Finite Group Databasebeta

← #16778459

Subgroups — #16778459

Order 3328.

462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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#13130764C211yesmaximal, characteristic
2#13130621C211yesmaximal, characteristic
3#13129654C214yesmaximal
4C4⋊Q8×Dic13C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×Q8×Dic13—21no—
7C2×#88112—21no—
8C2×#88110—21no—
9#11718891—21no—
10#11718646—21no—
11#11718646C2212yes—
12C4⋊C4×Dic13—21no—
13C4⋊C4×Dic13C412yes—
14#11718596C411yescharacteristic
15C42×Dic13C2211yescharacteristic
16#11718290—21no—
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×Q8×C13—21no—
21C22×#1057—22no—
22C22×#1057—22no—
23C13×C4⋊Q8—24no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27Q8×Dic13—44no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—22no—
31C2×C4⋊Dic13C2×C412yes—
32C2×C4×Dic13—22no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13C2311yescharacteristic
39#88112—24no—
40#88110—42no—
41#88071—22no—
42#88071—22no—
43#7622—131nomaximal, Sylow
44C2×Q8×C13—24no—
45C2×Q8×C13—42no—
46C2×Q8×C13—42no—
47C22×C4×C13—22no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C22⋊C411yescharacteristic
54C22×Dic13C2×D411yescharacteristic
55C22×Dic13C2×D411yescharacteristic
56C2×#1057—24no—
57C2×#1057—42no—
58C2×#1057—42no—
59C2×#1057—42no—
60C2×#1057—42no—
61C2×#1057—42no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—22no—
64C13×C4⋊C4M1614yes—
65C42×C13—22no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C4⋊Dic13—44no—
69C4⋊Dic13—42no—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13—41no—
74C4×Dic13—41no—
75C4×Dic13—44no—
76C4×Dic13SD1612yes—
77C4×Dic13Q1612yes—
78C4×C4⋊Q8—131no—
79#1839—131no—
80#1767—131no—
81#1271—134no—
82C23×C13C2×C22⋊C411yescharacteristic
83Q8×C13—48no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—24no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13#10312yes—
94C2×C4×C13#10412yes—
95C2×C4×C13C2×M1612yes—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13#10112yes—
108C2×Dic13#10312yes—
109C2×Dic13C2×SD1611yescharacteristic
110C2×Dic13C2×Q1611yescharacteristic
111C2×Dic13AGL(1,ℤ/8)12yes—
112#1057—44no—
113#1057—82no—
114C2×C4⋊Q8#26111yescharacteristic
115C2×C4×Q8—261no—
116C2×C4⋊C8—261no—
117C2×#97—261no—
118#391—261no—
119#389—132no—
120#389—261no—
121#384—131no—
122C4×C4⋊C4—132no—
123C4×C4⋊C4—261no—
124C43—131no—
125#336—132no—
126#336—132no—
127#336—261no—
128#336—261no—
129C22×C13#40711yescharacteristic
130C22×C13#41011yescharacteristic
131C22×C13C2×#10111yescharacteristic
132C22×C13C2×#10311yescharacteristic
133C22×C13#41811yescharacteristic
134C22×C13C2×#10411yescharacteristic
135C22×C13#42111yescharacteristic
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—22no—
139C4×C13—44no—
140Dic13—22no—
141Dic13—21no—
142Dic13—21no—
143Dic13—22no—
144Dic13—22no—
145Dic13—82no—
146C22×Q8—21no—
147C22×C8—262no—
148C22×C8—262no—
149C4⋊Q8—24no—
150C4×Q8—524no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4—262no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4C2×#26112yes—
157C2×C42—131no—
158C2×C42—131no—
159C2×C42—131no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—262no—
164C2×C42C2×#26111yescharacteristic
165C4⋊C8—264no—
166#97—522no—
167#95—262no—
168#95—262no—
169C2×C13#146711yescharacteristic
170C2×C13#148711yescharacteristic
171C2×C13#149011yescharacteristic
172C2×C13#150311yescharacteristic
173C2×C13#151411yescharacteristic
174C2×C13#153111yescharacteristic
175C2×C13#154911yescharacteristic
176C2×Q8—24no—
177C2×Q8—42no—
178C2×Q8—42no—
179C22×C4—22no—
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—262no—
185C22×C4C22⋊#26111yescharacteristic
186C22×C4C22⋊#26111yescharacteristic
187C22×C4C22×#26111yescharacteristic
188C2×C8—264no—
189C2×C8—522no—
190C2×C8—522no—
191C2×C8—522no—
192C2×C8—522no—
193C2×C8—522no—
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—522no—
197C4⋊C4—522no—
198C4⋊C4—522no—
199C4⋊C4—524no—
200C4⋊C4#612214yes—
201C42—22no—
202C42—132no—
203C42—132no—
204C42—262no—
205C42—262no—
206C42—262no—
207C42—521no—
208C42—521no—
209C42—524no—
210C13#762211yescharacteristic, complemented, Sylow
211C23C2×C22⋊#26111yescharacteristic
212Q8—48no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—24no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—132no—
223C2×C4—131no—
224C2×C4—132no—
225C2×C4—131no—
226C2×C4—132no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4—522no—
238C2×C4#8811612yes—
239C2×C4#8811712yes—
240C2×C4C2×#612212yes—
241C8—524no—
242C8—1042no—
243C22#1171913811yescharacteristic
244C22C2×#8811611yescharacteristic
245C22C2×#8811711yescharacteristic
246C22#1171915511yescharacteristic
247C22#1171915611yescharacteristic
248C22D13⋊#10111yescharacteristic
249C22#1171916911yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—44no—
254C4—262no—
255C4—262no—
256C4—262no—
257C4—261no—
258C4—261no—
259C4—1042no—
260C2#1313009911yescharacteristic
261C2#1313016411yescharacteristic
262C2#1313017511yescharacteristic
263C2#1313021911yescharacteristic
264C2#1313025711yescharacteristic
265C2#1313030911yescharacteristic
266C2#1313035211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#7622
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
210. C13#7622semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131306212
#131296542
C4⋊Q8×Dic132
#762213