Finite Group Databasebeta

← C2×#13076683 #14960311

Subgroups — C2×#13076683 #14960311

Order 2816.

2046 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic
2#13076683C2116yesmaximal, direct product factor
3C2×#10622599C212yesmaximal
4C2×#10622595C212yesmaximal
5C2×#10622597C214yesmaximal
6C2×#10622593C212yesmaximal
7C2×#10622596C212yesmaximal
8C2×#10622549C211yesmaximal, characteristic
9C22×C11×#125C211yesmaximal, characteristic
10C2×C11×#125—28no—
11C2×C11×#125C2218yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2214yes—
23C2×#66923—28no—
24C2×#66923C2218yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622599C22116yes—
31#10622597C22132yes—
32#10622596C22116yes—
33#10622595C22116yes—
34#10622593C22116yes—
35#10622549C2218yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2314yes—
44C11×#125—232no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—28no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4C2314yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C4⋊C4C2318yes—
52C2×C11×C4⋊C4C2318yes—
53C2×C42×C11D418yes—
54C2×C42×C11C2314yes—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11—24no—
57C2×C4⋊Dic11—44no—
58C2×C4⋊Dic11C2314yes—
59C2×C4⋊Dic11C2314yes—
60C2×C4⋊Dic11C2318yes—
61C2×Dic11⋊C4—28no—
62C2×Dic11⋊C4—28no—
63C2×Dic11⋊C4—48no—
64C2×Dic11⋊C4C2318yes—
65C2×Dic11⋊C4C2318yes—
66C2×Dic11⋊C4C23116yes—
67#66923—232no—
68C11⋊#95C2318yes—
69C11⋊#95C2318yes—
70C11⋊#95C23116yes—
71C11⋊#95C23116yes—
72C11⋊#95C23116yes—
73C2×#2822—111nomaximal, Sylow
74C24×C11C2411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—28no—
83C22×C4×C11—24no—
84C22×C4×C11C2×D414yes—
85C22×C4×C11C2×D414yes—
86C22×C4×C11C2×D414yes—
87C22×C4×C11C2414yes—
88C22×C4×C11C2414yes—
89C22×C4×C11C2412yes—
90C22×C4×C11C2412yes—
91C22×C4×C11C2412yes—
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11—24no—
95C22×Dic11—28no—
96C22×Dic11—28no—
97C22×Dic11—28no—
98C22×Dic11—28no—
99C22×Dic11—24no—
100C22×Dic11C2418yes—
101C22×Dic11C2414yes—
102C22×Dic11C2414yes—
103C11×C4⋊C4—28no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—216no—
106C11×C4⋊C4—216no—
107C42×C11C2×D4116yes—
108C4⋊Dic11—28no—
109C4⋊Dic11—28no—
110C4⋊Dic11—48no—
111Dic11⋊C4—216no—
112Dic11⋊C4—216no—
113Dic11⋊C4—416no—
114C22×#125—111no—
115C22×#125D1111yescharacteristic
116#2822—1116no—
117C2×#400—112no—
118C2×#400—112no—
119C2×#398—112no—
120C2×#398—112no—
121C2×#398—114no—
122C2×#382—111no—
123C23×C11C22×D412yes—
124C23×C11H(5,𝔽2)12yes—
125C23×C112−1+414yes—
126C23×C112−1+414yes—
127C23×C112−1+412yes—
128C23×C11C2511yescharacteristic
129C2×C4×C11—28no—
130C2×C4×C11—28no—
131C2×C4×C11—28no—
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—28no—
140C2×C4×C11—24no—
141C2×C4×C11—48no—
142C2×C4×C11—48no—
143C2×C4×C11C22×D414yes—
144C2×C4×C11C22×D414yes—
145C2×C4×C11C22×D414yes—
146C2×Dic11—24no—
147C2×Dic11—24no—
148C2×Dic11—24no—
149C2×Dic11—28no—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—24no—
153C2×Dic11—28no—
154C2×Dic11—48no—
155C2×Dic11—48no—
156C2×Dic11—416no—
157C2×#125—28no—
158C2×#125—118no—
159C2×#125—228no—
160C2×#125C2×D1118yes—
161C22×C4⋊C4—112no—
162C22×C4⋊C4—112no—
163C22×C4⋊C4—111no—
164C22×C4⋊C4—111no—
165C22×C4⋊C4—114no—
166C22×C4⋊C4—112no—
167C22×C4⋊C4C2×D1111yescharacteristic
168C22×C4⋊C4C2×D1112yes—
169C22×C4⋊C4C2×D1112yes—
170C22×C4⋊C4C2×D1111yescharacteristic
171C22×C42C2×D1111yescharacteristic
172#400—1116no—
173#400—1116no—
174#398—1116no—
175#398—1116no—
176#398—1132no—
177#382—118no—
178C2×#95—114no—
179C2×#95—114no—
180C2×#95—114no—
181C2×#95—112no—
182C2×#95—112no—
183C22×C11#53614yes—
184C22×C11#53614yes—
