Finite Group Databasebeta

← #14673305

Subgroups — #14673305

Order 2816.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#13070270C212yesmaximal
2#13069139C212yesmaximal
3#13068835C211yesmaximal, characteristic
4#13066737C211yesmaximal, characteristic
5C11×#3202C211yesmaximal, characteristic
6C11×#536C2212yes—
7#10623350C2211yescharacteristic
8C11×#485—22no—
9C11×#470—21no—
10C11×#467—21no—
11C11×#451—22no—
12C11×#408C2211yescharacteristic
13#10622853C2212yes—
14#10622850C2211yescharacteristic
15#10622838—22no—
16#10622737—21no—
17#10622190—21no—
18#10622177—24no—
19#10622169—22no—
20C2×C11×#41C2311yescharacteristic
21C22×Q8×C11D412yes—
22C2×C11×Q16—21no—
23C2×C11×Q16—21no—
24C2×C11×M16D411yescharacteristic
25C22×C8×C11D411yescharacteristic
26C11×C4⋊Q8—22no—
27C11×#124—22no—
28C11×#123—22no—
29C11×#123—22no—
30C11×C22⋊Q8—22no—
31C11×C22⋊Q8—22no—
32C11×#117D412yes—
33#67001—42no—
34#66979—22no—
35C2×#4318—22no—
36C2×#4318—21no—
37C2×#4318—21no—
38C11×#107—21no—
39C11×#106—21no—
40C11×#103—22no—
41C11×#103—22no—
42C11×C22⋊C8—22no—
43#66900—21no—
44#66899—44no—
45#66898—22no—
46#66898—22no—
47#66897D412yes—
48#66886—42no—
49#13438—111nomaximal, Sylow
50C11×#41—41no—
51C11×#41—41no—
52C2×Q8×C11—22no—
53C2×Q8×C11—22no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C2×Q8×C11#4111yescharacteristic
57C2×D4×C11C2×D411yescharacteristic
58C2×D4×C11#4112yes—
59C22×C4×C11—22no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C11×Q16—81no—
63C11×Q16—81no—
64C11×M16—41no—
65C2×C8×C11—21no—
66C2×C8×C11—21no—
67C2×C8×C11—41no—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C22⋊C4—22no—
72C11×C22⋊C4—42no—
73C11×C22⋊C4—42no—
74C42×C11—22no—
75C22⋊Dic11—42no—
76C4⋊Dic11—42no—
77C4×Dic11—42no—
78#4318—22no—
79#4318—22no—
80#4318—41no—
81#4318—42no—
82#4318—41no—
83C2×C11⋊C8—24no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86#3202D1111yescharacteristic
87#2123—112no—
88#1909—112no—
89#1858—111no—
90#1391—111no—
91C23×C11#12112yes—
92C23×C11#12411yescharacteristic
93Q8×C11—41no—
94Q8×C11—44no—
95Q8×C11—42no—
96Q8×C11—42no—
97D4×C11—41no—
98D4×C11—42no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—82no—
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11#12111yescharacteristic
108C2×C4×C11#12312yes—
109C2×Dic11—82no—
110C8×C11—41no—
111C8×C11—41no—
112C11⋊C8—42no—
113C11⋊C8—42no—
114#568—111no—
115#536C2×D1112yes—
116#485—22no—
117#470—21no—
118#467—21no—
119#451—22no—
120#430—221no—
121#419—222no—
122#413—111no—
123#410—112no—
124#408C2×D1111yescharacteristic
125#352—224no—
126#341—221no—
127H(3,ℤ/4)—222no—
128C22×C11—22no—
129C22×C11—21no—
130C22×C11—42no—
131C22×C11—41no—
132C22×C11#39411yescharacteristic
133C4×C11—21no—
134C4×C11—22no—
135C4×C11—82no—
136C4×C11—82no—
137C4×C11B(4,𝔽2)11yescharacteristic
138C4×C11#45811yescharacteristic
139Dic11—162no—
140C2×#41C22×D1111yescharacteristic
141C22×Q8C22⋊D1112yes—
142C2×Q16—21no—
143C2×Q16—21no—
144#131—442no—
145C2×M16—222no—
146C2×M16—221no—
147C2×M16—221no—
148C2×M16C22⋊D1111yescharacteristic
149C22×C8C22⋊D1111yescharacteristic
150C4⋊Q8—22no—
151#124—22no—
152#123—22no—
153#123—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156#117—222no—
157#117C22⋊D1112yes—
158#108—442no—
159#107—21no—
160#106—21no—
161#103—22no—
162#103—22no—
163#103—444no—
164#101—221no—
165#100—112no—
166#99—222no—
167#99—222no—
168C22⋊C8—22no—
169C2×C11—21no—
170C2×C11—42no—
171C2×C11—41no—
172C2×C11#204411yescharacteristic
173#41—41no—
174#41—41no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8#434111yescharacteristic
180C2×D4D4×D1111yescharacteristic
181C2×D4#434112yes—
182C22×C4—22no—
183C22×C4C2×C22⋊D1112yes—
184C22×C4C2×C22⋊D1111yescharacteristic
185Q16—81no—
186Q16—81no—
187M16—41no—
188M16—222no—
189M16—222no—
190M16—442no—
191M16—441no—
192M16—441no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—41no—
196C2×C8—224no—
197C2×C8—441no—
198C2×C8—441no—
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—442no—
203C22⋊C4—22no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—442no—
207C42—22no—
208C42—442no—
209C11#1343811yescharacteristic, complemented, Sylow
210C23#6698911yescharacteristic
211C23#6699212yes—
212Q8—41no—
213Q8—44no—
214Q8—42no—
215Q8—42no—
216D4—41no—
217D4—42no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4—882no—
226C2×C4#6698812yes—
227C2×C4#6699111yescharacteristic
228C2×C4#6700611yescharacteristic
229C8—41no—
230C8—41no—
231C8—442no—
232C8—442no—
233C22—22no—
234C22—21no—
235C22—41no—
236C22—42no—
237C22#1062283511yescharacteristic
238C4—21no—
239C4—22no—
240C4—82no—
241C4—82no—
242C4—1762no—
243C4#1062285611yescharacteristic
244C4#1062285711yescharacteristic
245C2—21no—
246C2—42no—
247C2—41no—
248C2#1306986411yescharacteristic
subgroupG/H
centerC2#13069864
commutator, prime radical, cosocleC2×C11×#41C23
FrattiniC2×#41C22×D11
FittingC11×#3202C2
socleC2×C11#2044
hypercenter#3202D11
hypocenterC11#13438
LCSG ▷ C2×C11×#41 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #3202

Complements

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

NH ≅ G/Ntype
209. C11#13438semidirect

Maximal subgroups

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

subgroupindex
#130702702
#130691392
#130688352
#130667372
C11×#32022
#1343811