Finite Group Databasebeta

← #15754668

Subgroups — #15754668

Order 3328.

706 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#11719275C211yesmaximal, characteristic
2#13113518C212yesmaximal
3#13113264C212yesmaximal
4#13113160C211yesmaximal, characteristic
5C13×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×Q8×Dic13—21no—
8#11719275—24no—
9#11719275—24no—
10C2×#88144—22no—
11C2×#88144—21no—
12C2×#88123C412yes—
13C2×#88123C2211yescharacteristic
14C2×C4×Dic26C412yes—
15C2×C4×Dic26C2211yescharacteristic
16C13×#423C2212yes—
17C2×C13×#101—21no—
18#11718586C2212yes—
19C13×#343—21no—
20#11718120—22no—
21#11718076—24no—
22#11718073—24no—
23C22×Q8×C13D411yescharacteristic
24C22×Dic26C2×C412yes—
25C22×Dic26C2×C411yescharacteristic
26C2×C13×M16—22no—
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C42×C13C2×C412yes—
32C2×C42×C13C2311yescharacteristic
33Q8×Dic13—28no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×#6101—22no—
40C2×#6101—21no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13—21no—
43#88144—216no—
44#88144—28no—
45#88123—24no—
46#88123—24no—
47#88123—22no—
48#88123D414yes—
49C4×Dic26—24no—
50C4×Dic26—22no—
51C4×Dic26—24no—
52C4×Dic26D414yes—
53C13×C4⋊C8—22no—
54C13×C4⋊C8—22no—
55C13×#101—42no—
56C22⋊#1055—22no—
57C4⋊#1055—22no—
58C4×#1055—22no—
59#8392—131nomaximal, Sylow
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13SD1612yes—
63C2×Q8×C13Q1612yes—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—22no—
71C22×Dic13—21no—
72C2×Dic26—21no—
73C2×Dic26—22no—
74C2×Dic26—42no—
75C2×Dic26—44no—
76C2×Dic26C22⋊C412yes—
77C2×Dic26C22⋊C414yes—
78C13×M16—42no—
79C13×M16—42no—
80C2×C8×C13—42no—
81C13×C4⋊C4—24no—
82C13×C4⋊C4—22no—
83C42×C13—22no—
84C42×C13—22no—
85C42×C13C2×D412yes—
86C42×C13C2×D412yes—
87C4⋊Dic13—28no—
88C4⋊Dic13—28no—
89C4⋊Dic13—21no—
90C4⋊Dic13—24no—
91C4⋊Dic13—24no—
92C4⋊Dic13C22⋊C412yes—
93#6101—28no—
94#6101—24no—
95C4×Dic13—28no—
96C4×Dic13—24no—
97C2×#1055—42no—
98C2×#557—131no—
99#1801D1311yescharacteristic
100#1548—132no—
101#1487—132no—
102#1461—131no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—24no—
105Q8×C13—24no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13#10314yes—
113C2×C4×C13C2×C22⋊C411yescharacteristic
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13#12012yes—
116C2×C4×C13#12012yes—
117C2×C4×C13C2×SD1611yescharacteristic
118C2×C4×C13C2×Q1611yescharacteristic
119C2×C4×C13#13712yes—
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—24no—
123C2×Dic13—42no—
124C2×Dic13—44no—
125C2×Dic13—42no—
126Dic26—24no—
127Dic26—42no—
128Dic26—44no—
129Dic26—44no—
130C8×C13—82no—
131#1055—82no—
132#557—264no—
133#557—264no—
134C2×C4⋊Q8—132no—
135C2×C4⋊Q8—131no—
136C2×#125—262no—
137C2×#125—261no—
138C2×C4×Q8—132no—
139C2×C4×Q8—131no—
140C2×C4×Q8—261no—
141C2×C4×Q8C2×D1311yescharacteristic
142#431—132no—
143#423C2×D1312yes—
144C2×#101—21no—
145#343—21no—
146#333—264no—
147Q8⋊C8—264no—
148#324—262no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13#37911yescharacteristic
152C22×C13C2×#10311yescharacteristic
153C22×C13#41911yescharacteristic
