Finite Group Databasebeta

← #14649539

Subgroups — #14649539

Order 2816.

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

normal subgroups only

This group has 586 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
1C2×#10622550C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3C2×#10622176C212yesmaximal
4#13066494C212yesmaximal
5C11×#2855C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C11×#391C412yescomplemented
9C11×#389C412yescomplemented
10C11×#387—22no—
11C11×#385—21no—
12C11×#381—21no—
13C11×#380C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18#10622550—24no—
19#10622176—24no—
20#10622162—22no—
21C22×Q8×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C23×Dic11—22no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C42×C11—22no—
35C2×C42×C11—22no—
36C2×C42×C11C2×C412yes—
37C2×C42×C11D412yes—
38C22×C11⋊C8—22no—
39C11×#95—22no—
40C11×#95—22no—
41C11×#95—22no—
42C11×#95—21no—
43C11⋊#95—24no—
44C11⋊#95—24no—
45C11⋊#95—22no—
46C11⋊#95D414yes—
47C22⋊(C11⋊C8)—22no—
48C22⋊(C11⋊C8)—22no—
49#9153—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C2×Q8×C11—22no—
52C2×Q8×C11—42no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11#4112yes—
70C22×Dic11—24no—
71C22×Dic11—44no—
72C22×Dic11—44no—
73C22×Dic11—42no—
74C22×Dic11—42no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—44no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—42no—
82C42×C11—24no—
83C42×C11—24no—
84C2×C11⋊C8—44no—
85C2×C11⋊C8—42no—
86#2855D1111yescharacteristic
87C2×#383—111no—
88#1817—111no—
89C2×#328—112no—
90#1294—112no—
91C23×C11—22no—
92C23×C11—22no—
93C23×C11C2×C22⋊C411yescharacteristic
94C23×C11#12011yescharacteristic
95C23×C11#12311yescharacteristic
96C23×C11#13512yes—
97C23×C11#13712yes—
98Q8×C11—82no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11C4×D412yes—
121C2×C4×C11#12112yes—
122C2×Dic11—44no—
123C2×Dic11—44no—
124C2×Dic11—44no—
125C2×Dic11—84no—
126C2×Dic11—84no—
127C11⋊C8—82no—
128C2×C22⋊Q8C2×D1111yescharacteristic
129C22×C42C2×D1111yescharacteristic
130C2×C22⋊C8—112no—
131#391Dic1112yescomplemented
132#389Dic1112yescomplemented
133#387—22no—
134#385—21no—
135#383—224no—
136#381—21no—
137#380C2×D1111yescharacteristic
138C2×#95—112no—
139C2×#95—221no—
140C2×#95—221no—
141#336—222no—
142#328—224no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—24no—
148C22×C11—24no—
149C22×C11#38611yescharacteristic
150C22×C11#41012yes—
151C22×C11#41611yescharacteristic
152C22×C11#41911yescharacteristic
153C22×C11#42112yes—
154C22×C11#45212yes—
155C22×C11#48512yes—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—42no—
159C4×C11—42no—
160C4×C11—81no—
161C4×C11—81no—
162C4×C11—82no—
163Dic11—84no—
164C22×Q8C2×Dic1111yescharacteristic
165C23×C4—222no—
166C23×C4C22⋊D1111yescharacteristic
167C23×C4C22⋊D1111yescharacteristic
168C23×C4C22×D1111yescharacteristic
169C22×C8—222no—
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×Dic1111yescharacteristic
175C2×C4⋊C4C2×Dic1112yes—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42—22no—
179C2×C42—22no—
180C2×C42C2×Dic1112yes—
181C2×C42C22⋊D1112yes—
182C22⋊C8—222no—
183C22⋊C8—222no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—21no—
188#95—114no—
189#95—224no—
190#95—224no—
191#95—222no—
192C2×C11—22no—
193C2×C11—22no—
194C2×C11#151512yes—
195C2×C11#152112yes—
196C2×C11#187311yescharacteristic
197C2×C11#189711yescharacteristic
198C2×C11#189911yescharacteristic
199C24C2×C22⋊D1111yescharacteristic
200C2×Q8—22no—
201C2×Q8—42no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—224no—
214C22×C4—444no—
215C22×C4—444no—
216C22×C4—442no—
217C22×C4—442no—
218C22×C4C22⋊Dic1112yes—
219C22×C4C22⋊Dic1112yes—
220C22×C4D4×D1112yes—
221C22×C4#434112yes—
222C22×C4C22×Dic1111yescharacteristic
223C22×C4C2×C22⋊D1111yescharacteristic
224C2×C8—444no—
225C2×C8—442no—
226C4⋊C4—22no—
227C4⋊C4—42no—
228C4⋊C4—44no—
229C4⋊C4—42no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—42no—
233C42—24no—
234C42—24no—
235C11#915311yescharacteristic, complemented, Sylow
236C23—22no—
237C23—22no—
238C23#6698811yescharacteristic
239C23#6699011yescharacteristic
240C23#6699512yes—
241C23#6700312yes—
242C23C2×C22⋊Dic1111yescharacteristic
243Q8—82no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—444no—
266C2×C4—444no—
267C2×C4—444no—
268C2×C4—884no—
269C2×C4—884no—
270C2×C4D4×Dic1112yes—
271C2×C4#6699212yes—
272C8—882no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—24no—
278C22—24no—
279C22#1062265812yes—
280C22#1062266012yes—
281C22#1062283311yescharacteristic
282C22#1062283811yescharacteristic
283C22#1062284611yescharacteristic
284C22#1062284912yes—
285C22#1062285312yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—81no—
291C4—81no—
292C4—82no—
293C4—884no—
294C2—22no—
295C2—22no—
296C2#1306716712yes—
297C2#1306719312yes—
298C2#1306892911yescharacteristic
299C2#1306906511yescharacteristic
300C2#1306907511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2855C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2855D11
hypocenterC11#9153
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
8. C11×#391C4semidirect
9. C11×#389C4semidirect
131. #391Dic11semidirect
132. #389Dic11semidirect
235. C11#9153semidirect

Maximal subgroups

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

subgroupindex
C2×#106225502
#130686842
C2×#106221762
#130664942
C11×#28552
#915311