Finite Group Databasebeta

← #14680548

Subgroups — #14680548

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622842C211yesmaximal, characteristic
2C2×#10622546C213yesmaximal
3#13066887C211yesmaximal, characteristic
4#13066875C213yesmaximal
5#13066866C213yesmaximal
6#13066843C213yesmaximal
7C22×C4×Q8×C11C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C2×C4×Q8×C11—212no—
10C22×C11×C4⋊C4C2213yes—
11C22×C42×C11C2213yes—
12C22×Dic11⋊C4C2211yescharacteristic
13C22×Dic11⋊C4C2213yes—
14#10622842C418yescomplemented
15C2×C11⋊#95C2213yes—
16C2×C11⋊#95C2213yes—
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2216yes—
21C2×C11⋊#95C2213yes—
22#10622546—212no—
23C22×Q8×C11—26no—
24C22×Q8×C11—26no—
25C22×Q8×C11C2×C414yes—
26C23×C4×C11C2313yes—
27C23×C4×C11C2313yes—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11C2311yescharacteristic
30C23×Dic11C2313yes—
31C23×Dic11C2311yescharacteristic
32C23×Dic11C2313yes—
33C4×Q8×C11—232no—
34C2×C11×C4⋊C4—212no—
35C2×C11×C4⋊C4—26no—
36C2×C42×C11—212no—
37C2×C42×C11D4112yes—
38C2×Dic11⋊C4—26no—
39C2×Dic11⋊C4—26no—
40C2×Dic11⋊C4—26no—
41C2×Dic11⋊C4C2×C4112yes—
42C11⋊#95—26no—
43C11⋊#95—26no—
44C11⋊#95—26no—
45C11⋊#95—26no—
46C11⋊#95—26no—
47C11⋊#95—46no—
48C11⋊#95C2×C4112yes—
49#14302—111nomaximal, Sylow
50C24×C11C2411yescharacteristic
51C2×Q8×C11—28no—
52C2×Q8×C11—224no—
53C2×Q8×C11—224no—
54C22×C4×C11—26no—
55C22×C4×C11—26no—
56C22×C4×C11—23no—
57C22×C4×C11—21no—
58C22×C4×C11—26no—
59C22×C4×C11—23no—
60C22×C4×C11—26no—
61C22×C4×C11—23no—
62C22×C4×C11C22×C416yes—
63C22×C4×C11C2×D416yes—
64C22×C4×C11C2×D416yes—
65C22×C4×C11C2×D416yes—
66C22×C4×C11#4116yes—
67C22×Dic11—23no—
68C22×Dic11—23no—
69C22×Dic11—23no—
70C22×Dic11—23no—
71C22×Dic11—23no—
72C22×Dic11—23no—
73C22×Dic11—26no—
74C22×Dic11—23no—
75C22×Dic11—23no—
76C22×Dic11—23no—
77C22×Dic11—23no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—26no—
81C22×Dic11—21no—
82C22×Dic11—23no—
83C22×Dic11C22×C416yes—
84C22×Dic11C22×C412yes—
85C11×C4⋊C4—224no—
86C42×C11—224no—
87Dic11⋊C4—224no—
88Dic11⋊C4—44no—
89C22×C4×Q8D1111yescharacteristic
90C2×#395—111no—
91C2×#387—113no—
92#1446—111no—
93#1442—113no—
94#1441—113no—
95#1434—113no—
96C23×C11C23×C411yescharacteristic
97C23×C11C22×D413yes—
98C23×C11C2×#4113yes—
99C23×C11H(5,𝔽2)11yescharacteristic
100C23×C112−1+413yes—
101C23×C112−1+411yescharacteristic
102C23×C112−1+413yes—
103Q8×C11—232no—
104C2×C4×C11—212no—
105C2×C4×C11—26no—
106C2×C4×C11—26no—
107C2×C4×C11—212no—
108C2×C4×C11—26no—
109C2×C4×C11—26no—
110C2×C4×C11—26no—
111C2×C4×C11—26no—
112C2×C4×C11—26no—
113C2×C4×C11—46no—
114C2×C4×C11—46no—
115C2×C4×C11C4×D4112yes—
116C2×C4×C11#12014yes—
117C2×Dic11—26no—
118C2×Dic11—26no—
119C2×Dic11—26no—
120C2×Dic11—26no—
121C2×Dic11—41no—
122C2×Dic11—43no—
123C2×Dic11—43no—
124C2×Dic11—43no—
125C2×Dic11—43no—
126C2×Dic11—43no—
127C2×Dic11—41no—
128C2×Dic11—43no—
129C2×Dic11—43no—
130C2×Dic11—43no—
131C2×Dic11—43no—
132C2×Dic11—43no—
133C2×Dic11—46no—
134C2×Dic11—46no—
135C23×Q8C2×D1111yescharacteristic
136C2×C4×Q8—212no—
137C22×C4⋊C4—113no—
138C22×C4⋊C4—111no—
139C22×C4⋊C4C2×D1113yes—
140C22×C42C2×D1113yes—
141#395—118no—
142#387—2212no—
143C2×#95—113no—
144C2×#95—113no—
145C2×#95—113no—
146C2×#95—113no—
147C2×#95—113no—
148C2×#95—113no—
149C2×#95—116no—
150C22×C11C2×C4×D413yes—
151C22×C11#51913yes—
152C22×C11#52011yescharacteristic
153C22×C11C2×#12011yescharacteristic
