Finite Group Databasebeta

← #15776795

Subgroups — #15776795

Order 3328.

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

normal subgroups only

This group has 288 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#13116975C211yesmaximal, characteristic
4#13112884C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic
6#13112799C211yesmaximal, characteristic
7C13×#1674C211yesmaximal, characteristic
8#11719275—21no—
9C13×#500C2211yescharacteristic
10C13×#462—21no—
11C8×Q8×C13C2211yescharacteristic
12#11718510—22no—
13#11718510—21no—
14#11718360—21no—
15#11718360C2211yescharacteristic
16C4×Dic52—21no—
17C4×Dic52C2211yescharacteristic
18C13×#335C2211yescharacteristic
19C13×#332—21no—
20#11718084—21no—
21#11718084—22no—
22#11718082—21no—
23C4⋊#6090C2211yescharacteristic
24C4×#6090C2211yescharacteristic
25C2×C13×Q16—41no—
26C13×C4⋊Q8—21no—
27C4×Q8×C13D411yescharacteristic
28Q8×Dic13—41no—
29C2×Dic52—21no—
30C2×Dic52—22no—
31C2×Dic52D411yescharacteristic
32C2×Dic52D412yes—
33#88144—42no—
34#88144—41no—
35#88123—22no—
36#88123—21no—
37C4×Dic26—22no—
38C4×Dic26—21no—
39C13×#107—21no—
40C13×#107—21no—
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#12382—131nomaximal, Sylow
53C2×Q8×C13—41no—
54C2×Q8×C13D811yescharacteristic
55C2×Dic26—21no—
56C2×Dic26—22no—
57C13×Q16—82no—
58C2×C8×C13—21no—
59C2×C8×C13—41no—
60C2×C8×C13C2×D411yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C13×C4⋊C4—21no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4D811yescharacteristic
66C42×C13—21no—
67C42×C13C2×D411yescharacteristic
68C4⋊Dic13—21no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4⋊Dic13—41no—
72C4⋊Dic13—41no—
73#6101—42no—
74#6101—41no—
75C4×Dic13—42no—
76C4×Dic13—41no—
77Dic52—21no—
78Dic52—21no—
79Dic52—42no—
80Dic52—41no—
81Dic52—41no—
82Dic52—82no—
83#6090—41no—
84#6090—41no—
85#3395—131no—
86#2241—131no—
87#2225—131no—
88#1674D1311yescharacteristic
89#1362—131no—
90Q8⋊C16—131no—
91#1332—131no—
92Q8×C13—21no—
93Q8×C13—81no—
94Q8×C13—81no—
95Q8×C13SD3212yes—
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—
104C2×Dic13—41no—
105Dic26—41no—
106Dic26—42no—
107Dic26—42no—
108Dic26—41no—
109C8×C13—21no—
110C8×C13—41no—
111C8×C13—81no—
112C8×C13#13511yescharacteristic
113C8×C13#13711yescharacteristic
114#557—261no—
115#500C2×D1311yescharacteristic
116#494—131no—
117#494—261no—
118#462—21no—
119#462—262no—
120#462—261no—
121C8×Q8C2×D1311yescharacteristic
122C4×Q16—131no—
123C4×Q16—261no—
124#367—261no—
125C4⋊C16—131no—
126#358—261no—
127#358—262no—
128C4×C16—131no—
129#335C2×D1311yescharacteristic
130#332—21no—
131C22×C13#44711yescharacteristic
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—41no—
135C4×C13—161no—
136C4×C13#45211yescharacteristic
137C4×C13#45511yescharacteristic
138C4×C13C2×SD3211yescharacteristic
139C4×C13#51011yescharacteristic
140Dic13—81no—
141Dic13—82no—
142Dic13—81no—
143C2×Q16—41no—
144C2×Q16—131no—
145C2×Q16—132no—
146C2×Q16—262no—
147C2×Q16—261no—
148C4⋊Q8—21no—
149C4⋊Q8—262no—
150C4⋊Q8—261no—
151#125—522no—
152#125—521no—
153C4×Q8—262no—
154C4×Q8—261no—
155C4×Q8—521no—
156C4×Q8C22⋊D1311yescharacteristic
157C2×C16—261no—
158C2×C16—261no—
159#107—21no—
160#107—21no—
161#107—131no—
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#164111yescharacteristic
171C2×C13#218511yescharacteristic
172C2×C13#219511yescharacteristic
173C2×Q8—41no—
174C2×Q8—261no—
175C2×Q8—262no—
176C2×Q8#610411yescharacteristic
177Q16—82no—
178Q16—261no—
179Q16—261no—
180Q16—522no—
181Q16—521no—
182Q16—521no—
183Q16—1042no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8D4×D1311yescharacteristic
187C2×C8D4×D1311yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—261no—
192C4⋊C4—522no—
193C4⋊C4—522no—
194C4⋊C4—522no—
195C4⋊C4—521no—
196C4⋊C4—521no—
197C4⋊C4—521no—
198C4⋊C4#610411yescharacteristic
199C42—21no—
200C42—522no—
201C42—521no—
202C42C2×C22⋊D1311yescharacteristic
203C16—521no—
204C16—521no—
205C13#1238211yescharacteristic, complemented, Sylow
206Q8—21no—
207Q8—81no—
208Q8—81no—
209Q8—521no—
210Q8—522no—
211Q8—522no—
212Q8—521no—
213Q8#8806712yes—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—81no—
217C2×C4—521no—
218C2×C4—522no—
219C2×C4—521no—
220C2×C4C2×#610411yescharacteristic
221C2×C4#8819111yescharacteristic
222C2×C4#8820311yescharacteristic
223C8—21no—
224C8—41no—
225C8—81no—
226C8#8817211yescharacteristic
227C8#8817311yescharacteristic
228C22#1171869711yescharacteristic
229C4—22no—
230C4—21no—
231C4—41no—
232C4—161no—
233C4—1041no—
234C4—1041no—
235C4—1042no—
236C4C2×#8806711yescharacteristic
237C4#1171884811yescharacteristic
238C4#1171885611yescharacteristic
239C4#1171886311yescharacteristic
240C2#1311402711yescharacteristic
241C2#1311675211yescharacteristic
242C2#1311681211yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1674C2
socle, prime radicalC22×C13#447
hypercenter#1674D13
hypocenterC13#12382
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1674

Complements

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

NH ≅ G/Ntype
205. C13#12382semidirect

Maximal subgroups

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

subgroupindex
#131278422
#131170652
#131169752
#131128842
Q8⋊#60902
#131127992
C13×#16742
#1238213