Finite Group Databasebeta

← #14649831

Subgroups — #14649831

Order 2816.

516 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 115 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#13074429C211yesmaximal, characteristic
2#13067187C212yesmaximal
3C2×#10622166C211yesmaximal, characteristic
4#13066483C212yesmaximal
5C11×#2313C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C11×#387—24no—
9C11×#381—21no—
10C11×#380C2212yes—
11C4×C11×C22⋊C4—21no—
12#10622825C2211yescharacteristic
13#10622824—21no—
14#10622823—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622599C412yescomplemented
17#10622597—22no—
18#10622592C412yescomplemented
19#10622166—22no—
20#10622090—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4C2×C412yes—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11—22no—
32C2×C22⋊Dic11—21no—
33C2×C22⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36#66977—22no—
37#66977—22no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—22no—
40C22×C11⋊C8—22no—
41C11×#95—22no—
42C11×#95—24no—
43C11×#95D414yes—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95C2×C412yes—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50#9202—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—21no—
58C22×C4×C11—24no—
59C22×C4×C11—81no—
60C22×C4×C11—81no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D412yes—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4112yes—
67C22×Dic11—21no—
68C22×Dic11—22no—
69C22×Dic11—21no—
70C2×Dic22—22no—
71C2×Dic22—81no—
72C11×C4⋊C4—24no—
73C11×C4⋊C4—24no—
74C11×C4⋊C4—82no—
75C11×C22⋊C4—42no—
76C11×C22⋊C4—42no—
77C42×C11—82no—
78C22⋊Dic11—41no—
79C22⋊Dic11—41no—
80C22⋊Dic11—42no—
81C4⋊Dic11—22no—
82C4⋊Dic11—81no—
83Dic11⋊C4—42no—
84Dic11⋊C4—82no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—82no—
87#2627—111no—
88#2313D1111yescharacteristic
89#1520—112no—
90C2×#324—111no—
91#1289—112no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11C2×C22⋊C411yescharacteristic
95C23×C11#12011yescharacteristic
96C23×C11#12311yescharacteristic
97C23×C11#13512yes—
98C23×C11#13712yes—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—44no—
112C2×C4×C11—44no—
113C2×C4×C11—44no—
114C2×C4×C11—81no—
115C2×C4×C11C4×D412yes—
116C2×C4×C11#12112yes—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—41no—
122C2×Dic11—41no—
123C2×Dic11—42no—
124Dic22—82no—
125C11⋊C8—82no—
126C2×C22⋊Q8—111no—
127C22×C4⋊C4C2×D1111yescharacteristic
128C2×C22⋊C8—112no—
129#400—112no—
130#398—222no—
131#395—112no—
132#387—24no—
133#385—221no—
134#381—21no—
135#381—221no—
136#380—111no—
137#380C2×D1112yes—
138C4×C22⋊C4—21no—
139#328—224no—
140#324—222no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11#38611yescharacteristic
150C22×C11#41611yescharacteristic
151C22×C11#41911yescharacteristic
152C22×C11#45212yes—
153C22×C11#48512yes—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—42no—
157C4×C11—42no—
158C4×C11—84no—
159Dic11—82no—
160Dic11—81no—
161Dic11—81no—
162C22×Q8—111no—
163C23×C4C22⋊D1111yescharacteristic
164C23×C4C22⋊D1111yescharacteristic
165C23×C4C22×D1111yescharacteristic
166C22×C8—222no—
167C22⋊Q8—222no—
168C22⋊Q8—222no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—111no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4C4×D1112yes—
177C2×C4⋊C4D4412yes—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—221no—
180C2×C22⋊C4—221no—
181C2×C42—22no—
182C22⋊C8—222no—
183C22⋊C8—222no—
184#95—22no—
185#95—24no—
186#95—112no—
187#95—222no—
188#95—222no—
189#95—222no—
190#95C22⋊D1114yes—
191C2×C11—21no—
192C2×C11—22no—
193C2×C11—21no—
194C2×C11—22no—
195C2×C11#187311yescharacteristic
196C2×C11#191211yescharacteristic
197C2×C11#191311yescharacteristic
198C24C2×C22⋊D1111yescharacteristic
199C2×Q8—222no—
200C2×Q8—881no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—24no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—222no—
211C22×C4—221no—
212C22×C4—221no—
213C22×C4(C2×D11)⋊C412yes—
214C22×C4(C2×D11)⋊C412yes—
215C22×C4C2×C4×D1111yescharacteristic
216C22×C4C2×D4411yescharacteristic
217C22×C4#433912yes—
218C22×C4C2×C22⋊D1112yes—
219C2×C8—442no—
220C2×C8—882no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—82no—
224C4⋊C4—222no—
225C4⋊C4—442no—
226C4⋊C4—882no—
227C4⋊C4—881no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—441no—
231C22⋊C4—442no—
232C22⋊C4—441no—
233C42—82no—
234C11#920211yescharacteristic, complemented, Sylow
235C23—41no—
236C23—41no—
237C23C2×(C2×D11)⋊C411yescharacteristic
238C23#6698211yescharacteristic
239C23#6700312yes—
240C23#6700412yes—
241C23#6700611yescharacteristic
242Q8—882no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—81no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—442no—
266C2×C4C4×C22⋊D1112yes—
267C2×C4#6698312yes—
268C8—882no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22#1062260912yes—
278C22#1062261511yescharacteristic
279C22#1062261711yescharacteristic
280C22#1062282611yescharacteristic
281C22#1062285212yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—84no—
287C4—882no—
288C4—881no—
289C4—881no—
290C2—22no—
291C2—21no—
292C2—22no—
293C2—21no—
294C2#1306892811yescharacteristic
295C2#1306915311yescharacteristic
296C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2313C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2313D11
hypocenterC11#9202
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
16. #10622599C4semidirect
18. #10622592C4semidirect
234. C11#9202semidirect

Maximal subgroups

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

subgroupindex
#130744292
#130671872
C2×#106221662
#130664832
C11×#23132
#920211