Finite Group Databasebeta

← C2×#13074493 #14920700

Subgroups — C2×#13074493 #14920700

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2#13074493C2116yesmaximal, direct product factor
3C2×#10622599C212yesmaximal
4C2×#10622595C212yesmaximal
5C2×#10622593C212yesmaximal
6C2×#10622592C212yesmaximal
7C2×#10622591C214yesmaximal
8C2×#10622550C211yesmaximal, characteristic
9C22×C11×#125C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C2×C11×#125—28no—
12C2×C11×#125C2218yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2214yes—
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2212yes—
22C2×C4×Dic22—28no—
23C2×C4×Dic22C2218yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30#10622599C22116yes—
31#10622595C22116yes—
32#10622593C22116yes—
33#10622592C22116yes—
34#10622591C22132yes—
35#10622550C2218yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2314yes—
43C23×Dic11C2312yes—
44C22×Dic22—24no—
45C22×Dic22—28no—
46C22×Dic22C2314yes—
47C11×#125—232no—
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4—24no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—28no—
52C2×C11×C4⋊C4C2318yes—
53C2×C11×C4⋊C4C2318yes—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C4⋊C4C2314yes—
56C2×C42×C11D418yes—
57C2×C42×C11C2314yes—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11C2314yes—
60C2×Dic11⋊C4—28no—
61C2×Dic11⋊C4—216no—
62C2×Dic11⋊C4C2318yes—
63C2×Dic11⋊C4C23116yes—
64C2×C4×Dic11—28no—
65C2×C4×Dic11C2318yes—
66C4×Dic22—232no—
67C11⋊#95C2318yes—
68C11⋊#95C2318yes—
69C11⋊#95C2318yes—
70C11⋊#95C23116yes—
71C11⋊#95C23116yes—
72C11⋊#95C23116yes—
73C2×#2634—111nomaximal, Sylow
74C24×C11C2411yescharacteristic
75C22×C4×C11—24no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—28no—
81C22×C4×C11—28no—
82C22×C4×C11C2×D414yes—
83C22×C4×C11C2×D414yes—
84C22×C4×C11C2×D414yes—
85C22×C4×C11C2414yes—
86C22×C4×C11C2414yes—
87C22×C4×C11C2412yes—
88C22×C4×C11C2412yes—
89C22×C4×C11C2412yes—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—28no—
94C22×Dic11—28no—
95C22×Dic11—28no—
96C22×Dic11—28no—
97C22×Dic11#4118yes—
98C22×Dic11C2418yes—
99C22×Dic11C2414yes—
100C22×Dic11C2414yes—
101C2×Dic22—232no—
102C2×Dic22—216no—
103C2×Dic22—28no—
104C11×C4⋊C4—216no—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4—216no—
108C42×C11C2×D4116yes—
109C4⋊Dic11—28no—
110Dic11⋊C4—232no—
111Dic11⋊C4—216no—
112C4×Dic11—216no—
113C22×#125D1111yescharacteristic
114C22×C4×Q8—111no—
115#2634—1116no—
116C2×#400—112no—
117C2×#400—112no—
118C2×#398—112no—
119C2×#395—112no—
120C2×#387—114no—
121C2×#383—111no—
122C23×C11C22×D412yes—
123C23×C11C2×#4114yes—
124C23×C112−1+414yes—
125C23×C112−1+414yes—
126C23×C11C2511yescharacteristic
127C2×C4×C11—28no—
128C2×C4×C11—28no—
129C2×C4×C11—28no—
130C2×C4×C11—24no—
131C2×C4×C11—24no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—28no—
136C2×C4×C11—28no—
137C2×C4×C11—48no—
138C2×C4×C11—48no—
139C2×C4×C11C22×D414yes—
140C2×C4×C11C22×D414yes—
141C2×C4×C11C22×D414yes—
142C2×Dic11—216no—
143C2×Dic11—24no—
144C2×Dic11—24no—
145C2×Dic11—24no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—28no—
150C2×Dic11—48no—
151C2×Dic11—416no—
152C2×Dic11C2×#4118yes—
153Dic22—232no—
154C23×Q8—111no—
155C2×#125—28no—
156C2×#125C2×D1118yes—
157C2×C4×Q8—118no—
158C2×C4×Q8—228no—
159C22×C4⋊C4—114no—
160C22×C4⋊C4—112no—
161C22×C4⋊C4—111no—
162C22×C4⋊C4C2×D1112yes—
163C22×C4⋊C4C2×D1111yescharacteristic
164C22×C4⋊C4C2×D1111yescharacteristic
165C22×C4⋊C4C2×D1112yes—
166C22×C42—112no—
167C22×C42C2×D1111yescharacteristic
168#400—1116no—
169#400—1116no—
170#398—1116no—
171#395—1116no—
