Finite Group Databasebeta

← C2×C11×#1886 #14598143

Subgroups — C2×C11×#1886 #14598143

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊Q8C211yesmaximal, characteristic
2C2×C11×#519C211yesmaximal, characteristic
3C2×C11×#419C212yesmaximal
4C22×C11×#101C211yesmaximal, characteristic
5C11×#1886C218yesmaximal, direct product factor
6C2×C11×#339C212yesmaximal
7C23×Q8×C11C2211yescharacteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×M16C2212yes—
10C2×C11×C4⋊Q8—24no—
11C2×C11×C4⋊Q8—22no—
12C2×C11×C4⋊Q8C418yescomplemented
13C2×C11×C4⋊Q8C2214yes—
14C11×#519—22no—
15C11×#519—24no—
16C11×#519C2214yes—
17C2×C4×Q8×C11—24no—
18C2×C11×#117—22no—
19C2×C11×#117C2212yes—
20C22×C11×C4⋊C4—22no—
21C22×C42×C11C2211yescharacteristic
22C11×#419—24no—
23C11×#419C2218yes—
24C2×C11×#103—24no—
25C2×C11×#101—24no—
26C2×C11×#101C2214yes—
27C11×#339C2218yes—
28C22×Q8×C11—22no—
29C22×Q8×C11—22no—
30C22×Q8×C11—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—24no—
33C22×Q8×C11—22no—
34C22×Q8×C11—22no—
35C22×Q8×C11—24no—
36C22×Q8×C11C2×C414yes—
37C22×Q8×C11C2×C414yes—
38C22×Q8×C11D414yes—
39C22×Q8×C11D412yes—
40C22×Q8×C11C2312yes—
41C22×Q8×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—22no—
47C2×C11×M16—24no—
48C2×C11×M16—24no—
49C2×C11×M16C2314yes—
50C22×C8×C11—22no—
51C11×C4⋊Q8—216no—
52C11×C4⋊Q8—28no—
53C11×C4⋊Q8C2×C4116yescomplemented
54C4×Q8×C11—216no—
55C4×Q8×C11—216no—
56C11×#117—28no—
57C11×#117—28no—
58C11×#117—22no—
59C11×#117—22no—
60C11×#117D414yes—
61C11×#117C2314yes—
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—216no—
64C2×C11×C4⋊C4—28no—
65C2×C11×C4⋊C4D414yes—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—24no—
68C2×C42×C11—21no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11C2×C414yes—
72C2×C42×C11C2312yes—
73C11×#103—216no—
74C11×#101—28no—
75C2×#1886C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2×D411yescharacteristic
77C2×Q8×C11—24no—
78C2×Q8×C11—28no—
79C2×Q8×C11—28no—
80C2×Q8×C11—24no—
81C2×Q8×C11—28no—
82C2×Q8×C11—28no—
83C2×Q8×C11—24no—
84C2×Q8×C11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—24no—
87C2×Q8×C11—28no—
88C2×Q8×C11—28no—
89C2×Q8×C11—24no—
90C2×Q8×C11—24no—
91C2×Q8×C11—42no—
92C2×Q8×C11—44no—
93C2×Q8×C11—44no—
94C2×Q8×C11—42no—
95C2×Q8×C11C22⋊C418yes—
96C2×Q8×C11C22×C414yes—
97C2×Q8×C11C22×C414yes—
98C2×Q8×C11C2×D414yes—
99C22×C4×C11—28no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—42no—
111C22×C4×C11C22⋊C418yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D414yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11#4114yes—
119C22×C4×C11C2411yescharacteristic
120C11×M16—24no—
121C11×M16—24no—
122C11×M16—44no—
123C2×C8×C11—24no—
124C2×C8×C11—44no—
125C11×C4⋊C4—216no—
126C11×C4⋊C4—232no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4C2×D418yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C42×C11—216no—
132C42×C11—24no—
133C42×C11—24no—
134C42×C11—22no—
135C42×C11—24no—
