Finite Group Databasebeta

← C11×#10153 #14587346

Subgroups — C11×#10153 #14587346

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic
2C11×#3165C211yesmaximal, characteristic, complemented
3C2×C11×#492C211yesmaximal, characteristic
4C11×#1965C211yesmaximal, characteristic
5C11×#1549C211yesmaximal, characteristic, complemented
6C11×#1493C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C22×C11×SD16—22no—
9C11×#533C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C11×#501—22no—
13C11×#500—21no—
14C11×#498—21no—
15C11×#492—21no—
16C11×#492—22no—
17C11×#492—22no—
18C11×#486—21no—
19C11×#460—22no—
20C11×#450—22no—
21C11×#431C2211yescharacteristic
22C11×#428—22no—
23C11×#423C2211yescharacteristic
24C2×C11×#100—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#332—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×C11×SD16—28no—
34C2×C11×SD16—24no—
35C2×C11×SD16—48no—
36C2×C11×M16—21no—
37C2×C11×M16D412yes—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D412yes—
44C11×C4⋊Q8D411yescharacteristic
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#125—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C11×#117—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—24no—
59C11×#106—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#102—24no—
64C11×#100—44no—
65C11×C22⋊C8—21no—
66C11×#97—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71#10153C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—21no—
76C2×Q8×C11—44no—
77C2×Q8×C11—41no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—82no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C11×SD16—416no—
93C11×SD16—84no—
94C11×M16—22no—
95C11×M16—42no—
96C11×M16SD1614yescomplemented
97C2×C8×C11—24no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118#3208C2×C1111yescharacteristic
119#3165C2×C1111yescharacteristic, complemented
120C2×#492C2×C1111yescharacteristic
121#1965C2×C1111yescharacteristic
122#1549C2×C1111yescharacteristic, complemented
123#1493C2×C1111yescharacteristic, complemented
124#1278C2×C1111yescharacteristic, complemented
125C23×C11—42no—
126C23×C11—44no—
127C23×C11—82no—
128C23×C11—82no—
129C23×C11#12111yescharacteristic
130Q8×C11—44no—
131Q8×C11—42no—
132Q8×C11—42no—
133Q8×C11—82no—
134D4×C11—44no—
135D4×C11—44no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—81no—
140D4×C11—81no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11C2×SD1612yes—
154C2×C4×C11#13712yes—
155C8×C11—24no—
156C8×C11—24no—
157C8×C11—42no—
158C8×C11—81no—
159C22×SD16—22no—
160#533C22×C1111yescharacteristic
161C2×C4⋊Q8C22×C1111yescharacteristic
162C2×#127C22×C1111yescharacteristic
163#501—22no—
164#500—21no—
165#498—21no—
166#492—22no—
167#492—21no—
168#492—22no—
169#486—21no—
170#460—22no—
171#450—22no—
172#431C22×C1111yescharacteristic
173#428—22no—
174#423C22×C1111yescharacteristic
175C2×#100—22no—
176C4×M16C22×C1111yescharacteristic
177C2×C4×C8C22×C1111yescharacteristic
178#332—22no—
179Q8⋊C8—22no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—82no—
185C22×C11—164no—
186C22×C11#39211yescharacteristic
187C22×C11#46112yes—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—82no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11#44812yes—
194C4×C11#45312yes—
195C4×C11#47112yes—
196C4×C11#49211yescharacteristic
197C4×C11#49711yescharacteristic
198C22×Q8—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4D4×C1112yes—
202C2×SD16—28no—
203C2×SD16—24no—
204C2×SD16—48no—
205C2×M16—21no—
206C2×M16D4×C1112yes—
207C22×C8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8D4×C1112yes—
212C4⋊Q8D4×C1111yescharacteristic
213C4⋊Q8D4×C1111yescharacteristic
214#127—21no—
215#127—21no—
216#127—21no—
217#127—21no—
218#125—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C42C23×C1111yescharacteristic
227#107—24no—
228#106—24no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8D4×C1112yes—
232#102—24no—
233#100—44no—
234C22⋊C8—21no—
235#97—21no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8D4×C1112yes—
240C2×C11—22no—
241C2×C11—162no—
242C2×C11#200211yescharacteristic
243C2×C11#201311yescharacteristic
244C2×C11#201911yescharacteristic
245C24—22no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—44no—
250C2×Q8—41no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—44no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—82no—
261C22×C4—41no—
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C11×#4111yescharacteristic
265SD16—416no—
266SD16—84no—
267M16—22no—
268M16—42no—
269M16C11×SD1614yescomplemented
270C2×C8—24no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—41no—
286C42—41no—
287C42C2×D4×C1111yescharacteristic
288C42C2×D4×C1111yescharacteristic
289C42C2×D4×C1111yescharacteristic
290C42C2×D4×C1111yescharacteristic
291C11#1015311yescharacteristic, direct product factor, Sylow
292C23—42no—
293C23—44no—
294C23—82no—
295C23—82no—
296C23C11×#12111yescharacteristic
297Q8—44no—
298Q8—42no—
299Q8—42no—
300Q8—82no—
301D4—44no—
302D4—44no—
303D4—82no—
304D4—81no—
305D4—81no—
306D4—82no—
307D4—82no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4C11×#12011yescharacteristic
315C2×C4C11×#12011yescharacteristic
316C2×C4C11×#12011yescharacteristic
317C2×C4C11×#12111yescharacteristic
318C2×C4C11×#12111yescharacteristic
319C2×C4C11×#12711yescharacteristic
320C2×C4C2×C11×SD1612yes—
321C2×C4C11×#13712yes—
322C8—24no—
323C8—24no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—82no—
329C22—82no—
330C22—82no—
331C22—164no—
332C22C11×#39211yescharacteristic
333C22C11×#46112yes—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—81no—
339C4C11×#44812yes—
340C4C11×#45312yes—
341C4C11×#47112yes—
342C4C11×#49211yescharacteristic
343C4C11×#49711yescharacteristic
344C2—22no—
345C2—162no—
346C2C11×#200211yescharacteristic
347C2C11×#201311yescharacteristic
348C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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
2. C11×#3165C2semidirect
5. C11×#1549C2semidirect
6. C11×#1493C2semidirect
7. C11×#1278C2semidirect
71. #10153C11direct (N × H)
96. C11×M16SD16semidirect
119. #3165C2×C11semidirect
122. #1549C2×C11semidirect
123. #1493C2×C11semidirect
124. #1278C2×C11semidirect
269. M16C11×SD16semidirect
291. C11#10153direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32082
C11×#31652
C2×C11×#4922
C11×#19652
C11×#15492
C11×#14932
C11×#12782
#1015311