Finite Group Databasebeta

← #15776741

Subgroups — #15776741

Order 3328.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#13117063C211yesmaximal, characteristic, complemented
2#13116988C211yesmaximal, characteristic, complemented
3#13114235C211yesmaximal, characteristic
4#13112885C211yesmaximal, characteristic, complemented
5#13112800C211yesmaximal, characteristic, complemented
6D4⋊#6090C211yesmaximal, characteristic
7D4×C13×Q16C211yesmaximal, characteristic
8C22×C13×Q16—21no—
9D4×Q8×C13—21no—
10C13×#494C2211yescharacteristic
11C13×#467—21no—
12C13×#462—21no—
13C13×#451—22no—
14C4×C13×Q16C2211yescharacteristic
15C8×D4×C13C2211yescharacteristic
16#11718669—21no—
17#11718343C2211yescharacteristic
18#11718156—21no—
19#11718156—22no—
20#11718081—21no—
21#11718073—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C22×Q8×C13—22no—
26C2×C13×Q16—22no—
27C2×C13×Q16—21no—
28C2×C13×Q16—42no—
29C2×C13×Q16—42no—
30C2×C13×Q16D411yescharacteristic
31C2×C13×Q16D412yes—
32C22×C8×C13—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—41no—
35C13×C22⋊Q8—22no—
36C13×C22⋊Q8—42no—
37C4×Q8×C13—21no—
38C4×D4×C13—41no—
39C4×D4×C13D411yescharacteristic
40#88123—21no—
41C13×#107D411yescharacteristic
42C13×C4⋊C8D411yescharacteristic
43C13×#103—22no—
44C13×#103—21no—
45C13×C22⋊C8—21no—
46C4×C8×C13C2311yescharacteristic
47#88072—41no—
48#88058—21no—
49#88058—21no—
50C2×#6090—21no—
51C2×#6090—21no—
52#88048—41no—
53C4⋊#1055—21no—
54#12374—131nomaximal, Sylow
55C2×Q8×C13—21no—
56C2×Q8×C13—22no—
57C2×Q8×C13—42no—
58C2×Q8×C13—44no—
59C2×Q8×C13—82no—
60C2×D4×C13D811yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C2×Dic26—41no—
64C13×Q16—21no—
65C13×Q16—42no—
66C13×Q16—44no—
67C13×Q16—41no—
68C13×Q16—41no—
69C13×Q16SD1612yes—
70C2×C8×C13—21no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13C2×D411yescharacteristic
74C2×C8×C13C2×D411yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4D811yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4—42no—
83C42×C13—41no—
84C42×C13C2×D411yescharacteristic
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C2×#1055—41no—
88#6090—41no—
89#6090—41no—
90D4×Q16D1311yescharacteristic
91#2241—131no—
92#2227—131no—
93#1675—131no—
94#1362—131no—
95#1332—131no—
96D4⋊C16—131no—
97C23×C13—21no—
98Q8×C13—22no—
99Q8×C13—41no—
100Q8×C13—42no—
101Q8×C13—42no—
102Q8×C13—84no—
103D4×C13—21no—
104D4×C13Q3212yes—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—84no—
112C2×C4×C13#12011yescharacteristic
113C2×C4×C13C2×D811yescharacteristic
114C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
115C2×Dic13—81no—
116Dic26—161no—
117C8×C13—21no—
118C8×C13—41no—
119C8×C13C2×SD1611yescharacteristic
120C8×C13AGL(1,ℤ/8)11yescharacteristic
121#1055—81no—
122C22×Q16—21no—
123D4×Q8—21no—
124#500—131no—
125#494C2×D1311yescharacteristic
126#476—261no—
127#467—21no—
128#462—21no—
129#451—22no—
130C4×Q16C2×D1311yescharacteristic
131C8×D4C2×D1311yescharacteristic
132#366—261no—
133C4⋊C16—131no—
134#358—261no—
135#358—262no—
136C4×C16—131no—
