Finite Group Databasebeta

← #15777061

Subgroups — #15777061

Order 3328.

234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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#13116983C211yesmaximal, characteristic
2#13114430C211yesmaximal, characteristic, complemented
3D8×#1055C211yesmaximal, characteristic
4#13112899C211yesmaximal, characteristic, complemented
5#13112893C211yesmaximal, characteristic, complemented
6#13112885C211yesmaximal, characteristic, complemented
7C13×#2208C211yesmaximal, characteristic
8C2×C13×SD32—21no—
9C13×#494C2211yescharacteristic
10C4×C13×D8C2211yescharacteristic
11#11718754—21no—
12#11718740—21no—
13D4×#1055—21no—
14#11718343C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#358—21no—
17#11718154—21no—
18D4⋊#1055—21no—
19#11718082—21no—
20C4⋊#6090C2211yescharacteristic
21#11718050C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C2×C13×D8D411yescharacteristic
26C13×C4⋊Q8—21no—
27C4×D4×C13—21no—
28C22×#1055—41no—
29#88123—21no—
30C13×SD32—42no—
31C2×C13×C16—21no—
32C13×#107D411yescharacteristic
33C13×#102—21no—
34C4×C8×C13C2311yescharacteristic
35C22⋊#1055—41no—
36#88058—21no—
37#88058—21no—
38C2×#6090—21no—
39#88050—42no—
40#88048—41no—
41#88048—41no—
42C4⋊#1055—21no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45#12420—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D4×C13—21no—
48C22×C4×C13—41no—
49C2×Dic26—41no—
50C13×Q16—41no—
51C13×Q16—41no—
52C13×Q16—81no—
53C13×D8—21no—
54C13×D8SD1612yes—
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13#4111yescharacteristic
57C13×C4⋊C4—21no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C13×C22⋊C4—41no—
61C42×C13C2×D411yescharacteristic
62C4⋊Dic13—41no—
63C4⋊Dic13—41no—
64C2×#1055—21no—
65C2×#1055—41no—
66C2×#1055—82no—
67C2×#1055D811yescharacteristic
68C2×#1055D811yescharacteristic
69C13×C16—41no—
70#6090—41no—
71#2226—131no—
72#2208D1311yescharacteristic
73#1707—131no—
74C8×D8—131no—
75#1367—131no—
76#1365—131no—
77#1362—131no—
78C23×C13—41no—
79Q8×C13—81no—
80Q8×C13—81no—
81D4×C13—22no—
82D4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13—81no—
87C2×C4×C13#12111yescharacteristic
88C2×C4×C13C2×D811yescharacteristic
89C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
90C2×Dic13—81no—
91Dic26—82no—
92C8×C13—21no—
93C8×C13C2×SD1611yescharacteristic
94C8×C13#13511yescharacteristic
95#1055—21no—
96#1055—41no—
97#1055—81no—
98#1055SD3212yescomplemented
99C2×SD32—21no—
100#500—131no—
101#498—261no—
102#494C2×D1311yescharacteristic
103#487—261no—
104C4×D8C2×D1311yescharacteristic
105C8×D4—261no—
106#367—261no—
107C4⋊C16—131no—
108C4⋊C16C2×D1311yescharacteristic
109#358—21no—
110#357—261no—
111#335—131no—
112D4⋊C8—261no—
113C82—131no—
114C22×C13—42no—
115C22×C13—81no—
116C22×C13—81no—
117C22×C13#45911yescharacteristic
118C4×C13—21no—
119C4×C13—81no—
120C4×C13—161no—
121C4×C13#46511yescharacteristic
122C4×C13#47111yescharacteristic
123C4×C13C2×SD3211yescharacteristic
124C4×C13#51011yescharacteristic
125Dic13—161no—
126C2×Q16—21no—
127C2×Q16—21no—
128C2×D8C22⋊D1311yescharacteristic
129C22×C8—521no—
130C4⋊Q8—21no—
131C4⋊Q8—261no—
132C4×D4—21no—
133SD32—42no—
134C2×C16—21no—
135C2×C16—261no—
136#107—261no—
137#107—261no—
138#107C22⋊D1311yescharacteristic
139#106—521no—
140#106—521no—
141C4⋊C8—261no—
142#103—522no—
143#102—21no—
144C22⋊C8—521no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8C22×D1311yescharacteristic
148C2×C13—82no—
149C2×C13#166511yescharacteristic
150C2×C13#220811yescharacteristic
151C2×C13#221211yescharacteristic
152C2×Q8—41no—
153C2×Q8—521no—
154C2×D4—21no—
155C22×C4—41no—
156Q16—41no—
157Q16—41no—
158Q16—81no—
159D8—21no—
160D8#610512yes—
161C2×C8—131no—
162C2×C8—131no—
163C2×C8—261no—
164C2×C8—521no—
165C2×C8—1042no—
166C2×C8#612911yescharacteristic
167C2×C8C2×C22⋊D1311yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C22⋊C4—41no—
174C42D4×D1311yescharacteristic
175C16—41no—
176C16—521no—
177C13#1242011yescharacteristic, complemented, Sylow
178C23—41no—
179Q8—81no—
180Q8—81no—
181Q8—1042no—
182D4—22no—
183D4—41no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—1041no—
189C2×C4D8×D1311yescharacteristic
190C2×C4#8816511yescharacteristic
191C2×C4#8819311yescharacteristic
192C8—21no—
193C8—132no—
194C8—261no—
195C8—521no—
196C8—1041no—
197C8C2×#610511yescharacteristic
198C8#8820411yescharacteristic
199C22—42no—
200C22—81no—
201C22—81no—
202C22#1171881111yescharacteristic
203C4—21no—
204C4—81no—
205C4—161no—
206C4—2081no—
207C4D13×SD3211yescharacteristic
208C4#1171857611yescharacteristic
209C4#1171870211yescharacteristic
210C4#1171886111yescharacteristic
211C2—82no—
212C2#1311417511yescharacteristic
213C2#1311687911yescharacteristic
214C2#1311690711yescharacteristic
subgroupG/H
centerC22#11718811
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2208C2
socleC22×C13#459
prime radicalC2×C13×D8D4
hypercenter#2208D13
hypocenterC13#12420
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #13114430C2semidirect
4. #13112899C2semidirect
5. #13112893C2semidirect
6. #13112885C2semidirect
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
#131169832
#131144302
D8×#10552
#131128992
#131128932
#131128852
C13×#22082
#1242013