Finite Group Databasebeta

← #16791313

Subgroups — #16791313

Order 3328.

312 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 60 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×#11718227C212yesmaximal
2#13129980C214yesmaximal, complemented
3#13125217C211yesmaximal, characteristic
4#11719175C411yescharacteristic
5C2×#88123C2211yescharacteristic
6C2×#88113—22no—
7C4×C13×M16C411yescharacteristic
8#11718781—22no—
9#11718364C412yes—
10#11718364C2212yes—
11#11718342—22no—
12#11718227—22no—
13#11718227C2214yes—
14C22×Dic26D412yes—
15C2×#6122—42no—
16C2×C13×M16—21no—
17C2×C42×C13C2×C411yescharacteristic
18#88180—21no—
19C2×C4⋊Dic13—41no—
20#88178—41no—
21#88124C2×C412yes—
22#88123—21no—
23#88123—41no—
24#88123C2×C411yescharacteristic
25#88123D412yes—
26#88123C2311yescharacteristic
27C4×Dic26—41no—
28#88113—24no—
29#88113—42no—
30C13×#97C2×C412yes—
31C4×C8×C13—21no—
32#88056—24no—
33#88056—24no—
34#13599—131nomaximal, Sylow
35C22×C4×C13—21no—
36C22×C4×C13C22⋊C411yescharacteristic
37C22×Dic13—22no—
38C2×Dic26—22no—
39C2×Dic26—42no—
40C2×Dic26—42no—
41C2×Dic26—41no—
42C2×Dic26C22⋊C412yes—
43C2×Dic26C2×D412yes—
44#6122—44no—
45#6122—82no—
46C2×#1057—82no—
47C13×M16—42no—
48C2×C8×C13—22no—
49C42×C13—21no—
50C42×C13C22⋊C411yescharacteristic
51C42×C13C22×C411yescharacteristic
52C22⋊Dic13—41no—
53C4⋊Dic13—22no—
54C4⋊Dic13—41no—
55C4⋊Dic13—42no—
56C4⋊Dic13—41no—
57C4⋊Dic13—41no—
58#6101—42no—
59C4×Dic13—41no—
60#3139—131no—
61C2×#356—132no—
62#1413—134no—
63C23×C13#9911yescharacteristic
64C2×C4×C13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—42no—
68C2×C4×C13#9911yescharacteristic
69C2×C4×C13C2×C22⋊C411yescharacteristic
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—42no—
73C2×Dic13—42no—
74C2×Dic13—42no—
75Dic26—42no—
76Dic26—42no—
77Dic26—82no—
78Dic26—82no—
79#1057—84no—
80C8×C13—42no—
81#533—131no—
82C2×C4⋊Q8—131no—
83#491—132no—
84#491—132no—
85#487—262no—
86#419—262no—
87C2×#101—262no—
88C4×M16#26111yescharacteristic
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—
98Dic13—42no—
99Dic13—42no—
100Dic13—82no—
101C22×Q8—132no—
102C2×M16—21no—
103C2×M16—522no—
104C4⋊Q8—132no—
105C4⋊Q8—131no—
106C4⋊Q8—131no—
107C4⋊Q8—261no—
108C4⋊Q8—521no—
109#125—132no—
110C22⋊Q8—521no—
111C4×Q8—521no—
112#117—261no—
113C2×C4⋊C4—521no—
114C2×C42C2×#26111yescharacteristic
115#103—264no—
116#103—264no—
117#101—264no—
118#101—522no—
119#97C2×#26112yes—
120C4×C8—21no—
121C2×C13—21no—
122C2×C13—22no—
123C2×C13C2×#35411yescharacteristic
124C2×Q8—132no—
125C2×Q8—132no—
126C2×Q8—262no—
127C2×Q8—521no—
128C2×Q8—522no—
129C2×Q8—522no—
130C22×C4—21no—
131C22×C4—262no—
132C22×C4C22⋊#26111yescharacteristic
133M16—42no—
134M16—524no—
135M16—1042no—
136C2×C8—22no—
137C2×C8—1042no—
138C4⋊C4—262no—
139C4⋊C4—522no—
140C4⋊C4—521no—
141C4⋊C4—521no—
142C4⋊C4—522no—
143C4⋊C4—521no—
144C22⋊C4—521no—
145C42—21no—
146C42—521no—
147C42C22⋊#26111yescharacteristic
148C42C22×#26111yescharacteristic
149C13#1359911yescharacteristic, complemented, Sylow
150C23#8810711yescharacteristic
151Q8—522no—
152Q8—522no—
153Q8—1042no—
154Q8—1042no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—262no—
160C2×C4—262no—
161C2×C4—522no—
162C2×C4—522no—
163C2×C4—522no—
164C2×C4#8810711yescharacteristic
165C2×C4C2×C22⋊#26111yescharacteristic
166C8—42no—
167C8—1044no—
168C22—41no—
169C22#1171822612yes—
170C22C2×#8810711yescharacteristic
171C4—22no—
172C4—21no—
173C4—21no—
174C4—41no—
175C4—522no—
176C4—522no—
177C4—1042no—
178C2—21no—
179C2—22no—
180C2C2×#1171822611yescharacteristic
subgroupG/H
centerC2C2×#11718226
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC4×C13×M16C4
socleC2×C13C2×#354
prime radicalC23×C13#99
cosocle#88123C23
hypercenterC4×M16#261
hypocenterC13#13599
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #13129980C2semidirect
149. C13#13599semidirect

Maximal subgroups

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

subgroupindex
C2×#117182272
#131299802
#131252172
#1359913