Finite Group Databasebeta

← #15782028

Subgroups — #15782028

Order 3328.

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

normal subgroups only

This group has 402 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
1C2×#11718341C211yesmaximal, characteristic, complemented
2C2×#11718110C212yesmaximal
3#13115724C211yesmaximal, characteristic
4#13112935C212yesmaximal, complemented
5C13×#1376C211yesmaximal, characteristic, complemented
6C2×#88158C2211yescharacteristic
7C2×#88123—21no—
8C2×C13×M32C2212yes—
9C2×C4×C8×C13C2211yescharacteristic
10#11718771—21no—
11C2×#88059C2211yescharacteristic
12C2×#88057—21no—
13C2×#88057C2212yes—
14C2×#88045—21no—
15#11718341—24no—
16#11718110—24no—
17C2×#6127—21no—
18C22×Dic26—41no—
19C22×C8×C13D411yescharacteristic
20C22×C8×C13C2311yescharacteristic
21C2×C42×C13D411yescharacteristic
22C2×C4⋊Dic13—22no—
23C2×C4⋊Dic13—41no—
24C2×#6099—21no—
25C2×Dic52Q811yescharacteristic, complemented
26#88158—22no—
27#88158—22no—
28C2×D104Q811yescharacteristic, complemented
29C2×#6095—21no—
30#88123—24no—
31#88123—42no—
32C13×M32—22no—
33C13×M32—22no—
34C2×C13×C16—22no—
35C4×C8×C13—22no—
36#88060—42no—
37#88059—22no—
38#88057—24no—
39#88057—22no—
40#88057D414yes—
41#88045—42no—
42#13371—131nomaximal, Sylow
43C22×C4×C13—21no—
44C22×C4×C13C2×D411yescharacteristic
45C2×C22⋊D13—41no—
46C22×Dic13—42no—
47#6127—41no—
48#6127—41no—
49#6127—41no—
50#6127—41no—
51C2×D52—21no—
52C2×C4×D13—41no—
53C2×Dic26—21no—
54C2×Dic26—44no—
55C2×Dic26—84no—
56C2×C8×C13—21no—
57C2×C8×C13—21no—
58C2×C8×C13SD1612yes—
59C2×C8×C13C2×D412yes—
60C2×C8×C13C2×Q811yescharacteristic
61C2×C8×C13#4112yes—
62C2×C8×C13#4111yescharacteristic
63C42×C13—21no—
64C42×C13D812yes—
65C4⋊Dic13—24no—
66C4⋊Dic13—44no—
67C4⋊Dic13—42no—
68#6099—41no—
69#6099—41no—
70C2×#1055—41no—
71Dic52—22no—
72D104—22no—
73#6095—42no—
74C13×C16—42no—
75C2×#498—131no—
76C2×#360—132no—
77#1974—131no—
78#1383—132no—
79#1376D1311yescharacteristic, complemented
80C23×C13AGL(1,ℤ/8)11yescharacteristic
81C22×D13—41no—
82C2×C4×C13—24no—
83C2×C4×C13—22no—
84C2×C4×C13#12011yescharacteristic
85C2×C4×C13C22⋊Q811yescharacteristic
86C2×C4×C13#12411yescharacteristic
87C2×C4×C13C2×D811yescharacteristic
88C2×C4×C13C2×SD1611yescharacteristic
89C2×C4×C13#13711yescharacteristic
90C22⋊D13—81no—
91C22⋊D13—81no—
92C2×Dic13—44no—
93C2×Dic13—41no—
94C2×Dic13—84no—
95D52—41no—
96D52—41no—
97C4×D13—81no—
98C4×D13—81no—
99Dic26—41no—
100Dic26—41no—
101Dic26—88no—
102C8×C13—22no—
103C8×C13C22⋊Q812yes—
104C8×C13#12412yes—
105#1055—81no—
106C2×#135—131no—
107C2×C4⋊Q8—261no—
108C2×M32C2×D1312yes—
109#498—264no—
110C2×#108—131no—
111C2×#106—132no—
112C2×#106—261no—
113C2×#104—261no—
114#408—261no—
115C2×C4×C8C2×D1311yescharacteristic
116#360—264no—
117C22×C13—22no—
118C22×C13#44711yescharacteristic
119C22×C13#47611yescharacteristic
120C22×C13#48911yescharacteristic
121C2×D13—82no—
122C2×D13—81no—
123C4×C13—24no—
124C4×C13#39311yescharacteristic
