Finite Group Databasebeta

← #13127767

Subgroups — #13127767

Order 1664.

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

normal subgroups only

This group has 326 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#11719426C211yesmaximal, characteristic
2Q8×Dic26C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic
4#11718740C211yesmaximal, characteristic
5C4×#6107C211yesmaximal, characteristic
6#11718517C212yesmaximal
7#11718515C212yesmaximal
8#11718511C211yesmaximal, characteristic
9#11718492C211yesmaximal, characteristic
10#11718457C212yesmaximal
11#11718450C212yesmaximal
12C13×C4⋊Q8C2211yescharacteristic
13C4×Q8×C13C2211yescharacteristic
14Q8×Dic13—21no—
15Q8×Dic13C2212yes—
16#88198—21no—
17C2×#6107C2211yescharacteristic
18#88144C2212yes—
19#88143—22no—
20#88142—22no—
21#88142C2212yes—
22#88141C2212yes—
23#88123—21no—
24#88123C2211yescharacteristic
25C4×Dic26—21no—
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C13×#106C2212yes—
29C13×C4⋊C8C2211yescharacteristic
30C13×#103C2212yes—
31#88075C2211yescharacteristic
32#88058C2212yes—
33#88056C2212yes—
34#88055C2212yes—
35#88054C2212yes—
36#88050C2211yescharacteristic
37#88048C2212yes—
38#88048C2212yes—
39#88047C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43C2×Dic26—21no—
44C2×Dic26—22no—
45C2×Dic26D411yescharacteristic
46C2×Dic26C2311yescharacteristic
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4C2312yes—
51C13×C4⋊C4C2311yescharacteristic
52C42×C13—21no—
53C42×C13C2311yescharacteristic
54#6107Q814yescomplemented
55C4⋊Dic13—21no—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13D411yescharacteristic
59C4⋊Dic13C2311yescharacteristic
60C4⋊Dic13C2312yes—
61#6101—21no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65#6101D412yes—
66C4×Dic13—21no—
67C4×Dic13—22no—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72#3387—131nomaximal, Sylow
73Q8×C13—21no—
74Q8×C13—42no—
75Q8×C13C2×Q812yes—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2411yescharacteristic
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13C2×D412yes—
86C2×Dic13C2×D412yes—
87Dic26—22no—
88Dic26—21no—
89Dic26—82no—
90Dic26—81no—
91Dic26C2×Q812yes—
92C8×C13—22no—
93#1055—21no—
94#1055C2×Q812yes—
95Q82—131no—
96#557—131no—
97#501—132no—
98#498—131no—
99#479—132no—
100#477—131no—
101#475—132no—
102#475D1311yescharacteristic
103#446—131no—
104#441—132no—
105C4×Q16—131no—
106C22×C13C22×D411yescharacteristic
107C4×C13—22no—
108C4×C13—21no—
109C4×C13—42no—
110C4×C13—41no—
111C4×C13#13712yes—
112C4×C13C22×Q811yescharacteristic
113C4×C132−1+411yescharacteristic
114Dic13—22no—
115Dic13—22no—
116Dic13—22no—
117Dic13—42no—
118Dic13—41no—
119C2×Q16—131no—
120C4⋊Q8—132no—
121C4⋊Q8—131no—
122C4⋊Q8—261no—
123C4⋊Q8—262no—
124C4⋊Q8—261no—
125C4⋊Q8C2×D1311yescharacteristic
126#125—132no—
127#125—262no—
128C4×Q8—131no—
129C4×Q8—132no—
130C4×Q8—132no—
131C4×Q8—131no—
132C4×Q8—261no—
133C4×Q8—261no—
134C4×Q8C2×D1311yescharacteristic
135#107—132no—
136#107—131no—
137#106—132no—
138#106—132no—
139#106C2×D1312yes—
140C4⋊C8—132no—
141C4⋊C8C2×D1311yescharacteristic
142#103—131no—
143#103—132no—
144#103—131no—
145#103C2×D1312yes—
146#97—132no—
147C4×C8—131no—
148C2×C13D4×Q811yescharacteristic
149C2×C13C2×#13711yescharacteristic
150C2×C13#57711yescharacteristic
151C2×Q8—21no—
152C2×Q8—131no—
153C2×Q8—131no—
154C2×Q8—262no—
155C2×Q8—261no—
156C2×Q8C22×D1311yescharacteristic
157Q16—134no—
158C2×C8—131no—
159C2×C8—131no—
160C2×C8C22×D1312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—131no—
164C4⋊C4—132no—
165C4⋊C4—132no—
166C4⋊C4—131no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—261no—
173C4⋊C4—261no—
174C4⋊C4C22×D1311yescharacteristic
175C4⋊C4C22×D1312yes—
176C42—21no—
177C42—132no—
178C42—262no—
179C42—262no—
180C42—261no—
181C42C22×D1311yescharacteristic
182C13#338711yescharacteristic, complemented, Sylow
183Q8—21no—
184Q8—42no—
185Q8—132no—
186Q8—262no—
187Q8—261no—
188Q8—1041no—
189Q8—1042no—
190Q8Q8×D1312yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—132no—
195C2×C4—132no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—262no—
199C2×C4D4×D1311yescharacteristic
200C2×C4D4×D1311yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—22no—
203C8—132no—
204C8—261no—
205C22C2×D4×D1311yescharacteristic
206C4—21no—
207C4—22no—
208C4—42no—
209C4—41no—
210C4—262no—
211C4—262no—
212C4—262no—
213C4—521no—
214C4—522no—
215C4#8816912yes—
216C4C2×Q8×D1311yescharacteristic
217C4#8825711yescharacteristic
218C2#1171933711yescharacteristic
219C2C2×#8816911yescharacteristic
220C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socle, prime radicalC22×C13C22×D4
hypercenter#475D13
hypocenterC13#3387
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
54. #6107Q8semidirect
182. C13#3387semidirect

Maximal subgroups

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

subgroupindex
#117194262
Q8×Dic262
C13×#4752
#117187402
C4×#61072
#117185172
#117185152
#117185112
#117184922
#117184572
#117184502
#338713