Finite Group Databasebeta

← #15780560

Subgroups — #15780560

Order 3328.

246 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 95 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#13116601C211yesmaximal, characteristic
2#13116441C211yesmaximal, characteristic
3#13114721C211yesmaximal, characteristic
4#13112923C211yesmaximal, characteristic
5#13112919C211yesmaximal, characteristic
6#13112915C211yesmaximal, characteristic
7C13×#1378C211yesmaximal, characteristic
8C2×C13×M32C2211yescharacteristic
9C2×C13×M32C2211yescharacteristic
10C13×#405C2211yescharacteristic
11C2×#88062C411yescharacteristic
12#11718762C2211yescharacteristic
13C2×#88055C2211yescharacteristic
14C2×#88052C2211yescharacteristic
15C2×#88052C2211yescharacteristic
16#11718659C411yescharacteristic
17#11718147C411yescharacteristic
18#11718124C411yescharacteristic
19#11718103—22no—
20#11718058—22no—
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13C2311yescharacteristic
23C13×#117C2×C411yescharacteristic
24#88180C2×C411yescharacteristic
25C2×C4×Dic13C2×C411yescharacteristic
26C2×#6099C2×C411yescharacteristic
27C22×#1055C2×C411yescharacteristic
28C13×M32—21no—
29C13×M32—21no—
30C13×M32—21no—
31C13×M32—21no—
32C2×C13×C16—21no—
33C2×C13×C16—21no—
34C13×#97—21no—
35C4×C8×C13—21no—
36#88062—22no—
37#88055—21no—
38#88055—21no—
39#88055—21no—
40C8×Dic13—21no—
41#88052—21no—
42#88052—21no—
43#88052—21no—
44#88052D412yes—
45C2×#6090—21no—
46C2×#6090Q812yes—
47#88048—21no—
48#88047—21no—
49#13108—131nomaximal, Sylow
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—21no—
52C13×M16—21no—
53C13×M16—21no—
54C2×C8×C13—21no—
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13C2×Q811yescharacteristic
57C2×C8×C13#4111yescharacteristic
58C2×C8×C13#4111yescharacteristic
59C2×C8×C13#4111yescharacteristic
60C2×C8×C13#4111yescharacteristic
61C13×C4⋊C4—21no—
62C13×C22⋊C4—21no—
63C42×C13—21no—
64C22⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4×Dic13—21no—
67C4×Dic13—21no—
68C4×Dic13—21no—
69#6099—21no—
70#6099M1612yes—
71C2×#1055—21no—
72C2×#1055—21no—
73C2×#1055—21no—
74C2×#1055M1611yescharacteristic
75C2×#1055M1611yescharacteristic
76C13×C16—41no—
77C13×C16—41no—
78#6090—22no—
79#6090—22no—
80#2153—131no—
81#2110—131no—
82#1773—131no—
83#1378—131no—
84#1378D1311yescharacteristic
85#1377—131no—
86#1375—131no—
87C23×C13#13111yescharacteristic
88C2×C4×C13—41no—
89C2×C4×C13#11711yescharacteristic
90C2×C4×C13C4×D411yescharacteristic
91C2×C4×C13C4×Q811yescharacteristic
92C2×C4×C13C2×M1611yescharacteristic
93C2×C4×C13C2×M1611yescharacteristic
94C2×C4×C13#13111yescharacteristic
95C2×Dic13—41no—
96C2×Dic13—41no—
97C2×Dic13—81no—
98C8×C13—41no—
99C8×C13C22⋊Q811yescharacteristic
100C8×C13#12311yescharacteristic
101C8×C13#12511yescharacteristic
102C8×C13#12611yescharacteristic
103#1055—21no—
104#1055—21no—
105#1055—22no—
106C2×M32—131no—
107C2×M32—131no—
108C2×M32C2×D1311yescharacteristic
109C2×M32C2×D1311yescharacteristic
110C2×#108—131no—
111#427—131no—
112#405—131no—
