Finite Group Databasebeta

← C4×#10623350 #15617190

Subgroups — C4×#10623350 #15617190

Order 2816.

3250 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623350C212yesmaximal
2#13077044C218yesmaximal, complemented
3C4×#67001C218yesmaximal, complemented
4#13077035C216yesmaximal, complemented
5C2×C4×#4318C216yesmaximal, complemented
6C2×C4×C11×#41C211yesmaximal, characteristic
7C22×C11×#41C2211yescharacteristic
8C4×C11×#41C418yes—
9C4×C11×#41C2214yes—
10C4×C11×#41C2214yes—
11C2×C4×Q8×C11C412yes—
12C2×C4×D4×C11C416yes—
13C2×C11×#117C2213yes—
14C22×C42×C11C2213yes—
15#10623350C4132yesdirect product factor
16C2×#67001C22116yes—
17C22×#4318C22112yes—
18#10622610C22148yescomplemented
19C4×#4318C2214yes—
20C4×#4318C22112yes—
21C4×#4318C22112yescomplemented
22C4×#4318C22112yescomplemented
23C2×#66867C22112yescomplemented
24C2×C4×C11⋊C8C22112yescomplemented
25C2×C11×#41C2×C4116yes—
26C2×C11×#41C2×C414yes—
27C2×C11×#41C2314yes—
28C22×Q8×C11C2×C411yescharacteristic
29C22×D4×C11C2×C413yes—
30C23×C4×C11C2×C416yes—
31C23×C4×C11C2313yes—
32C4×Q8×C11C2×C418yes—
33C4×Q8×C11C2×C418yes—
34C4×D4×C11C2×C4124yes—
35C4×D4×C11C2×C4124yes—
36C11×#117C2×C4112yes—
37C11×#117C23112yes—
38C2×C11×C4⋊C4C2×C416yes—
39C2×C11×C22⋊C4C2×C416yes—
40C2×C42×C11C2×C416yes—
41C2×C42×C11C2×C4112yes—
42C2×C42×C11C2316yes—
43C2×C42×C11C2316yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2313yes—
46#67001C2×C41128yescomplemented
47C2×#4318C2×C4196yescomplemented
48C2×#4318C2318yes—
49C2×#4318C23124yes—
50C22×C11⋊C8C23124yes—
51#66867C2318yes—
52#66867C23124yes—
53C4×C11⋊C8C2318yes—
54C4×C11⋊C8C23124yes—
55C4×#568—111nomaximal, Sylow
56C24×C11C22×C413yes—
57C11×#41C42132yes—
58C11×#41C22×C4132yes—
59C2×Q8×C11C4218yes—
60C2×Q8×C11C22×C414yes—
61C2×D4×C11C42124yes—
62C2×D4×C11C22×C4112yes—
63C22×C4×C11—412no—
64C22×C4×C11C22×C412yes—
65C22×C4×C11C22×C4112yes—
66C22×C4×C11C22×C416yes—
67C22×C4×C11C22×C4112yes—
68C22×C4×C11C22×C413yes—
69C22×C4×C11C22×C416yes—
70C22×C4×C11C22×C4124yes—
71C22×C4×C11C2416yes—
72C22×C4×C11C2411yescharacteristic
73C11×C4⋊C4C22×C4124yes—
74C11×C22⋊C4C22×C4124yes—
75C42×C11C22×C412yes—
76C42×C11C22×C416yes—
77C42×C11C22×C4112yes—
78C42×C11C22×C4112yes—
79C42×C11C2416yes—
80C42×C11C2411yescharacteristic
81C42×C11C2411yescharacteristic
82#4318C22×C4132yes—
83#4318C22×C4196yescomplemented
84C2×C11⋊C8C22×C4196yescomplemented
85C2×C11⋊C8C24116yes—
86C2×#568—112no—
87C2×C4×#41D1111yescharacteristic
88#2875—118no—
89C4×#131—118no—
90#2873—116no—
91C2×C4×M16—116no—
92C23×C11—46no—
93C23×C11C2×C42112yes—
94C23×C11C23×C416yes—
95C23×C11C23×C411yescharacteristic
96Q8×C11C2×C42116yes—
97D4×C11C2×C42148yes—
98C2×C4×C11—24no—
99C2×C4×C11—224no—
100C2×C4×C11—412no—
101C2×C4×C11—46no—
102C2×C4×C11C2×C42112yes—
103C2×C4×C11C2×C42124yes—
104C2×C4×C11C23×C4124yes—
105C2×C4×C11C23×C414yes—
106C2×C4×C11C23×C412yes—
107C2×C4×C11C23×C4112yes—
108C2×C4×C11C23×C412yes—
109C2×C4×C11C23×C411yescharacteristic
110C2×C4×C11C23×C416yes—
111C2×C4×C11C2511yescharacteristic
112C11⋊C8C23×C4132yes—
113C22×#41C2×D1111yescharacteristic
114#568—1132no—
115C2×#131—1116no—
116C22×M16—1112no—
117C4×#41Dic1118yes—
118C4×#41C2×D1114yes—
119C4×#41C2×D1114yes—
120C2×C4×Q8Dic1112yes—
121C2×C4×D4Dic1116yes—
122C2×#117C2×D1113yes—
123C22×C42C2×D1113yes—
124#405—1148no—
125C4×M16—114no—
126C4×M16—1112no—
127C4×M16—1112no—
128C4×M16—1112no—
129C2×#97—1112no—
130C2×C4×C8—1112no—
131C22×C11—22no—
132C22×C11—212no—
133C22×C11—412no—
