Finite Group Databasebeta

← #13113303

Subgroups — #13113303

Order 1664.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#11719253C211yesmaximal, characteristic
2#11718496C211yesmaximal, characteristic, complemented
3#11718346C211yesmaximal, characteristic, complemented
4C13×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊#1055C211yesmaximal, characteristic, complemented
6#11718075C211yesmaximal, characteristic, complemented
7#11718051C211yesmaximal, characteristic, complemented
8C2×#6127—21no—
9C4×D4×C13C2211yescharacteristic
10#88194C411yescharacteristic
11#88192C411yescharacteristic
12C4×C22⋊D13—21no—
13#88149C411yescharacteristic
14#88142C411yescharacteristic
15#88139—21no—
16#88138—21no—
17C4×D52C2211yescharacteristic
18C42×D13C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20C4×C8×C13C2211yescharacteristic
21#88060—21no—
22#88060—21no—
23#88055—21no—
24#88054—21no—
25C4⋊#1055C2211yescharacteristic
26C4×#1055C2211yescharacteristic
27C2×D4×C13C2×C411yescharacteristic
28C22×C4×C13—21no—
29C2×C22⋊D13—21no—
30C2×C22⋊D13—21no—
31C2×C22⋊D13—21no—
32#6127—42no—
33#6127—42no—
34C2×D52—21no—
35C2×D52C2×C411yescharacteristic
36C2×C4×D13—21no—
37C2×C4×D13C2×C411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×C4×D13D411yescharacteristic
40C2×Dic26—21no—
41C2×C8×C13—21no—
42C2×C8×C13—21no—
43C13×C4⋊C4C2×C411yescharacteristic
44C13×C22⋊C4—21no—
45C42×C13C2311yescharacteristic
46C22⋊Dic13—21no—
47#6103—21no—
48#6103—21no—
49C4⋊Dic13C2×C411yescharacteristic
50#6101—21no—
51C4×Dic13C2×C411yescharacteristic
52C4×Dic13D411yescharacteristic
53C4×Dic13D411yescharacteristic
54C2×#1055—21no—
55C2×#1055—21no—
56#1496—131nomaximal, Sylow
57C23×C13—21no—
58C22×D13—21no—
59C22×D13C22⋊C411yescharacteristic
60D4×C13—21no—
61D4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13C22×C411yescharacteristic
66C2×C4×C13C2×D411yescharacteristic
67C2×C4×C13C2×D411yescharacteristic
68C22⋊D13—42no—
69C22⋊D13—42no—
70C22⋊D13—42no—
71C2×Dic13—21no—
72C2×Dic13C22⋊C411yescharacteristic
73C2×Dic13C22⋊C411yescharacteristic
74C2×Dic13C22⋊C411yescharacteristic
75D52—21no—
76D52—21no—
77D52—42no—
78C4×D13—21no—
79C4×D13—21no—
80C4×D13—21no—
81C4×D13—21no—
82C4×D13—41no—
83C4×D13—41no—
84C4×D13—41no—
85Dic26—42no—
86C8×C13—41no—
87C8×C13—41no—
88#1055—41no—
89#1055—41no—
90#532—131no—
91#432—131no—
92#431—131no—
93D4⋊C8—131no—
94D4⋊C8—131no—
95D4⋊C8—131no—
96D4⋊C8D1311yescharacteristic, complemented
97C22×C13—41no—
98C22×C13—41no—
99C22×C13—41no—
100C22×C13C2×C22⋊C411yescharacteristic
101C2×D13—21no—
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—41no—
105C2×D13—41no—
106C2×D13—41no—
107C4×C13—21no—
108C4×C13—41no—
109C4×C13#13111yescharacteristic
110C4×C13#13111yescharacteristic
111C4×C13AGL(1,ℤ/8)11yescharacteristic
112C4×C13AGL(1,ℤ/8)11yescharacteristic
113Dic13—21no—
114Dic13—21no—
115Dic13—21no—
116Dic13—41no—
117C2×#41—261no—
118C4⋊Q8—131no—
119#127—131no—
120#124—261no—
121#121—131no—
122#121—131no—
123#121—261no—
124C4×D4—131no—
125C4×D4—261no—
126C4×D4C2×D1311yescharacteristic
127C2×C42—131no—
128C4⋊C8—131no—
129C4⋊C8—261no—
130C4⋊C8C2×D1311yescharacteristic
131C22⋊C8—261no—
132C22⋊C8—261no—
133#97—261no—
134C4×C8—131no—
135C4×C8C2×D1311yescharacteristic
136C2×C13—81no—
137C2×C13#40811yescharacteristic
138C2×C13#41811yescharacteristic
139C2×C13#42111yescharacteristic
140D13—41no—
141D13—81no—
142#41—522no—
143#41—522no—
144C2×Q8—261no—
145C2×D4—131no—
146C2×D4—261no—
147C2×D4—261no—
148C2×D4—261no—
149C2×D4—261no—
150C2×D4C4×D1311yescharacteristic
151C22×C4—21no—
152C22×C4—131no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—261no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—261no—
159C2×C8—261no—
160C4⋊C4—131no—
161C4⋊C4—261no—
162C4⋊C4C4×D1311yescharacteristic
163C22⋊C4—21no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—261no—
167C42—131no—
168C42—131no—
169C42—131no—
170C42C22×D1311yescharacteristic
171C13#149611yescharacteristic, complemented, Sylow
172C23—21no—
173C23—131no—
174C23—261no—
175Q8—522no—
176D4—21no—
177D4—21no—
178D4—261no—
179D4—261no—
180D4—522no—
181D4—522no—
182D4—522no—
183D4—522no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—261no—
195C2×C4—521no—
196C2×C4—521no—
197C2×C4—521no—
198C2×C4C2×C4×D1311yescharacteristic
199C2×C4D4×D1311yescharacteristic
200C2×C4D4×D1311yescharacteristic
201C8—41no—
202C8—41no—
203C8—521no—
204C8—521no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—261no—
209C22—261no—
210C22—261no—
211C22—521no—
212C22—521no—
213C22—521no—
214C22C22⋊C4×D1311yescharacteristic
215C4—21no—
216C4—41no—
217C4—261no—
218C4—261no—
219C4—261no—
220C4—521no—
221C4#8815511yescharacteristic
222C4#8816111yescharacteristic
223C4#8816511yescharacteristic
224C4#8816811yescharacteristic
225C2—81no—
226C2—521no—
227C2—1041no—
228C2#1171838811yescharacteristic
229C2#1171843111yescharacteristic
230C2#1171848211yescharacteristic
subgroupG/H
centerC2×C4D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×D4⋊C8C2
socleC22×C13C2×C22⋊C4
prime radical#11719253C2
cosocleC42×C13C23
hypercenterD4⋊C8D13
hypocenterC13#1496
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11718496C2semidirect
3. #11718346C2semidirect
4. C13×D4⋊C8C2semidirect
5. D4⋊#1055C2semidirect
6. #11718075C2semidirect
7. #11718051C2semidirect
96. D4⋊C8D13semidirect
171. C13#1496semidirect

Maximal subgroups

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

subgroupindex
#117192532
#117184962
#117183462
C13×D4⋊C82
D4⋊#10552
#117180752
#117180512
#149613