Finite Group Databasebeta

← C2×C4×#66923 #14912264

Subgroups — C2×C4×#66923 #14912264

Order 2816.

2622 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66923C211yesmaximal, characteristic
2C4×#66923C2116yesmaximal, direct product factor
3C2×#10622541C212yesmaximal
4C2×#10622546C214yesmaximal
5C2×#10622549C211yesmaximal, characteristic
6C2×C4×Dic11⋊C4C214yesmaximal
7C2×C4×C4⋊Dic11C212yesmaximal
8C2×C43×C11C211yesmaximal, characteristic
9C22×C42×C11C2212yes—
10C22×C42×C11C2212yes—
11C22×C42×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4⋊Dic11C2212yes—
16C22×Dic11⋊C4C2214yes—
17C22×Dic11⋊C4C2214yes—
18C22×C4×Dic11C2214yes—
19C2×#66923C4116yesdirect product factor
20C2×#66923C2218yes—
21C43×C11C2218yes—
22C2×C11⋊#95C2214yes—
23C2×C11⋊#95C2214yes—
24C2×C11⋊#95C2214yes—
25#10622549C2218yes—
26C4×C4⋊Dic11C22116yes—
27#10622546C22132yes—
28C4×Dic11⋊C4C22132yes—
29#10622541C22116yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2311yescharacteristic
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2314yes—
36C23×Dic11C2314yes—
37C2×C42×C11—28no—
38C2×C42×C11—24no—
39C2×C42×C11—28no—
40C2×C42×C11C2×C418yes—
41C2×C42×C11Q818yes—
42C2×C42×C11C2314yes—
43C2×C42×C11C2318yes—
44C2×C42×C11C2318yes—
45C2×C42×C11C2314yes—
46C2×C42×C11C2314yes—
47C2×C4⋊Dic11—28no—
48C2×C4⋊Dic11C2×C4116yes—
49C2×C4⋊Dic11C2318yes—
50C2×C4⋊Dic11C2318yes—
51C2×Dic11⋊C4—216no—
52C2×Dic11⋊C4C2×C4132yes—
53C2×Dic11⋊C4C23116yes—
54C2×Dic11⋊C4C23116yes—
55C2×C4×Dic11—216no—
56C2×C4×Dic11C23116yes—
57#66923C2×C4164yesdirect product factor
58C11⋊#95C23116yes—
59C11⋊#95C23116yes—
60C11⋊#95C23116yes—
61C2×C4×#125—111nomaximal, Sylow
62C24×C11C2411yescharacteristic
63C22×C4×C11—24no—
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11C22×C418yes—
69C22×C4×C11C22×C414yes—
70C22×C4×C11C2×Q814yes—
71C22×C4×C11C2×Q814yes—
72C22×C4×C11C2×Q814yes—
73C22×C4×C11#4118yes—
74C22×C4×C11#4114yes—
75C22×C4×C11#4118yes—
76C22×C4×C11C2414yes—
77C22×C4×C11C2412yes—
78C22×C4×C11C2414yes—
79C22×C4×C11C2412yes—
80C22×C4×C11C2412yes—
81C22×Dic11—28no—
82C22×Dic11—28no—
83C22×Dic11—28no—
84C22×Dic11—28no—
85C22×Dic11—28no—
86C22×Dic11C22×C4116yes—
87C22×Dic11C2418yes—
88C22×Dic11C2418yes—
89C42×C11—216no—
90C42×C11—28no—
91C42×C11—216no—
92C42×C11C22×C4116yes—
93C42×C11C2×Q8116yes—
94C4⋊Dic11—216no—
95C4⋊Dic11C22×C4132yes—
96Dic11⋊C4—232no—
97Dic11⋊C4C22×C4164yes—
98C4×Dic11—232no—
99C22×#125—111no—
100C4×#125—1116no—
101C2×#389—112no—
102C2×#387—114no—
103C2×#382—111no—
104C2×C4×C4⋊C4—112no—
105C2×C4×C4⋊C4—114no—
