Finite Group Databasebeta

← C2×#13070179 #14783681

Subgroups — C2×#13070179 #14783681

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×#10622548C211yesmaximal, characteristic
2#13070179C218yesmaximal, direct product factor
3C2×#10622167C212yesmaximal
4C2×#10622167C212yesmaximal
5C2×#10622162C211yesmaximal, characteristic
6C2×C11×#389C211yesmaximal, characteristic
7C22×C11×C4⋊C4—21no—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11—21no—
12C22×C4⋊Dic11—21no—
13C22×C4⋊Dic11C2212yes—
14C23×C11⋊C8C2212yes—
15C11×#389—22no—
16C11×#389C2214yes—
17C2×C11×#95—21no—
18#10622548—22no—
19#10622548C2214yes—
20#10622167C2218yes—
21#10622167C2218yes—
22#10622162C2214yes—
23C23×C4×C11—21no—
24C23×C4×C11—21no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—24no—
32C2×C11×C4⋊C4—24no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—44no—
35C2×C11×C4⋊C4Q814yes—
36C2×C11×C4⋊C4C2312yes—
37C2×C11×C4⋊C4C2312yes—
38C2×C42×C11—24no—
39C2×C42×C11D412yes—
40C2×C42×C11C2312yes—
41C2×C4⋊Dic11—28no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11—24no—
44C2×C4⋊Dic11—24no—
45C2×C4⋊Dic11—44no—
46C2×C4⋊Dic11—44no—
47C2×C4⋊Dic11C2314yes—
48C22×C11⋊C8—24no—
49C22×C11⋊C8—24no—
50C22×C11⋊C8—24no—
51C22×C11⋊C8C2314yes—
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×C11—24no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11SD1614yes—
68C22×C4×C11Q1614yes—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×Q812yes—
73C22×C4×C11#4112yes—
74C22×C4×C11#4114yes—
75C22×C4×C11#4114yes—
76C22×C4×C11C2411yescharacteristic
77C22×Dic11—24no—
78C22×Dic11—44no—
79C22×Dic11—44no—
80C22×Dic11—44no—
81C11×C4⋊C4—24no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—24no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—48no—
86C11×C4⋊C4C2×Q814yes—
87C42×C11—24no—
88C42×C11—24no—
89C4⋊Dic11—28no—
90C4⋊Dic11—48no—
91C4⋊Dic11—48no—
92C4⋊Dic11—44no—
93C2×C11⋊C8—24no—
94C2×C11⋊C8—24no—
95C2×C11⋊C8—24no—
96C2×C11⋊C8—48no—
97C2×#389D1111yescharacteristic
98C2×#384—111no—
99#2100—118no—
100C2×#340—112no—
101C2×#340—112no—
102C2×#336—111no—
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×C11—24no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—48no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—84no—
125C2×C4×C11C22⋊Q812yes—
126C2×C4×C11#12312yes—
127C2×C4×C11#12412yes—
128C2×C4×C11#12518yes—
129C2×C4×C11#12618yes—
130C2×C4×C11C2×SD1614yes—
131C2×C4×C11C2×Q1614yes—
132C2×C4×C11C22×Q811yescharacteristic
133C2×C4×C11C2×#4111yescharacteristic
134C2×C4×C11C2×#4112yes—
135C2×C4×C11C2×#4112yes—
136C2×Dic11—44no—
137C2×Dic11—44no—
138C2×Dic11—44no—
139C2×Dic11—88no—
140C11⋊C8—44no—
141C23×C8—112no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—112no—
144C22×C4⋊C4—221no—
145C22×C4⋊C4—221no—
146C22×C4⋊C4C2×D1111yescharacteristic
147C22×C4⋊C4C2×D1111yescharacteristic
148C22×C42C2×D1111yescharacteristic
149#389—22no—
150#389C2×D1114yes—
151#384—114no—
152#384—222no—
153C2×#95—21no—
154#340—118no—
155#340—118no—
156#336—114no—
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—44no—
174C4×C11—82no—
175C4×C11#40014yes—
176C4×C11C2×#12512yes—
177C4×C11C2×#12612yes—
178Dic11—84no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—222no—
