Finite Group Databasebeta

← #15757870

Subgroups — #15757870

Order 3328.

376 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 89 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#13125358C211yesmaximal, characteristic
2#13123941C211yesmaximal, characteristic
3#13113500C211yesmaximal, characteristic
4#13113309C211yesmaximal, characteristic
5#13112736C211yesmaximal, characteristic
6#13112734C211yesmaximal, characteristic
7C13×#1497C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#432C2211yescharacteristic
11C13×#431C2211yescharacteristic
12#11718741C412yes—
13#11718741C412yes—
14#11718726—21no—
15#11718726—21no—
16#11718659—22no—
17#11718587C2211yescharacteristic
18#11718586C2211yescharacteristic
19C2×#88043C2211yescharacteristic
20#11718489—22no—
21#11718381—22no—
22#11718362—22no—
23C13×Q8⋊C8—22no—
24Q8⋊#1055—22no—
25#11718078—21no—
26#11718074—21no—
27C13×C4⋊Q8C2×C411yescharacteristic
28C13×C4⋊Q8C2×C411yescharacteristic
29C13×#125—21no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13—21no—
34C13×#117—21no—
35C2×C42×C13C2311yescharacteristic
36#88180D412yes—
37#88178—21no—
38#88178—21no—
39C22×#1055—21no—
40#88124C2×C412yes—
41#88123D411yescharacteristic
42#88123D411yescharacteristic
43C4×Dic26—21no—
44C4×Dic26—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8D412yes—
47C13×C22⋊C8—21no—
48C13×C22⋊C8—21no—
49C13×#97—21no—
50C4×C8×C13—21no—
51C22⋊#1055—21no—
52C22⋊#1055—21no—
53#88055—22no—
54#88054—24no—
55C8×Dic13—22no—
56#88048—22no—
57#88048—22no—
58#88047—22no—
59#88047—22no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62#88043—21no—
63#88043—21no—
64#88043C2×C412yes—
65C4×#1055—21no—
66#9006—131nomaximal, Sylow
67C2×Q8×C13—21no—
68C2×Q8×C13—21no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×C8×C13—22no—
75C2×C8×C13—41no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—41no—
83C42×C13—41no—
84C42×C13C22×C411yescharacteristic
85C42×C13C2×D411yescharacteristic
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C22⋊Dic13—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13C22⋊C412yes—
92C4⋊Dic13C22⋊C412yes—
93#6101—22no—
94#6101—22no—
95C4×Dic13—22no—
96C2×#1055—24no—
97C2×#1055—22no—
98C2×#1055—22no—
99C2×#1055—41no—
100#3162—131no—
101#2987—131no—
102#1544—131no—
103#1497—131no—
104#1497D1311yescharacteristic
105#1302—131no—
106#1302—131no—
107C23×C13#12311yescharacteristic
108Q8×C13—42no—
109Q8×C13—42no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13C4×D411yescharacteristic
117C2×C4×C13C4×D411yescharacteristic
118C2×C4×C13#12011yescharacteristic
119C2×C4×C13#12111yescharacteristic
120C2×C4×C13#12111yescharacteristic
121C2×Dic13—22no—
122C2×Dic13—22no—
123Dic26—81no—
124Dic26—81no—
125C8×C13—42no—
126C8×C13—81no—
127#1055—24no—
128#1055—42no—
129#1055—81no—
130#533—131no—
131#533C2×D1311yescharacteristic
132#501—132no—
133#501—132no—
134#501—261no—
135#501—261no—
136#446—262no—
137#446—262no—
138#433—262no—
139#432—131no—
140#432C2×D1311yescharacteristic
141#431—131no—
142#431C2×D1311yescharacteristic
143#427—262no—
144C2×#97—131no—
145#332—261no—
146#332—261no—
147Q8⋊C8—22no—
148Q8⋊C8—262no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13#38611yescharacteristic
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—81no—
159C4×C13—81no—
160C4×C13#45612yes—
161Dic13—42no—
162Dic13—42no—
163C22×C8—261no—
164C4⋊Q8—131no—
165C4⋊Q8—131no—
166C4⋊Q8C4×D1311yescharacteristic
167C4⋊Q8C4×D1311yescharacteristic
168#125—21no—
169#125—132no—
170C22⋊Q8—21no—
171C22⋊Q8—21no—
172C22⋊Q8—261no—
173C22⋊Q8—261no—
174C4×Q8—21no—
175C4×Q8—21no—
176C4×Q8—261no—
177C4×Q8—261no—
178#117—21no—
179#117—132no—
180C2×C42C22×D1311yescharacteristic
181#107—262no—
182#107—262no—
183#106—262no—
184#106—262no—
185C4⋊C8—21no—
186C4⋊C8—132no—
187C4⋊C8—264no—
188C4⋊C8—261no—
189C4⋊C8C22⋊D1312yes—
190C22⋊C8—21no—
191C22⋊C8—21no—
192C22⋊C8—261no—
193C22⋊C8—261no—
194#97—21no—
195#97—132no—
196#97—262no—
197#97—261no—
198#97—261no—
199C4×C8—21no—
200C4×C8—262no—
201C4×C8—261no—
202C2×C13—41no—
203C2×C13#188111yescharacteristic
204C2×C13#188111yescharacteristic
205C2×C13#188611yescharacteristic
206C2×Q8—21no—
207C2×Q8—21no—
208C2×Q8—261no—
209C2×Q8—261no—
210C22×C4#612711yescharacteristic
211C22×C4D4×D1311yescharacteristic
212C22×C4#612911yescharacteristic
213C2×C8—22no—
214C2×C8—41no—
215C2×C8—264no—
216C2×C8—262no—
217C2×C8—262no—
218C2×C8—521no—
219C4⋊C4—21no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—132no—
226C4⋊C4—132no—
227C4⋊C4—262no—
228C4⋊C4—261no—
229C4⋊C4—262no—
230C4⋊C4—261no—
231C22⋊C4—41no—
232C22⋊C4—262no—
233C42—41no—
234C42—262no—
235C42C2×C4×D1311yescharacteristic
236C42D4×D1311yescharacteristic
237C42D4×D1311yescharacteristic
238C42C2×C22⋊D1311yescharacteristic
239C13#900611yescharacteristic, complemented, Sylow
240C23#8813711yescharacteristic
241Q8—42no—
242Q8—42no—
243Q8—1041no—
244Q8—1041no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4C22⋊C4×D1311yescharacteristic
253C2×C4#8813511yescharacteristic
254C2×C4#8813811yescharacteristic
255C2×C4C4×C22⋊D1311yescharacteristic
256C2×C4#8819111yescharacteristic
257C2×C4#8819211yescharacteristic
258C8—42no—
259C8—81no—
260C8—264no—
261C8—522no—
262C8—1041no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22#1171861711yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—21no—
272C4—81no—
273C4—81no—
274C4—522no—
275C4—522no—
276C4#1171886612yes—
277C2—41no—
278C2#1311519511yescharacteristic
279C2#1311520111yescharacteristic
280C2#1311522611yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1497C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#1497D13
hypocenterC13#9006
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
239. C13#9006semidirect

Maximal subgroups

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

subgroupindex
#131253582
#131239412
#131135002
#131133092
#131127362
#131127342
C13×#14972
#900613