106C2×C43D1111yescharacteristic
107C23×C11C23×C412yes—
108C23×C11C22×Q812yes—
109C23×C11C2×#4112yes—
110C23×C11C2×#4114yes—
111C23×C11C2×#4114yes—
112C23×C11C2511yescharacteristic
113C2×C4×C11—216no—
114C2×C4×C11—216no—
115C2×C4×C11—28no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—24no—
121C2×C4×C11C4×Q8116yes—
122C2×C4×C11#125116yescomplemented
123C2×C4×C11C23×C418yes—
124C2×C4×C11C23×C414yes—
125C2×C4×C11C22×Q814yes—
126C2×C4×C11C22×Q814yes—
127C2×C4×C11C22×Q814yes—
128C2×C4×C11C2×#4118yes—
129C2×C4×C11C2×#4114yes—
130C2×C4×C11C2×#4118yes—
131C2×Dic11—232no—
132C2×Dic11—28no—
133C2×Dic11—28no—
134C2×Dic11—28no—
135C2×Dic11—28no—
136C2×Dic11—28no—
137C2×Dic11—416no—
138C2×Dic11C23×C4116yes—
139C2×#125—118no—
140C2×#125—1116no—
141C22×C4⋊C4—114no—
142C22×C4⋊C4—112no—
143C22×C4⋊C4—114no—
144C22×C4⋊C4—112no—
145C22×C42—114no—
146C22×C42C2×D1112yes—
147C22×C42C2×D1111yescharacteristic
148C22×C42C2×D1112yes—
149C22×C42C2×D1111yescharacteristic
150C22×C42C2×D1111yescharacteristic
151#389—1116no—
152#387—1132no—
153#382—118no—
154C4×C4⋊C4—1132no—
155C4×C4⋊C4—1116no—
156C2×#95—114no—
157C2×#95—114no—
158C2×#95—114no—
159C43C2×D1118yes—
160C22×C11C2×C4×Q814yes—
161C22×C11C4×#4118yes—
162C22×C11C2×#12514yes—
163C22×C11#52918yes—
164C22×C11#53314yes—
165C22×C11C24×C411yescharacteristic
166C22×C11C23×Q811yescharacteristic
167C22×C11C22×#4111yescharacteristic
168C22×C11C22×#4112yes—
169C22×C11C22×#4112yes—
170C4×C11—28no—
171C4×C11—28no—
172C4×C11—24no—
173C4×C11C2×C4×Q818yes—
174C4×C11C2×#12518yescomplemented
175Dic11—216no—
176Dic11—48no—
177C23×C4—114no—
178C23×C4—114no—
179C23×C4C22×D1111yescharacteristic
180C23×C4C22×D1112yes—
181C23×C4C22×D1112yes—
182C23×C4C22×D1111yescharacteristic
183C23×C4C22×D1111yescharacteristic
184#125—1164no—
185C2×C4⋊C4—1132no—
186C2×C4⋊C4—1116no—
187C2×C4⋊C4—1116no—
188C2×C4⋊C4—118no—
189C2×C4⋊C4—118no—
190C2×C4⋊C4—1116no—
191C2×C4⋊C4—2216no—
192C2×C4⋊C4—228no—
193C2×C42—28no—
194C2×C42—24no—
195C2×C42—28no—
196C2×C42—1116no—
197C2×C42—2216no—
198C2×C42Dic2218yes—
199C2×C42C4×D1118yes—
200C2×C42C22×D1118yes—
201C2×C42C22×D1118yes—
202C2×C42C22×D1114yes—
203C2×C42C22×D1114yes—
204C2×C42C22×D1114yes—
205#95—1116no—
206#95—1116no—
207#95—1116no—
208C2×C11C4×#12518yescomplemented
209C2×C11C22×C4×Q811yescharacteristic
210C2×C11C2×C4×#4112yes—
211C2×C11C22×#12511yescharacteristic
212C2×C11C2×#52912yes—
213C2×C11C2×#53311yescharacteristic
214C24C23×D1111yescharacteristic
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—1116no—
