Finite Group Databasebeta

← #28309579

Subgroups — #28309579

Order 13568.

388 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#20290581C211yesmaximal, characteristic
2#20289957C211yesmaximal, characteristic
3#20289715C214yesmaximal
4#20279923C211yesmaximal, characteristic
5#16811640—21no—
6#16811626—21no—
7C2×#13133278—21no—
8#16811503C2212yes—
9#16811469C2212yes—
10#16811468—21no—
11C2×#13133217C411yescharacteristic
12C2×C4×Dic106C2211yescharacteristic
13#16810544C412yes—
14#16810544C2212yes—
15#16810529—21no—
16#16810522—21no—
17#16810522—21no—
18#16810493—21no—
19C4×C4⋊C4×C53C411yescharacteristic
20C2×#11719940—22no—
21#13133284—41no—
22#13133284—41no—
23C4⋊#88324—41no—
24#13133278—42no—
25C22⋊#88324—22no—
26C4×#88324—41no—
27C22×Dic106C2×C412yes—
28C22×Dic106D411yescharacteristic
29#13133217—41no—
30#13133217—41no—
31C4×Dic106—41no—
32C4×Dic106—41no—
33C2×C4⋊Dic53—21no—
34C2×C4⋊Dic53—21no—
35C2×C4⋊Dic53—22no—
36C2×C4⋊Dic53—22no—
37C2×C4⋊Dic53D411yescharacteristic
38C2×#11719919C2×C411yescharacteristic
39C2×#11719919C2311yescharacteristic
40C2×C4×Dic53D411yescharacteristic
41C2×C4×Dic53D411yescharacteristic
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—41no—
58C2×Dic106—41no—
59C2×Dic106—42no—
60C2×Dic106—82no—
61C2×Dic106SD1612yes—
62C2×Dic106Q1612yes—
63#11719940—42no—
64#11719940—42no—
65C2×#88324—42no—
66C2×#88324—42no—
67C4⋊C4×C53—24no—
68C42×C53—21no—
69C42×C53—21no—
70C42×C53—42no—
71C4⋊Dic53—41no—
72C4⋊Dic53—42no—
73C4⋊Dic53—41no—
74C4⋊Dic53—41no—
75C4⋊Dic53—82no—
76C4⋊Dic53—82no—
77#11719919—41no—
78#11719919—41no—
79C4×Dic53—21no—
80C4×Dic53—21no—
81C4×Dic53—21no—
82C4×Dic53—21no—
83C23×C53C2×C22⋊C411yescharacteristic
84C2×C4×C53—21no—
85C2×C4×C53—21no—
86C2×C4×C53—22no—
87C2×C4×C53—24no—
88C2×C4×C53—21no—
89C2×C4×C53—42no—
90C2×C4×C53—42no—
91C2×C4×C53—41no—
92C2×C4×C53#9911yescharacteristic
93C2×C4×C53#9911yescharacteristic
94C2×C4×C53#10312yes—
95C2×Dic53—21no—
96C2×Dic53—21no—
97C2×Dic53—21no—
98C2×Dic53—21no—
99C2×Dic53—21no—
100C2×Dic53—21no—
101C2×Dic53—41no—
102C2×Dic53—41no—
103C2×Dic53—42no—
104C2×Dic53—42no—
105C2×Dic53—42no—
106C2×Dic53#10312yes—
107C2×Dic53C2×SD1611yescharacteristic
108C2×Dic53C2×Q1611yescharacteristic
109Dic106—42no—
110Dic106—42no—
111Dic106—84no—
112#88324—82no—
113#88324—82no—
114#11908—531nomaximal, Sylow
115C22×C53—21no—
116C22×C53—21no—
117C22×C53C2×#9911yescharacteristic
118C22×C53C2×#10311yescharacteristic
119C22×C53#42111yescharacteristic
120C4×C53—21no—
121C4×C53—22no—
122C4×C53—44no—
123C4×C53—41no—
124C4×C53#35612yes—
125Dic53—21no—
126Dic53—22no—
127Dic53—21no—
128Dic53—41no—
129Dic53—41no—
130Dic53—82no—
131#2567—531no—
132#1801—531no—
133#1461—531no—
134#1354—534no—
135C2×C53—21no—
136C2×C53—21no—
137C2×C53#152011yescharacteristic
