Finite Group Databasebeta

← #13130986

Subgroups — #13130986

Order 1664.

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

normal subgroups only

This group has 340 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×SD16×D13C211yesmaximal, characteristic
2(C2×#261)⋊Q8C211yesmaximal, characteristic, complemented
3C2×#88117C211yesmaximal, characteristic, complemented
4#11719151C211yesmaximal, characteristic
5C2×#88115C211yesmaximal, characteristic
6C2×#88102C211yesmaximal, characteristic, complemented
7C2×#88100C211yesmaximal, characteristic, complemented
8C2×Q8×D13C2211yescharacteristic
9C2×D4×D13C2211yescharacteristic
10C2×C22⋊#261—22no—
11C2×C4⋊#261C2211yescharacteristic
12C2×C4⋊#261C2211yescharacteristic
13C2×C4×#261C2211yescharacteristic
14C2×D13⋊C8C2211yescharacteristic
15C2×C13×SD16C411yescharacteristic, complemented
16C2×#6106C411yescharacteristic, complemented
17C2×#6105C411yescharacteristic, complemented
18SD16×D13—22no—
19SD16×D13—22no—
20C2×#6095C411yescharacteristic, complemented
21C2×C8×D13C2211yescharacteristic
22#88117—22no—
23#88115—22no—
24(C2×#261)⋊C4—22no—
25#88102—22no—
26#88100—22no—
27C23×D13—21no—
28C22×#261—21no—
29C22×#261—21no—
30C22×#261D412yes—
31C2×Q8×C13C2×C411yescharacteristic
32C2×D4×C13C2×C411yescharacteristic
33C2×C22⋊D13—21no—
34Q8×D13—21no—
35Q8×D13—21no—
36Q8×D13—21no—
37Q8×D13—21no—
38D4×D13—21no—
39D4×D13—21no—
40D4×D13—21no—
41D4×D13—21no—
42C2×D52C2×C411yescharacteristic
43C2×C4×D13—21no—
44C2×C4×D13C2311yescharacteristic
45C2×Dic26—21no—
46C2×Dic26C2×C411yescharacteristic
47C22⋊#261—44no—
48C2×#1057—21no—
49C4⋊#261—21no—
50C4⋊#261—21no—
51C4⋊#261—21no—
52C4⋊#261—21no—
53C4×#261—21no—
54C4×#261—21no—
55D13⋊C8—21no—
56D13⋊C8D412yes—
57C13×SD16—22no—
58C2×C8×C13C2×C411yescharacteristic
59#6106—22no—
60#6105—22no—
61C2×#1055C2×C411yescharacteristic
62#6095—22no—
63C8×D13D412yes—
64C8×D13D412yes—
65#1973—131nomaximal, Sylow
66C23×C13—21no—
67C22×D13—21no—
68C22×D13—41no—
69C22×D13—41no—
70C22×D13—42no—
71C22×D13—42no—
72C22×D13C2×D411yescharacteristic
73C2×#261—22no—
74C2×#261—22no—
75C2×#261—22no—
76C2×#261—41no—
77C2×#261—41no—
78C2×#261—42no—
79C2×#261—42no—
80Q8×C13—21no—
81Q8×C13—21no—
82D4×C13—21no—
83D4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13C22×C411yescharacteristic
86C22⋊D13—41no—
87C22⋊D13—41no—
88C2×Dic13—21no—
89C2×Dic13#4111yescharacteristic
90D52—21no—
91D52—21no—
92C4×D13—41no—
93C4×D13—41no—
94C4×D13C2×D411yescharacteristic
95C4×D13C2×D411yescharacteristic
96C4×D13C2×D411yescharacteristic
97C4×D13#4111yescharacteristic
98Dic26—21no—
99Dic26—21no—
100Dic26—41no—
101Dic26—41no—
102#1057—22no—
103C8×C13C22⋊C412yescomplemented
104#1055C22⋊C412yescomplemented
105C22×SD16—131no—
106C2×#107—131no—
107C2×#103—131no—
108C2×#102—131no—
109C2×#97—131no—
110#391—131no—
111#390—131no—
112C22×C13—41no—
113C22×C13—42no—
114C22×C13C4×D411yescharacteristic
115C2×D13—41no—
116C2×D13—42no—
117C2×D13—82no—
118C2×D13—81no—
119C2×D13—81no—
120C2×D13#12111yescharacteristic
121C2×D13#12711yescharacteristic
122C2×D13AGL(1,ℤ/8)12yes—
123C2×D13#13712yes—
124#261—42no—
125#261—81no—
126#261—81no—
127C4×C13—41no—