154C22×C11#52513yes—
155C22×C11#53613yes—
156C22×C11#53613yes—
157C22×C11#53613yes—
158C22×C11#53713yes—
159C22×C11#54113yes—
160C22×C11#54116yes—
161C22×C11#54213yes—
162C4×C11—24no—
163C4×C11—212no—
164C4×C11—46no—
165Dic11—46no—
166Dic11—42no—
167Dic11—81no—
168Dic11—83no—
169C22×Q8—26no—
170C22×Q8—26no—
171C22×Q8C4×D1114yes—
172C23×C4—111no—
173C23×C4—113no—
174C23×C4—111no—
175C23×C4—113no—
176C23×C4C22×D1113yes—
177C23×C4C22×D1113yes—
178C23×C4C22×D1111yescharacteristic
179C4×Q8—232no—
180C2×C4⋊C4—212no—
181C2×C4⋊C4—26no—
182C2×C4⋊C4—1112no—
183C2×C4⋊C4—226no—
184C2×C4⋊C4—226no—
185C2×C4⋊C4—226no—
186C2×C42—212no—
187C2×C42C22⋊D11112yes—
188#95—1112no—
189#95—226no—
190#95—226no—
191#95—226no—
192#95—226no—
193#95—226no—
194#95—446no—
195C2×C11C4×#12011yescharacteristic
196C2×C11#232313yes—
197C2×C11#232713yes—
198C2×C11#261411yescharacteristic
199C2×C11#261611yescharacteristic
200C2×C11#263413yes—
201C2×C11#263713yes—
202C24C23×D1111yescharacteristic
203C2×Q8—28no—
204C2×Q8—224no—
205C2×Q8—224no—
206C22×C4—26no—
207C22×C4—23no—
208C22×C4—21no—
209C22×C4—26no—
210C22×C4—23no—
211C22×C4—26no—
212C22×C4—23no—
213C22×C4—26no—
214C22×C4—116no—
215C22×C4—112no—
216C22×C4—223no—
217C22×C4—223no—
218C22×C4—223no—
219C22×C4—223no—
220C22×C4—223no—
221C22×C4—223no—
222C22×C4—223no—
223C22×C4—223no—
224C22×C4—226no—
225C22×C4—223no—
226C22×C4—221no—
227C22×C4—226no—
228C22×C4—223no—
229C22×C4—223no—
230C22×C4—223no—
231C22×C4—223no—
232C22×C4C2×C4×D1116yes—
233C22×C4#433916yes—
234C22×C4C2×C22⋊D1116yes—
235C22×C4C2×C22⋊D1116yes—
236C22×C4C2×C22⋊D1116yes—
237C4⋊C4—224no—
238C4⋊C4—2224no—
239C4⋊C4—444no—
240C42—224no—
241C11#1430211yescharacteristic, complemented, Sylow
242C23C22×C4×D1111yescharacteristic
243C23C2×#433913yes—
244C23#6704013yes—
245C23#6704011yescharacteristic
246C23#6704211yescharacteristic
247C23#6704313yes—
248C23C22×C22⋊D1113yes—
249Q8—232no—
250C2×C4—212no—
251C2×C4—212no—
252C2×C4—26no—
253C2×C4—26no—
254C2×C4—26no—
255C2×C4—26no—
256C2×C4—26no—
257C2×C4—26no—
258C2×C4—26no—
259C2×C4—46no—
260C2×C4—46no—
261C2×C4—226no—
262C2×C4—226no—
263C2×C4—226no—
264C2×C4—226no—
265C2×C4—443no—
266C2×C4—443no—
267C2×C4—443no—
268C2×C4—443no—
269C2×C4—443no—
270C2×C4—441no—
271C2×C4—443no—
272C2×C4—443no—
273C2×C4—443no—
274C2×C4—443no—
275C2×C4—443no—
276C2×C4—446no—
277C2×C4—446no—
278C2×C4—441no—
279C2×C4C4×C22⋊D11112yes—
280C2×C4#6700614yes—
281C22#1062310313yes—
282C22#1062310511yescharacteristic
283C22#1062311313yes—
284C22#1062311413yes—
285C22#1062311416yes—
286C22C2×C4×C22⋊D1113yes—
287C22#1062332213yes—
288C22#1062334713yes—
289C22#1062334713yes—
290C22#1062335613yes—
291C22#1062336413yes—
292C22C2×#6700611yescharacteristic
293C4—212no—
294C4—24no—
295C4—46no—
296C4—442no—
297C4—446no—
298C4—883no—
299C4—881no—
300C2C4×#6700611yescharacteristic
301C2#1307129213yes—
302C2#1307133213yes—
303C2#1307433511yescharacteristic
304C2#1307434511yescharacteristic
305C2#1307449213yes—
306C2#1307452213yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×Q8×C11C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11#14302
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
14. #10622842C4semidirect
241. C11#14302semidirect

Maximal subgroups

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

subgroupindex
C2×#106228422
C2×#106225462
#130668872
#130668752
#130668662
#130668432
C22×C4×Q8×C112
#1430211