Finite Group Databasebeta

← #15761858

Subgroups — #15761858

Order 3328.

434 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×C4×Dic52C211yesmaximal, characteristic
2#13113232C212yesmaximal
3#13113159C212yesmaximal
4#13113128C211yesmaximal, characteristic
5C13×#1564C211yesmaximal, characteristic
6C22×Dic52C411yescharacteristic
7C2×C4×Dic26C2212yes—
8C13×#431C2212yes—
9C2×C4×C8×C13C2211yescharacteristic
10C2×#88058C411yescharacteristic
11C2×#88056C412yes—
12#11718586C2211yescharacteristic
13#11718586C2211yescharacteristic
14C4×Dic52—21no—
15C4×Dic52—21no—
16C4×Dic52—21no—
17C4×Dic52—21no—
18C13×#335—21no—
19C13×#334—21no—
20#11718061—24no—
21#11718048—24no—
22#11718046—21no—
23#11718046—21no—
24C22×Dic26C2×C412yes—
25C22×C8×C13C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13C2×C412yes—
29C2×#6101—22no—
30C2×C4×Dic13—22no—
31C2×Dic52—24no—
32C2×Dic52—21no—
33C2×Dic52—21no—
34C4×Dic26—22no—
35C4×Dic26—22no—
36C4×Dic26—22no—
37C4×Dic26—22no—
38C13×C4⋊C8—22no—
39C13×C22⋊C8—22no—
40C4×C8×C13—22no—
41C4×C8×C13D411yescharacteristic
42C4×C8×C13D411yescharacteristic
43C4×C8×C13D411yescharacteristic
44C4×C8×C13D411yescharacteristic
45C22⋊#1055—21no—
46C22⋊#1055D412yes—
47#88058—21no—
48#88058—21no—
49#88056—22no—
50#88056—22no—
51C4⋊#1055—21no—
52C4⋊#1055D412yes—
53C4×#1055—21no—
54C4×#1055—21no—
55#9671—131nomaximal, Sylow
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13#4111yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C2×Dic26—22no—
62C2×Dic26—22no—
63C2×Dic26—22no—
64C2×Dic26—22no—
65C2×Dic26—22no—
66C2×Dic26M1614yes—
67C2×C8×C13—22no—
68C2×C8×C13—22no—
69C2×C8×C13—42no—
70C2×C8×C13C22⋊C411yescharacteristic
71C2×C8×C13C22⋊C411yescharacteristic
72C2×C8×C13C22⋊C411yescharacteristic
73C2×C8×C13C22⋊C411yescharacteristic
74C42×C13C2×D411yescharacteristic
75C42×C13C2×D411yescharacteristic
76C42×C13C2×D411yescharacteristic
77C42×C13#4111yescharacteristic
78C4⋊Dic13—22no—
79C4⋊Dic13—22no—
80#6101—42no—
81#6101—42no—
82C4×Dic13—42no—
83C4×Dic13—42no—
84C2×#1055—22no—
85C2×#1055—22no—
86Dic52—24no—
87Dic52—24no—
88C2×C4×Q16—131no—
89#1564D1311yescharacteristic
90#1479—132no—
91#1461—132no—
92#1452—131no—
93C23×C13C4×D411yescharacteristic
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13C4×D411yescharacteristic
98C2×C4×C13#12111yescharacteristic
99C2×C4×C13#12111yescharacteristic
100C2×C4×C13#12411yescharacteristic
101C2×C4×C13#12711yescharacteristic
102C2×C4×C13C2×M1612yes—
103C2×C4×C13#13112yes—
104C2×Dic13—24no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—82no—
109Dic26—24no—
110Dic26—24no—
111Dic26—42no—
112Dic26—42no—
113C8×C13—21no—
114C8×C13—21no—
115C8×C13—21no—
116C8×C13—21no—
117C8×C13—82no—
118#1055—42no—
119#1055—42no—
120C22×Q16—131no—
121C2×C4×Q8—132no—
122C4×Q16—261no—
123C4×Q16—261no—
124C4×Q16—261no—
125C4×Q16—261no—
126#431—131no—
127#431—131no—
128#431C2×D1312yes—
129C2×#107—131no—
130C2×#103—132no—
131C2×C4×C8C2×D1311yescharacteristic
132#335—21no—
133#334—21no—
134Q8⋊C8—264no—
135#324—264no—
136#322—261no—
