Finite Group Databasebeta

← #13118491

Subgroups — #13118491

Order 1664.

852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×Q8×D13C211yesmaximal, characteristic, complemented
2C2×C13×#124C211yesmaximal, characteristic, complemented
3C2×#88192C211yesmaximal, characteristic
4C2×#88190C211yesmaximal, characteristic, complemented
5#11718891C211yesmaximal, characteristic, complemented
6#11718617C214yesmaximal, complemented
7#11718608C214yesmaximal, complemented
8C4×#6103C211yesmaximal, characteristic, complemented
9#11718590C211yesmaximal, characteristic, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic
12C22×C22⋊D13C2212yes—
13C2×Q8×D13—24no—
14C2×Q8×D13—24no—
15C2×Q8×D13—24no—
16C22×C4×D13C2212yes—
17C22×C4×D13C2211yescharacteristic
18C22×Dic26C2212yes—
19C22×Dic26C2211yescharacteristic
20C13×#124—24no—
21C2×C13×C22⋊C4C2214yes—
22C2×C42×C13C2211yescharacteristic
23C2×C22⋊Dic13C2214yes—
24C2×C22⋊Dic13C2212yes—
25#88192—24no—
26#88190—24no—
27C2×#6103C2212yes—
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30#88071C2214yes—
31#88071C2212yes—
32#88071C2214yes—
33C24×C13C2312yes—
34C23×D13C2311yescharacteristic
35C2×Q8×C13—22no—
36C2×Q8×C13—22no—
37C2×Q8×C13D414yescomplemented
38C2×D4×C13—22no—
39C2×D4×C13—22no—
40C2×D4×C13—22no—
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13—24no—
45C2×C22⋊D13—28no—
46C22×Dic13C2312yes—
47C22×Dic13C2312yes—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2312yes—
50Q8×D13—232no—
51C2×C4×D13—24no—
52C2×C4×D13—24no—
53C2×C4×D13—22no—
54C2×C4×D13—22no—
55C2×C4×D13—24no—
56C2×C4×D13D414yes—
57C2×Dic26—24no—
58C2×Dic26—22no—
59C2×Dic26—22no—
60C2×Dic26—24no—
61C2×Dic26—24no—
62C2×Dic26D414yescomplemented
63C13×C22⋊C4—28no—
64C42×C13—22no—
65C22⋊Dic13—28no—
66C22⋊Dic13—24no—
67#6103—24no—
68C4⋊Dic13—22no—
69C4×Dic13—22no—
70#2436—131nomaximal, Sylow
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—24no—
75C23×C13—24no—
76C23×C13C2411yescharacteristic
77C22×D13—21no—
78C22×D13—21no—
79C22×D13—22no—
80C22×D13C2×D412yes—
81C22×D13#4114yes—
82Q8×C13—28no—
83D4×C13—44no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13C2×D414yes—
90C2×C4×C13C2×D412yes—
91C2×C4×C13C2×D412yes—
92C2×C4×C13C2×D412yes—
93C22⋊D13—48no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—24no—
102C2×Dic13—22no—
103C2×Dic13C2×D412yes—
104C2×Dic13C2×D414yes—
105C4×D13—216no—
106C4×D13—28no—
107Dic26—216no—
108Dic26—28no—
109C23×Q8—131no—
110C2×#124—131no—
111C2×#124D1311yescharacteristic, complemented
112C2×#121—131no—
113#393—134no—
114#391—131no—
115#391—131no—
116#386—134no—
117C4×C22⋊C4—131no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—44no—
122C22×C13—44no—
123C22×C13C22×D411yescharacteristic
124C22×C13C22×D411yescharacteristic
125C22×C13C22×D411yescharacteristic
126C22×C13C2×#4112yes—
127C22×C132−1+412yes—
128C2×D13—22no—
129C2×D13—22no—
130C2×D13—24no—
131C2×D13—24no—
132C2×D13#12414yescomplemented
133C4×C13—24no—
134C4×C13—42no—
135C4×C13#12014yes—
136Dic13—22no—
137Dic13—24no—
138Dic13—42no—
139Dic13—42no—
140C22×Q8—131no—
141C22×Q8—132no—
142C22×Q8—264no—
143C22×Q8—264no—
