Finite Group Databasebeta

← #15779750

Subgroups — #15779750

Order 3328.

424 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 103 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#13118017C211yesmaximal, characteristic
2#13115230C211yesmaximal, characteristic
3#13115053C212yesmaximal
4#13112962C212yesmaximal
5C2×C13×#356C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7#11719517C2211yescharacteristic
8C2×C13×#101C2212yes—
9#11718891—21no—
10#11718891C2212yes—
11C2×#88076C2211yescharacteristic
12#11718886—21no—
13#11718782—22no—
14#11718642—22no—
15#11718642—22no—
16#11718598—21no—
17C13×#356C414yescomplemented
18#11718147—22no—
19#11718115—21no—
20C22×Q8×C13D411yescharacteristic
21C22×Q8×C13C2311yescharacteristic
22C2×C13×M16—22no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8C2×C412yes—
25C13×C4⋊Q8Q812yes—
26C2×C13×C4⋊C4—22no—
27C2×C42×C13D411yescharacteristic
28Q8×Dic13—42no—
29#88180—22no—
30#88180—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13D412yes—
33C2×C4×Dic13—21no—
34C2×C4×Dic13D412yes—
35C2×#6099—21no—
36C13×#101—22no—
37C13×#101C2×C414yes—
38#88076—22no—
39#88075—42no—
40#88071—21no—
41#88071—22no—
42#88071—21no—
43#88071—22no—
44#88071—22no—
45#88071—22no—
46#88058—42no—
47#88057—42no—
48#12971—131nomaximal, Sylow
49C2×Q8×C13—21no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13C4⋊C412yes—
55C2×Q8×C13C22×C411yescharacteristic
56C2×Q8×C13C2×Q811yescharacteristic
57C2×Q8×C13#4112yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C22×Dic13—22no—
63C22×Dic13—22no—
64C13×M16—24no—
65C13×M16—42no—
66C2×C8×C13—42no—
67C13×C4⋊C4—24no—
68C13×C4⋊C4—24no—
69C42×C13—21no—
70C42×C13C4⋊C412yes—
71C22⋊Dic13—41no—
72C4⋊Dic13—22no—
73C4⋊Dic13—22no—
74C4⋊Dic13—22no—
75C4⋊Dic13—42no—
76C4⋊Dic13—81no—
77C4×Dic13—41no—
78C4×Dic13—42no—
79C4×Dic13—42no—
80C4×Dic13—81no—
81#6099—41no—
82#6099—41no—
83C2×#1055—41no—
84#2381—131no—
85C2×#356D1311yescharacteristic
86#1886—131no—
87#1857—132no—
88#1394—132no—
89C23×C13#12011yescharacteristic
90Q8×C13—41no—
91Q8×C13—41no—
92Q8×C13—42no—
93Q8×C13—42no—
94Q8×C13—81no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13C2×C4⋊C411yescharacteristic
105C2×C4×C13C4×D412yes—
106C2×C4×C13C22⋊Q812yes—
107C2×C4×C13#12311yescharacteristic
108C2×Dic13—44no—
109C2×Dic13—44no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C8×C13—44no—
114#1055—81no—
115C2×C4⋊Q8C2×D1311yescharacteristic
116#519—131no—
117#428—262no—
118#419—261no—
119C2×#101—131no—
120C2×#101C2×D1312yes—
121#391—132no—
122#391—261no—
123#387—262no—
124#387—262no—
125#383—261no—
126#356Dic1314yescomplemented
127#339—262no—
128#339—261no—
129C22×C13—22no—
130C22×C13#38511yescharacteristic
131C22×C13B(4,𝔽2)11yescharacteristic
132C22×C13#45811yescharacteristic
133C4×C13—21no—
134C4×C13—22no—
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—42no—
138C4×C13—42no—
139Dic13—82no—
140Dic13—82no—
141Dic13—82no—
142C22×Q8D5211yescharacteristic
143C22×Q8C22×D1311yescharacteristic
144C2×M16—22no—
145C2×M16—261no—
146C4⋊Q8—22no—
147C4⋊Q8Dic2612yes—
148C4⋊Q8C2×Dic1312yes—
149C4×Q8—522no—
150#117—261no—
151#117—262no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—132no—
154C2×C4⋊C4—261no—
155C2×C42—132no—
156C2×C42—261no—
157C2×C42D5211yescharacteristic
158#107—522no—
159#106—522no—
160#103—522no—
161#101—22no—
162#101—262no—
163#101C2×Dic1314yes—
164#95—261no—
165#95—262no—
166#95—261no—
167#95—262no—
168#95—262no—
169#95—262no—
170C2×C13—21no—
171C2×C13—21no—
172C2×C13#186711yescharacteristic
173C2×C13#220312yes—
174C2×Q8—21no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C4⋊Dic1312yes—
180C2×Q8C2×Dic2611yescharacteristic
181C2×Q8#612912yes—
182C2×Q8C22×Dic1311yescharacteristic
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—262no—
186C22×C4—262no—
187C22×C4C2×D5211yescharacteristic
188C22×C4D4×D1312yes—
189M16—24no—
190M16—42no—
191M16—521no—
192M16—521no—
193C2×C8—42no—
194C2×C8—521no—
195C4⋊C4—24no—
196C4⋊C4—24no—
197C4⋊C4—262no—
198C4⋊C4—262no—
199C4⋊C4—262no—
200C4⋊C4—522no—
201C4⋊C4—1041no—
202C22⋊C4—521no—
203C42—21no—
204C42—522no—
205C42—522no—
206C42—521no—
207C42—1041no—
208C42C4⋊Dic1312yes—
209C13#1297111yescharacteristic, complemented, Sylow
210C23#8813611yescharacteristic
211Q8—41no—
212Q8—42no—
213Q8—41no—
214Q8—42no—
215Q8—81no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—524no—
226C2×C4—524no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4#8813212yes—
231C2×C4#8814011yescharacteristic
232C2×C4C2×C4⋊Dic1311yescharacteristic
233C2×C4D4×Dic1312yes—
234C8—44no—
235C8—1041no—
236C22—22no—
237C22#1171840211yescharacteristic
238C22#1171840311yescharacteristic
239C22#1171861111yescharacteristic
240C4—22no—
241C4—21no—
242C4—22no—
243C4—21no—
244C4—42no—
245C4—42no—
246C4—1042no—
247C4—1042no—
248C4—1042no—
249C2—21no—
250C2—21no—
251C2#1311511911yescharacteristic
252C2#1311685812yes—
subgroupG/H
centerC22#11718402
commutatorC2×Q8×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC2×C13×#356C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
cosocleC22×Q8×C13C23
hypercenterC2×#356D13
hypocenterC13#12971
LCSG ▷ C2×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
17. C13×#356C4semidirect
126. #356Dic13semidirect
209. C13#12971semidirect

Maximal subgroups

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

subgroupindex
#131180172
#131152302
#131150532
#131129622
C2×C13×#3562
#1297113