Finite Group Databasebeta

← #15767200

Subgroups — #15767200

Order 3328.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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#13115559C211yesmaximal, characteristic
3#13113491C212yesmaximal
4#13113336C212yesmaximal
5C13×#1275C211yesmaximal, characteristic
6#11719175C2212yes—
7C13×#431C2212yes—
8C2×C13×#97C2211yescharacteristic
9#11718767—21no—
10#11718767—21no—
11C2×#88054—21no—
12C4×C4⋊Dic13C2211yescharacteristic
13C2×C4⋊#1055C2211yescharacteristic
14#11718363—22no—
15#11718363—22no—
16#11718142—21no—
17#11718074—22no—
18#11718073—22no—
19#11718059—22no—
20#11718059—22no—
21C22×C8×C13D411yescharacteristic
22C22×C8×C13D411yescharacteristic
23C2×C42×C13C2311yescharacteristic
24#88180—22no—
25C2×C4⋊Dic13—21no—
26#88178—22no—
27#88178—22no—
28C2×C4×Dic13—21no—
29C22×#1055—21no—
30#88124—22no—
31#88123D412yes—
32#88123D412yes—
33C4×Dic26—22no—
34C4×Dic26—22no—
35C13×C4⋊C8—22no—
36C13×C22⋊C8—22no—
37C13×#97—22no—
38C4×C8×C13—22no—
39#88071D411yescharacteristic
40#88071D411yescharacteristic
41#88058—21no—
42#88058—21no—
43#88058—21no—
44#88058—21no—
45#88057—22no—
46#88057—22no—
47#88054—42no—
48C4⋊#1055—22no—
49#10548—131nomaximal, Sylow
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C22×Dic13—21no—
54C22×Dic13—21no—
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—42no—
62C2×C8×C13SD1612yes—
63C2×C8×C13Q1612yes—
64C42×C13C2×D412yes—
65C42×C13#4112yes—
66C22⋊Dic13—42no—
67C4⋊Dic13—22no—
68C4⋊Dic13—22no—
69C4⋊Dic13—22no—
70C4⋊Dic13—22no—
71C4⋊Dic13—42no—
72#6101—42no—
73#6101—42no—
74C4×Dic13—42no—
75C4×Dic13—41no—
76C4×Dic13—41no—
77C2×#1055—41no—
78C2×#1055—41no—
79C2×#1055—41no—
80#3162—131no—
81#1940—131no—
82#1542—132no—
83#1503—132no—
84#1275D1311yescharacteristic
85C23×C13#12111yescharacteristic
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13#12011yescharacteristic
89C2×C4×C13#12112yes—
90C2×C4×C13#12312yes—
91C2×C4×C13#12411yescharacteristic
92C2×C4×C13C2×SD1611yescharacteristic
93C2×C4×C13C2×Q1611yescharacteristic
94C2×C4×C13#13711yescharacteristic
95C2×C4×C13#13711yescharacteristic
96C2×Dic13—22no—
97C2×Dic13—41no—
98C2×Dic13—41no—
99C2×Dic13—41no—
100C2×Dic13—41no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103C2×Dic13—41no—
104Dic26—82no—
105Dic26—82no—
106C8×C13—22no—
107C8×C13—22no—
108C8×C13—82no—
109#1055—81no—
110#533—132no—
111#501—262no—
112#501—262no—
113#431C2×D1312yes—
114#427—261no—
115#427—261no—
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#44811yescharacteristic
133C4×C13#45111yescharacteristic
134C4×C13#48711yescharacteristic
135C4×C13#49111yescharacteristic
136Dic13—42no—
137Dic13—81no—
138Dic13—82no—
139Dic13—82no—
140C22×C8—261no—
141C22×C8D5211yescharacteristic
142C22×C8D5211yescharacteristic
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—261no—
152C2×C42—261no—
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—262no—
162C4⋊C8—522no—
163C22⋊C8—22no—
164#97—22no—
165C4×C8—22no—
166#95—131no—
167#95—131no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#204311yescharacteristic
171C2×C13#205011yescharacteristic
172C2×C13#205311yescharacteristic
173C2×Q8—262no—
174C2×Q8—262no—
175C22×C4—261no—
176C22×C4—261no—
177C22×C4C2×D5211yescharacteristic
178C22×C4D4×D1311yescharacteristic
179C22×C4#613111yescharacteristic
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—42no—
185C2×C8—521no—
186C2×C8—521no—
187C2×C8—521no—
188C2×C8#609512yes—
189C2×C8Dic5212yes—
190C4⋊C4—262no—
191C4⋊C4—262no—
192C4⋊C4—262no—
193C4⋊C4—262no—
194C4⋊C4—522no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C22⋊C4—522no—
198C42—522no—
199C42—521no—
200C42—521no—
201C42#612712yes—
202C42D4×D1312yes—
203C13#1054811yescharacteristic, complemented, Sylow
204C23#8814911yescharacteristic
205Q8—1042no—
206Q8—1042no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—262no—
210C2×C4—521no—
211C2×C4—521no—
212C2×C4—521no—
213C2×C4—521no—
214C2×C4—521no—
215C2×C4—522no—
216C2×C4—522no—
217C2×C4#8812911yescharacteristic
218C2×C4#8813611yescharacteristic
219C2×C4#8813812yes—
220C2×C4#8814812yes—
221C2×C4C2×#609511yescharacteristic
222C2×C4C2×Dic5211yescharacteristic
223C2×C4#8816311yescharacteristic
224C2×C4#8816311yescharacteristic
225C8—22no—
226C8—22no—
227C8—82no—
228C8—1041no—
229C22—21no—
230C22—21no—
231C22#1171833311yescharacteristic
232C22#1171850211yescharacteristic
233C22#1171851011yescharacteristic
234C4—22no—
235C4—22no—
236C4—522no—
237C4—1041no—
238C4—1042no—
239C4—1042no—
240C4#1171834211yescharacteristic
241C4#1171836411yescharacteristic
242C4#1171839911yescharacteristic
243C4#1171840011yescharacteristic
244C2—21no—
245C2—21no—
246C2#1311608311yescharacteristic
247C2#1311612411yescharacteristic
248C2#1311614311yescharacteristic
subgroupG/H
centerC2×C4#88129
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1275C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#1275D13
hypocenterC13#10548
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

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
#131155592
#131134912
#131133362
C13×#12752
#1054813