Finite Group Databasebeta

← #16791310

Subgroups — #16791310

Order 3328.

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

normal subgroups only

This group has 318 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
1#13131129C212yesmaximal
2#13129980C214yesmaximal, complemented
3#13125182C211yesmaximal, characteristic
4#11719182C2211yescharacteristic
5#11719175C411yescharacteristic
6#11719132—22no—
7C2×C13×#97C411yescharacteristic
8#11718774—22no—
9#11718375—22no—
10#11718374C412yes—
11#11718364C2212yes—
12#11718228—22no—
13#11718227C2214yes—
14C2×#6127D412yes—
15D13⋊M16—42no—
16C22×C8×C13—21no—
17C2×C42×C13C2×C411yescharacteristic
18#88184—41no—
19#88180—21no—
20#88178—41no—
21#88129D412yes—
22#88128C2×C411yescharacteristic
23C4×D52—41no—
24#88124C2×C412yes—
25#88123—21no—
26#88123C2311yescharacteristic
27C4×Dic26—41no—
28#88121—42no—
29#88113—24no—
30C13×#97—21no—
31C13×#97C2×C412yes—
32#88061—24no—
33#88056—24no—
34#13598—131nomaximal, Sylow
35C22×C4×C13—21no—
36C22×C4×C13C22⋊C411yescharacteristic
37C2×C22⋊D13—22no—
38#6127—42no—
39#6127—42no—
40C2×D52—41no—
41C2×D52C22⋊C412yes—
42C2×C4×D13—22no—
43C2×Dic26—41no—
44C2×Dic26C2×D412yes—
45#6122—44no—
46#6118—82no—
47D13⋊C8—82no—
48C2×C8×C13—22no—
49C2×C8×C13—41no—
50C2×C8×C13—41no—
51C42×C13—21no—
52C42×C13C22⋊C411yescharacteristic
53C42×C13C22×C411yescharacteristic
54C22⋊Dic13—41no—
55#6103—42no—
56C4⋊Dic13—22no—
57C4⋊Dic13—41no—
58C4⋊Dic13—41no—
59#6101—42no—
60C4×Dic13—41no—
61#3135—131no—
62#2132—132no—
63#1413—134no—
64C23×C13#9911yescharacteristic
65C22×D13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—81no—
71C2×C4×C13#9911yescharacteristic
72C2×C4×C13C2×C22⋊C411yescharacteristic
73C22⋊D13—82no—
74C2×Dic13—22no—
75C2×Dic13—42no—
76D52—42no—
77D52—82no—
78C4×D13—42no—
79C4×D13—42no—
80Dic26—42no—
81Dic26—82no—
82#1057—84no—
83C8×C13—42no—
84#533—131no—
85#532—131no—
86#491—132no—
87#490—132no—
88#489—262no—
89#416—262no—
90#413—262no—
91C2×#97#26111yescharacteristic
92#356—134no—
93#355—262no—
94C22×C13—21no—
95C22×C13—41no—
96C22×C13C2×#9911yescharacteristic
97C2×D13—42no—
98C2×D13—82no—
99C4×C13—21no—
100C4×C13—41no—
101C4×C13—41no—
102C4×C13#35411yescharacteristic
103C4×C13#35411yescharacteristic
104Dic13—42no—
105Dic13—82no—
106C2×#41—132no—
107C2×M16—522no—
108C22×C8—21no—
109C4⋊Q8—131no—
110C4⋊Q8—261no—
111#127—131no—
112#125—132no—
113#124—132no—
114C22⋊Q8—521no—
115#121—521no—
116C4×Q8—521no—
117C4×D4—521no—
118#117—261no—
119C2×C42C2×#26111yescharacteristic
120#103—264no—
121#102—264no—
122#101—264no—
123#100—522no—
124#97—21no—
125#97C2×#26112yes—
126C2×C13—21no—
127C2×C13—41no—
128C2×C13C2×#35411yescharacteristic
129D13—82no—
130#41—522no—
131#41—522no—
132C2×Q8—132no—
133C2×Q8—521no—
134C2×D4—132no—
135C2×D4—262no—
136C2×D4—521no—
137C22×C4—21no—
138C22×C4—262no—
139C22×C4C22⋊#26111yescharacteristic
140M16—524no—
141M16—1042no—
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C2×C8—1042no—
146C4⋊C4—262no—
147C4⋊C4—521no—
148C4⋊C4—522no—
149C4⋊C4—521no—
150C22⋊C4—522no—
151C22⋊C4—521no—
152C42—21no—
153C42—521no—
154C42C22⋊#26111yescharacteristic
155C42C22×#26111yescharacteristic
156C13#1359811yescharacteristic, complemented, Sylow
157C23—262no—
158C23#8810711yescharacteristic
159Q8—522no—
160Q8—1042no—
161D4—522no—
162D4—1042no—
163D4—1042no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—262no—
170C2×C4—522no—
171C2×C4—522no—
172C2×C4—522no—
173C2×C4#8810711yescharacteristic
174C2×C4C2×C22⋊#26111yescharacteristic
175C8—42no—
176C8—1044no—
177C22—21no—
178C22—41no—
179C22—522no—
180C22—1042no—
181C22C2×#8810711yescharacteristic
182C4—21no—
183C4—41no—
184C4—41no—
185C4—522no—
186C4—1042no—
187C4#1171822611yescharacteristic
188C4#1171822611yescharacteristic
189C2—21no—
190C2—41no—
191C2—1042no—
192C2C2×#1171822611yescharacteristic
subgroupG/H
centerC4#11718226
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×#97C4
socleC2×C13C2×#354
prime radical#11719182C22
cosocle#88123C23
hypercenterC2×#97#261
hypocenterC13#13598
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #13129980C2semidirect
156. C13#13598semidirect

Maximal subgroups

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

subgroupindex
#131311292
#131299802
#131251822
#1359813