137#335—131no—
138#333—261no—
139C22×C13—22no—
140C22×C13—41no—
141C22×C13—41no—
142C22×C13#44711yescharacteristic
143C4×C13—21no—
144C4×C13—41no—
145C4×C13—42no—
146C4×C13—82no—
147C4×C13—81no—
148C4×C13#45011yescharacteristic
149C4×C13#45511yescharacteristic
150C4×C13C2×Q3211yescharacteristic
151C4×C13#51011yescharacteristic
152Dic13—161no—
153C22×Q8—22no—
154C2×Q16—22no—
155C2×Q16—21no—
156C2×Q16—42no—
157C2×Q16—42no—
158C2×Q16C22⋊D1311yescharacteristic
159C2×Q16C22⋊D1312yes—
160C22×C8—21no—
161C4⋊Q8—21no—
162C4⋊Q8—41no—
163C4⋊Q8—261no—
164C22⋊Q8—22no—
165C22⋊Q8—42no—
166C4×Q8—21no—
167C4×D4—41no—
168C4×D4C22⋊D1311yescharacteristic
169C2×C16—261no—
170C2×C16—261no—
171#107—261no—
172#107—261no—
173#107C22⋊D1311yescharacteristic
174#106—521no—
175C4⋊C8—261no—
176C4⋊C8C22⋊D1311yescharacteristic
177#103—22no—
178#103—21no—
179#102—521no—
180C22⋊C8—21no—
181C4×C8C22×D1311yescharacteristic
182C2×C13—42no—
183C2×C13#163911yescharacteristic
184C2×C13#218811yescharacteristic
185C2×C13#219311yescharacteristic
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—42no—
189C2×Q8—44no—
190C2×Q8—82no—
191C2×Q8—521no—
192C2×D4#610411yescharacteristic
193C22×C4—21no—
194C22×C4—42no—
195Q16—21no—
196Q16—42no—
197Q16—44no—
198Q16—41no—
199Q16—41no—
200Q16#610512yes—
201C2×C8—21no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—521no—
205C2×C8C2×C22⋊D1311yescharacteristic
206C2×C8C2×C22⋊D1311yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—521no—
213C4⋊C4—521no—
214C4⋊C4#610411yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—42no—
217C42—41no—
218C42C2×C22⋊D1311yescharacteristic
219C16—521no—
220C16—521no—
221C13#1237411yescharacteristic, complemented, Sylow
222C23—21no—
223Q8—22no—
224Q8—41no—
225Q8—42no—
226Q8—42no—
227Q8—84no—
228Q8—2081no—
229D4—21no—
230D4#8806912yes—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—84no—
238C2×C4—1041no—
239C2×C4C2×#610411yescharacteristic
240C2×C4#8818611yescharacteristic
241C2×C4#8820711yescharacteristic
242C8—21no—
243C8—41no—
244C8—1041no—
245C8#8818611yescharacteristic
246C8C2×#610511yescharacteristic
247C22—22no—
248C22—41no—
249C22—41no—
250C22#1171887811yescharacteristic
251C4—21no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4—82no—
256C4—2081no—
257C4#1171884011yescharacteristic
258C4C2×#8806911yescharacteristic
259C4#1171887911yescharacteristic
260C4#1171890311yescharacteristic
261C2—42no—
262C2#1311401511yescharacteristic
263C2#1311677011yescharacteristic
264C2#1311680011yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingD4×C13×Q16C2
socleC22×C13#447
prime radicalC2×D4×C13D8
hypercenterD4×Q16D13
hypocenterC13#12374
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
1. #13117063C2semidirect
2. #13116988C2semidirect
4. #13112885C2semidirect
5. #13112800C2semidirect
221. C13#12374semidirect

Maximal subgroups

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

subgroupindex
#131170632
#131169882
#131142352
#131128852
#131128002
D4⋊#60902
D4×C13×Q162
#1237413