Finite Group Databasebeta

← C2×C11×#1671 #14596295

Subgroups — C2×C11×#1671 #14596295

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#498C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C2×C11×#461C211yesmaximal, characteristic
4C2×C8×D4×C11C211yesmaximal, characteristic
5C11×#1671C218yesmaximal, direct product factor
6C2×C11×#334C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×#332C211yesmaximal, characteristic, complemented
9C22×C11×SD16—21no—
10C23×C8×C11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C11×#498—22no—
15C11×#498C2214yescomplemented
16C11×#476—22no—
17C11×#476C2214yes—
18C11×#461—22no—
19C11×#461C2214yes—
20C8×D4×C11—22no—
21C8×D4×C11C2214yes—
22C2×C11×#106—21no—
23C2×C11×#106—21no—
24C2×C11×#106—21no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103—21no—
29C2×C11×#102—21no—
30C2×C11×C22⋊C8—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#334C2214yescomplemented
33C11×#333C2214yescomplemented
34C11×#332C2214yescomplemented
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C2×C11×SD16—24no—
40C2×C11×SD16—44no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C22×C8×C11—21no—
44C22×C8×C11—24no—
45C22×C8×C11—44no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11D411yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8C2312yes—
55C11×C4⋊Q8C2312yes—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D412yes—
59C4×D4×C11C2312yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C11×#106—24no—
68C11×#106—24no—
69C11×#106—24no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×C4⋊C8C2312yes—
76C11×#103—24no—
77C11×#102—24no—
78C11×C22⋊C8—24no—
79C4×C8×C11D412yes—
80C4×C8×C11C2312yes—
81C2×#1671C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×Q8×C11—82no—
90C2×D4×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11SD1614yes—
93C2×D4×C11C2×D412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C11×SD16—48no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—48no—
110C2×C8×C11—42no—
111C2×C8×C11—42no—
112C2×C8×C11—42no—
113C2×C8×C11SD1614yescomplemented
114C2×C8×C11C2×D412yes—
115C2×C8×C11C2×D412yes—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4C2×D412yes—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—22no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132C2×#498C2×C1111yescharacteristic, complemented
133C2×#476C2×C1111yescharacteristic
134C2×#461C2×C1111yescharacteristic
135C2×C8×D4C2×C1111yescharacteristic
136#1671C2×C1118yesdirect product factor
137C2×#334C2×C1111yescharacteristic, complemented
138C2×#333C2×C1111yescharacteristic, complemented
139C2×#332C2×C1111yescharacteristic, complemented
140C23×C11—22no—
141C23×C11—24no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11#12111yescharacteristic
145Q8×C11—42no—
146Q8×C11—42no—
147Q8×C11—82no—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—22no—
151D4×C11—24no—
152D4×C11C2×SD1614yes—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—44no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—82no—
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11C2×SD1612yes—
167C2×C4×C11C2×SD1612yes—
168C2×C4×C11#13512yes—
169C2×C4×C11#13712yes—
170C2×C4×C11C22×D411yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C8×C11—22no—
174C8×C11—42no—
175C8×C11—42no—
176C8×C11—42no—
177C8×C11C2×SD1614yescomplemented
178C22×SD16—21no—
179C23×C8—21no—
180C2×C4⋊Q8C22×C1111yescharacteristic
181C2×C4⋊Q8C22×C1111yescharacteristic
182C2×C4×D4C22×C1111yescharacteristic
183#498—22no—
184#498C22×C1114yescomplemented
185#476—22no—
186#476C22×C1114yes—
187#461—22no—
188#461C22×C1114yes—
189C8×D4—22no—
190C8×D4C22×C1114yes—
191C2×#106—21no—
192C2×#106—21no—
193C2×#106—21no—
194C2×C4⋊C8C22×C1111yescharacteristic
195C2×C4⋊C8C22×C1111yescharacteristic
196C2×C4⋊C8C22×C1111yescharacteristic
197C2×#103—21no—
198C2×#102—21no—
199C2×C22⋊C8—21no—
200C2×C4×C8C22×C1111yescharacteristic
201#334C22×C1114yescomplemented
202#333C22×C1114yescomplemented
203#332C22×C1114yescomplemented
204C22×C11—24no—
205C22×C11—48no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11#46112yes—
