Finite Group Databasebeta

← C11×#10144 #14587337

Subgroups — C11×#10144 #14587337

Order 2816.

758 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
1C11×#3205C211yesmaximal, characteristic, complemented
2C11×#3151C211yesmaximal, characteristic, complemented
3C2×C11×#493C211yesmaximal, characteristic, complemented
4C11×#1965C211yesmaximal, characteristic, complemented
5C11×#1545C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—22no—
9C22×C11×D8—22no—
10C11×#532C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C11×#127C2211yescharacteristic
13C11×#496—22no—
14C11×#493—21no—
15C11×#493—21no—
16C11×#493—22no—
17C11×#493—22no—
18C11×#492—21no—
19C11×#486—21no—
20C11×#459—22no—
21C11×#447—22no—
22C11×#431C2211yescharacteristic
23C11×#423C2211yescharacteristic
24C2×C11×#100—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#331—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11D412yes—
36C11×AGL(1,ℤ/8)—44no—
37C11×AGL(1,ℤ/8)—44no—
38C2×C11×SD16—24no—
39C2×C11×D8—28no—
40C2×C11×D8—24no—
41C2×C11×D8—24no—
42C2×C11×D8—48no—
43C2×C11×M16—21no—
44C2×C11×M16D412yes—
45C22×C8×C11—21no—
46C11×C4⋊Q8D411yescharacteristic
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127—21no—
54C11×#127D411yescharacteristic
55C11×#127D412yes—
56C11×#124—21no—
57C11×#121—21no—
58C11×#121—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×#102—24no—
66C11×#100—44no—
67C11×C22⋊C8—21no—
68C11×#97—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71C4×C8×C11—21no—
72C4×C8×C11D412yes—
73#10144C1111yesmaximal, characteristic, direct product factor, Sylow
74C24×C11—22no—
75C24×C11—41no—
76C11×#41—42no—
77C11×#41—42no—
78C2×Q8×C11—21no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—44no—
88C2×D4×C11—44no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11—82no—
102C2×D4×C11—82no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C11×SD16—48no—
108C11×D8—416no—
109C11×D8—48no—
110C11×D8—84no—
111C11×M16—22no—
112C11×M16—42no—
113C11×M16D814yescomplemented
114C2×C8×C11—24no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—41no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127#3205C2×C1111yescharacteristic, complemented
128#3151C2×C1111yescharacteristic, complemented
129C2×#493C2×C1111yescharacteristic, complemented
130#1965C2×C1111yescharacteristic, complemented
131#1545C2×C1111yescharacteristic, complemented
132#1492C2×C1111yescharacteristic, complemented
133#1278C2×C1111yescharacteristic, complemented
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—44no—
138C23×C11—82no—
139C23×C11—82no—
140C23×C11—82no—
141C23×C11—82no—
142C23×C11—82no—
143C23×C11#12111yescharacteristic
144Q8×C11—42no—
145D4×C11—44no—
146D4×C11—44no—
147D4×C11—42no—
148D4×C11—44no—
149D4×C11—42no—
150D4×C11—44no—
151D4×C11—42no—
152D4×C11—82no—
153D4×C11—82no—
154D4×C11—82no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—81no—
162D4×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×D812yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C8×C11—24no—
177C8×C11—24no—
178C8×C11—42no—
179C8×C11—81no—
180C2×AGL(1,ℤ/8)—22no—
181C22×D8—22no—
182#532C22×C1111yescharacteristic
183C2×#127C22×C1111yescharacteristic
184C2×#127C22×C1111yescharacteristic
185#496—22no—
186#493—22no—
187#493—21no—
188#493—21no—
189#493—22no—
190#492—21no—
191#486—21no—
192#459—22no—
193#447—22no—
194#431C22×C1111yescharacteristic
195#423C22×C1111yescharacteristic
196C2×#100—22no—
197C4×M16C22×C1111yescharacteristic
198C2×C4×C8C22×C1111yescharacteristic
199#331—22no—
200D4⋊C8—22no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—81no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—164no—
213C22×C11—164no—
214C22×C11#39211yescharacteristic
215C22×C11#45912yes—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—81no—