134C22×C11C22×C4212yes—
135C22×C11C22×C42112yes—
136C22×C11C24×C411yescharacteristic
137C4×C11—22no—
138C4×C11—212no—
139C4×C11C22×C4212yes—
140C4×C11C22×C42112yes—
141C4×C11#56814yescomplemented
142C4×C11C24×C412yes—
143C2×#41C4×D11116yes—
144C2×#41C2×Dic1114yes—
145C2×#41C22×D1114yes—
146C22×Q8C2×Dic1111yescharacteristic
147C22×D4C2×Dic1113yes—
148C23×C4C2×Dic1116yes—
149C23×C4C22×D1113yes—
150#131—11128no—
151C2×M16—1196no—
152C2×M16—118no—
153C2×M16—1124no—
154C22×C8—1124no—
155C4×Q8C2×Dic1118yes—
156C4×Q8C2×Dic1118yes—
157C4×D4C2×Dic11124yes—
158C4×D4C2×Dic11124yes—
159#117C2×Dic11112yes—
160#117C22×D11112yes—
161C2×C4⋊C4C2×Dic1116yes—
162C2×C22⋊C4C2×Dic1116yes—
163C2×C42C2×Dic1116yes—
164C2×C42C2×Dic11112yes—
165C2×C42C22×D1113yes—
166C2×C42C22×D1116yes—
167C2×C42C22×D1116yes—
168C2×C42C22×D1111yescharacteristic
169#97—118no—
170#97—1124no—
171C4×C8—1124no—
172C4×C8—118no—
173C2×C11—22no—
174C2×C11—212no—
175C2×C11C23×C4211yescharacteristic
176C2×C11C2×#56812yes—
177C24C22×Dic1113yes—
178#41C4×Dic11132yes—
179#41C2×C4×D11132yes—
180C2×Q8C4×Dic1118yes—
181C2×Q8C22×Dic1114yes—
182C2×D4C4×Dic11124yes—
183C2×D4C22×Dic11112yes—
184C22×C4—412no—
185C22×C4C2×C4×D11124yes—
186C22×C4C22×Dic1112yes—
187C22×C4C22×Dic11112yes—
188C22×C4C22×Dic1116yes—
189C22×C4C22×Dic11112yes—
190C22×C4C22×Dic1113yes—
191C22×C4C22×Dic1116yes—
192C22×C4C23×D1111yescharacteristic
193C22×C4C23×D1116yes—
194M16—1132no—
195M16—1196no—
196C2×C8—1196no—
197C2×C8—1116no—
198C4⋊C4C22×Dic11124yes—
199C22⋊C4C22×Dic11124yes—
200C42C22×Dic1112yes—
201C42C22×Dic1116yes—
202C42C22×Dic11112yes—
203C42C22×Dic11112yes—
204C42C23×D1116yes—
205C42C23×D1111yescharacteristic
206C42C23×D1111yescharacteristic
207C11C4×#56811yescharacteristic, complemented, Sylow
208C23—46no—
209C23C2×C4×Dic11112yes—
210C23C23×Dic1116yes—
211C23C23×Dic1111yescharacteristic
212Q8C2×C4×Dic11116yes—
213D4C2×C4×Dic11148yes—
214C2×C4—24no—
215C2×C4—224no—
216C2×C4—412no—
217C2×C4—46no—
218C2×C4C2×C4×Dic11112yes—
219C2×C4C2×C4×Dic11124yes—
220C2×C4C22×C4×D11124yes—
221C2×C4C22×C4×D1114yes—
222C2×C4C23×Dic1112yes—
223C2×C4C23×Dic11112yes—
224C2×C4C23×Dic1111yescharacteristic
225C2×C4C23×Dic1116yes—
226C2×C4C23×Dic1112yes—
227C2×C4C24×D1111yescharacteristic
228C8—1132no—
229C22—22no—
230C22—212no—
231C22—412no—
232C22C22×C4×Dic1112yes—
233C22C22×C4×Dic11112yes—
234C22C24×Dic1111yescharacteristic
235C4—22no—
236C4—212no—
237C4C22×C4×Dic1112yes—
238C4C22×C4×Dic11112yes—
239C4#1062335014yesdirect product factor
240C4C23×C4×D1112yes—
241C2—22no—
242C2—212no—
243C2C23×C4×Dic1111yescharacteristic
244C2C2×#1062335012yes—
subgroupG/H
centerC42C23×D11
commutatorC2×C11C23×C42
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC22×C11C24×C4
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC2×C4×#41D11
hypocenterC11C4×#568
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. #13077044C2semidirect
3. C4×#67001C2semidirect
4. #13077035C2semidirect
5. C2×C4×#4318C2semidirect
15. #10623350C4direct (N × H)
18. #10622610C22semidirect
21. C4×#4318C22semidirect
22. C4×#4318C22semidirect
23. C2×#66867C22semidirect
24. C2×C4×C11⋊C8C22semidirect
46. #67001C2×C4semidirect
47. C2×#4318C2×C4semidirect
83. #4318C22×C4semidirect
84. C2×C11⋊C8C22×C4semidirect
141. C4×C11#568semidirect
207. C11C4×#568semidirect
239. C4#10623350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233502
#130770442
C4×#670012
#130770352
C2×C4×#43182
C2×C4×C11×#412
C4×#56811