Finite Group Databasebeta

← C2×#13066642 #14664069

Subgroups — C2×#13066642 #14664069

Order 2816.

500 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 123 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×#10622599C211yesmaximal, characteristic
2C2×#10622166C211yesmaximal, characteristic
3#13066642C214yesmaximal, direct product factor
4C2×C11×#343C211yesmaximal, characteristic
5C22×C11×M16—21no—
6C22×C11×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C2×C11⋊#95—21no—
9C2×C11⋊#95—21no—
10C2×C11⋊#95C411yescharacteristic
11C2×C22⋊(C11⋊C8)—21no—
12#10622599—21no—
13#10622599—21no—
14#10622599C412yes—
15#10622599C2212yes—
16C11×#343—21no—
17C11×#343C2212yes—
18#10622166—21no—
19#10622166C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C2×C11×M16—24no—
26C2×C11×M16—22no—
27C2×C11×M16—41no—
28C2×C11×M16—42no—
29C22×C8×C11—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—41no—
38C2×C4⋊Dic11—41no—
39C2×C4⋊Dic11C2×C412yes—
40C22×C11⋊C8—41no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95C2×C412yes—
47C22⋊(C11⋊C8)—22no—
48C22⋊(C11⋊C8)—41no—
49C2×#1353—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11SD1612yes—
64C22×C4×C11Q1612yes—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—22no—
69C22×Dic11—22no—
70C22×Dic11—42no—
71C22×Dic11—42no—
72C22×Dic11—44no—
73C22×Dic11—41no—
74C22×Dic11—41no—
75C22×Dic11—42no—
76C11×M16—24no—
77C11×M16—44no—
78C11×M16—42no—
79C2×C8×C11—44no—
80C2×C8×C11—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C4⋊Dic11—42no—
86C4⋊Dic11—42no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—82no—
89C2×#400—111no—
90C2×#343D1111yescharacteristic
91C2×#324—111no—
92#1353—114no—
93C23×C11—22no—
94C23×C11—22no—
95C23×C11#9911yescharacteristic
96C23×C11#9911yescharacteristic
97C23×C11#10312yes—
98C23×C11#10412yes—
99C23×C11C2×C22⋊C411yescharacteristic
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—81no—
120C2×C4×C11#10312yes—
121C2×C4×C11C2×SD1611yescharacteristic
122C2×C4×C11C2×Q1611yescharacteristic
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—44no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—84no—
129C2×Dic11—82no—
130C2×Dic11—82no—
131C8×C11—44no—
132C11⋊C8—82no—
133C22×M16—21no—
134C22×C4⋊C4—111no—
135C22×C4⋊C4C2×D1111yescharacteristic
136C2×C22⋊C8—221no—
137#400—112no—
138#400—112no—
139#400—221no—
140#400—221no—
141C2×#95—111no—
142C2×#95—221no—
143C2×#95—221no—
144#343—21no—
145#343C2×D1112yes—
146#324—112no—
147#324—221no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—24no—
151C22×C11—24no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11#32812yes—
155C22×C11#32812yes—
156C22×C11#35212yes—
157C22×C11#35512yes—
158C22×C11C2×#9911yescharacteristic
159C22×C11C2×#10311yescharacteristic
160C22×C11C2×#10411yescharacteristic
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168Dic11—82no—
169Dic11—82no—
170C23×C4—221no—
171C23×C4—221no—
172C23×C4C4×D1111yescharacteristic
173C23×C4D4411yescharacteristic
174C23×C4C22⋊D1111yescharacteristic
175C2×M16—24no—
176C2×M16—22no—
177C2×M16—41no—
178C2×M16—42no—
179C22×C8—41no—
180C22×C8—441no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—112no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—441no—
186C2×C4⋊C4—441no—
187C2×C4⋊C4C4×D1111yescharacteristic
188C2×C4⋊C4D4411yescharacteristic
189C2×C4⋊C4C22⋊D1111yescharacteristic
190C2×C4⋊C4C22×D1111yescharacteristic
191C22⋊C8—222no—
192C22⋊C8—441no—
193#95—112no—
194#95—221no—
195#95—222no—
196#95—222no—
197#95—222no—
198#95—222no—
199C2×C11—21no—
200C2×C11—22no—
201C2×C11—21no—
202C2×C11#135314yescomplemented
203C2×C11C2×#32811yescharacteristic
204C2×C11C2×#35211yescharacteristic
205C2×C11C2×#35511yescharacteristic
206C24(C2×D11)⋊C411yescharacteristic
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—222no—
217C22×C4—222no—
218C22×C4—442no—
219C22×C4—442no—
220C22×C4—444no—
221C22×C4—442no—
222C22×C4—441no—
223C22×C4—441no—
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4(C2×D11)⋊C411yescharacteristic
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4#432412yes—
228C22×C4#432612yes—
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4C2×D4411yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232M16—24no—
233M16—44no—
234M16—42no—
235C2×C8—42no—
236C2×C8—44no—
237C2×C8—442no—
238C2×C8—882no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—442no—
244C4⋊C4—442no—
245C11C2×#135311yescharacteristic, complemented, Sylow
246C23—22no—
247C23—22no—
248C23#6686912yes—
249C23#6687011yescharacteristic
250C23#6687011yescharacteristic
251C23#6687412yes—
252C23C2×(C2×D11)⋊C411yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—444no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—884no—
279C2×C4—882no—
280C2×C4—882no—
281C2×C4#6687412yes—
282C2×C4C2×#432411yescharacteristic
283C2×C4C2×#432611yescharacteristic
284C8—44no—
285C8—882no—
286C22—24no—
287C22—24no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22#1062209012yes—
293C22#1062209012yes—
294C22#1062211412yes—
295C22#1062211512yes—
296C22C2×#6686911yescharacteristic
297C22C2×#6687011yescharacteristic
298C22C2×#6687411yescharacteristic
299C4—21no—
300C4—22no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—882no—
307C4—882no—
308C2—21no—
309C2—21no—
310C2—22no—
311C2#1306664214yesdirect product factor
312C2C2×#1062209011yescharacteristic
313C2C2×#1062211411yescharacteristic
314C2C2×#1062211511yescharacteristic
subgroupG/H
centerC23#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC2×C11×#343C2
socleC23×C11#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenterC2×#343D11
hypocenterC11C2×#1353
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
3. #13066642C2direct (N × H)
202. C2×C11#1353semidirect
245. C11C2×#1353semidirect
311. C2#13066642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225992
C2×#106221662
#130666422
C2×C11×#3432
C2×#135311