Finite Group Databasebeta

← #15783282

Subgroups — #15783282

Order 3328.

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

normal subgroups only

This group has 312 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
1C2×#11718140C212yesmaximal
2#13113009C214yesmaximal, complemented
3C13×#3139C211yesmaximal, characteristic
4C13×#533C411yescharacteristic
5C2×C13×C4⋊Q8C2211yescharacteristic
6C13×#491C412yes—
7C13×#491C2212yes—
8C13×#487—22no—
9C13×#419—22no—
10C4×C13×M16C411yescharacteristic
11C2×#88076—22no—
12#11718140—22no—
13#11718140C2214yes—
14C22×Q8×C13D412yes—
15C2×C13×M16—21no—
16C13×C4⋊Q8—21no—
17C13×C4⋊Q8—41no—
18C13×C4⋊Q8C2×C411yescharacteristic
19C13×C4⋊Q8D412yes—
20C13×C4⋊Q8C2311yescharacteristic
21C13×#125C2×C412yes—
22C13×C22⋊Q8—41no—
23C4×Q8×C13—41no—
24C13×#117—21no—
25C2×C13×C4⋊C4—41no—
26C2×C42×C13C2×C411yescharacteristic
27C2×#6099—42no—
28C13×#103—24no—
29C13×#103—24no—
30C13×#97C2×C412yes—
31C4×C8×C13—21no—
32#88076—24no—
33#88076—42no—
34#13599—131nomaximal, Sylow
35C2×Q8×C13—22no—
36C2×Q8×C13—41no—
37C2×Q8×C13—42no—
38C2×Q8×C13—42no—
39C2×Q8×C13C22⋊C412yes—
40C2×Q8×C13C2×D412yes—
41C22×C4×C13—22no—
42C22×C4×C13—21no—
43C22×C4×C13C22⋊C411yescharacteristic
44C13×M16—42no—
45C2×C8×C13—22no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—41no—
48C13×C4⋊C4—42no—
49C13×C4⋊C4—41no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—41no—
52C13×C22⋊C4—41no—
53C42×C13—21no—
54C42×C13—41no—
55C42×C13C22⋊C411yescharacteristic
56C42×C13C22×C411yescharacteristic
57#6099—44no—
58#6099—82no—
59C2×#1055—82no—
60#3139D1311yescharacteristic
61C2×#356—132no—
62#1413—134no—
63C23×C13#9911yescharacteristic
64Q8×C13—42no—
65Q8×C13—42no—
66Q8×C13—82no—
67Q8×C13—82no—
68C2×C4×C13—22no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—42no—
74C2×C4×C13—42no—
75C2×C4×C13—42no—
76C2×C4×C13—42no—
77C2×C4×C13#9911yescharacteristic
78C2×C4×C13C2×C22⋊C411yescharacteristic
79C8×C13—42no—
80#1055—84no—
81#533Dic1311yescharacteristic
82C2×C4⋊Q8C2×D1311yescharacteristic
83#491Dic1312yes—
84#491C2×D1312yes—
85#487—22no—
86#419—22no—
87C2×#101—262no—
88C4×M16Dic1311yescharacteristic
89#356—134no—
90#356—262no—
91C22×C13—41no—
92C22×C13#35412yes—
93C22×C13C2×#9911yescharacteristic
94C4×C13—22no—
95C4×C13—21no—
96C4×C13—21no—
97C4×C13—41no—
98C4×C13—42no—
99C4×C13—42no—
100C4×C13—82no—
101C22×Q8C22⋊D1312yes—
102C2×M16—21no—
103C2×M16—522no—
104C4⋊Q8—21no—
105C4⋊Q8—41no—
106C4⋊Q8C2×Dic1311yescharacteristic
107C4⋊Q8C22⋊D1312yes—
108C4⋊Q8C22×D1311yescharacteristic
109#125C2×Dic1312yes—
110C22⋊Q8—41no—
111C4×Q8—41no—
112#117—21no—
113C2×C4⋊C4—41no—
114C2×C42C2×Dic1311yescharacteristic
115#103—24no—
116#103—24no—
117#101—264no—
118#101—522no—
119#97C2×Dic1312yes—
120C4×C8—21no—
121C2×C13—21no—
122C2×C13—22no—
123C2×C13C2×#35411yescharacteristic
124C2×Q8—22no—
125C2×Q8—41no—
126C2×Q8—42no—
127C2×Q8—42no—
128C2×Q8C22⋊Dic1312yes—
129C2×Q8C2×C22⋊D1312yes—
130C22×C4—21no—
131C22×C4—22no—
132C22×C4C22⋊Dic1311yescharacteristic
133M16—42no—
134M16—524no—
135M16—1042no—
136C2×C8—22no—
137C2×C8—1042no—
138C4⋊C4—22no—
139C4⋊C4—41no—
140C4⋊C4—42no—
141C4⋊C4—41no—
142C4⋊C4—42no—
143C4⋊C4—41no—
144C22⋊C4—41no—
145C42—21no—
146C42—41no—
147C42C22⋊Dic1311yescharacteristic
148C42C22×Dic1311yescharacteristic
149C13#1359911yescharacteristic, complemented, Sylow
150C23#8807411yescharacteristic
151Q8—42no—
152Q8—42no—
153Q8—82no—
154Q8—82no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4#8807411yescharacteristic
165C2×C4C2×C22⋊Dic1311yescharacteristic
166C8—42no—
167C8—1044no—
168C22—41no—
169C22#1171813312yes—
170C22C2×#8807411yescharacteristic
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—42no—
176C4—42no—
177C4—82no—
178C2—21no—
179C2—22no—
180C2C2×#1171813311yescharacteristic
subgroupG/H
centerC2C2×#11718133
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC13×#3139C2
socleC2×C13C2×#354
prime radicalC23×C13#99
cosocleC13×C4⋊Q8C23
hypercenter#3139D13
hypocenterC13#13599
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ #3139

Complements

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

NH ≅ G/Ntype
2. #13113009C2semidirect
149. C13#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131130092
C13×#31392
#1359913