Finite Group Databasebeta

← #15774841

Subgroups — #15774841

Order 3328.

240 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×D208C211yesmaximal, characteristic
2#13113720C211yesmaximal, characteristic, complemented
3#13113630C211yesmaximal, characteristic, complemented
4#13112796C211yesmaximal, characteristic, complemented
5#13112796C211yesmaximal, characteristic, complemented
6#13112755C211yesmaximal, characteristic, complemented
7C13×#1372C211yesmaximal, characteristic, complemented
8C2×D208C411yescharacteristic
9#11718499—21no—
10#11718495—21no—
11C4×D104C2211yescharacteristic
12C4×D104C2211yescharacteristic
13C4×C13×C16C2211yescharacteristic
14C13×#335C2211yescharacteristic
15C13×#335C2211yescharacteristic
16#11718101C411yescharacteristic
17#11718101C411yescharacteristic
18#11718096C411yescharacteristic
19#11718075—21no—
20#11718075—21no—
21C4×#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×D104C2×C411yescharacteristic
24C2×D104C2×C411yescharacteristic
25C2×#6094—41no—
26C2×C8×D13—41no—
27C4×D52—21no—
28C4×D52—21no—
29C2×C13×C16C2×C411yescharacteristic
30C2×C13×C16C2×C411yescharacteristic
31C13×C4⋊C8—21no—
32C13×C4⋊C8—21no—
33C4×C8×C13C2311yescharacteristic
34#88061—21no—
35#88061—21no—
36#88060—41no—
37#88060—41no—
38#88058C2×C411yescharacteristic
39#88058C2×C411yescharacteristic
40C2×#6090—21no—
41C4×#1055D411yescharacteristic
42C4×#1055D411yescharacteristic
43D208—22no—
44#12073—131nomaximal, Sylow
45C2×D52—21no—
46C2×D52—21no—
47C2×C4×D13—41no—
48C2×C4×D13—41no—
49C2×C8×C13—41no—
50C2×C8×C13—41no—
51C2×C8×C13C22×C411yescharacteristic
52C2×C8×C13#4111yescharacteristic
53C42×C13C2×D411yescharacteristic
54#6103—41no—
55#6103—41no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C2×#1055—21no—
59C2×#1055D811yescharacteristic
60C2×#1055D811yescharacteristic
61D104—21no—
62D104—21no—
63D104—21no—
64D104M1612yescomplemented
65#6094—82no—
66C8×D13—82no—
67C13×C16—21no—
68C13×C16—21no—
69#6090—41no—
70C4×D16—131no—
71#1589—131no—
72C8×D8—131no—
73#1372D1311yescharacteristic, complemented
74#1331—131no—
75#1331—131no—
76#1312—131no—
77C22×D13—41no—
78C22×D13—41no—
79C2×C4×C13C4×D411yescharacteristic
80C2×C4×C13C2×D811yescharacteristic
81C2×C4×C13#13511yescharacteristic
82C2×Dic13—41no—
83C2×Dic13—41no—
84D52—22no—
85D52—41no—
86D52—41no—
87D52—41no—
88C4×D13—81no—
89C4×D13—81no—
90C4×D13—81no—
91C4×D13—81no—
92C8×C13—21no—
93C8×C13—81no—
94C8×C13—81no—
95C8×C13C2×M1611yescharacteristic
96C8×C13#13111yescharacteristic
97#1055—22no—
98#1055—21no—
99#1055—21no—
100C2×D16—131no—
101C4×D8—131no—
102C4×D8—131no—
103#436—261no—
104C8×D4—261no—
105#366—131no—
106#357—131no—
107#357—131no—
108C4×C16—131no—
109C4×C16C2×D1311yescharacteristic
110#335C2×D1311yescharacteristic
111#335C2×D1311yescharacteristic
112D4⋊C8—261no—
113D4⋊C8—261no—
114C82—131no—
115C22×C13C4×D811yescharacteristic
116C2×D13—42no—
117C2×D13—81no—
118C2×D13—81no—
119C2×D13—81no—
120C2×D13—81no—
121C2×D13—81no—
122C4×C13—21no—
123C4×C13#43511yescharacteristic
124C4×C13#44411yescharacteristic
125C4×C13#50911yescharacteristic
126C4×C13#50911yescharacteristic
127Dic13—81no—
128Dic13—81no—
129C2×D8—131no—
130C2×D8—131no—
131C2×M16—521no—
132C22×C8—521no—
133C4×D4—261no—
134C4×D4—261no—
135D16—262no—
136C2×C16—261no—
137C2×C16C4×D1311yescharacteristic
138C2×C16C4×D1311yescharacteristic
139#107—131no—
140#107—131no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143#102—261no—
144#102—261no—
145C22⋊C8—521no—
146C22⋊C8—521no—
147C4×C8—131no—
148C4×C8—131no—
149C4×C8C22×D1311yescharacteristic
150C2×C13#158111yescharacteristic
151C2×C13#217711yescharacteristic
152C2×C13#217811yescharacteristic
153D13—82no—
154D13—161no—
155C2×D4—261no—
156C2×D4—261no—
157C22×C4—521no—
158C22×C4—521no—
159D8—132no—
160D8—261no—
161D8—261no—
162D8—261no—
163M16—1042no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—261no—
169C2×C8—1042no—
170C2×C8C2×C4×D1311yescharacteristic
171C2×C8#613111yescharacteristic
172C4⋊C4—261no—
173C4⋊C4—261no—
174C22⋊C4—521no—
175C22⋊C4—521no—
176C42D4×D1311yescharacteristic
177C16—21no—
178C16—21no—
179C16—521no—
180C13#1207311yescharacteristic, complemented, Sylow
181C23—521no—
182C23—521no—
183D4—262no—
184D4—521no—
185D4—521no—
186D4—521no—
187C2×C4—521no—
188C2×C4—521no—
189C2×C4—1041no—
190C2×C4—1041no—
191C2×C4—1041no—
192C2×C4—1041no—
193C2×C4#8814711yescharacteristic
194C2×C4D8×D1311yescharacteristic
195C2×C4#8817311yescharacteristic
196C8—21no—
197C8—81no—
198C8—81no—
199C8—262no—
200C8—261no—
201C8—261no—
202C8#8815511yescharacteristic
203C8M16×D1311yescharacteristic
204C22—522no—
205C22—1041no—
206C22—1041no—
207C22—1041no—
208C22—1041no—
209C22—1041no—
210C22#1171853311yescharacteristic
211C4—21no—
212C4—1041no—
213C4—1041no—
214C4#1171849711yescharacteristic
215C4#1171855511yescharacteristic
216C4#1171857511yescharacteristic
217C4#1171857511yescharacteristic
218C2—1042no—
219C2—2081no—
220C2#1311366411yescharacteristic
221C2#1311671111yescharacteristic
222C2#1311671611yescharacteristic
subgroupG/H
centerC2×C4D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1372C2
socleC22×C13C4×D8
prime radicalC2×D208C4
cosocleC4×C8×C13C23
hypercenter#1372D13
hypocenterC13#12073
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
2. #13113720C2semidirect
3. #13113630C2semidirect
4. #13112796C2semidirect
5. #13112796C2semidirect
6. #13112755C2semidirect
7. C13×#1372C2semidirect
64. D104M16semidirect
73. #1372D13semidirect
180. C13#12073semidirect

Maximal subgroups

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

subgroupindex
C4×D2082
#131137202
#131136302
#131127962
#131127552
C13×#13722
#1207313