Finite Group Databasebeta

← C11×#10515 #14587708

Subgroups — C11×#10515 #14587708

Order 2816.

366 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3246C211yesmaximal, characteristic
2C11×#1832C211yesmaximal, characteristic, complemented
3C11×#1552C211yesmaximal, characteristic, complemented
4C11×#1551C211yesmaximal, characteristic
5C11×#1506C211yesmaximal, characteristic, complemented
6C11×#1505C211yesmaximal, characteristic
7C11×#1290C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C11×#476—21no—
11C11×#475—21no—
12C11×#465—22no—
13C11×#461—21no—
14C11×#460—21no—
15C11×#432C2211yescharacteristic
16C11×#432C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#376C2211yescharacteristic
20C11×#336—22no—
21C11×#333—21no—
22C11×#332—21no—
23C11×#332—21no—
24C11×#331—21no—
25C11×#328—22no—
26C11×#327—22no—
27C2×C11×#41—21no—
28C2×C11×SD16—22no—
29C22×C8×C11—21no—
30C22×C8×C11D412yes—
31C11×C4⋊Q8D411yescharacteristic
32C11×C4⋊Q8D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#125—21no—
36C11×#124—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×#121—21no—
40C11×#121—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C11×#117—21no—
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48C11×#106—22no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×#103—22no—
56C11×#102—22no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#97—21no—
61C11×#95—21no—
62C11×#95D412yes—
63#10515C1111yesmaximal, characteristic, direct product factor, Sylow
64C11×#41—82no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—41no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C11×SD16—82no—
78C2×C8×C11—22no—
79C2×C8×C11—42no—
80C2×C8×C11—42no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102#3246C2×C1111yescharacteristic
103#1832C2×C1111yescharacteristic, complemented
104#1552C2×C1111yescharacteristic, complemented
105#1551C2×C1111yescharacteristic
106#1506C2×C1111yescharacteristic, complemented
107#1505C2×C1111yescharacteristic
108#1290C2×C1111yescharacteristic, complemented
109C23×C11—41no—
110C23×C11#12111yescharacteristic
111Q8×C11—41no—
112Q8×C11—41no—
113Q8×C11—81no—
114Q8×C11—81no—
115D4×C11—41no—
116D4×C11—41no—
117D4×C11—81no—
118D4×C11—81no—
119D4×C11—82no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—82no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C8×C11—42no—
138C8×C11—81no—
139C8×C11—81no—
140C8×C11—81no—
141#533C22×C1111yescharacteristic
142#532C22×C1111yescharacteristic
143#476—21no—
144#475—21no—
145#465—22no—
146#461—21no—
147#460—21no—
148#432C22×C1111yescharacteristic
149#432C22×C1111yescharacteristic
150C2×C4⋊C8C22×C1111yescharacteristic
151C2×C4⋊C8C22×C1111yescharacteristic
152#376C22×C1111yescharacteristic
153#336—22no—
154#333—21no—
155#332—21no—
156#332—21no—
157#331—21no—
158#328—22no—
159#327—22no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11—81no—
165C22×C11#39411yescharacteristic
166C22×C11#47112yes—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—82no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11—81no—
176C4×C11#45411yescharacteristic
177C4×C11#45511yescharacteristic
178C2×#41—21no—
179C2×SD16—22no—
180C22×C8—21no—
181C22×C8D4×C1112yes—
182C4⋊Q8D4×C1111yescharacteristic
183C4⋊Q8D4×C1111yescharacteristic
184C4⋊Q8D4×C1111yescharacteristic
185#127D4×C1111yescharacteristic
186#125—21no—
187#124—21no—
188C22⋊Q8—21no—
189C22⋊Q8—21no—
190#121—21no—
191#121—21no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×D4—21no—
195C4×D4—21no—
196#117—21no—
197C2×C42—21no—
198C2×C42C23×C1111yescharacteristic
199#106—22no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206#103—22no—
207#102—22no—
208C22⋊C8—21no—
209C22⋊C8—21no—
210#97—21no—
211#97—21no—
212#95—21no—
213#95D4×C1112yes—
214C2×C11—22no—
215C2×C11—161no—
216C2×C11#204011yescharacteristic
217C2×C11#204611yescharacteristic
218C2×C11#205311yescharacteristic
219#41—82no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—41no—
227C22×C4—22no—
228C22×C4—41no—
229C22×C4C2×D4×C1111yescharacteristic
230C22×C4C2×D4×C1111yescharacteristic
231C22×C4C11×#4111yescharacteristic
232SD16—82no—
233C2×C8—22no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C42C2×D4×C1111yescharacteristic
254C42C2×D4×C1111yescharacteristic
255C42C11×#4111yescharacteristic
256C42C11×#4111yescharacteristic
257C11#1051511yescharacteristic, direct product factor, Sylow
258C23—41no—
259C23C11×#12111yescharacteristic
260Q8—41no—
261Q8—41no—
262Q8—81no—
263Q8—81no—
264D4—41no—
265D4—41no—
266D4—81no—
267D4—81no—
268D4—82no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—82no—
280C2×C4C11×#12011yescharacteristic
281C2×C4C11×#12111yescharacteristic
282C2×C4C11×#12111yescharacteristic
283C2×C4C11×#12311yescharacteristic
284C2×C4C11×#12311yescharacteristic
285C2×C4C11×#12411yescharacteristic
286C8—42no—
287C8—81no—
288C8—81no—
289C8—81no—
290C22—21no—
291C22—21no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22C11×#39411yescharacteristic
296C22C11×#47112yes—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—82no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4C11×#45411yescharacteristic
307C4C11×#45511yescharacteristic
308C2—22no—
309C2—161no—
310C2C11×#204011yescharacteristic
311C2C11×#204611yescharacteristic
312C2C11×#205311yescharacteristic
subgroupG/H
center, socleC22×C11#394
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
2. C11×#1832C2semidirect
3. C11×#1552C2semidirect
5. C11×#1506C2semidirect
7. C11×#1290C2semidirect
63. #10515C11direct (N × H)
103. #1832C2×C11semidirect
104. #1552C2×C11semidirect
106. #1506C2×C11semidirect
108. #1290C2×C11semidirect
257. C11#10515direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32462
C11×#18322
C11×#15522
C11×#15512
C11×#15062
C11×#15052
C11×#12902
#1051511