Finite Group Databasebeta

← #13127764

Subgroups — #13127764

Order 1664.

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

normal subgroups only

This group has 326 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
1Q82×C13C211yesmaximal, characteristic
2#11719272C211yesmaximal, characteristic
3#11718755C212yesmaximal
4#11718752C211yesmaximal, characteristic
5#11718741C212yesmaximal
6#11718740C211yesmaximal, characteristic
7#11718691C212yesmaximal
8C4×#6107C211yesmaximal, characteristic
9#11718685C211yesmaximal, characteristic
10#11718683C212yesmaximal
11#11718681C211yesmaximal, characteristic
12C13×C4⋊Q8—21no—
13C13×C4⋊Q8—22no—
14C13×C4⋊Q8C2211yescharacteristic
15C13×C4⋊Q8C2212yes—
16C4×Q8×C13—21no—
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2212yes—
19C4×Q8×C13C2211yescharacteristic
20#88198—21no—
21C2×#6107C2211yescharacteristic
22#88143—22no—
23#88141—21no—
24#88124C2212yes—
25#88123C2211yescharacteristic
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2212yes—
28#88075C2212yes—
29#88075C2211yescharacteristic
30#88050C2211yescharacteristic
31#88050C2212yes—
32#88048C2212yes—
33#88048C2212yes—
34#88048C2212yes—
35#88047C2212yes—
36#88047C2211yescharacteristic
37C4⋊#1055C2211yescharacteristic
38C4⋊#1055C2212yes—
39#88043C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—21no—
43C2×Q8×C13D411yescharacteristic
44C2×Q8×C13C2311yescharacteristic
45C2×Dic26—21no—
46C2×Dic26C2311yescharacteristic
47C13×C4⋊C4—22no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4D411yescharacteristic
52C13×C4⋊C4D412yes—
53C13×C4⋊C4C2311yescharacteristic
54C13×C4⋊C4C2312yes—
55C42×C13—22no—
56C42×C13—21no—
57C42×C13C2311yescharacteristic
58C42×C13C2312yes—
59#6107Q814yescomplemented
60C4⋊Dic13—21no—
61C4⋊Dic13C2312yes—
62C4⋊Dic13C2311yescharacteristic
63#6101—21no—
64#6101—22no—
65#6101—22no—
66#6101—22no—
67C4×Dic13—22no—
68C4×Dic13—21no—
69C2×#1055C2311yescharacteristic
70C2×#1055C2312yes—
71C2×#1055C2311yescharacteristic
72#3387—131nomaximal, Sylow
73Q8×C13—22no—
74Q8×C13—21no—
75Q8×C13—82no—
76Q8×C13—81no—
77Q8×C13C2×Q812yes—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13C2×D412yes—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89Dic26—21no—
90Dic26—42no—
91Dic26C2×Q812yes—
92#1055—21no—
93#1055—22no—
94#1055C2×Q812yes—
95Q82D1311yescharacteristic
96#557—131no—
97#501—132no—
98#498—131no—
99#479—132no—
100#477—131no—
101#475—132no—
102#475—131no—
103#446—131no—
104#441—132no—
105C4×Q16—131no—
106C22×C13C22×D411yescharacteristic
107C4×C13—22no—
108C4×C13—22no—
109C4×C13—22no—
110C4×C13—21no—
111C4×C13—42no—
112C4×C13—41no—
113C4×C13#13712yes—
114C4×C13C22×Q811yescharacteristic
115C4×C132−1+411yescharacteristic
116Dic13—22no—
117Dic13—42no—
118Dic13—41no—
119C2×Q16—131no—
120C4⋊Q8—21no—
121C4⋊Q8—22no—
122C4⋊Q8—131no—
123C4⋊Q8—261no—
124C4⋊Q8C2×D1312yes—
125C4⋊Q8C2×D1311yescharacteristic
126#125—132no—
127#125—262no—
128C4×Q8—21no—
129C4×Q8—131no—
130C4×Q8—132no—
131C4×Q8—261no—
132C4×Q8C2×D1311yescharacteristic
133C4×Q8C2×D1312yes—
134C4×Q8C2×D1311yescharacteristic
135#107—131no—
136#107—132no—
137#106—132no—
138#106—132no—
139#106—132no—
140C4⋊C8—131no—
141C4⋊C8—132no—
142#103—131no—
143#103—132no—
144#103—131no—
145#103—132no—
146#97—132no—
147C4×C8—131no—
148C2×C13D4×Q811yescharacteristic
149C2×C13C2×#13711yescharacteristic
150C2×C13#57711yescharacteristic
151C2×Q8—22no—
152C2×Q8—21no—
153C2×Q8—131no—
154C2×Q8—261no—
155C2×Q8C22⋊D1311yescharacteristic
156C2×Q8C22×D1311yescharacteristic
157Q16—134no—
158C2×C8—131no—
159C2×C8—131no—
160C2×C8—132no—
161C4⋊C4—22no—
162C4⋊C4—21no—
163C4⋊C4—22no—
164C4⋊C4—21no—
165C4⋊C4—132no—
166C4⋊C4—131no—
167C4⋊C4—261no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—261no—
172C4⋊C4C22⋊D1311yescharacteristic
173C4⋊C4C22⋊D1312yes—
174C4⋊C4C22×D1311yescharacteristic
175C4⋊C4C22×D1312yes—
176C42—22no—
177C42—21no—
178C42—262no—
179C42—261no—
180C42C22×D1311yescharacteristic
181C42C22×D1312yes—
182C13#338711yescharacteristic, complemented, Sylow
183Q8—22no—
184Q8—21no—
185Q8—82no—
186Q8—81no—
187Q8—132no—
188Q8—261no—
189Q8—522no—
190Q8Q8×D1312yes—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—262no—
197C2×C4C2×C22⋊D1312yes—
198C2×C4C2×C22⋊D1312yes—
199C2×C4C2×C22⋊D1311yescharacteristic
200C2×C4C2×C22⋊D1311yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—132no—
203C8—261no—
204C8—262no—
205C22C22×C22⋊D1311yescharacteristic
206C4—22no—
207C4—22no—
208C4—22no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—262no—
213C4—522no—
214C4—521no—
215C4#8819612yes—
216C4C2×Q8×D1311yescharacteristic
217C4#8825411yescharacteristic
218C2C2×#8819611yescharacteristic
219C2Q8×C22⋊D1311yescharacteristic
220C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingQ82×C13C2
socle, prime radicalC22×C13C22×D4
hypercenterQ82D13
hypocenterC13#3387
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
59. #6107Q8semidirect
182. C13#3387semidirect

Maximal subgroups

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

subgroupindex
Q82×C132
#117192722
#117187552
#117187522
#117187412
#117187402
#117186912
C4×#61072
#117186852
#117186832
#117186812
#338713