Finite Group Databasebeta

← #13130830

Subgroups — #13130830

Order 1664.

338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 80 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×Q8×#261C211yesmaximal, characteristic
2C2×Q16×D13C211yesmaximal, characteristic
3(C2×#261)⋊Q8C211yesmaximal, characteristic
4C2×#88117C211yesmaximal, characteristic
5C2×#88117C211yesmaximal, characteristic
6#11718265C211yesmaximal, characteristic
7(C2×#261)⋊C8C211yesmaximal, characteristic
8C2×Q8×D13C2211yescharacteristic
9C2×Q8×D13C2211yescharacteristic
10Q8×#261—22no—
11Q8×#261—22no—
12C2×C4⋊#261—21no—
13C2×C4⋊#261C2211yescharacteristic
14C2×C4⋊#261C2211yescharacteristic
15C2×C4×#261—21no—
16C2×C4×#261C2211yescharacteristic
17C2×D13⋊C8C2211yescharacteristic
18C2×C13×Q16C411yescharacteristic, complemented
19C2×#6107C411yescharacteristic, complemented
20C2×#6107C411yescharacteristic, complemented
21Q16×D13—22no—
22Q16×D13—22no—
23C2×Dic52C411yescharacteristic, complemented
24C2×C8×D13C2211yescharacteristic
25#88117—22no—
26#88117—22no—
27(C2×#261)⋊C4—21no—
28(C2×#261)⋊C4—21no—
29C22×#261—21no—
30C22×#261—21no—
31C22×#261D411yescharacteristic
32C22×#261D411yescharacteristic
33C2×Q8×C13C2×C411yescharacteristic
34C2×Q8×C13C2×C411yescharacteristic
35Q8×D13—21no—
36Q8×D13—21no—
37Q8×D13—21no—
38Q8×D13—21no—
39Q8×D13—21no—
40Q8×D13—21no—
41Q8×D13D412yes—
42Q8×D13D412yes—
43C2×C4×D13—21no—
44C2×C4×D13—21no—
45C2×C4×D13C2311yescharacteristic
46C2×Dic26—21no—
47C2×Dic26—21no—
48C2×Dic26C2×C411yescharacteristic
49C2×Dic26C2×C411yescharacteristic
50C2×#1057—21no—
51C4⋊#261—24no—
52C4⋊#261—21no—
53C4⋊#261—21no—
54C4⋊#261—21no—
55C4⋊#261D412yes—
56C4×#261—24no—
57C4×#261—21no—
58C4×#261—21no—
59D13⋊C8—21no—
60D13⋊C8—21no—
61C13×Q16—22no—
62C2×C8×C13C2×C411yescharacteristic
63#6107—22no—
64#6107—22no—
65C2×#1055C2×C411yescharacteristic
66Dic52—22no—
67C8×D13—21no—
68C8×D13—21no—
69#1878—131nomaximal, Sylow
70C22×D13C2×D411yescharacteristic
71C2×#261—21no—
72C2×#261—21no—
73C2×#261—21no—
74C2×#261—22no—
75C2×#261—21no—
76C2×#261—21no—
77C2×#261—41no—
78C2×#261—41no—
79C2×#261—41no—
80C2×#261—41no—
81C2×#261—41no—
82C2×#261Q1612yescomplemented
83Q8×C13—21no—
84Q8×C13—21no—
85Q8×C13—21no—
86Q8×C13C22⋊C412yes—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13C22×C411yescharacteristic
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13#4111yescharacteristic
93C4×D13—22no—
94C4×D13—22no—
95C4×D13—41no—
96C4×D13—41no—
97C4×D13C2×D411yescharacteristic
98C4×D13C2×D411yescharacteristic
99C4×D13C2×D411yescharacteristic
100C4×D13#4111yescharacteristic
101Dic26—21no—
102Dic26—22no—
103Dic26—22no—
104Dic26—21no—
105Dic26—21no—
106Dic26—41no—
107Dic26—41no—
108Dic26C22⋊C412yes—
109#1057—41no—
110C8×C13—21no—
111#1055—21no—
112C22×Q16—131no—
113C2×C4×Q8—131no—
114C2×#103—131no—
115C2×#103—131no—
116#391—131no—
117#340—131no—
118#336—131no—
119C22×C13C4×D411yescharacteristic
120C2×D13#12011yescharacteristic
121C2×D13#12111yescharacteristic
122C2×D13C2×Q1611yescharacteristic
123C2×D13#13511yescharacteristic
124C2×D13#13711yescharacteristic
125C2×D13#13711yescharacteristic
126#261—22no—
127#261—41no—
128#261—42no—