209C22×C11#46512yes—
210C22×C11#47112yes—
211C22×C11C2×#12111yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—82no—
216C4×C11—82no—
217C4×C11#46112yes—
218C4×C11#46512yes—
219C4×C11C22×SD1611yescharacteristic
220C4×C11C22×SD1611yescharacteristic
221C4×C11C2×#13511yescharacteristic
222C4×C11C2×#13711yescharacteristic
223C22×Q8—21no—
224C22×Q8—21no—
225C22×D4D4×C1111yescharacteristic
226C23×C4—21no—
227C2×SD16—24no—
228C2×SD16—44no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—24no—
233C22×C8—44no—
234C22×C8D4×C1111yescharacteristic
235C22×C8D4×C1111yescharacteristic
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8C23×C1112yes—
243C4⋊Q8C23×C1112yes—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4D4×C1112yes—
247C4×D4C23×C1112yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C1111yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C23×C1111yescharacteristic
255#106—24no—
256#106—24no—
257#106—24no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8C23×C1112yes—
262C4⋊C8C23×C1112yes—
263C4⋊C8C23×C1112yes—
264#103—24no—
265#102—24no—
266C22⋊C8—24no—
267C4×C8D4×C1112yes—
268C4×C8C23×C1112yes—
269C2×C11—44no—
270C2×C11#167114yesdirect product factor
271C2×C11C2×#46111yescharacteristic
272C2×C11C2×#46511yescharacteristic
273C2×C11C2×#47111yescharacteristic
274C24—21no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—82no—
282C2×D4—21no—
283C2×D4—22no—
284C2×D4C11×SD1614yes—
285C2×D4C2×D4×C1112yes—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295C22×C4C11×#4111yescharacteristic
296SD16—48no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—48no—
305C2×C8C11×SD1614yescomplemented
306C2×C8C2×D4×C1112yes—
307C2×C8C2×D4×C1112yes—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4C2×D4×C1112yes—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C42C2×D4×C1111yescharacteristic
321C42C2×D4×C1111yescharacteristic
322C42C11×#4111yescharacteristic
323C42C24×C1111yescharacteristic
324C11C2×#167111yescharacteristic, direct product factor, Sylow
325C23—22no—
326C23—24no—
327C23—42no—
328C23—42no—
329C23C11×#12111yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—82no—
334Q8—82no—
335D4—22no—
336D4—24no—
337D4C2×C11×SD1614yes—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4C11×#12111yescharacteristic
349C2×C4C11×#12111yescharacteristic
350C2×C4C11×#12111yescharacteristic
351C2×C4C2×C11×SD1612yes—
352C2×C4C2×C11×SD1612yes—
353C2×C4C11×#13512yes—
354C2×C4C11×#13712yes—
355C2×C4C22×D4×C1111yescharacteristic
356C2×C4C22×D4×C1111yescharacteristic
357C2×C4C2×C11×#4111yescharacteristic
358C8—22no—
359C8—42no—
360C8—42no—
361C8—42no—
362C8C2×C11×SD1614yescomplemented
363C22—24no—
364C22—48no—
365C22—42no—
366C22—42no—
367C22C11×#46112yes—
368C22C11×#46512yes—
369C22C11×#47112yes—
370C22C2×C11×#12111yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4C11×#46112yes—
377C4C11×#46512yes—
378C4C22×C11×SD1611yescharacteristic
379C4C22×C11×SD1611yescharacteristic
380C4C2×C11×#13511yescharacteristic
381C4C2×C11×#13711yescharacteristic
382C2—44no—
383C2C11×#167114yesdirect product factor
384C2C2×C11×#46111yescharacteristic
385C2C2×C11×#46511yescharacteristic
386C2C2×C11×#47111yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#498C2semidirect
5. C11×#1671C2direct (N × H)
6. C2×C11×#334C2semidirect
7. C2×C11×#333C2semidirect
8. C2×C11×#332C2semidirect
15. C11×#498C22semidirect
32. C11×#334C22semidirect
33. C11×#333C22semidirect
34. C11×#332C22semidirect
81. C2×#1671C11direct (N × H)
113. C2×C8×C11SD16semidirect
132. C2×#498C2×C11semidirect
136. #1671C2×C11direct (N × H)
137. C2×#334C2×C11semidirect
138. C2×#333C2×C11semidirect
139. C2×#332C2×C11semidirect
177. C8×C11C2×SD16semidirect
184. #498C22×C11semidirect
201. #334C22×C11semidirect
202. #333C22×C11semidirect
203. #332C22×C11semidirect
270. C2×C11#1671direct (N × H)
305. C2×C8C11×SD16semidirect
324. C11C2×#1671direct (N × H)
362. C8C2×C11×SD16semidirect
383. C2C11×#1671direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C2×C11×#4762
C2×C11×#4612
C2×C8×D4×C112
C11×#16712
C2×C11×#3342
C2×C11×#3332
C2×C11×#3322
C2×#167111