Finite Group Databasebeta

← #15766866

Subgroups — #15766866

Order 3328.

344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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#13125982C211yesmaximal, characteristic
2#13115825C211yesmaximal, characteristic
3#13113624C211yesmaximal, characteristic
4#13113573C211yesmaximal, characteristic
5#13113522C211yesmaximal, characteristic
6#13113258C211yesmaximal, characteristic
7C13×#1299C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C4×C13×M16C2211yescharacteristic
13#11718586C2211yescharacteristic
14#11718585C2211yescharacteristic
15#11718512—21no—
16#11718512—21no—
17#11718382—22no—
18#11718342—21no—
19#11718341—21no—
20#11718146—22no—
21#11718078—22no—
22#11718078—21no—
23#11718074—21no—
24#11718072—21no—
25#11718071—21no—
26#11718048—22no—
27C22×Dic26—21no—
28C2×C13×M16—21no—
29C2×C13×M16—21no—
30C2×C42×C13C2311yescharacteristic
31#88180—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13D412yes—
34#88178—21no—
35#88178—21no—
36C2×#6099—21no—
37#88124—21no—
38#88123—21no—
39#88123—21no—
40#88123—21no—
41#88123—21no—
42#88123D411yescharacteristic
43#88123D411yescharacteristic
44C4×Dic26—21no—
45C4×Dic26—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8D411yescharacteristic
49C13×C4⋊C8D411yescharacteristic
50C13×C22⋊C8—21no—
51C13×#97—21no—
52C4×C8×C13—21no—
53C4×C8×C13—21no—
54C22⋊#1055—21no—
55#88057—22no—
56#88057—22no—
57#88056—22no—
58#88056—22no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62C4×#1055—21no—
63#10494—131nomaximal, Sylow
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13#4111yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×Dic13—22no—
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26—41no—
71C2×Dic26—41no—
72C2×Dic26—82no—
73C13×M16—22no—
74C13×M16—41no—
75C13×M16—81no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C42×C13C2×D411yescharacteristic
81C42×C13C2×D411yescharacteristic
82C42×C13C2×D411yescharacteristic
83C42×C13#4111yescharacteristic
84C22⋊Dic13—41no—
85C4⋊Dic13—21no—
86C4⋊Dic13—22no—
87C4⋊Dic13—21no—
88C4⋊Dic13—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—41no—
94#6101—41no—
95C4×Dic13—41no—
96#6099—42no—
97C2×#1055—22no—
98C2×#1055—41no—
99#3229—131no—
100#1997—131no—
101#1574—131no—
102#1561—131no—
103#1549—131no—
104#1485—131no—
105#1299D1311yescharacteristic
106C23×C13#12311yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13#12011yescharacteristic
113C2×C4×C13#12111yescharacteristic
114C2×C4×C13#12111yescharacteristic
115C2×C4×C13#12111yescharacteristic
116C2×C4×C13#12311yescharacteristic
117C2×C4×C13#12411yescharacteristic
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—42no—
121C2×Dic13—82no—
122Dic26—41no—
123Dic26—41no—
124Dic26—41no—
125Dic26—41no—
126Dic26—82no—
127Dic26—82no—
128C8×C13—42no—
129C8×C13—41no—
130C8×C13—41no—
131C8×C13—81no—
132#1055—42no—
133#1055—81no—
134#533—131no—
135C2×C4⋊Q8—131no—
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×M16C2×D1311yescharacteristic
146#343—262no—
147#335—261no—
148#334—261no—
149#332—262no—
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#45411yescharacteristic
161C4×C13#45611yescharacteristic
162C4×C13#47111yescharacteristic
163C4×C13#47112yes—
164C4×C13#47311yescharacteristic
165Dic13—81no—
166Dic13—81no—
167Dic13—82no—
168C22×Q8—261no—
169C2×M16—21no—
170C2×M16—21no—
171C2×M16—261no—
172C4⋊Q8—131no—
173C4⋊Q8—131no—
174C4⋊Q8—261no—
175C4⋊Q8—261no—
176C4⋊Q8—261no—
177C4⋊Q8—261no—
178#125—261no—
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181C4×Q8—261no—
182C4×Q8—261no—
183#117—261no—
184C2×C4⋊C4—132no—
185C2×C4⋊C4—261no—
186C2×C42C22×D1311yescharacteristic
187#106—262no—
188#106—262no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8—132no—
192C4⋊C8—261no—
193C4⋊C8—261no—
194C4⋊C8D5211yescharacteristic
195C4⋊C8D5211yescharacteristic
196#103—262no—
197#103—262no—
198C22⋊C8—21no—
199C22⋊C8—261no—
200#97—21no—
201C4×C8—21no—
202C4×C8—21no—
203C4×C8—261no—
204C2×C13—41no—
205C2×C13#203811yescharacteristic
206C2×C13#204611yescharacteristic
207C2×C13#205211yescharacteristic
208C2×Q8—261no—
209C2×Q8—261no—
210C2×Q8—521no—
211C2×Q8—521no—
212C2×Q8—1042no—
213C22×C4—262no—
214C22×C4#612711yescharacteristic
215C22×C4D4×D1311yescharacteristic
216C22×C4#613111yescharacteristic
217M16—22no—
218M16—41no—
219M16—81no—
220M16—522no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—262no—
226C2×C8—521no—
227C4⋊C4—262no—
228C4⋊C4—261no—
229C4⋊C4—262no—
230C4⋊C4—261no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C22⋊C4—521no—
238C42—521no—
239C42C2×D5211yescharacteristic
240C42#612711yescharacteristic
241C42D4×D1311yescharacteristic
242C42D4×D1311yescharacteristic
243C13#1049411yescharacteristic, complemented, Sylow
244C23#8814811yescharacteristic
245Q8—521no—
246Q8—521no—
247Q8—521no—
248Q8—521no—
249Q8—1042no—
250Q8—1042no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—522no—
259C2×C4—1042no—
260C2×C4#8812911yescharacteristic
261C2×C4#8813611yescharacteristic
262C2×C4#8813811yescharacteristic
263C2×C4#8813811yescharacteristic
264C2×C4#8814811yescharacteristic
265C2×C4#8814911yescharacteristic
266C8—42no—
267C8—41no—
268C8—41no—
269C8—81no—
270C8—522no—
271C8—1041no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#1171833311yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—1041no—
280C4—1042no—
281C4—1041no—
282C4#1171840911yescharacteristic
283C4#1171841611yescharacteristic
284C4#1171848711yescharacteristic
285C4#1171848811yescharacteristic
286C4#1171855912yes—
287C2—41no—
288C2#1311605611yescharacteristic
289C2#1311610011yescharacteristic
290C2#1311613811yescharacteristic
subgroupG/H
centerC22#11718333
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1299C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1299D13
hypocenterC13#10494
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1299

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
#131259822
#131158252
#131136242
#131135732
#131135222
#131132582
C13×#12992
#1049413