Finite Group Databasebeta

← #28309178

Subgroups — #28309178

Order 13568.

378 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C4×#13133278C211yesmaximal, characteristic
2#20289977C211yesmaximal, characteristic
3#20289713C214yesmaximal
4#20279930C211yesmaximal, characteristic
5#16811644—21no—
6C2×#13133278—21no—
7C4×#11719940—21no—
8#16811503C2212yes—
9#16811469C2212yes—
10#16811468—21no—
11C2×#13133217C411yescharacteristic
12C2×C4×Dic106C2211yescharacteristic
13#16810563C412yes—
14#16810563C2212yes—
15#16810529—21no—
16#16810528—21no—
17#16810528—21no—
18#16810489—21no—
19C4×C4⋊C4×C53C411yescharacteristic
20C2×#11719940—22no—
21C4⋊#88324—41no—
22#13133278—24no—
23C22⋊#88324—22no—
24#13133272—41no—
25#13133272—41no—
26C4×#88324—41no—
27C22×Dic106—21no—
28C22×Dic106D411yescharacteristic
29#13133217—41no—
30#13133217—41no—
31C4×Dic106—41no—
32C4×Dic106—41no—
33C2×C4⋊Dic53—21no—
34C2×C4⋊Dic53C2×C412yes—
35C2×C4⋊Dic53D411yescharacteristic
36C2×#11719919C2×C411yescharacteristic
37C2×#11719919C2311yescharacteristic
38C2×C4×Dic53D411yescharacteristic
39C2×C4×Dic53D411yescharacteristic
40#13133124—22no—
41#13133124—22no—
42#13133124—22no—
43#13133124—22no—
44C2×C4⋊C4×C53—21no—
45C2×C42×C53—21no—
46C2×C42×C53C2×C411yescharacteristic
47#95×C53C2×C412yes—
48C22×C4×C53—22no—
49C22×C4×C53C22⋊C411yescharacteristic
50C22×C4×C53C22⋊C411yescharacteristic
51C22×C4×C53C22×C411yescharacteristic
52C22×Dic53—22no—
53C22×Dic53C22⋊C411yescharacteristic
54C22×Dic53C22⋊C411yescharacteristic
55C22×Dic53C2×D411yescharacteristic
56C22×Dic53C2×D411yescharacteristic
57C2×Dic106—22no—
58C2×Dic106—22no—
59C2×Dic106—41no—
60C2×Dic106—44no—
61C2×Dic106—41no—
62C2×Dic106—41no—
63#11719940—24no—
64#11719940—42no—
65C2×#88324—42no—
66C2×#88324—42no—
67C4⋊C4×C53—42no—
68C42×C53—21no—
69C42×C53—21no—
70C42×C53—42no—
71C4⋊Dic53—41no—
72C4⋊Dic53—42no—
73C4⋊Dic53—42no—
74#11719919—41no—
75#11719919—41no—
76C4×Dic53—21no—
77C4×Dic53—21no—
78C4×Dic53—21no—
79C4×Dic53—21no—
80C23×C53C2×C22⋊C411yescharacteristic
81C2×C4×C53—21no—
82C2×C4×C53—21no—
83C2×C4×C53—22no—
84C2×C4×C53—21no—
85C2×C4×C53—41no—
86C2×C4×C53—42no—
87C2×C4×C53—42no—
88C2×C4×C53—42no—
89C2×C4×C53#9911yescharacteristic
90C2×C4×C53#9911yescharacteristic
91C2×C4×C53#10412yes—
92C2×Dic53—21no—
93C2×Dic53—21no—
94C2×Dic53—21no—
95C2×Dic53—21no—
96C2×Dic53—21no—
97C2×Dic53—21no—
98C2×Dic53—21no—
99C2×Dic53—41no—
100C2×Dic53—41no—
101C2×Dic53—44no—
102C2×Dic53—42no—
103C2×Dic53#13712yes—
104Dic106—44no—
105Dic106—82no—
106Dic106—82no—
107#88324—44no—
108#88324—82no—
109#11794—531nomaximal, Sylow
110C22×C53—21no—
111C22×C53—21no—
112C22×C53C2×#9911yescharacteristic
113C22×C53#41911yescharacteristic
114C22×C53C2×#10411yescharacteristic
115C4×C53—21no—
116C4×C53—22no—
117C4×C53—41no—
118C4×C53—82no—
119C4×C53#35512yes—
120Dic53—22no—
121Dic53—41no—
122Dic53—41no—
123Dic53—41no—
124Dic53—82no—
125#2568—531no—
126C4×#101—531no—
