Finite Group Databasebeta

← #14649784

Subgroups — #14649784

Order 2816.

504 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 127 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#13077180C211yesmaximal, characteristic
2#13074437C211yesmaximal, characteristic
3#13067300C212yesmaximal, complemented
4#13066475C212yesmaximal, complemented
5C11×#1458C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C22×#4318—21no—
8C2×#66922C2211yescharacteristic
9C11×#431C2212yes—
10#10622825—21no—
11#10622612—24no—
12#10622599C412yes—
13#10622592—21no—
14#10622562C412yes—
15#10622560—21no—
16#10622549C2211yescharacteristic
17#10622541—21no—
18#10622537—21no—
19#10622537C2212yes—
20C11×#324—21no—
21C11×#323—21no—
22#10622120—24no—
23C23×C4×C11D411yescharacteristic
24C22×Dic22—21no—
25C11×#117—22no—
26C11×#117—22no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C412yes—
37C2×Dic11⋊C4—22no—
38C2×#4318—22no—
39C2×#4318—22no—
40C2×#4318—42no—
41C2×#4318—42no—
42C22×C11⋊C8—22no—
43#66922—22no—
44#66922—22no—
45C11×C4⋊C8—22no—
46C11×C22⋊C8—22no—
47C4×C8×C11—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—21no—
51C11⋊#95C2×C412yes—
52C4⋊(C11⋊C8)—24no—
53C4⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)D414yes—
55#9193—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11SD1612yes—
65C22×C4×C11Q1612yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—22no—
70C22×Dic11—22no—
71C2×Dic22—42no—
72C2×Dic22—82no—
73C2×C8×C11—42no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C22⋊C4—22no—
77C11×C22⋊C4—22no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11C2×D412yes—
81C42×C11#4112yes—
82C22⋊Dic11—82no—
83C4⋊Dic11—24no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88Dic11⋊C4—82no—
89#4318—44no—
90#4318—42no—
91#4318—42no—
92C2×C11⋊C8—24no—
93C2×C11⋊C8—44no—
94#2905—111no—
95#2628—111no—
96#1549—112no—
97#1458D1111yescharacteristic
98#1286—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11#10312yes—
104C23×C11C2×C22⋊C411yescharacteristic
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11#10312yes—
118C2×C4×C11C4×D412yes—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12112yes—
121C2×C4×C11#12311yescharacteristic
122C2×C4×C11C2×SD1611yescharacteristic
123C2×C4×C11C2×Q1611yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132Dic22—84no—
133C8×C11—82no—
134C11⋊C8—44no—
135C22×M16—221no—
136C2×C4⋊Q8—111no—
137C2×#117C2×D1111yescharacteristic
138#431C2×D1112yes—
139#424—224no—
140#423—112no—
141#423—221no—
142#400—112no—
143#399—112no—
144#395—221no—
145#393—221no—
146#389—221no—
147#382—111no—
148#380—221no—
149#332—224no—
150#324—21no—
151#323—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—22no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—81no—
159C22×C11#38611yescharacteristic
160C22×C11C2×#10311yescharacteristic
161C22×C11#41711yescharacteristic
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—22no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11#45011yescharacteristic
168C4×C11#45111yescharacteristic
169C4×C11#48311yescharacteristic
170C4×C11#48411yescharacteristic
171Dic11—82no—
172Dic11—82no—
173C22×Q8—221no—
174C23×C4D4411yescharacteristic
175C2×M16—222no—
176C2×M16—222no—
177C2×M16—442no—
178C2×M16—442no—
179C22×C8—222no—
180C4⋊Q8—222no—
181C4⋊Q8—222no—
182#117—22no—
183#117—22no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4C4×D1111yescharacteristic
189C2×C4⋊C4C22⋊D1111yescharacteristic
190C2×C22⋊C4—222no—
191C2×C22⋊C4C4×D1111yescharacteristic
192C2×C22⋊C4C22⋊D1111yescharacteristic
193C2×C42D4411yescharacteristic
194C2×C42C22×D1111yescharacteristic
195C4⋊C8—22no—
196C4⋊C8—114no—
197C4⋊C8—224no—
198C4⋊C8—222no—
199C22⋊C8—22no—
200C4×C8—22no—
201#95—112no—
202#95—222no—
203#95—222no—
204#95—221no—
205C2×C11—21no—
206C2×C11—21no—
207C2×C11—42no—
208C2×C11#187211yescharacteristic
209C2×C11#191011yescharacteristic
210C2×C11#191511yescharacteristic
211C24(C2×D11)⋊C411yescharacteristic
212C2×Q8—442no—
213C2×Q8—882no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—222no—
219C22×C4—222no—
220C22×C4#431412yes—
221C22×C4Dic4412yes—
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—444no—
229M16—442no—
230M16—442no—
231C2×C8—42no—
232C2×C8—224no—
233C2×C8—444no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—224no—
237C4⋊C4—441no—
238C4⋊C4—441no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C4⋊C4—882no—
242C22⋊C4—22no—
243C22⋊C4—22no—
244C22⋊C4—882no—
245C42—21no—
246C42—21no—
247C42D4×D1112yes—
248C42#434112yes—
249C11#919311yescharacteristic, complemented, Sylow
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23#6688012yes—
255C23C2×(C2×D11)⋊C411yescharacteristic
256Q8—884no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—442no—
270C2×C4—442no—
271C2×C4—442no—
272C2×C4—442no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4#6688012yes—
276C2×C4(C22⋊D11)⋊C412yes—
277C2×C4#6693511yescharacteristic
278C2×C4#6693911yescharacteristic
279C2×C4C2×#431411yescharacteristic
280C2×C4C2×Dic4411yescharacteristic
281C2×C4#6696111yescharacteristic
282C2×C4#6696211yescharacteristic
283C2×C4#6699212yes—
284C8—82no—
285C8—444no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22#1062257111yescharacteristic
294C22C2×#6688011yescharacteristic
295C22#1062274611yescharacteristic
296C4—22no—
297C4—22no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—882no—
302C4—882no—
303C4#1062233411yescharacteristic
304C4#1062233511yescharacteristic
305C4#1062234411yescharacteristic
306C4#1062235211yescharacteristic
307C2—21no—
308C2—21no—
309C2—42no—
310C2#1306892111yescharacteristic
311C2#1306914111yescharacteristic
312C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1458C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1458D11
hypocenterC11#9193
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13067300C2semidirect
4. #13066475C2semidirect
249. C11#9193semidirect

Maximal subgroups

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

subgroupindex
#130771802
#130744372
#130673002
#130664752
C11×#14582
#919311