Finite Group Databasebeta

← #16791084

Subgroups — #16791084

Order 3328.

354 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 104 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#13131043C211yesmaximal, characteristic
2#13130773C211yesmaximal, characteristic
3#13129907C214yesmaximal
4#13125347C211yesmaximal, characteristic
5#11719433—21no—
6C2×#88102—21no—
7C2×#88101C2212yes—
8C2×#88098C2212yes—
9#11719060—21no—
10C13×#500C411yescharacteristic, complemented
11#11718740—21no—
12#11718541—21no—
13#11718541C2212yes—
14#11718539—21no—
15#11718539C412yescomplemented
16C4×C8×D13C2211yescharacteristic
17#11718343C411yescharacteristic, complemented
18#11718257—21no—
19#11718231—21no—
20C2×C4⋊#261—22no—
21C13×C4⋊Q8—21no—
22#88200—41no—
23Q8×Dic13—41no—
24C2×C8×D13D411yescharacteristic
25C2×C8×D13C2311yescharacteristic
26#88151—41no—
27#88146—22no—
28#88144—22no—
29#88141—41no—
30C42×D13D411yescharacteristic
31#88123—21no—
32(C2×#261)⋊C4—41no—
33(C2×#261)⋊C4—41no—
34C2×#6092—22no—
35#88102—42no—
36#88101—24no—
37#88098—22no—
38#88098Q814yescomplemented
39C13×#107—21no—
40C13×#107C2×C412yes—
41C4×C8×C13C2×C411yescharacteristic
42#88058—21no—
43#88058C2×C412yes—
44C8×Dic13C2×C411yescharacteristic
45C8×Dic13D411yescharacteristic
46#88048—22no—
47#88048—22no—
48C4×#1055D411yescharacteristic
49#13288—131nomaximal, Sylow
50C22×#261—42no—
51C2×Q8×C13—41no—
52C2×C4×D13D811yescharacteristic
53C2×C4×D13D811yescharacteristic
54C2×C4×D13C2×D411yescharacteristic
55C2×Dic26—41no—
56C4⋊#261—42no—
57C4⋊#261—42no—
58C2×C8×C13C22⋊C411yescharacteristic
59C2×C8×C13C22×C411yescharacteristic
60C13×C4⋊C4—22no—
61C13×C4⋊C4—41no—
62C42×C13C22⋊C411yescharacteristic
63#6103—42no—
64C4⋊Dic13—22no—
65C4⋊Dic13—41no—
66C4⋊Dic13—42no—
67#6101—42no—
68C4×Dic13—42no—
69C4×Dic13C22⋊C411yescharacteristic
70C4×Dic13SD1611yescharacteristic
71C4×Dic13SD1611yescharacteristic
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C2×D411yescharacteristic
74C8×D13SD1612yes—
75C8×D13Q1612yes—
76C8×D13C2×Q812yes—
77C8×D13#4112yes—
78#6092—24no—
79#3160—131no—
80C4×M32—131no—
81#1846—131no—
82#1386—134no—
83C22×D13C2×D811yescharacteristic
84C2×#261—82no—
85C2×#261—82no—
86C2×#261—82no—
87Q8×C13—82no—
88C2×C4×C13—42no—
89C2×C4×C13#10211yescharacteristic
90C2×C4×C13#10211yescharacteristic
91C2×C4×C13C2×C22⋊C411yescharacteristic
92C2×Dic13—42no—
93C2×Dic13#10211yescharacteristic
94C2×Dic13#10211yescharacteristic
95C2×Dic13C2×SD1611yescharacteristic
96C4×D13—41no—
97C4×D13—41no—
98C4×D13#12411yescharacteristic
99C4×D13C4⋊Q811yescharacteristic
100C4×D13C2×SD1611yescharacteristic
101C4×D13C2×Q1611yescharacteristic
102Dic26—82no—
103C8×C13#10312yes—
104C8×C13C4×Q812yes—
105#1055#10312yes—
106#1055C22⋊Q812yes—
107#533—261no—
108C2×M32—132no—
109#500—131no—
110#500#26111yescharacteristic, complemented
111#499—132no—
112#499—261no—
113#498—261no—
114#427—132no—
115#427—261no—
116C2×#107—261no—
117C2×#106—132no—
118C2×C4×C8—131no—
119#382—261no—