182C23×C4C22⋊D1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C23×C4C22×D1111yescharacteristic
185C22×C8—114no—
186C22×C8—224no—
187C22×C8—224no—
188C22×C8—224no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—114no—
196C2×C4⋊C4—228no—
197C2×C4⋊C4—222no—
198C2×C4⋊C4—224no—
199C2×C4⋊C4—224no—
200C2×C4⋊C4—444no—
201C2×C4⋊C4—444no—
202C2×C4⋊C4Dic2214yes—
203C2×C4⋊C4C22×D1112yes—
204C2×C4⋊C4C22×D1112yes—
205C2×C42—24no—
206C2×C42C22⋊D1112yes—
207C2×C42C22×D1112yes—
208#95—24no—
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×C22⋊D1111yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—224no—
231C22×C4—444no—
232C22×C4—444no—
233C22×C4—444no—
234C22×C4#432414yes—
235C22×C4#432614yes—
236C22×C4C2×Dic2212yes—
237C22×C4#433912yes—
238C22×C4#434114yes—
239C22×C4#434314yes—
240C22×C4C2×C22⋊D1112yes—
241C22×C4C2×C22⋊D1112yes—
242C22×C4C2×C22⋊D1111yescharacteristic
243C22×C4C23×D1111yescharacteristic
244C2×C8—224no—
245C2×C8—224no—
246C2×C8—224no—
247C2×C8—448no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4—24no—
251C4⋊C4—48no—
252C4⋊C4—42no—
253C4⋊C4—228no—
254C4⋊C4—448no—
255C4⋊C4—448no—
256C4⋊C4—444no—
257C4⋊C4C2×Dic2214yes—
258C42—24no—
259C42—24no—
260C11C2×#210011yescharacteristic, complemented, Sylow
261C23#6697712yes—
262C23C2×#432412yes—
263C23#6698812yes—
264C23C2×#432612yes—
265C23#6700012yes—
266C23#6700212yes—
267C23#6700212yes—
268C23C22×C22⋊D1111yescharacteristic
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—24no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—48no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—84no—
283C2×C4—444no—
284C2×C4—444no—
285C2×C4—444no—
286C2×C4—888no—
287C2×C4#6694318yes—
288C2×C4#6695118yes—
289C2×C4#6697712yes—
290C2×C4C2×#432414yes—
291C2×C4#6698812yes—
292C2×C4C2×#432614yes—
293C2×C4#6700012yes—
294C2×C4C22×Dic2211yescharacteristic
295C2×C4C2×#433911yescharacteristic
296C2×C4C2×#434112yes—
297C2×C4C2×#434312yes—
298C8—444no—
299C22#1062259914yes—
300C22#1062262114yes—
301C22#1062263414yes—
302C22#1062264714yes—
303C22#1062265714yes—
304C22#1062268014yes—
305C22#1062270614yes—
306C22C2×#6697711yescharacteristic
307C22C22×#432411yescharacteristic
308C22C2×#6698811yescharacteristic
309C22C22×#432611yescharacteristic
310C22C2×#6700011yescharacteristic
311C22C2×#6700211yescharacteristic
312C22C2×#6700211yescharacteristic
313C4—24no—
314C4—24no—
315C4—44no—
316C4—82no—
317C4—884no—
318C4#1062259914yes—
319C4C2×#6694312yes—
320C4C2×#6695112yes—
321C2#1307017918yesdirect product factor
322C2C2×#1062259911yescharacteristic
323C2C2×#1062262111yescharacteristic
324C2C2×#1062263411yescharacteristic
325C2C2×#1062264711yescharacteristic
326C2C2×#1062265711yescharacteristic
327C2C2×#1062270611yescharacteristic
328C2C2×#1062268011yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#389C2
socle, prime radicalC24×C11C2×D4
hypercenterC2×#389D11
hypocenterC11C2×#2100
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #13070179C2direct (N × H)
209. C2×C11#2100semidirect
260. C11C2×#2100semidirect
321. C2#13070179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225482
#130701792
C2×#106221672
C2×#106221622
C2×C11×#3892
C2×#210011