Finite Group Databasebeta

← #13113307

Subgroups — #13113307

Order 1664.

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

normal subgroups only

This group has 202 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#11719283C211yesmaximal, characteristic
2#11718496C211yesmaximal, characteristic
3#11718346C211yesmaximal, characteristic
4C13×Q8⋊C8C211yesmaximal, characteristic, complemented
5Q8⋊#1055C211yesmaximal, characteristic, complemented
6#11718076C211yesmaximal, characteristic, complemented
7#11718048C211yesmaximal, characteristic, complemented
8C4×Q8×C13C2211yescharacteristic
9#88200C411yescharacteristic
10#88198C411yescharacteristic
11#88151C411yescharacteristic
12#88150—21no—
13#88143—21no—
14#88142C411yescharacteristic
15#88126—21no—
16C42×D13C2211yescharacteristic
17C4×Dic26—21no—
18C4×Dic26C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20C4×C8×C13C2211yescharacteristic
21#88060—21no—
22#88060—21no—
23#88055—21no—
24#88054—21no—
25C4⋊#1055C2211yescharacteristic
26C4×#1055C2211yescharacteristic
27C2×Q8×C13C2×C411yescharacteristic
28C2×C4×D13C2×C411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13D411yescharacteristic
31C2×Dic26—21no—
32C2×Dic26C2×C411yescharacteristic
33C2×C8×C13—21no—
34C2×C8×C13—21no—
35C13×C4⋊C4—21no—
36C13×C4⋊C4C2×C411yescharacteristic
37C42×C13—21no—
38C42×C13C2311yescharacteristic
39#6103—21no—
40#6103—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13C2×C411yescharacteristic
43#6101—21no—
44#6101—21no—
45#6101—21no—
46#6101—21no—
47#6101—21no—
48C4×Dic13—21no—
49C4×Dic13C2×C411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13D411yescharacteristic
52C2×#1055—21no—
53C2×#1055—21no—
54#1497—131nomaximal, Sylow
55C22×D13C22⋊C411yescharacteristic
56Q8×C13—21no—
57Q8×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13C22×C411yescharacteristic
61C2×C4×C13C2×D411yescharacteristic
62C2×C4×C13C2×D411yescharacteristic
63C2×Dic13—21no—
64C2×Dic13—21no—
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C22⋊C411yescharacteristic
68C4×D13—21no—
69C4×D13—21no—
70C4×D13—21no—
71C4×D13—21no—
72C4×D13—41no—
73Dic26—21no—
74Dic26—21no—
75Dic26—42no—
76C8×C13—41no—
77C8×C13—41no—
78#1055—41no—
79#1055—41no—
80#533—131no—
81#432—131no—
82#431—131no—
83Q8⋊C8—131no—
84Q8⋊C8—131no—
85Q8⋊C8—131no—
86Q8⋊C8D1311yescharacteristic, complemented
87C22×C13C2×C22⋊C411yescharacteristic
88C2×D13—21no—
89C2×D13—21no—
90C2×D13—21no—
91C4×C13—21no—
92C4×C13—41no—
93C4×C13—41no—
94C4×C13#13111yescharacteristic
95C4×C13#13111yescharacteristic
96C4×C13#13711yescharacteristic
97C4×C13#13711yescharacteristic
98Dic13—21no—
99Dic13—21no—
100Dic13—21no—
101Dic13—41no—
102Dic13—41no—
103C4⋊Q8—131no—
104C4⋊Q8—131no—
105#125—261no—
106C22⋊Q8—131no—
107C22⋊Q8—131no—
108C22⋊Q8—261no—
109C4×Q8—131no—
110C4×Q8—261no—
111C4×Q8C2×D1311yescharacteristic
112#117—261no—
113C2×C42—131no—
114C4⋊C8—131no—
115C4⋊C8—261no—
116C4⋊C8C2×D1311yescharacteristic
117C22⋊C8—261no—
118C22⋊C8—261no—
119#97—261no—
120C4×C8—131no—
121C4×C8C2×D1311yescharacteristic
122C2×C13#40811yescharacteristic
123C2×C13#41911yescharacteristic
124C2×C13#42111yescharacteristic
125D13—41no—
126C2×Q8—131no—
127C2×Q8—261no—
128C2×Q8C4×D1311yescharacteristic
129C22×C4—131no—
130C22×C4—131no—
131C22×C4—131no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—261no—
135C2×C8—261no—
136C4⋊C4—21no—
137C4⋊C4—131no—
138C4⋊C4—261no—
139C4⋊C4—261no—
140C4⋊C4—261no—
141C4⋊C4—261no—
142C4⋊C4—261no—
143C4⋊C4—261no—
144C4⋊C4C4×D1311yescharacteristic
145C22⋊C4—261no—
146C22⋊C4—261no—
147C42—21no—
148C42—131no—
149C42—131no—
150C42—131no—
151C42—261no—
152C42C22×D1311yescharacteristic
153C13#149711yescharacteristic, complemented, Sylow
154C23—131no—
155Q8—21no—
156Q8—21no—
157Q8—261no—
158Q8—261no—
159Q8—522no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—131no—
165C2×C4—261no—
166C2×C4—261no—
167C2×C4—261no—
168C2×C4—261no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4—521no—
172C2×C4C2×C4×D1311yescharacteristic
173C2×C4D4×D1311yescharacteristic
174C2×C4D4×D1311yescharacteristic
175C8—41no—
176C8—41no—
177C8—521no—
178C8—521no—
179C22—261no—
180C22—261no—
181C22—261no—
182C22C22⋊C4×D1311yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—261no—
187C4—261no—
188C4—261no—
189C4—521no—
190C4—521no—
191C4#8815511yescharacteristic
192C4#8816111yescharacteristic
193C4#8816911yescharacteristic
194C4#8817211yescharacteristic
195C2—521no—
196C2#1171838811yescharacteristic
197C2#1171846311yescharacteristic
198C2#1171848211yescharacteristic
subgroupG/H
centerC2×C4D4×D13
commutatorC2×C4×C13C22×C4
FrattiniC42C22×D13
FittingC13×Q8⋊C8C2
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC42×C13C23
hypercenterQ8⋊C8D13
hypocenterC13#1497
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C13×Q8⋊C8C2semidirect
5. Q8⋊#1055C2semidirect
6. #11718076C2semidirect
7. #11718048C2semidirect
86. Q8⋊C8D13semidirect
153. C13#1497semidirect

Maximal subgroups

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

subgroupindex
#117192832
#117184962
#117183462
C13×Q8⋊C82
Q8⋊#10552
#117180762
#117180482
#149713