219C4×C11#44712yes—
220C4×C11#45312yes—
221C4×C11#47212yes—
222C4×C11#49311yescharacteristic
223C4×C11#49611yescharacteristic
224C2×#41—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4D4×C1112yes—
231AGL(1,ℤ/8)—44no—
232AGL(1,ℤ/8)—44no—
233C2×SD16—24no—
234C2×D8—28no—
235C2×D8—24no—
236C2×D8—24no—
237C2×D8—48no—
238C2×M16—21no—
239C2×M16D4×C1112yes—
240C22×C8—21no—
241C4⋊Q8D4×C1111yescharacteristic
242#127—21no—
243#127—21no—
244#127—21no—
245#127—21no—
246#127—21no—
247#127—21no—
248#127—21no—
249#127D4×C1112yes—
250#127D4×C1111yescharacteristic
251#124—21no—
252#121—21no—
253#121—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C42C23×C1111yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C1112yes—
260#102—24no—
261#100—44no—
262C22⋊C8—21no—
263#97—21no—
264C4×C8—21no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8D4×C1112yes—
268C2×C11—22no—
269C2×C11—161no—
270C2×C11—162no—
271C2×C11—162no—
272C2×C11#200211yescharacteristic
273C2×C11#201111yescharacteristic
274C2×C11#201811yescharacteristic
275C24—22no—
276C24—41no—
277#41—42no—
278#41—42no—
279C2×Q8—21no—
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—22no—
288C2×D4—44no—
289C2×D4—44no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—82no—
303C2×D4—82no—
304C22×C4—41no—
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×D4×C1111yescharacteristic
307C22×C4C11×#4111yescharacteristic
308SD16—48no—
309D8—416no—
310D8—48no—
311D8—84no—
312M16—22no—
313M16—42no—
314M16C11×D814yescomplemented
315C2×C8—24no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—41no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C42C2×D4×C1111yescharacteristic
325C42C2×D4×C1111yescharacteristic
326C42C2×D4×C1111yescharacteristic
327C42C2×D4×C1111yescharacteristic
328C11#1014411yescharacteristic, direct product factor, Sylow
329C23—41no—
330C23—42no—
331C23—42no—
332C23—44no—
333C23—82no—
334C23—82no—
335C23—82no—
336C23—82no—
337C23—82no—
338C23C11×#12111yescharacteristic
339Q8—42no—
340D4—44no—
341D4—44no—
342D4—42no—
343D4—44no—
344D4—42no—
345D4—44no—
346D4—42no—
347D4—82no—
348D4—82no—
349D4—82no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—82no—
355D4—82no—
356D4—82no—
357D4—82no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4C11×#12011yescharacteristic
364C2×C4C11×#12011yescharacteristic
365C2×C4C11×#12011yescharacteristic
366C2×C4C11×#12111yescharacteristic
367C2×C4C11×#12111yescharacteristic
368C2×C4C11×#12711yescharacteristic
369C2×C4C2×C11×D812yes—
370C2×C4C11×AGL(1,ℤ/8)12yes—
371C8—24no—
372C8—24no—
373C8—42no—
374C8—81no—
375C22—21no—
376C22—21no—
377C22—82no—
378C22—82no—
379C22—81no—
380C22—81no—
381C22—82no—
382C22—82no—
383C22—81no—
384C22—82no—
385C22—82no—
386C22—164no—
387C22—164no—
388C22C11×#39211yescharacteristic
389C22C11×#45912yes—
390C4—21no—
391C4—21no—
392C4—81no—
393C4C11×#44712yes—
394C4C11×#45312yes—
395C4C11×#47212yes—
396C4C11×#49311yescharacteristic
397C4C11×#49611yescharacteristic
398C2—22no—
399C2—162no—
400C2—162no—
401C2—161no—
402C2C11×#200211yescharacteristic
403C2C11×#201111yescharacteristic
404C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3205C2semidirect
2. C11×#3151C2semidirect
3. C2×C11×#493C2semidirect
4. C11×#1965C2semidirect
5. C11×#1545C2semidirect
6. C11×#1492C2semidirect
7. C11×#1278C2semidirect
73. #10144C11direct (N × H)
113. C11×M16D8semidirect
127. #3205C2×C11semidirect
128. #3151C2×C11semidirect
129. C2×#493C2×C11semidirect
130. #1965C2×C11semidirect
131. #1545C2×C11semidirect
132. #1492C2×C11semidirect
133. #1278C2×C11semidirect
314. M16C11×D8semidirect
328. C11#10144direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#31512
C2×C11×#4932
C11×#19652
C11×#15452
C11×#14922
C11×#12782
#1014411