Finite Group Databasebeta

← C11×#22188 #14599381

Subgroups — C11×#22188 #14599381

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#470C211yesmaximal, characteristic
2C4×C11×C22⋊Q8C212yesmaximal
3C11×#1927C212yesmaximal, complemented
4C11×#1920C212yesmaximal, complemented
5C11×#1894C212yesmaximal
6C11×#1878C212yesmaximal, complemented
7C11×#1863C212yesmaximal, complemented
8C11×#1809C211yesmaximal, characteristic
9C11×#1728C211yesmaximal, characteristic
10C22×C11×Q16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C4×Q8×C11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C11×#470C418yescomplemented
17C2×C11×#107C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C11×#391C2212yes—
24C11×#389C2212yes—
25C11×#387—22no—
26C11×#385—22no—
27C11×#380C2212yes—
28C4×C11×C4⋊C4—22no—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C22⋊C4—22no—
31C11×#340C2212yes—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2212yes—
35C11×#336C2212yes—
36C22×Q8×C11C2312yes—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C2×C11×Q16—41no—
41C2×C11×Q16—41no—
42C2×C11×Q16C2×C414yescomplemented
43C2×C11×M16—22no—
44C2×C11×M16—41no—
45C2×C11×M16—41no—
46C2×C11×M16—41no—
47C2×C11×M16—41no—
48C2×C11×M16C2×C414yes—
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8C2×C418yes—
54C4×Q8×C11—42no—
55C4×Q8×C11—42no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—41no—
67C2×C42×C11—41no—
68C2×C42×C11D412yes—
69C2×C42×C11C2312yes—
70C11×#107—41no—
71C11×#106—41no—
72C11×#106C2×C414yescomplemented
73C11×#103—42no—
74C11×#103—42no—
75C11×#103C2×C418yescomplemented
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81#22188C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11C22×C414yes—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—42no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C11×Q16—44no—
108C11×M16—44no—
109C11×M16—44no—
110C2×C8×C11—22no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11C22×C412yes—
118C2×C8×C11C22×C412yes—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4—44no—
127C11×C4⋊C4C22×C414yes—
128C11×C22⋊C4—28no—
129C11×C22⋊C4—44no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—42no—
133C42×C11—44no—
134C42×C11—44no—
135C2×#470C2×C1111yescharacteristic
136C4×C22⋊Q8C2×C1112yes—
137#1927C2×C1112yescomplemented
138#1920C2×C1112yescomplemented
139#1894C2×C1112yes—
140#1878C2×C1112yescomplemented
141#1863C2×C1112yescomplemented
142#1809C2×C1111yescharacteristic
143#1728C2×C1111yescharacteristic
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11C4×D412yes—
149C23×C11C22×D411yescharacteristic
150Q8×C11—24no—
151Q8×C11—24no—
152Q8×C11—42no—
153Q8×C11—42no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11C4×D412yes—
180C2×C4×C11#13714yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11H(5,𝔽2)11yescharacteristic
184C2×C4×C11H(5,𝔽2)11yescharacteristic
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C2×C4×C112−1+411yescharacteristic
187C8×C11—22no—
188C8×C11—22no—
189C8×C11—42no—
190C22×Q16C22×C1111yescharacteristic
191C22×M16C22×C1111yescharacteristic
192C22×M16C22×C1111yescharacteristic
193C2×C22⋊Q8C22×C1112yes—
194C2×C4×Q8C22×C1112yes—
195C22×C42C22×C1111yescharacteristic
196#470C4×C1118yescomplemented
197C2×#107C22×C1111yescharacteristic
198C2×#106C22×C1111yescharacteristic
199C2×#106C22×C1111yescharacteristic
200C2×#103C22×C1112yes—
201C2×#103C22×C1112yes—
202C2×#103C22×C1112yes—
203#391C22×C1112yes—
204#389C22×C1112yes—
205#387—22no—
206#385—22no—
207#380C22×C1112yes—
208C4×C4⋊C4—22no—
209C4×C4⋊C4C22×C1112yes—
210C4×C22⋊C4—22no—
211#340C22×C1112yes—
212#340C22×C1112yes—
213#340C22×C1112yes—
214#336C22×C1112yes—
215#336C22×C1112yes—
216C22×C11—22no—
217C22×C11—24no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—42no—
221C22×C11C2×C4×D411yescharacteristic
222C22×C11#53411yescharacteristic
223C22×C11#53711yescharacteristic
224C22×C11C2×#13712yes—
