Finite Group Databasebeta

← #15766557

Subgroups — #15766557

Order 3328.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11718512C211yesmaximal, characteristic
2#13114829C211yesmaximal, characteristic
3#13113520C211yesmaximal, characteristic
4#13113518C211yesmaximal, characteristic
5#13113230C211yesmaximal, characteristic
6#13112733C211yesmaximal, characteristic
7C13×#1570C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×#88064—21no—
14C2×#88057—21no—
15C2×#88056—21no—
16#11718586C2211yescharacteristic
17#11718585C2211yescharacteristic
18#11718512—22no—
19#11718512—22no—
20C13×#334—22no—
21#11718146—21no—
22#11718076—22no—
23#11718074—22no—
24#11718073—22no—
25C22×Dic26—21no—
26C22×Dic26D411yescharacteristic
27C2×C13×M16—21no—
28C22×C8×C13—21no—
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13D411yescharacteristic
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×#6099—21no—
36#88123—21no—
37#88123—21no—
38#88123—21no—
39#88123D412yes—
40C4×Dic26—21no—
41C4×Dic26—21no—
42C4×Dic26—21no—
43C4×Dic26—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8D412yes—
48C13×C4⋊C8D412yes—
49C13×C22⋊C8—21no—
50C4×C8×C13—21no—
51C22⋊#1055—21no—
52#88064—42no—
53#88057—24no—
54#88056—24no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4×#1055—21no—
59#10450—131nomaximal, Sylow
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×C4×C13#4111yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—41no—
66C2×Dic26—21no—
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26—22no—
72C2×Dic26—41no—
73C2×Dic26—82no—
74C2×Dic26SD1612yes—
75C13×M16—41no—
76C13×M16—41no—
77C2×C8×C13—22no—
78C2×C8×C13—22no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C42×C13C2×D411yescharacteristic
83C42×C13C2×D411yescharacteristic
84C42×C13C2×D411yescharacteristic
85C42×C13#4111yescharacteristic
86C4⋊Dic13—21no—
87C4⋊Dic13—22no—
88C4⋊Dic13—21no—
89C4⋊Dic13—22no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92#6101—41no—
93#6101—41no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96#6099—41no—
97#6099—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#475—131no—
101#1801—131no—
102#1570D1311yescharacteristic
103#1549—131no—
104#1548—131no—
105#1479—131no—
106#1301—131no—
107C23×C13#12311yescharacteristic
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13#12011yescharacteristic
111C2×C4×C13#12111yescharacteristic
112C2×C4×C13#12111yescharacteristic
113C2×C4×C13#12111yescharacteristic
114C2×C4×C13#12311yescharacteristic
115C2×C4×C13#12411yescharacteristic
116C2×C4×C13C2×SD1611yescharacteristic
117C2×C4×C13#13511yescharacteristic
118C2×C4×C13#13711yescharacteristic
119C2×C4×C13#13711yescharacteristic
120C2×Dic13—22no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—42no—
125C2×Dic13—82no—
126C2×Dic13—81no—
127Dic26—22no—
128Dic26—22no—
129Dic26—41no—
130Dic26—41no—
131Dic26—82no—
132Dic26—82no—
133C8×C13—42no—
134C8×C13—42no—
135C8×C13—81no—
136#1055—81no—
137#1055—81no—
138C2×C4⋊Q8—131no—
139C2×C4×Q8—131no—
140#475—262no—
141#475—262no—
142#431—131no—
143#431C2×D1311yescharacteristic
144C2×#106—261no—
145#423—131no—
146#423C2×D1311yescharacteristic
147C2×C4⋊C8C2×D1311yescharacteristic
148C2×#103—261no—
149C2×#101—261no—
150#343—261no—
151#334—22no—
152#333—262no—
153#332—262no—
154Q8⋊C8—262no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13#39411yescharacteristic
158C22×C13#48311yescharacteristic
