Finite Group Databasebeta

← #13118124

Subgroups — #13118124

Order 1664.

568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 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×D4×Dic13C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic
4#11718883C211yesmaximal, characteristic
5#11718647C211yesmaximal, characteristic, complemented
6#11718613C212yesmaximal, complemented
7#11718608C212yesmaximal, complemented
8C22⋊C4×Dic13C212yesmaximal, complemented
9C22⋊C4×Dic13C212yesmaximal, complemented
10#11718320C211yesmaximal, characteristic, complemented
11#11718309C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×Dic13C2212yes—
14C22×Dic26C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21D4×Dic13—24no—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29#88141—24no—
30C13×#95C2211yescharacteristic
31#88071C2212yes—
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2312yes—
38C2×D4×C13—24no—
39C2×D4×C13—22no—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13—24no—
45C22×Dic13—24no—
46C22×Dic13—24no—
47C22×Dic13C2312yes—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C2×Dic26—22no—
54C2×Dic26—22no—
55C2×Dic26—22no—
56C13×C4⋊C4—22no—
57C13×C22⋊C4—24no—
58C13×C22⋊C4—24no—
59C22⋊Dic13—24no—
60C22⋊Dic13—24no—
61C22⋊Dic13—24no—
62C4⋊Dic13—22no—
63#6101—22no—
64#6101—22no—
65C4×Dic13—22no—
66C4×Dic13—22no—
67C4×Dic13—24no—
68C4×Dic13D414yes—
69#2398—131nomaximal, Sylow
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13#4114yes—
77C23×C13C2411yescharacteristic
78D4×C13—28no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13#4112yes—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—48no—
102C2×Dic13C2×D412yes—
103C2×Dic13C2×D412yes—
104C2×Dic13#4112yes—
105C2×Dic13#4114yes—
106Dic26—28no—
107C2×C4×Q8—131no—
108C2×C4×D4—131no—
109#400—131no—
110#400—131no—
111#397—132no—
112#394—131no—
113#394D1311yescharacteristic
114#393—132no—
115C4×C22⋊C4—132no—
116C4×C22⋊C4—132no—
117#376—131no—
118C22×C13—24no—
119C22×C13—24no—
120C22×C13—24no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13C22×D411yescharacteristic
126C22×C13C2×#4112yes—
127C22×C13C2×#4111yescharacteristic
128C22×C13C2×#4111yescharacteristic
129C22×C13C2×#4112yes—
130C4×C13—22no—
131C4×C13—22no—
132C4×C13—41no—
133C4×C13—42no—
134Dic13—22no—
135Dic13—22no—
136Dic13—41no—
137Dic13—42no—
138Dic13—42no—
139Dic13#12414yes—
140C22×Q8—131no—
141C22×D4C2×D1311yescharacteristic
142C23×C4—132no—
143C4×Q8—264no—
144C4×D4—264no—
145C2×C4⋊C4—131no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4C2×D1311yescharacteristic
149C2×C22⋊C4—132no—
150C2×C22⋊C4—132no—
151C2×C22⋊C4—132no—
152C2×C22⋊C4C2×D1312yes—
153C2×C22⋊C4C2×D1312yes—
154C2×C42—131no—
155C2×C42—131no—
156C2×C42—131no—
157C2×C42—132no—
158#95—132no—
159#95—131no—
160#95—132no—
161#95—132no—
162#95—132no—
163#95—132no—
164#95C2×D1311yescharacteristic
165C2×C13—44no—
166C2×C13#52511yescharacteristic
167C2×C13#52511yescharacteristic
168C2×C13C2×#12411yescharacteristic
169C2×C13#52912yes—
170C2×C13#52912yes—
171C24C22×D1312yes—
172C2×Q8—262no—
173C2×Q8—262no—
174C2×Q8—262no—
175C2×D4—24no—
176C2×D4—22no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—132no—
181C22×C4—132no—
182C22×C4—131no—
183C22×C4—264no—
184C22×C4—264no—
185C22×C4—264no—
186C22×C4C22×D1312yes—
187C22×C4C22×D1311yescharacteristic
188C22×C4C22×D1311yescharacteristic
189C22×C4C22×D1311yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—262no—
192C4⋊C4—262no—
193C4⋊C4—262no—
194C22⋊C4—24no—
195C22⋊C4—24no—
196C22⋊C4—264no—
197C22⋊C4—264no—
198C22⋊C4—264no—
199C42—134no—
200C42—262no—
201C42—262no—
202C42—264no—
203C13#239811yescharacteristic, complemented, Sylow
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23#612914yes—
211C23C23×D1311yescharacteristic
212Q8—268no—
213D4—28no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—132no—
223C2×C4—134no—
224C2×C4—132no—
225C2×C4—132no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—528no—
239C2×C4D4×D1312yes—
240C2×C4#612912yes—
241C22—24no—
242C22—24no—
243C22—24no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×D4×D1311yescharacteristic
249C22C2×#612912yes—
250C22C2×#612911yescharacteristic
251C22#41×D1312yes—
252C22#41×D1311yescharacteristic
253C4—22no—
254C4—22no—
255C4—41no—
256C4—42no—
257C4—134no—
258C4—262no—
259C4—262no—
260C4—521no—
261C4—522no—
262C4—522no—
263C2—44no—
264C2#1171929111yescharacteristic
265C2#1171930512yes—
266C2#1171931111yescharacteristic
267C2#1171935412yes—
268C2D13×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2398
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88141C2semidirect
5. #11718647C2semidirect
6. #11718613C2semidirect
7. #11718608C2semidirect
8. C22⋊C4×Dic13C2semidirect
9. C22⋊C4×Dic13C2semidirect
10. #11718320C2semidirect
11. #11718309C2semidirect
203. C13#2398semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881412
C13×#3942
#117188832
#117186472
#117186132
#117186082
C22⋊C4×Dic132
#117183202
#117183092
#239813