Finite Group Databasebeta

← #15774404

Subgroups — #15774404

Order 3328.

314 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 115 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#13125422C211yesmaximal, characteristic
2#13113595C211yesmaximal, characteristic
3#13112893C212yesmaximal, complemented
4#13112886C212yesmaximal, complemented
5C2×C13×C4⋊C16C211yesmaximal, characteristic
6#11719175—21no—
7C22×C13×C16—21no—
8C2×C4×C8×C13C2211yescharacteristic
9#11718777—21no—
10#11718777C412yes—
11#11718585—21no—
12#11718360C2211yescharacteristic
13C4×Dic52—21no—
14C4×Dic52C412yes—
15#11718343C2211yescharacteristic
16#11718342—21no—
17C13×C4⋊C16—21no—
18C13×C4⋊C16C2212yes—
19#11718050—21no—
20#11718050C2212yes—
21C22×C8×C13C2×C411yescharacteristic
22C22×C8×C13D411yescharacteristic
23C2×C42×C13D411yescharacteristic
24#88180—41no—
25#88178—22no—
26#88178—41no—
27C2×#6099—41no—
28C2×Dic52—21no—
29C2×Dic52C2×C412yes—
30#88124—41no—
31#88123—21no—
32#88123—21no—
33C4×Dic26—22no—
34C4×Dic26—41no—
35C2×C13×C16—22no—
36C2×C13×C16—42no—
37C4×C8×C13C2×C411yescharacteristic
38C4×C8×C13D411yescharacteristic
39C4×C8×C13D411yescharacteristic
40C4×C8×C13C2311yescharacteristic
41#88058—21no—
42#88058C2×C412yes—
43#88056—22no—
44#88056—22no—
45C4⋊#1055—22no—
46C4⋊#1055—41no—
47#11983—131nomaximal, Sylow
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13D811yescharacteristic
50C22×C4×C13SD1611yescharacteristic
51C2×Dic26—22no—
52C2×Dic26—41no—
53C2×C8×C13—21no—
54C2×C8×C13—21no—
55C2×C8×C13—41no—
56C2×C8×C13C22⋊C411yescharacteristic
57C2×C8×C13C22⋊C411yescharacteristic
58C2×C8×C13C22×C411yescharacteristic
59C2×C8×C13C2×D411yescharacteristic
60C42×C13C22⋊C411yescharacteristic
61C42×C13D811yescharacteristic
62C42×C13SD1611yescharacteristic
63C42×C13C2×D411yescharacteristic
64C22⋊Dic13—42no—
65C4⋊Dic13—22no—
66C4⋊Dic13—41no—
67C4⋊Dic13—41no—
68C4⋊Dic13—41no—
69#6101—42no—
70#6101—42no—
71C4×Dic13—42no—
72#6099—82no—
73C2×#1055—42no—
74Dic52—42no—
75Dic52—41no—
76Dic52—41no—
77C13×C16—42no—
78#3170—131no—
79C2×C4⋊C16D1311yescharacteristic
80#1567—131no—
81#1365—132no—
82#1362—132no—
83C23×C13#10211yescharacteristic
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—41no—
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13#10211yescharacteristic
89C2×C4×C13#10211yescharacteristic
90C2×C4×C13SD3212yes—
91C2×C4×C13Q3212yes—
92C2×C4×C13C2×C22⋊C411yescharacteristic
93C2×C4×C13C2×D811yescharacteristic
94C2×C4×C13C2×SD1611yescharacteristic
95C2×Dic13—42no—
96C2×Dic13—42no—
97Dic26—42no—
98Dic26—42no—
99Dic26—82no—
100C8×C13—21no—
101C8×C13—21no—
102C8×C13—21no—
103C8×C13AGL(1,ℤ/8)11yescharacteristic
104C8×C13#13711yescharacteristic
105#1055—82no—
106#533—261no—
107C22×C16—21no—
108#500—131no—
109#494—131no—
110#487—261no—
111#467—132no—
112#467—261no—
113C4×Q16—132no—
114C4×Q16—261no—
115#423—261no—
116C2×C4×C8C2×D1311yescharacteristic
117C4⋊C16—21no—
118C4⋊C16C2×D1312yes—
119#335—132no—
120#335—261no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#35812yes—
124C22×C13C2×#10211yescharacteristic