125C4×C13#44811yescharacteristic
126C4×C13#47411yescharacteristic
127C4×C13#48611yescharacteristic
128Dic13—84no—
129Dic13—81no—
130C2×#41—261no—
131C22×Q8—521no—
132#135—262no—
133#135—262no—
134C2×Q16—131no—
135C2×SD16—261no—
136C2×D8—131no—
137C2×M16—261no—
138C22×C8D5211yescharacteristic
139C22×C8C22×D1311yescharacteristic
140C4⋊Q8—264no—
141C4⋊Q8—522no—
142C2×C4⋊C4—262no—
143C2×C4⋊C4—521no—
144C2×C42D5211yescharacteristic
145M32—22no—
146M32—22no—
147C2×C16—22no—
148#108—262no—
149#106—134no—
150#106—264no—
151#106—262no—
152#104—522no—
153C22⋊C8—522no—
154C4×C8—22no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#202311yescharacteristic
158C2×C13#223012yes—
159D13—161no—
160#41—521no—
161#41—521no—
162#41—521no—
163#41—521no—
164C2×Q8—261no—
165C2×Q8—524no—
166C2×Q8—1044no—
167C2×D4—261no—
168C2×D4—521no—
169C22×C4—21no—
170C22×C4—522no—
171C22×C4—521no—
172C22×C4C2×D5211yescharacteristic
173Q16—262no—
174SD16—522no—
175D8—262no—
176M16—521no—
177M16—521no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—521no—
181C2×C8#609512yes—
182C2×C8#612712yes—
183C2×C8D4×D1312yes—
184C2×C8#612911yescharacteristic
185C2×C8Q8×D1311yescharacteristic
186C4⋊C4—264no—
187C4⋊C4—524no—
188C4⋊C4—522no—
189C42—21no—
190C42D10412yes—
191C16—42no—
192C13#1337111yescharacteristic, complemented, Sylow
193C23—521no—
194C23#8816211yescharacteristic
195Q8—521no—
196Q8—521no—
197Q8—1048no—
198D4—521no—
199D4—521no—
200D4—1041no—
201D4—1041no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—521no—
205C2×C4—524no—
206C2×C4—1044no—
207C2×C4—1041no—
208C2×C4—1041no—
209C2×C4#8812911yescharacteristic
210C2×C4#8813611yescharacteristic
211C2×C4#8815111yescharacteristic
212C2×C4C2×#609511yescharacteristic
213C2×C4C2×D10411yescharacteristic
214C2×C4#8816311yescharacteristic
215C8—22no—
216C8—1041no—
217C8#8813912yes—
218C8#8815012yes—
219C22—22no—
220C22—1041no—
221C22—1042no—
222C22#1171837511yescharacteristic
223C22#1171839311yescharacteristic
224C22#1171850311yescharacteristic
225C4—24no—
226C4—1044no—
227C4—1041no—
228C4#1171833411yescharacteristic
229C4#1171835511yescharacteristic
230C4#1171839911yescharacteristic
231C4#1171850711yescharacteristic
232C2—21no—
233C2—21no—
234C2—2081no—
235C2#1311597311yescharacteristic
236C2#1311700812yes—
subgroupG/H
centerC22#11718503
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#1376C2
socleC22×C13#476
prime radicalC2×#88158C22
hypercenter#1376D13
hypocenterC13#13371
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1376

Complements

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

NH ≅ G/Ntype
1. C2×#11718341C2semidirect
4. #13112935C2semidirect
5. C13×#1376C2semidirect
25. C2×Dic52Q8semidirect
28. C2×D104Q8semidirect
79. #1376D13semidirect
192. C13#13371semidirect

Maximal subgroups

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

subgroupindex
C2×#117183412
C2×#117181102
#131157242
#131129352
C13×#13762
#1337113