Finite Group Databasebeta

← #16778397

Subgroups — #16778397

Order 3328.

440 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 118 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#13130763C212yesmaximal
2#13129656C214yesmaximal
3C4⋊Q8×Dic13C211yesmaximal, characteristic
4C2×C13×C4⋊Q8C411yescharacteristic
5C2×Q8×Dic13C412yes—
6#11718891C2212yes—
7#11718646—22no—
8C4⋊C4×Dic13—22no—
9#11718596C411yescharacteristic
10C42×Dic13C2211yescharacteristic
11#11718290—22no—
12#11718290—22no—
13#11718290C2214yes—
14C22×Q8×C13C2×C412yes—
15C22×#1057—24no—
16C13×C4⋊Q8—22no—
17C13×C4⋊Q8C814yescomplemented
18C2×C13×C4⋊C4—22no—
19C2×C42×C13C2×C411yescharacteristic
20Q8×Dic13—44no—
21C2×C4⋊Dic13—22no—
22C2×C4⋊Dic13—22no—
23C2×C4⋊Dic13C2×C412yes—
24C2×C4×Dic13—22no—
25C2×C4×Dic13C2×C411yescharacteristic
26C2×C4×Dic13D412yes—
27C2×C4×Dic13D412yes—
28C2×C4×Dic13C2311yescharacteristic
29#88071—24no—
30#7605—131nomaximal, Sylow
31C2×Q8×C13—22no—
32C2×Q8×C13—42no—
33C2×Q8×C13—42no—
34C2×Q8×C13C2×C814yes—
35C22×C4×C13—22no—
36C22×C4×C13C22⋊C412yes—
37C22×C4×C13C22×C411yescharacteristic
38C22×Dic13—22no—
39C22×Dic13C22⋊C411yescharacteristic
40C22×Dic13C22⋊C411yescharacteristic
41C22×Dic13C2×D412yes—
42C2×#1057—44no—
43C2×#1057—44no—
44C2×#1057—44no—
45C13×C4⋊C4—28no—
46C42×C13C2×C812yes—
47C42×C13M1612yes—
48C4⋊Dic13—44no—
49C4⋊Dic13—44no—
50C4⋊Dic13—42no—
51C4×Dic13—22no—
52C4×Dic13—24no—
53C4×Dic13—42no—
54C4×Dic13—41no—
55C4×Dic13—44no—
56C4×C4⋊Q8—131no—
57#1839—132no—
58#1272—134no—
59C23×C13C2×C22⋊C411yescharacteristic
60Q8×C13—44no—
61Q8×C13—44no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—24no—
67C2×C4×C13—42no—
68C2×C4×C13—42no—
69C2×C4×C13C22⋊C814yes—
70C2×C4×C13C22×C811yescharacteristic
71C2×C4×C13C2×M1611yescharacteristic
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—21no—
76C2×Dic13—22no—
77C2×Dic13—42no—
78C2×Dic13—44no—
79C2×Dic13#10012yes—
80C2×Dic13#13714yes—
81#1057—84no—
82C2×C4⋊Q8#26111yescharacteristic
83C2×C4×Q8—132no—
84#391—132no—
85#389—262no—
86#384—131no—
87C4×C4⋊C4—262no—
88C43—131no—
89#336—134no—
90#336—262no—
91#336—262no—
92C22×C13C2×C22⋊C811yescharacteristic
93C22×C13#41011yescharacteristic
94C22×C13C2×#10011yescharacteristic
95C22×C13#41912yes—
96C22×C13#42112yes—
97C4×C13—21no—
98C4×C13—21no—
99C4×C13—24no—
100C4×C13—44no—
101Dic13—22no—
102Dic13—24no—
103Dic13—41no—
104Dic13—82no—
105C22×Q8C2×#26112yes—
106C22×C8—264no—
107C4⋊Q8—22no—
108C4⋊Q8#105714yescomplemented
109C4×Q8—524no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—132no—
112C2×C4⋊C4—262no—
113C2×C4⋊C4—262no—
114C2×C42—132no—
115C2×C42—131no—
116C2×C42—132no—
117C2×C42—131no—
118C2×C42—262no—
119C2×C42C2×#26111yescharacteristic
120#95—264no—
121C2×C13#146011yescharacteristic
122C2×C13#147912yes—
123C2×C13#151512yes—
124C2×C13#153611yescharacteristic
125C2×C13#155811yescharacteristic
126C2×Q8—22no—
127C2×Q8—42no—
128C2×Q8—42no—
129C2×Q8C2×#105714yes—
130C22×C4—22no—
131C22×C4—132no—
132C22×C4—131no—
133C22×C4—131no—
134C22×C4—262no—
135C22×C4C22⋊#26112yes—
136C22×C4C22×#26111yescharacteristic
137C2×C8—524no—
138C2×C8—524no—
139C2×C8—524no—
140C4⋊C4—28no—
141C4⋊C4—522no—
142C4⋊C4—524no—
143C4⋊C4—524no—
144C42—262no—
145C42—264no—
146C42—521no—
147C42—522no—
148C42—524no—
149C42C2×#105712yes—
150C42#612212yes—
151C13#760511yescharacteristic, complemented, Sylow
152C23C2×C22⋊#26111yescharacteristic
153Q8—44no—
154Q8—44no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—132no—
163C2×C4—134no—
164C2×C4—262no—
165C2×C4—262no—
166C2×C4—262no—
167C2×C4—261no—
168C2×C4—262no—
169C2×C4—522no—
170C2×C4—524no—
171C2×C4C22⋊#105714yes—
172C2×C4C22×#105711yescharacteristic
173C2×C4C2×#612211yescharacteristic
174C8—1044no—
175C22#1171914211yescharacteristic
176C22D13⋊#10011yescharacteristic
177C22#1171915312yes—
178C22#1171915512yes—
179C22C2×C22⋊#105711yescharacteristic
180C4—21no—
181C4—21no—
182C4—24no—
183C4—44no—
184C4—264no—
185C4—262no—
186C4—521no—
187C4—1042no—
188C2#1313007611yescharacteristic
189C2#1313013812yes—
190C2#1313026012yes—
191C2#1313032611yescharacteristic
192C2#1313037011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#7605
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
17. C13×C4⋊Q8C8semidirect
108. C4⋊Q8#1057semidirect
151. C13#7605semidirect

Maximal subgroups

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

subgroupindex
#131307632
#131296562
C4⋊Q8×Dic132
#760513