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13#35812yes—
129C4×C13#41311yescharacteristic
130C4×C13#41711yescharacteristic
131C4×C13C2×SD3211yescharacteristic
132C4×C13C2×Q3211yescharacteristic
133Dic13—82no—
134Dic13—82no—
135C2×Q16—132no—
136C2×Q16—261no—
137C2×M16—521no—
138C22×C8C4×D1311yescharacteristic
139C22×C8C22⋊D1311yescharacteristic
140C4⋊Q8—261no—
141C4⋊Q8—261no—
142#125—521no—
143C22⋊Q8—262no—
144C22⋊Q8—521no—
145C4×Q8—262no—
146C4×Q8—521no—
147#117—521no—
148C2×C42D5211yescharacteristic
149C2×C16—22no—
150C2×C16—42no—
151#107—132no—
152#107—261no—
153C4⋊C8—262no—
154C4⋊C8—521no—
155#103—262no—
156#103—262no—
157C4×C8C4×D1311yescharacteristic
158C4×C8D5211yescharacteristic
159C4×C8C22⋊D1311yescharacteristic
160C4×C8C22×D1311yescharacteristic
161C2×C13—22no—
162C2×C13#154711yescharacteristic
163C2×C13C2×#35811yescharacteristic
164C2×C13#214811yescharacteristic
165C2×Q8—262no—
166C2×Q8—521no—
167C22×C4#609511yescharacteristic
168C22×C4D10411yescharacteristic
169C22×C4#610311yescharacteristic
170Q16—522no—
171Q16—521no—
172Q16—521no—
173M16—1042no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—41no—
177C2×C8—522no—
178C2×C8#610311yescharacteristic
179C2×C8#610311yescharacteristic
180C2×C8C2×C4×D1311yescharacteristic
181C2×C8C2×C22⋊D1311yescharacteristic
182C4⋊C4—262no—
183C4⋊C4—521no—
184C4⋊C4—521no—
185C4⋊C4—521no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C22⋊C4—522no—
189C42—522no—
190C42#609511yescharacteristic
191C42D10411yescharacteristic
192C42#610311yescharacteristic
193C42C2×D5211yescharacteristic
194C16—42no—
195C13#1198311yescharacteristic, complemented, Sylow
196C23#8806111yescharacteristic
197Q8—522no—
198Q8—522no—
199Q8—1042no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4#8804012yes—
206C2×C4Dic10412yes—
207C2×C4#8806111yescharacteristic
208C2×C4#8806111yescharacteristic
209C2×C4#8806111yescharacteristic
210C2×C4C2×#609511yescharacteristic
211C2×C4C2×D10411yescharacteristic
212C2×C4C2×#610311yescharacteristic
213C8—21no—
214C8—21no—
215C8—21no—
216C8—1042no—
217C8#8818611yescharacteristic
218C8#8819611yescharacteristic
219C22—21no—
220C22—21no—
221C22#1171809512yes—
222C22C2×#8806111yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—1042no—
227C4—1042no—
228C4#1171809512yes—
229C4C2×#8804011yescharacteristic
230C4C2×Dic10411yescharacteristic
231C4#1171862711yescharacteristic
232C4#1171879311yescharacteristic
233C2—22no—
234C2#1311351111yescharacteristic
235C2C2×#1171809511yescharacteristic
236C2#1311658611yescharacteristic
subgroupG/H
centerC22C2×#88061
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC2×C13×C4⋊C16C2
socleC22×C13C2×#102
prime radicalC23×C13#102
cosocleC4×C8×C13C23
hypercenterC2×C4⋊C16D13
hypocenterC13#11983
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
3. #13112893C2semidirect
4. #13112886C2semidirect
195. C13#11983semidirect

Maximal subgroups

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

subgroupindex
#131254222
#131135952
#131128932
#131128862
C2×C13×C4⋊C162
#1198313