Finite Group Databasebeta

← #15776642

Subgroups — #15776642

Order 3328.

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

normal subgroups only

This group has 296 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#13127704C211yesmaximal, characteristic
2#13117063C211yesmaximal, characteristic, complemented
3#13116878C211yesmaximal, characteristic
4#13112895C211yesmaximal, characteristic, complemented
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112796C211yesmaximal, characteristic
7C13×#1670C211yesmaximal, characteristic, complemented
8#11719284—21no—
9C13×#494C2211yescharacteristic
10C13×#475—21no—
11C8×Q8×C13C2211yescharacteristic
12C2×#88068—21no—
13#11718508—22no—
14#11718503—21no—
15C4×D104—21no—
16C4×D104C2211yescharacteristic
17#11718344—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
29#88200—41no—
30C2×D104D411yescharacteristic
31#88150—42no—
32C4⋊C4×D13—41no—
33C4×D52—22no—
34C4×D52—21no—
35#88124—22no—
36#88123—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#88068—42no—
45#88061—22no—
46#88061—21no—
47#88058—21no—
48#88058D412yes—
49#88058D411yescharacteristic
50#88057—22no—
51C2×#6090—21no—
52C2×#6090—21no—
53#12359—131nomaximal, Sylow
54C2×Q8×C13—41no—
55C2×Q8×C13D811yescharacteristic
56C2×D52—21no—
57C2×C4×D13—41no—
58C2×C4×D13—42no—
59C2×Dic26—41no—
60C13×Q16—42no—
61C13×Q16—41no—
62C13×Q16—41no—
63C2×C8×C13—21no—
64C2×C8×C13—41no—
65C2×C8×C13C2×D411yescharacteristic
66C2×C8×C13C2×D411yescharacteristic
67C13×C4⋊C4—21no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4D811yescharacteristic
71C42×C13—21no—
72C42×C13C2×D411yescharacteristic
73#6103—42no—
74#6103—41no—
75C4⋊Dic13—22no—
76C4⋊Dic13—21no—
77C4⋊Dic13—41no—
78#6101—42no—
79#6101—42no—
80D104—21no—
81D104SD1612yes—
82#6090—41no—
83#6090—41no—
84#3380—131no—
85#2241—131no—
86#2208—131no—
87#1670D1311yescharacteristic, complemented
88#1365—131no—
89Q8⋊C16—131no—
90#1331—131no—
91C22×D13—41no—
92Q8×C13—21no—
93Q8×C13—21no—
94Q8×C13—81no—
95Q8×C13—81no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—81no—
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13C2×D811yescharacteristic
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×Dic13—41no—
103C2×Dic13—42no—
104D52—22no—
105D52—41no—
106C4×D13—81no—
107C4×D13—81no—
108C4×D13—162no—
109Dic26—161no—
110C8×C13—21no—
111C8×C13—41no—
112C8×C13—81no—
113C8×C13C2×SD1611yescharacteristic
114C8×C13#13711yescharacteristic
115#554—261no—
116C2×SD32—261no—
117#500—131no—
118#499—261no—
119#494C2×D1311yescharacteristic
120#478—262no—
121#476—261no—
122#475—21no—
123C8×Q8C2×D1311yescharacteristic
124C4×D8—131no—
125C4×D8—261no—
126C4⋊C16—131no—
127#358—261no—
128#358—262no—
129C4×C16—131no—
130#335C2×D1311yescharacteristic
131#332—21no—
132C22×C13#44711yescharacteristic
133C2×D13—42no—
134C2×D13—81no—
135C2×D13—81no—
136C4×C13—21no—
137C4×C13—41no—
138C4×C13—41no—
139C4×C13—161no—
140C4×C13#44811yescharacteristic
141C4×C13#45411yescharacteristic
142C4×C13#50811yescharacteristic
143C4×C13#51011yescharacteristic
144Dic13—81no—
145Dic13—82no—
146C2×Q16—21no—
147C2×Q16—21no—
148C2×D8—131no—
149C4⋊Q8—21no—
150C4⋊Q8—261no—
151#125—262no—
152C22⋊Q8—522no—
153C22⋊Q8—521no—
154C4×Q8C22⋊D1311yescharacteristic
155C4×D4—262no—
156C4×D4—261no—
157C2×C4⋊C4—521no—
158SD32—522no—
159C2×C16—261no—
160C2×C16—261no—
161#107—131no—
162#107—132no—
163#107—261no—
164#106—41no—
165#106—262no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8C22⋊D1311yescharacteristic
169#103—41no—
170#102—262no—
171#102—261no—
172C4×C8—21no—
173C4×C8C22×D1311yescharacteristic
174C2×C13#162711yescharacteristic
175C2×C13#218911yescharacteristic
176C2×C13#219411yescharacteristic
177D13—82no—
178C2×Q8—41no—
179C2×Q8—521no—
180C2×Q8#610411yescharacteristic
181C2×D4—261no—
182C22×C4—522no—
183C22×C4—521no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187D8—132no—
188D8—261no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8D4×D1311yescharacteristic
192C2×C8D4×D1311yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—261no—
197C4⋊C4—262no—
198C4⋊C4—522no—
199C4⋊C4—522no—
200C4⋊C4—521no—
201C4⋊C4#610411yescharacteristic
202C22⋊C4—522no—
203C22⋊C4—521no—
204C42—21no—
205C42C2×C22⋊D1311yescharacteristic
206C16—521no—
207C16—521no—
208C13#1235911yescharacteristic, complemented, Sylow
209C23—521no—
210Q8—21no—
211Q8—21no—
212Q8—81no—
213Q8—81no—
214Q8—2081no—
215D4—262no—
216D4—521no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—81no—
220C2×C4—521no—
221C2×C4—522no—
222C2×C4—1041no—
223C2×C4—1041no—
224C2×C4—2082no—
225C2×C4C2×#610411yescharacteristic
226C2×C4#8819111yescharacteristic
227C2×C4#8820311yescharacteristic
228C8—21no—
229C8—41no—
230C8—81no—
231C8SD16×D1311yescharacteristic
232C8#8816911yescharacteristic
233C22—522no—
234C22—1041no—
235C22—1041no—
236C22#1171869711yescharacteristic
237C4—21no—
238C4—41no—
239C4—41no—
240C4—161no—
241C4—1041no—
242C4—1042no—
243C4#1171883111yescharacteristic
244C4#1171884011yescharacteristic
245C4#1171885511yescharacteristic
246C4#1171886211yescharacteristic
247C2—1042no—
248C2#1311393711yescharacteristic
249C2#1311677411yescharacteristic
250C2#1311680511yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1670C2
socleC22×C13#447
prime radicalC2×D104D4
hypercenter#1670D13
hypocenterC13#12359
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
2. #13117063C2semidirect
4. #13112895C2semidirect
5. Q8⋊#6090C2semidirect
7. C13×#1670C2semidirect
87. #1670D13semidirect
208. C13#12359semidirect

Maximal subgroups

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

subgroupindex
#131277042
#131170632
#131168782
#131128952
Q8⋊#60902
#131127962
C13×#16702
#1235913