129#261—81no—
130C4×C13—22no—
131C4×C13—41no—
132C4×C13C2×C22⋊C411yescharacteristic
133C4×C13C4×D411yescharacteristic
134Dic13—22no—
135Dic13—41no—
136Dic13#12111yescharacteristic
137Dic13#12311yescharacteristic
138C22×Q8—131no—
139C22×Q8—131no—
140C2×Q16—131no—
141C2×Q16—131no—
142C2×Q16—131no—
143C2×Q16—262no—
144C2×Q16—262no—
145C2×Q16#26111yescharacteristic, complemented
146C22×C8—131no—
147C22×C8—131no—
148C4×Q8—262no—
149C4×Q8—262no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—261no—
153C2×C42—131no—
154C2×C42—261no—
155#103—262no—
156#103—262no—
157#95—261no—
158#95—261no—
159C2×C13#38611yescharacteristic
160C2×C13C4×Q1611yescharacteristic
161C2×C13#44111yescharacteristic
162D13#45111yescharacteristic
163D13#45211yescharacteristic
164D13#46211yescharacteristic
165D13#46411yescharacteristic
166C2×Q8—132no—
167C2×Q8—132no—
168C2×Q8—131no—
169C2×Q8—131no—
170C2×Q8—261no—
171C2×Q8—261no—
172C2×Q8—261no—
173C2×Q8—261no—
174C2×Q8—261no—
175C2×Q8—261no—
176C2×Q8—261no—
177C2×Q8—261no—
178C2×Q8C2×#26111yescharacteristic
179C2×Q8C2×#26111yescharacteristic
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4—261no—
186C22×C4—261no—
187Q16—22no—
188Q16—262no—
189Q16—262no—
190Q16—262no—
191C2×C8—131no—
192C2×C8—261no—
193C2×C8—261no—
194C2×C8—261no—
195C2×C8—261no—
196C2×C8—261no—
197C2×C8C2×#26111yescharacteristic
198C4⋊C4—132no—
199C4⋊C4—261no—
200C4⋊C4—261no—
201C4⋊C4—261no—
202C4⋊C4—264no—
203C42—261no—
204C42—261no—
205C42—264no—
206C13#187811yescharacteristic, complemented, Sylow
207C23—131no—
208Q8—21no—
209Q8—21no—
210Q8—21no—
211Q8—132no—
212Q8—262no—
213Q8—262no—
214Q8—261no—
215Q8—261no—
216Q8—261no—
217Q8—521no—
218Q8—521no—
219Q8C22⋊#26112yes—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—131no—
223C2×C4—131no—
224C2×C4—131no—
225C2×C4—131no—
226C2×C4—131no—
227C2×C4—132no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—261no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—521no—
239C2×C4—521no—
240C2×C4—521no—
241C2×C4—521no—
242C2×C4—521no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4C22×#26111yescharacteristic
246C8—21no—
247C8—261no—
248C8—521no—
249C22—131no—
250C22—131no—
251C22—131no—
252C22—131no—
253C22—131no—
254C22—131no—
255C22D4×#26111yescharacteristic
256C4—22no—
257C4—41no—
258C4—131no—
259C4—131no—
260C4—262no—
261C4—262no—
262C4—521no—
263C4—522no—
264C4—521no—
265C4—1041no—
266C4D4×#26111yescharacteristic
267C4C2×C22⋊#26111yescharacteristic
268C2—131no—
269C2—131no—
270C2—131no—
271C2—131no—
272C2Q16×#26111yescharacteristic
273C2#1171911011yescharacteristic
274C2#1171915011yescharacteristic
subgroupG/H
centerC22D4×#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×Q16C4
socleC22×C13C4×D4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenterC2×Q16#261
hypocenterC13#1878
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
18. C2×C13×Q16C4semidirect
19. C2×#6107C4semidirect
20. C2×#6107C4semidirect
23. C2×Dic52C4semidirect
82. C2×#261Q16semidirect
145. C2×Q16#261semidirect
206. C13#1878semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#2612
C2×Q16×D132
(C2×#261)⋊Q82
C2×#881172
#117182652
(C2×#261)⋊C82
#187813