154C4×C13—22no—
155C4×C13—21no—
156C4×C13—24no—
157C4×C13—42no—
158C4×C13#41312yes—
159C4×C13#44812yes—
160C4×C13#45112yes—
161Dic13—42no—
162Dic13—42no—
163Dic13—44no—
164C22×Q8—131no—
165C22×Q8—132no—
166C22×Q8C22⋊D1311yescharacteristic
167C2×M16—22no—
168C4⋊Q8—134no—
169C4⋊Q8—264no—
170C4⋊Q8—264no—
171C4⋊Q8—262no—
172#125—2616no—
173#125—268no—
174C4×Q8—22no—
175C4×Q8—22no—
176C4×Q8—134no—
177C4×Q8—264no—
178C4×Q8—264no—
179C4×Q8—268no—
180C4×Q8—262no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—262no—
183C2×C4⋊C4—262no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4D5212yes—
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C42—262no—
191C2×C42—261no—
192C2×C42C4×D1312yes—
193C2×C42C22×D1311yescharacteristic
194C4⋊C8—22no—
195C4⋊C8—22no—
196C4⋊C8—262no—
197#101—42no—
198C22⋊C8—262no—
199C4×C8—262no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13#178511yescharacteristic
203C2×C13#178711yescharacteristic
204C2×C13#179611yescharacteristic
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8—132no—
208C2×Q8—134no—
209C2×Q8—261no—
210C2×Q8—262no—
211C2×Q8—522no—
212C2×Q8—524no—
213C2×Q8#610512yes—
214C2×Q8#610712yes—
215C22×C4—261no—
216C22×C4—262no—
217C22×C4—261no—
218C22×C4#610312yes—
219C22×C4#610312yes—
220C22×C4C2×C4×D1311yescharacteristic
221C22×C4C2×D5211yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223M16—42no—
224M16—42no—
225C2×C8—42no—
226C2×C8—522no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C4⋊C4—132no—
230C4⋊C4—268no—
231C4⋊C4—268no—
232C4⋊C4—268no—
233C4⋊C4—261no—
234C4⋊C4—264no—
235C4⋊C4—264no—
236C4⋊C4—264no—
237C42—22no—
238C42—22no—
239C42—268no—
240C42—264no—
241C42D4×D1312yes—
242C42D4×D1312yes—
243C13#839211yescharacteristic, complemented, Sylow
244C23C2×#610311yescharacteristic
245Q8—24no—
246Q8—24no—
247Q8—264no—
248Q8—524no—
249Q8—522no—
250Q8—524no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—264no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4—524no—
263C2×C4#8805014yes—
264C2×C4C22⋊C4×D1311yescharacteristic
265C2×C4C22⋊C4×D1311yescharacteristic
266C2×C4#8813612yes—
267C2×C4C2×#610511yescharacteristic
268C2×C4#8819112yes—
269C2×C4C2×#610711yescharacteristic
270C2×C4#8820512yes—
271C8—82no—
272C8—1042no—
273C22—21no—
274C22—21no—
275C22#1171861611yescharacteristic
276C22C2×#8805011yescharacteristic
277C22#1171866511yescharacteristic
278C4—21no—
279C4—24no—
280C4—22no—
281C4—42no—
282C4—522no—
283C4—524no—
284C4—522no—
285C4#1171841212yes—
286C4#1171870112yes—
287C4#1171871112yes—
288C2—21no—
289C2—21no—
290C2#1311476311yescharacteristic
291C2#1311477011yescharacteristic
292C2#1311481211yescharacteristic
subgroupG/H
centerC22#11718616
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1801C2
socleC22×C13#379
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1801D13
hypocenterC13#8392
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
243. C13#8392semidirect

Maximal subgroups

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

subgroupindex
C2×#117192752
#131135182
#131132642
#131131602
C13×#18012
#839213