138C2×C53#212211yescharacteristic
139C2×C53C2×#35611yescharacteristic
140C2×C4⋊Q8—531no—
141C2×C4×Q8—531no—
142#431—1061no—
143#423—1061no—
144C2×#101—1061no—
145#395—532no—
146#395—532no—
147#391—1061no—
148#389—1061no—
149#389—1061no—
150#384—1061no—
151C4×C4⋊C4#615711yescharacteristic
152#343—532no—
153#324—532no—
154#324—1061no—
155C53#1190811yescharacteristic, complemented, Sylow
156C22×Q8—531no—
157C22×Q8—532no—
158C2×M16—1062no—
159C4⋊Q8—2121no—
160C4⋊Q8—2121no—
161C4×Q8—2121no—
162C4×Q8—2121no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—531no—
165C2×C4⋊C4—531no—
166C2×C4⋊C4—531no—
167C2×C4⋊C4—1062no—
168C2×C4⋊C4—1062no—
169C2×C4⋊C4—1061no—
170C2×C4⋊C4—1061no—
171C2×C42—21no—
172C2×C42—531no—
173C2×C42—531no—
174C2×C42C2×#615711yescharacteristic
175C4⋊C8—2121no—
176C4⋊C8—2121no—
177C4⋊C8—2121no—
178#101—2122no—
179C22⋊C8—1062no—
180C4×C8—2121no—
181#95—1062no—
182#95—1062no—
183#95C2×#615712yes—
184C2×Q8—532no—
185C2×Q8—532no—
186C2×Q8—4242no—
187C2×Q8—2121no—
188C2×Q8—2121no—
189C2×Q8—2122no—
190C22×C4—22no—
191C22×C4—531no—
192C22×C4—531no—
193C22×C4—531no—
194C22×C4—531no—
195C22×C4—1062no—
196C22×C4C22⋊#615711yescharacteristic
197C22×C4C22⋊#615711yescharacteristic
198C22×C4C22×#615711yescharacteristic
199M16—2122no—
200M16—2122no—
201C2×C8—2122no—
202C2×C8—2122no—
203C4⋊C4—24no—
204C4⋊C4—4242no—
205C4⋊C4—4242no—
206C4⋊C4—2121no—
207C4⋊C4—2121no—
208C4⋊C4—2121no—
209C4⋊C4—2122no—
210C4⋊C4—2121no—
211C4⋊C4—2121no—
212C42—21no—
213C42—21no—
214C42—42no—
215C42—1061no—
216C42—1061no—
217C42—1061no—
218C42—1061no—
219C23C2×C22⋊#615711yescharacteristic
220Q8—4244no—
221Q8—2122no—
222Q8—2122no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—532no—
232C2×C4—531no—
233C2×C4—531no—
234C2×C4—1061no—
235C2×C4—1061no—
236C2×C4—1061no—
237C2×C4—1061no—
238C2×C4—1061no—
239C2×C4—1061no—
240C2×C4—2122no—
241C2×C4—2122no—
242C2×C4—2122no—
243C2×C4—2121no—
244C2×C4—2121no—
245C2×C4#1313327611yescharacteristic
246C2×C4#1313327611yescharacteristic
247C2×C4#1313328012yes—
248C8—4242no—
249C8—4242no—
250C22—21no—
251C22—21no—
252C22C2×#1313327611yescharacteristic
253C22C2×#1313328011yescharacteristic
254C22#1681162111yescharacteristic
255C4—22no—
256C4—21no—
257C4—44no—
258C4—41no—
259C4—1061no—
260C4—1062no—
261C4—1061no—
262C4—4242no—
263C4—2121no—
264C4—2121no—
265C4#1681153412yes—
266C2—21no—
267C2—21no—
268C2#2029015411yescharacteristic
269C2#2029097611yescharacteristic
270C2C2×#1681153411yescharacteristic
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#11908
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
155. C53#11908semidirect

Maximal subgroups

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

subgroupindex
#202905812
#202899572
#202897152
#202799232
#1190853