137#322—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#39011yescharacteristic
141C22×C13#43512yes—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—21no—
145C4×C13#40711yescharacteristic
146C4×C13#40811yescharacteristic
147C4×C13#43512yes—
148C4×C13#47312yes—
149Dic13—44no—
150Dic13—82no—
151C22×Q8—132no—
152C2×Q16—264no—
153C2×Q16—261no—
154C2×Q16—261no—
155C22×C8C4×D1311yescharacteristic
156C22×C8C4×D1311yescharacteristic
157C4×Q8—262no—
158C4×Q8—262no—
159C4×Q8—262no—
160C4×Q8—262no—
161C2×C4⋊C4—132no—
162C2×C4⋊C4—262no—
163C2×C42—262no—
164C2×C42C22×D1311yescharacteristic
165#107—261no—
166#107—261no—
167C4⋊C8—22no—
168C4⋊C8—132no—
169C4⋊C8—261no—
170#103—262no—
171#103—262no—
172C22⋊C8—22no—
173C22⋊C8—132no—
174C22⋊C8—261no—
175C4×C8—22no—
176C4×C8—261no—
177C4×C8—261no—
178C4×C8D5211yescharacteristic
179C4×C8D5211yescharacteristic
180C4×C8C22⋊D1311yescharacteristic
181C4×C8C22⋊D1311yescharacteristic
182C2×C13—22no—
183C2×C13#195511yescharacteristic
184C2×C13#197611yescharacteristic
185C2×C13#197911yescharacteristic
186C2×Q8—134no—
187C2×Q8—262no—
188C2×Q8—262no—
189C2×Q8—262no—
190C2×Q8—262no—
191C2×Q8—262no—
192C22×C4—262no—
193C22×C4—262no—
194C22×C4C2×C4×D1311yescharacteristic
195C22×C4D4×D1311yescharacteristic
196C22×C4#613111yescharacteristic
197Q16—264no—
198Q16—264no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—42no—
202C2×C8—262no—
203C2×C8—262no—
204C2×C8#610311yescharacteristic
205C2×C8#610311yescharacteristic
206C2×C8#610311yescharacteristic
207C2×C8#610311yescharacteristic
208C4⋊C4—262no—
209C4⋊C4—262no—
210C4⋊C4—522no—
211C4⋊C4—522no—
212C42—522no—
213C42—522no—
214C42C2×D5211yescharacteristic
215C42D4×D1311yescharacteristic
216C42#613111yescharacteristic
217C42C2×C22⋊D1311yescharacteristic
218C13#967111yescharacteristic, complemented, Sylow
219C23#8814711yescharacteristic
220Q8—264no—
221Q8—264no—
222Q8—522no—
223Q8—522no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—264no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4—1042no—
231C2×C4#8814711yescharacteristic
232C2×C4#8814911yescharacteristic
233C2×C4#8814911yescharacteristic
234C2×C4#8815512yes—
235C2×C4M16×D1312yes—
236C2×C4C2×#610311yescharacteristic
237C2×C4#8819411yescharacteristic
238C2×C4#8820111yescharacteristic
239C8—21no—
240C8—21no—
241C8—21no—
242C8—21no—
243C8—82no—
244C8—522no—
245C8—522no—
246C22—21no—
247C22—21no—
248C22#1171849712yes—
249C22#1171864911yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—524no—
254C4—1042no—
255C4#1171849712yes—
256C4#1171855712yes—
257C4#1171877111yescharacteristic
258C4#1171878711yescharacteristic
259C2—22no—
260C2#1311563311yescharacteristic
261C2#1311573211yescharacteristic
262C2#1311574911yescharacteristic
subgroupG/H
centerC2×C4#88149
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1564C2
socleC22×C13#390
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#1564D13
hypocenterC13#9671
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
218. C13#9671semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic522
#131132322
#131131592
#131131282
C13×#15642
#967113