Finite Group Databasebeta

← #14668974

Subgroups — #14668974

Order 2816.

452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 121 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#13077334C211yesmaximal, characteristic
2#13070301C211yesmaximal, characteristic
3#13068418C212yesmaximal, complemented
4#13066744C212yesmaximal, complemented
5C11×#2126C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C2×#67001C411yescharacteristic, complemented
8C2×#67001C2211yescharacteristic
9C11×#410C2212yes—
10#10622850C2212yes—
11#10622847C411yescharacteristic, complemented
12#10622847C2211yescharacteristic
13#10622624—22no—
14#10622624—22no—
15#10622610—22no—
16#10622537C411yescharacteristic, complemented
17C2×#66867C411yescharacteristic, complemented
18C11×#354C412yes—
19C11×#353C412yes—
20#10622186C412yescomplemented
21#10622180C412yescomplemented
22#10622171—22no—
23C2×C11×#41C2×C411yescharacteristic
24C2×C11×#41C2311yescharacteristic
25C11×C4⋊Q8C2×C411yescharacteristic
26C11×#127C2×C411yescharacteristic
27C11×#124C2×C411yescharacteristic
28C11×#124C2×C411yescharacteristic
29C11×#121—22no—
30C4×D4×C11—22no—
31C11×#117—22no—
32C2×C42×C11C2×C411yescharacteristic
33#67001—42no—
34#67001—42no—
35C2×#4318—21no—
36C2×#4318—22no—
37C2×#4318C2×C411yescharacteristic
38C2×#4318C2×C411yescharacteristic
39C2×#4318D412yes—
40C22×C11⋊C8—21no—
41C22×C11⋊C8C2×C411yescharacteristic
42C22×C11⋊C8C2×C411yescharacteristic
43C22×C11⋊C8D412yes—
44C11×#99—22no—
45C11×#99C2×C414yes—
46#66900C2×C414yes—
47#66897—22no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51#66867—21no—
52#66867—21no—
53#66867—42no—
54C4×C11⋊C8—42no—
55#12634—111nomaximal, Sylow
56C11×#41—41no—
57C11×#41—41no—
58C11×#41—41no—
59C11×#41—41no—
60C2×Q8×C11C4211yescharacteristic
61C2×Q8×C11C22×C411yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—22no—
64C2×D4×C11C4211yescharacteristic
65C2×D4×C11C22×C411yescharacteristic
66C2×D4×C11#4112yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D412yes—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—42no—
73C11×C22⋊C4—22no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—24no—
76C42×C11—21no—
77C42×C11—42no—
78C42×C11C4211yescharacteristic
79C42×C11C4211yescharacteristic
80#4318—24no—
81#4318—41no—
82#4318—42no—
83#4318—41no—
84#4318—42no—
85#4318—42no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—22no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8—42no—
93C2×C11⋊C8—42no—
94C2×C11⋊C8C22⋊C411yescharacteristic
95C2×C11⋊C8C22⋊C412yes—
96C2×C11⋊C8C22⋊C411yescharacteristic
97#2932—111no—
98#2132—111no—
99#2126D1111yescharacteristic
100#1757—112no—
101#1395—112no—
102C23×C11—21no—
103C23×C11#11711yescharacteristic
104C23×C11C4×D412yes—
105Q8×C11—41no—
106Q8×C11—41no—
107D4×C11—41no—
108D4×C11—42no—
109D4×C11—41no—
110D4×C11—42no—
111D4×C11—82no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—44no—
122C2×C4×C11—81no—
123C2×C4×C11C2×C4211yescharacteristic
124C2×C4×C11C2×C22⋊C411yescharacteristic
125C2×C4×C11C4×D412yes—
126C11⋊C8—21no—
127C11⋊C8—22no—
128C11⋊C8—44no—
129C11⋊C8—41no—
130C11⋊C8—41no—
131C11⋊C8#9912yes—
132C2×#131—111no—
133C2×#131—111no—
134#532C2×D1111yescharacteristic
135#435—222no—
136#435—222no—
137#423—111no—
138#413—112no—
139#410C2×D1112yes—
140#408—111no—
141#408—111no—
142#405—222no—
143C2×#97—111no—
144#356—112no—
145#355—112no—
146#354Dic1112yes—
