Finite Group Databasebeta

← #15750709

Subgroups — #15750709

Order 3328.

270 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 59 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#13116501C211yesmaximal, characteristic
2#13115669C211yesmaximal, characteristic
3C13×#2132C211yesmaximal, characteristic
4C13×#532C2211yescharacteristic
5C13×#413—21no—
6#11718901—21no—
7C2×#88077—21no—
8C2×#88077—21no—
9#11718593C411yescharacteristic, complemented
10#11718585C411yescharacteristic, complemented
11C13×#356C412yescomplemented
12C13×#355—21no—
13#11718137C412yescomplemented
14#11718133—21no—
15C2×C13×#41D411yescharacteristic
16C2×C13×#41D411yescharacteristic
17C2×C13×M16—41no—
18C13×C4⋊Q8C2×C411yescharacteristic
19C13×#127C2×C411yescharacteristic
20C13×#124D411yescharacteristic
21C13×#124Q811yescharacteristic
22C13×#121—41no—
23C4×D4×C13—41no—
24C2×C42×C13C2×C411yescharacteristic
25#88180—41no—
26C2×C4×Dic13—21no—
27C2×#6099—21no—
28C13×#101—22no—
29C13×#100—41no—
30#88077—42no—
31#88077—42no—
32#88074—22no—
33#88074—41no—
34#88071—41no—
35C4⋊#1055—41no—
36#7503—131nomaximal, Sylow
37C13×#41—41no—
38C13×#41—41no—
39C13×#41—41no—
40C13×#41—41no—
41C2×Q8×C13C22⋊C411yescharacteristic
42C2×Q8×C13C4⋊C411yescharacteristic
43C2×D4×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13C22⋊C411yescharacteristic
47C2×D4×C13C4⋊C411yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×Dic13—41no—
53C13×M16—42no—
54C13×M16—81no—
55C2×C8×C13—81no—
56C13×C4⋊C4—41no—
57C13×C22⋊C4—41no—
58C13×C22⋊C4—41no—
59C42×C13—21no—
60C42×C13C4211yescharacteristic
61C42×C13C4⋊C411yescharacteristic
62C22⋊Dic13—42no—
63C4⋊Dic13—81no—
64C4×Dic13—22no—
65C4×Dic13—41no—
66C4×Dic13—81no—
67#6099—41no—
68#6099—41no—
69C2×#1055—41no—
70#2132D1311yescharacteristic
71#2126—131no—
72#1963—131no—
73C23×C13—21no—
74C23×C13—21no—
75C23×C13#9911yescharacteristic
76Q8×C13—41no—
77Q8×C13—41no—
78D4×C13—41no—
79D4×C13—41no—
80D4×C13—81no—
81D4×C13—81no—
82D4×C13—82no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—81no—
94C2×C4×C13#9511yescharacteristic
95C2×C4×C13#9911yescharacteristic
96C2×Dic13—42no—
97C2×Dic13—82no—
98C2×Dic13—82no—
99C8×C13—82no—
100#1055—81no—
101#532C2×D1311yescharacteristic
102#423—131no—
103C2×#104—261no—
104C2×#104—261no—
105#413—21no—
106#410—261no—
107#376—131no—
108#356Dic1312yescomplemented
109#355—21no—
110#354—261no—
111#353—132no—
112C22×C13—21no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—81no—
117C22×C13—81no—
118C22×C13#34211yescharacteristic
119C4×C13—21no—
120C4×C13—41no—
121C4×C13—41no—
122C4×C13—41no—
123C4×C13—41no—
124C4×C13#35311yescharacteristic
125C4×C13#35411yescharacteristic
126Dic13—82no—
127Dic13—162no—
128C2×#41D5211yescharacteristic
129C2×#41C22⋊D1311yescharacteristic
130C2×M16—41no—
131C2×M16—261no—
132C4⋊Q8C2×Dic1311yescharacteristic
133#127C4×D1311yescharacteristic
134#124Dic2611yescharacteristic
135#124C22⋊D1311yescharacteristic
136#121—41no—
137C4×D4—41no—
138#117—521no—
139C2×C42—261no—
140C2×C42C4×D1311yescharacteristic
141C4⋊C8—521no—
142#104—522no—
143#104—522no—
144#101—22no—
145#100—41no—
146#99—262no—
147#99—521no—
148#95—521no—
149C2×C13—21no—
150C2×C13—41no—
151C2×C13—81no—
152C2×C13—81no—
153C2×C13#139311yescharacteristic
154#41—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158C2×Q8C4⋊Dic1311yescharacteristic
159C2×Q8C22⋊Dic1311yescharacteristic
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4#610111yescharacteristic
164C2×D4#610311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—521no—
169C22×C4#610311yescharacteristic
170M16—42no—
171M16—81no—
172M16—521no—
173M16—521no—
174C2×C8—81no—
175C2×C8—521no—
176C4⋊C4—41no—
177C4⋊C4—1041no—
178C22⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—522no—
181C42—21no—
182C42—262no—
183C42—521no—
184C42—1041no—
185C42C4×Dic1311yescharacteristic
186C42#610111yescharacteristic
187C13#750311yescharacteristic, complemented, Sylow
188C23—21no—
189C23—21no—
190C23#8804611yescharacteristic
191Q8—41no—
192Q8—41no—
193D4—41no—
194D4—41no—
195D4—81no—
196D4—81no—
197D4—82no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—81no—
209C2×C4—522no—
210C2×C4—1042no—
211C2×C4—1042no—
212C2×C4#8804611yescharacteristic
213C2×C4#8807111yescharacteristic
214C8—82no—
215C8—1041no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22#1171811911yescharacteristic
223C4—21no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—41no—
228C4—1042no—
229C4—2082no—
230C4#1171806511yescharacteristic
231C4#1171806611yescharacteristic
232C2—21no—
233C2—41no—
234C2—81no—
235C2—81no—
236C2#1311296011yescharacteristic
subgroupG/H
centerC4#11718065
commutatorC42×C13C42
Frattini#532C2×D13
FittingC13×#2132C2
socleC2×C13#1393
prime radical, cosocleC13×#532C22
hypercenter#2132D13
hypocenterC13#7503
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
9. #11718593C4semidirect
10. #11718585C4semidirect
11. C13×#356C4semidirect
13. #11718137C4semidirect
108. #356Dic13semidirect
187. C13#7503semidirect

Maximal subgroups

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

subgroupindex
#131165012
#131156692
C13×#21322
#750313