Finite Group Databasebeta

← #15754658

Subgroups — #15754658

Order 3328.

706 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11719272C211yesmaximal, characteristic
2#13113509C212yesmaximal
3#13113264C212yesmaximal
4#13113160C211yesmaximal, characteristic
5C13×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88198—21no—
8#11719272—24no—
9#11719272—24no—
10C2×#88143—22no—
11C2×#88141—21no—
12C2×#88124C412yes—
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#11718074—24no—
23C22×Q8×C13D411yescharacteristic
24C22×Dic26—21no—
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
33#88198—28no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C412yes—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—22no—
38C2×#6101—22no—
39C2×#6101—22no—
40C2×#6101—21no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13—21no—
43#88143—216no—
44#88141—28no—
45#88124—24no—
46#88124—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#8390—131nomaximal, Sylow
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
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—21no—
71C22×Dic13—22no—
72C2×Dic26—21no—
73C2×Dic26—24no—
74C2×Dic26—24no—
75C2×Dic26—42no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26C22⋊C412yes—
79C13×M16—42no—
80C13×M16—42no—
81C2×C8×C13—42no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—24no—
84C42×C13—22no—
85C42×C13—22no—
86C42×C13C2×D412yes—
87C42×C13C2×D412yes—
88C4⋊Dic13—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13—24no—
91C4⋊Dic13C22⋊C414yes—
92C4⋊Dic13C22⋊C412yes—
93#6101—28no—
94#6101—28no—
95#6101—28no—
96#6101—24no—
97C4×Dic13—28no—
98C4×Dic13—24no—
99C2×#1055—42no—
100C2×#557—131no—
101#1801D1311yescharacteristic
102#1546—132no—
103#1487—132no—
104#1461—131no—
105C23×C13C2×C22⋊C411yescharacteristic
106Q8×C13—42no—
107Q8×C13—42no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13C2×C22⋊C411yescharacteristic
117C2×C4×C13#12012yes—
118C2×C4×C13#12012yes—
119C2×C4×C13#13512yes—
120C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C13#13711yescharacteristic
122C2×Dic13—24no—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—24no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129Dic26—24no—
130Dic26—22no—
131Dic26—44no—
132Dic26—44no—
133Dic26#10114yescomplemented
134C8×C13—82no—
135#1055—82no—
136#557—264no—
137#557—264no—
138C2×C4⋊Q8—131no—
139C2×C4⋊Q8—261no—
140C2×#125—132no—
141C2×#125—262no—
142C2×C4×Q8—132no—
143C2×C4×Q8—131no—
144C2×C4×Q8—261no—
145C2×C4×Q8C2×D1311yescharacteristic
146#431—132no—
147#423C2×D1312yes—
148C2×#101—21no—
149#343—21no—
150#332—264no—
151Q8⋊C8—264no—
152#324—262no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13#37911yescharacteristic
156C22×C13#41611yescharacteristic
157C22×C13#41711yescharacteristic
158C4×C13—22no—
159C4×C13—21no—
160C4×C13—42no—
161C4×C13—42no—
162C4×C13C2×#10112yes—
163C4×C13#44912yes—
164C4×C13#45212yes—
165Dic13—24no—
166Dic13—42no—
167Dic13—44no—
168C22×Q8—131no—
169C22×Q8—261no—
170C22×Q8C22⋊D1311yescharacteristic
171C2×M16—22no—
172C4⋊Q8—134no—
173C4⋊Q8—268no—
174C4⋊Q8—262no—
175#125—264no—
176#125—264no—
177#125—2616no—
178C4×Q8—22no—
179C4×Q8—22no—
180C4×Q8—134no—
181C4×Q8—264no—
182C4×Q8—264no—
183C4×Q8—268no—
184C4×Q8—262no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—132no—
187C2×C4⋊C4—262no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4D5212yes—
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C42—262no—
195C2×C42—261no—
196C2×C42C4×D1312yes—
197C2×C42C22×D1311yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—22no—
200C4⋊C8—262no—
201#101—42no—
202C22⋊C8—262no—
203C4×C8—262no—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13#178411yescharacteristic
207C2×C13#178811yescharacteristic
208C2×C13#179611yescharacteristic
209C2×Q8—21no—
210C2×Q8—22no—
211C2×Q8—21no—
212C2×Q8—22no—
213C2×Q8—132no—
214C2×Q8—264no—
215C2×Q8—261no—
216C2×Q8—264no—
217C2×Q8—521no—
218C2×Q8—521no—
219C2×Q8—522no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4—262no—
223C22×C4#610312yes—
224C22×C4#610312yes—
225C22×C4C2×C4×D1311yescharacteristic
226C22×C4C2×D5211yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228M16—42no—
229M16—42no—
230C2×C8—42no—
231C2×C8—522no—
232C4⋊C4—24no—
233C4⋊C4—22no—
234C4⋊C4—132no—
235C4⋊C4—134no—
236C4⋊C4—268no—
237C4⋊C4—268no—
238C4⋊C4—268no—
239C4⋊C4—261no—
240C4⋊C4—262no—
241C4⋊C4—264no—
242C4⋊C4—264no—
243C42—22no—
244C42—22no—
245C42—268no—
246C42—264no—
247C42D4×D1312yes—
248C42D4×D1312yes—
249C13#839011yescharacteristic, complemented, Sylow
250C23C2×#610311yescharacteristic
251Q8—42no—
252Q8—42no—
253Q8—134no—
254Q8—264no—
255Q8—262no—
256Q8—524no—
257Q8—524no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—264no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—264no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4C22⋊C4×D1311yescharacteristic
273C2×C4C22⋊C4×D1311yescharacteristic
274C2×C4#8813612yes—
275C2×C4#8818611yescharacteristic
276C2×C4#8819112yes—
277C2×C4#8819611yescharacteristic
278C2×C4#8820412yes—
279C8—82no—
280C8—1042no—
281C22—21no—
282C22—21no—
283C22#1171861611yescharacteristic
284C22#1171862711yescharacteristic
285C22#1171866311yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—264no—
291C4—524no—
292C4—522no—
293C4D13×#10112yes—
294C4#1171869812yes—
295C4#1171870812yes—
296C2—21no—
297C2—21no—
298C2#1311475811yescharacteristic
299C2#1311477411yescharacteristic
300C2#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#8390
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
133. Dic26#101semidirect
249. C13#8390semidirect

Maximal subgroups

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

subgroupindex
C2×#117192722
#131135092
#131132642
#131131602
C13×#18012
#839013