147#353Dic1112yes—
148#344—222no—
149C22×C11—22no—
150C22×C11—21no—
151C22×C11—41no—
152C22×C11—42no—
153C22×C11—42no—
154C22×C11—41no—
155C22×C11C4×C22⋊C411yescharacteristic
156C4×C11—21no—
157C4×C11—22no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—84no—
162C4×C11C2×#9911yescharacteristic
163C4×C11#41011yescharacteristic
164C2×#41C4×D1111yescharacteristic
165C2×#41C22×D1111yescharacteristic
166#131—442no—
167#131—442no—
168C2×M16—111no—
169C2×M16—112no—
170C2×M16—111no—
171C2×M16—221no—
172C2×M16—222no—
173C22×C8—111no—
174C22×C8—112no—
175C22×C8—111no—
176C22×C8—221no—
177C4⋊Q8C4×D1111yescharacteristic
178#127C2×Dic1111yescharacteristic
179#124C4×D1111yescharacteristic
180#124C2×Dic1111yescharacteristic
181#121—22no—
182C4×D4—22no—
183#117—22no—
184C2×C42C4×D1111yescharacteristic
185C4⋊C8—222no—
186#101—114no—
187#100—222no—
188#99—22no—
189#99C2×Dic1114yes—
190C22⋊C8—222no—
191C22⋊C8—222no—
192#97—221no—
193#97—221no—
194#97—442no—
195C4×C8—442no—
196C2×C11—21no—
197C2×C11—42no—
198C2×C11—41no—
199C2×C11—81no—
200C2×C11C4×#9911yescharacteristic
201#41—41no—
202#41—41no—
203#41—41no—
204#41—41no—
205C2×Q8C4×Dic1111yescharacteristic
206C2×Q8C2×C4×D1111yescharacteristic
207C2×D4—21no—
208C2×D4—22no—
209C2×D4C4×Dic1111yescharacteristic
210C2×D4#434112yes—
211C2×D4C22×Dic1111yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C2×C4×D1111yescharacteristic
215C22×C4D4×D1112yes—
216M16—224no—
217M16—442no—
218M16—442no—
219M16—441no—
220M16—442no—
221M16—441no—
222C2×C8—111no—
223C2×C8—111no—
224C2×C8—112no—
225C2×C8—222no—
226C2×C8—222no—
227C2×C8—222no—
228C2×C8—221no—
229C2×C8—221no—
230C2×C8—442no—
231C2×C8—442no—
232C2×C8—441no—
233C4⋊C4—22no—
234C4⋊C4—42no—
235C22⋊C4—22no—
236C22⋊C4—22no—
237C22⋊C4—24no—
238C42—21no—
239C42—42no—
240C42C4×Dic1111yescharacteristic
241C42C4×Dic1111yescharacteristic
242C11#1263411yescharacteristic, complemented, Sylow
243C23—21no—
244C23#6693011yescharacteristic
245C23D4×Dic1112yes—
246Q8—41no—
247Q8—41no—
248D4—42no—
249D4—41no—
250D4—41no—
251D4—42no—
252D4—82no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—81no—
264C2×C4C22⋊C4×D1111yescharacteristic
265C2×C4(C22⋊D11)⋊C412yes—
266C2×C4C2×C4×Dic1111yescharacteristic
267C8—112no—
268C8—221no—
269C8—222no—
270C8—444no—
271C8—441no—
272C8—441no—
273C22—22no—
274C22—21no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22C22⋊C4×Dic1111yescharacteristic
280C4—22no—
281C4—21no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—84no—
286C4#1062235311yescharacteristic
287C4D11×#9911yescharacteristic
288C2—21no—
289C2—42no—
290C2—41no—
291C2—81no—
292C2#99×Dic1111yescharacteristic
subgroupG/H
centerC4D11×#99
commutatorC2×C4×C11C2×C42
FrattiniC2×#41C22×D11
FittingC11×#2126C2
socleC2×C11C4×#99
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#2126D11
hypocenterC11#12634
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2126

Complements

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

NH ≅ G/Ntype
3. #13068418C2semidirect
4. #13066744C2semidirect
7. C2×#67001C4semidirect
11. #10622847C4semidirect
16. #10622537C4semidirect
17. C2×#66867C4semidirect
20. #10622186C4semidirect
21. #10622180C4semidirect
242. C11#12634semidirect

Maximal subgroups

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

subgroupindex
#130773342
#130703012
#130684182
#130667442
C11×#21262
#1263411