Finite Group Databasebeta

← #13127748

Subgroups — #13127748

Order 1664.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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#11719284C211yesmaximal, characteristic
2Q8×Dic26C211yesmaximal, characteristic, complemented
3C13×#446C211yesmaximal, characteristic, complemented
4#11718511C211yesmaximal, characteristic, complemented
5#11718507C212yesmaximal
6#11718503C211yesmaximal, characteristic
7#11718490C212yesmaximal, complemented
8#11718371C212yesmaximal
9#11718363C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic
11#11718343C211yesmaximal, characteristic, complemented
12C4×Q8×C13C2211yescharacteristic
13#88200—21no—
14Q8×Dic13—21no—
15C2×#6095C2211yescharacteristic
16#88150—22no—
17C4⋊C4×D13—21no—
18#88142—21no—
19#88142—22no—
20C4×D52C2211yescharacteristic
21C4×D52C2212yes—
22#88124C2212yes—
23#88123C2211yescharacteristic
24#88123C2212yes—
25#88123C2211yescharacteristic
26C4×Dic26C2212yes—
27C4×Dic26C2211yescharacteristic
28C13×C4⋊C8C2212yes—
29C13×C4⋊C8C2211yescharacteristic
30C13×#97C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88061C2212yes—
33#88061C2211yescharacteristic
34#88058C2212yes—
35#88058C2212yes—
36#88058C2212yes—
37#88057C2212yes—
38#88057C2211yescharacteristic
39#88056C2211yescharacteristic
40#88056C2212yes—
41C2×Q8×C13D411yescharacteristic
42C2×D52C2311yescharacteristic
43C2×C4×D13—21no—
44C2×C4×D13—22no—
45C2×Dic26—22no—
46C2×Dic26—21no—
47C2×Dic26—21no—
48C2×Dic26C2311yescharacteristic
49C2×C8×C13C2311yescharacteristic
50C2×C8×C13C2312yes—
51C2×C8×C13C2311yescharacteristic
52C13×C4⋊C4D411yescharacteristic
53C13×C4⋊C4D412yes—
54C42×C13C2311yescharacteristic
55C42×C13C2312yes—
56#6103—21no—
57#6103—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—21no—
60C4⋊Dic13—21no—
61C4⋊Dic13C2312yes—
62C4⋊Dic13C2311yescharacteristic
63C4⋊Dic13C2312yes—
64C4⋊Dic13C2311yescharacteristic
65#6101—22no—
66#6101—21no—
67#6101—22no—
68#6101—22no—
69C4×Dic13—22no—
70C4×Dic13—21no—
71#6095Q814yescomplemented
72#3385—131nomaximal, Sylow
73C22×D13—21no—
74Q8×C13—22no—
75C2×C4×C13C2×D412yes—
76C2×C4×C13C2×D412yes—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2411yescharacteristic
80C2×Dic13—21no—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85D52—21no—
86D52C2×Q812yes—
87C4×D13—42no—
88C4×D13—82no—
89Dic26—21no—
90Dic26—81no—
91Dic26—82no—
92Dic26—81no—
93Dic26C2×Q812yes—
94C8×C13—21no—
95C8×C13—22no—
96C8×C13C2×Q812yes—
97Q82—131no—
98#554—131no—
99#501—132no—
100#500—131no—
101#479—132no—
102#477—131no—
103#476—131no—
104#474—132no—
105#446D1311yescharacteristic, complemented
106#440—132no—
107C4×SD16—131no—
108C22×C13C22×D411yescharacteristic
109C2×D13—22no—
110C2×D13—41no—
111C2×D13—41no—
112C4×C13—22no—
113C4×C13—21no—
114C4×C13—22no—
115C4×C13#13712yes—
116C4×C13C22×Q811yescharacteristic
117C4×C132−1+411yescharacteristic
118Dic13—22no—
119Dic13—41no—
120Dic13—42no—
121Dic13—41no—
122Dic13—42no—
123C2×SD16—131no—
124C4⋊Q8—131no—
125C4⋊Q8—132no—
126C4⋊Q8—131no—
127C4⋊Q8—261no—
128C4⋊Q8—262no—
129#125—132no—
130C22⋊Q8—261no—
131C22⋊Q8—262no—
132C4×Q8—131no—
133C4×Q8—132no—
134C4×Q8—261no—
135C4×Q8C2×D1311yescharacteristic
136C4×D4—131no—
137C4×D4—132no—
138C2×C4⋊C4—261no—
139#107—132no—
140#107—132no—
141#107—132no—
142#106—131no—
143#106—132no—
144C4⋊C8C2×D1312yes—
145C4⋊C8C2×D1311yescharacteristic
146#103—131no—
147#103—132no—
148#102—131no—
149#102—132no—
150#97C2×D1312yes—
151C4×C8C2×D1311yescharacteristic
152C2×C13D4×Q811yescharacteristic
153C2×C13C2×#13711yescharacteristic
154C2×C13#57611yescharacteristic
155D13—42no—
156C2×Q8—131no—
157C2×Q8—261no—
158C2×Q8—261no—
159C2×Q8—262no—
160C2×Q8D5211yescharacteristic
161C2×D4—131no—
162C22×C4—261no—
163C22×C4—262no—
164SD16—134no—
165C2×C8C22×D1311yescharacteristic
166C2×C8C22×D1312yes—
167C2×C8C22×D1311yescharacteristic
168C4⋊C4—131no—
169C4⋊C4—132no—
170C4⋊C4—131no—
171C4⋊C4—132no—
172C4⋊C4—262no—
173C4⋊C4—261no—
174C4⋊C4—261no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—261no—
178C4⋊C4—262no—
179C4⋊C4D5211yescharacteristic
180C4⋊C4D5212yes—
181C22⋊C4—261no—
182C22⋊C4—262no—
183C42—262no—
184C42—261no—
185C42C22×D1311yescharacteristic
186C42C22×D1312yes—
187C13#338511yescharacteristic, complemented, Sylow
188C23—261no—
189Q8—22no—
190Q8—132no—
191Q8—261no—
192Q8—1042no—
193Q8—1041no—
194Q8—1041no—
195D4—132no—
196D4—261no—
197C2×C4—261no—
198C2×C4—262no—
199C2×C4—261no—
200C2×C4—261no—
201C2×C4—262no—
202C2×C4—522no—
203C2×C4—1042no—
204C2×C4C2×D5212yes—
205C2×C4C2×D5211yescharacteristic
206C2×C4C2×D5212yes—
207C2×C4C2×D5211yescharacteristic
208C2×C4C23×D1311yescharacteristic
209C8—21no—
210C8—22no—
211C8Q8×D1312yes—
212C22—262no—
213C22—521no—
214C22—521no—
215C22C22×D5211yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—262no—
220C4—521no—
221C4—522no—
222C4—521no—
223C4—522no—
224C4#8816312yes—
225C4C2×Q8×D1311yescharacteristic
226C4#8825711yescharacteristic
227C2—522no—
228C2Q8×D5211yescharacteristic
229C2C2×#8816311yescharacteristic
230C2#1171945711yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#446C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#446D13
hypocenterC13#3385
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. Q8×Dic26C2semidirect
3. C13×#446C2semidirect
4. #11718511C2semidirect
7. #11718490C2semidirect
9. #11718363C2semidirect
11. #11718343C2semidirect
71. #6095Q8semidirect
105. #446D13semidirect
187. C13#3385semidirect

Maximal subgroups

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

subgroupindex
#117192842
Q8×Dic262
C13×#4462
#117185112
#117185072
#117185032
#117184902
#117183712
#117183632
C4×#60952
#117183432
#338513