Finite Group Databasebeta

← #14670296

Subgroups — #14670296

Order 2816.

424 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 135 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#13077206C211yesmaximal, characteristic
2#13070404C212yesmaximal, complemented
3#13068649C211yesmaximal, characteristic
4#13066722C212yesmaximal, complemented
5C2×C11×#349C211yesmaximal, characteristic
6C22×C11×M16C2211yescharacteristic
7C2×#66979—21no—
8C2×C11×M32C2212yes—
9#10622825—21no—
10#10622734—22no—
11#10622734—22no—
12#10622719—21no—
13#10622719C2212yes—
14C2×#66882C2211yescharacteristic
15C2×#66881C2211yescharacteristic
16C11×#349C414yescomplemented
17#10622189—21no—
18#10622143—22no—
19#10622142—22no—
20C23×C4×C11D411yescharacteristic
21C2×C11×M16—22no—
22C2×C11×M16—22no—
23C2×C11×M16C2×C412yes—
24C2×C11×M16Q812yes—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11C2311yescharacteristic
27C2×C22⋊Dic11—41no—
28C2×C22⋊Dic11—41no—
29#66979—22no—
30#66979—22no—
31#66979—41no—
32#66979—41no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4×Dic11—41no—
38C11×M32—22no—
39C11×M32C2×C414yescomplemented
40C2×C11×C16—22no—
41C11⋊#95—41no—
42#66882—21no—
43#66882—21no—
44#66882—22no—
45#66882D412yes—
46#66882D412yes—
47#66881—22no—
48#66881—22no—
49#66881—22no—
50#12923—111nomaximal, Sylow
51C24×C11D811yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11C4⋊C412yes—
57C22×C4×C11D811yescharacteristic
58C22×C4×C11Q1612yes—
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—41no—
61C22×Dic11—41no—
62C22×Dic11—41no—
63C22×Dic11—41no—
64C11×M16—24no—
65C11×M16—24no—
66C2×C8×C11—21no—
67C2×C8×C11—21no—
68C2×C8×C11C4⋊C412yes—
69C2×C8×C11C22×C411yescharacteristic
70C2×C8×C11C2×D412yes—
71C2×C8×C11C2×Q811yescharacteristic
72C2×C8×C11#4112yes—
73C22⋊Dic11—42no—
74C22⋊Dic11—42no—
75C22⋊Dic11—82no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84C4×Dic11—42no—
85C4×Dic11—42no—
86C11×C16—24no—
87#2911—111no—
88#2159—112no—
89C2×#349D1111yescharacteristic
90#1809—111no—
91#1386—112no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11#10712yes—
97C23×C11C2×D811yescharacteristic
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11#10712yes—
105C2×C4×C11C2×C4⋊C411yescharacteristic
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11C2×Q1611yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C11#13711yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—82no—
114C2×Dic11—82no—
115C2×Dic11—81no—
116C2×Dic11—81no—
117C2×Dic11—81no—
118C2×Dic11—81no—
119C2×Dic11—81no—
120C2×Dic11—81no—
121C8×C11—22no—
122C8×C11C4×D412yes—
123C8×C11C22⋊Q812yes—
124C22×M16C2×D1111yescharacteristic
125C2×#117—221no—
126C2×M32C2×D1112yes—
127#428—222no—
128#428—222no—
129#427—112no—
130#427—221no—
131C2×#107—111no—
132C2×#106—111no—
133#380—221no—
134#367—222no—
135#366—222no—
136#349Dic1114yescomplemented
137#340—221no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—22no—
141C22×C11—42no—
142C22×C11—41no—
143C22×C11—41no—
144C22×C11—81no—
145C22×C11C2×#10711yescharacteristic
146C22×C11#44711yescharacteristic
147C22×C11#48011yescharacteristic
148C4×C11—22no—
149C4×C11#38511yescharacteristic
150C4×C11#42811yescharacteristic
151C4×C11#45111yescharacteristic
