Finite Group Databasebeta

← C11×#10161 #14587354

Subgroups — C11×#10161 #14587354

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 346 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×#486C211yesmaximal, characteristic
4C11×#1965C211yesmaximal, characteristic
5C11×#1548C211yesmaximal, characteristic, complemented
6C11×#1493C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#492—21no—
15C11×#486—21no—
16C11×#486—22no—
17C11×#486—22no—
18C11×#460—22no—
19C11×#450—22no—
20C11×#431C2211yescharacteristic
21C11×#428—22no—
22C11×#423C2211yescharacteristic
23C2×C11×#102—22no—
24C2×C11×#100—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#333—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×C11×SD16—24no—
34C2×C11×M16—21no—
35C2×C11×M16D412yes—
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D412yes—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#125—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C11×#107—24no—
57C11×#106—24no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×#102—28no—
62C11×#102—24no—
63C11×#100—44no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11D412yes—
70#10161C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—82no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—44no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—82no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C11×SD16—84no—
92C11×M16—22no—
93C11×M16—42no—
94C11×M16SD1614yescomplemented
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—42no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116#3208C2×C1111yescharacteristic
117#3165C2×C1111yescharacteristic, complemented
118C2×#486C2×C1111yescharacteristic
119#1965C2×C1111yescharacteristic
120#1548C2×C1111yescharacteristic, complemented
121#1493C2×C1111yescharacteristic, complemented
122#1278C2×C1111yescharacteristic, complemented
123C23×C11—42no—
124C23×C11—44no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11#12111yescharacteristic
128Q8×C11—42no—
129Q8×C11—42no—
130Q8×C11—82no—
131Q8×C11—82no—
132D4×C11—44no—
133D4×C11—44no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—82no—
137D4×C11—81no—
138D4×C11—81no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—82no—
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×C4×C11C2×SD1612yes—
152C2×C4×C11#13712yes—
153C8×C11—24no—
154C8×C11—42no—
155C8×C11—42no—
156C8×C11—81no—
157#533C22×C1111yescharacteristic
158C2×C4⋊Q8C22×C1111yescharacteristic
159C2×#127C22×C1111yescharacteristic
160#501—22no—
161#500—21no—
162#498—21no—
163#492—21no—
164#486—22no—
165#486—21no—
166#486—22no—
167#460—22no—
168#450—22no—
169#431C22×C1111yescharacteristic
170#428—22no—
171#423C22×C1111yescharacteristic
172C2×#102—22no—
173C2×#100—22no—
174C4×M16C22×C1111yescharacteristic
175C2×C4×C8C22×C1111yescharacteristic
176#333—22no—
177Q8⋊C8—22no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—164no—
184C22×C11#39211yescharacteristic
185C22×C11#46112yes—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—81no—
189C4×C11—82no—
190C4×C11—81no—
191C4×C11#44812yes—
192C4×C11#45512yes—
193C4×C11#47212yes—
194C4×C11#49211yescharacteristic
195C4×C11#49711yescharacteristic
196C22×Q8—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4D4×C1112yes—
200C2×SD16—24no—
201C2×M16—21no—
202C2×M16D4×C1112yes—
203C22×C8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8D4×C1112yes—
208C4⋊Q8D4×C1111yescharacteristic
209C4⋊Q8D4×C1111yescharacteristic
210#127—21no—
211#127—21no—
212#127—21no—
213#127—21no—
214#125—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219#117—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C42C23×C1111yescharacteristic
223#107—24no—
224#106—24no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8D4×C1112yes—
228#102—28no—
229#102—24no—
230#100—44no—
231C22⋊C8—21no—
232#97—21no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8D4×C1112yes—
237C2×C11—22no—
238C2×C11—162no—
239C2×C11#200411yescharacteristic
240C2×C11#201311yescharacteristic
241C2×C11#201811yescharacteristic
242C24—22no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—82no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—82no—
258C22×C4—41no—
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C2×D4×C1111yescharacteristic
261C22×C4C11×#4111yescharacteristic
262SD16—84no—
263M16—22no—
264M16—42no—
265M16C11×SD1614yescomplemented
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—42no—
270C2×C8—41no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42C2×D4×C1111yescharacteristic
284C42C2×D4×C1111yescharacteristic
285C42C2×D4×C1111yescharacteristic
286C42C2×D4×C1111yescharacteristic
287C11#1016111yescharacteristic, direct product factor, Sylow
288C23—42no—
289C23—44no—
290C23—82no—
291C23—82no—
292C23C11×#12111yescharacteristic
293Q8—42no—
294Q8—42no—
295Q8—82no—
296Q8—82no—
297D4—44no—
298D4—44no—
299D4—82no—
300D4—81no—
301D4—81no—
302D4—82no—
303D4—82no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4C11×#12011yescharacteristic
311C2×C4C11×#12011yescharacteristic
312C2×C4C11×#12011yescharacteristic
313C2×C4C11×#12111yescharacteristic
314C2×C4C11×#12111yescharacteristic
315C2×C4C11×#12711yescharacteristic
316C2×C4C2×C11×SD1612yes—
317C2×C4C11×#13712yes—
318C8—24no—
319C8—42no—
320C8—42no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—164no—
328C22C11×#39211yescharacteristic
329C22C11×#46112yes—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—82no—
334C4—81no—
335C4C11×#44812yes—
336C4C11×#45512yes—
337C4C11×#47212yes—
338C4C11×#49211yescharacteristic
339C4C11×#49711yescharacteristic
340C2—22no—
341C2—162no—
342C2C11×#200411yescharacteristic
343C2C11×#201311yescharacteristic
344C2C11×#201811yescharacteristic
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×#1548C2semidirect
6. C11×#1493C2semidirect
7. C11×#1278C2semidirect
70. #10161C11direct (N × H)
94. C11×M16SD16semidirect
117. #3165C2×C11semidirect
120. #1548C2×C11semidirect
121. #1493C2×C11semidirect
122. #1278C2×C11semidirect
265. M16C11×SD16semidirect
287. C11#10161direct (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×#4862
C11×#19652
C11×#15482
C11×#14932
C11×#12782
#1016111