Finite Group Databasebeta

← #15776825

Subgroups — #15776825

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#13117063C211yesmaximal, characteristic
2#13116988C211yesmaximal, characteristic
3#13114240C211yesmaximal, characteristic
4#13112885C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112800C211yesmaximal, characteristic
7C13×#3395C211yesmaximal, characteristic
8C13×#557—21no—
9C13×#494—21no—
10C13×#494C2211yescharacteristic
11C13×#462—22no—
12C13×#462—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×Q16—21no—
15C4×C13×Q16C2211yescharacteristic
16#11718682—21no—
17#11718343C2211yescharacteristic
18#11718156—21no—
19#11718156—22no—
20#11718081—21no—
21#11718073—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16—22no—
26C2×C13×Q16—21no—
27C2×C13×Q16D411yescharacteristic
28C2×C13×Q16D412yes—
29C13×C4⋊Q8—22no—
30C13×C4⋊Q8—21no—
31C13×#125—42no—
32C13×#125—41no—
33C4×Q8×C13—22no—
34C4×Q8×C13—21no—
35C4×Q8×C13—41no—
36C4×Q8×C13D411yescharacteristic
37#88123—21no—
38C13×#107D411yescharacteristic
39C13×C4⋊C8—21no—
40C13×C4⋊C8D411yescharacteristic
41C13×#103—22no—
42C13×#103—21no—
43C4×C8×C13—21no—
44C4×C8×C13C2311yescharacteristic
45#88075—41no—
46#88058—21no—
47#88058—21no—
48C2×#6090—21no—
49C2×#6090—21no—
50#88047—41no—
51C4⋊#1055—21no—
52#12386—131nomaximal, Sylow
53C2×Q8×C13—21no—
54C2×Q8×C13—22no—
55C2×Q8×C13D811yescharacteristic
56C2×Dic26—41no—
57C13×Q16—21no—
58C13×Q16—21no—
59C13×Q16—42no—
60C13×Q16—41no—
61C13×Q16—41no—
62C13×Q16—82no—
63C2×C8×C13—21no—
64C2×C8×C13C2×D411yescharacteristic
65C2×C8×C13C2×D411yescharacteristic
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4D811yescharacteristic
75C42×C13—21no—
76C42×C13—42no—
77C42×C13—41no—
78C42×C13C2×D411yescharacteristic
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81C2×#1055—41no—
82#6090—41no—
83#6090—41no—
84#3395D1311yescharacteristic
85#2241—131no—
86#2227—131no—
87#1676—131no—
88#1362—131no—
89Q8⋊C16—131no—
90#1332—131no—
91Q8×C13—21no—
92Q8×C13—41no—
93Q8×C13—42no—
94Q8×C13—42no—
95Q8×C13—41no—
96Q8×C13Q3212yes—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13#12011yescharacteristic
103C2×C4×C13C2×D811yescharacteristic
104C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
105C2×Dic13—81no—
106Dic26—161no—
107C8×C13—21no—
108C8×C13—41no—
109C8×C13#13511yescharacteristic
110C8×C13#13711yescharacteristic
111#1055—81no—
112#557—21no—
113#500—131no—
114#494—21no—
115#494C2×D1311yescharacteristic
116#477—261no—
117#462—22no—
118#462—21no—
119C8×Q8C2×D1311yescharacteristic
120C4×Q16—21no—
121C4×Q16C2×D1311yescharacteristic
122#366—261no—
123C4⋊C16—131no—
124#358—261no—
125#358—262no—
126C4×C16—131no—
127#335—131no—
128#333—261no—
129C22×C13#44711yescharacteristic
130C4×C13—22no—
131C4×C13—21no—
132C4×C13—41no—
133C4×C13—81no—
134C4×C13—82no—
135C4×C13—81no—
136C4×C13#45211yescharacteristic
137C4×C13#45511yescharacteristic
138C4×C13C2×Q3211yescharacteristic
139C4×C13#51011yescharacteristic
140Dic13—161no—
141C2×Q16—22no—
142C2×Q16—21no—
143C2×Q16C22⋊D1311yescharacteristic
144C2×Q16C22⋊D1312yes—
145C4⋊Q8—22no—
146C4⋊Q8—21no—
147C4⋊Q8—261no—
148#125—42no—
149#125—41no—
150C4×Q8—22no—
151C4×Q8—21no—
152C4×Q8—41no—
153C4×Q8C22⋊D1311yescharacteristic
154C2×C16—261no—
155C2×C16—261no—
156#107—261no—
157#107—261no—
158#107—521no—
159#107C22⋊D1311yescharacteristic
160C4⋊C8—21no—
161C4⋊C8—261no—
162C4⋊C8C22⋊D1311yescharacteristic
163#103—22no—
164#103—21no—
165#103—521no—
166C4×C8—21no—
167C4×C8C22×D1311yescharacteristic
168C2×C13#164111yescharacteristic
169C2×C13#218811yescharacteristic
170C2×C13#219311yescharacteristic
171C2×Q8—21no—
172C2×Q8—22no—
173C2×Q8—521no—
174C2×Q8#610411yescharacteristic
175Q16—21no—
176Q16—21no—
177Q16—42no—
178Q16—41no—
179Q16—41no—
180Q16—82no—
181C2×C8—21no—
182C2×C8—521no—
183C2×C8C2×C22⋊D1311yescharacteristic
184C2×C8C2×C22⋊D1311yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—521no—
194C4⋊C4—521no—
195C4⋊C4#610411yescharacteristic
196C42—21no—
197C42—42no—
198C42—41no—
199C42C2×C22⋊D1311yescharacteristic
200C16—521no—
201C16—521no—
202C13#1238611yescharacteristic, complemented, Sylow
203Q8—21no—
204Q8—41no—
205Q8—42no—
206Q8—42no—
207Q8—41no—
208Q8—2081no—
209Q8#8806912yes—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—1041no—
216C2×C4C2×#610411yescharacteristic
217C2×C4#8818611yescharacteristic
218C2×C4#8820711yescharacteristic
219C8—21no—
220C8—41no—
221C8—1041no—
222C8#8820411yescharacteristic
223C8#8820511yescharacteristic
224C22#1171887811yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—81no—
229C4—81no—
230C4—82no—
231C4—2081no—
232C4#1171884011yescharacteristic
233C4C2×#8806911yescharacteristic
234C4#1171890011yescharacteristic
235C4#1171890311yescharacteristic
236C2#1311402911yescharacteristic
237C2#1311677011yescharacteristic
238C2#1311680011yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3395C2
socle, prime radicalC22×C13#447
hypercenter#3395D13
hypocenterC13#12386
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3395

Complements

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

NH ≅ G/Ntype
202. C13#12386semidirect

Maximal subgroups

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

subgroupindex
#131170632
#131169882
#131142402
#131128852
Q8⋊#60902
#131128002
C13×#33952
#1238613