172#387—1132no—
173#383—118no—
174C2×#95—112no—
175C2×#95—114no—
176C2×#95—112no—
177C2×#95—114no—
178C2×#95—114no—
179C2×#95—112no—
180C22×C11#52514yes—
181C22×C11#53614yes—
182C22×C11#53614yes—
183C22×C11#541116yes—
184C22×C11C23×D411yescharacteristic
185C22×C11C22×#4112yes—
186C22×C11C2×2−1+412yes—
187C22×C11C2×2−1+412yes—
188C4×C11—24no—
189C4×C11—24no—
190C4×C11—24no—
191C4×C11—44no—
192C4×C11—44no—
193Dic11—28no—
194Dic11—44no—
195Dic11—48no—
196C22×Q8—114no—
197C22×Q8—228no—
198C22×Q8—224no—
199C23×C4—112no—
200C23×C4—112no—
201C23×C4—114no—
202C23×C4C22×D1112yes—
203C23×C4C22×D1112yes—
204C23×C4C22×D1111yescharacteristic
205C23×C4C22×D1111yescharacteristic
206C23×C4C22×D1111yescharacteristic
207#125—232no—
208C4×Q8—2232no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—28no—
213C2×C4⋊C4—118no—
214C2×C4⋊C4—114no—
215C2×C4⋊C4—1116no—
216C2×C4⋊C4—2216no—
217C2×C4⋊C4—228no—
218C2×C4⋊C4—224no—
219C2×C4⋊C4C22×D1118yes—
220C2×C4⋊C4C22×D1118yes—
221C2×C4⋊C4C22×D1114yes—
222C2×C4⋊C4C22×D1114yes—
223C2×C42—118no—
224C2×C42—228no—
225C2×C42C22⋊D1118yes—
226C2×C42C22×D1114yes—
227#95—118no—
228#95—118no—
229#95—118no—
230#95—1116no—
231#95—1116no—
232#95—1116no—
233C2×C11#263418yescomplemented
234C2×C11C2×#52511yescharacteristic
235C2×C11C2×#53611yescharacteristic
236C2×C11C2×#53611yescharacteristic
237C2×C11C2×#54114yes—
238C24C23×D1111yescharacteristic
239C2×Q8—2216no—
240C2×Q8—2232no—
241C2×Q8—228no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—28no—
246C22×C4—28no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—118no—
250C22×C4—114no—
251C22×C4—118no—
252C22×C4—114no—
253C22×C4—224no—
254C22×C4—224no—
255C22×C4—228no—
256C22×C4—228no—
257C22×C4—228no—
258C22×C4—228no—
259C22×C4—224no—
260C22×C4C2×C22⋊D1114yes—
261C22×C4C2×C22⋊D1114yes—
262C22×C4C2×C22⋊D1114yes—
263C22×C4C23×D1114yes—
264C22×C4C23×D1114yes—
265C22×C4C23×D1112yes—
266C22×C4C23×D1112yes—
267C22×C4C23×D1112yes—
268C4⋊C4—216no—
269C4⋊C4—28no—
270C4⋊C4—28no—
271C4⋊C4—216no—
272C4⋊C4—2232no—
273C4⋊C4—2216no—
274C4⋊C4—228no—
275C42—2216no—
276C42C2×C22⋊D11116yes—
277C11C2×#263411yescharacteristic, complemented, Sylow
278C23#6704014yes—
279C23#41×D1114yes—
280C23#6704314yes—
281C23C22×C22⋊D1112yes—
282C23C24×D1111yescharacteristic
283Q8—2232no—
284C2×C4—28no—
285C2×C4—28no—
286C2×C4—28no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—48no—
295C2×C4—48no—
296C2×C4—118no—
297C2×C4—2216no—
298C2×C4—224no—
299C2×C4—224no—
300C2×C4—228no—
301C2×C4—228no—
302C2×C4—228no—
303C2×C4—228no—
304C2×C4—224no—
305C2×C4—448no—
306C2×C4—4416no—
307C2×C4C22×C22⋊D1114yes—
308C2×C4C22×C22⋊D1114yes—
309C2×C4C22×C22⋊D1114yes—
310C22#10623227116yes—
311C22#1062334714yes—
312C22#1062335614yes—
313C22#1062335914yes—
314C22C2×#6704012yes—
315C22C2×#41×D1112yes—
316C22C2×#6704312yes—
317C22C23×C22⋊D1111yescharacteristic
318C4—24no—
319C4—24no—
320C4—24no—
321C4—44no—
322C4—44no—
323C4—228no—
324C4—444no—
325C4—448no—
326C2#1307449318yesdirect product factor
327C2C2×#1062335911yescharacteristic
328C2C2×#1062335611yescharacteristic
329C2C2×#1062334711yescharacteristic
330C2C2×#1062322714yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#125C2
socle, prime radicalC24×C11C24
hypercenterC22×#125D11
hypocenterC11C2×#2634
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13074493C2direct (N × H)
233. C2×C11#2634semidirect
277. C11C2×#2634semidirect
326. C2#13074493direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
#130744932
C2×#106225992
C2×#106225952
C2×#106225932
C2×#106225922
C2×#106225912
C2×#106225502
C22×C11×#1252
C2×#263411