120#346—261no—
121C4×C16—261no—
122C22×C13C2×#10211yescharacteristic
123C2×D13—21no—
124C2×D13—21no—
125C2×D13#48611yescharacteristic
126C2×D13#50011yescharacteristic
127#261—162no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—82no—
131C4×C13#39111yescharacteristic
132C4×C13C2×#10311yescharacteristic
133Dic13—21no—
134Dic13—21no—
135Dic13—82no—
136Dic13#48711yescharacteristic
137Dic13#49811yescharacteristic
138C22×C8—131no—
139C22×C8—131no—
140C4⋊Q8—21no—
141C4⋊Q8—261no—
142#125—262no—
143C22⋊Q8—521no—
144C22⋊Q8—521no—
145C4×Q8—521no—
146C4×Q8—521no—
147#117—262no—
148C2×C4⋊C4—262no—
149C2×C42—131no—
150M32—134no—
151M32—262no—
152C2×C16—262no—
153#107—21no—
154#107—132no—
155#107—261no—
156#107—522no—
157#107C2×#26112yes—
158#106—262no—
159#106—262no—
160#106—264no—
161C4×C8—131no—
162C4×C8—131no—
163C4×C8—131no—
164C4×C8C2×#26111yescharacteristic
165#95—521no—
166#95—521no—
167C2×C13#199011yescharacteristic
168C2×C13#214511yescharacteristic
169C2×C13#214511yescharacteristic
170D13—21no—
171D13—21no—
172C2×Q8—41no—
173C2×Q8—521no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—131no—
177C22×C4—522no—
178C2×C8—131no—
179C2×C8—131no—
180C2×C8—132no—
181C2×C8—132no—
182C2×C8—132no—
183C2×C8—132no—
184C2×C8C22⋊#26111yescharacteristic
185C2×C8C22×#26111yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—262no—
189C4⋊C4—522no—
190C4⋊C4—522no—
191C4⋊C4—522no—
192C4⋊C4—522no—
193C4⋊C4—521no—
194C22⋊C4—522no—
195C42—131no—
196C42—131no—
197C42—131no—
198C42—522no—
199C42C22⋊#26111yescharacteristic
200C16—264no—
201C13#1328811yescharacteristic, complemented, Sylow
202C23—131no—
203Q8—82no—
204Q8—1042no—
205C2×C4—42no—
206C2×C4—131no—
207C2×C4—131no—
208C2×C4—131no—
209C2×C4—131no—
210C2×C4—131no—
211C2×C4—131no—
212C2×C4—131no—
213C2×C4—521no—
214C2×C4—521no—
215C2×C4—522no—
216C2×C4—1042no—
217C2×C4—1042no—
218C2×C4—1042no—
219C2×C4#8811511yescharacteristic
220C2×C4#8811511yescharacteristic
221C2×C4C2×C22⋊#26111yescharacteristic
222C8—132no—
223C8—132no—
224C8#8811712yes—
225C8Q8×#26112yes—
226C22—131no—
227C22—131no—
228C22—261no—
229C22—261no—
230C22C2×#8811511yescharacteristic
231C4—21no—
232C4—21no—
233C4—82no—
234C4—131no—
235C4—131no—
236C4—261no—
237C4—261no—
238C4—1042no—
239C4—2082no—
240C4C2×#8811711yescharacteristic
241C4(C2×#261)⋊Q811yescharacteristic
242C2—261no—
243C2—261no—
244C2#1313101711yescharacteristic
245C2#1313115711yescharacteristic
246C2#1313115811yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#500C4
socleC22×C13C2×#102
prime radicalC22×D13C2×D8
cosocleC2×C8×D13C23
hypercenter#500#261
hypocenterC13#13288
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
10. C13×#500C4semidirect
15. #11718539C4semidirect
17. #11718343C4semidirect
38. #88098Q8semidirect
110. #500#261semidirect
201. C13#13288semidirect

Maximal subgroups

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

subgroupindex
#131310432
#131307732
#131299072
#131253472
#1328813