Finite Group Databasebeta

← #16778469

Subgroups — #16778469

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—42no—
28Q8×Dic13—42no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—22no—
32C2×C4⋊Dic13C2×C412yes—
33C2×C4×Dic13—22no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13C2311yescharacteristic
40#88112—24no—
41#88110—42no—
42#88071—22no—
43#88071—22no—
44#7625—131nomaximal, Sylow
45C2×Q8×C13—24no—
46C2×Q8×C13—42no—
47C2×Q8×C13—42no—
48C22×C4×C13—22no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13—22no—
53C22×Dic13C22⋊C411yescharacteristic
54C22×Dic13C22⋊C411yescharacteristic
55C22×Dic13C2×D411yescharacteristic
56C22×Dic13C2×D411yescharacteristic
57C2×#1057—24no—
58C2×#1057—42no—
59C2×#1057—42no—
60C2×#1057—42no—
61C2×#1057—42no—
62C2×#1057—42no—
63C13×C4⋊C4—24no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4M1614yes—
66C42×C13—22no—
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4⋊Dic13—42no—
72C4×Dic13—22no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C4×Dic13—41no—
76C4×Dic13—41no—
77C4×Dic13—44no—
78C4×Dic13D812yes—
79C4×Dic13SD1612yes—
80C4×C4⋊Q8—131no—
81#1839—131no—
82#1767—131no—
83#1271—134no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—48no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—24no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13#10212yes—
96C2×C4×C13#10412yes—
97C2×C4×C13C2×M1612yes—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13#10112yes—
110C2×Dic13#10212yes—
111C2×Dic13C2×D811yescharacteristic
112C2×Dic13C2×SD1611yescharacteristic
113C2×Dic13#13712yes—
114#1057—44no—
115#1057—82no—
116C2×C4⋊Q8#26111yescharacteristic
117C2×C4×Q8—261no—
118C2×C4⋊C8—261no—
119C2×#97—261no—
120#391—261no—
121#389—132no—
122#389—261no—
123#384—131no—
124C4×C4⋊C4—132no—
125C4×C4⋊C4—261no—
126C43—131no—
127#336—132no—
128#336—132no—
129#336—261no—
130#336—261no—
131C22×C13#40711yescharacteristic
132C22×C13#41011yescharacteristic
133C22×C13C2×#10111yescharacteristic
134C22×C13C2×#10211yescharacteristic
135C22×C13#41911yescharacteristic
136C22×C13C2×#10411yescharacteristic
137C22×C13#42111yescharacteristic
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—44no—
142Dic13—22no—
143Dic13—21no—
144Dic13—21no—
145Dic13—22no—
146Dic13—22no—
147Dic13—82no—
148C22×Q8—21no—
149C22×C8—262no—
150C22×C8—262no—
151C4⋊Q8—24no—
152C4×Q8—522no—
153C4×Q8—522no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4—262no—
157C2×C4⋊C4—261no—
158C2×C4⋊C4—261no—
159C2×C4⋊C4C2×#26112yes—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—131no—
164C2×C42—131no—
165C2×C42—131no—
166C2×C42—262no—
167C2×C42C2×#26111yescharacteristic
168C4⋊C8—264no—
169#97—522no—
170#95—262no—
171#95—262no—
172C2×C13#146711yescharacteristic
173C2×C13#148611yescharacteristic
174C2×C13#149111yescharacteristic
175C2×C13#150211yescharacteristic
176C2×C13#151511yescharacteristic
177C2×C13#153111yescharacteristic
178C2×C13#154611yescharacteristic
179C2×Q8—24no—
180C2×Q8—42no—
181C2×Q8—42no—
182C22×C4—22no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—131no—
186C22×C4—131no—
187C22×C4—262no—
188C22×C4C22⋊#26111yescharacteristic
189C22×C4C22⋊#26111yescharacteristic
190C22×C4C22×#26111yescharacteristic
191C2×C8—264no—
192C2×C8—522no—
193C2×C8—522no—
194C2×C8—522no—
195C2×C8—522no—
196C2×C8—522no—
197C4⋊C4—24no—
198C4⋊C4—22no—
199C4⋊C4—522no—
200C4⋊C4—522no—
201C4⋊C4—522no—
202C4⋊C4—522no—
203C4⋊C4—522no—
204C4⋊C4#612214yes—
205C42—22no—
206C42—132no—
207C42—132no—
208C42—262no—
209C42—262no—
210C42—262no—
211C42—521no—
212C42—521no—
213C42—524no—
214C13#762511yescharacteristic, complemented, Sylow
215C23C2×C22⋊#26111yescharacteristic
216Q8—48no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—24no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—132no—
227C2×C4—131no—
228C2×C4—131no—
229C2×C4—132no—
230C2×C4—132no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4#8811512yes—
243C2×C4#8811812yes—
244C2×C4C2×#612212yes—
245C8—524no—
246C8—1042no—
247C22C2×#8811511yescharacteristic
248C22#1171914011yescharacteristic
249C22#1171915311yescharacteristic
250C22C2×#8811811yescharacteristic
251C22#1171915611yescharacteristic
252C22D13⋊#10111yescharacteristic
253C22#1171916911yescharacteristic
254C4—22no—
255C4—22no—
256C4—22no—
257C4—44no—
258C4—262no—
259C4—262no—
260C4—262no—
261C4—261no—
262C4—261no—
263C4—1042no—
264C2#1313009911yescharacteristic
265C2#1313016111yescharacteristic
266C2#1313017811yescharacteristic
267C2#1313021711yescharacteristic
268C2#1313025911yescharacteristic
269C2#1313031011yescharacteristic
270C2#1313034611yescharacteristic
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#7625
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
214. C13#7625semidirect

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
#762513