Finite Group Databasebeta

← C11×#10148 #14587341

Subgroups — C11×#10148 #14587341

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic, complemented
2C11×#3151C211yesmaximal, characteristic
3C2×C11×#486C211yesmaximal, characteristic, complemented
4C11×#1997C211yesmaximal, characteristic, complemented
5C11×#1545C211yesmaximal, characteristic, complemented
6C11×#1492C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—22no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C11×#498—21no—
13C11×#496—22no—
14C11×#493—21no—
15C11×#492—21no—
16C11×#486—21no—
17C11×#486—22no—
18C11×#486—22no—
19C11×#481—22no—
20C11×#476—22no—
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C2×C11×#102—22no—
24C4×C11×M16C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#343—22no—
27C11×#331—22no—
28C11×D4⋊C8—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C11×AGL(1,ℤ/8)—44no—
35C11×AGL(1,ℤ/8)—44no—
36C2×C11×SD16—24no—
37C2×C11×D8—24no—
38C2×C11×M16—21no—
39C2×C11×M16D412yes—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D411yescharacteristic
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127D411yescharacteristic
50C11×#127D412yes—
51C11×#124—21no—
52C11×#121—21no—
53C11×#121—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D412yes—
58C2×C42×C11C2311yescharacteristic
59C11×#106—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#102—28no—
64C11×#102—24no—
65C11×C22⋊C8—21no—
66C11×#97—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71#10148C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—41no—
73C11×#41—42no—
74C11×#41—42no—
75C2×Q8×C11—21no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C2×D4×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—21no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—44no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—82no—
93C22×C4×C11—22no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C11×SD16—48no—
99C11×D8—48no—
100C11×M16—22no—
101C11×M16—42no—
102C11×M16SD1614yes—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—42no—
107C2×C8×C11—41no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120#3227C2×C1111yescharacteristic, complemented
121#3151C2×C1111yescharacteristic
122C2×#486C2×C1111yescharacteristic, complemented
123#1997C2×C1111yescharacteristic, complemented
124#1545C2×C1111yescharacteristic, complemented
125#1492C2×C1111yescharacteristic, complemented
126#1278C2×C1111yescharacteristic, complemented
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—82no—
130C23×C11—82no—
131C23×C11—82no—
132C23×C11#12111yescharacteristic
133Q8×C11—42no—
134Q8×C11—82no—
135Q8×C11—82no—
136D4×C11—44no—
137D4×C11—42no—
138D4×C11—44no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—82no—
142D4×C11—82no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—81no—
146D4×C11—81no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—82no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11AGL(1,ℤ/8)12yes—
162C8×C11—24no—
163C8×C11—42no—
164C8×C11—42no—
165C8×C11—81no—
166C2×AGL(1,ℤ/8)—22no—
167#532C22×C1111yescharacteristic
168C2×C4⋊Q8C22×C1111yescharacteristic
169C2×#127C22×C1111yescharacteristic
170#498—21no—
171#496—22no—
172#493—21no—
173#492—21no—
174#486—22no—
175#486—21no—
176#486—22no—
177#481—22no—
178#476—22no—
179#431C22×C1111yescharacteristic
180#423C22×C1111yescharacteristic
181C2×#102—22no—
182C4×M16C22×C1111yescharacteristic
183C2×C4×C8C22×C1111yescharacteristic
184#343—22no—
185#331—22no—
186D4⋊C8—22no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—82no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—82no—
193C22×C11—81no—
194C22×C11—82no—
195C22×C11—164no—
