Finite Group Databasebeta

← #15765544

Subgroups — #15765544

Order 3328.

510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#11718343C211yesmaximal, characteristic
2C2×#11718682C212yesmaximal
3C2×#11718073C212yesmaximal
4#13112671C211yesmaximal, characteristic
5C13×#1984C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88123C2212yes—
8C2×C13×C4⋊C8C2211yescharacteristic
9C2×C4×C8×C13C2211yescharacteristic
10C2×#88075—22no—
11C2×#88058—22no—
12#11718682—24no—
13#11718682—24no—
14C2×#88047—22no—
15C2×C4⋊#1055C2212yes—
16#11718343—24no—
17C13×#336—22no—
18#11718073—24no—
19C22×Q8×C13D411yescharacteristic
20C22×Dic26—22no—
21C22×C8×C13—21no—
22C22×C8×C13D412yes—
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C42×C13—21no—
28C2×C42×C13C2311yescharacteristic
29C2×C4⋊Dic13—22no—
30C2×C4⋊Dic13—22no—
31C22×#1055—22no—
32#88123—22no—
33#88123—22no—
34#88123—22no—
35#88123D414yes—
36C13×C4⋊C8—22no—
37C4×C8×C13—22no—
38#88075—28no—
39#88058—28no—
40#88047—28no—
41C4⋊#1055—22no—
42C4⋊#1055D414yes—
43#10279—131nomaximal, Sylow
44C2×Q8×C13—21no—
45C2×Q8×C13—22no—
46C2×Q8×C13—22no—
47C2×Q8×C13Q1612yes—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C22×Dic13—42no—
54C2×Dic26—24no—
55C2×Dic26—42no—
56C2×Dic26—84no—
57C2×C8×C13—22no—
58C2×C8×C13—22no—
59C2×C8×C13—41no—
60C2×C8×C13—42no—
61C2×C8×C13Q1614yes—
62C13×C4⋊C4—22no—
63C13×C4⋊C4—42no—
64C42×C13—41no—
65C42×C13—41no—
66C42×C13C2×D412yes—
67C42×C13C2×D412yes—
68C4⋊Dic13—24no—
69C4⋊Dic13—24no—
70C4⋊Dic13—42no—
71C4⋊Dic13—42no—
72C2×#1055—24no—
73C2×#1055—42no—
74C2×#1055—42no—
75C2×#500—131no—
76C2×#477—132no—
77#1984D1311yescharacteristic
78C2×#333—132no—
79#1277—131no—
80C23×C13#12111yescharacteristic
81Q8×C13—24no—
82Q8×C13—42no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—42no—
89C2×C4×C13#12011yescharacteristic
90C2×C4×C13#12012yes—
91C2×C4×C13#12112yes—
92C2×C4×C13#12711yescharacteristic
93C2×C4×C13C2×Q1611yescharacteristic
94C2×C4×C13C2×Q1612yes—
95C2×C4×C13#13511yescharacteristic
96C2×C4×C13#13712yes—
97C2×C4×C13#13712yes—
98C2×Dic13—44no—
99C2×Dic13—84no—
100Dic26—84no—
101Dic26—84no—
102C8×C13—24no—
103C8×C13—81no—
104#1055—44no—
105C2×C4⋊Q8—132no—
106C2×C4×Q8C2×D1311yescharacteristic
107#500—264no—
108#477—264no—
109#477—264no—
110C2×#107—262no—
111C2×#107—262no—
112C2×C4⋊C8—132no—
113C2×C4⋊C8C2×D1311yescharacteristic
114C2×#103—262no—
115C2×C4×C8C2×D1311yescharacteristic
116#336—22no—
117#333—264no—
118C22×C13#39211yescharacteristic
119C22×C13#46212yes—
120C22×C13#46711yescharacteristic
121C22×C13#47011yescharacteristic
122C22×C13#47212yes—
123C4×C13—22no—
124C4×C13—42no—
125C4×C13—81no—
126C4×C13#45112yes—
127C4×C13#45112yes—
128C4×C13#45212yes—
129C4×C13#49411yescharacteristic
130C4×C13#49711yescharacteristic
131Dic13—84no—
132C22×Q8—262no—
133C22×Q8D5211yescharacteristic
134C22×C8—21no—
135C22×C8—262no—
136C22×C8C22⋊D1312yes—
137C4⋊Q8—134no—
138C4⋊Q8—262no—
139C4⋊Q8—262no—
140C4⋊Q8—262no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4—262no—
146C2×C4⋊C4D5211yescharacteristic
147C2×C42—21no—
148C2×C42C22×D1311yescharacteristic
149#107—268no—
150#107—268no—
151C4⋊C8—22no—
152C4⋊C8—134no—
153C4⋊C8—262no—
154#103—268no—
155C4×C8—22no—
156C2×C13#167612yes—
157C2×C13#169612yes—
158C2×C13#200111yescharacteristic
159C2×C13#201611yescharacteristic
160C2×C13#201811yescharacteristic
161C2×Q8—21no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8—264no—
165C2×Q8—522no—
166C2×Q8—1044no—
167C2×Q8Dic5212yes—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—522no—
171C22×C4C2×D5211yescharacteristic
172C22×C4#612711yescharacteristic
173C22×C4C2×C22⋊D1311yescharacteristic
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—264no—
179C2×C8—522no—
180C2×C8—522no—
181C2×C8#610714yes—
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—264no—
185C4⋊C4—264no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C42—41no—
189C42—41no—
190C42D4×D1312yes—
191C42D4×D1312yes—
192C13#1027911yescharacteristic, complemented, Sylow
193C23#8818411yescharacteristic
194Q8—24no—
195Q8—42no—
196Q8—1044no—
197Q8—1044no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—524no—
205C2×C4—1044no—
206C2×C4#8813612yes—
207C2×C4#8813812yes—
208C2×C4#8815811yescharacteristic
209C2×C4C2×Dic5211yescharacteristic
210C2×C4#8816312yes—
211C2×C4#8819111yescharacteristic
212C2×C4#8819411yescharacteristic
213C2×C4C2×#610712yes—
214C2×C4#8820512yes—
215C8—24no—
216C8—81no—
217C8—524no—
218C22#1171862111yescharacteristic
219C22#1171869212yes—
220C22#1171877711yescharacteristic
221C22#1171879811yescharacteristic
222C22#1171880312yes—
223C4—22no—
224C4—42no—
225C4—81no—
226C4—1044no—
227C4#1171839412yes—
228C4#1171840012yes—
229C4#1171871112yes—
230C4#1171872111yescharacteristic
231C4#1171875311yescharacteristic
232C2#1311424012yes—
233C2#1311436412yes—
234C2#1311584611yescharacteristic
235C2#1311593511yescharacteristic
236C2#1311594511yescharacteristic
subgroupG/H
centerC23#88184
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1984C2
socle, prime radicalC23×C13#121
hypercenter#1984D13
hypocenterC13#10279
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
192. C13#10279semidirect

Maximal subgroups

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

subgroupindex
C2×#117183432
C2×#117186822
C2×#117180732
#131126712
C13×#19842
#1027913