Finite Group Databasebeta

← #16791267

Subgroups — #16791267

Order 3328.

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

normal subgroups only

This group has 406 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#13131109C212yesmaximal
2#13129969C214yesmaximal, complemented
3#13125293C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C411yescharacteristic, complemented
5C2×#88196—22no—
6#11719182C2211yescharacteristic
7#11719116—22no—
8#11718753C412yescomplemented
9#11718747—22no—
10#11718746C2212yes—
11C4×#6099C411yescharacteristic, complemented
12#11718226—22no—
13#11718225C2214yes—
14C22×Q8×C13—21no—
15C2×#6127D412yes—
16#88237—42no—
17C13×C4⋊Q8—21no—
18C13×C4⋊Q8—41no—
19C13×C4⋊Q8C2×C412yes—
20C2×C13×C4⋊C4—41no—
21C2×C42×C13C2×C411yescharacteristic
22C2×#6107—24no—
23#88196—44no—
24#88196—44no—
25C2×#6106—24no—
26#88184—41no—
27C2×#6099—21no—
28#88129D412yes—
29#88128C2311yescharacteristic
30C4×D52—41no—
31#88123C2×C411yescharacteristic
32#88119—42no—
33#88107—24no—
34#88043—21no—
35C4×#1055C2×C412yes—
36#13586—131nomaximal, Sylow
37C2×Q8×C13—22no—
38C2×Q8×C13—42no—
39C2×Q8×C13—42no—
40C2×Q8×C13—41no—
41C22×C4×C13—21no—
42C22×C4×C13—41no—
43C22×C4×C13C22⋊C411yescharacteristic
44C2×C22⋊D13—22no—
45#6127—42no—
46#6127—42no—
47C2×D52—41no—
48C2×D52C2×D412yes—
49C2×C4×D13—22no—
50C2×Dic26C22⋊C412yes—
51C22⋊#261—44no—
52C4⋊#261—82no—
53C4×#261—82no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—42no—
56C42×C13—21no—
57C42×C13C22⋊C411yescharacteristic
58C42×C13C22×C411yescharacteristic
59#6107—48no—
60#6106—48no—
61#6103—42no—
62C4⋊Dic13—41no—
63#6099—24no—
64C2×#1055—22no—
65#3152—131no—
66#2126—132no—
67#1409—134no—
68C23×C13#9911yescharacteristic
69C22×D13—22no—
70C2×#261—84no—
71Q8×C13—44no—
72Q8×C13—82no—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—81no—
79C2×C4×C13—81no—
80C2×C4×C13#9911yescharacteristic
81C2×C4×C13C2×C22⋊C411yescharacteristic
82C22⋊D13—82no—
83C2×Dic13—22no—
84D52—42no—
85D52—82no—
86C4×D13—42no—
87C4×D13—42no—
88Dic26—42no—
89#1055—24no—
90C2×#137—262no—
91#532—131no—
92C2×C4⋊Q8#26111yescharacteristic, complemented
93#497—262no—
94#494—132no—
95#492—132no—
96#410—262no—
97C4×M16—131no—
98#354—262no—
99#353—134no—
100C22×C13—21no—
101C22×C13—41no—
102C22×C13C2×#9911yescharacteristic
103C2×D13—42no—
104C2×D13—82no—
105#261—164no—
106C4×C13—22no—
107C4×C13—21no—
108C4×C13—41no—
109C4×C13—82no—
110C4×C13#35312yes—
111Dic13—42no—
112C2×#41—132no—
113C22×Q8—21no—
114#137—524no—
115#137—524no—
116C2×Q16—264no—
117C2×SD16—264no—
118C2×M16—261no—
119C4⋊Q8—21no—
120C4⋊Q8—41no—
121C4⋊Q8—131no—
122C4⋊Q8C2×#26112yes—
123#127—131no—
124#124—132no—
125#121—521no—
126C4×D4—521no—
127#117—522no—
128C2×C4⋊C4—41no—
129C2×C42C2×#26111yescharacteristic
130#99—264no—
131#99—522no—
132#97—261no—
133C4×C8—132no—
134C2×C13—21no—
135C2×C13—41no—
136C2×C13C2×#35311yescharacteristic
137D13—82no—
138#41—522no—
139#41—522no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—41no—
144C2×Q8—132no—
145C2×D4—132no—
146C2×D4—262no—
147C2×D4—521no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—262no—
151C22×C4C22⋊#26111yescharacteristic
152Q16—528no—
153SD16—528no—
154M16—264no—
155C2×C8—262no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—521no—
159C4⋊C4—1042no—
160C22⋊C4—522no—
161C22⋊C4—524no—
162C42—21no—
163C42—1042no—
164C42C22⋊#26111yescharacteristic
165C42C22×#26111yescharacteristic
166C13#1358611yescharacteristic, complemented, Sylow
167C23—262no—
168C23#8811911yescharacteristic
169Q8—44no—
170Q8—82no—
171Q8—522no—
172D4—522no—
173D4—1042no—
174D4—1042no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—262no—
183C2×C4—522no—
184C2×C4—522no—
185C2×C4—1044no—
186C2×C4#8811911yescharacteristic
187C2×C4C2×C22⋊#26111yescharacteristic
188C8—264no—
189C22—21no—
190C22—41no—
191C22—522no—
192C22—1042no—
193C22C2×#8811911yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—82no—
198C4—522no—
199C4—2084no—
200C4#1171829412yes—
201C2—21no—
202C2—41no—
203C2—1042no—
204C2C2×#1171829411yescharacteristic
subgroupG/H
centerC2C2×#11718294
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC2×C13×C4⋊Q8C4
socleC2×C13C2×#353
prime radical#11719182C22
cosocle#88128C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#13586
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13129969C2semidirect
4. C2×C13×C4⋊Q8C4semidirect
8. #11718753C4semidirect
11. C4×#6099C4semidirect
92. C2×C4⋊Q8#261semidirect
166. C13#13586semidirect

Maximal subgroups

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

subgroupindex
#131311092
#131299692
#131252932
#1358613