159C22×C13#48511yescharacteristic
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13#44811yescharacteristic
164C4×C13#45211yescharacteristic
165C4×C13#46511yescharacteristic
166C4×C13#47011yescharacteristic
167C4×C13#47112yes—
168Dic13—42no—
169Dic13—81no—
170Dic13—82no—
171C22×Q8—131no—
172C22×Q8—261no—
173C2×M16—21no—
174C2×M16—261no—
175C22×C8—21no—
176C4⋊Q8—132no—
177C4⋊Q8—261no—
178C4⋊Q8—261no—
179C4⋊Q8—261no—
180C4×Q8—261no—
181C4×Q8—261no—
182C4×Q8—261no—
183C4×Q8—261no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C42—261no—
189C2×C42C22×D1311yescharacteristic
190#106—264no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—261no—
195C4⋊C8—261no—
196C4⋊C8—261no—
197C4⋊C8D5212yes—
198C4⋊C8C22⋊D1312yes—
199#103—264no—
200#101—522no—
201C22⋊C8—21no—
202C22⋊C8—261no—
203C4×C8—21no—
204C4×C8—261no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13#203511yescharacteristic
208C2×C13#204611yescharacteristic
209C2×C13#204911yescharacteristic
210C2×Q8—132no—
211C2×Q8—261no—
212C2×Q8—262no—
213C2×Q8—261no—
214C2×Q8—261no—
215C2×Q8—261no—
216C2×Q8—261no—
217C2×Q8—521no—
218C2×Q8—1042no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4—521no—
222C22×C4#612711yescharacteristic
223C22×C4D4×D1311yescharacteristic
224C22×C4#613111yescharacteristic
225M16—41no—
226M16—41no—
227M16—521no—
228M16—521no—
229C2×C8—22no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—521no—
235C2×C8—521no—
236C4⋊C4—261no—
237C4⋊C4—262no—
238C4⋊C4—262no—
239C4⋊C4—261no—
240C4⋊C4—521no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—521no—
244C42—521no—
245C42—521no—
246C42C2×D5211yescharacteristic
247C42D4×D1311yescharacteristic
248C42#613111yescharacteristic
249C42C2×C22⋊D1311yescharacteristic
250C13#1045011yescharacteristic, complemented, Sylow
251C23#8814811yescharacteristic
252Q8—262no—
253Q8—262no—
254Q8—521no—
255Q8—521no—
256Q8—1042no—
257Q8—1042no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—262no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—522no—
265C2×C4—1042no—
266C2×C4—1041no—
267C2×C4#8814811yescharacteristic
268C2×C4#8814911yescharacteristic
269C2×C4#8814911yescharacteristic
270C2×C4SD16×D1311yescharacteristic
271C2×C4#8816911yescharacteristic
272C2×C4#8816911yescharacteristic
273C2×C4#8817011yescharacteristic
274C2×C4#8818411yescharacteristic
275C2×C4#8819111yescharacteristic
276C2×C4#8820111yescharacteristic
277C8—42no—
278C8—42no—
279C8—81no—
280C8—1041no—
281C8—1041no—
282C22—21no—
283C22—21no—
284C22#1171852311yescharacteristic
285C22#1171852811yescharacteristic
286C22#1171865211yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—522no—
291C4—1042no—
292C4—1041no—
293C4#1171852511yescharacteristic
294C4#1171852911yescharacteristic
295C4#1171880212yes—
296C4#1171883111yescharacteristic
297C4#1171883411yescharacteristic
298C2—21no—
299C2—21no—
300C2#1311603411yescharacteristic
301C2#1311609911yescharacteristic
302C2#1311611811yescharacteristic
subgroupG/H
centerC22#11718652
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1570C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1570D13
hypocenterC13#10450
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
250. C13#10450semidirect

Maximal subgroups

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

subgroupindex
C2×#117185122
#131148292
#131135202
#131135182
#131132302
#131127332
C13×#15702
#1045013