Finite Group Databasebeta

← C4×#10622842 #14675582

Subgroups — C4×#10622842 #14675582

Order 2816.

1942 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
1C2×#10622842C211yesmaximal, characteristic
2C2×C4×Dic11⋊C4C213yesmaximal
3#13066887C211yesmaximal, characteristic
4#13066879C213yesmaximal
5#13066866C213yesmaximal
6C4×C11⋊#95C213yesmaximal
7C22×C4×Q8×C11C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C2×C4×Q8×C11—212no—
10C22×C11×C4⋊C4C2213yes—
11C22×C42×C11C2213yes—
12C22×Dic11⋊C4C2213yes—
13C22×Dic11⋊C4C2213yes—
14C22×C4×Dic11C2211yescharacteristic
15C22×C4×Dic11C2213yes—
16#10622842C418yesdirect product factor
17C2×C11⋊#95C2216yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22C4×Dic11⋊C4—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⋊C4—26no—
42C2×Dic11⋊C4—26no—
43C2×Dic11⋊C4C2×C4112yes—
44C2×C4×Dic11—26no—
45C2×C4×Dic11—26no—
46C2×C4×Dic11—26no—
47C2×C4×Dic11Q8112yescomplemented
48C11⋊#95—26no—
49C11⋊#95—26no—
50C11⋊#95—26no—
51C11⋊#95—212no—
52C11⋊#95C2×C4112yes—
53C4×#395—111nomaximal, Sylow
54C24×C11C2411yescharacteristic
55C2×Q8×C11—28no—
56C2×Q8×C11—224no—
57C2×Q8×C11—224no—
58C22×C4×C11—26no—
59C22×C4×C11—26no—
60C22×C4×C11—26no—
61C22×C4×C11—26no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11C22×C416yes—
65C22×C4×C11C2×D416yes—
66C22×C4×C11C2×D416yes—
67C22×C4×C11C2×D416yes—
68C22×C4×C11C2×Q816yes—
69C22×C4×C11#4116yes—
70C22×C4×C11#4112yes—
71C22×Dic11—23no—
72C22×Dic11—23no—
73C22×Dic11—23no—
74C22×Dic11—23no—
75C22×Dic11—23no—
76C22×Dic11—23no—
77C22×Dic11—23no—
78C22×Dic11—26no—
79C22×Dic11—26no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11C22×C412yes—
84C22×Dic11C22×C416yes—
85C22×Dic11C2×Q816yes—
86C22×Dic11C2×Q816yes—
87C22×Dic11#4112yes—
88C22×Dic11#4116yes—
89C11×C4⋊C4—224no—
90C42×C11—224no—
91Dic11⋊C4—224no—
92Dic11⋊C4—224no—
93C4×Dic11—224no—
94C4×Dic11—44no—
95C22×C4×Q8D1111yescharacteristic
96C2×#395—111no—
97C2×C4×C4⋊C4—113no—
98#1446—111no—
99#1444—113no—
100#1441—113no—
101C4×#95—113no—
102C23×C11C23×C411yescharacteristic
103C23×C11C22×D413yes—
104C23×C11C22×Q813yes—
105C23×C11C2×#4113yes—
106C23×C11C2×#4111yescharacteristic
107C23×C11C2×#4113yes—
108C23×C11C2×#4111yescharacteristic
109Q8×C11—232no—
110C2×C4×C11—212no—
111C2×C4×C11—26no—
112C2×C4×C11—26no—
113C2×C4×C11—212no—
114C2×C4×C11—26no—
115C2×C4×C11—26no—
116C2×C4×C11—26no—
117C2×C4×C11—46no—
118C2×C4×C11—46no—
119C2×C4×C11C4×D4112yes—
120C2×C4×C11#12014yes—
121C2×C4×C11C22⋊Q8112yes—
122C2×C4×C11C4⋊Q8112yes—
123C2×Dic11—26no—
124C2×Dic11—26no—
125C2×Dic11—26no—
126C2×Dic11—26no—
127C2×Dic11—26no—
128C2×Dic11—26no—
129C2×Dic11—26no—
130C2×Dic11—26no—
131C2×Dic11—26no—
132C2×Dic11—212no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—43no—
136C2×Dic11—43no—
137C2×Dic11—46no—
138C2×Dic11—43no—
139C2×Dic11—43no—
140C2×Dic11C4×Q8112yescomplemented
141C23×Q8C2×D1111yescharacteristic
142C2×C4×Q8—212no—
143C22×C4⋊C4—113no—
144C22×C4⋊C4—113no—
145C22×C4⋊C4C2×D1113yes—
146C22×C42—113no—
147C22×C42—111no—
148C22×C42C2×D1113yes—
149#395—118no—
150C4×C4⋊C4—2212no—
151C2×#95—113no—
152C2×#95—116no—
153C2×#95—113no—
154C2×#95—113no—
155C2×#95—113no—
156C22×C11C2×C4×D413yes—
157C22×C11C2×C4×Q813yes—
158C22×C11C4×#4111yescharacteristic
159C22×C11C2×#12011yescharacteristic
160C22×C11C2×C22⋊Q813yes—
161C22×C11#52513yes—
162C22×C11#52513yes—
163C22×C11#52913yes—
164C22×C11C2×C4⋊Q813yes—
165C22×C11#53213yes—
166C22×C11#53316yes—
167C22×C11#53313yes—
168C4×C11—212no—
169C4×C11—46no—