127#1467—531no—
128#1353—534no—
129C2×C53—21no—
130C2×C53—21no—
131C2×C53#150811yescharacteristic
132C2×C53#212311yescharacteristic
133C2×C53C2×#35511yescharacteristic
134C2×C4⋊Q8—531no—
135C2×C4×Q8—531no—
136#432—1061no—
137C2×#101—1061no—
138C4×M16—1061no—
139#400—532no—
140#400—532no—
141#391—1061no—
142#391—1061no—
143#391—1061no—
144#382—1061no—
145C4×C4⋊C4#615711yescharacteristic
146#343—532no—
147#324—532no—
148#324—1061no—
149C53#1179411yescharacteristic, complemented, Sylow
150C22×Q8—531no—
151C22×Q8—1061no—
152C2×M16—1062no—
153C4⋊Q8—2121no—
154C4⋊Q8—2121no—
155C4×Q8—2121no—
156C4×Q8—2121no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—531no—
159C2×C4⋊C4—531no—
160C2×C4⋊C4—531no—
161C2×C4⋊C4—532no—
162C2×C4⋊C4—1061no—
163C2×C42—21no—
164C2×C42—531no—
165C2×C42—531no—
166C2×C42C2×#615711yescharacteristic
167C4⋊C8—2121no—
168#101—1064no—
169C22⋊C8—1062no—
170#97—2121no—
171#97—2121no—
172C4×C8—2121no—
173#95—1062no—
174#95—1062no—
175#95—1062no—
176#95—1062no—
177#95C2×#615712yes—
178C2×Q8—1062no—
179C2×Q8—1062no—
180C2×Q8—2121no—
181C2×Q8—2124no—
182C2×Q8—2121no—
183C2×Q8—2121no—
184C22×C4—22no—
185C22×C4—531no—
186C22×C4—531no—
187C22×C4—531no—
188C22×C4—531no—
189C22×C4—1062no—
190C22×C4C22⋊#615711yescharacteristic
191C22×C4C22⋊#615711yescharacteristic
192C22×C4C22×#615711yescharacteristic
193M16—1064no—
194M16—2122no—
195C2×C8—2122no—
196C2×C8—2122no—
197C4⋊C4—42no—
198C4⋊C4—2121no—
199C4⋊C4—2121no—
200C4⋊C4—2121no—
201C4⋊C4—2122no—
202C4⋊C4—2122no—
203C42—21no—
204C42—21no—
205C42—42no—
206C42—1061no—
207C42—1061no—
208C42—1061no—
209C42—1061no—
210C23C2×C22⋊#615711yescharacteristic
211Q8—4242no—
212Q8—4242no—
213Q8—2124no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—532no—
223C2×C4—1061no—
224C2×C4—1061no—
225C2×C4—1061no—
226C2×C4—1061no—
227C2×C4—1061no—
228C2×C4—1061no—
229C2×C4—1061no—
230C2×C4—2124no—
231C2×C4—2122no—
232C2×C4—2121no—
233C2×C4—2121no—
234C2×C4#1313327611yescharacteristic
235C2×C4#1313327611yescharacteristic
236C2×C4#1313328112yes—
237C8—4242no—
238C8—2124no—
239C22—21no—
240C22—21no—
241C22C2×#1313327611yescharacteristic
242C22#1681161611yescharacteristic
243C22C2×#1313328111yescharacteristic
244C4—22no—
245C4—21no—
246C4—41no—
247C4—82no—
248C4—1062no—
249C4—4242no—
250C4—2121no—
251C4—2121no—
252C4—2121no—
253C4#1681153212yes—
254C2—21no—
255C2—21no—
256C2#2029011411yescharacteristic
257C2#2029097911yescharacteristic
258C2C2×#1681153211yescharacteristic
subgroupG/H
centerC22C2×#13133276
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC4×C4⋊C4×C53C4
socleC22×C53C2×#99
prime radicalC23×C53C2×C22⋊C4
cosocleC2×#11719919C23
hypercenterC4×C4⋊C4#6157
hypocenterC53#11794
LCSG ▷ C22×C4×C53 ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
149. C53#11794semidirect

Maximal subgroups

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

subgroupindex
C4×#131332782
#202899772
#202897132
#202799302
#1179453