Finite Group Databasebeta

← #15783279

Subgroups — #15783279

Order 3328.

318 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 79 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#13116521C212yesmaximal
2#13113009C214yesmaximal, complemented
3C13×#3135C211yesmaximal, characteristic
4C13×#533C411yescharacteristic
5C13×#532C2211yescharacteristic
6C13×#491C2212yes—
7C13×#490C412yes—
8C13×#489—22no—
9C13×#416—22no—
10C2×C13×#97C411yescharacteristic
11#11718898—22no—
12#11718140C2214yes—
13#11718134—22no—
14C2×C13×#41D412yes—
15C22×C8×C13—21no—
16C13×C4⋊Q8—21no—
17C13×C4⋊Q8C2311yescharacteristic
18C13×#127C2×C411yescharacteristic
19C13×#125C2×C412yes—
20C13×#124D412yes—
21C13×C22⋊Q8—41no—
22C13×#121—41no—
23C4×Q8×C13—41no—
24C4×D4×C13—41no—
25C13×#117—21no—
26C2×C42×C13C2×C411yescharacteristic
27C2×#6099—42no—
28C13×#103—24no—
29C13×#102—24no—
30C13×#97—21no—
31C13×#97C2×C412yes—
32#88076—24no—
33#88073—42no—
34#13598—131nomaximal, Sylow
35C13×#41—42no—
36C13×#41—42no—
37C2×Q8×C13—41no—
38C2×Q8×C13C2×D412yes—
39C2×D4×C13—22no—
40C2×D4×C13—41no—
41C2×D4×C13C22⋊C412yes—
42C22×C4×C13—21no—
43C22×C4×C13—22no—
44C22×C4×C13C22⋊C411yescharacteristic
45C2×C8×C13—22no—
46C2×C8×C13—41no—
47C2×C8×C13—41no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—41no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—41no—
52C13×C22⋊C4—42no—
53C13×C22⋊C4—41no—
54C42×C13—21no—
55C42×C13—41no—
56C42×C13C22⋊C411yescharacteristic
57C42×C13C22×C411yescharacteristic
58#6099—44no—
59#6099—82no—
60C2×#1055—82no—
61#3135D1311yescharacteristic
62#2132—132no—
63#1413—134no—
64C23×C13—22no—
65C23×C13#9911yescharacteristic
66Q8×C13—42no—
67Q8×C13—82no—
68D4×C13—42no—
69D4×C13—82no—
70D4×C13—82no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13—81no—
80C2×C4×C13#9911yescharacteristic
81C2×C4×C13C2×C22⋊C411yescharacteristic
82C8×C13—42no—
83#1055—84no—
84#533Dic1311yescharacteristic
85#532C2×D1311yescharacteristic
86#491C2×D1312yes—
87#490Dic1312yes—
88#489—22no—
89#416—22no—
90#413—262no—
91C2×#97Dic1311yescharacteristic
92#356—134no—
93#355—262no—
94C22×C13—21no—
95C22×C13—41no—
96C22×C13—42no—
97C22×C13—82no—
98C22×C13C2×#9911yescharacteristic
99C4×C13—21no—
100C4×C13—41no—
101C4×C13—41no—
102C4×C13—42no—
103C4×C13—82no—
104C4×C13#35411yescharacteristic
105C4×C13#35411yescharacteristic
106C2×#41C22⋊D1312yes—
107C2×M16—522no—
108C22×C8—21no—
109C4⋊Q8—21no—
110C4⋊Q8C22×D1311yescharacteristic
111#127C2×Dic1311yescharacteristic
112#125C2×Dic1312yes—
113#124C22⋊D1312yes—
114C22⋊Q8—41no—
115#121—41no—
116C4×Q8—41no—
117C4×D4—41no—
118#117—21no—
119C2×C42C2×Dic1311yescharacteristic
120#103—24no—
121#102—24no—
122#101—264no—
123#100—522no—
124#97—21no—
125#97C2×Dic1312yes—
126C2×C13—21no—
127C2×C13—41no—
128C2×C13—82no—
129C2×C13C2×#35411yescharacteristic
130#41—42no—
131#41—42no—
132C2×Q8—41no—
133C2×Q8C2×C22⋊D1312yes—
134C2×D4—22no—
135C2×D4—41no—
136C2×D4C22⋊Dic1312yes—
137C22×C4—21no—
138C22×C4—22no—
139C22×C4C22⋊Dic1311yescharacteristic
140M16—524no—
141M16—1042no—
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C2×C8—1042no—
146C4⋊C4—22no—
147C4⋊C4—41no—
148C4⋊C4—42no—
149C4⋊C4—41no—
150C22⋊C4—42no—
151C22⋊C4—41no—
152C42—21no—
153C42—41no—
154C42C22⋊Dic1311yescharacteristic
155C42C22×Dic1311yescharacteristic
156C13#1359811yescharacteristic, complemented, Sylow
157C23—22no—
158C23#8807411yescharacteristic
159Q8—42no—
160Q8—82no—
161D4—42no—
162D4—82no—
163D4—82no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—81no—
173C2×C4#8807411yescharacteristic
174C2×C4C2×C22⋊Dic1311yescharacteristic
175C8—42no—
176C8—1044no—
177C22—21no—
178C22—41no—
179C22—42no—
180C22—82no—
181C22C2×#8807411yescharacteristic
182C4—21no—
183C4—41no—
184C4—41no—
185C4—42no—
186C4—82no—
187C4#1171813311yescharacteristic
188C4#1171813311yescharacteristic
189C2—21no—
190C2—41no—
191C2—82no—
192C2C2×#1171813311yescharacteristic
subgroupG/H
centerC4#11718133
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC13×#3135C2
socleC2×C13C2×#354
prime radicalC13×#532C22
cosocleC13×C4⋊Q8C23
hypercenter#3135D13
hypocenterC13#13598
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3135

Complements

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

NH ≅ G/Ntype
2. #13113009C2semidirect
156. C13#13598semidirect

Maximal subgroups

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

subgroupindex
#131165212
#131130092
C13×#31352
#1359813