Finite Group Databasebeta

← C2×C4×#14519710 #29678058

Subgroups — C2×C4×#14519710 #29678058

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519710C212yesmaximal
2C22×C4×#92418C211yesmaximal, characteristic
3C2×C4×C4⋊Dic61C211yesmaximal, characteristic
4C4×#14519710C218yesmaximal, direct product factor
5C2×#16839524C212yesmaximal
6C2×C4×C4⋊C4×C61C211yesmaximal, characteristic
7C23×#92418C2211yescharacteristic
8C23×#92418C2211yescharacteristic
9C22×C4⋊Dic61C2212yes—
10C22×C4×Dic61—21no—
11C2×#14519710C4116yesdirect product factor
12C2×#14519710C2218yes—
13C2×C4×#92418C418yescomplemented
14C2×C4×#92418C2214yes—
15C4×C4⋊Dic61—22no—
16C4×C4⋊Dic61C2214yes—
17C2×#14519684—21no—
18#16839524C2218yes—
19C22×C4⋊C4×C61C2212yes—
20C22×C42×C61—21no—
21C22×C42×C61C2211yescharacteristic
22C4×C4⋊C4×C61—22no—
23C4×C4⋊C4×C61C2214yes—
24C2×#95×C61—21no—
25C23×Dic61—22no—
26C22×#92418—24no—
27C22×#92418C2×C414yes—
28C22×#92418C2×C414yes—
29C22×#92418C2×C418yes—
30C22×#92418C2312yes—
31C22×#92418C2312yes—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61—24no—
34C2×C4⋊Dic61C2×C418yes—
35C2×C4⋊Dic61C2314yes—
36C2×C4×Dic61—24no—
37C2×C4×Dic61—44no—
38#14519710C2×C4132yesdirect product factor
39C4×#92418C2×C4116yescomplemented
40#14519684—24no—
41C23×C4×C61—22no—
42C23×C4×C61D411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C2×C4⋊C4×C61—22no—
46C2×C4⋊C4×C61—24no—
47C2×C4⋊C4×C61C2×C418yes—
48C2×C4⋊C4×C61C2314yes—
49C2×C42×C61—24no—
50C2×C42×C61—44no—
51C2×C42×C61C2×C414yes—
52C2×C42×C61D412yes—
53C2×C42×C61Q814yes—
54C2×C42×C61C2312yes—
55#95×C61—24no—
56C24×C61C2×D411yescharacteristic
57C22×C4×C61—24no—
58C22×C4×C61—28no—
59C22×C4×C61—24no—
60C22×C4×C61—44no—
61C22×C4×C61—44no—
62C22×C4×C61C4⋊C414yes—
63C22×C4×C61C4⋊C414yes—
64C22×C4×C61D814yes—
65C22×C4×C61Q1614yes—
66C22×C4×C61C22×C412yes—
67C22×C4×C61C22×C414yes—
68C22×C4×C61C2×D412yes—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D412yes—
71C22×C4×C61C2×Q812yes—
72C22×C4×C61#4114yes—
73C22×C4×C61C2411yescharacteristic
74C22×Dic61—28no—
75C22×Dic61—24no—
76C22×Dic61—44no—
77C22×Dic61—44no—
78C4⋊C4×C61—28no—
79C4⋊C4×C61—24no—
80C4⋊C4×C61C22×C418yes—
81C42×C61—48no—
82C42×C61C4⋊C418yes—
83C42×C61C22×C414yes—
84C42×C61C2×Q814yes—
85C4⋊Dic61—28no—
86C4⋊Dic61—24no—
87C4⋊Dic61C22×C418yes—
88C4×Dic61—48no—
89C2×#92418—28no—
90C2×#92418—24no—
91C2×#92418C42116yescomplemented
92C2×#92418C22×C414yes—
93C2×#92418C22×C414yes—
94C2×#92418C22×C418yes—
95C23×C61C2×C4⋊C412yes—
96C23×C61C4×D414yes—
97C23×C61C2×D812yes—
98C23×C61C2×Q1612yes—
99C23×C61#13514yes—
100C23×C61C22×D411yescharacteristic
101C2×C4×C61—24no—
102C2×C4×C61—28no—
103C2×C4×C61—28no—
104C2×C4×C61—44no—
105C2×C4×C61—44no—
106C2×C4×C61—416no—
107C2×C4×C61#107116yescomplemented
