Finite Group Databasebeta

← #16788584

Subgroups — #16788584

Order 3328.

288 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 78 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#13131195C211yesmaximal, characteristic
2#13130399C211yesmaximal, characteristic
3#13129855C212yesmaximal, complemented
4#13129854C212yesmaximal, complemented
5#13125349C211yesmaximal, characteristic
6#11719393—21no—
7#11719054—21no—
8C13×#499C411yescharacteristic
9#11718725—21no—
10#11718541C411yescharacteristic
11#11718541C411yescharacteristic
12#11718535C2211yescharacteristic
13#11718535C2211yescharacteristic
14#11718521—21no—
15#11718516—21no—
16C4×C8×D13C2211yescharacteristic
17#11718344C411yescharacteristic
18#11718260C2212yes—
19#11718259—21no—
20#11718256C2212yes—
21#11718255—21no—
22C4×#6092—21no—
23C13×#125—21no—
24C2×C8×D13C2×C411yescharacteristic
25C2×C8×D13D411yescharacteristic
26#88150—41no—
27#88150—41no—
28#88146—21no—
29#88146—21no—
30#88142—21no—
31#88142—21no—
32#88141—41no—
33#88141—41no—
34C42×D13D411yescharacteristic
35#88124—21no—
36#88111—41no—
37#88110—41no—
38C4⋊#1057—22no—
39C2×#6092—22no—
40C13×#107C2×C411yescharacteristic
41C13×#107C2×C411yescharacteristic
42C13×#106—21no—
43C4×C8×C13C2×C411yescharacteristic
44#88058C2×C411yescharacteristic
45#88058C2×C411yescharacteristic
46#88057—21no—
47C8×Dic13D411yescharacteristic
48C8×Dic13C2311yescharacteristic
49#88048—21no—
50#88048—21no—
51#88047—21no—
52#88047—21no—
53C4×#1055D411yescharacteristic
54#11973—131nomaximal, Sylow
55C2×C4×D13C22⋊C411yescharacteristic
56C2×C4×D13D811yescharacteristic
57C2×C4×D13SD1611yescharacteristic
58C2×Dic26—41no—
59C2×Dic26—41no—
60C2×#1057—42no—
61C2×C8×C13C22⋊C411yescharacteristic
62C2×C8×C13C22×C411yescharacteristic
63C13×C4⋊C4—21no—
64C13×C4⋊C4—21no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C42×C13C22⋊C411yescharacteristic
68#6103—41no—
69#6103—41no—
70C4⋊Dic13—21no—
71C4⋊Dic13—21no—
72#6101—41no—
73#6101—41no—
74#6101—41no—
75#6101—41no—
76C4×Dic13—41no—
77C4×Dic13—41no—
78C4×Dic13D811yescharacteristic
79C4×Dic13SD1611yescharacteristic
80C4×Dic13C2×D411yescharacteristic
81C2×#1055C22⋊C411yescharacteristic
82C2×#1055C2×D411yescharacteristic
83C8×D13—22no—
84C8×D13—22no—
85#6092—42no—
86#3160—131no—
87#2162—131no—
88#1568—131no—
89#1365—132no—
90#1364—132no—
91C22×D13#10211yescharacteristic
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13#10211yescharacteristic
95C2×C4×C13#10211yescharacteristic
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×Dic13—41no—
98C2×Dic13—41no—
99C2×Dic13#10211yescharacteristic
100C2×Dic13C2×D811yescharacteristic
101C2×Dic13C2×SD1611yescharacteristic
102C4×D13—21no—
103C4×D13—21no—
104C4×D13—22no—
105C4×D13—41no—
106Dic26—82no—
107Dic26—82no—
108#1057—82no—
109C8×C13—21no—
110C8×C13—21no—
111#1055#10112yes—
112#1055#13712yes—
113#533—261no—
114#500—131no—
115#500—131no—
116#499—131no—
117#499—261no—
118#499#26111yescharacteristic
119#498—261no—
120#432—261no—
121#427—131no—
122#427—131no—
123#427—261no—
124C2×C4×C8—131no—
125C4⋊C16—132no—
126C22⋊C16—261no—
127C4×C16—261no—
128#335—132no—
129#334—261no—
130C22×C13C2×#10211yescharacteristic
131C2×D13—21no—
132C2×D13—21no—
133C2×D13—21no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—81no—
137C4×C13—81no—
138C4×C13C2×#10111yescharacteristic
139C4×C13#41911yescharacteristic
140Dic13—21no—
141Dic13—21no—
142Dic13—81no—
143Dic13—81no—
144Dic13#50812yes—
145C22×C8—131no—
146C22×C8—131no—
147C4⋊Q8—261no—
148C4⋊Q8—261no—
149#125—21no—
150#125—261no—
151C22⋊Q8—521no—
152C22⋊Q8—521no—
153C4×Q8—521no—
154C4×Q8—521no—
155#117—261no—
156#117—261no—
157C2×C42—131no—
158C2×C16—262no—
159#107—131no—
160#107—131no—
161#107—261no—
162#107—261no—
163#107C2×#26111yescharacteristic
164#107C2×#26111yescharacteristic
165#106—21no—
166#106—261no—
167#106—261no—
168#106—261no—
169C4⋊C8—262no—
170C22⋊C8—521no—
171#97—521no—
172C4×C8—131no—
173C4×C8—131no—
174C4×C8—131no—
175C4×C8C2×#26111yescharacteristic
176C2×C13#154611yescharacteristic
177C2×C13#213811yescharacteristic
178C2×C13#214811yescharacteristic
179D13—41no—
180C2×Q8—521no—
181C2×Q8—521no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C2×C8—131no—
186C2×C8—131no—
187C2×C8—262no—
188C2×C8—262no—
189C2×C8—522no—
190C2×C8C22⋊#26111yescharacteristic
191C2×C8C22×#26111yescharacteristic
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—521no—
199C4⋊C4—521no—
200C4⋊C4—521no—
201C4⋊C4—521no—
202C22⋊C4—521no—
203C22⋊C4—521no—
204C42—131no—
205C42—131no—
206C42—131no—
207C42—521no—
208C42—521no—
209C42C22⋊#26111yescharacteristic
210C16—522no—
211C13#1197311yescharacteristic, complemented, Sylow
212C23—131no—
213Q8—1042no—
214Q8—1042no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—131no—
218C2×C4—131no—
219C2×C4—131no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—521no—
224C2×C4—521no—
225C2×C4—521no—
226C2×C4#8811511yescharacteristic
227C2×C4#8811511yescharacteristic
228C2×C4C2×C22⋊#26111yescharacteristic
229C8—21no—
230C8—21no—
231C8—132no—
232C8—132no—
233C8—1042no—
234C22—261no—
235C22—261no—
236C22—261no—
237C22C2×#8811511yescharacteristic
238C4—21no—
239C4—21no—
240C4—81no—
241C4—81no—
242C4—132no—
243C4—261no—
244C4—261no—
245C4—1041no—
246C4—1041no—
247C4#1171915311yescharacteristic
248C4D13⋊#10111yescharacteristic
249C2—521no—
250C2#1313034611yescharacteristic
251C2#1313114311yescharacteristic
252C2#1313116311yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#499C4
socleC22×C13C2×#102
prime radicalC22×D13#102
cosocleC8×Dic13C23
hypercenter#499#261
hypocenterC13#11973
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
3. #13129855C2semidirect
4. #13129854C2semidirect
211. C13#11973semidirect

Maximal subgroups

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

subgroupindex
#131311952
#131303992
#131298552
#131298542
#131253492
#1197313