Finite Group Databasebeta

← #16787113

Subgroups — #16787113

Order 3328.

376 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 70 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#13130099C212yesmaximal
2#13129777C212yesmaximal
3#13129767C212yesmaximal
4#13117554C211yesmaximal, characteristic
5C2×Q8×Dic13C2211yescharacteristic
6C2×#88198C411yescharacteristic
7C2×#88141C411yescharacteristic
8#11719128—22no—
9C13×#391C411yescharacteristic
10#11718638C2211yescharacteristic
11#11718593C411yescharacteristic
12#11718590C2211yescharacteristic
13#11718316—22no—
14#11718313—22no—
15#11718285—22no—
16#11718285C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×Dic26C2×C411yescharacteristic
19C2×C13×C4⋊C4C2×C411yescharacteristic
20C2×C42×C13C2×C411yescharacteristic
21Q8×Dic13—42no—
22#88198—22no—
23#88198—22no—
24C2×C4⋊Dic13D412yes—
25C2×C4⋊Dic13C2311yescharacteristic
26C2×#6101—22no—
27C2×#6101—21no—
28C2×C4×Dic13—21no—
29C2×C4×Dic13C2×C411yescharacteristic
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13D412yes—
32#88141—42no—
33C22⋊#1057—24no—
34#88112—42no—
35#88110—42no—
36C13×#95—22no—
37#88071—21no—
38#88071—21no—
39#88071—22no—
40#88071—22no—
41#11536—131nomaximal, Sylow
42C2×Q8×C13—21no—
43C2×Q8×C13—21no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C22⋊C412yes—
49C22×C4×C13C22×C411yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C22⋊C411yescharacteristic
54C22×Dic13C2×D412yes—
55C2×Dic26—21no—
56C2×Dic26—41no—
57C2×Dic26—41no—
58C2×Dic26M1612yes—
59C2×#1057—44no—
60C13×C4⋊C4—41no—
61C42×C13—41no—
62C4⋊Dic13—42no—
63C4⋊Dic13—41no—
64#6101—28no—
65#6101—42no—
66C4×Dic13—21no—
67C4×Dic13—22no—
68C4×Dic13—22no—
69C4×Dic13—22no—
70C4×Dic13—42no—
71C4×Dic13M1612yes—
72#2327—131no—
73#1467—132no—
74#1324—132no—
75#1319—132no—
76C23×C13C2×C22⋊C411yescharacteristic
77Q8×C13—42no—
78Q8×C13—42no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—42no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13C2×M1611yescharacteristic
90C2×C4×C13C2×M1611yescharacteristic
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—41no—
96C2×Dic13—41no—
97C2×Dic13—41no—
98C2×Dic13—41no—
99C2×Dic13—41no—
100C2×Dic13—41no—
101C2×Dic13—42no—
102C2×Dic13#9912yes—
103Dic26—42no—
104Dic26—42no—
105#1057—84no—
106C2×C4⋊Q8—131no—
107C2×C4×Q8—131no—
108C2×C4×Q8—131no—
109#432—262no—
110#391—131no—
111#391#26111yescharacteristic
112#387—262no—
113#387—262no—
114#382—131no—
115#376—131no—
116#324—134no—
117#324—262no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13#40711yescharacteristic
121C22×C13C2×#9911yescharacteristic
122C22×C13#41311yescharacteristic
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—42no—
126C4×C13—81no—
127C4×C13—81no—
128Dic13—22no—
129Dic13—42no—
130Dic13—42no—
131Dic13—41no—
132Dic13—42no—
133C22×Q8—131no—
134C22×Q8C2×#26111yescharacteristic
135C4⋊Q8—262no—
136C4⋊Q8—262no—
137C4×Q8—522no—
138C4×Q8—522no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4—131no—
141C2×C4⋊C4—262no—
142C2×C4⋊C4—261no—
143C2×C4⋊C4C2×#26111yescharacteristic
144C2×C42—131no—
145C2×C42—132no—
146C2×C42—131no—
147C2×C42—261no—
148C2×C42C2×#26111yescharacteristic
149C4⋊C8—522no—
150C22⋊C8—264no—
151#97—522no—
152#95—22no—
153#95—261no—
154#95—261no—
155#95—262no—
156#95—262no—
157C2×C13—21no—
158C2×C13—21no—
159C2×C13#146511yescharacteristic
160C2×C13#212911yescharacteristic
161C2×C13#213311yescharacteristic
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—132no—
167C2×Q8—261no—
168C2×Q8—521no—
169C2×Q8—521no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—131no—
173C22×C4—132no—
174C22×C4—131no—
175C22×C4—261no—
176C22×C4—261no—
177C22×C4C22⋊#26112yes—
178C22×C4C22×#26111yescharacteristic
179C2×C8—524no—
180C4⋊C4—41no—
181C4⋊C4—268no—
182C4⋊C4—521no—
183C4⋊C4—522no—
184C4⋊C4—522no—
185C42—41no—
186C42—132no—
187C42—262no—
188C42—262no—
189C42—262no—
190C42—261no—
191C42—522no—
192C13#1153611yescharacteristic, complemented, Sylow
193C23C2×C22⋊#26111yescharacteristic
194Q8—42no—
195Q8—42no—
196Q8—522no—
197Q8—522no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—132no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—261no—
212C2×C4—262no—
213C2×C4—521no—
214C2×C4—521no—
215C2×C4—521no—
216C2×C4—521no—
217C2×C4—521no—
218C2×C4—522no—
219C2×C4—521no—
220C2×C4D13⋊M1611yescharacteristic
221C2×C4D13⋊M1611yescharacteristic
222C8—1044no—
223C22—21no—
224C22—21no—
225C22#1171912611yescharacteristic
226C22D13⋊#9911yescharacteristic
227C22#1171914811yescharacteristic
228C4—21no—
229C4—21no—
230C4—42no—
231C4—81no—
232C4—81no—
233C4—262no—
234C4—522no—
235C4—522no—
236C4—522no—
237C4—521no—
238C2—21no—
239C2—21no—
240C2#1313009411yescharacteristic
241C2#1313111911yescharacteristic
242C2#1313113211yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#391C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenter#391#261
hypocenterC13#11536
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
192. C13#11536semidirect

Maximal subgroups

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

subgroupindex
#131300992
#131297772
#131297672
#131175542
#1153613