Finite Group Databasebeta

← #15776635

Subgroups — #15776635

Order 3328.

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

normal subgroups only

This group has 288 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
1Q8×Dic52C211yesmaximal, characteristic
2#13117063C211yesmaximal, characteristic
3#13116883C211yesmaximal, characteristic
4#13112895C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112799C211yesmaximal, characteristic
7C13×#1670C211yesmaximal, characteristic
8Q8×Dic26—21no—
9C13×#494C2211yescharacteristic
10C13×#475—21no—
11C8×Q8×C13C2211yescharacteristic
12C2×#88069—21no—
13#11718511—22no—
14#11718511—21no—
15C4×Dic52—21no—
16C4×Dic52C2211yescharacteristic
17#11718343—21no—
18#11718343C2211yescharacteristic
19C13×#335C2211yescharacteristic
20C13×#332—21no—
21#11718156—22no—
22#11718156—21no—
23C4⋊#6090C2211yescharacteristic
24C4×#6090C2211yescharacteristic
25C2×C13×Q16—21no—
26C2×C13×Q16—21no—
27C13×C4⋊Q8—21no—
28C4×Q8×C13D411yescharacteristic
29Q8×Dic13—41no—
30C2×Dic52D411yescharacteristic
31#88142—42no—
32#88142—41no—
33#88123—22no—
34#88123—21no—
35C4×Dic26—22no—
36C4×Dic26—21no—
37C13×#106—41no—
38C13×C4⋊C8—21no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8D411yescharacteristic
41C13×#103—41no—
42C4×C8×C13—21no—
43C4×C8×C13C2311yescharacteristic
44#88069—42no—
45#88058—22no—
46#88058—21no—
47#88058D412yes—
48#88058D411yescharacteristic
49#88056—22no—
50#88056—21no—
51C2×#6090—21no—
52C2×#6090—21no—
53#12358—131nomaximal, Sylow
54C2×Q8×C13—41no—
55C2×Q8×C13D811yescharacteristic
56C2×Dic26—21no—
57C2×Dic26—42no—
58C2×Dic26—41no—
59C13×Q16—42no—
60C13×Q16—41no—
61C13×Q16—41no—
62C2×C8×C13—21no—
63C2×C8×C13—41no—
64C2×C8×C13C2×D411yescharacteristic
65C2×C8×C13C2×D411yescharacteristic
66C13×C4⋊C4—21no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4D811yescharacteristic
70C42×C13—21no—
71C42×C13C2×D411yescharacteristic
72C4⋊Dic13—22no—
73C4⋊Dic13—21no—
74C4⋊Dic13—42no—
75C4⋊Dic13—41no—
76#6101—42no—
77#6101—41no—
78C4×Dic13—42no—
79C4×Dic13—41no—
80Dic52—21no—
81Dic52SD1612yes—
82#6090—41no—
83#6090—41no—
84Q8×Q16—131no—
85#2241—131no—
86#2209—131no—
87#1670D1311yescharacteristic
88#1365—131no—
89Q8⋊C16—131no—
90#1332—131no—
91Q8×C13—21no—
92Q8×C13—81no—
93Q8×C13—81no—
94Q8×C13Q3212yescomplemented
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—81no—
98C2×C4×C13#12011yescharacteristic
99C2×C4×C13C2×D811yescharacteristic
100C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
101C2×Dic13—41no—
102C2×Dic13—42no—
103C2×Dic13—41no—
104Dic26—22no—
105Dic26—41no—
106Dic26—161no—
107Dic26—162no—
108C8×C13—21no—
109C8×C13—41no—
110C8×C13—81no—
111C8×C13C2×SD1611yescharacteristic
112C8×C13#13711yescharacteristic
113Q82—261no—
114C2×Q32—261no—
115#500—131no—
116#500—261no—
117#494C2×D1311yescharacteristic
118#477—262no—
119#477—261no—
120#475—21no—
121C8×Q8C2×D1311yescharacteristic
122C4×Q16—131no—
123C4×Q16—261no—
124C4⋊C16—131no—
125#358—261no—
126#358—262no—
127C4×C16—131no—
128#335C2×D1311yescharacteristic
129#332—21no—
130C22×C13#44711yescharacteristic
131C4×C13—22no—
132C4×C13—21no—
133C4×C13—41no—
134C4×C13—161no—
135C4×C13#44811yescharacteristic
136C4×C13#45411yescharacteristic
137C4×C13C2×Q3211yescharacteristic
138C4×C13#51011yescharacteristic
139Dic13—42no—
140Dic13—82no—
141Dic13—81no—
142C2×Q16—21no—
143C2×Q16—21no—
144C2×Q16—131no—
145C4⋊Q8—21no—
146C4⋊Q8—262no—
147C4⋊Q8—261no—
148C4⋊Q8—522no—
149C4⋊Q8—521no—
150C4×Q8—262no—
151C4×Q8—261no—
152C4×Q8—521no—
153C4×Q8C22⋊D1311yescharacteristic
154Q32—522no—
155C2×C16—261no—
156C2×C16—261no—
157#107—131no—
158#107—132no—
159#107—262no—
160#107—261no—
161#106—41no—
162C4⋊C8—21no—
163C4⋊C8—21no—
164C4⋊C8C22⋊D1311yescharacteristic
165#103—41no—
166#103—262no—
167#103—261no—
168C4×C8—21no—
169C4×C8C22×D1311yescharacteristic
170C2×C13#162711yescharacteristic
171C2×C13#218811yescharacteristic
172C2×C13#219411yescharacteristic
173C2×Q8—41no—
174C2×Q8—261no—
175C2×Q8—522no—
176C2×Q8—521no—
177C2×Q8#610411yescharacteristic
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—132no—
182Q16—261no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8D4×D1311yescharacteristic
186C2×C8D4×D1311yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4—522no—
193C4⋊C4—522no—
194C4⋊C4—521no—
195C4⋊C4—521no—
196C4⋊C4#610411yescharacteristic
197C42—21no—
198C42—522no—
199C42—521no—
200C42C2×C22⋊D1311yescharacteristic
201C16—521no—
202C16—521no—
203C13#1235811yescharacteristic, complemented, Sylow
204Q8—21no—
205Q8—81no—
206Q8—81no—
207Q8—262no—
208Q8—521no—
209Q8—2081no—
210Q8—2082no—
211Q8#8806912yescomplemented
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—81no—
215C2×C4—521no—
216C2×C4—522no—
217C2×C4—521no—
218C2×C4C2×#610411yescharacteristic
219C2×C4#8819111yescharacteristic
220C2×C4#8820311yescharacteristic
221C8—21no—
222C8—41no—
223C8—81no—
224C8SD16×D1311yescharacteristic
225C8#8816911yescharacteristic
226C22#1171869711yescharacteristic
227C4—22no—
228C4—21no—
229C4—41no—
230C4—161no—
231C4—522no—
232C4—1042no—
233C4—1041no—
234C4#1171883111yescharacteristic
235C4C2×#8806911yescharacteristic
236C4#1171885611yescharacteristic
237C4#1171886211yescharacteristic
238C2#1311393711yescharacteristic
239C2#1311676911yescharacteristic
240C2#1311680511yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1670C2
socle, prime radicalC22×C13#447
hypercenter#1670D13
hypocenterC13#12358
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
94. Q8×C13Q32semidirect
203. C13#12358semidirect
211. Q8#88069semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic522
#131170632
#131168832
#131128952
Q8⋊#60902
#131127992
C13×#16702
#1235813