharacteristic
231C25D4×C1111yescharacteristic
232C22×Q8—22no—
233C22×Q8—21no—
234C22×Q8—24no—
235C22×Q8—24no—
236C22×Q8C2×C4×C1114yes—
237C22×Q8C23×C1112yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—22no—
243C23×C4C2×C4×C1114yes—
244C23×C4D4×C1111yescharacteristic
245C23×C4D4×C1112yes—
246C23×C4D4×C1114yes—
247C23×C4C23×C1112yes—
248C23×C4C23×C1111yescharacteristic
249C2×M16—232no—
250C2×M16—28no—
251C2×M16—216no—
252C22×C8—24no—
253C22×C8—24no—
254C22×C8D4×C1118yes—
255C22×C8C23×C1114yes—
256C22⋊Q8—216no—
257C22⋊Q8—28no—
258C22⋊Q8C2×C4×C11116yescomplemented
259C2×C4⋊C4—28no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4C2×C4×C1114yes—
267C2×C4⋊C4C23×C1114yes—
268C2×C4⋊C4C23×C1112yes—
269C2×C22⋊C4—28no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—44no—
273#103—216no—
274#95—24no—
275C2×C11—44no—
276C2×C11#189418yesdirect product factor
277C2×C11C2×#38611yescharacteristic
278C2×C11C2×#41911yescharacteristic
279C2×C11C2×#41711yescharacteristic
280C2×C11C2×#46812yes—
281C2×C11C2×#47012yes—
282C24—24no—
283C24—22no—
284C24—22no—
285C24—24no—
286C24C11×C22⋊C414yes—
287C24C2×D4×C1112yes—
288C24C2×D4×C1111yescharacteristic
289C2×Q8—24no—
290C2×Q8—22no—
291C2×Q8—216no—
292C2×Q8—24no—
293C2×Q8—24no—
294C2×Q8—44no—
295C2×Q8—44no—
296C2×Q8—44no—
297C2×Q8C22×C4×C1114yes—
298C22×C4—24no—
299C22×C4—216no—
300C22×C4—28no—
301C22×C4—28no—
302C22×C4—28no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—24no—
310C22×C4—44no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—44no—
315C22×C4—44no—
316C22×C4C11×C22⋊C414yes—
317C22×C4C11×C22⋊C418yes—
318C22×C4C22×C4×C1114yes—
319C22×C4C22×C4×C1112yes—
320C22×C4C2×D4×C1112yes—
321C22×C4C2×D4×C1114yes—
322C22×C4C2×D4×C1111yescharacteristic
323C22×C4C2×D4×C1112yes—
324C22×C4C2×D4×C1114yes—
325C22×C4C11×#4114yes—
326C22×C4C24×C1111yescharacteristic
327M16—232no—
328C2×C8—216no—
329C2×C8—24no—
330C2×C8—24no—
331C2×C8C2×D4×C1118yes—
332C4⋊C4—216no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—44no—
338C4⋊C4C22×C4×C1114yes—
339C22⋊C4—216no—
340C22⋊C4—48no—
341C11C2×#189411yescharacteristic, direct product factor, Sylow
342C23—24no—
343C23—28no—
344C23—28no—
345C23—28no—
346C23—22no—
347C23—24no—
348C23—22no—
349C23—48no—
350C23—48no—
351C23C2×C11×C22⋊C414yes—
352C23C2×C11×C22⋊C412yes—
353C23C11×#12114yes—
354C23C11×AGL(1,ℤ/8)12yes—
355C23C11×#13712yes—
356C23C11×#13714yes—
357C23C22×D4×C1111yescharacteristic
358Q8—28no—
359Q8—42no—
360Q8—48no—
361Q8—42no—
362C2×C4—24no—
363C2×C4—28no—
364C2×C4—28no—
365C2×C4—24no—
366C2×C4—216no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—44no—
371C2×C4—48no—
372C2×C4—48no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—88no—
379C2×C4C2×C11×C22⋊C414yes—
380C2×C4C2×C11×C22⋊C412yes—
381C2×C4C4×D4×C1118yes—
382C2×C4C11×#12014yes—
383C2×C4C11×#12114yes—
384C2×C4C11×#12314yes—
385C2×C4C23×C4×C1111yescharacteristic
386C2×C4C22×D4×C1112yes—
387C2×C4C22×D4×C1111yescharacteristic
388C2×C4C2×C11×#4112yes—
389C8—28no—
390C22—24no—
391C22—24no—
392C22—24no—
393C22—416no—
394C22—44no—
395C22—44no—
396C22C11×#38614yes—
397C22C11×#41714yes—
398C22C11×#41914yes—
399C22C11×#46818yes—
400C22C11×#47018yes—
401C22C22×C11×C22⋊C411yescharacteristic
402C22C2×C11×#12112yes—
403C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
404C22C2×C11×#13712yes—
405C22C2×C11×#13711yescharacteristic
406C4—24no—
407C4—44no—
408C4—44no—
409C4—84no—
410C4C11×#38614yes—
411C4C2×C4×D4×C1112yes—
412C4C2×C11×#12011yescharacteristic
413C4C2×C11×#12311yescharacteristic
414C2—44no—
415C2C11×#189418yesdirect product factor
416C2C2×C11×#38611yescharacteristic
417C2C2×C11×#41911yescharacteristic
418C2C2×C11×#41711yescharacteristic
419C2C2×C11×#46812yes—
420C2C2×C11×#47012yes—
subgroupG/H
center, socleC24×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C11×#103C2semidirect
5. C11×#1894C2direct (N × H)
6. C2×C11×#340C2semidirect
15. C2×C11×C22⋊Q8C4semidirect
23. C2×C11×#103C22semidirect
27. C11×#340C22semidirect
55. C11×C22⋊Q8C2×C4semidirect
72. C2×#1894C11direct (N × H)
134. C22×#103C2×C11semidirect
136. #1894C2×C11direct (N × H)
137. C2×#340C2×C11semidirect
194. C2×C22⋊Q8C4×C11semidirect
202. C2×#103C22×C11semidirect
206. #340C22×C11semidirect
258. C22⋊Q8C2×C4×C11semidirect
276. C2×C11#1894direct (N × H)
341. C11C2×#1894direct (N × H)
415. C2C11×#1894direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C11×M162
C22×C11×C22⋊Q82
C22×C11×#1032
C2×C11×#3802
C11×#18942
C2×C11×#3402
C2×#189411