136C42×C11C22×C414yes—
137C22×C4⋊Q8C2×C1111yescharacteristic
138C2×#519C2×C1111yescharacteristic
139C2×#419C2×C1112yes—
140C22×#101C2×C1111yescharacteristic
141#1886C2×C1118yesdirect product factor
142C2×#339C2×C1112yes—
143C23×C11—24no—
144C23×C11C2×C22⋊C412yes—
145C23×C11#12011yescharacteristic
146C23×C11#12011yescharacteristic
147C23×C11#12312yes—
148C23×C11C22×D411yescharacteristic
149Q8×C11—28no—
150Q8×C11—28no—
151Q8×C11—216no—
152Q8×C11—28no—
153Q8×C11—44no—
154Q8×C11—48no—
155C2×C4×C11—216no—
156C2×C4×C11—28no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—28no—
161C2×C4×C11—28no—
162C2×C4×C11—24no—
163C2×C4×C11—28no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—44no—
167C2×C4×C11—44no—
168C2×C4×C11—48no—
169C2×C4×C11C2×C22⋊C418yes—
170C2×C4×C11C2×C22⋊C412yes—
171C2×C4×C11C4×D414yes—
172C2×C4×C11C4×D414yes—
173C2×C4×C11#12012yes—
174C2×C4×C11#12114yes—
175C2×C4×C11#12114yes—
176C2×C4×C11#12312yes—
177C2×C4×C11C23×C411yescharacteristic
178C2×C4×C11C22×D412yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4112yes—
181C8×C11—44no—
182C23×Q8C22×C1111yescharacteristic
183C23×Q8C22×C1111yescharacteristic
184C22×M16C22×C1112yes—
185C2×C4⋊Q8—24no—
186C2×C4⋊Q8—22no—
187C2×C4⋊Q8C4×C1118yescomplemented
188C2×C4⋊Q8C22×C1114yes—
189#519—22no—
190#519—24no—
191#519C22×C1114yes—
192C2×C4×Q8—24no—
193C2×#117—22no—
194C2×#117C22×C1112yes—
195C22×C4⋊C4—22no—
196C22×C42C22×C1111yescharacteristic
197#419—24no—
198#419C22×C1118yes—
199C2×#103—24no—
200C2×#101—24no—
201C2×#101C22×C1114yes—
202#339C22×C1118yes—
203C22×C11—24no—
204C22×C11—24no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11#38612yes—
208C22×C11#38612yes—
209C22×C11#45614yes—
210C22×C11C22×C22⋊C411yescharacteristic
211C22×C11C2×#12011yescharacteristic
212C22×C11C2×#12311yescharacteristic
213C4×C11—28no—
214C4×C11—28no—
215C4×C11—48no—
216C4×C11—44no—
217C4×C11#38614yes—
218C4×C11C2×C4×D412yes—
219C4×C11C2×#12112yes—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—21no—
224C22×Q8—24no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8C2×C4×C1114yes—
229C22×Q8C2×C4×C1114yes—
230C22×Q8D4×C1114yes—
231C22×Q8D4×C1112yes—
232C22×Q8C23×C1112yes—
233C22×Q8C23×C1112yes—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4D4×C1112yes—
237C23×C4C23×C1111yescharacteristic
238C2×M16—22no—
239C2×M16—24no—
240C2×M16—24no—
241C2×M16C23×C1114yes—
242C22×C8—22no—
243C4⋊Q8—216no—
244C4⋊Q8—28no—
245C4⋊Q8C2×C4×C11116yescomplemented
246C4×Q8—216no—
247C4×Q8—216no—
248#117—28no—
249#117—28no—
250#117—22no—
251#117—22no—
252#117D4×C1114yes—
253#117C23×C1114yes—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—216no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4D4×C1114yes—
258C2×C22⋊C4—22no—
259C2×C42—24no—
260C2×C42—22no—
261C2×C42—21no—
262C2×C42—22no—
263C2×C42C2×C4×C1114yes—
264C2×C42C23×C1112yes—
265#103—216no—
266#101—28no—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—22no—
