Finite Group Databasebeta

← #14647809

Subgroups — #14647809

Order 2816.

418 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077645C211yesmaximal, characteristic
2#13067399C212yesmaximal, complemented
3#13066937C211yesmaximal, characteristic
4#13066515C212yesmaximal, complemented
5C11×#1955C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C11×C4⋊C8C2211yescharacteristic
8C2×C11×C22⋊C8—21no—
9C2×C11×C22⋊C8—21no—
10C2×C11×#97C2211yescharacteristic
11#10622820—21no—
12C2×C22⋊(C11⋊C8)—21no—
13#10622624—22no—
14#10622624—22no—
15#10622539C2212yes—
16#10622538C2212yes—
17#10622163C412yes—
18#10622163C412yes—
19#10622118—22no—
20#10622117—22no—
21C22×D4×C11Q811yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C22×C8×C11—21no—
25C22×C8×C11—21no—
26C4×D4×C11—22no—
27C4×D4×C11—22no—
28C2×C11×C4⋊C4Q811yescharacteristic
29C2×C11×C22⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4C2×C411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×#4318—21no—
33C2×#4318—21no—
34C22×C11⋊C8—21no—
35C22×C11⋊C8—21no—
36C11×C4⋊C8—22no—
37C11×C22⋊C8—42no—
38C11×C22⋊C8—42no—
39C11×#97—22no—
40C22⋊(C11⋊C8)—22no—
41C22⋊(C11⋊C8)—22no—
42C22⋊(C11⋊C8)—22no—
43C22⋊(C11⋊C8)C2×C414yes—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D412yes—
46C4⋊(C11⋊C8)D412yes—
47#66867—22no—
48C4×C11⋊C8—22no—
49#8864—111nomaximal, Sylow
50C24×C11C4⋊C411yescharacteristic
51C24×C11C4⋊C411yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11C4⋊C411yescharacteristic
64C22×C4×C11C4⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×Q811yescharacteristic
68C2×C8×C11—22no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—22no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4—22no—
77C42×C11C2×D412yes—
78C42×C11#4112yes—
79#4318—81no—
80#4318—81no—
81C2×C11⋊C8—24no—
82C2×C11⋊C8—22no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—81no—
85C2×C11⋊C8—81no—
86#2973—111no—
87#1955D1111yescharacteristic
88#1573—112no—
89#1460—111no—
90#1302—112no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11#10812yes—
101C23×C11C2×C4⋊C411yescharacteristic
102D4×C11—44no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11C4×D412yes—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11C22⋊Q812yes—
121C2×C4×C11#12311yescharacteristic
122C8×C11—42no—
123C8×C11—81no—
124C11⋊C8—44no—
125C11⋊C8—42no—
126C11⋊C8—42no—
127C2×C4×D4C2×D1111yescharacteristic
128#435—222no—
129#435—222no—
130#432—112no—
131#431—112no—
132C2×C4⋊C8C2×D1111yescharacteristic
133#407—221no—
134C2×C22⋊C8—21no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—221no—
137C2×#97C2×D1111yescharacteristic
138#335—222no—
139#334—222no—
140#323—112no—
141#323—112no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—22no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—81no—
153C22×C11—81no—
154C22×C11#38511yescharacteristic
155C22×C11C2×#10811yescharacteristic
156C22×C11#43011yescharacteristic
157C4×C11—22no—
158C4×C11—21no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11#45311yescharacteristic
163C4×C11#45511yescharacteristic
164C22×D4Dic2211yescharacteristic
165C23×C4C22⋊D1111yescharacteristic
166C23×C4C22⋊D1111yescharacteristic
167C2×M16—221no—
168C2×M16—221no—
169C22×C8—21no—
170C22×C8—21no—
171C22×C8—221no—
172C22×C8—221no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C4⋊C4Dic2211yescharacteristic
176C2×C22⋊C4C4×D1111yescharacteristic
177C2×C22⋊C4C4×D1111yescharacteristic
178C2×C42C22×D1111yescharacteristic
179C4⋊C8—22no—
180C4⋊C8—112no—
181C4⋊C8—112no—
182C4⋊C8—222no—
183C22⋊C8—42no—
184C22⋊C8—42no—
185C22⋊C8—114no—
186C22⋊C8—222no—
187C22⋊C8—222no—
188C22⋊C8—222no—
189#97—22no—
190#97—222no—
191C4×C8—222no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11—42no—
195C2×C11—81no—
196C2×C11#185511yescharacteristic
197C2×C11#185611yescharacteristic
198C2×C11#186811yescharacteristic
199C24Dic11⋊C411yescharacteristic
200C24Dic11⋊C411yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4Dic11⋊C411yescharacteristic
213C22×C4Dic11⋊C411yescharacteristic
214C22×C4C2×Dic2211yescharacteristic
215C22×C4C2×C4×D1111yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217M16—881no—
218M16—881no—
219C2×C8—22no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—224no—
226C2×C8—222no—
227C2×C8—222no—
228C2×C8—881no—
229C2×C8—881no—
230C4⋊C4—22no—
231C22⋊C4—22no—
232C22⋊C4—22no—
233C42D4×D1112yes—
234C42#434112yes—
235C11#886411yescharacteristic, complemented, Sylow
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23#6688612yes—
246C23C2×Dic11⋊C411yescharacteristic
247D4—44no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4#6693112yes—
264C2×C4(C22⋊D11)⋊C412yes—
265C2×C4#6698811yescharacteristic
266C2×C4#6699011yescharacteristic
267C8—42no—
268C8—81no—
269C8—444no—
270C8—442no—
271C8—442no—
272C22—21no—
273C22—21no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22—81no—
284C22#1062255911yescharacteristic
285C22C2×#6688611yescharacteristic
286C22#1062273711yescharacteristic
287C4—22no—
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4#1062267411yescharacteristic
293C4#1062269011yescharacteristic
294C2—21no—
295C2—21no—
296C2—42no—
297C2—81no—
298C2#1306882011yescharacteristic
299C2#1306882511yescharacteristic
300C2#1306890111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1955C2
socleC22×C11#385
prime radicalC22×D4×C11Q8
cosocleC2×C42×C11C23
hypercenter#1955D11
hypocenterC11#8864
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #13067399C2semidirect
4. #13066515C2semidirect
235. C11#8864semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130673992
#130669372
#130665152
C11×#19552
#886411