Finite Group Databasebeta

← C2×C11×#1683 #14596302

Subgroups — C2×C11×#1683 #14596302

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#487C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C2×C11×#474C211yesmaximal, characteristic
4C2×C8×D4×C11C211yesmaximal, characteristic
5C11×#1683C218yesmaximal, direct product factor
6C2×C11×#335C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×#332C211yesmaximal, characteristic, complemented
9C23×C8×C11—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#487—22no—
14C11×#487C2214yescomplemented
15C11×#476—22no—
16C11×#476C2214yes—
17C11×#474—22no—
18C11×#474C2214yes—
19C8×D4×C11—22no—
20C8×D4×C11C2214yes—
21C2×C11×#107—21no—
22C2×C11×#106—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103—21no—
27C2×C11×#103—21no—
28C2×C11×#102—21no—
29C2×C11×#102—21no—
30C2×C11×C22⋊C8—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#335C2214yescomplemented
33C11×#333C2214yescomplemented
34C11×#332C2214yescomplemented
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—24no—
43C22×C8×C11—44no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11D411yescharacteristic
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8C2312yes—
53C11×C4⋊Q8C2312yes—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11D412yes—
57C4×D4×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C11×#107—24no—
66C11×#106—24no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×#103—24no—
74C11×#103—24no—
75C11×#102—24no—
76C11×#102—24no—
77C11×C22⋊C8—24no—
78C4×C8×C11D412yes—
79C4×C8×C11C2312yes—
80C2×#1683C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—82no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11Q1614yes—
92C2×D4×C11C2×D412yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—48no—
109C2×C8×C11—42no—
110C2×C8×C11—42no—
111C2×C8×C11—42no—
112C2×C8×C11C2×D412yes—
113C2×C8×C11C2×D412yes—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4C2×D412yes—
124C11×C22⋊C4—22no—
125C11×C22⋊C4—22no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11C2411yescharacteristic
130C2×#487C2×C1111yescharacteristic, complemented
131C2×#476C2×C1111yescharacteristic
132C2×#474C2×C1111yescharacteristic
133C2×C8×D4C2×C1111yescharacteristic
134#1683C2×C1118yesdirect product factor
135C2×#335C2×C1111yescharacteristic, complemented
136C2×#333C2×C1111yescharacteristic, complemented
137C2×#332C2×C1111yescharacteristic, complemented
138C23×C11—22no—
139C23×C11—24no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11#12111yescharacteristic
143Q8×C11—42no—
144Q8×C11—42no—
145Q8×C11—82no—
146Q8×C11—82no—
147Q8×C11—82no—
148D4×C11—22no—
149D4×C11—24no—
150D4×C11C2×Q1614yes—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—44no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11C2×Q1612yes—
165C2×C4×C11#13512yes—
166C2×C4×C11#13512yes—
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C8×C11—22no—
172C8×C11—22no—
173C8×C11—42no—
174C8×C11—42no—
175C8×C11—42no—
176C23×C8—21no—
177C2×C4⋊Q8C22×C1111yescharacteristic
178C2×C4⋊Q8C22×C1111yescharacteristic
179C2×C4×D4C22×C1111yescharacteristic
180#487—22no—
181#487C22×C1114yescomplemented
182#476—22no—
183#476C22×C1114yes—
184#474—22no—
185#474C22×C1114yes—
186C8×D4—22no—
187C8×D4C22×C1114yes—
188C2×#107—21no—
189C2×#106—21no—
190C2×C4⋊C8C22×C1111yescharacteristic
191C2×C4⋊C8C22×C1111yescharacteristic
192C2×C4⋊C8C22×C1111yescharacteristic
193C2×#103—21no—
194C2×#103—21no—
195C2×#102—21no—
196C2×#102—21no—
197C2×C22⋊C8—21no—
198C2×C4×C8C22×C1111yescharacteristic
199#335C22×C1114yescomplemented
200#333C22×C1114yescomplemented
201#332C22×C1114yescomplemented
202C22×C11—24no—
203C22×C11—48no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11#46312yes—
207C22×C11#46712yes—
208C22×C11#47112yes—
209C22×C11C2×#12111yescharacteristic
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—82no—