128C4×C13C2×C22⋊C411yescharacteristic
129C4×C13C4×D411yescharacteristic
130Dic13—41no—
131Dic13#12111yescharacteristic
132Dic13#12411yescharacteristic
133C22×Q8—131no—
134C22×D4—131no—
135C2×SD16—131no—
136C2×SD16—131no—
137C2×SD16—131no—
138C2×SD16—262no—
139C2×SD16—262no—
140C2×SD16#26111yescharacteristic, complemented
141C22×C8—131no—
142C22×C8—131no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—131no—
145C2×C22⋊C4—262no—
146C2×C42—131no—
147#107—262no—
148#103—262no—
149#102—262no—
150#97—262no—
151#95—262no—
152C2×C13—81no—
153C2×C13#39011yescharacteristic
154C2×C13#44012yes—
155D13—81no—
156D13#46812yes—
157D13#49611yescharacteristic
158D13#49711yescharacteristic
159C24—261no—
160C2×Q8—131no—
161C2×Q8—261no—
162C2×Q8—261no—
163C2×Q8—261no—
164C2×Q8—261no—
165C2×Q8—261no—
166C2×Q8C2×#26111yescharacteristic
167C2×D4—131no—
168C2×D4—261no—
169C2×D4—261no—
170C2×D4—261no—
171C2×D4—261no—
172C2×D4—261no—
173C2×D4C2×#26111yescharacteristic
174C22×C4—131no—
175C22×C4—132no—
176C22×C4—261no—
177C22×C4—261no—
178C22×C4—261no—
179SD16—22no—
180SD16—262no—
181SD16—262no—
182SD16—262no—
183C2×C8—131no—
184C2×C8—132no—
185C2×C8—132no—
186C2×C8—132no—
187C2×C8—261no—
188C2×C8—261no—
189C2×C8C2×#26111yescharacteristic
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C22⋊C4—524no—
195C42—261no—
196C42—261no—
197C13#197311yescharacteristic, complemented, Sylow
198C23—21no—
199C23—131no—
200C23—261no—
201C23—522no—
202C23—521no—
203C23—521no—
204C23—522no—
205Q8—21no—
206Q8—21no—
207Q8—261no—
208Q8—261no—
209Q8—521no—
210Q8—521no—
211D4—21no—
212D4—21no—
213D4—261no—
214D4—261no—
215D4—521no—
216D4—521no—
217C2×C4—21no—
218C2×C4—131no—
219C2×C4—131no—
220C2×C4—131no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—261no—
227C2×C4—521no—
228C2×C4—521no—
229C2×C4—522no—
230C2×C4—521no—
231C2×C4—521no—
232C2×C4—522no—
233C2×C4C22×#26111yescharacteristic
234C8—132no—
235C8—262no—
236C8C22⋊#26112yescomplemented
237C22—42no—
238C22—41no—
239C22—132no—
240C22—132no—
241C22—131no—
242C22—131no—
243C22—522no—
244C22—521no—
245C22—1042no—
246C22—1041no—
247C22—1041no—
248C22D4×#26111yescharacteristic
249C4—41no—
250C4—131no—
251C4—131no—
252C4—522no—
253C4—521no—
254C4—1041no—
255C4—1041no—
256C4D4×#26111yescharacteristic
257C4C2×C22⋊#26111yescharacteristic
258C2—81no—
259C2—132no—
260C2—131no—
261C2—131no—
262C2—1041no—
263C2#1171910612yes—
264C2#1171915111yescharacteristic
subgroupG/H
centerC22D4×#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×SD16C4
socleC22×C13C4×D4
prime radicalC2×D4×D13C22
cosocleC2×C4×D13C23
hypercenterC2×SD16#261
hypocenterC13#1973
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. (C2×#261)⋊Q8C2semidirect
3. C2×#88117C2semidirect
6. C2×#88102C2semidirect
7. C2×#88100C2semidirect
15. C2×C13×SD16C4semidirect
16. C2×#6106C4semidirect
17. C2×#6105C4semidirect
20. C2×#6095C4semidirect
103. C8×C13C22⋊C4semidirect
104. #1055C22⋊C4semidirect
140. C2×SD16#261semidirect
197. C13#1973semidirect
236. C8C22⋊#261semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D132
(C2×#261)⋊Q82
C2×#881172
#117191512
C2×#881152
C2×#881022
C2×#881002
#197313