Finite Group Databasebeta

← #13124642

Subgroups — #13124642

Order 1664.

376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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
1#11719433C211yesmaximal, characteristic
2C4×Q8×D13C211yesmaximal, characteristic
3C13×#477C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718681C211yesmaximal, characteristic, complemented
6#11718542C212yesmaximal
7#11718538C212yesmaximal, complemented
8#11718512C211yesmaximal, characteristic, complemented
9#11718498C211yesmaximal, characteristic
10#11718463C212yesmaximal
11#11718460C212yesmaximal, complemented
12C2×Q8×D13C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88200—21no—
16Q8×Dic13—21no—
17Q8×Dic13C2211yescharacteristic
18C2×#6094C2212yes—
19#88151—21no—
20#88146C2212yes—
21C4⋊C4×D13—21no—
22C4⋊C4×D13C2211yescharacteristic
23#88144C2212yes—
24#88141—21no—
25#88141—21no—
26#88141C2211yescharacteristic
27C42×D13—21no—
28C42×D13C2211yescharacteristic
29#88123C2211yescharacteristic
30C4×Dic26—21no—
31C4×Dic26C2211yescharacteristic
32C13×#107C2212yes—
33C13×C4⋊C8C2211yescharacteristic
34C13×#103C2212yes—
35#88075C2212yes—
36#88057C2212yes—
37#88056C2212yes—
38#88054C2212yes—
39#88050C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42C4⋊#1055C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45Q8×D13—22no—
46Q8×D13Q814yescomplemented
47C2×C4×D13—21no—
48C2×C4×D13—21no—
49C2×C4×D13D411yescharacteristic
50C2×C4×D13D411yescharacteristic
51C2×C4×D13C2311yescharacteristic
52C2×Dic26—21no—
53C2×Dic26—21no—
54C2×Dic26C2311yescharacteristic
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C13×C4⋊C4C2311yescharacteristic
60C42×C13—21no—
61C42×C13C2311yescharacteristic
62#6103—22no—
63C4⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4⋊Dic13C2312yes—
67C4⋊Dic13C2311yescharacteristic
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—21no—
74C4×Dic13—21no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C2×#1055C2312yes—
80#6094—24no—
81#3078—131nomaximal, Sylow
82C22×D13C2×D411yescharacteristic
83Q8×C13—21no—
84Q8×C13—42no—
85Q8×C13C2×Q812yes—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2411yescharacteristic
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98C4×D13—24no—
99C4×D13—22no—
100C4×D13—41no—
101C4×D13—42no—
102C4×D13C2×Q812yes—
103C4×D13#4112yes—
104Dic26—21no—
105Dic26—24no—
106Dic26—42no—
107Dic26C2×Q812yes—
108C8×C13—22no—
109#1055—22no—
110#533—131no—
111C2×C4×Q8—131no—
112#479—132no—
113#479—132no—
114#477—131no—
115#477D1311yescharacteristic, complemented
116#475—131no—
117#475—131no—
118#428—132no—
119#423—131no—
120#419—132no—
121C22×C13C22×D411yescharacteristic
122C2×D13—21no—
123C2×D13—21no—
124C2×D13C22⋊Q812yes—
125C4×C13—22no—
126C4×C13—21no—
127C4×C13—41no—
128C4×C13—42no—
129C4×C13#13712yes—
130C4×C13C22×Q811yescharacteristic
131C4×C13C2×#4111yescharacteristic
132Dic13—22no—
133Dic13—21no—
134Dic13—21no—
135Dic13—42no—
136Dic13—41no—
137Dic13C22⋊Q812yes—
138C22×Q8—131no—
139C2×M16—132no—
140C4⋊Q8—131no—
141C4⋊Q8C2×D1311yescharacteristic
142#125—132no—
143C22⋊Q8—261no—
144C22⋊Q8—261no—
145C4×Q8—131no—
146C4×Q8—131no—
147C4×Q8—131no—
148C4×Q8—261no—
149C4×Q8—261no—
150C4×Q8—261no—
151C4×Q8—261no—
152C4×Q8C2×D1311yescharacteristic
153#117—132no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—261no—
156C2×C42—131no—
157C2×C42—261no—
158#107—132no—
159#107C2×D1312yes—
160#106—132no—
161#106—132no—
162C4⋊C8—132no—
163C4⋊C8—131no—
164C4⋊C8C2×D1311yescharacteristic
165#103—132no—
166#103—132no—
167#103—132no—
168#103C2×D1312yes—
169C2×C13C2×C22⋊Q811yescharacteristic
170C2×C13C2×#13711yescharacteristic
171C2×C13#57511yescharacteristic
172D13—22no—
173C2×Q8—21no—
174C2×Q8—134no—
175C2×Q8—131no—
176C2×Q8—261no—
177C2×Q8—262no—
178C2×Q8—261no—
179C2×Q8C22×D1311yescharacteristic
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—261no—
184C22×C4—261no—
185M16—264no—
186C2×C8—132no—
187C2×C8C22×D1312yes—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—132no—
191C4⋊C4—131no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4—262no—
196C4⋊C4—262no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4C22×D1312yes—
200C4⋊C4C22×D1311yescharacteristic
201C22⋊C4—262no—
202C42—21no—
203C42—131no—
204C42—131no—
205C42—131no—
206C42—261no—
207C42—261no—
208C42—262no—
209C42—261no—
210C42C22×D1311yescharacteristic
211C13#307811yescharacteristic, complemented, Sylow
212C23—131no—
213Q8—21no—
214Q8—42no—
215Q8—132no—
216Q8—264no—
217Q8—261no—
218Q8—522no—
219Q8Q8×D1312yes—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—131no—
224C2×C4—132no—
225C2×C4—132no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—264no—
229C2×C4—261no—
230C2×C4—262no—
231C2×C4—261no—
232C2×C4—262no—
233C2×C4—521no—
234C2×C4—522no—
235C2×C4D4×D1311yescharacteristic
236C2×C4D4×D1311yescharacteristic
237C2×C4C23×D1311yescharacteristic
238C8—22no—
239C8—262no—
240C22—132no—
241C22—261no—
242C22—261no—
243C22C2×D4×D1311yescharacteristic
244C4—21no—
245C4—22no—
246C4—41no—
247C4—42no—
248C4—132no—
249C4—261no—
250C4—261no—
251C4—262no—
252C4—522no—
253C4—521no—
254C4#8817212yes—
255C4C2×Q8×D1311yescharacteristic
256C4#41×D1311yescharacteristic
257C2—262no—
258C2D13×C22⋊Q811yescharacteristic
259C2C2×#8817211yescharacteristic
260C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#477C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#477D13
hypocenterC13#3078
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. C13×#477C2semidirect
4. #11718752C2semidirect
5. #11718681C2semidirect
7. #11718538C2semidirect
8. #11718512C2semidirect
11. #11718460C2semidirect
46. Q8×D13Q8semidirect
115. #477D13semidirect
211. C13#3078semidirect

Maximal subgroups

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

subgroupindex
#117194332
C4×Q8×D132
C13×#4772
#117187522
#117186812
#117185422
#117185382
#117185122
#117184982
#117184632
#117184602
#307813