152C4×C11#48411yescharacteristic
153Dic11—82no—
154Dic11—82no—
155Dic11—161no—
156Dic11—161no—
157C23×C4D4411yescharacteristic
158C2×M16—22no—
159C2×M16—22no—
160C2×M16Dic2212yes—
161C2×M16C2×Dic1112yes—
162C22×C8D4411yescharacteristic
163C22×C8C22×D1111yescharacteristic
164#117—222no—
165#117—222no—
166#117—441no—
167#117—441no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4—221no—
171C2×C4⋊C4—221no—
172C2×C22⋊C4—441no—
173C2×C22⋊C4—441no—
174C2×C42—441no—
175M32—22no—
176M32C2×Dic1114yescomplemented
177C2×C16—22no—
178#107—112no—
179#107—112no—
180#107—221no—
181#107—221no—
182#107—222no—
183#106—222no—
184#106—222no—
185#106—222no—
186#95—441no—
187C2×C11—21no—
188C2×C11—21no—
189C2×C11—42no—
190C2×C11#185211yescharacteristic
191C2×C11#219011yescharacteristic
192C2×C11#219111yescharacteristic
193C24D8811yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—441no—
199C22×C4—441no—
200C22×C4—441no—
201C22×C4—441no—
202C22×C4D8811yescharacteristic
203C22×C4Dic4412yes—
204C22×C4C4⋊Dic1112yes—
205C22×C4C2×D4411yescharacteristic
206M16—24no—
207M16—24no—
208C2×C8—21no—
209C2×C8—21no—
210C2×C8C4⋊Dic1112yes—
211C2×C8C2×Dic2211yescharacteristic
212C2×C8D4×D1112yes—
213C2×C8#434112yes—
214C2×C8C22×Dic1111yescharacteristic
215C4⋊C4—222no—
216C4⋊C4—222no—
217C4⋊C4—441no—
218C4⋊C4—441no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C22⋊C4—442no—
224C22⋊C4—442no—
225C22⋊C4—882no—
226C42—442no—
227C42—442no—
228C16—24no—
229C11#1292311yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—41no—
233C23—41no—
234C23#6688212yes—
235C23C2×D8811yescharacteristic
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—882no—
245C2×C4—882no—
246C2×C4—881no—
247C2×C4—881no—
248C2×C4—881no—
249C2×C4—881no—
250C2×C4—881no—
251C2×C4—881no—
252C2×C4#6688212yes—
253C2×C4#6693511yescharacteristic
254C2×C4#6693911yescharacteristic
255C2×C4C2×Dic4411yescharacteristic
256C2×C4#6696111yescharacteristic
257C2×C4#6696211yescharacteristic
258C2×C4C2×C4⋊Dic1111yescharacteristic
259C8—22no—
260C8#6693112yes—
261C8D4×Dic1112yes—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—42no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1062234511yescharacteristic
270C22#1062234911yescharacteristic
271C22C2×#6688211yescharacteristic
272C4—22no—
273C4—882no—
274C4—882no—
275C4—1761no—
276C4—1761no—
277C4#1062233511yescharacteristic
278C4#1062235211yescharacteristic
279C4#1062256311yescharacteristic
280C4#1062273411yescharacteristic
281C2—21no—
282C2—21no—
283C2—42no—
284C2#1306880611yescharacteristic
285C2#1307056411yescharacteristic
286C2#1307056911yescharacteristic
subgroupG/H
centerC22#10622345
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#349C2
socleC22×C11#447
prime radicalC24×C11D8
cosocleC22×C8×C11C23
hypercenterC2×#349D11
hypocenterC11#12923
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. #13070404C2semidirect
4. #13066722C2semidirect
16. C11×#349C4semidirect
39. C11×M32C2×C4semidirect
136. #349Dic11semidirect
176. M32C2×Dic11semidirect
229. C11#12923semidirect

Maximal subgroups

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

subgroupindex
#130772062
#130704042
#130686492
#130667222
C2×C11×#3492
#1292311