Finite Group Databasebeta

← #15767196

Subgroups — #15767196

Order 3328.

364 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 101 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#13115559C211yesmaximal, characteristic
2#13113493C212yesmaximal
3#13113335C212yesmaximal
4#13112667C211yesmaximal, characteristic
5C13×#3162C211yesmaximal, characteristic
6C13×#533C2212yes—
7C13×#501—22no—
8C13×#501—22no—
9C13×#427—21no—
10C13×#427—21no—
11C2×C13×#97C2211yescharacteristic
12C2×#88054—21no—
13C4×C4⋊Dic13C2211yescharacteristic
14#11718586C2212yes—
15C2×C4⋊#1055C2211yescharacteristic
16#11718142—21no—
17#11718139—22no—
18#11718138—22no—
19#11718130—22no—
20#11718130—22no—
21C22×C8×C13D411yescharacteristic
22C22×C8×C13D411yescharacteristic
23C13×C4⋊Q8D412yes—
24C13×C4⋊Q8D412yes—
25C13×#125—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C13×#117—22no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4×Dic13—21no—
34C22×#1055—21no—
35C13×#107—21no—
36C13×#107—21no—
37C13×#107—21no—
38C13×#107—21no—
39C13×#106—22no—
40C13×#106—22no—
41C13×#97—22no—
42#88071D411yescharacteristic
43#88071D411yescharacteristic
44C22⋊#1055—22no—
45#88054—42no—
46C4⋊#1055—22no—
47C4⋊#1055—22no—
48C4×#1055—22no—
49#10548—131nomaximal, Sylow
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C22×C4×C13C2×D411yescharacteristic
53C22×C4×C13C2×D411yescharacteristic
54C22×C4×C13#4111yescharacteristic
55C22×Dic13—21no—
56C22×Dic13—21no—
57C2×C8×C13—21no—
58C2×C8×C13—21no—
59C2×C8×C13—21no—
60C2×C8×C13—21no—
61C2×C8×C13SD1612yes—
62C2×C8×C13Q1612yes—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C22⋊C4—42no—
70C42×C13—42no—
71C42×C13C2×D412yes—
72C42×C13#4112yes—
73C4⋊Dic13—42no—
74C4×Dic13—41no—
75C4×Dic13—41no—
76C2×#1055—41no—
77C2×#1055—42no—
78C2×#1055—41no—
79C2×#1055—41no—
80#3162D1311yescharacteristic
81#1940—131no—
82#1542—132no—
83#1503—132no—
84#1275—131no—
85C23×C13#12111yescharacteristic
86Q8×C13—82no—
87Q8×C13—82no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13#12011yescharacteristic
93C2×C4×C13#12112yes—
94C2×C4×C13#12312yes—
95C2×C4×C13#12411yescharacteristic
96C2×C4×C13C2×SD1611yescharacteristic
97C2×C4×C13C2×Q1611yescharacteristic
98C2×C4×C13#13711yescharacteristic
99C2×C4×C13#13711yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—41no—
102C2×Dic13—41no—
103C2×Dic13—41no—
104C2×Dic13—41no—
105C2×Dic13—41no—
106C8×C13—22no—
107C8×C13—22no—
108#1055—82no—
109#1055—81no—
110#533C2×D1312yes—
111#501—22no—
112#501—22no—
113#431—132no—
114#427—21no—
115#427—21no—
116C2×C4⋊C8—131no—
117C2×C4⋊C8—261no—
118C2×#97C2×D1311yescharacteristic
119C4×C4⋊C4—131no—
120#336—261no—
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—82no—
133C4×C13—82no—
134C4×C13#44811yescharacteristic
135C4×C13#45111yescharacteristic
136C4×C13#48711yescharacteristic
137C4×C13#49111yescharacteristic
138Dic13—42no—
139Dic13—81no—
140C22×C8—261no—
141C22×C8C22⋊D1311yescharacteristic
142C22×C8C22⋊D1311yescharacteristic
143C4⋊Q8C22⋊D1312yes—
144C4⋊Q8C22⋊D1312yes—
145#125—22no—
146C22⋊Q8—22no—
147C22⋊Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150#117—22no—
151C2×C4⋊C4—261no—
152C2×C42—261no—
153C2×C42C22×D1311yescharacteristic
154#107—21no—
155#107—21no—
156#107—21no—
157#107—21no—
158#106—22no—
159#106—22no—
160C4⋊C8—262no—
161C4⋊C8—262no—
162C4⋊C8—522no—
163C22⋊C8—262no—
164#97—22no—
165C4×C8—262no—
166#95—131no—
167#95—131no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#204311yescharacteristic
171C2×C13#205011yescharacteristic
172C2×C13#205311yescharacteristic
173C2×Q8—22no—
174C2×Q8—22no—
175C22×C4—261no—
176C22×C4—261no—
177C22×C4D4×D1311yescharacteristic
178C22×C4#612911yescharacteristic
179C22×C4C2×C22⋊D1311yescharacteristic
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—522no—
185C2×C8—521no—
186C2×C8—521no—
187C2×C8—521no—
188C2×C8#610612yes—
189C2×C8#610712yes—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—522no—
197C22⋊C4—42no—
198C42—42no—
199C42—521no—
200C42—521no—
201C42#612912yes—
202C42C2×C22⋊D1312yes—
203C13#1054811yescharacteristic, complemented, Sylow
204C23#8819211yescharacteristic
205Q8—82no—
206Q8—82no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—262no—
212C2×C4—521no—
213C2×C4—521no—
214C2×C4—521no—
215C2×C4—521no—
216C2×C4—521no—
217C2×C4#8818912yes—
218C2×C4#8819011yescharacteristic
219C2×C4#8819312yes—
220C2×C4C2×#610611yescharacteristic
221C2×C4#8819611yescharacteristic
222C2×C4#8819611yescharacteristic
223C2×C4C2×#610711yescharacteristic
224C2×C4#8820711yescharacteristic
225C8—22no—
226C8—22no—
227C8—1042no—
228C8—1041no—
229C22—21no—
230C22—21no—
231C22#1171874411yescharacteristic
232C22#1171875111yescharacteristic
233C22#1171888311yescharacteristic
234C4—22no—
235C4—22no—
236C4—82no—
237C4—82no—
238C4—522no—
239C4—1041no—
240C4#1171874211yescharacteristic
241C4#1171874311yescharacteristic
242C4#1171888811yescharacteristic
243C4#1171888911yescharacteristic
244C2—21no—
245C2—21no—
246C2#1311607911yescharacteristic
247C2#1311612011yescharacteristic
248C2#1311613911yescharacteristic
subgroupG/H
centerC2×C4#88190
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3162C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#3162D13
hypocenterC13#10548
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

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
#131155592
#131134932
#131133352
#131126672
C13×#31622
#1054813