Finite Group Databasebeta

← #14664403

Subgroups — #14664403

Order 2816.

444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#66897C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066643C214yesmaximal, complemented
4C11×#2487C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C22×C11×C4⋊C4C411yescharacteristic
7C11×#400C2212yes—
8C11×#399C412yes—
9C11×#389—21no—
10C11×#386—21no—
11C11×#385—21no—
12C11×#380—21no—
13C11×#380C411yescharacteristic
14C2×#66897—21no—
15#10622820—21no—
16C4×#4318—21no—
17#10622168C2212yes—
18#10622166C2212yes—
19#10622163—21no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×#4318—22no—
39C2×#4318—41no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95C2×C412yes—
43#66897—24no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—41no—
46#66867—41no—
47C4×C11⋊C8—41no—
48#11790—111nomaximal, Sylow
49C24×C11C22⋊C411yescharacteristic
50C24×C11C22⋊C411yescharacteristic
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—82no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C11×C4⋊C4—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—82no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—82no—
79C42×C11—21no—
80C42×C11—21no—
81#4318—24no—
82#4318—42no—
83#4318—82no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86#2487D1111yescharacteristic
87C4×#100—111no—
88#1465—111no—
89#1353—114no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11#10412yes—
100C23×C11C2×C22⋊C411yescharacteristic
101D4×C11—44no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—81no—
121C2×C4×C11—84no—
122C2×C4×C11#9911yescharacteristic
123C2×C4×C11#9911yescharacteristic
124C2×C4×C11#13712yes—
125C11⋊C8—44no—
126C11⋊C8—82no—
127C2×C4×D4C2×D1111yescharacteristic
128C22×C4⋊C4Dic1111yescharacteristic
129C2×#100—221no—
130#407—221no—
131C4×M16—221no—
132#400C2×D1112yes—
133#399Dic1112yes—
134#389—21no—
135#386—21no—
136#385—21no—
137#380—21no—
138#380Dic1111yescharacteristic
139#343—112no—
140#324—112no—
141#323—221no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—81no—
154C22×C11C2×#9911yescharacteristic
155C22×C11#41911yescharacteristic
156C22×C11C2×#10411yescharacteristic
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—82no—
163C4×C11—82no—
164C4×C11#35212yes—
165C22×D4C22⋊D1111yescharacteristic
166C23×C4—21no—
167C23×C4C2×Dic1111yescharacteristic
168C23×C4C22⋊D1111yescharacteristic
169C2×M16—222no—
170C2×M16—441no—
171C4×D4—41no—
172C4×D4—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4C2×Dic1112yes—
179C2×C4⋊C4C22×D1111yescharacteristic
180C2×C22⋊C4—21no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4C2×Dic1111yescharacteristic
183C2×C22⋊C4C22⋊D1111yescharacteristic
184C2×C42C22⋊D1111yescharacteristic
185#100—224no—
186C22⋊C8—222no—
187C22⋊C8—441no—
188#97—441no—
189C4×C8—441no—
190#95—22no—
191#95—22no—
192#95C2×Dic1112yes—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11—42no—
196C2×C11—81no—
197C2×C11#150811yescharacteristic
198C2×C11C2×#35211yescharacteristic
199C2×C11#213411yescharacteristic
200C24C22⋊Dic1111yescharacteristic
201C24C22⋊Dic1111yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—82no—
215C22×C4C22⋊Dic1111yescharacteristic
216C22×C4C22⋊Dic1111yescharacteristic
217C22×C4C22×Dic1111yescharacteristic
218C22×C4C2×C22⋊D1111yescharacteristic
219C22×C4C2×C22⋊D1111yescharacteristic
220M16—224no—
221M16—442no—
222M16—882no—
223C2×C8—442no—
224C2×C8—442no—
225C4⋊C4—41no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—82no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C22⋊C4—82no—
235C42—21no—
236C42—21no—
237C11#1179011yescharacteristic, complemented, Sylow
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23#6690112yes—
248C23C2×C22⋊Dic1111yescharacteristic
249D4—44no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—84no—
270C2×C4#6689811yescharacteristic
271C2×C4#6689811yescharacteristic
272C2×C4#6699512yes—
273C8—444no—
274C8—882no—
275C22—21no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—81no—
287C22C2×#6689811yescharacteristic
288C22#1062283811yescharacteristic
289C22C2×#6690111yescharacteristic
290C4—22no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—82no—
296C4—82no—
297C4#1062217712yes—
298C2—21no—
299C2—21no—
300C2—42no—
301C2—81no—
302C2#1306713611yescharacteristic
303C2C2×#1062217711yescharacteristic
304C2#1307030811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2487C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C4⋊C4C23
hypercenter#2487D11
hypocenterC11#11790
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #13066643C2semidirect
237. C11#11790semidirect

Maximal subgroups

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

subgroupindex
C4×#668972
#130669542
#130666432
C11×#24872
#1179011