Finite Group Databasebeta

← C2×#13070180 #14783682

Subgroups — C2×#13070180 #14783682

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic
2C2×#10622548C211yesmaximal, characteristic
3#13070180C218yesmaximal, direct product factor
4C2×#10622189C212yesmaximal
5C2×#10622189C212yesmaximal
6C2×C11×#336C211yesmaximal, characteristic
7C23×C8×C11C2212yes—
8C22×C42×C11C2211yescharacteristic
9C22×C4⋊Dic11—21no—
10C22×C4⋊Dic11—21no—
11C22×C4⋊Dic11C2212yes—
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4—21no—
15C2×C11⋊#95—21no—
16#10622548—22no—
17#10622548C2214yes—
18#10622541—22no—
19#10622541C2214yes—
20C11×#336C2214yes—
21#10622189C2218yes—
22#10622189C2218yes—
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C23×Dic11—21no—
28C23×Dic11—22no—
29C22×C8×C11—24no—
30C22×C8×C11—24no—
31C22×C8×C11—24no—
32C22×C8×C11C2314yes—
33C2×C42×C11—24no—
34C2×C42×C11D412yes—
35C2×C42×C11C2312yes—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—28no—
39C2×C4⋊Dic11—24no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11—24no—
43C2×C4⋊Dic11—24no—
44C2×C4⋊Dic11—44no—
45C2×C4⋊Dic11—44no—
46C2×C4⋊Dic11Q814yes—
47C2×C4⋊Dic11C2312yes—
48C2×C4⋊Dic11C2314yes—
49C2×C4⋊Dic11C2312yes—
50C2×Dic11⋊C4—24no—
51C2×Dic11⋊C4—44no—
52C11⋊#95—24no—
53C2×#2100—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11SD1614yes—
60C22×C4×C11Q1614yes—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×Q812yes—
65C22×C4×C11#4112yes—
66C22×C4×C11#4114yes—
67C22×C4×C11#4114yes—
68C22×C4×C11C2411yescharacteristic
69C22×Dic11—24no—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C22×Dic11—24no—
73C22×Dic11—42no—
74C22×Dic11—44no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—44no—
79C22×Dic11—44no—
80C22×Dic11—42no—
81C2×C8×C11—24no—
82C2×C8×C11—24no—
83C2×C8×C11—24no—
84C2×C8×C11—48no—
85C42×C11—24no—
86C42×C11—24no—
87C4⋊Dic11—24no—
88C4⋊Dic11—22no—
89C4⋊Dic11—28no—
90C4⋊Dic11—24no—
91C4⋊Dic11—48no—
92C4⋊Dic11—48no—
93C4⋊Dic11—42no—
94C4⋊Dic11—44no—
95C4⋊Dic11C2×Q814yes—
96Dic11⋊C4—48no—
97C2×#389—111no—
98C2×#384—111no—
99#2100—118no—
100C2×#340—112no—
101C2×#340—112no—
102C2×#336D1111yescharacteristic
103C23×C11C22⋊Q812yes—
104C23×C11#12312yes—
105C23×C11#12412yes—
106C23×C11C2×SD1612yes—
107C23×C11C2×Q1612yes—
108C23×C11AGL(1,ℤ/8)12yes—
109C23×C11AGL(1,ℤ/8)12yes—
110C23×C11C22×D411yescharacteristic
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—28no—
116C2×C4×C11—28no—
117C2×C4×C11C22⋊Q812yes—
118C2×C4×C11#12312yes—
119C2×C4×C11#12412yes—
120C2×C4×C11#12518yes—
121C2×C4×C11#12618yes—
122C2×C4×C11C2×SD1614yes—
123C2×C4×C11C2×Q1614yes—
124C2×C4×C11C22×Q811yescharacteristic
125C2×C4×C11C2×#4112yes—
126C2×C4×C11C2×#4112yes—
127C2×C4×C11C2×#4111yescharacteristic
128C2×Dic11—24no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—48no—
132C2×Dic11—42no—
133C2×Dic11—44no—
134C2×Dic11—42no—
135C2×Dic11—44no—
136C2×Dic11—44no—
137C2×Dic11—42no—
138C2×Dic11—84no—
139C2×Dic11—88no—
140C8×C11—44no—
141C23×C8C2×D1112yes—
142C22×C4⋊C4—111no—
143C22×C4⋊C4—112no—
144C22×C4⋊C4—111no—
145C22×C4⋊C4—221no—
146C22×C4⋊C4—221no—
147C22×C4⋊C4—221no—
148C22×C42C2×D1111yescharacteristic
149#389—114no—
150#389—222no—
151#384—114no—
152#384—222no—
153C2×#95—221no—
154#340—118no—
155#340—118no—
156#336C2×D1114yes—
157C22×C11#40014yes—
158C22×C11#47614yes—
159C22×C11#47714yes—
160C22×C11#48114yes—
161C22×C11#48414yes—
162C22×C11#48714yes—
163C22×C11#49014yes—
164C22×C11C2×C22⋊Q811yescharacteristic
165C22×C11C2×#12311yescharacteristic
166C22×C11C2×#12411yescharacteristic
167C22×C11C22×SD1611yescharacteristic
168C22×C11C22×Q1611yescharacteristic
169C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
170C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
171C4×C11—24no—
172C4×C11—24no—