108C2×C4×C61C2×C4214yes—
109C2×C4×C61C2×C4⋊C414yes—
110C2×C4×C61C2×C4⋊C412yes—
111C2×C4×C61C2×C4⋊C414yes—
112C2×C4×C61#11714yes—
113C2×C4×C61C4×D414yes—
114C2×C4×C61C4×Q818yes—
115C2×C4×C61C2×D814yes—
116C2×C4×C61C2×Q1614yes—
117C2×C4×C61C23×C411yescharacteristic
118C2×C4×C61C23×C412yes—
119C2×C4×C61C22×Q811yescharacteristic
120C2×C4×C61C2×#4112yes—
121C2×Dic61—28no—
122C2×Dic61—44no—
123C2×Dic61—44no—
124C2×Dic61—416no—
125#92418—24no—
126#92418C2×C4218yescomplemented
127C2×C4×#107—611nomaximal, Sylow
128C22×C61C4×C4⋊C414yes—
129C22×C61C2×#10714yes—
130C22×C61#42714yes—
131C22×C61C4×D818yes—
132C22×C61C4×Q1618yes—
133C22×C61C22×C4⋊C411yescharacteristic
134C22×C61C2×C4×D412yes—
135C22×C61C22×D811yescharacteristic
136C22×C61C22×Q1611yescharacteristic
137C22×C61C2×#13512yes—
138C4×C61—24no—
139C4×C61—48no—
140C4×C61C4×C4⋊C414yes—
141C4×C61C2×#10718yescomplemented
142C4×C61C22×C4211yescharacteristic
143C4×C61C2×#11711yescharacteristic
144C4×C61C2×C4×Q812yes—
145Dic61—48no—
146C22×#107—612no—
147C22×C4×C8—611no—
148C2×C4×C4⋊C4—611no—
149C2×C4×C4⋊C4D6111yescharacteristic
150C4×#107—618no—
151C2×#340—612no—
152C2×C61C4×#10718yescomplemented
153C2×C61C2×C4×C4⋊C411yescharacteristic
154C2×C61C22×#10711yescharacteristic
155C2×C61C2×#42711yescharacteristic
156C2×C61C2×C4×D812yes—
157C2×C61C2×C4×Q1612yes—
158C23×C8—611no—
159C23×C8—611no—
160C22×C4⋊C4—612no—
161C22×C4⋊C4C2×D6112yes—
162C22×C42—21no—
163C22×C42—1221no—
164C22×C42C2×D6111yescharacteristic
165C2×#107—6116no—
166C2×#107—618no—
167C2×C4×C8—618no—
168C2×C4×C8—614no—
169C4×C4⋊C4—22no—
170C4×C4⋊C4—614no—
171C4×C4⋊C4—1222no—
172C4×C4⋊C4C2×D6114yes—
173C2×#95—21no—
174C2×#95—1221no—
175#340—618no—
176C61C2×C4×#10711yescharacteristic, complemented, Sylow
177C23×C4—22no—
178C23×C4—1222no—
179C23×C4C22⋊D6111yescharacteristic
180C23×C4C22⋊D6111yescharacteristic
181C23×C4C22×D6111yescharacteristic
182C22×C8—614no—
183C22×C8—618no—
184C22×C8—612no—
185C22×C8—614no—
186C22×C8—612no—
187C22×C8—1224no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—618no—
191C2×C4⋊C4—614no—
192C2×C4⋊C4—1224no—
193C2×C4⋊C4—1222no—
194C2×C4⋊C4C4×D6118yes—
195C2×C4⋊C4C22×D6114yes—
196C2×C42—24no—
197C2×C42—44no—
198C2×C42—1224no—
199C2×C42—2444no—
200C2×C42Dic12214yes—
201C2×C42C4×D6114yes—
202C2×C42C22⋊D6112yes—
203C2×C42C22×D6112yes—
204#107—6132no—
205C4×C8—6116no—
206#95—24no—
207#95—1224no—
208C24C2×C22⋊D6111yescharacteristic
209C22×C4—24no—
210C22×C4—24no—
211C22×C4—28no—
212C22×C4—44no—
213C22×C4—44no—
214C22×C4—1224no—
215C22×C4—1228no—
216C22×C4—2444no—
217C22×C4—2444no—
218C22×C4#1175819614yes—
219C22×C4#1175819614yes—
220C22×C4#1175819914yes—
221C22×C4#1175820214yes—
222C22×C4C2×Dic12212yes—
223C22×C4C2×C4×D6112yes—
224C22×C4C2×C4×D6114yes—