185C22×C11#53714yes—
186C22×C11#56318yes—
187C22×C11#56418yes—
188C22×C11C23×D411yescharacteristic
189C22×C11C2×H(5,𝔽2)11yescharacteristic
190C22×C11C2×2−1+412yes—
191C22×C11C2×2−1+412yes—
192C22×C11C2×2−1+411yescharacteristic
193C4×C11—24no—
194C4×C11—24no—
195C4×C11—24no—
196C4×C11—44no—
197C4×C11—44no—
198Dic11—44no—
199Dic11—44no—
200Dic11—48no—
201C23×C4—112no—
202C23×C4—112no—
203C23×C4—114no—
204C23×C4C22×D1112yes—
205C23×C4C22×D1112yes—
206C23×C4C22×D1111yescharacteristic
207C23×C4C22×D1111yescharacteristic
208C23×C4C22×D1111yescharacteristic
209#125—232no—
210#125—2232no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—28no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—118no—
216C2×C4⋊C4—114no—
217C2×C4⋊C4—118no—
218C2×C4⋊C4—114no—
219C2×C4⋊C4—118no—
220C2×C4⋊C4—1116no—
221C2×C4⋊C4—228no—
222C2×C4⋊C4—228no—
223C2×C4⋊C4—224no—
224C2×C4⋊C4—224no—
225C2×C4⋊C4—448no—
226C2×C4⋊C4—444no—
227C2×C4⋊C4C22×D1118yes—
228C2×C4⋊C4C22×D1114yes—
229C2×C4⋊C4C22×D1118yes—
230C2×C4⋊C4C22×D1114yes—
231C2×C42C22⋊D1118yes—
232C2×C42C22×D1114yes—
233#95—118no—
234#95—118no—
235#95—1116no—
236#95—1116no—
237#95—1116no—
238C2×C11#282218yescomplemented
239C2×C11C2×#53611yescharacteristic
240C2×C11C2×#53611yescharacteristic
241C2×C11C2×#53711yescharacteristic
242C2×C11C2×#56312yes—
243C2×C11C2×#56412yes—
244C24C23×D1111yescharacteristic
245C22×C4—24no—
246C22×C4—22no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—118no—
255C22×C4—114no—
256C22×C4—114no—
257C22×C4—228no—
258C22×C4—228no—
259C22×C4—224no—
260C22×C4—228no—
261C22×C4—224no—
262C22×C4—228no—
263C22×C4—224no—
264C22×C4—224no—
265C22×C4C2×C22⋊D1114yes—
266C22×C4C2×C22⋊D1114yes—
267C22×C4C2×C22⋊D1114yes—
268C22×C4C23×D1114yes—
269C22×C4C23×D1114yes—
270C22×C4C23×D1112yes—
271C22×C4C23×D1112yes—
272C22×C4C23×D1112yes—
273C4⋊C4—216no—
274C4⋊C4—28no—
275C4⋊C4—216no—
276C4⋊C4—28no—
277C4⋊C4—2216no—
278C4⋊C4—2216no—
279C4⋊C4—228no—
280C4⋊C4—228no—
281C4⋊C4—4416no—
282C4⋊C4—448no—
283C42C2×C22⋊D11116yes—
284C11C2×#282211yescharacteristic, complemented, Sylow
285C23#6704014yes—
286C23#6704212yes—
287C23#6704314yes—
288C23#6704312yes—
289C23C22×C22⋊D1112yes—
290C23C24×D1111yescharacteristic
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—28no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—48no—
304C2×C4—48no—
305C2×C4—228no—
306C2×C4—228no—
307C2×C4—224no—
308C2×C4—228no—
309C2×C4—224no—
310C2×C4—228no—
311C2×C4—224no—
312C2×C4—224no—
313C2×C4—448no—
314C2×C4—448no—
315C2×C4—4416no—
316C2×C4C22×C22⋊D1114yes—
317C2×C4C22×C22⋊D1114yes—
318C2×C4C22×C22⋊D1114yes—
319C22C11⋊#56418yes—
320C22#1062323018yes—
321C22#1062334714yes—
322C22#1062335614yes—
323C22#1062336414yes—
324C22C2×#6704012yes—
325C22C2×#6704211yescharacteristic
326C22C2×#6704312yes—
327C22C2×#6704311yescharacteristic
328C22C23×C22⋊D1111yescharacteristic
329C4—24no—
330C4—24no—
331C4—24no—
332C4—44no—
333C4—44no—
334C4—444no—
335C4—444no—
336C4—448no—
337C2#1307668318yesdirect product factor
338C2C2×#1062335611yescharacteristic
339C2C2×#1062334711yescharacteristic
340C2C2×#1062336411yescharacteristic
341C2C2×#1062323012yes—
342C2C2×C11⋊#56412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#125C2
socle, prime radicalC24×C11C24
hypercenterC22×#125D11
hypocenterC11C2×#2822
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13076683C2direct (N × H)
238. C2×C11#2822semidirect
284. C11C2×#2822semidirect
337. C2#13076683direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
#130766832
C2×#106225992
C2×#106225952
C2×#106225972
C2×#106225932
C2×#106225962
C2×#106225492
C22×C11×#1252
C2×#282211