214C4×C11—82no—
215C4×C11#46312yes—
216C4×C11#46712yes—
217C4×C11C22×Q1611yescharacteristic
218C4×C11C2×#13511yescharacteristic
219C4×C11C2×#13511yescharacteristic
220C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C22×Q8—21no—
222C22×Q8—21no—
223C22×D4D4×C1111yescharacteristic
224C23×C4—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—24no—
229C22×C8—44no—
230C22×C8D4×C1111yescharacteristic
231C22×C8D4×C1111yescharacteristic
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8C23×C1112yes—
239C4⋊Q8C23×C1112yes—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4D4×C1112yes—
243C4×D4C23×C1112yes—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42C23×C1111yescharacteristic
251#107—24no—
252#106—24no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8C23×C1112yes—
257C4⋊C8C23×C1112yes—
258C4⋊C8C23×C1112yes—
259#103—24no—
260#103—24no—
261#102—24no—
262#102—24no—
263C22⋊C8—24no—
264C4×C8D4×C1112yes—
265C4×C8C23×C1112yes—
266C2×C11—44no—
267C2×C11#168314yesdirect product factor
268C2×C11C2×#46311yescharacteristic
269C2×C11C2×#46711yescharacteristic
270C2×C11C2×#47111yescharacteristic
271C24—21no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—82no—
279C2×D4—21no—
280C2×D4—22no—
281C2×D4C11×Q1614yes—
282C2×D4C2×D4×C1112yes—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C11×#4111yescharacteristic
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—48no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8C2×D4×C1112yes—
303C2×C8C2×D4×C1112yes—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4C2×D4×C1112yes—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C42C2×D4×C1111yescharacteristic
317C42C2×D4×C1111yescharacteristic
318C42C11×#4111yescharacteristic
319C42C24×C1111yescharacteristic
320C11C2×#168311yescharacteristic, direct product factor, Sylow
321C23—22no—
322C23—24no—
323C23—42no—
324C23—42no—
325C23C11×#12111yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—82no—
329Q8—82no—
330Q8—82no—
331D4—22no—
332D4—24no—
333D4C2×C11×Q1614yes—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4C11×#12111yescharacteristic
345C2×C4C11×#12111yescharacteristic
346C2×C4C11×#12111yescharacteristic
347C2×C4C2×C11×Q1612yes—
348C2×C4C11×#13512yes—
349C2×C4C11×#13512yes—
350C2×C4C11×AGL(1,ℤ/8)12yes—
351C2×C4C22×D4×C1111yescharacteristic
352C2×C4C22×D4×C1111yescharacteristic
353C2×C4C2×C11×#4111yescharacteristic
354C8—22no—
355C8—22no—
356C8—42no—
357C8—42no—
358C8—42no—
359C22—24no—
360C22—48no—
361C22—42no—
362C22—42no—
363C22C11×#46312yes—
364C22C11×#46712yes—
365C22C11×#47112yes—
366C22C2×C11×#12111yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—82no—
371C4—82no—
372C4C11×#46312yes—
373C4C11×#46712yes—
374C4C22×C11×Q1611yescharacteristic
375C4C2×C11×#13511yescharacteristic
376C4C2×C11×#13511yescharacteristic
377C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
378C2—44no—
379C2C11×#168314yesdirect product factor
380C2C2×C11×#46311yescharacteristic
381C2C2×C11×#46711yescharacteristic
382C2C2×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×#487C2semidirect
5. C11×#1683C2direct (N × H)
6. C2×C11×#335C2semidirect
7. C2×C11×#333C2semidirect
8. C2×C11×#332C2semidirect
14. C11×#487C22semidirect
32. C11×#335C22semidirect
33. C11×#333C22semidirect
34. C11×#332C22semidirect
80. C2×#1683C11direct (N × H)
130. C2×#487C2×C11semidirect
134. #1683C2×C11direct (N × H)
135. C2×#335C2×C11semidirect
136. C2×#333C2×C11semidirect
137. C2×#332C2×C11semidirect
181. #487C22×C11semidirect
199. #335C22×C11semidirect
200. #333C22×C11semidirect
201. #332C22×C11semidirect
267. C2×C11#1683direct (N × H)
320. C11C2×#1683direct (N × H)
379. C2C11×#1683direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4872
C2×C11×#4762
C2×C11×#4742
C2×C8×D4×C112
C11×#16832
C2×C11×#3352
C2×C11×#3332
C2×C11×#3322
C2×#168311