270C2×C11#188614yesdirect product factor
271C2×C11C2×#38611yescharacteristic
272C2×C11C2×#45612yes—
273C24C2×D4×C1111yescharacteristic
274C2×Q8—24no—
275C2×Q8—28no—
276C2×Q8—28no—
277C2×Q8—24no—
278C2×Q8—28no—
279C2×Q8—28no—
280C2×Q8—24no—
281C2×Q8—24no—
282C2×Q8—22no—
283C2×Q8—24no—
284C2×Q8—28no—
285C2×Q8—28no—
286C2×Q8—24no—
287C2×Q8—24no—
288C2×Q8—42no—
289C2×Q8—44no—
290C2×Q8—44no—
291C2×Q8—42no—
292C2×Q8C11×C22⋊C418yes—
293C2×Q8C22×C4×C1114yes—
294C2×Q8C22×C4×C1114yes—
295C2×Q8C2×D4×C1114yes—
296C22×C4—28no—
297C22×C4—24no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4C11×C22⋊C418yes—
309C22×C4C22×C4×C1112yes—
310C22×C4C2×D4×C1114yes—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1112yes—
313C22×C4C2×D4×C1112yes—
314C22×C4C2×D4×C1112yes—
315C22×C4C11×#4114yes—
316C22×C4C24×C1111yescharacteristic
317M16—24no—
318M16—24no—
319M16—44no—
320C2×C8—24no—
321C2×C8—44no—
322C4⋊C4—216no—
323C4⋊C4—232no—
324C4⋊C4—24no—
325C4⋊C4C2×D4×C1118yes—
326C22⋊C4—24no—
327C22⋊C4—24no—
328C42—216no—
329C42—24no—
330C42—24no—
331C42—22no—
332C42—24no—
333C42C22×C4×C1114yes—
334C11C2×#188611yescharacteristic, direct product factor, Sylow
335C23—24no—
336C23C2×C11×C22⋊C412yes—
337C23C11×#12011yescharacteristic
338C23C11×#12011yescharacteristic
339C23C11×#12312yes—
340C23C22×D4×C1111yescharacteristic
341Q8—28no—
342Q8—28no—
343Q8—216no—
344Q8—28no—
345Q8—44no—
346Q8—48no—
347C2×C4—216no—
348C2×C4—28no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—28no—
352C2×C4—28no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—28no—
356C2×C4—42no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—48no—
361C2×C4C2×C11×C22⋊C418yes—
362C2×C4C2×C11×C22⋊C412yes—
363C2×C4C4×D4×C1114yes—
364C2×C4C4×D4×C1114yes—
365C2×C4C11×#12012yes—
366C2×C4C11×#12114yes—
367C2×C4C11×#12114yes—
368C2×C4C11×#12312yes—
369C2×C4C23×C4×C1111yescharacteristic
370C2×C4C22×D4×C1112yes—
371C2×C4C22×D4×C1111yescharacteristic
372C2×C4C2×C11×#4112yes—
373C8—44no—
374C22—24no—
375C22—24no—
376C22—22no—
377C22—22no—
378C22C11×#38612yes—
379C22C11×#38612yes—
380C22C11×#45614yes—
381C22C22×C11×C22⋊C411yescharacteristic
382C22C2×C11×#12011yescharacteristic
383C22C2×C11×#12311yescharacteristic
384C4—28no—
385C4—28no—
386C4—48no—
387C4—44no—
388C4C11×#38614yes—
389C4C2×C4×D4×C1112yes—
390C4C2×C11×#12112yes—
391C2—21no—
392C2—22no—
393C2—21no—
394C2C11×#188614yesdirect product factor
395C2C2×C11×#38611yescharacteristic
396C2C2×C11×#45612yes—
subgroupG/H
center, socleC23×C11#120
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#1886C2direct (N × H)
12. C2×C11×C4⋊Q8C4semidirect
53. C11×C4⋊Q8C2×C4semidirect
75. C2×#1886C11direct (N × H)
141. #1886C2×C11direct (N × H)
187. C2×C4⋊Q8C4×C11semidirect
245. C4⋊Q8C2×C4×C11semidirect
270. C2×C11#1886direct (N × H)
334. C11C2×#1886direct (N × H)
394. C2C11×#1886direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊Q82
C2×C11×#5192
C2×C11×#4192
C22×C11×#1012
C11×#18862
C2×C11×#3392
C2×#188611