Finite Group Databasebeta

← C11×#32967 #14610160

Subgroups — C11×#32967 #14610160

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#519C211yesmaximal, characteristic
2C2×C11×#479C212yesmaximal, complemented
3C11×#2629C211yesmaximal, characteristic
4C11×#1865C212yesmaximal, complemented
5C11×#1863C212yesmaximal, complemented
6C11×#1854C212yesmaximal
7C11×#1803C212yesmaximal, complemented
8C11×#1798C211yesmaximal, characteristic
9C11×#1787C212yesmaximal
10C23×Q8×C11C2211yescharacteristic
11C2×C11×#125C2211yescharacteristic
12C11×#519—28no—
13C2×C4×Q8×C11—22no—
14C2×C4×Q8×C11C2212yes—
15C2×C4×Q8×C11C2212yes—
16C2×C11×#117—22no—
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C11×#479—28no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2212yes—
28C11×#398—22no—
29C11×#396—22no—
30C11×#389C2212yes—
31C11×#384C2211yescharacteristic
32C11×#380C2212yes—
33C11×#340C2212yes—
34C11×#340C2212yes—
35C11×#336C2211yescharacteristic
36C11×#336C2211yescharacteristic
37C22×Q8×C11—24no—
38C22×Q8×C11—24no—
39C22×Q8×C11—21no—
40C22×Q8×C11—22no—
41C22×Q8×C11Q814yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2312yes—
47C11×#125—24no—
48C4×Q8×C11—216no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11D418yes—
53C11×#117—216no—
54C11×#117—24no—
55C11×#117—24no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C11×#107—24no—
74C11×#106—24no—
75C11×C4⋊C8—24no—
76C11×#103—24no—
77C11×#103—24no—
78C11×#103—24no—
79C11×#103—24no—
80C11×C22⋊C8—24no—
81C11×#95—22no—
82C11×#95—22no—
83#32967C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11C2×D411yescharacteristic
85C2×Q8×C11—24no—
86C2×Q8×C11—216no—
87C2×Q8×C11—24no—
88C2×Q8×C11—216no—
89C2×Q8×C11—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11C2×D414yes—
94C2×Q8×C11C2×Q814yes—
95C2×Q8×C11#4114yes—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×Q812yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C11×C4⋊C4—28no—
118C11×C4⋊C4—28no—
119C11×C4⋊C4—24no—
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—82no—
127C11×C4⋊C4—82no—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—82no—
132C42×C11—28no—
133C42×C11—24no—
134C42×C11—28no—
135C42×C11—22no—
136C42×C11C2×D414yes—
137C2×#519C2×C1111yescharacteristic
138C2×#479C2×C1112yescomplemented
139#2629C2×C1111yescharacteristic
140#1865C2×C1112yescomplemented
141#1863C2×C1112yescomplemented
142#1854C2×C1112yes—
143#1803C2×C1112yescomplemented
144#1798C2×C1111yescharacteristic
145#1787C2×C1112yes—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11C22⋊Q812yes—
151C23×C11C22×D411yescharacteristic
152Q8×C11—216no—
153Q8×C11—24no—
154Q8×C11—24no—
155Q8×C11—24no—
156Q8×C11C22⋊Q818yes—
157C2×C4×C11—216no—
158C2×C4×C11—24no—
159C2×C4×C11—21no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
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×C11#12014yes—
180C2×C4×C11C22⋊Q812yes—
181C2×C4×C11C22×D412yes—
182C2×C4×C11C22×Q811yescharacteristic
183C2×C4×C11C2×#4112yes—
184C2×C4×C11C2×#4111yescharacteristic
185C8×C11—42no—
186C8×C11—42no—
187C23×Q8C22×C1111yescharacteristic
188C2×#125C22×C1111yescharacteristic
189#519—28no—
190C2×C4×Q8—22no—
191C2×C4×Q8C22×C1112yes—
192C2×C4×Q8C22×C1112yes—
193C2×#117—22no—
194C2×#117C22×C1111yescharacteristic
195C2×#117C22×C1111yescharacteristic
196#479—28no—
197C2×#107C22×C1112yes—
198C2×#106C22×C1112yes—
199C2×C4⋊C8C22×C1112yes—
200C2×#103C22×C1112yes—
201C2×#103C22×C1112yes—
202C2×#103C22×C1112yes—
203C2×#103C22×C1112yes—
204C2×C22⋊C8C22×C1112yes—
205#398—22no—
206#396—22no—
207#389C22×C1112yes—
208#384C22×C1111yescharacteristic
209#380C22×C1112yes—
210#340C22×C1112yes—
211#340C22×C1112yes—
212#336C22×C1111yescharacteristic
