Finite Group Databasebeta

← C11×#11905 #14589098

Subgroups — C11×#11905 #14589098

Order 2816.

372 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2581C211yesmaximal, characteristic
2C11×#1801C211yesmaximal, characteristic
3C11×#1461C211yesmaximal, characteristic
4C11×#1354C212yesmaximal
5C11×#1353C212yesmaximal
6C2×C4×Q8×C11C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#431—21no—
9C11×#423—21no—
10C2×C11×#101—21no—
11C11×#400C411yescharacteristic
12C11×#400C2211yescharacteristic
13C11×#395C411yescharacteristic
14C11×#395C2211yescharacteristic
15C11×#391—21no—
16C11×#389—21no—
17C11×#387—21no—
18C11×#387—21no—
19C11×#382C411yescharacteristic
20C11×#343C2212yes—
21C11×#324—21no—
22C11×#324C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Q8×C11D411yescharacteristic
25C2×C11×M16—22no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C11×C4⋊C8—41no—
43C11×C4⋊C8—41no—
44C11×C4⋊C8—41no—
45C11×#101—42no—
46C11×C22⋊C8—22no—
47C4×C8×C11—41no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11905C1111yesmaximal, characteristic, direct product factor, Sylow
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—42no—
61C2×Q8×C11—41no—
62C2×Q8×C11SD1612yes—
63C2×Q8×C11Q1612yes—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C11×M16—42no—
76C11×M16—42no—
77C2×C8×C11—42no—
78C2×C8×C11—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11—42no—
95#2581C2×C1111yescharacteristic
96#1801C2×C1111yescharacteristic
97#1461C2×C1111yescharacteristic
98#1354C2×C1112yes—
99#1353C2×C1112yes—
100C23×C11C2×C22⋊C411yescharacteristic
101Q8×C11—42no—
102Q8×C11—42no—
103Q8×C11—42no—
104Q8×C11—42no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#10312yes—
132C2×C4×C11#10312yes—
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C8×C11—82no—
136C8×C11—82no—
137C2×C4×Q8C4×C1111yescharacteristic
138C2×C4×Q8C22×C1111yescharacteristic
139#431—21no—
140#423—21no—
141C2×#101—21no—
142#400C4×C1111yescharacteristic
143#400C22×C1111yescharacteristic
144#395C4×C1111yescharacteristic
145#395C22×C1111yescharacteristic
146#391—21no—
147#389—21no—
148#387—21no—
149#387—21no—
150#382C4×C1111yescharacteristic
151#343C22×C1112yes—
152#324—21no—
153#324C22×C1112yes—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11C2×#9911yescharacteristic
157C22×C11C2×#10311yescharacteristic
158C22×C11#42111yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—22no—
162C4×C11—22no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—42no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—81no—
170C4×C11—81no—
171C4×C11—81no—
172C22×Q8C2×C4×C1111yescharacteristic
173C22×Q8D4×C1111yescharacteristic
174C2×M16—22no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—41no—
178C4×Q8—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C1111yescharacteristic
184C2×C4⋊C4C2×C4×C1111yescharacteristic
185C2×C4⋊C4D4×C1111yescharacteristic
186C2×C4⋊C4C23×C1111yescharacteristic
187C2×C42—21no—
188C2×C42C2×C4×C1111yescharacteristic
189C2×C42D4×C1111yescharacteristic
190C2×C42D4×C1111yescharacteristic
191C4⋊C8—41no—
192C4⋊C8—41no—
193C4⋊C8—41no—
194#101—42no—
195C22⋊C8—22no—
196C4×C8—41no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95C2×C4×C1111yescharacteristic
205#95C2×C4×C1111yescharacteristic
206C2×C11—21no—
207C2×C11—21no—
208C2×C11#152011yescharacteristic
209C2×C11#212011yescharacteristic
210C2×C11#213311yescharacteristic
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—42no—
214C2×Q8—41no—
215C2×Q8C11×SD1612yes—
216C2×Q8C11×Q1612yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4C11×C22⋊C411yescharacteristic
222C22×C4C11×C22⋊C411yescharacteristic
223C22×C4C11×C22⋊C411yescharacteristic
224C22×C4C11×C22⋊C411yescharacteristic
225C22×C4C22×C4×C1111yescharacteristic
226C22×C4C2×D4×C1111yescharacteristic
227C22×C4C2×D4×C1111yescharacteristic
228M16—42no—
229M16—42no—
230C2×C8—42no—
231C2×C8—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—42no—
248C11#1190511yescharacteristic, direct product factor, Sylow
249C23C2×C11×C22⋊C411yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4C11×#9911yescharacteristic
279C2×C4C11×#9911yescharacteristic
280C2×C4C11×#10312yes—
281C2×C4C11×#10312yes—
282C2×C4C2×C11×SD1611yescharacteristic
283C2×C4C2×C11×Q1611yescharacteristic
284C8—82no—
285C8—82no—
286C22—21no—
287C22—21no—
288C22C2×C11×#9911yescharacteristic
289C22C2×C11×#10311yescharacteristic
290C22C11×#42111yescharacteristic
291C4—21no—
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—21no—
297C4—41no—
298C4—42no—
299C4—41no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2C11×#152011yescharacteristic
307C2C11×#212011yescharacteristic
308C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×C11C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
57. #11905C11direct (N × H)
248. C11#11905direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25812
C11×#18012
C11×#14612
C11×#13542
C11×#13532
#1190511