Finite Group Databasebeta

← #15777066

Subgroups — #15777066

Order 3328.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#13116980C211yesmaximal, characteristic
2#13116882C211yesmaximal, characteristic
3#13114434C211yesmaximal, characteristic, complemented
4#13113630C211yesmaximal, characteristic
5#13112899C211yesmaximal, characteristic, complemented
6#13112884C211yesmaximal, characteristic, complemented
7C13×#1365C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9#11718742—21no—
10#11718740—21no—
11C2×#88040—21no—
12#11718495—21no—
13#11718360C2211yescharacteristic
14C4×D104C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718095—21no—
18#11718083—21no—
19#11718082—21no—
20#11718075—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C13×C4⋊Q8—21no—
24C2×Dic52—21no—
25C2×Dic52—21no—
26C2×D104D411yescharacteristic
27C2×C8×D13—41no—
28C4×D52—21no—
29#88123—21no—
30C2×C13×C16—21no—
31C13×#107—21no—
32C13×#107—21no—
33C13×C4⋊C8—21no—
34C4×C8×C13C2311yescharacteristic
35#88075—42no—
36#88061—21no—
37#88060—41no—
38#88058D411yescharacteristic
39C2×#6090—21no—
40#88048—41no—
41#88048—41no—
42C4×#1055D411yescharacteristic
43C4×#1055D411yescharacteristic
44#88040—42no—
45#12420—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D52—21no—
48C2×C4×D13—41no—
49C2×Dic26—41no—
50C2×C8×C13—41no—
51C2×C8×C13C2×D411yescharacteristic
52C2×C8×C13#4111yescharacteristic
53C13×C4⋊C4—41no—
54C13×C4⋊C4—41no—
55C42×C13C2×D411yescharacteristic
56#6103—41no—
57C4⋊Dic13—21no—
58C4⋊Dic13—41no—
59C4⋊Dic13—41no—
60C2×#1055—21no—
61C2×#1055D811yescharacteristic
62C2×#1055D811yescharacteristic
63Dic52—41no—
64Dic52—41no—
65Dic52—81no—
66D104—21no—
67D104SD1612yes—
68C8×D13—82no—
69C13×C16—41no—
70#6090—41no—
71#2226—131no—
72#2208—131no—
73#1707—131no—
74C8×D8—131no—
75#1367—131no—
76#1365D1311yescharacteristic, complemented
77#1362—131no—
78C22×D13—41no—
79Q8×C13—82no—
80C2×C4×C13—81no—
81C2×C4×C13#12111yescharacteristic
82C2×C4×C13C2×D811yescharacteristic
83C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
84C2×Dic13—41no—
85C2×Dic13—81no—
86D52—22no—
87D52—41no—
88C4×D13—81no—
89C4×D13—81no—
90Dic26—81no—
91Dic26—81no—
92C8×C13—21no—
93C8×C13—81no—
94C8×C13C2×SD1611yescharacteristic
95C8×C13#13511yescharacteristic
96#1055—21no—
97#1055—41no—
98#1055SD3212yescomplemented
99C2×SD32—261no—
100#500C2×D1311yescharacteristic
101#498—261no—
102#494—131no—
103#487—261no—
104C4×D8—131no—
105C8×D4—261no—
106#367—261no—
107C4⋊C16—131no—
108C4⋊C16C2×D1311yescharacteristic
109#358—261no—
110#357—261no—
111#335C2×D1311yescharacteristic
112D4⋊C8—261no—
113C82—131no—
114C22×C13#45911yescharacteristic
115C2×D13—42no—
116C2×D13—81no—
117C2×D13—81no—
118C4×C13—21no—
119C4×C13—161no—
120C4×C13#46511yescharacteristic
121C4×C13#47111yescharacteristic
122C4×C13C2×SD3211yescharacteristic
123C4×C13#51011yescharacteristic
124Dic13—81no—
125Dic13—161no—
126C2×Q16—261no—
127C2×Q16—261no—
128C2×D8—131no—
129C22×C8—521no—
130C4⋊Q8—21no—
131C4⋊Q8—261no—
132C4×D4—261no—
133SD32—522no—
134C2×C16—21no—
135C2×C16—261no—
136#107—21no—
137#107—21no—
138#107—131no—
139#106—521no—
140#106—521no—
141C4⋊C8—21no—
142#103—522no—
143#102—261no—
144C22⋊C8—521no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8C22×D1311yescharacteristic
148C2×C13#166511yescharacteristic
149C2×C13#220811yescharacteristic
150C2×C13#221211yescharacteristic
151D13—82no—
152C2×Q8—41no—
153C2×Q8—521no—
154C2×D4—261no—
155C22×C4—521no—
156Q16—521no—
157Q16—521no—
158Q16—1041no—
159D8—132no—
160D8—261no—
161C2×C8—41no—
162C2×C8—131no—
163C2×C8—131no—
164C2×C8—261no—
165C2×C8—1042no—
166C2×C8#612711yescharacteristic
167C2×C8D4×D1311yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—261no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C22⋊C4—521no—
174C42D4×D1311yescharacteristic
175C16—41no—
176C16—521no—
177C13#1242011yescharacteristic, complemented, Sylow
178C23—521no—
179Q8—82no—
180Q8—1041no—
181Q8—1041no—
182D4—262no—
183D4—521no—
184C2×C4—81no—
185C2×C4—521no—
186C2×C4—1041no—
187C2×C4—1041no—
188C2×C4—1041no—
189C2×C4#8813811yescharacteristic
190C2×C4D8×D1311yescharacteristic
191C2×C4#8816811yescharacteristic
192C8—21no—
193C8—81no—
194C8—132no—
195C8—261no—
196C8—521no—
197C8SD16×D1311yescharacteristic
198C8#8817311yescharacteristic
199C22—522no—
200C22—1041no—
201C22—1041no—
202C22#1171844711yescharacteristic
203C4—21no—
204C4—161no—
205C4—1041no—
206C4—2081no—
207C4#1171841511yescharacteristic
208C4#1171846811yescharacteristic
209C4D13×SD3211yescharacteristic
210C4#1171857911yescharacteristic
211C2—1042no—
212C2#1311418011yescharacteristic
213C2#1311688011yescharacteristic
214C2#1311690411yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1365C2
socleC22×C13#459
prime radicalC2×D104D4
hypercenter#1365D13
hypocenterC13#12420
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
3. #13114434C2semidirect
5. #13112899C2semidirect
6. #13112884C2semidirect
7. C13×#1365C2semidirect
76. #1365D13semidirect
98. #1055SD32semidirect
177. C13#12420semidirect

Maximal subgroups

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

subgroupindex
#131169802
#131168822
#131144342
#131136302
#131128992
#131128842
C13×#13652
#1242013