213#336C22×C1111yescharacteristic
214C22×C11—24no—
215C22×C11—22no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—42no—
219C22×C11C2×#12011yescharacteristic
220C22×C11C2×C22⋊Q811yescharacteristic
221C22×C11#52511yescharacteristic
222C22×C11#57712yes—
223C22×C11#57812yes—
224C4×C11—28no—
225C4×C11—22no—
226C4×C11—24no—
227C4×C11—42no—
228C4×C11—44no—
229C4×C11—82no—
230C4×C11—82no—
231C4×C11C2×C22⋊Q812yes—
232C4×C11#52512yes—
233C22×Q8—24no—
234C22×Q8—24no—
235C22×Q8—21no—
236C22×Q8—22no—
237C22×Q8Q8×C1114yes—
238C22×Q8C23×C1112yes—
239C23×C4—21no—
240C23×C4C23×C1111yescharacteristic
241C22×C8C23×C1112yes—
242C22×C8C23×C1112yes—
243#125—24no—
244C4×Q8—216no—
245C4×Q8—24no—
246C4×Q8—24no—
247C4×Q8—24no—
248C4×Q8D4×C1118yes—
249#117—216no—
250#117—24no—
251#117—24no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4D4×C1112yes—
258C2×C4⋊C4C23×C1112yes—
259C2×C4⋊C4C23×C1112yes—
260C2×C4⋊C4C23×C1112yes—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4D4×C1112yes—
264C2×C42—22no—
265C2×C42—22no—
266C2×C42—21no—
267C2×C42C23×C1111yescharacteristic
268C2×C42C23×C1111yescharacteristic
269#107—24no—
270#106—24no—
271C4⋊C8—24no—
272#103—24no—
273#103—24no—
274#103—24no—
275#103—24no—
276C22⋊C8—24no—
277#95—22no—
278#95—22no—
279C2×C11—42no—
280C2×C11#284811yescharacteristic
281C2×C11#301312yes—
282C2×C11#308212yes—
283C2×C11#312611yescharacteristic
284C2×C11#312711yescharacteristic
285C24C2×D4×C1111yescharacteristic
286C2×Q8—24no—
287C2×Q8—216no—
288C2×Q8—24no—
289C2×Q8—216no—
290C2×Q8—24no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8C2×D4×C1114yes—
295C2×Q8C2×Q8×C1114yes—
296C2×Q8C11×#4114yes—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4C2×D4×C1112yes—
307C22×C4C2×D4×C1112yes—
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C2×Q8×C1112yes—
310C22×C4C11×#4112yes—
311C22×C4C24×C1111yescharacteristic
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C4⋊C4—28no—
319C4⋊C4—28no—
320C4⋊C4—24no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—44no—
327C4⋊C4—82no—
328C4⋊C4—82no—
329C4⋊C4C2×D4×C1114yes—
330C22⋊C4—24no—
331C22⋊C4—24no—
332C22⋊C4—82no—
333C42—28no—
334C42—24no—
335C42—28no—
336C42—22no—
337C42C2×D4×C1114yes—
338C11#3296711yescharacteristic, direct product factor, Sylow
339C23—21no—
340C23—21no—
341C23—22no—
342C23—22no—
343C23C11×C22⋊Q812yes—
344C23C22×D4×C1111yescharacteristic
345Q8—216no—
346Q8—24no—
347Q8—24no—
348Q8—24no—
349Q8C11×C22⋊Q818yes—
350C2×C4—216no—
351C2×C4—24no—
352C2×C4—21no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4C11×#12014yes—
373C2×C4C11×C22⋊Q812yes—
374C2×C4C22×D4×C1112yes—
375C2×C4C22×Q8×C1111yescharacteristic
376C2×C4C2×C11×#4112yes—
377C2×C4C2×C11×#4111yescharacteristic
378C8—42no—
379C8—42no—
380C22—24no—
381C22—22no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22C2×C11×#12011yescharacteristic
386C22C2×C11×C22⋊Q811yescharacteristic
387C22C11×#52511yescharacteristic
388C22C11×#57712yes—
389C22C11×#57812yes—
390C4—24no—
391C4—28no—
392C4—22no—
393C4—42no—
394C4—44no—
395C4—82no—
396C4—82no—
397C4C2×C11×C22⋊Q812yes—
398C4C11×#52512yes—
399C2—42no—
400C2C11×#284811yescharacteristic
401C2C11×#301312yes—
402C2C11×#308212yes—
403C2C11×#312611yescharacteristic
404C2C11×#312711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
4. C11×#1865C2semidirect
5. C11×#1863C2semidirect
7. C11×#1803C2semidirect
83. #32967C11direct (N × H)
138. C2×#479C2×C11semidirect
140. #1865C2×C11semidirect
141. #1863C2×C11semidirect
143. #1803C2×C11semidirect
338. C11#32967direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5192
C2×C11×#4792
C11×#26292
C11×#18652
C11×#18632
C11×#18542
C11×#18032
C11×#17982
C11×#17872
#3296711