Finite Group Databasebeta

← C11×#10283 #14587476

Subgroups — C11×#10283 #14587476

Order 2816.

626 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×#3227C211yesmaximal, characteristic
2C11×#3206C211yesmaximal, characteristic
3C11×#2868C211yesmaximal, characteristic, complemented
4C11×#1962C211yesmaximal, characteristic
5C11×#1549C211yesmaximal, characteristic, complemented
6C11×#1548C211yesmaximal, characteristic, complemented
7C11×#1276C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8—22no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C11×#498—21no—
13C11×#492—21no—
14C11×#487—21no—
15C11×#486—21no—
16C11×#481—22no—
17C11×#476—22no—
18C11×#461—22no—
19C11×#448—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C2×C11×#104—22no—
24C11×#384—22no—
25C11×#384—22no—
26C43×C11C2211yescharacteristic
27C11×#333—22no—
28C11×#332—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D412yes—
32C2×C11×SD16—24no—
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—48no—
43C11×C4⋊Q8D411yescharacteristic
44C11×#127D411yescharacteristic
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—28no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C42×C11—21no—
56C2×C42×C11—21no—
57C2×C42×C11D412yes—
58C2×C42×C11C2311yescharacteristic
59C11×#106—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C4⋊C8D412yes—
64C11×#104—44no—
65C11×#103—24no—
66C11×#102—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71#10283C1111yesmaximal, characteristic, direct product factor, Sylow
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—22no—
75C2×Q8×C11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—44no—
78C2×Q8×C11—44no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C11×SD16—84no—
93C11×M16—42no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—41no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—416no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—24no—
111C42×C11—24no—
112C42×C11—22no—
113C42×C11SD1614yescomplemented
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118#3227C2×C1111yescharacteristic
119#3206C2×C1111yescharacteristic
120#2868C2×C1111yescharacteristic, complemented
121#1962C2×C1111yescharacteristic
122#1549C2×C1111yescharacteristic, complemented
123#1548C2×C1111yescharacteristic, complemented
124#1276C2×C1111yescharacteristic, complemented
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127Q8×C11—44no—
128Q8×C11—42no—
129Q8×C11—82no—
130Q8×C11—82no—
131Q8×C11—82no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—42no—
135D4×C11—82no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—44no—
142C2×C4×C11—44no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C2×C4×C11C2×SD1612yes—
155C2×C4×C11#13712yes—
156C8×C11—42no—
157C8×C11—42no—
158C8×C11—81no—
159#532C22×C1111yescharacteristic
160C2×C4⋊Q8—22no—
161C2×C4⋊Q8C22×C1111yescharacteristic
162C2×C4⋊Q8C22×C1111yescharacteristic
163#498—21no—
164#492—21no—
165#487—21no—
166#486—21no—
167#481—22no—
168#476—22no—
169#461—22no—
170#448—22no—
171#431C22×C1111yescharacteristic
172#431C22×C1111yescharacteristic
173#423C22×C1111yescharacteristic
174C2×#104—22no—
175#384—22no—
176#384—22no—
177C43C22×C1111yescharacteristic
178#333—22no—
179#332—22no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#39211yescharacteristic
186C22×C11#44812yes—
187C4×C11—28no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—82no—
191C4×C11—82no—
192C4×C11—81no—
193C4×C11#45312yes—
194C4×C11#45612yes—
195C4×C11#46112yes—
196C4×C11#49211yescharacteristic
197C4×C11#49711yescharacteristic
198C2×#41—21no—
199C22×Q8—21no—
200C22×Q8D4×C1112yes—
201C2×SD16—24no—
202C2×M16—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—48no—
212C4⋊Q8D4×C1111yescharacteristic
213#127D4×C1111yescharacteristic
214#124—21no—
215#121—21no—
216#121—21no—
217C4×D4—21no—
218C4×D4—21no—
219C2×C4⋊C4—28no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C1112yes—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42D4×C1112yes—
227C2×C42C23×C1111yescharacteristic
228#106—24no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8D4×C1112yes—
232C4⋊C8D4×C1112yes—
233#104—44no—
234#103—24no—
235#102—24no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C2×C11—22no—
241C2×C11—161no—
242C2×C11#200211yescharacteristic
243C2×C11#200511yescharacteristic
244C2×C11#201311yescharacteristic
245#41—42no—
246#41—42no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—44no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4C2×D4×C1111yescharacteristic
263C22×C4C2×D4×C1111yescharacteristic
264C22×C4C2×D4×C1111yescharacteristic
265SD16—84no—
266M16—42no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—41no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—416no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—24no—
284C42—24no—
285C42—22no—
286C42C11×SD1614yescomplemented
287C42C2×D4×C1111yescharacteristic
288C42C2×D4×C1111yescharacteristic
289C42C2×D4×C1111yescharacteristic
290C42C11×#4111yescharacteristic
291C11#1028311yescharacteristic, direct product factor, Sylow
292C23—41no—
293C23C11×#12011yescharacteristic
294Q8—44no—
295Q8—42no—
296Q8—82no—
297Q8—82no—
298Q8—82no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4C11×#12011yescharacteristic
316C2×C4C11×#12011yescharacteristic
317C2×C4C11×#12111yescharacteristic
318C2×C4C11×#12111yescharacteristic
319C2×C4C11×#12111yescharacteristic
320C2×C4C11×#12711yescharacteristic
321C2×C4C2×C11×SD1612yes—
322C2×C4C11×#13712yes—
323C8—42no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22C11×#39211yescharacteristic
332C22C11×#44812yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—82no—
338C4—81no—
339C4C11×#45312yes—
340C4C11×#45612yes—
341C4C11×#46112yes—
342C4C11×#49211yescharacteristic
343C4C11×#49711yescharacteristic
344C2—22no—
345C2—161no—
346C2C11×#200211yescharacteristic
347C2C11×#200511yescharacteristic
348C2C11×#201311yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
3. C11×#2868C2semidirect
5. C11×#1549C2semidirect
6. C11×#1548C2semidirect
7. C11×#1276C2semidirect
71. #10283C11direct (N × H)
113. C42×C11SD16semidirect
120. #2868C2×C11semidirect
122. #1549C2×C11semidirect
123. #1548C2×C11semidirect
124. #1276C2×C11semidirect
286. C42C11×SD16semidirect
291. C11#10283direct (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×#32062
C11×#28682
C11×#19622
C11×#15492
C11×#15482
C11×#12762
#1028311