225C22×C4#1175822214yes—
226C22×C4C2×C22⋊D6112yes—
227C22×C4C2×C22⋊D6111yescharacteristic
228C22×C4C2×C22⋊D6112yes—
229C22×C4C23×D6111yescharacteristic
230C2×C8—614no—
231C2×C8—618no—
232C2×C8—6116no—
233C2×C8—614no—
234C2×C8—1224no—
235C2×C8—1228no—
236C4⋊C4—24no—
237C4⋊C4—28no—
238C4⋊C4—618no—
239C4⋊C4—1224no—
240C4⋊C4—1228no—
241C4⋊C4C2×C4×D6118yes—
242C42—48no—
243C42—2448no—
244C42#1175819618yes—
245C42C2×Dic12214yes—
246C42C2×C4×D6114yes—
247C23C2×#1175819612yes—
248C23C4×C22⋊D6114yes—
249C23C2×#1175819912yes—
250C23C2×#1175820212yes—
251C23#1451979714yes—
252C23C22×C22⋊D6111yescharacteristic
253C2×C4—24no—
254C2×C4—28no—
255C2×C4—28no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—416no—
259C2×C4—1228no—
260C2×C4—2444no—
261C2×C4—2444no—
262C2×C4—24416no—
263C2×C4#14519710116yesdirect product factor
264C2×C4C42×D6114yes—
265C2×C4C2×#1175819614yes—
266C2×C4C2×#1175819614yes—
267C2×C4C2×#1175819612yes—
268C2×C4#1451973414yes—
269C2×C4C4×C22⋊D6114yes—
270C2×C4C4×Dic12218yes—
271C2×C4C2×#1175819914yes—
272C2×C4C2×#1175820214yes—
273C2×C4C22×C4×D6111yescharacteristic
274C2×C4C22×C4×D6112yes—
275C2×C4C22×Dic12211yescharacteristic
276C2×C4C2×#1175822212yes—
277C8—618no—
278C8—1224no—
279C22C4×#1175819614yes—
280C22C2×#1451971014yes—
281C22#1683979814yes—
282C22C4×#1175819918yes—
283C22C4×#1175820218yes—
284C22C22×#1175819611yescharacteristic
285C22C2×C4×C22⋊D6112yes—
286C22C22×#1175819911yescharacteristic
287C22C22×#1175820211yescharacteristic
288C22C2×#1451979712yes—
289C4—24no—
290C4—48no—
291C4—2448no—
292C4C4×#1175819614yes—
293C4C2×#1451971018yesdirect product factor
294C4C2×C42×D6111yescharacteristic
295C4C2×#1451973411yescharacteristic
296C4C2×C4×Dic12212yes—
297C2C4×#1451971018yesdirect product factor
298C2C2×C4×#1175819611yescharacteristic
299C2C22×#1451971011yescharacteristic
300C2C2×#1683979811yescharacteristic
301C2C2×C4×#1175819912yes—
302C2C2×C4×#1175820212yes—
subgroupG/H
centerC23×C4C22⋊D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC2×C4×C4⋊C4×C61C2
socle, prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenterC2×C4×C4⋊C4D61
hypocenterC61C2×C4×#107
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C4×#14519710C2direct (N × H)
11. C2×#14519710C4direct (N × H)
13. C2×C4×#92418C4semidirect
38. #14519710C2×C4direct (N × H)
39. C4×#92418C2×C4semidirect
91. C2×#92418C42semidirect
107. C2×C4×C61#107semidirect
126. #92418C2×C42semidirect
141. C4×C61C2×#107semidirect
152. C2×C61C4×#107semidirect
176. C61C2×C4×#107semidirect
263. C2×C4#14519710direct (N × H)
293. C4C2×#14519710direct (N × H)
297. C2C4×#14519710direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197102
C22×C4×#924182
C2×C4×C4⋊Dic612
C4×#145197102
C2×#168395242
C2×C4×C4⋊C4×C612
C2×C4×#10761