Finite Group Databasebeta

← #15776823

Subgroups — #15776823

Order 3328.

282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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#13127842C211yesmaximal, characteristic
2#13117065C211yesmaximal, characteristic
3#13116985C211yesmaximal, characteristic
4#13112884C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112799C211yesmaximal, characteristic
7C13×#1676C211yesmaximal, characteristic
8#11719275—21no—
9C13×#500C2211yescharacteristic
10C13×#477—21no—
11C8×Q8×C13C2211yescharacteristic
12#11718510—22no—
13#11718510—21no—
14#11718360—21no—
15#11718360C2211yescharacteristic
16C4×Dic52—21no—
17C4×Dic52C2211yescharacteristic
18C13×#335C2211yescharacteristic
19C13×#333—21no—
20#11718084—21no—
21#11718084—22no—
22#11718081—21no—
23C4⋊#6090C2211yescharacteristic
24C4×#6090C2211yescharacteristic
25C13×C4⋊Q8—21no—
26C4×Q8×C13D411yescharacteristic
27Q8×Dic13—41no—
28C2×Dic52—21no—
29C2×Dic52—22no—
30C2×Dic52D411yescharacteristic
31C2×Dic52D412yes—
32#88144—42no—
33#88144—41no—
34#88123—22no—
35#88123—21no—
36C4×Dic26—22no—
37C4×Dic26—21no—
38C13×#107—21no—
39C13×#107—21no—
40C13×#107—41no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8D411yescharacteristic
44C13×#103—41no—
45C4×C8×C13—21no—
46C4×C8×C13C2311yescharacteristic
47#88058D411yescharacteristic
48#88056—22no—
49#88056—21no—
50C2×#6090—21no—
51C2×#6090—21no—
52#12386—131nomaximal, Sylow
53C2×Q8×C13—41no—
54C2×Q8×C13D811yescharacteristic
55C2×Dic26—21no—
56C2×Dic26—22no—
57C2×C8×C13—21no—
58C2×C8×C13—41no—
59C2×C8×C13C2×D411yescharacteristic
60C2×C8×C13C2×D411yescharacteristic
61C13×C4⋊C4—21no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4D811yescharacteristic
65C42×C13—21no—
66C42×C13C2×D411yescharacteristic
67C4⋊Dic13—21no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70C4⋊Dic13—41no—
71C4⋊Dic13—41no—
72#6101—42no—
73#6101—41no—
74C4×Dic13—42no—
75C4×Dic13—41no—
76Dic52—21no—
77Dic52—21no—
78Dic52—42no—
79Dic52—41no—
80Dic52—41no—
81Dic52—82no—
82#6090—41no—
83#6090—41no—
84#3395—131no—
85#2241—131no—
86#2227—131no—
87#1676D1311yescharacteristic
88#1362—131no—
89Q8⋊C16—131no—
90#1332—131no—
91Q8×C13—21no—
92Q8×C13—161no—
93Q8×C13Q3212yes—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—81no—
97C2×C4×C13#12011yescharacteristic
98C2×C4×C13C2×D811yescharacteristic
99C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
100C2×Dic13—41no—
101C2×Dic13—42no—
102C2×Dic13—41no—
103Dic26—41no—
104Dic26—42no—
105Dic26—42no—
106Dic26—41no—
107C8×C13—21no—
108C8×C13—41no—
109C8×C13—81no—
110C8×C13#13511yescharacteristic
111C8×C13#13711yescharacteristic
112#557—261no—
113#500C2×D1311yescharacteristic
114#494—131no—
115#494—261no—
116#477—21no—
117#462—262no—
118#462—261no—
119C8×Q8C2×D1311yescharacteristic
120C4×Q16—131no—
121C4×Q16—261no—
122#366—261no—
123C4⋊C16—131no—
124#358—261no—
125#358—262no—
126C4×C16—131no—
127#335C2×D1311yescharacteristic
128#333—21no—
129C22×C13#44711yescharacteristic
130C4×C13—22no—
131C4×C13—21no—
132C4×C13—41no—
133C4×C13—161no—
134C4×C13#45211yescharacteristic
135C4×C13#45511yescharacteristic
136C4×C13C2×Q3211yescharacteristic
137C4×C13#51011yescharacteristic
138Dic13—81no—
139Dic13—82no—
140Dic13—81no—
141C2×Q16—131no—
142C2×Q16—132no—
143C2×Q16—262no—
144C2×Q16—261no—
145C4⋊Q8—21no—
146C4⋊Q8—262no—
147C4⋊Q8—261no—
148#125—522no—
149#125—521no—
150C4×Q8—262no—
151C4×Q8—261no—
152C4×Q8—521no—
153C4×Q8C22⋊D1311yescharacteristic
154C2×C16—261no—
155C2×C16—261no—
156#107—21no—
157#107—21no—
158#107—41no—
159#107—131no—
160C4⋊C8—21no—
161C4⋊C8—21no—
162C4⋊C8C22⋊D1311yescharacteristic
163#103—41no—
164#103—262no—
165#103—261no—
166C4×C8—21no—
167C4×C8C22×D1311yescharacteristic
168C2×C13#164111yescharacteristic
169C2×C13#218811yescharacteristic
170C2×C13#219311yescharacteristic
171C2×Q8—41no—
172C2×Q8—261no—
173C2×Q8—262no—
174C2×Q8#610411yescharacteristic
175Q16—261no—
176Q16—261no—
177Q16—522no—
178Q16—521no—
179Q16—521no—
180Q16—1042no—
181C2×C8—21no—
182C2×C8—41no—
183C2×C8D4×D1311yescharacteristic
184C2×C8D4×D1311yescharacteristic
185C4⋊C4—21no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—261no—
189C4⋊C4—522no—
190C4⋊C4—522no—
191C4⋊C4—522no—
192C4⋊C4—521no—
193C4⋊C4—521no—
194C4⋊C4—521no—
195C4⋊C4#610411yescharacteristic
196C42—21no—
197C42—522no—
198C42—521no—
199C42C2×C22⋊D1311yescharacteristic
200C16—521no—
201C16—521no—
202C13#1238611yescharacteristic, complemented, Sylow
203Q8—21no—
204Q8—161no—
205Q8—521no—
206Q8—522no—
207Q8—522no—
208Q8—521no—
209Q8#8806912yes—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—81no—
213C2×C4—521no—
214C2×C4—522no—
215C2×C4—521no—
216C2×C4C2×#610411yescharacteristic
217C2×C4#8819111yescharacteristic
218C2×C4#8820311yescharacteristic
219C8—21no—
220C8—41no—
221C8—81no—
222C8#8817211yescharacteristic
223C8#8817311yescharacteristic
224C22#1171869711yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—161no—
229C4—1041no—
230C4—1041no—
231C4—1042no—
232C4C2×#8806911yescharacteristic
233C4#1171884811yescharacteristic
234C4#1171885611yescharacteristic
235C4#1171886311yescharacteristic
236C2#1311402711yescharacteristic
237C2#1311676911yescharacteristic
238C2#1311679811yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1676C2
socle, prime radicalC22×C13#447
hypercenter#1676D13
hypocenterC13#12386
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1676

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
#131278422
#131170652
#131169852
#131128842
Q8⋊#60902
#131127992
C13×#16762
#1238613