Finite Group Databasebeta

← #14853480

Subgroups — #14853480

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077003C211yesmaximal, characteristic, complemented
2#13070173C212yesmaximal, complemented
3#13069847C212yesmaximal
4#13069316C214yesmaximal, complemented
5#13068626C212yesmaximal, complemented
6#13068626C212yesmaximal, complemented
7#13068469C211yesmaximal, characteristic, complemented
8C4×C11×#127C211yesmaximal, characteristic
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11—22no—
11C2×C4×D4×C11C2212yes—
12C11×#390—22no—
13C11×#390C2212yes—
14C11×#384C2211yescharacteristic
15C43×C11C2211yescharacteristic
16C2×#66896C2214yes—
17C2×#66896C2214yes—
18#10622549C2211yescharacteristic
19#10622549C2211yescharacteristic
20#10622546—22no—
21#10622546—22no—
22#10622541C2212yes—
23#10622541C2212yes—
24C2×C4⋊(C11⋊C8)C2212yes—
25C2×#66867C2212yes—
26#10622167C2214yes—
27#10622167C2214yes—
28#10622162C2212yes—
29C22×D4×C11—22no—
30C22×D4×C11C2312yes—
31C23×C4×C11—22no—
32C11×#127—24no—
33C4×D4×C11—24no—
34C4×D4×C11—24no—
35C4×D4×C11—48no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4C2312yes—
38C2×C11×C22⋊C4—24no—
39C2×C11×C22⋊C4—22no—
40C2×C42×C11D412yes—
41C2×C42×C11D412yes—
42C2×C42×C11C2311yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C2×C4⋊Dic11C2312yes—
46C2×C4⋊Dic11C2312yes—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4—22no—
49C22×C11⋊C8C2314yes—
50#66896—28no—
51#66896—44no—
52C11⋊#95—22no—
53C11⋊#95—22no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C4⋊(C11⋊C8)—24no—
59#66867—42no—
60#29127—111nomaximal, Sylow
61C24×C11—22no—
62C2×D4×C11—28no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—44no—
69C2×D4×C11—44no—
70C2×D4×C11#4114yes—
71C22×C4×C11—22no—
72C22×C4×C11—48no—
73C22×C4×C11—44no—
74C22×C4×C11C2×D412yes—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2411yescharacteristic
79C22×Dic11—22no—
80C22×Dic11—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—44no—
84C11×C22⋊C4—48no—
85C11×C22⋊C4—44no—
86C42×C11—24no—
87C42×C11—22no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—42no—
91C42×C11#4114yes—
92C4⋊Dic11—24no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95Dic11⋊C4—44no—
96Dic11⋊C4—44no—
97C2×C11⋊C8—24no—
98C2×C11⋊C8—24no—
99C2×C11⋊C8—24no—
100#2864—111no—
101C4×#127D1111yescharacteristic
102#2099—112no—
103#2041—112no—
104#1936—114no—
105#1804—112no—
106#1804—112no—
107#1767—111no—
108C23×C11—24no—
109C23×C11—42no—
110C23×C11—42no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11C22×D411yescharacteristic
114D4×C11—24no—
115D4×C11—24no—
116D4×C11—416no—
117D4×C11—42no—
118D4×C11—42no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—42no—
127C2×C4×C11—44no—
128C2×C4×C11—88no—
129C2×C4×C11#12412yes—
130C2×C4×C11#12412yes—
131C2×C4×C11AGL(1,ℤ/8)14yes—
132C2×C4×C11C2×#4112yes—
133C2×C4×C11C2×#4112yes—
134C2×C4×C11H(5,𝔽2)11yescharacteristic
135C2×C4×C112−1+411yescharacteristic
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C11⋊C8—44no—
143C2×#127C2×D1111yescharacteristic
144C2×C4×D4—22no—
145C2×C4×D4C2×D1112yes—
146C2×C4⋊C8—112no—
147C2×#102—114no—
148C2×#102—114no—
149C2×#97—112no—
150#390—22no—
151#390C2×D1112yes—
152#389—112no—
153#389—112no—
154#387—222no—
155#387—222no—
156#384C2×D1111yescharacteristic
157#382—111no—
158#382—111no—
159C43C2×D1111yescharacteristic
160#340—114no—
161#340—114no—