225C22×C11#57512yes—
226C4×C11—22no—
227C4×C11—24no—
228C4×C11—44no—
229C4×C11—42no—
230C4×C11—44no—
231C4×C11—82no—
232C4×C11—82no—
233C4×C11#51811yescharacteristic
234C4×C11#52011yescharacteristic
235C4×C11#53811yescharacteristic
236C4×C11#53911yescharacteristic
237C22×Q8C23×C1112yes—
238C23×C4D4×C1111yescharacteristic
239C23×C4D4×C1111yescharacteristic
240C23×C4C23×C1111yescharacteristic
241C2×Q16—41no—
242C2×Q16—41no—
243C2×Q16C2×C4×C1114yescomplemented
244C2×M16—22no—
245C2×M16—41no—
246C2×M16—41no—
247C2×M16—41no—
248C2×M16—41no—
249C2×M16C2×C4×C1114yes—
250C22×C8C23×C1112yes—
251C22×C8C23×C1111yescharacteristic
252C22×C8C23×C1111yescharacteristic
253C22⋊Q8—24no—
254C22⋊Q8C2×C4×C1118yes—
255C4×Q8—42no—
256C4×Q8—42no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4C23×C1112yes—
261C2×C4⋊C4C23×C1112yes—
262C2×C4⋊C4C23×C1112yes—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C42—22no—
266C2×C42—22no—
267C2×C42—41no—
268C2×C42—41no—
269C2×C42D4×C1112yes—
270C2×C42C23×C1112yes—
271#107—41no—
272#106—41no—
273#106C2×C4×C1114yescomplemented
274#103—42no—
275#103—42no—
276#103C2×C4×C1118yescomplemented
277#95—22no—
278#95—22no—
279#95—22no—
280#95—22no—
281#95—22no—
282C2×C11—42no—
283C2×C11#232511yescharacteristic
284C2×C11C4×#13712yes—
285C2×C11#319511yescharacteristic
286C2×C11#319711yescharacteristic
287C2×C11#325212yes—
288C24C2×D4×C1111yescharacteristic
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8C22×C4×C1114yes—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4C22×C4×C1112yes—
308C22×C4C2×D4×C1112yes—
309C22×C4C2×D4×C1111yescharacteristic
310C22×C4C2×D4×C1112yes—
311C22×C4C11×#4112yes—
312C22×C4C24×C1111yescharacteristic
313Q16—44no—
314M16—44no—
315M16—44no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8C22×C4×C1112yes—
324C2×C8C22×C4×C1112yes—
325C4⋊C4—28no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—44no—
332C4⋊C4—44no—
333C4⋊C4C22×C4×C1114yes—
334C22⋊C4—28no—
335C22⋊C4—44no—
336C42—22no—
337C42—22no—
338C42—42no—
339C42—44no—
340C42—44no—
341C11#2218811yescharacteristic, direct product factor, Sylow
342C23—21no—
343C23—21no—
344C23—22no—
345C23—22no—
346C23C4×D4×C1112yes—
347C23C22×D4×C1111yescharacteristic
348Q8—24no—
349Q8—24no—
350Q8—42no—
351Q8—42no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4C4×D4×C1112yes—
378C2×C4C11×#13714yes—
379C2×C4C23×C4×C1111yescharacteristic
380C2×C4C2×C11×#4111yescharacteristic
381C2×C4C11×H(5,𝔽2)11yescharacteristic
382C2×C4C11×H(5,𝔽2)11yescharacteristic
383C2×C4C11×H(5,𝔽2)11yescharacteristic
384C2×C4C11×2−1+411yescharacteristic
385C8—22no—
386C8—22no—
387C8—42no—
388C22—24no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—42no—
393C22C2×C4×D4×C1111yescharacteristic
394C22C11×#53411yescharacteristic
395C22C11×#53711yescharacteristic
396C22C2×C11×#13712yes—
397C22C11×#57512yes—
398C4—24no—
399C4—22no—
400C4—42no—
401C4—44no—
402C4—44no—
403C4—82no—
404C4—82no—
405C4C11×#51811yescharacteristic
406C4C11×#52011yescharacteristic
407C4C11×#53811yescharacteristic
408C4C11×#53911yescharacteristic
409C2—42no—
410C2C11×#232511yescharacteristic
411C2C4×C11×#13712yes—
412C2C11×#319511yescharacteristic
413C2C11×#319711yescharacteristic
414C2C11×#325212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1927C2semidirect
4. C11×#1920C2semidirect
6. C11×#1878C2semidirect
7. C11×#1863C2semidirect
16. C11×#470C4semidirect
42. C2×C11×Q16C2×C4semidirect
72. C11×#106C2×C4semidirect
75. C11×#103C2×C4semidirect
81. #22188C11direct (N × H)
137. #1927C2×C11semidirect
138. #1920C2×C11semidirect
140. #1878C2×C11semidirect
141. #1863C2×C11semidirect
196. #470C4×C11semidirect
243. C2×Q16C2×C4×C11semidirect
273. #106C2×C4×C11semidirect
276. #103C2×C4×C11semidirect
341. C11#22188direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4702
C4×C11×C22⋊Q82
C11×#19272
C11×#19202
C11×#18942
C11×#18782
C11×#18632
C11×#18092
C11×#17282
#2218811