196C22×C11#39211yescharacteristic
197C22×C11#46012yes—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—82no—
202C4×C11#45012yes—
203C4×C11#45412yes—
204C4×C11#47212yes—
205C4×C11#49211yescharacteristic
206C4×C11#49611yescharacteristic
207C2×#41—21no—
208C22×Q8—21no—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212AGL(1,ℤ/8)—44no—
213AGL(1,ℤ/8)—44no—
214C2×SD16—24no—
215C2×D8—24no—
216C2×M16—21no—
217C2×M16D4×C1112yes—
218C22×C8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8D4×C1111yescharacteristic
224#127—21no—
225#127—21no—
226#127—21no—
227#127D4×C1112yes—
228#127D4×C1111yescharacteristic
229#124—21no—
230#121—21no—
231#121—21no—
232C4×D4—21no—
233C4×D4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4D4×C1112yes—
236C2×C42C23×C1111yescharacteristic
237#106—24no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C1112yes—
241#102—28no—
242#102—24no—
243C22⋊C8—21no—
244#97—21no—
245C4×C8—21no—
246C4×C8—21no—
247C4×C8—21no—
248C4×C8D4×C1112yes—
249C2×C11—22no—
250C2×C11—161no—
251C2×C11—162no—
252C2×C11#200311yescharacteristic
253C2×C11#201411yescharacteristic
254C2×C11#201811yescharacteristic
255C24—41no—
256#41—42no—
257#41—42no—
258C2×Q8—21no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—82no—
262C2×D4—21no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—22no—
266C2×D4—21no—
267C2×D4—22no—
268C2×D4—44no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—82no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4C2×D4×C1111yescharacteristic
279C22×C4C2×D4×C1111yescharacteristic
280C22×C4C11×#4111yescharacteristic
281SD16—48no—
282D8—48no—
283M16—22no—
284M16—42no—
285M16C11×SD1614yes—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—42no—
290C2×C8—41no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42C2×D4×C1111yescharacteristic
300C42C2×D4×C1111yescharacteristic
301C42C2×D4×C1111yescharacteristic
302C42C2×D4×C1111yescharacteristic
303C11#1014811yescharacteristic, direct product factor, Sylow
304C23—41no—
305C23—42no—
306C23—82no—
307C23—82no—
308C23—82no—
309C23C11×#12111yescharacteristic
310Q8—42no—
311Q8—82no—
312Q8—82no—
313D4—44no—
314D4—42no—
315D4—44no—
316D4—42no—
317D4—42no—
318D4—82no—
319D4—82no—
320D4—81no—
321D4—81no—
322D4—82no—
323D4—82no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4C11×#12011yescharacteristic
332C2×C4C11×#12011yescharacteristic
333C2×C4C11×#12011yescharacteristic
334C2×C4C11×#12111yescharacteristic
335C2×C4C11×#12111yescharacteristic
336C2×C4C11×#12711yescharacteristic
337C2×C4C2×C11×SD1612yes—
338C2×C4C11×AGL(1,ℤ/8)12yes—
339C8—24no—
340C8—42no—
341C8—42no—
342C8—81no—
343C22—21no—
344C22—21no—
345C22—82no—
346C22—81no—
347C22—81no—
348C22—82no—
349C22—81no—
350C22—82no—
351C22—164no—
352C22C11×#39211yescharacteristic
353C22C11×#46012yes—
354C4—21no—
355C4—21no—
356C4—81no—
357C4—82no—
358C4C11×#45012yes—
359C4C11×#45412yes—
360C4C11×#47212yes—
361C4C11×#49211yescharacteristic
362C4C11×#49611yescharacteristic
363C2—22no—
364C2—162no—
365C2—161no—
366C2C11×#200311yescharacteristic
367C2C11×#201411yescharacteristic
368C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3151C2
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×#3227C2semidirect
3. C2×C11×#486C2semidirect
4. C11×#1997C2semidirect
5. C11×#1545C2semidirect
6. C11×#1492C2semidirect
7. C11×#1278C2semidirect
71. #10148C11direct (N × H)
120. #3227C2×C11semidirect
122. C2×#486C2×C11semidirect
123. #1997C2×C11semidirect
124. #1545C2×C11semidirect
125. #1492C2×C11semidirect
126. #1278C2×C11semidirect
303. C11#10148direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C11×#31512
C2×C11×#4862
C11×#19972
C11×#15452
C11×#14922
C11×#12782
#1014811