Finite Group Databasebeta

← C2×#13070041 #14782594

Subgroups — C2×#13070041 #14782594

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66882C211yesmaximal, characteristic, complemented
2C22×(C2×D11)⋊C8C211yesmaximal, characteristic
3C2×#10622600C212yesmaximal
4#13070041C218yesmaximal, direct product factor
5C2×#10622167C212yesmaximal, complemented
6C2×C11×#340C211yesmaximal, characteristic, complemented
7C23×C4×D11C2211yescharacteristic
8C23×C8×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×(C2×D11)⋊C4—22no—
11C22×C4⋊Dic11C2212yes—
12C23×C11⋊C8C2211yescharacteristic
13C2×C11⋊#95—22no—
14C2×(C2×D11)⋊C8—24no—
15C2×(C2×D11)⋊C8C2214yes—
16C2×#66882—24no—
17C2×#66882C2214yescomplemented
18#10622600—24no—
19#10622600C2218yes—
20C11×#340C2214yescomplemented
21#10622167C2218yescomplemented
22C24×D11D411yescharacteristic
23C23×C4×C11—22no—
24C23×C4×C11C2311yescharacteristic
25C23×Dic11—22no—
26C23×Dic11D411yescharacteristic
27C22×C4×D11—22no—
28C22×C4×D11—24no—
29C22×C4×D11—24no—
30C22×C4×D11—22no—
31C22×C4×D11D412yes—
32C22×C4×D11C2312yes—
33C22×C8×C11—24no—
34C22×C8×C11D414yes—
35C22×C8×C11C2312yes—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4C2314yes—
40C2×(C2×D11)⋊C4—28no—
41C2×(C2×D11)⋊C4—48no—
42C2×C4⋊Dic11—24no—
43C2×C4⋊Dic11—24no—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11C2314yes—
46C22×C11⋊C8—22no—
47C22×C11⋊C8—24no—
48C22×C11⋊C8C2312yes—
49C11⋊#95—28no—
50(C2×D11)⋊C8—28no—
51#66882—28no—
52C2×#2075—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C23×D11—22no—
55C23×D11—24no—
56C23×D11—22no—
57C23×D11—24no—
58C23×D11D814yes—
59C23×D11C2×D412yes—
60C22×C4×C11—24no—
61C22×C4×C11—44no—
62C22×C4×C11—44no—
63C22×C4×C11—44no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C22×C4×C11#4112yes—
67C22×C4×C11#4114yes—
68C22×C4×C11#4114yes—
69C22×C4×C11C2411yescharacteristic
70C22×Dic11—22no—
71C22×Dic11—24no—
72C22×Dic11—24no—
73C22×Dic11—44no—
74C22×Dic11—44no—
75C22×Dic11—44no—
76C22×Dic11C2×D412yes—
77C2×C4×D11—24no—
78C2×C4×D11—28no—
79C2×C4×D11—22no—
80C2×C4×D11—24no—
81C2×C4×D11—24no—
82C2×C4×D11—22no—
83C2×C4×D11—44no—
84C2×C4×D11—44no—
85C2×C4×D11—48no—
86C2×C8×C11—28no—
87C2×C8×C11—24no—
88C2×C8×C11C2×D414yes—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—44no—
92(C2×D11)⋊C4—416no—
93C4⋊Dic11—24no—
94C4⋊Dic11—24no—
95C4⋊Dic11—44no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—24no—
98C2×C11⋊C8—44no—
99C22×#107—111no—
100C22×C22⋊C8—111no—
101C2×#380—112no—
102#2075—118no—
103C2×#340—112no—
104C2×#340D1111yescharacteristic, complemented
105C23×C11#12112yes—
106C23×C11#12314yes—
107C23×C11C2×D812yes—
108C23×C11#13512yes—
109C23×C11#13714yes—
110C23×C11C22×D411yescharacteristic
111C22×D11—22no—
112C22×D11—24no—
113C22×D11—22no—
114C22×D11—24no—
115C22×D11—28no—
116C22×D11—216no—
117C22×D11—44no—
118C22×D11—44no—
119C22×D11—48no—
120C22×D11C2×D814yes—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—88no—
125C2×C4×C11#12112yes—
126C2×C4×C11#12314yes—
127C2×C4×C11#12314yes—
128C2×C4×C11#12414yes—
129C2×C4×C11#12618yes—
130C2×C4×C11C22×D411yescharacteristic
131C2×C4×C11C2×#4112yes—
132C2×C4×C11C2×#4112yes—
133C2×C4×C11C2×#4111yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—24no—
136C2×Dic11—44no—
137C2×Dic11—44no—
138C2×Dic11—44no—
139C2×Dic11—44no—
140C2×Dic11—88no—
141C4×D11—42no—
142C4×D11—42no—
143C4×D11—44no—
144C4×D11—48no—
145C8×C11—24no—
146C11⋊C8—42no—
147C24×C4—111no—
148C23×C8—111no—
149C23×C8C2×D1111yescharacteristic
150C22×C4⋊C4—112no—
151C22×C4⋊C4C2×D1112yes—
152C22×C22⋊C4—222no—
153C2×#107—114no—
154C2×#107—224no—
155C2×C22⋊C8—114no—
156C2×C22⋊C8—224no—
157#380—118no—
158#380—224no—
159C2×#95—222no—
160#340—118no—
161#340C2×D1114yescomplemented
162C22×C11#39714yes—
163C22×C11#46614yes—
164C22×C11#47014yes—
165C22×C11#48018yes—
166C22×C11#48518yes—
167C22×C11C2×#12111yescharacteristic
168C22×C11C2×#12312yes—
169C22×C11C22×D811yescharacteristic
170C22×C11C2×#13511yescharacteristic
171C22×C11C2×#13712yes—
