Finite Group Databasebeta

← #13127750

Subgroups — #13127750

Order 1664.

340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719427C211yesmaximal, characteristic, complemented
2#11719248C211yesmaximal, characteristic
3C13×#476C211yesmaximal, characteristic
4#11718739C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic
6#11718518C212yesmaximal, complemented
7#11718517C212yesmaximal, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718420C212yesmaximal
11#11718418C212yesmaximal
12C13×C4⋊Q8C2211yescharacteristic
13C4×D4×C13C2211yescharacteristic
14#88198—22no—
15D4×Dic13C2212yes—
16C2×#6105C2211yescharacteristic
17C2×C4⋊Dic13—21no—
18#88178—21no—
19#88144C2212yes—
20#88142—21no—
21#88142C2212yes—
22#88141—21no—
23#88141C2212yes—
24#88132—22no—
25#88123C2211yescharacteristic
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C13×#106C2212yes—
29C13×C4⋊C8C2211yescharacteristic
30C13×#102C2212yes—
31#88072C2211yescharacteristic
32#88058C2212yes—
33#88056C2212yes—
34#88055C2212yes—
35#88054C2212yes—
36#88050C2211yescharacteristic
37#88048C2211yescharacteristic
38#88047C2212yes—
39#88047C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×Dic13—22no—
45C2×Dic26—21no—
46C2×Dic26—22no—
47C2×Dic26D411yescharacteristic
48C2×Dic26C2311yescharacteristic
49C2×C8×C13C2312yes—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C13×C4⋊C4C2311yescharacteristic
53C13×C22⋊C4—21no—
54C42×C13C2311yescharacteristic
55C22⋊Dic13—22no—
56#6105Q814yescomplemented
57C4⋊Dic13—21no—
58C4⋊Dic13—22no—
59C4⋊Dic13D411yescharacteristic
60C4⋊Dic13C2311yescharacteristic
61C4⋊Dic13C2312yes—
62#6101—21no—
63#6101—22no—
64#6101—22no—
65#6101—22no—
66#6101D412yes—
67C4×Dic13—21no—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72#3385—131nomaximal, Sylow
73C23×C13—21no—
74Q8×C13—81no—
75D4×C13—21no—
76D4×C13C2×Q812yes—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—42no—
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2411yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13—82no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89Dic26—22no—
90Dic26—21no—
91Dic26—82no—
92Dic26—81no—
93Dic26C2×Q812yes—
94C8×C13—22no—
95#1055—21no—
96#1055C2×Q812yes—
97Q82—131no—
98#554—131no—
99#501—132no—
100#500—131no—
101#479—132no—
102#477—131no—
103#476D1311yescharacteristic
104#474—132no—
105#446—131no—
106#440—132no—
107C4×SD16—131no—
108C22×C13—22no—
109C22×C13—41no—
110C22×C13—41no—
111C22×C13C22×D411yescharacteristic
112C4×C13—21no—
113C4×C13—41no—
114C4×C13—42no—
115C4×C13#13712yes—
116C4×C13C22×Q811yescharacteristic
117C4×C132−1+411yescharacteristic
118Dic13—22no—
119Dic13—22no—
120Dic13—22no—
121Dic13—41no—
122Dic13—42no—
123C2×SD16—131no—
124C4⋊Q8—132no—
125C4⋊Q8—131no—
126C4⋊Q8—261no—
127C4⋊Q8—262no—
128C4⋊Q8C2×D1311yescharacteristic
129#125—132no—
130C22⋊Q8—262no—
131C22⋊Q8—261no—
132C4×Q8—131no—
133C4×Q8—132no—
134C4×Q8—131no—
135C4×Q8—261no—
136C4×D4—132no—
137C4×D4C2×D1311yescharacteristic
138C2×C4⋊C4—261no—
139#107—132no—
140#107—132no—
141#107—132no—
142#106—131no—
143#106C2×D1312yes—
144C4⋊C8—132no—
145C4⋊C8C2×D1311yescharacteristic
146#103—132no—
147#103—131no—
148#102—131no—
149#102C2×D1312yes—
150#97—132no—
151C4×C8—131no—
152C2×C13—42no—
153C2×C13D4×Q811yescharacteristic
154C2×C13C2×#13711yescharacteristic
155C2×C13#57611yescharacteristic
156C2×Q8—21no—
157C2×Q8—131no—
158C2×Q8—131no—
159C2×Q8—262no—
160C2×Q8—261no—
161C2×D4C22×D1311yescharacteristic
162C22×C4—21no—
163C22×C4—262no—
164SD16—134no—
165C2×C8—131no—
166C2×C8—131no—
167C2×C8C22×D1312yes—
168C4⋊C4—21no—
169C4⋊C4—131no—
170C4⋊C4—132no—
171C4⋊C4—131no—
172C4⋊C4—132no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—261no—
178C4⋊C4—261no—
179C4⋊C4C22×D1312yes—
180C4⋊C4C22×D1311yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—262no—
183C42—132no—
184C42—262no—
185C42—261no—
186C42C22×D1311yescharacteristic
187C13#338511yescharacteristic, complemented, Sylow
188C23—21no—
189Q8—81no—
190Q8—132no—
191Q8—262no—
192Q8—261no—
193Q8—1041no—
194Q8—1042no—
195D4—21no—
196D4Q8×D1312yes—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—132no—
201C2×C4—132no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4—262no—
205C2×C4—1042no—
206C2×C4D4×D1311yescharacteristic
207C2×C4D4×D1311yescharacteristic
208C2×C4C23×D1311yescharacteristic
209C8—22no—
210C8—132no—
211C8—261no—
212C22—22no—
213C22—41no—
214C22—41no—
215C22C2×D4×D1311yescharacteristic
216C4—21no—
217C4—41no—
218C4—42no—
219C4—262no—
220C4—262no—
221C4—262no—
222C4—522no—
223C4—521no—
224C4#8816912yes—
225C4C2×Q8×D1311yescharacteristic
226C4#8825711yescharacteristic
227C2—42no—
228C2#1171933711yescharacteristic
229C2C2×#8816911yescharacteristic
230C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#476C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#476D13
hypocenterC13#3385
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11719427C2semidirect
4. #11718739C2semidirect
6. #11718518C2semidirect
7. #11718517C2semidirect
8. #11718511C2semidirect
9. #11718492C2semidirect
56. #6105Q8semidirect
187. C13#3385semidirect

Maximal subgroups

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

subgroupindex
#117194272
#117192482
C13×#4762
#117187392
C4×#61052
#117185182
#117185172
#117185112
#117184922
#117184202
#117184182
#338513