Finite Group Databasebeta

← #15766864

Subgroups — #15766864

Order 3328.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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#13125980C211yesmaximal, characteristic
2#13115826C211yesmaximal, characteristic
3#13113625C211yesmaximal, characteristic
4#13113573C211yesmaximal, characteristic
5#13113256C211yesmaximal, characteristic
6#13112725C211yesmaximal, characteristic
7C13×#1549C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12#11718755—21no—
13#11718755—21no—
14#11718754—21no—
15#11718740—21no—
16#11718632—22no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19C4×#6099C2211yescharacteristic
20C13×#332—22no—
21#11718122—22no—
22#11718078—21no—
23#11718076—22no—
24#11718074—21no—
25#11718050—21no—
26#11718049—21no—
27C22×Q8×C13—21no—
28C2×C13×M16—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D412yes—
35C2×C42×C13C2311yescharacteristic
36#88180—21no—
37#88178—21no—
38#88178—21no—
39C2×#6099—21no—
40C2×#6099—21no—
41#88124—21no—
42#88123D411yescharacteristic
43#88123D411yescharacteristic
44C4×Dic26—21no—
45C4×Dic26—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8D412yes—
49C13×C22⋊C8—21no—
50C4×C8×C13—21no—
51C22⋊#1055—21no—
52#88050—22no—
53#88050—22no—
54#88048—22no—
55#88048—22no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4⋊#1055D411yescharacteristic
59C4⋊#1055D411yescharacteristic
60#88043—21no—
61C4×#1055—21no—
62C4×#1055—21no—
63#10494—131nomaximal, Sylow
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13—82no—
67C22×C4×C13—22no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4111yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C2×Dic26—21no—
72C2×Dic26—21no—
73C13×M16—81no—
74C2×C8×C13—22no—
75C2×C8×C13—41no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C42×C13C2×D411yescharacteristic
81C42×C13C2×D411yescharacteristic
82C42×C13C2×D411yescharacteristic
83C42×C13#4111yescharacteristic
84C22⋊Dic13—41no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—41no—
92#6099—22no—
93#6099—41no—
94#6099—42no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—41no—
98C2×#1055—41no—
99#3229—131no—
100#1997—131no—
101#1574—131no—
102#1561—131no—
103#1549D1311yescharacteristic
104#1485—131no—
105#1299—131no—
106C23×C13#12311yescharacteristic
107Q8×C13—82no—
108Q8×C13—82no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—82no—
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13#12111yescharacteristic
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12111yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13#12411yescharacteristic
122C2×Dic13—41no—
123C2×Dic13—41no—
124Dic26—41no—
125Dic26—41no—
126Dic26—41no—
127Dic26—41no—
128C8×C13—42no—
129C8×C13—81no—
130#1055—42no—
131#1055—41no—
132#1055—41no—
133#1055—81no—
134#533—131no—
135C2×C4⋊Q8C2×D1311yescharacteristic
136#498—261no—
137#487—261no—
138#483—262no—
139#475—261no—
140#475—261no—
141#431—131no—
142#431C2×D1311yescharacteristic
143#423—131no—
144#423C2×D1311yescharacteristic
145C4×M16—131no—
146#343—262no—
147#335—261no—
148#334—261no—
149#332—22no—
150#332—261no—
151#332—261no—
152Q8⋊C8—262no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13#39411yescharacteristic
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—82no—
161C4×C13#45411yescharacteristic
162C4×C13#45611yescharacteristic
163C4×C13#47111yescharacteristic
164C4×C13#47112yes—
165C4×C13#47311yescharacteristic
166Dic13—81no—
167Dic13—81no—
168C22×Q8—21no—
169C2×M16—21no—
170C2×M16—261no—
171C2×M16—261no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—131no—
177C4⋊Q8—131no—
178#125—261no—
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181C4×Q8—261no—
182C4×Q8—261no—
183#117—261no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4D5212yes—
186C2×C42C22×D1311yescharacteristic
187#106—262no—
188#106—262no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—131no—
192C4⋊C8—131no—
193C4⋊C8—261no—
194C4⋊C8—261no—
195C4⋊C8C22⋊D1312yes—
196#103—262no—
197#103—262no—
198C22⋊C8—21no—
199C22⋊C8—261no—
200#97—261no—
201C4×C8—21no—
202C4×C8—261no—
203C4×C8—261no—
204C2×C13—41no—
205C2×C13#203811yescharacteristic
206C2×C13#204611yescharacteristic
207C2×C13#205211yescharacteristic
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8—82no—
211C2×Q8—261no—
212C2×Q8—261no—
213C22×C4—22no—
214C22×C4C2×D5211yescharacteristic
215C22×C4#612911yescharacteristic
216C22×C4#612911yescharacteristic
217M16—81no—
218M16—262no—
219M16—521no—
220M16—522no—
221C2×C8—22no—
222C2×C8—41no—
223C2×C8—261no—
224C2×C8—261no—
225C2×C8—521no—
226C2×C8—521no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4—261no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C22⋊C4—521no—
238C42—521no—
239C42#612711yescharacteristic
240C42D4×D1311yescharacteristic
241C42D4×D1311yescharacteristic
242C42C2×C22⋊D1311yescharacteristic
243C13#1049411yescharacteristic, complemented, Sylow
244C23#8814011yescharacteristic
245Q8—82no—
246Q8—82no—
247Q8—521no—
248Q8—521no—
249Q8—521no—
250Q8—521no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—82no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4#8813611yescharacteristic
261C2×C4#8813711yescharacteristic
262C2×C4#8813911yescharacteristic
263C2×C4#8818411yescharacteristic
264C2×C4#8819211yescharacteristic
265C2×C4#8819311yescharacteristic
266C8—42no—
267C8—81no—
268C8—522no—
269C8—521no—
270C8—521no—
271C8—1041no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#1171862211yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—82no—
280C4—1041no—
281C4—1041no—
282C4#1171841311yescharacteristic
283C4#1171841411yescharacteristic
284C4#1171883811yescharacteristic
285C4#1171885311yescharacteristic
286C4#1171886112yes—
287C2—41no—
288C2#1311605411yescharacteristic
289C2#1311609811yescharacteristic
290C2#1311613611yescharacteristic
subgroupG/H
centerC22#11718622
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1549C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1549D13
hypocenterC13#10494
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
243. C13#10494semidirect

Maximal subgroups

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

subgroupindex
#131259802
#131158262
#131136252
#131135732
#131132562
#131127252
C13×#15492
#1049413