Finite Group Databasebeta

← #13130851

Subgroups — #13130851

Order 1664.

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

normal subgroups only

This group has 360 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
1C2×D13⋊M16C211yesmaximal, characteristic
2D13×C22⋊Q8C211yesmaximal, characteristic
3C2×#88117C212yesmaximal, complemented
4#11719136C211yesmaximal, characteristic
5#11718246C212yesmaximal, complemented
6C2×Q8×D13C2211yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×#6122—21no—
10C2×C4⋊#261C2212yes—
11D13⋊M16—24no—
12C2×#6118—21no—
13C2×D13⋊C8C2212yes—
14C13×C22⋊Q8C411yescharacteristic, complemented
15#88200C411yescharacteristic, complemented
16#88178C411yescharacteristic, complemented
17#88151C411yescharacteristic, complemented
18#88150—21no—
19C4⋊C4×D13—21no—
20C4⋊C4×D13C2211yescharacteristic
21C22⋊C4×D13—21no—
22#88132—21no—
23#88117—24no—
24(C2×#261)⋊C4—21no—
25C23×D13D411yescharacteristic
26C22×#261—22no—
27C2×Q8×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C22×Dic13D411yescharacteristic
30Q8×D13—22no—
31Q8×D13—22no—
32C2×C4×D13—22no—
33C2×C4×D13—22no—
34C2×C4×D13—21no—
35C2×C4×D13—21no—
36C2×C4×D13C2×C411yescharacteristic
37C2×C4×D13D411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×C4×D13C2311yescharacteristic
40C2×Dic26—21no—
41C2×Dic26C2×C411yescharacteristic
42C22⋊#261—42no—
43#6122—24no—
44C2×#1057—22no—
45C4⋊#261—22no—
46C4⋊#261—22no—
47#6118—24no—
48D13⋊C8—22no—
49D13⋊C8D414yes—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2×C411yescharacteristic
52C13×C22⋊C4—21no—
53C22⋊Dic13—21no—
54#6103—21no—
55#6103—21no—
56C4⋊Dic13—21no—
57C4⋊Dic13C2×C411yescharacteristic
58#6101—21no—
59#6101—21no—
60#6101—21no—
61#1894—131nomaximal, Sylow
62C23×C13C22⋊C411yescharacteristic
63C22×D13—22no—
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—22no—
67C22×D13C22⋊C411yescharacteristic
68C22×D13C2×D411yescharacteristic
69C2×#261—42no—
70C2×#261—42no—
71C2×#261—42no—
72Q8×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13C22⋊C411yescharacteristic
77C2×C4×C13C22×C411yescharacteristic
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13C22⋊C411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84C4×D13—22no—
85C4×D13—22no—
86C4×D13—21no—
87C4×D13—21no—
88C4×D13—42no—
89C4×D13—41no—
90C4×D13—41no—
91C4×D13C2×D412yes—
92C4×D13#4112yes—
93Dic26—22no—
94Dic26—41no—
95Dic26—41no—
96#1057—24no—
97C22×M16—131no—
98C2×C22⋊Q8—131no—
99C2×#103—132no—
100#380—131no—
101#340—132no—
102C22×C13—21no—
103C22×C13—21no—
104C22×C13—21no—
105C22×C13C2×C22⋊C411yescharacteristic
106C2×D13—21no—
107C2×D13—21no—
108C2×D13—21no—
109C2×D13—42no—
110C2×D13—42no—
111C2×D13#12112yes—
112C2×D13AGL(1,ℤ/8)11yescharacteristic
113C2×D13#13712yes—
114C2×D13#13711yescharacteristic
115#261—82no—
116C4×C13—21no—
117C4×C13—41no—
118C4×C13—41no—
119C4×C13C4×D412yes—
120Dic13—21no—
121Dic13—41no—
122Dic13—41no—
123Dic13#12011yescharacteristic
124Dic13#12311yescharacteristic
125C22×Q8—131no—
126C23×C4—131no—
127C2×M16—264no—
128C2×M16—261no—
129C2×M16—261no—
130C22×C8—132no—
131C22⋊Q8—131no—
132C22⋊Q8—131no—
133C22⋊Q8—131no—
134C22⋊Q8—261no—
135C22⋊Q8—261no—
136C22⋊Q8#26111yescharacteristic, complemented
137C2×C4⋊C4—131no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—261no—
140C2×C22⋊C4—261no—
141C2×C22⋊C4—261no—
142#103—264no—
143#95—261no—
144C2×C13—41no—
145C2×C13#38611yescharacteristic
146C2×C13#41711yescharacteristic
147C2×C13#41911yescharacteristic
148D13—41no—
149D13#46812yes—
150D13#47012yes—
151C24—131no—
152C2×Q8—131no—
153C2×Q8—261no—
154C2×Q8—262no—
155C2×Q8—262no—
156C2×Q8C2×#26111yescharacteristic
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—262no—
163C22×C4—262no—
164C22×C4—261no—
165C22×C4—261no—
166C22×C4—262no—
167C22×C4C2×#26111yescharacteristic
168M16—264no—
169M16—264no—
170C2×C8—134no—
171C2×C8—262no—
172C2×C8—262no—
173C4⋊C4—21no—
174C4⋊C4—131no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4—261no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—261no—
181C4⋊C4C2×#26111yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—261no—
184C22⋊C4—261no—
185C22⋊C4—261no—
186C22⋊C4—522no—
187C13#189411yescharacteristic, complemented, Sylow
188C23—131no—
189C23—131no—
190C23—261no—
191C23—262no—
192C23—262no—
193C23—261no—
194C23C22⋊#26111yescharacteristic
195Q8—22no—
196Q8—262no—
197Q8—521no—
198Q8—521no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—131no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—131no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—262no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—521no—
215C2×C4—521no—
216C2×C4—522no—
217C2×C4—522no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4C22⋊#26111yescharacteristic
221C2×C4C22×#26111yescharacteristic
222C8—264no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—132no—
227C22—132no—
228C22—131no—
229C22—131no—
230C22—261no—
231C22—261no—
232C22—261no—
233C22—522no—
234C22—522no—
235C22C2×C22⋊#26111yescharacteristic
236C4—21no—
237C4—41no—
238C4—41no—
239C4—131no—
240C4—131no—
241C4—261no—
242C4—521no—
243C4—521no—
244C4—1042no—
245C4D4×#26112yes—
246C2—41no—
247C2—132no—
248C2—132no—
249C2—521no—
250C2#1171915011yescharacteristic
251C2#1171915311yescharacteristic
252C2#1171916411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC22⋊Q8#261
hypocenterC13#1894
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#88117C2semidirect
5. #11718246C2semidirect
14. C13×C22⋊Q8C4semidirect
15. #88200C4semidirect
16. #88178C4semidirect
17. #88151C4semidirect
136. C22⋊Q8#261semidirect
187. C13#1894semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊M162
D13×C22⋊Q82
C2×#881172
#117191362
#117182462
#189413