221C22×C4—118no—
222C22×C4—118no—
223C22×C4—228no—
224C22×C4—228no—
225C22×C4—228no—
226C22×C4—228no—
227C22×C4—228no—
228C22×C4C2×Dic2214yes—
229C22×C4C2×Dic2214yes—
230C22×C4C2×Dic2214yes—
231C22×C4C2×C4×D1118yes—
232C22×C4C2×C4×D1114yes—
233C22×C4#433918yes—
234C22×C4#433914yes—
235C22×C4#433918yes—
236C22×C4C23×D1112yes—
237C22×C4C23×D1114yes—
238C22×C4C23×D1114yes—
239C22×C4C23×D1112yes—
240C22×C4C23×D1112yes—
241C4⋊C4—1164no—
242C4⋊C4—1132no—
243C4⋊C4—2232no—
244C4⋊C4—2216no—
245C42—216no—
246C42—28no—
247C42—216no—
248C42—2232no—
249C42C2×Dic22116yes—
250C42C2×C4×D11116yes—
251C11C2×C4×#12511yescharacteristic, complemented, Sylow
252C23C22×Dic2212yes—
253C23C22×C4×D1112yes—
254C23C2×#433912yes—
255C23C2×#433914yes—
256C23C2×#433914yes—
257C23C24×D1111yescharacteristic
258C2×C4—28no—
259C2×C4—216no—
260C2×C4—216no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—1116no—
267C2×C4—2232no—
268C2×C4—228no—
269C2×C4—228no—
270C2×C4—228no—
271C2×C4—228no—
272C2×C4—228no—
273C2×C4—4416no—
274C2×C4C4×Dic22116yes—
275C2×C4#66923116yesdirect product factor
276C2×C4C22×Dic2214yes—
277C2×C4C22×Dic2214yes—
278C2×C4C22×Dic2214yes—
279C2×C4C22×C4×D1118yes—
280C2×C4C22×C4×D1114yes—
281C2×C4C2×#433918yes—
282C2×C4C2×#433914yes—
283C2×C4C2×#433918yes—
284C22C2×C4×Dic2214yes—
285C22C2×#6692314yes—
286C22#1062300114yes—
287C22C4×#433918yes—
288C22#1062301018yes—
289C22C23×Dic2211yescharacteristic
290C22C23×C4×D1111yescharacteristic
291C22C22×#433912yes—
292C22C22×#433911yescharacteristic
293C22C22×#433912yes—
294C4—28no—
295C4—24no—
296C4—28no—
297C4—2216no—
298C4—448no—
299C4C2×C4×Dic2218yes—
300C4C2×#6692318yesdirect product factor
301C2C4×#6692318yesdirect product factor
302C2C22×C4×Dic2211yescharacteristic
303C2C2×C4×#433912yes—
304C2C22×#6692311yescharacteristic
305C2C2×#1062301012yes—
306C2C2×#1062300111yescharacteristic
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C43×C11C2
socle, prime radicalC24×C11C24
cosocleC23×C11C25
hypercenterC2×C43D11
hypocenterC11C2×C4×#125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
2. C4×#66923C2direct (N × H)
19. C2×#66923C4direct (N × H)
57. #66923C2×C4direct (N × H)
122. C2×C4×C11#125semidirect
174. C4×C11C2×#125semidirect
208. C2×C11C4×#125semidirect
251. C11C2×C4×#125semidirect
275. C2×C4#66923direct (N × H)
300. C4C2×#66923direct (N × H)
301. C2C4×#66923direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669232
C4×#669232
C2×#106225412
C2×#106225462
C2×#106225492
C2×C4×Dic11⋊C42
C2×C4×C4⋊Dic112
C2×C43×C112
C2×C4×#12511