Finite Group Databasebeta

← #15767199

Subgroups — #15767199

Order 3328.

364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125360C211yesmaximal, characteristic
2#13113494C212yesmaximal
3#13113334C212yesmaximal
4#13112667C211yesmaximal, characteristic
5C13×#1940C211yesmaximal, characteristic
6#11719175C2212yes—
7C2×C13×C4⋊C8—21no—
8C2×C13×C4⋊C8C2211yescharacteristic
9C2×C13×#97C2211yescharacteristic
10C4×C13×C4⋊C4C2211yescharacteristic
11#11718767—21no—
12#11718767—21no—
13#11718586C2212yes—
14#11718363—22no—
15#11718363—22no—
16C13×#336—21no—
17#11718078—22no—
18#11718073—22no—
19#11718044—22no—
20#11718044—22no—
21C22×C8×C13—21no—
22C22×C8×C13D411yescharacteristic
23C22×C8×C13D411yescharacteristic
24C2×C13×C4⋊C4—21no—
25C2×C42×C13—21no—
26C2×C42×C13C2311yescharacteristic
27#88180—22no—
28#88178—22no—
29#88178—22no—
30#88124—22no—
31#88123D412yes—
32#88123D412yes—
33C4×Dic26—22no—
34C4×Dic26—22no—
35C13×C4⋊C8—22no—
36C13×C4⋊C8—42no—
37C13×#97—22no—
38C13×#95D411yescharacteristic
39C13×#95D411yescharacteristic
40C22⋊#1055—22no—
41#88058—21no—
42#88058—21no—
43#88058—21no—
44#88058—21no—
45#88057—22no—
46#88057—22no—
47C4⋊#1055—22no—
48C4×#1055—22no—
49#10548—131nomaximal, Sylow
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13C2×D411yescharacteristic
53C22×C4×C13C2×D411yescharacteristic
54C22×C4×C13#4111yescharacteristic
55C2×Dic26—22no—
56C2×Dic26—22no—
57C2×C8×C13—21no—
58C2×C8×C13—21no—
59C2×C8×C13—21no—
60C2×C8×C13—21no—
61C2×C8×C13—41no—
62C2×C8×C13—41no—
63C2×C8×C13—41no—
64C2×C8×C13SD1612yes—
65C2×C8×C13Q1612yes—
66C13×C4⋊C4—42no—
67C42×C13—41no—
68C42×C13—41no—
69C42×C13C2×D412yes—
70C42×C13#4112yes—
71C22⋊Dic13—42no—
72C4⋊Dic13—22no—
73C4⋊Dic13—22no—
74C4⋊Dic13—22no—
75C4⋊Dic13—22no—
76#6101—42no—
77#6101—42no—
78C4×Dic13—42no—
79C2×#1055—42no—
80#3162—131no—
81#1940D1311yescharacteristic
82#1542—132no—
83#1503—132no—
84#1275—131no—
85C23×C13#12111yescharacteristic
86C2×C4×C13—22no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13#12011yescharacteristic
95C2×C4×C13#12112yes—
96C2×C4×C13#12312yes—
97C2×C4×C13#12411yescharacteristic
98C2×C4×C13C2×SD1611yescharacteristic
99C2×C4×C13C2×Q1611yescharacteristic
100C2×C4×C13#13711yescharacteristic
101C2×C4×C13#13711yescharacteristic
102C2×Dic13—42no—
103C2×Dic13—42no—
104Dic26—82no—
105Dic26—82no—
106C8×C13—22no—
107C8×C13—22no—
108C8×C13—81no—
109#1055—82no—
110#533—132no—
111#501—262no—
112#501—262no—
113#431—132no—
114#427—261no—
115#427—261no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8C2×D1311yescharacteristic
118C2×#97C2×D1311yescharacteristic
119C4×C4⋊C4C2×D1311yescharacteristic
120#336—21no—
121#333—262no—
122#332—262no—
123#328—262no—
124#328—262no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#39411yescharacteristic
128C22×C13#46111yescharacteristic
129C22×C13#46211yescharacteristic
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—42no—
133C4×C13—81no—
134C4×C13#44811yescharacteristic
135C4×C13#45111yescharacteristic
136C4×C13#48711yescharacteristic
137C4×C13#49111yescharacteristic
138Dic13—82no—
139Dic13—82no—
140C22×C8—21no—
141C22×C8C22⋊D1311yescharacteristic
142C22×C8C22⋊D1311yescharacteristic
143C4⋊Q8—132no—
144C4⋊Q8—132no—
145#125—262no—
146C22⋊Q8—262no—
147C22⋊Q8—262no—
148C4×Q8—262no—
149C4×Q8—262no—
150#117—262no—
151C2×C4⋊C4—21no—
152C2×C42—21no—
153C2×C42C22×D1311yescharacteristic
154#107—261no—
155#107—261no—
156#107—261no—
157#107—261no—
158#106—262no—
159#106—262no—
160C4⋊C8—22no—
161C4⋊C8—42no—
162C4⋊C8—262no—
163C22⋊C8—262no—
164#97—22no—
165C4×C8—262no—
166#95D5211yescharacteristic
167#95D5211yescharacteristic
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#204311yescharacteristic
171C2×C13#205011yescharacteristic
172C2×C13#205311yescharacteristic
173C2×Q8—262no—
174C2×Q8—262no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D5211yescharacteristic
178C22×C4#612711yescharacteristic
179C22×C4C2×C22⋊D1311yescharacteristic
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—522no—
188C2×C8#610512yes—
189C2×C8#610712yes—
190C4⋊C4—42no—
191C4⋊C4—262no—
192C4⋊C4—262no—
193C4⋊C4—262no—
194C4⋊C4—262no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C22⋊C4—522no—
198C42—41no—
199C42—41no—
200C42—522no—
201C42D4×D1312yes—
202C42#613112yes—
203C13#1054811yescharacteristic, complemented, Sylow
204C23#8818411yescharacteristic
205Q8—1042no—
206Q8—1042no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—522no—
216C2×C4—522no—
217C2×C4#8814812yes—
218C2×C4#8814912yes—
219C2×C4C2×#610511yescharacteristic
220C2×C4#8819111yescharacteristic
221C2×C4C2×#610711yescharacteristic
222C2×C4#8820111yescharacteristic
223C2×C4#8820511yescharacteristic
224C2×C4#8820511yescharacteristic
225C8—22no—
226C8—22no—
227C8—81no—
228C8—1042no—
229C22—21no—
230C22—21no—
231C22#1171865211yescharacteristic
232C22#1171868011yescharacteristic
233C22#1171869211yescharacteristic
234C4—22no—
235C4—22no—
236C4—42no—
237C4—81no—
238C4—1042no—
239C4—1042no—
240C4#1171870111yescharacteristic
241C4#1171871111yescharacteristic
242C4#1171873011yescharacteristic
243C4#1171875411yescharacteristic
244C2—21no—
245C2—21no—
246C2#1311608211yescharacteristic
247C2#1311612311yescharacteristic
248C2#1311614211yescharacteristic
subgroupG/H
centerC2×C4#88201
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1940C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#1940D13
hypocenterC13#10548
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1940

Complements

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

NH ≅ G/Ntype
203. C13#10548semidirect

Maximal subgroups

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

subgroupindex
#131253602
#131134942
#131133342
#131126672
C13×#19402
#1054813