172C2×D11—28no—
173C2×D11—24no—
174C2×D11—44no—
175C2×D11—416no—
176C2×D11—42no—
177C2×D11—42no—
178C4×C11—84no—
179C4×C11#39714yes—
180C4×C11C2×#12311yescharacteristic
181C4×C11C2×#12411yescharacteristic
182C4×C11C2×#12612yes—
183Dic11—42no—
184Dic11—84no—
185C25—111no—
186C23×C4—22no—
187C23×C4—111no—
188C23×C4—112no—
189C23×C4—112no—
190C23×C4—222no—
191C23×C4—224no—
192C23×C4—224no—
193C23×C4—222no—
194C23×C4—222no—
195C23×C4C22×D1111yescharacteristic
196C22×C8—24no—
197C22×C8—112no—
198C22×C8—222no—
199C22×C8—224no—
200C22×C8D4414yes—
201C22×C8C22×D1112yes—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—114no—
206C2×C4⋊C4—224no—
207C2×C4⋊C4—224no—
208C2×C4⋊C4—222no—
209C2×C4⋊C4C22×D1114yes—
210C2×C22⋊C4—228no—
211C2×C22⋊C4—448no—
212#107—228no—
213C22⋊C8—228no—
214#95—228no—
215C2×C11#207518yescomplemented
216C2×C11C2×#39711yescharacteristic
217C2×C11C2×#46611yescharacteristic
218C2×C11C2×#47011yescharacteristic
219C2×C11C2×#48012yes—
220C2×C11C2×#48512yes—
221D11—44no—
222C24—114no—
223C24—112no—
224C24—224no—
225C24—222no—
226C24—224no—
227C24—222no—
228C24D4×D1111yescharacteristic
229C22×C4—24no—
230C22×C4—44no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—112no—
234C22×C4—224no—
235C22×C4—222no—
236C22×C4—228no—
237C22×C4—224no—
238C22×C4—222no—
239C22×C4—224no—
240C22×C4—224no—
241C22×C4—222no—
242C22×C4—224no—
243C22×C4—444no—
244C22×C4—444no—
245C22×C4—448no—
246C22×C4—444no—
247C22×C4—444no—
248C22×C4—444no—
249C22×C4C2×D4412yes—
250C22×C4#433914yes—
251C22×C4D4×D1111yescharacteristic
252C22×C4#434114yes—
253C22×C4#434312yes—
254C22×C4C23×D1111yescharacteristic
255C2×C8—28no—
256C2×C8—24no—
257C2×C8—222no—
258C2×C8—224no—
259C2×C8—444no—
260C2×C8C2×D4414yes—
261C4⋊C4—24no—
262C4⋊C4—24no—
263C4⋊C4—44no—
264C4⋊C4—224no—
265C4⋊C4—224no—
266C4⋊C4—444no—
267C22⋊C4—4416no—
268C11C2×#207511yescharacteristic, complemented, Sylow
269C23—114no—
270C23—228no—
271C23—224no—
272C23—224no—
273C23—222no—
274C23—222no—
275C23—2216no—
276C23—444no—
277C23—444no—
278C23—448no—
279C23#6693614yes—
280C23#6694812yes—
281C23D8×D1112yes—
282C23#6696814yes—
283C23#6697212yes—
284C23C2×D4×D1111yescharacteristic
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—88no—
289C2×C4—224no—
290C2×C4—222no—
291C2×C4—444no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—444no—
295C2×C4—448no—
296C2×C4—444no—
297C2×C4—444no—
298C2×C4—444no—
299C2×C4—888no—
300C2×C4#6692814yes—
301C2×C4#6693614yes—
302C2×C4#6693914yes—
303C2×C4#6694812yes—
304C2×C4#6695118yes—
305C2×C4C22×D4411yescharacteristic
306C2×C4C2×#433912yes—
307C2×C4C2×#434112yes—
308C2×C4C2×#434311yescharacteristic
309C8—24no—
310C8—442no—
311C22—224no—
312C22—228no—
313C22—442no—
314C22—4416no—
315C22—442no—
316C22—444no—
317C22#1062228714yes—
318C22#1062238718yes—
319C22#1062242718yes—
320C22#1062248114yes—
321C22#1062249614yes—
322C22C2×#6693612yes—
323C22C2×#6694811yescharacteristic
324C22C2×D8×D1111yescharacteristic
325C22C2×#6696812yes—
326C22C2×#6697211yescharacteristic
327C4—84no—
328C4—442no—
329C4—884no—
330C4#1062228714yes—
331C4C2×#6692811yescharacteristic
332C4C2×#6693911yescharacteristic
333C4C2×#6695112yes—
334C2—444no—
335C2#1307004118yesdirect product factor
336C2C2×#1062228711yescharacteristic
337C2C2×#1062249611yescharacteristic
338C2C2×#1062248111yescharacteristic
339C2C2×#1062238712yes—
340C2C2×#1062242712yes—
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC24×D11D4
hypercenterC2×#340D11
hypocenterC11C2×#2075
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#66882C2semidirect
4. #13070041C2direct (N × H)
5. C2×#10622167C2semidirect
6. C2×C11×#340C2semidirect
17. C2×#66882C22semidirect
20. C11×#340C22semidirect
21. #10622167C22semidirect
104. C2×#340D11semidirect
161. #340C2×D11semidirect
215. C2×C11#2075semidirect
268. C11C2×#2075semidirect
335. C2#13070041direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668822
C22×(C2×D11)⋊C82
C2×#106226002
#130700412
C2×#106221672
C2×C11×#3402
C2×#207511