170C4×C11#39518yescomplemented
171Dic11—212no—
172Dic11—42no—
173Dic11—46no—
174Dic11—42no—
175C22×Q8—26no—
176C22×Q8—26no—
177C22×Q8C4×D1114yes—
178C23×C4—113no—
179C23×C4—111no—
180C23×C4—111no—
181C23×C4—113no—
182C23×C4C22×D1113yes—
183C23×C4C22×D1113yes—
184C23×C4C22×D1111yescharacteristic
185C4×Q8—232no—
186C2×C4⋊C4—212no—
187C2×C4⋊C4—26no—
188C2×C4⋊C4—1112no—
189C2×C4⋊C4—226no—
190C2×C4⋊C4—226no—
191C2×C4⋊C4—226no—
192C2×C4⋊C4—226no—
193C2×C4⋊C4—226no—
194C2×C42—212no—
195C2×C42—1112no—
196C2×C42—226no—
197C2×C42—226no—
198C2×C42—226no—
199C2×C42C22⋊D11112yes—
200#95—1112no—
201#95—2212no—
202#95—226no—
203#95—226no—
204#95—226no—
205C2×C11C4×#12011yescharacteristic
206C2×C11C4×C22⋊Q813yes—
207C2×C11C4×C4⋊Q813yes—
208C2×C11C2×#39511yescharacteristic
209C2×C11#238811yescharacteristic
210C2×C11#239613yes—
211C2×C11#239913yes—
212C24C23×D1111yescharacteristic
213C2×Q8—28no—
214C2×Q8—224no—
215C2×Q8—224no—
216C22×C4—26no—
217C22×C4—26no—
218C22×C4—26no—
219C22×C4—23no—
220C22×C4—23no—
221C22×C4—26no—
222C22×C4—116no—
223C22×C4—116no—
224C22×C4—116no—
225C22×C4—112no—
226C22×C4—116no—
227C22×C4—112no—
228C22×C4—223no—
229C22×C4—223no—
230C22×C4—223no—
231C22×C4—223no—
232C22×C4—226no—
233C22×C4—223no—
234C22×C4—223no—
235C22×C4—226no—
236C22×C4—223no—
237C22×C4—223no—
238C22×C4—223no—
239C22×C4—223no—
240C22×C4C2×C4×D1116yes—
241C22×C4#433916yes—
242C22×C4Q8×D1116yes—
243C22×C4#434312yes—
244C22×C4C2×C22⋊D1116yes—
245C22×C4C2×C22⋊D1116yes—
246C22×C4C2×C22⋊D1116yes—
247C4⋊C4—224no—
248C4⋊C4—2224no—
249C4⋊C4—2224no—
250C42—224no—
251C42—2224no—
252C42—444no—
253C11C4×#39511yescharacteristic, complemented, Sylow
254C23C22×C4×D1111yescharacteristic
255C23C2×#433913yes—
256C23C2×Q8×D1113yes—
257C23C2×#434311yescharacteristic
258C23#41×D1113yes—
259C23#41×D1111yescharacteristic
260C23C22×C22⋊D1113yes—
261Q8—232no—
262C2×C4—212no—
263C2×C4—212no—
264C2×C4—26no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—26no—
268C2×C4—26no—
269C2×C4—46no—
270C2×C4—46no—
271C2×C4—1112no—
272C2×C4—226no—
273C2×C4—226no—
274C2×C4—226no—
275C2×C4—226no—
276C2×C4—226no—
277C2×C4—226no—
278C2×C4—226no—
279C2×C4—226no—
280C2×C4—226no—
281C2×C4—2212no—
282C2×C4—443no—
283C2×C4—443no—
284C2×C4—443no—
285C2×C4—443no—
286C2×C4—446no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4C4×C22⋊D11112yes—
290C2×C4#66997112yes—
291C2×C4#66999112yes—
292C2×C4#6700614yes—
293C22C4×Q8×D1113yes—
294C22C4×#434311yescharacteristic
295C22#1062310916yes—
296C22#1062310913yes—
297C22#1062311113yes—
298C22C2×C4×C22⋊D1113yes—
299C22#1062332213yes—
300C22C2×#6699713yes—
301C22C2×#6699913yes—
302C22#1062335913yes—
303C22#1062336313yes—
304C22C2×#6700611yescharacteristic
305C4—212no—
306C4—46no—
307C4—2212no—
308C4—442no—
309C4—446no—
310C4—442no—
311C4#1062284218yesdirect product factor
312C2C4×#6700611yescharacteristic
313C2C4×#6699913yes—
314C2C4×#6699713yes—
315C2C2×#1062284211yescharacteristic
316C2#1307182911yescharacteristic
317C2#1307188613yes—
318C2#1307190713yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC22×C4×Q8×C11C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11C4×#395
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
16. #10622842C4direct (N × H)
47. C2×C4×Dic11Q8semidirect
140. C2×Dic11C4×Q8semidirect
170. C4×C11#395semidirect
253. C11C4×#395semidirect
311. C4#10622842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228422
C2×C4×Dic11⋊C42
#130668872
#130668792
#130668662
C4×C11⋊#952
C22×C4×Q8×C112
C4×#39511