Finite Group Databasebeta

← #15767059

Subgroups — #15767059

Order 3328.

370 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 77 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#13114976C211yesmaximal, characteristic, complemented
2#13113558C212yesmaximal, complemented
3#13113447C212yesmaximal, complemented
4#13112747C211yesmaximal, characteristic, complemented
5C13×#3253C211yesmaximal, characteristic
6C13×#532C2212yes—
7C13×#476—22no—
8C13×#469—22no—
9C13×#459—22no—
10C13×#423C2211yescharacteristic
11#11718587C2212yes—
12#11718585C2211yescharacteristic
13C2×#88043C2211yescharacteristic
14#11718150—22no—
15#11718139—22no—
16#11718136—22no—
17#11718132—24no—
18C2×C13×#41—22no—
19C2×C13×D8—22no—
20C2×C13×M16D412yes—
21C13×C4⋊Q8D412yes—
22C13×#127D412yes—
23C13×#124—22no—
24C13×#121—22no—
25C13×#121—22no—
26C4×D4×C13—22no—
27C4×D4×C13—22no—
28C2×C42×C13C2311yescharacteristic
29C2×#6099—21no—
30C22×#1055—21no—
31C13×#106—22no—
32C13×C4⋊C8—22no—
33C13×#102—24no—
34C22⋊#1055—22no—
35C4⋊#1055—22no—
36C4⋊#1055—22no—
37#88043—21no—
38#88043—22no—
39#88043D412yes—
40#10525—131nomaximal, Sylow
41C13×#41—84no—
42C2×Q8×C13—22no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13—42no—
47C22×C4×C13—42no—
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13#4112yes—
50C13×D8—82no—
51C13×M16—42no—
52C2×C8×C13—22no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C22⋊C4—42no—
56C13×C22⋊C4—42no—
57C42×C13C2×D411yescharacteristic
58C42×C13C2×D412yes—
59C42×C13#4111yescharacteristic
60#6099—42no—
61C2×#1055—22no—
62C2×#1055—41no—
63C2×#1055—41no—
64C2×#1055—41no—
65C2×#1055—42no—
66#3253D1311yescharacteristic
67#1838—131no—
68#1557—132no—
69#1530—132no—
70#1307—131no—
71C23×C13—42no—
72C23×C13#12411yescharacteristic
73Q8×C13—82no—
74D4×C13—42no—
75D4×C13—42no—
76D4×C13—82no—
77D4×C13—82no—
78D4×C13—84no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—84no—
84C2×C4×C13#12011yescharacteristic
85C2×C4×C13#12111yescharacteristic
86C2×C4×C13#12112yes—
87C2×C4×C13#12312yes—
88C8×C13—42no—
89#1055—42no—
90#1055—82no—
91#1055—81no—
92#532C2×D1312yes—
93#476—22no—
94#469—22no—
95#459—22no—
96#432—132no—
97#423—131no—
98#423C2×D1311yescharacteristic
99C2×#97—131no—
100#341—262no—
101#332—262no—
102#331—262no—
103#329—264no—
104C22×C13—22no—
105C22×C13—21no—
106C22×C13—82no—
107C22×C13—82no—
108C22×C13—82no—
109C22×C13#39411yescharacteristic
110C4×C13—22no—
111C4×C13—22no—
112C4×C13—21no—
113C4×C13—82no—
114C4×C13#45411yescharacteristic
115C4×C13#45511yescharacteristic
116C2×#41—22no—
117C2×D8—22no—
118C2×M16—261no—
119C2×M16C22⋊D1312yes—
120C22×C8—261no—
121C4⋊Q8C22⋊D1312yes—
122#127C22⋊D1312yes—
123#124—22no—
124#121—22no—
125#121—22no—
126C4×D4—22no—
127C4×D4—22no—
128C2×C42C22×D1311yescharacteristic
129#106—22no—
130C4⋊C8—22no—
131C4⋊C8—262no—
132C4⋊C8—262no—
133#102—24no—
134C22⋊C8—262no—
135#97—132no—
136#97—262no—
137#97—261no—
138C2×C13—41no—
139C2×C13—162no—
140C2×C13#204011yescharacteristic
141C2×C13#204812yes—
142#41—84no—
143C2×Q8—22no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—42no—
148C22×C4—42no—
149C22×C4#612912yes—
150C22×C4C2×C22⋊D1311yescharacteristic
151D8—82no—
152M16—42no—
153M16—522no—
154C2×C8—22no—
155C2×C8—262no—
156C2×C8—521no—
157C2×C8—521no—
158C2×C8—522no—
159C2×C8—521no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C22⋊C4—42no—
163C22⋊C4—42no—
164C42D4×D1311yescharacteristic
165C42#612911yescharacteristic
166C42C2×C22⋊D1312yes—
167C13#1052511yescharacteristic, complemented, Sylow
168C23—42no—
169C23#8819011yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—82no—
175D4—84no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—84no—
181C2×C4#8818912yes—
182C2×C4#8819211yescharacteristic
183C2×C4#8819312yes—
184C2×C4#8820711yescharacteristic
185C8—42no—
186C8—522no—
187C8—1042no—
188C8—1041no—
189C22—21no—
190C22—22no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22#1171888311yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—82no—
199C4#1171890311yescharacteristic
200C4#1171890611yescharacteristic
201C2—41no—
202C2—162no—
203C2#1311606211yescharacteristic
204C2#1311610612yes—
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3253C2
socleC22×C13#394
hypercenter#3253D13
hypocenterC13#10525
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #13114976C2semidirect
2. #13113558C2semidirect
3. #13113447C2semidirect
4. #13112747C2semidirect
167. C13#10525semidirect

Maximal subgroups

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

subgroupindex
#131149762
#131135582
#131134472
#131127472
C13×#32532
#1052513