Finite Group Databasebeta

← C11×#11907 #14589100

Subgroups — C11×#11907 #14589100

Order 2816.

372 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2568C211yesmaximal, characteristic
2C11×#1801C211yesmaximal, characteristic
3C11×#1461C211yesmaximal, characteristic
4C11×#1353C214yesmaximal
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#431—21no—
8C11×#423—21no—
9C2×C11×#101—21no—
10C11×#400C412yes—
11C11×#400C2212yes—
12C11×#391—21no—
13C11×#391—21no—
14C11×#391—21no—
15C11×#382—21no—
16C4×C11×C4⋊C4C411yescharacteristic
17C11×#343C2212yes—
18C11×#324—21no—
19C11×#324C2212yes—
20C22×Q8×C11—21no—
21C22×Q8×C11D411yescharacteristic
22C2×C11×M16—22no—
23C11×C4⋊Q8—41no—
24C11×C4⋊Q8—41no—
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C11×C4⋊C8—41no—
38C11×C4⋊C8—41no—
39C11×C4⋊C8—41no—
40C11×#101—42no—
41C11×C22⋊C8—22no—
42C4×C8×C11—41no—
43C11×#95—22no—
44C11×#95—22no—
45C11×#95—22no—
46C11×#95—22no—
47C11×#95C2×C412yes—
48#11907C1111yesmaximal, characteristic, direct product factor, Sylow
49C2×Q8×C11—41no—
50C2×Q8×C11—41no—
51C2×Q8×C11—44no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11SD1612yes—
55C2×Q8×C11Q1612yes—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×M16—42no—
66C11×M16—42no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—42no—
82#2568C2×C1111yescharacteristic
83#1801C2×C1111yescharacteristic
84#1461C2×C1111yescharacteristic
85#1353C2×C1114yes—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—42no—
88Q8×C11—42no—
89Q8×C11—82no—
90Q8×C11—82no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—44no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11#10312yes—
112C2×C4×C11#10312yes—
113C2×C4×C11C2×SD1611yescharacteristic
114C2×C4×C11C2×Q1611yescharacteristic
115C8×C11—82no—
116C8×C11—82no—
117C2×C4⋊Q8C4×C1111yescharacteristic
118C2×C4×Q8C22×C1111yescharacteristic
119#431—21no—
120#423—21no—
121C2×#101—21no—
122#400C4×C1112yes—
123#400C22×C1112yes—
124#391—21no—
125#391—21no—
126#391—21no—
127#382—21no—
128C4×C4⋊C4C4×C1111yescharacteristic
129#343C22×C1112yes—
130#324—21no—
131#324C22×C1112yes—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11C2×#9911yescharacteristic
135C22×C11C2×#10311yescharacteristic
136C22×C11#42111yescharacteristic
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—22no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—41no—
143C4×C11—41no—
144C4×C11—41no—
145C4×C11—82no—
146C4×C11—82no—
147C4×C11#35512yes—
148C22×Q8—21no—
149C22×Q8D4×C1111yescharacteristic
150C2×M16—22no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×C4×C1112yes—
158C2×C4⋊C4C2×C4×C1111yescharacteristic
159C2×C4⋊C4D4×C1111yescharacteristic
160C2×C4⋊C4C23×C1111yescharacteristic
161C2×C42—21no—
162C2×C42C2×C4×C1111yescharacteristic
163C2×C42D4×C1111yescharacteristic
164C2×C42D4×C1111yescharacteristic
165C4⋊C8—41no—
166C4⋊C8—41no—
167C4⋊C8—41no—
168#101—42no—
169C22⋊C8—22no—
170C4×C8—41no—
171#95—22no—
172#95—22no—
173#95—22no—
174#95—22no—
175#95C2×C4×C1112yes—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11#152011yescharacteristic
179C2×C11#212311yescharacteristic
180C2×C11C2×#35511yescharacteristic
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—44no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8C11×SD1612yes—
187C2×Q8C11×Q1612yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4C11×C22⋊C411yescharacteristic
191C22×C4C11×C22⋊C411yescharacteristic
192C22×C4C11×C22⋊C411yescharacteristic
193C22×C4C11×C22⋊C411yescharacteristic
194C22×C4C22×C4×C1111yescharacteristic
195C22×C4C2×D4×C1111yescharacteristic
196C22×C4C2×D4×C1111yescharacteristic
197M16—42no—
198M16—42no—
199C2×C8—42no—
200C2×C8—42no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—42no—
214C11#1190711yescharacteristic, direct product factor, Sylow
215C23C2×C11×C22⋊C411yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—82no—
219Q8—82no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4C11×#9911yescharacteristic
239C2×C4C11×#9911yescharacteristic
240C2×C4C11×#10312yes—
241C2×C4C11×#10312yes—
242C2×C4C2×C11×SD1611yescharacteristic
243C2×C4C2×C11×Q1611yescharacteristic
244C8—82no—
245C8—82no—
246C22—21no—
247C22—21no—
248C22C2×C11×#9911yescharacteristic
249C22C2×C11×#10311yescharacteristic
250C22C11×#42111yescharacteristic
251C4—21no—
252C4—21no—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—82no—
260C4—82no—
261C4C11×#35512yes—
262C2—21no—
263C2—21no—
264C2C11×#152011yescharacteristic
265C2C11×#212311yescharacteristic
266C2C2×C11×#35511yescharacteristic
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
48. #11907C11direct (N × H)
214. C11#11907direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25682
C11×#18012
C11×#14612
C11×#13532
#1190711