173C4×C11#40014yes—
174C4×C11C2×#12512yes—
175C4×C11C2×#12612yes—
176Dic11—44no—
177Dic11—82no—
178Dic11—84no—
179C23×C4—221no—
180C23×C4—222no—
181C23×C4—221no—
182C23×C4D4411yescharacteristic
183C23×C4D4411yescharacteristic
184C23×C4C22×D1111yescharacteristic
185C22×C8—24no—
186C22×C8—24no—
187C22×C8—24no—
188C22×C8C22×D1114yes—
189C2×C4⋊C4—114no—
190C2×C4⋊C4—112no—
191C2×C4⋊C4—114no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—228no—
196C2×C4⋊C4—224no—
197C2×C4⋊C4—222no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—224no—
200C2×C4⋊C4—224no—
201C2×C4⋊C4—224no—
202C2×C4⋊C4—444no—
203C2×C4⋊C4—444no—
204C2×C4⋊C4—444no—
205C2×C42—24no—
206C2×C42D4412yes—
207C2×C42C22×D1112yes—
208#95—224no—
209C2×C11#210018yescomplemented
210C2×C11C2×#40011yescharacteristic
211C2×C11C2×#47611yescharacteristic
212C2×C11C2×#47711yescharacteristic
213C2×C11C2×#48111yescharacteristic
214C2×C11C2×#48411yescharacteristic
215C2×C11C2×#48711yescharacteristic
216C2×C11C2×#49011yescharacteristic
217C24C2×D4411yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—224no—
223C22×C4—222no—
224C22×C4—222no—
225C22×C4—224no—
226C22×C4—442no—
227C22×C4—442no—
228C22×C4—444no—
229C22×C4—442no—
230C22×C4—442no—
231C22×C4—444no—
232C22×C4—444no—
233C22×C4—442no—
234C22×C4#431414yes—
235C22×C4Dic4414yes—
236C22×C4C2×D4412yes—
237C22×C4C2×D4412yes—
238C22×C4C2×D4411yescharacteristic
239C22×C4#433914yes—
240C22×C4#434112yes—
241C22×C4#434114yes—
242C22×C4Q8×D1112yes—
243C22×C4C23×D1111yescharacteristic
244C2×C8—24no—
245C2×C8—24no—
246C2×C8—24no—
247C2×C8—48no—
248C4⋊C4—114no—
249C4⋊C4—224no—
250C4⋊C4—222no—
251C4⋊C4—228no—
252C4⋊C4—224no—
253C4⋊C4—448no—
254C4⋊C4—448no—
255C4⋊C4—444no—
256C4⋊C4—442no—
257C4⋊C4—448no—
258C42—24no—
259C42—24no—
260C11C2×#210011yescharacteristic, complemented, Sylow
261C23#6692812yes—
262C23#6693912yes—
263C23#6695012yes—
264C23C2×#431412yes—
265C23C2×Dic4412yes—
266C23#6696112yes—
267C23#6696112yes—
268C23C22×D4411yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—224no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4—448no—
279C2×C4—444no—
280C2×C4—442no—
281C2×C4—444no—
282C2×C4—444no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—888no—
286C2×C4—884no—
287C2×C4#6692812yes—
288C2×C4#6693218yes—
289C2×C4#6693912yes—
290C2×C4#6694218yes—
291C2×C4#6695012yes—
292C2×C4C2×#431414yes—
293C2×C4C2×Dic4414yes—
294C2×C4C2×#433912yes—
295C2×C4C2×#434111yescharacteristic
296C2×C4C2×#434112yes—
297C2×C4C2×Q8×D1111yescharacteristic
298C8—44no—
299C22#1062227214yes—
300C22#1062229414yes—
301C22#1062232614yes—
302C22#1062233514yes—
303C22#1062234814yes—
304C22#1062245514yes—
305C22#1062246314yes—
306C22C2×#6692811yescharacteristic
307C22C2×#6693911yescharacteristic
308C22C2×#6695011yescharacteristic
309C22C22×#431411yescharacteristic
310C22C22×Dic4411yescharacteristic
311C22C2×#6696111yescharacteristic
312C22C2×#6696111yescharacteristic
313C4—24no—
314C4—24no—
315C4—444no—
316C4—884no—
317C4—882no—
318C4#1062227214yes—
319C4C2×#6693212yes—
320C4C2×#6694212yes—
321C2#1307018018yesdirect product factor
322C2C2×#1062227211yescharacteristic
323C2C2×#1062245511yescharacteristic
324C2C2×#1062246311yescharacteristic
325C2C2×#1062234811yescharacteristic
326C2C2×#1062233511yescharacteristic
327C2C2×#1062229411yescharacteristic
328C2C2×#1062232611yescharacteristic
subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#336C2
socle, prime radicalC24×C11C2×D4
hypercenterC2×#336D11
hypocenterC11C2×#2100
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #13070180C2direct (N × H)
209. C2×C11#2100semidirect
260. C11C2×#2100semidirect
321. C2#13070180direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106225482
#130701802
C2×#106221892
C2×C11×#3362
C2×#210011