113#405C2×D1311yescharacteristic
114C2×#97—131no—
115#364—262no—
116#347—262no—
117#339—131no—
118#339—131no—
119C22×C13—41no—
120C22×C13#43311yescharacteristic
121C22×C13#43611yescharacteristic
122C22×C13#44611yescharacteristic
123C4×C13—81no—
124C4×C13#38711yescharacteristic
125C4×C13#43211yescharacteristic
126C4×C13#43511yescharacteristic
127C4×C13#44611yescharacteristic
128Dic13—81no—
129Dic13—81no—
130C2×M16—131no—
131C2×M16C4×D1311yescharacteristic
132C22×C8—131no—
133C22×C8C22×D1311yescharacteristic
134#117—131no—
135#117C4×D1311yescharacteristic
136C2×C42—131no—
137M32—21no—
138M32—21no—
139M32—21no—
140M32—21no—
141M32—132no—
142M32—261no—
143M32—261no—
144M32—261no—
145C2×C16—21no—
146C2×C16—21no—
147C2×C16—132no—
148C2×C16—261no—
149#108—262no—
150#107—261no—
151#106—261no—
152#97—21no—
153#97—261no—
154#97—261no—
155#97—261no—
156C4×C8—21no—
157C4×C8—261no—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—21no—
161C2×C13#191711yescharacteristic
162C22×C4—261no—
163C22×C4C2×C4×D1311yescharacteristic
164M16—21no—
165M16—21no—
166M16—132no—
167M16—261no—
168C2×C8—21no—
169C2×C8—131no—
170C2×C8—131no—
171C2×C8—261no—
172C2×C8—261no—
173C2×C8—261no—
174C2×C8#612711yescharacteristic
175C2×C8#612711yescharacteristic
176C2×C8D4×D1311yescharacteristic
177C2×C8#612911yescharacteristic
178C2×C8#612911yescharacteristic
179C2×C8Q8×D1311yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—261no—
182C22⋊C4—21no—
183C22⋊C4—261no—
184C42—21no—
185C42—261no—
186C42—261no—
187C42—261no—
188C16—41no—
189C16—41no—
190C16—262no—
191C16—262no—
192C13#1310811yescharacteristic, complemented, Sylow
193C23#8815511yescharacteristic
194C2×C4—41no—
195C2×C4—521no—
196C2×C4—521no—
197C2×C4—1041no—
198C2×C4#8812611yescharacteristic
199C2×C4#8813511yescharacteristic
200C2×C4#8814111yescharacteristic
201C2×C4#8815511yescharacteristic
202C2×C4M16×D1311yescharacteristic
203C2×C4M16×D1311yescharacteristic
204C8—41no—
205C8—261no—
206C8—261no—
207C8—262no—
208C8#8813311yescharacteristic
209C8#8813711yescharacteristic
210C8#8814311yescharacteristic
211C8#8815011yescharacteristic
212C22—41no—
213C22#1171835111yescharacteristic
214C22#1171839011yescharacteristic
215C22#1171848911yescharacteristic
216C4—81no—
217C4—1041no—
218C4—1041no—
219C4#1171831311yescharacteristic
220C4#1171836611yescharacteristic
221C4#1171838911yescharacteristic
222C4#1171848911yescharacteristic
223C2—21no—
224C2—21no—
225C2—21no—
226C2#1311539811yescharacteristic
subgroupG/H
centerC4#11718313
commutatorC22×C4×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1378C2
socleC2×C13#1917
prime radicalC23×C13#131
cosocleC22×C8×C13C23
hypercenter#1378D13
hypocenterC13#13108
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C8 ◁ #1378

Complements

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

NH ≅ G/Ntype
192. C13#13108semidirect

Maximal subgroups

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

subgroupindex
#131166012
#131164412
#131147212
#131129232
#131129192
#131129152
C13×#13782
#1310813