Finite Group Databasebeta

← C11×#9979 #14587172

Subgroups — C11×#9979 #14587172

Order 2816.

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3189C211yesmaximal, characteristic
2C11×#3095C212yesmaximal
3C11×#1818C211yesmaximal, characteristic
4C11×#1472C212yesmaximal
5C11×#1293C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2212yes—
7C2×C11×#117C2211yescharacteristic
8C11×#485—24no—
9C11×#484—22no—
10C11×#484—22no—
11C11×#483—22no—
12C11×#467—22no—
13C11×#451—22no—
14C11×#428—22no—
15C11×#419—22no—
16C11×#407C2212yes—
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C11×#336—22no—
20C11×#324—24no—
21C22×Q8×C11D412yes—
22C23×C4×C11C2311yescharacteristic
23C2×C11×Q16—22no—
24C2×C11×M16—22no—
25C22×C8×C11—21no—
26C22×C8×C11D412yes—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—22no—
29C11×C22⋊Q8—22no—
30C11×C22⋊Q8—22no—
31C11×#117—22no—
32C11×#117—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D412yes—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—22no—
39C2×C42×C11—21no—
40C11×#107—24no—
41C11×#107—22no—
42C11×#106—24no—
43C11×#103—24no—
44C11×#103—24no—
45C11×#103—24no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8D414yes—
50#9979C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11#4111yescharacteristic
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—44no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—42no—
60C22×C4×C11C2×D412yes—
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C11×Q16—82no—
65C11×M16—44no—
66C2×C8×C11—22no—
67C2×C8×C11—24no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C2×C8×C11—41no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C42×C11—41no—
81C42×C11—41no—
82#3189C2×C1111yescharacteristic
83#3095C2×C1112yes—
84#1818C2×C1111yescharacteristic
85#1472C2×C1112yes—
86#1293C2×C1111yescharacteristic
87C23×C11—22no—
88C23×C11—41no—
89C23×C11—41no—
90C23×C11#12112yes—
91C23×C11#12111yescharacteristic
92Q8×C11—44no—
93Q8×C11—44no—
94C2×C4×C11—22no—
95C2×C4×C11—24no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—44no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—82no—
106C2×C4×C11#12012yes—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11#12711yescharacteristic
109C8×C11—44no—
110C8×C11—42no—
111C8×C11—81no—
112C2×C22⋊Q8C22×C1112yes—
113C2×#117C22×C1111yescharacteristic
114#485—24no—
115#484—22no—
116#484—22no—
117#483—22no—
118#467—22no—
119#451—22no—
120#428—22no—
121#419—22no—
122#407C22×C1112yes—
123C2×C22⋊C8C22×C1111yescharacteristic
124C2×C22⋊C8C22×C1111yescharacteristic
125#336—22no—
126#324—24no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—22no—
132C22×C11—82no—
133C22×C11#39211yescharacteristic
134C22×C11#47312yes—
135C4×C11—22no—
136C4×C11—21no—
137C4×C11—81no—
138C4×C11—82no—
139C4×C11—81no—
140C4×C11—82no—
141C4×C11#45812yes—
142C22×Q8D4×C1112yes—
143C23×C4C23×C1111yescharacteristic
144C2×Q16—22no—
145C2×M16—22no—
146C22×C8—21no—
147C22×C8D4×C1112yes—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152#117—22no—
153#117—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4D4×C1111yescharacteristic
156C2×C4⋊C4D4×C1111yescharacteristic
157C2×C4⋊C4D4×C1112yes—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—22no—
160C2×C42—21no—
161#107—24no—
162#107—22no—
163#106—24no—
164#103—24no—
165#103—24no—
166#103—24no—
167C22⋊C8—22no—
168C22⋊C8—22no—
169C22⋊C8—22no—
170C22⋊C8D4×C1114yes—
171C2×C11—22no—
172C2×C11—42no—
173C2×C11#201711yescharacteristic
174C2×C11#202011yescharacteristic
175C2×C11#202211yescharacteristic
176C24C11×#4111yescharacteristic
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—44no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4C2×D4×C1112yes—
186C22×C4C2×D4×C1111yescharacteristic
187C22×C4C2×D4×C1111yescharacteristic
188C22×C4C2×D4×C1112yes—
189Q16—82no—
190M16—44no—
191C2×C8—22no—
192C2×C8—24no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—41no—
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C42—41no—
206C42—41no—
207C11#997911yescharacteristic, direct product factor, Sylow
208C23—22no—
209C23—41no—
210C23—41no—
211C23C11×#12112yes—
212C23C11×#12111yescharacteristic
213Q8—44no—
214Q8—44no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4C11×#12012yes—
228C2×C4C11×#12011yescharacteristic
229C2×C4C11×#12711yescharacteristic
230C8—44no—
231C8—42no—
232C8—81no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22C11×#39211yescharacteristic
240C22C11×#47312yes—
241C4—22no—
242C4—21no—
243C4—81no—
244C4—82no—
245C4—81no—
246C4—82no—
247C4C11×#45812yes—
248C2—22no—
249C2—42no—
250C2C11×#201711yescharacteristic
251C2C11×#202011yescharacteristic
252C2C11×#202211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
50. #9979C11direct (N × H)
207. C11#9979direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31892
C11×#30952
C11×#18182
C11×#14722
C11×#12932
#997911