162#336—112no—
163C22×C11—44no—
164C22×C11—48no—
165C22×C11—82no—
166C22×C11—82no—
167C22×C11—84no—
168C22×C11#52511yescharacteristic
169C22×C11C2×#12411yescharacteristic
170C22×C11#53711yescharacteristic
171C22×C11C2×AGL(1,ℤ/8)12yes—
172C22×C11#57512yes—
173C4×C11—24no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—42no—
177C4×C11—82no—
178C4×C11#55212yes—
179C4×C11#55312yes—
180Dic11—82no—
181Dic11—82no—
182C22×D4—22no—
183C22×D4C22×D1112yes—
184C23×C4—22no—
185C22×C8—114no—
186#127—24no—
187C4×D4—24no—
188C4×D4—24no—
189C4×D4—48no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4C22×D1112yes—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—22no—
198C2×C42C22⋊D1112yes—
199C2×C42C22⋊D1112yes—
200C2×C42C22×D1111yescharacteristic
201C2×C42C22×D1111yescharacteristic
202C2×C42C22×D1111yescharacteristic
203C4⋊C8—224no—
204#102—228no—
205#102—444no—
206#97—442no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211#95—222no—
212#95—222no—
213C2×C11—84no—
214C2×C11#256211yescharacteristic
215C2×C11#311412yes—
216C2×C11#313511yescharacteristic
217C2×C11#313811yescharacteristic
218C2×C11#325112yes—
219C24—22no—
220C2×D4—28no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—44no—
227C2×D4—44no—
228C2×D4#433914yes—
229C22×C4—22no—
230C22×C4—48no—
231C22×C4—44no—
232C22×C4—222no—
233C22×C4—222no—
234C22×C4C2×C22⋊D1112yes—
235C22×C4C2×C22⋊D1112yes—
236C22×C4C2×C22⋊D1111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238C22×C4C23×D1111yescharacteristic
239C2×C8—224no—
240C2×C8—224no—
241C2×C8—224no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—44no—
245C4⋊C4—224no—
246C4⋊C4—222no—
247C4⋊C4—222no—
248C4⋊C4—444no—
249C4⋊C4—444no—
250C22⋊C4—48no—
251C22⋊C4—44no—
252C42—24no—
253C42—22no—
254C42—21no—
255C42—21no—
256C42—42no—
257C42#434114yes—
258C11#2912711yescharacteristic, complemented, Sylow
259C23—24no—
260C23—44no—
261C23—42no—
262C23—44no—
263C23—42no—
264C23C22×C22⋊D1111yescharacteristic
265D4—24no—
266D4—24no—
267D4—416no—
268D4—42no—
269D4—42no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—88no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—442no—
286C2×C4#6698514yes—
287C2×C4#6698912yes—
288C2×C4#6698912yes—
289C2×C4C2×#433912yes—
290C2×C4C2×#434112yes—
291C2×C4#6704211yescharacteristic
292C2×C4#6704311yescharacteristic
293C8—444no—
294C22—44no—
295C22—48no—
296C22—84no—
297C22—82no—
298C22—82no—
299C22#1062332211yescharacteristic
300C22C2×#6698512yes—
301C22C2×#6698911yescharacteristic
302C22#1062335312yes—
303C22#1062336411yescharacteristic
304C4—22no—
305C4—22no—
306C4—24no—
307C4—42no—
308C4—82no—
309C4—882no—
310C4—882no—
311C4#1062307212yes—
312C4#1062309612yes—
313C2—84no—
314C2#1307378211yescharacteristic
315C2#1307875412yes—
316C2#1307896111yescharacteristic
317C2#1307899011yescharacteristic
318C2#1307997212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#127C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC4×#127D11
hypocenterC11#29127
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. #13077003C2semidirect
2. #13070173C2semidirect
4. #13069316C2semidirect
5. #13068626C2semidirect
6. #13068626C2semidirect
7. #13068469C2semidirect
258. C11#29127semidirect

Maximal subgroups

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

subgroupindex
#130770032
#130701732
#130698472
#130693162
#130686262
#130684692
C4×C11×#1272
#2912711