Finite Group Databasebeta

← C4×#16811533 #28310633

Subgroups — C4×#16811533 #28310633

Order 13568.

500 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811533C212yesmaximal
2C4×#13133278C212yesmaximal
3#20289813C212yesmaximal
4C4×#13133215C211yesmaximal, characteristic
5C2×#13133278C2214yes—
6C4×#11719940—22no—
7#16811533C418yesdirect product factor
8#16811503—22no—
9C2×#13133215C2211yescharacteristic
10C2×C4×Dic106C2211yescharacteristic
11#16810530C411yescharacteristic
12#16810528C2211yescharacteristic
13#16810518—22no—
14#16810492C411yescharacteristic
15C4×#11719919—22no—
16C42×Dic53C411yescharacteristic
17C2×C4×Q8×C53C411yescharacteristic
18C2×#11719940—24no—
19#13133278—24no—
20#13133278C2×C418yes—
21#13133272—42no—
22C4×#88324—42no—
23C22×Dic106C2311yescharacteristic
24#13133215—22no—
25#13133215C2×C414yes—
26C4×Dic106—41no—
27C4×Dic106—41no—
28C2×C4⋊Dic53C2×C411yescharacteristic
29C2×#11719919—22no—
30C2×#11719919—22no—
31C2×#11719919D412yes—
32C2×C4×Dic53—21no—
33C2×C4×Dic53—21no—
34C2×C4×Dic53C2×C411yescharacteristic
35C2×C4×Dic53C2×C411yescharacteristic
36C2×C4×Dic53D412yes—
37#13133124—22no—
38#13133124—22no—
39C22×Q8×C53C2×C411yescharacteristic
40C4×Q8×C53—41no—
41C4×Q8×C53—41no—
42C2×C4⋊C4×C53—21no—
43C2×C4⋊C4×C53C2×C411yescharacteristic
44C2×C42×C53—21no—
45C2×C42×C53C2×C411yescharacteristic
46C2×Q8×C53—21no—
47C2×Q8×C53—41no—
48C2×Q8×C53—41no—
49C2×Q8×C53C4212yes—
50C22×C4×C53—21no—
51C22×C4×C53—21no—
52C22×C4×C53C22⋊C411yescharacteristic
53C22×C4×C53C22⋊C411yescharacteristic
54C22×C4×C53C22×C411yescharacteristic
55C22×Dic53—21no—
56C22×Dic53—21no—
57C22×Dic53C22⋊C412yes—
58C22×Dic53C2×D412yes—
59C2×Dic106—41no—
60C2×Dic106—41no—
61C2×Dic106C22×C412yes—
62C2×Dic106#4112yes—
63#11719940—28no—
64#11719940—44no—
65C2×#88324—44no—
66C4⋊C4×C53—42no—
67C4⋊C4×C53—41no—
68C42×C53—21no—
69C42×C53—21no—
70C42×C53—41no—
71C42×C53—41no—
72C4⋊Dic53—41no—
73#11719919—28no—
74#11719919—42no—
75#11719919—44no—
76C4×Dic53—24no—
77C4×Dic53—22no—
78C4×Dic53—22no—
79C4×Dic53—21no—
80C4×Dic53—42no—
81C4×Dic53—41no—
82C4×Dic53C4212yes—
83C23×C53C2×C22⋊C411yescharacteristic
84Q8×C53—42no—
85Q8×C53—42no—
86C2×C4×C53—21no—
87C2×C4×C53—21no—
88C2×C4×C53—22no—
89C2×C4×C53—22no—
90C2×C4×C53—21no—
91C2×C4×C53—41no—
92C2×C4×C53—41no—
93C2×C4×C53—41no—
94C2×C4×C53—42no—
95C2×C4×C53—41no—
96C2×C4×C53#9911yescharacteristic
97C2×C4×C53#9911yescharacteristic
98C2×C4×C53C2×C4211yescharacteristic
99C2×C4×C53#11711yescharacteristic
100C2×Dic53—22no—
101C2×Dic53—22no—
102C2×Dic53—22no—
103C2×Dic53—22no—
104C2×Dic53—22no—
105C2×Dic53—22no—
106C2×Dic53—22no—
107C2×Dic53—41no—
108C2×Dic53—41no—
109C2×Dic53—42no—
110C2×Dic53C4×D414yes—
111Dic106—42no—
112Dic106—42no—
113#88324—48no—
114C4×#356—531nomaximal, Sylow
115C22×C53—21no—
116C22×C53—21no—
117C22×C53C4×C22⋊C411yescharacteristic
118C22×C53C2×#9911yescharacteristic
119C22×C53#41011yescharacteristic
120C4×C53—21no—
121C4×C53—21no—
122C4×C53—21no—
123C4×C53—41no—
124C4×C53—42no—
125C4×C53—81no—
126C4×C53#35612yescomplemented
127Dic53—24no—
128Dic53—24no—
129Dic53—42no—
130Dic53—42no—
131C4×C4⋊Q8—531no—
132C2×#356—532no—
