Finite Group Databasebeta

← #15775762

Subgroups — #15775762

Order 3328.

380 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 63 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#13115997C211yesmaximal, characteristic
2#13113809C212yesmaximal
3#13112866C212yesmaximal
4#13112770C211yesmaximal, characteristic
5C13×#2811C211yesmaximal, characteristic
6#11719205C2211yescharacteristic
7C13×#395—22no—
8C13×#395C2212yes—
9C13×#391—21no—
10C13×#391—21no—
11C13×#391—22no—
12C13×#391C2211yescharacteristic
13#11718889—22no—
14#11718886—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13—21no—
20C22×Q8×C13D411yescharacteristic
21C22×Q8×C13D412yes—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C42×C13—21no—
27C2×C42×C13D411yescharacteristic
28C2×#6107—42no—
29#88180—21no—
30#88178—22no—
31C2×#6099—21no—
32#88144—41no—
33#88142—41no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95D412yes—
39#88075—41no—
40#88075—41no—
41#88075—42no—
42C22⋊#1055—22no—
43#12224—131nomaximal, Sylow
44C2×Q8×C13—24no—
45C2×Q8×C13—21no—
46C2×Q8×C13—41no—
47C2×Q8×C13—42no—
48C2×Q8×C13—41no—
49C2×Q8×C13—82no—
50C2×Q8×C13—81no—
51C2×Q8×C13—81no—
52C2×Q8×C13Q1612yescomplemented
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D412yes—
59C2×Dic26—22no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—82no—
62C13×C4⋊C4—81no—
63C13×C4⋊C4—81no—
64C42×C13—41no—
65C42×C13—81no—
66C22⋊Dic13—41no—
67#6107—84no—
68C4⋊Dic13—21no—
69C4⋊Dic13—22no—
70C4⋊Dic13—21no—
71#6101—42no—
72C4×Dic13—41no—
73#6099—41no—
74#6099—41no—
75C2×#1055—42no—
76C2×#1055—41no—
77#2811D1311yescharacteristic
78#2028—131no—
79#1605—132no—
80#1354—132no—
81#1319—131no—
82C23×C13#12011yescharacteristic
83Q8×C13—42no—
84Q8×C13—44no—
85Q8×C13—81no—
86Q8×C13—84no—
87Q8×C13—82no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—24no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13C2×Q1611yescharacteristic
105C2×C4×C13#13711yescharacteristic
106C2×Dic13—41no—
107C2×Dic13—41no—
108Dic26—82no—
109#1055—81no—
110#1055—82no—
111#544—131no—
112#451—262no—
113#419—261no—
114#395—22no—
115#395C2×D1312yes—
116#391—21no—
117#391—21no—
118#391—22no—
119#391C2×D1311yescharacteristic
120#343—131no—
121#339—261no—
122#328—262no—
123#324—132no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13#45111yescharacteristic
127C22×C13#45511yescharacteristic
128C22×C13B(4,𝔽2)11yescharacteristic
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—42no—
132C4×C13—44no—
133C4×C13—42no—
134C4×C13—42no—
135C4×C13—82no—
136Dic13—81no—
137Dic13—81no—
138C22×Q8—21no—
139C22×Q8C22⋊D1311yescharacteristic
140C22×Q8C22⋊D1312yes—
141C2×Q16—522no—
142C2×M16—261no—
143C4⋊Q8—521no—
144#125—521no—
145C22⋊Q8—262no—
146#117—261no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4C22×D1311yescharacteristic
151C2×C42—21no—
152C2×C42C22⋊D1311yescharacteristic
153#103—521no—
154#103—521no—
155#103—522no—
156C22⋊C8—262no—
157#95—22no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95C22⋊D1312yes—
162C2×C13—21no—
163C2×C13—21no—
164C2×C13#160211yescharacteristic
165C2×C13#219911yescharacteristic
166C2×C13#220511yescharacteristic
167C2×Q8—24no—
168C2×Q8—21no—
169C2×Q8—41no—
170C2×Q8—42no—
171C2×Q8—41no—
172C2×Q8—82no—
173C2×Q8—81no—
174C2×Q8—81no—
175C2×Q8—262no—
176C2×Q8#610712yescomplemented
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C2×C22⋊D1311yescharacteristic
182C22×C4C2×C22⋊D1312yes—
183Q16—1044no—
184M16—521no—
185M16—521no—
186C2×C8—522no—
187C2×C8—521no—
188C4⋊C4—41no—
189C4⋊C4—82no—
190C4⋊C4—81no—
191C4⋊C4—81no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—262no—
195C4⋊C4—522no—
196C22⋊C4—521no—
197C42—41no—
198C42—81no—
199C42—521no—
200C13#1222411yescharacteristic, complemented, Sylow
201C23#8820711yescharacteristic
202Q8—42no—
203Q8—44no—
204Q8—81no—
205Q8—84no—
206Q8—82no—
207Q8—1042no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—521no—
225C2×C4—521no—
226C2×C4#8819611yescharacteristic
227C2×C4C2×#610711yescharacteristic
228C8—1041no—
229C8—1042no—
230C22—21no—
231C22—21no—
232C22#1171888911yescharacteristic
233C22#1171890311yescharacteristic
234C22#1171890511yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—44no—
239C4—42no—
240C4—42no—
241C4—82no—
242C4—1041no—
243C4—1041no—
244C2—21no—
245C2—21no—
246C2#1311379311yescharacteristic
247C2#1311683711yescharacteristic
248C2#1311686611yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2811C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2811D13
hypocenterC13#12224
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2811

Complements

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

NH ≅ G/Ntype
52. C2×Q8×C13Q16semidirect
176. C2×Q8#6107semidirect
200. C13#12224semidirect

Maximal subgroups

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

subgroupindex
#131159972
#131138092
#131128662
#131127702
C13×#28112
#1222413