Finite Group Databasebeta

← #15766986

Subgroups — #15766986

Order 3328.

408 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 81 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#13114989C211yesmaximal, characteristic, complemented
2#13113531C212yesmaximal, complemented
3#13113344C212yesmaximal, complemented
4#13112706C211yesmaximal, characteristic, complemented
5C13×#3245C211yesmaximal, characteristic
6C13×#532C2212yes—
7C13×#474—22no—
8C13×#466—22no—
9C13×#459—22no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×#88054—22no—
12#11718593C2211yescharacteristic
13#11718587C2212yes—
14C2×C4⋊#1055C2211yescharacteristic
15#11718138—22no—
16#11718136—22no—
17#11718129—24no—
18C2×C13×#41—22no—
19C2×C13×D8—22no—
20C22×C8×C13D412yes—
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×C4×Dic13—21no—
30C22×#1055—21no—
31C13×#107—22no—
32C13×C4⋊C8—22no—
33C13×#102—24no—
34#88071—21no—
35#88071D412yes—
36C22⋊#1055—22no—
37#88054—44no—
38C4⋊#1055—22no—
39C4⋊#1055—22no—
40#88043—22no—
41#10512—131nomaximal, Sylow
42C13×#41—84no—
43C2×Q8×C13—22no—
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13—22no—
47C2×D4×C13—42no—
48C22×C4×C13—42no—
49C22×C4×C13C2×D411yescharacteristic
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13#4111yescharacteristic
52C22×Dic13—22no—
53C13×D8—82no—
54C2×C8×C13—22no—
55C2×C8×C13—42no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—22no—
58C13×C22⋊C4—42no—
59C13×C22⋊C4—42no—
60C42×C13C2×D412yes—
61C42×C13#4112yes—
62C4×Dic13—22no—
63C4×Dic13—22no—
64C2×#1055—42no—
65C2×#1055—41no—
66C2×#1055—42no—
67#3245D1311yescharacteristic
68#1843—131no—
69#1551—132no—
70#1505—132no—
71#1290—131no—
72C23×C13—42no—
73C23×C13#12111yescharacteristic
74Q8×C13—82no—
75D4×C13—42no—
76D4×C13—42no—
77D4×C13—82no—
78D4×C13—82no—
79D4×C13—84no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—41no—
84C2×C4×C13—42no—
85C2×C4×C13—84no—
86C2×C4×C13#12011yescharacteristic
87C2×C4×C13#12112yes—
88C2×C4×C13#12312yes—
89C2×C4×C13#12411yescharacteristic
90C2×Dic13—24no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93C8×C13—42no—
94#1055—82no—
95#1055—81no—
96#532C2×D1312yes—
97#474—22no—
98#466—22no—
99#459—22no—
100#432—132no—
101C2×C4⋊C8—131no—
102C2×C4⋊C8—262no—
103C2×C4⋊C8C2×D1311yescharacteristic
104#376—131no—
105#333—262no—
106#331—262no—
107#327—264no—
108C22×C13—21no—
109C22×C13—21no—
110C22×C13—82no—
111C22×C13—82no—
112C22×C13—82no—
113C22×C13#39411yescharacteristic
114C22×C13#47212yes—
115C4×C13—22no—
116C4×C13—21no—
117C4×C13—22no—
118C4×C13—82no—
119C4×C13#45311yescharacteristic
120C4×C13#45611yescharacteristic
121Dic13—44no—
122C2×#41—22no—
123C2×D8—22no—
124C22×C8—261no—
125C22×C8C22⋊D1312yes—
126C4⋊Q8C22⋊D1312yes—
127#127C22⋊D1312yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42—261no—
134C2×C42C22×D1311yescharacteristic
135#107—22no—
136C4⋊C8—22no—
137C4⋊C8—262no—
138C4⋊C8—262no—
139C4⋊C8—524no—
140#102—24no—
141C22⋊C8—262no—
142#97—262no—
143#95—132no—
144#95—261no—
145C2×C13—22no—
146C2×C13—162no—
147C2×C13#203911yescharacteristic
148C2×C13#204511yescharacteristic
149C2×C13#205311yescharacteristic
150#41—84no—
151C2×Q8—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—42no—
156C22×C4—42no—
157C22×C4—262no—
158C22×C4D4×D1311yescharacteristic
159C22×C4#612911yescharacteristic
160C22×C4C2×C22⋊D1311yescharacteristic
161D8—82no—
162C2×C8—22no—
163C2×C8—42no—
164C2×C8—522no—
165C2×C8—522no—
166C2×C8—521no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—262no—
172C42—262no—
173C42#612912yes—
174C42C2×C22⋊D1312yes—
175C13#1051211yescharacteristic, complemented, Sylow
176C23—42no—
177C23#8819211yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—82no—
182D4—82no—
183D4—84no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4—264no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4#8818912yes—
194C2×C4#8819011yescharacteristic
195C2×C4#8819312yes—
196C2×C4#8820711yescharacteristic
197C8—42no—
198C8—1042no—
199C8—1041no—
200C22—21no—
201C22—21no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1171882112yes—
206C22#1171888311yescharacteristic
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—524no—
212C4#1171890211yescharacteristic
213C4#1171890711yescharacteristic
214C2—22no—
215C2—162no—
216C2#1311605711yescharacteristic
217C2#1311608911yescharacteristic
218C2#1311613911yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3245C2
socleC22×C13#394
hypercenter#3245D13
hypocenterC13#10512
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13114989C2semidirect
2. #13113531C2semidirect
3. #13113344C2semidirect
4. #13112706C2semidirect
175. C13#10512semidirect

Maximal subgroups

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

subgroupindex
#131149892
#131135312
#131133442
#131127062
C13×#32452
#1051213