133C4×#101—532no—
134#1394—532no—
135C2×C53—21no—
136C2×C53—21no—
137C2×C53C4×#9911yescharacteristic
138C2×C53C2×#35611yescharacteristic
139C2×C53#213211yescharacteristic
140C2×C4⋊Q8—531no—
141C2×C4×Q8—531no—
142C2×C4×Q8#615711yescharacteristic
143C2×#101—534no—
144C4×M16—1062no—
145#391—531no—
146#391—531no—
147#389—1062no—
148#384—531no—
149C4×C4⋊C4—1062no—
150C43—531no—
151#356—538no—
152#343—1062no—
153C53C4×#35611yescharacteristic, complemented, Sylow
154C22×Q8—531no—
155C22×Q8C2×#615711yescharacteristic
156C2×M16—1064no—
157C4⋊Q8—534no—
158C4⋊Q8—1062no—
159C4×Q8—41no—
160C4×Q8—41no—
161C4×Q8—2121no—
162C4×Q8—2121no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—532no—
165C2×C4⋊C4—531no—
166C2×C4⋊C4—1062no—
167C2×C4⋊C4—1062no—
168C2×C4⋊C4C2×#615711yescharacteristic
169C2×C42—21no—
170C2×C42—531no—
171C2×C42—532no—
172C2×C42—531no—
173C2×C42—1061no—
174C2×C42—1061no—
175C2×C42C2×#615711yescharacteristic
176#101—538no—
177#101—1064no—
178#97—2122no—
179C4×C8—2122no—
180#95—1062no—
181#95—1062no—
182C2×Q8—21no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—532no—
186C2×Q8—532no—
187C2×Q8—2121no—
188C2×Q8—2121no—
189C2×Q8C4×#615712yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—532no—
193C22×C4—532no—
194C22×C4—1061no—
195C22×C4—1061no—
196C22×C4C22⋊#615711yescharacteristic
197C22×C4C22⋊#615711yescharacteristic
198C22×C4C22×#615711yescharacteristic
199M16—1068no—
200M16—2124no—
201C2×C8—2124no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—1068no—
205C4⋊C4—2122no—
206C4⋊C4—2121no—
207C4⋊C4—2124no—
208C42—21no—
209C42—21no—
210C42—41no—
211C42—41no—
212C42—532no—
213C42—1064no—
214C42—1062no—
215C42—1062no—
216C42—1061no—
217C42—2121no—
218C42—2122no—
219C23C2×C22⋊#615711yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—2122no—
223Q8—2122no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—534no—
235C2×C4—1062no—
236C2×C4—1062no—
237C2×C4—1062no—
238C2×C4—1062no—
239C2×C4—1062no—
240C2×C4—1062no—
241C2×C4—1062no—
242C2×C4—2121no—
243C2×C4—2121no—
244C2×C4—2122no—
245C2×C4#1313327511yescharacteristic
246C2×C4#1313327511yescharacteristic
247C2×C4C2×C4×#615711yescharacteristic
248C2×C4#1313329611yescharacteristic
249C8—2128no—
250C22—21no—
251C22—21no—
252C22C4×C22⋊#615711yescharacteristic
253C22C2×#1313327511yescharacteristic
254C22#1681160211yescharacteristic
255C4—21no—
256C4—21no—
257C4—21no—
258C4—42no—
259C4—41no—
260C4—81no—
261C4—1064no—
262C4—1064no—
263C4—2122no—
264C4—2122no—
265C4#1681153312yesdirect product factor
266C2—21no—
267C2—21no—
268C2C4×#1313327511yescharacteristic
269C2C2×#1681153311yescharacteristic
270C2#2029100611yescharacteristic
subgroupG/H
centerC2×C4#13133275
commutatorC2×C4×C53C2×C42
FrattiniC22×C4C22×#6157
FittingC2×C4×Q8×C53C4
socleC22×C53C2×#99
prime radicalC23×C53C2×C22⋊C4
cosocleC22×Dic106C23
hypercenterC2×C4×Q8#6157
hypocenterC53C4×#356
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
7. #16811533C4direct (N × H)
126. C4×C53#356semidirect
153. C53C4×#356semidirect
265. C4#16811533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168115332
C4×#131332782
#202898132
C4×#131332152
C4×#35653