Finite Group Databasebeta

← #15772354

Subgroups — #15772354

Order 3328.

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

normal subgroups only

This group has 284 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#13123473C211yesmaximal, characteristic
2#13116645C212yesmaximal, complemented
3#13112787C211yesmaximal, characteristic, complemented
4#13112771C212yesmaximal
5C13×#1327C211yesmaximal, characteristic, complemented
6C2×#88126C411yescharacteristic
7C13×#423C2211yescharacteristic
8#11718787C411yescharacteristic
9#11718787C2211yescharacteristic
10M16×Dic13C411yescharacteristic
11M16×Dic13C2211yescharacteristic
12#11718585C411yescharacteristic
13#11718501—22no—
14#11718501—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C22×C4×D13C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C2×C13×M16C2311yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×#6103—21no—
24C2×#6101—21no—
25C2×C4×Dic13C2×C411yescharacteristic
26C2×#6099C2×C411yescharacteristic
27C2×#6099C2×C411yescharacteristic
28#88126—22no—
29#88126—21no—
30#88126—21no—
31C13×M32—22no—
32C13×C4⋊C8—22no—
33#88060—22no—
34#88060—22no—
35#88055—21no—
36#88055D412yes—
37C8×Dic13—21no—
38C8×Dic13D412yes—
39#88052—22no—
40C4⋊#1055—22no—
41#11522—131nomaximal, Sylow
42C23×D13M1611yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13—21no—
46C22×Dic13M1611yescharacteristic
47C2×C4×D13—21no—
48C2×C4×D13—21no—
49C2×C4×D13—41no—
50C2×C4×D13—41no—
51C13×M16—41no—
52C13×M16—41no—
53C2×C8×C13—21no—
54C2×C8×C13C2×D412yes—
55C42×C13—21no—
56C42×C13M1612yes—
57#6103—22no—
58#6103—22no—
59#6101—22no—
60#6101—22no—
61C4×Dic13—21no—
62C4×Dic13C22⋊C411yescharacteristic
63C4×Dic13C22⋊C411yescharacteristic
64#6099—41no—
65#6099—41no—
66C2×#1055—21no—
67C2×#1055C22⋊C412yes—
68C13×C16—42no—
69#6090—42no—
70#2921—131no—
71#2165—132no—
72#1327—131no—
73#1327D1311yescharacteristic, complemented
74#1320—132no—
75C23×C13C2×M1611yescharacteristic
76C22×D13—21no—
77C22×D13—41no—
78C22×D13—81no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—81no—
83C2×C4×C13C2×C22⋊C411yescharacteristic
84C2×C4×C13C2×M1611yescharacteristic
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—41no—
89C2×Dic13—81no—
90C4×D13—42no—
91C4×D13—41no—
92C4×D13—41no—
93C8×C13—22no—
94C8×C13—41no—
95#1055—22no—
96#1055—41no—
97C2×#117—131no—
98#433—262no—
99#433—262no—
100#423—131no—
101#423C2×D1311yescharacteristic
102#407—131no—
103#407—131no—
104C4×M16—131no—
105C4×M16—131no—
106#364—262no—
107#349—132no—
108#349C2×D1312yes—
109#347—262no—
110C22×C13—21no—
111C22×C13—41no—
112C22×C13#40711yescharacteristic
113C2×D13—42no—
114C2×D13—41no—
115C2×D13—82no—
116C4×C13—21no—
117C4×C13—42no—
118C4×C13#41011yescharacteristic
119C4×C13#41311yescharacteristic
120Dic13—41no—
121Dic13—41no—
122Dic13—41no—
123C23×C4—131no—
124C2×M16—131no—
125C2×M16—131no—
126C2×M16C4×D1311yescharacteristic
127C2×M16C22×D1311yescharacteristic
128#117—261no—
129#117—261no—
130#117—262no—
131C2×C4⋊C4—261no—
132C2×C22⋊C4—261no—
133C2×C42—131no—
134C2×C42C4×D1311yescharacteristic
135M32—22no—
136M32—262no—
137C4⋊C8—22no—
138C4⋊C8—262no—
139C22⋊C8—262no—
140C22⋊C8—262no—
141#97—132no—
142#97—261no—
143C4×C8—132no—
144C4×C8—261no—
145C2×C13—21no—
146C2×C13—41no—
147C2×C13#146411yescharacteristic
148D13—81no—
149C24—131no—
150C22×C4—21no—
151C22×C4—131no—
152C22×C4—261no—
153C22×C4—261no—
154C22×C4—261no—
155C22×C4—521no—
156C22×C4—521no—
157C22×C4C2×C4×D1311yescharacteristic
158M16—41no—
159M16—41no—
160M16—521no—
161M16—521no—
162C2×C8—21no—
163C2×C8—132no—
164C2×C8—261no—
165C2×C8D4×D1312yes—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C42—21no—
171C42—131no—
172C42—131no—
173C42—261no—
174C42#609412yes—
175C16—42no—
176C16—522no—
177C13#1152211yescharacteristic, complemented, Sylow
178C23—261no—
179C23—521no—
180C23—1041no—
181C23M16×D1311yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—81no—
186C2×C4—261no—
187C2×C4—261no—
188C2×C4—261no—
189C2×C4—522no—
190C2×C4—521no—
191C2×C4—521no—
192C2×C4—521no—
193C2×C4—1041no—
194C2×C4C22⋊C4×D1311yescharacteristic
195C2×C4C2×#609411yescharacteristic
196C8—22no—
197C8—41no—
198C8—262no—
199C8—521no—
200C22—21no—
201C22—41no—
202C22—522no—
203C22—521no—
204C22—1042no—
205C22#1171838711yescharacteristic
206C4—21no—
207C4—42no—
208C4—521no—
209C4—521no—
210C4—521no—
211C4#1171840111yescharacteristic
212C4#1171841211yescharacteristic
213C2—21no—
214C2—41no—
215C2—1041no—
216C2#1311316911yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1327C2
socleC2×C13#1464
prime radicalC23×D13M16
cosocleC2×C13×M16C23
hypercenter#1327D13
hypocenterC13#11522
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #13116645C2semidirect
3. #13112787C2semidirect
5. C13×#1327C2semidirect
73. #1327D13semidirect
177. C13#11522semidirect

Maximal subgroups

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

subgroupindex
#131234732
#131166452
#131127872
#131127712
C13×#13272
#1152213