Finite Group Databasebeta

← #13127927

Subgroups — #13127927

Order 1664.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#11719386C212yesmaximal, complemented
2C13×#495C211yesmaximal, characteristic, complemented
3#11718846C212yesmaximal, complemented
4#11718837C212yesmaximal, complemented
5#11718825C212yesmaximal, complemented
6#11718811C212yesmaximal, complemented
7#11718718C212yesmaximal, complemented
8C4×D104C211yesmaximal, characteristic, complemented
9#11718340C211yesmaximal, characteristic, complemented
10C2×C13×Q16C2211yescharacteristic
11C2×C13×SD16C2212yes—
12C2×C13×D8C2211yescharacteristic
13C13×#124C2212yes—
14#88201C2212yes—
15Q8×Dic13C2212yes—
16C2×#6106C2212yes—
17#88194C2212yes—
18D4×Dic13C2212yes—
19C2×#6104C2212yes—
20C2×D104C2211yescharacteristic
21#88140—22no—
22#88139—22no—
23#88137—22no—
24#88135—22no—
25C4×D52C2212yes—
26C4×Dic26C2211yescharacteristic
27C4×C8×C13C2211yescharacteristic
28#88075C2212yes—
29#88072C2212yes—
30#88061C2212yes—
31#88058C2211yescharacteristic
32#88055C2212yes—
33#88054C2212yes—
34C4⋊#1055C2211yescharacteristic
35C2×Q8×C13C2312yes—
36C2×D4×C13C2312yes—
37C2×C22⋊D13—22no—
38C2×C22⋊D13—22no—
39C22×Dic13—22no—
40C2×D52C2312yes—
41C2×C4×D13—22no—
42C2×Dic26D411yescharacteristic
43C13×Q16—41no—
44C13×SD16—24no—
45C13×D8—41no—
46C2×C8×C13C2311yescharacteristic
47C2×C8×C13C2311yescharacteristic
48C13×C22⋊C4—22no—
49C13×C22⋊C4—22no—
50C42×C13C2311yescharacteristic
51C22⋊Dic13—22no—
52#6106—42no—
53#6104—42no—
54#6103—22no—
55#6103—22no—
56#6103—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13D411yescharacteristic
59C4⋊Dic13C2312yes—
60#6101D412yes—
61C4×Dic13—22no—
62C4×Dic13C2312yes—
63C2×#1055C2312yes—
64D104—22no—
65#3403—131nomaximal, Sylow
66C23×C13—22no—
67C22×D13—22no—
68Q8×C13—22no—
69Q8×C13—22no—
70D4×C13—22no—
71D4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2411yescharacteristic
76C22⋊D13—44no—
77C22⋊D13—82no—
78C2×Dic13—22no—
79C2×Dic13—82no—
80C2×Dic13C2×D412yes—
81C2×Dic13C2×D412yes—
82D52—22no—
83D52—22no—
84C4×D13—82no—
85Dic26—41no—
86C8×C13—21no—
87C8×C13#4112yes—
88#1055—22no—
89#559—132no—
90#496—132no—
91#495D1311yescharacteristic, complemented
92#464—132no—
93#463—132no—
94#459—132no—
95#446—131no—
96#440—132no—
97C4×D8—131no—
98C22×C13—42no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13C22×D411yescharacteristic
102C2×D13—42no—
103C2×D13—42no—
104C2×D13—42no—
105C4×C13—21no—
106C4×C13—21no—
107C4×C13—42no—
108C4×C13C2×#4111yescharacteristic
109C4×C13H(5,𝔽2)11yescharacteristic
110Dic13—22no—
111Dic13—22no—
112Dic13—42no—
113C2×Q16C2×D1311yescharacteristic
114C2×SD16—132no—
115C2×SD16C2×D1312yes—
116C2×D8—132no—
117C2×D8—131no—
118C2×D8C2×D1311yescharacteristic
119#127—132no—
120#124—132no—
121#124—262no—
122#124C2×D1312yes—
123#123—262no—
124#123—262no—
125C4×Q8—131no—
126C4×Q8—132no—
127C4×D4—132no—
128C4×D4—132no—
129C4×D4—262no—
130#107—131no—
131C4⋊C8—132no—
132C4⋊C8—131no—
133#103—132no—
134#102—132no—
135#102—132no—
136#97—132no—
137C4×C8C2×D1311yescharacteristic
138C2×C13—82no—
139C2×C13#55011yescharacteristic
140C2×C13#57511yescharacteristic
141C2×C13#57611yescharacteristic
142D13—82no—
143C2×Q8—131no—
144C2×Q8C22×D1312yes—
145C2×D4—132no—
146C2×D4—262no—
147C2×D4—262no—
148C2×D4C22×D1312yes—
149C22×C4—262no—
150C22×C4—262no—
151Q16—41no—
152SD16—24no—
153SD16—522no—
154D8—41no—
155D8—262no—
156D8—522no—
157C2×C8—132no—
158C2×C8C22×D1311yescharacteristic
159C2×C8C22×D1311yescharacteristic
160C4⋊C4—132no—
161C4⋊C4—131no—
162C4⋊C4—132no—
163C4⋊C4—262no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—262no—
167C22⋊C4—262no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C42—132no—
171C42—262no—
172C42C22×D1311yescharacteristic
173C13#340311yescharacteristic, complemented, Sylow
174C23—22no—
175C23—262no—
176Q8—22no—
177Q8—22no—
178Q8—521no—
179D4—22no—
180D4—22no—
181D4—262no—
182D4—262no—
183D4—524no—
184D4—1042no—
185C2×C4—22no—
186C2×C4—132no—
187C2×C4—132no—
188C2×C4—262no—
189C2×C4—1042no—
190C2×C4—1042no—
191C2×C4D4×D1311yescharacteristic
192C2×C4D4×D1311yescharacteristic
193C2×C4C23×D1311yescharacteristic
194C8—21no—
195C8—262no—
196C8#612912yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—522no—
201C22—522no—
202C22—522no—
203C22C2×D4×D1311yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—262no—
208C4—262no—
209C4—522no—
210C4C2×#612911yescharacteristic
211C4#8825111yescharacteristic
212C2—82no—
213C2—1042no—
214C2#1171942311yescharacteristic
215C2#1171947311yescharacteristic
216C2#1171947411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#495C2
socleC22×C13C22×D4
hypercenter#495D13
hypocenterC13#3403
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #11719386C2semidirect
2. C13×#495C2semidirect
3. #11718846C2semidirect
4. #11718837C2semidirect
5. #11718825C2semidirect
6. #11718811C2semidirect
7. #11718718C2semidirect
8. C4×D104C2semidirect
9. #11718340C2semidirect
91. #495D13semidirect
173. C13#3403semidirect

Maximal subgroups

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

subgroupindex
#117193862
C13×#4952
#117188462
#117188372
#117188252
#117188112
#117187182
C4×D1042
#117183402
#340313