Finite Group Databasebeta

← #15776630

Subgroups — #15776630

Order 3328.

282 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 75 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#13117065C211yesmaximal, characteristic
2#13116886C211yesmaximal, characteristic
3#13114206C211yesmaximal, characteristic
4#13112891C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#3383C211yesmaximal, characteristic
8C13×#557—21no—
9C13×#500C2211yescharacteristic
10C13×#499—21no—
11C13×#479—22no—
12C13×#475—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×Q16—21no—
15C4×C13×Q16C2211yescharacteristic
16C2×#88069—21no—
17#11718681—21no—
18#11718360C2211yescharacteristic
19#11718084—22no—
20#11718084—21no—
21#11718074—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16D411yescharacteristic
26C13×C4⋊Q8—21no—
27C13×C4⋊Q8—41no—
28C13×#125—22no—
29C13×#125—42no—
30C4×Q8×C13—22no—
31C4×Q8×C13—21no—
32C4×Q8×C13—41no—
33C4×Q8×C13D411yescharacteristic
34C2×Dic52—21no—
35C2×Dic52—21no—
36#88123—21no—
37C13×#107—21no—
38C13×#107D411yescharacteristic
39C13×#107D412yes—
40C13×#106—22no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8D411yescharacteristic
43C13×#103—22no—
44C13×#103—21no—
45C4×C8×C13—21no—
46C4×C8×C13C2311yescharacteristic
47#88075—41no—
48#88069—42no—
49C2×#6090—21no—
50C2×#6090—21no—
51#88048—41no—
52C4⋊#1055—21no—
53#12357—131nomaximal, Sylow
54C2×Q8×C13—21no—
55C2×Q8×C13—41no—
56C2×Q8×C13D811yescharacteristic
57C2×Dic26—41no—
58C13×Q16—21no—
59C13×Q16SD1612yes—
60C2×C8×C13—21no—
61C2×C8×C13C2×D411yescharacteristic
62C2×C8×C13C2×D411yescharacteristic
63C13×C4⋊C4—21no—
64C13×C4⋊C4—21no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4D811yescharacteristic
72C42×C13—21no—
73C42×C13—42no—
74C42×C13—41no—
75C42×C13C2×D411yescharacteristic
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78C2×#1055—41no—
79Dic52—42no—
80Dic52—41no—
81Dic52—41no—
82#6090—41no—
83#6090—41no—
84#3383D1311yescharacteristic
85#2241—131no—
86#2209—131no—
87#1670—131no—
88#1364—131no—
89Q8⋊C16—131no—
90#1332—131no—
91Q8×C13—22no—
92Q8×C13—21no—
93Q8×C13—21no—
94Q8×C13—41no—
95Q8×C13—81no—
96Q8×C13—81no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13#12011yescharacteristic
103C2×C4×C13C2×D811yescharacteristic
104C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
105C2×Dic13—81no—
106Dic26—81no—
107Dic26—81no—
108C8×C13—21no—
109C8×C13—41no—
110C8×C13C2×SD1611yescharacteristic
111C8×C13#13711yescharacteristic
112#1055—81no—
113#557—21no—
114C2×Q32—261no—
115#500C2×D1311yescharacteristic
116#499—21no—
117#494—131no—
118#479—22no—
119#475—21no—
120#475—261no—
121C8×Q8C2×D1311yescharacteristic
122C4×Q16—21no—
123C4×Q16C2×D1311yescharacteristic
124C4⋊C16—131no—
125#358—261no—
126#358—262no—
127C4×C16—131no—
128#335—131no—
129#332—261no—
130C22×C13#44711yescharacteristic
131C4×C13—21no—
132C4×C13—42no—
133C4×C13—41no—
134C4×C13—41no—
135C4×C13—82no—
136C4×C13—81no—
137C4×C13#44811yescharacteristic
138C4×C13#45411yescharacteristic
139C4×C13#50811yescharacteristic
140C4×C13#51011yescharacteristic
141Dic13—161no—
142C2×Q16—261no—
143C2×Q16—261no—
144C2×Q16C22⋊D1311yescharacteristic
145C4⋊Q8—21no—
146C4⋊Q8—41no—
147C4⋊Q8—261no—
148#125—22no—
149#125—42no—
150C4×Q8—22no—
151C4×Q8—21no—
152C4×Q8—41no—
153C4×Q8C22⋊D1311yescharacteristic
154Q32—522no—
155C2×C16—261no—
156C2×C16—261no—
157#107—21no—
158#107C22⋊D1311yescharacteristic
159#107C22⋊D1312yes—
160#106—22no—
161#106—521no—
162C4⋊C8—21no—
163C4⋊C8—261no—
164C4⋊C8C22⋊D1311yescharacteristic
165#103—22no—
166#103—21no—
167#103—521no—
168C4×C8—21no—
169C4×C8C22×D1311yescharacteristic
170C2×C13#162711yescharacteristic
171C2×C13#218911yescharacteristic
172C2×C13#219511yescharacteristic
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—521no—
176C2×Q8#610411yescharacteristic
177Q16—21no—
178Q16—522no—
179Q16—521no—
180Q16—521no—
181Q16#610612yes—
182C2×C8—21no—
183C2×C8—521no—
184C2×C8C2×C22⋊D1311yescharacteristic
185C2×C8C2×C22⋊D1311yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—521no—
195C4⋊C4—521no—
196C4⋊C4#610411yescharacteristic
197C42—21no—
198C42—42no—
199C42—41no—
200C42C2×C22⋊D1311yescharacteristic
201C16—521no—
202C16—521no—
203C13#1235711yescharacteristic, complemented, Sylow
204Q8—21no—
205Q8—21no—
206Q8—22no—
207Q8—41no—
208Q8—81no—
209Q8—81no—
210Q8—1041no—
211Q8—1041no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—1041no—
218C2×C4C2×#610411yescharacteristic
219C2×C4#8818611yescharacteristic
220C2×C4#8820711yescharacteristic
221C8—21no—
222C8—41no—
223C8—1041no—
224C8C2×#610611yescharacteristic
225C8#8819611yescharacteristic
226C22#1171887811yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—82no—
232C4—81no—
233C4—2081no—
234C4#1171885511yescharacteristic
235C4#1171885611yescharacteristic
236C4#1171888811yescharacteristic
237C4#1171890611yescharacteristic
238C2#1311393911yescharacteristic
239C2#1311677611yescharacteristic
240C2#1311681411yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3383C2
socle, prime radicalC22×C13#447
hypercenter#3383D13
hypocenterC13#12357
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
203. C13#12357semidirect

Maximal subgroups

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

subgroupindex
#131170652
#131168862
#131142062
#131128912
Q8⋊#60902
#131128002
C13×#33832
#1235713