144C22×Q8—264no—
145C22×Q8C2×D1311yescharacteristic
146C22×D4—132no—
147C22×D4C2×D1311yescharacteristic
148C23×C4—131no—
149C23×C4—132no—
150#124—24no—
151#124—264no—
152#121—264no—
153C2×C4⋊C4—131no—
154C2×C22⋊C4—132no—
155C2×C22⋊C4—134no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4C2×D1314yes—
158C2×C42—131no—
159C2×C42C2×D1311yescharacteristic
160#95—132no—
161#95—134no—
162#95—134no—
163C2×C13—82no—
164C2×C13C2×#12011yescharacteristic
165C2×C13C2×#12411yescharacteristic
166C2×C13#53611yescharacteristic
167C2×C13#54812yes—
168C2×C13#54812yes—
169D13—24no—
170C24—131no—
171C24C22×D1312yes—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—134no—
175C2×Q8—264no—
176C2×Q8—264no—
177C2×Q8—2632no—
178C2×Q8—262no—
179C2×Q8—264no—
180C2×Q8—262no—
181C2×Q8C22⋊D1314yescomplemented
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—264no—
186C2×D4—268no—
187C22×C4—131no—
188C22×C4—132no—
189C22×C4—134no—
190C22×C4—132no—
191C22×C4—132no—
192C22×C4—264no—
193C22×C4—264no—
194C22×C4—262no—
195C22×C4—264no—
196C22×C4—262no—
197C22×C4C22×D1312yes—
198C22×C4C22×D1312yes—
199C22×C4C22×D1311yescharacteristic
200C4⋊C4—262no—
201C22⋊C4—28no—
202C22⋊C4—264no—
203C22⋊C4—264no—
204C22⋊C4—268no—
205C42—22no—
206C42—262no—
207C13#243611yescharacteristic, complemented, Sylow
208C23—22no—
209C23—22no—
210C23—24no—
211C23—24no—
212C23—22no—
213C23—132no—
214C23—134no—
215C23—261no—
216C23—262no—
217C23—261no—
218C23C23×D1311yescharacteristic
219Q8—28no—
220Q8—2616no—
221Q8—268no—
222D4—44no—
223D4—528no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—132no—
230C2×C4—134no—
231C2×C4—2616no—
232C2×C4—262no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—262no—
236C2×C4—268no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—264no—
241C2×C4—262no—
242C2×C4D4×D1312yes—
243C2×C4D4×D1312yes—
244C2×C4C2×C22⋊D1314yes—
245C2×C4C2×C22⋊D1312yes—
246C22—42no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—44no—
251C22—134no—
252C22—262no—
253C22—264no—
254C22—262no—
255C22—264no—
256C22C2×D4×D1311yescharacteristic
257C22C2×D4×D1311yescharacteristic
258C22#41×D1312yes—
259C22#8825712yes—
260C22C22×C22⋊D1311yescharacteristic
261C4—24no—
262C4—42no—
263C4—262no—
264C4—264no—
265C4—522no—
266C4—522no—
267C4#8819114yes—
268C2—82no—
269C2—264no—
270C2D13×#12411yescharacteristic
271C2#1171938011yescharacteristic
272C2#1171938212yes—
273C2C2×#8819111yescharacteristic
274C2#1171953612yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#124C2
prime radicalC2×#88192C2
hypercenterC2×#124D13
hypocenterC13#2436
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D13C2semidirect
2. C2×C13×#124C2semidirect
4. C2×#88190C2semidirect
5. #11718891C2semidirect
6. #11718617C2semidirect
7. #11718608C2semidirect
8. C4×#6103C2semidirect
9. #11718590C2semidirect
37. C2×Q8×C13D4semidirect
62. C2×Dic26D4semidirect
111. C2×#124D13semidirect
132. C2×D13#124semidirect
181. C2×Q8C22⋊D13semidirect
207. C13#2436semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D132
C2×C13×#1242
C2×#881922
C2×#881902
#117188912
#117186172
#117186082
C4×#61032
#117185902
#243613