Finite Group Databasebeta

← #16819467

Subgroups — #16819467

Order 3712.

536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 121 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#14271180C212yesmaximal, complemented
2#14271172C212yesmaximal, complemented
3#14271147C211yesmaximal, characteristic, complemented
4#14271137C211yesmaximal, characteristic, complemented
5C2×C29×2−1+4C211yesmaximal, characteristic
6C29×2−1+4—24no—
7C29×2−1+4—24no—
8C2×#41×C29—21no—
9C2×#41×C29—22no—
10C2×#41×C29C412yescomplemented
11C2×#41×C29C2211yescharacteristic
12C2×#41×C29C2211yescharacteristic
13C22×Q8×C29—21no—
14C22×Q8×C29C412yescomplemented
15C22×Q8×C29C2211yescharacteristic
16#11745288C2212yes—
17C2×#90777C2212yes—
18#11745185—24no—
19#11745184—21no—
20#11745183—24no—
21#11745182—22no—
22#11745181—21no—
23#41×C29—216no—
24#41×C29—28no—
25#41×C29—24no—
26#41×C29—24no—
27#41×C29—22no—
28#41×C29—22no—
29#41×C29—22no—
30#41×C29D414yes—
31C2×Q8×C29—28no—
32C2×Q8×C29—24no—
33C2×Q8×C29—24no—
34C2×Q8×C29—22no—
35C2×Q8×C29—21no—
36C2×Q8×C29—22no—
37C2×Q8×C29C2×C411yescharacteristic
38C2×Q8×C29C2×C412yes—
39C2×Q8×C29D414yes—
40C2×Q8×C29D411yescharacteristic
41C2×D4×C29—22no—
42C2×D4×C29—21no—
43C2×D4×C29C2×C411yescharacteristic
44C2×D4×C29D412yes—
45C2×D4×C29D411yescharacteristic
46C22×C4×C29—22no—
47C22×C4×C29—21no—
48C22×C4×C29—22no—
49C22×C4×C29—21no—
50C22×C4×C29C2×C412yes—
51C22×C4×C29C2311yescharacteristic
52C22⋊Dic29—22no—
53C4⋊Dic29—22no—
54C4×Dic29—22no—
55#90777—22no—
56#90777—22no—
57C2×#6597—22no—
58C23×C29—21no—
59C23×C29C22⋊C412yes—
60C23×C29C2×D411yescharacteristic
61Q8×C29—28no—
62Q8×C29—21no—
63Q8×C29—22no—
64Q8×C29—24no—
65Q8×C29—22no—
66Q8×C29C22⋊C412yes—
67Q8×C29C22⋊C414yes—
68D4×C29—28no—
69D4×C29—24no—
70D4×C29—24no—
71D4×C29—21no—
72D4×C29—22no—
73D4×C29C22⋊C412yes—
74C2×C4×C29—28no—
75C2×C4×C29—28no—
76C2×C4×C29—21no—
77C2×C4×C29—22no—
78C2×C4×C29—24no—
79C2×C4×C29—22no—
80C2×C4×C29—22no—
81C2×C4×C29—24no—
82C2×C4×C29C22⋊C412yes—
83C2×C4×C29C22×C411yescharacteristic
84C2×C4×C29C2×D412yes—
85C2×C4×C29C2×D412yes—
86C2×C4×C29C2×D411yescharacteristic
87C2×Dic29—42no—
88#6597—42no—
89#1796—291nomaximal, Sylow
90C22×C29—22no—
91C22×C29—22no—
92C22×C29—41no—
93C22×C29—42no—
94C22×C29—42no—
95C22×C29C2×C22⋊C411yescharacteristic
96C22×C29#12012yes—
97C4×C29—24no—
98C4×C29—22no—
99C4×C29—22no—
100C4×C29C2×C22⋊C411yescharacteristic
101C4×C29C2×C22⋊C411yescharacteristic
102C4×C29#12012yes—
103Dic29—82no—
104C2×2−1+4D2911yescharacteristic
105#421—292no—
106#419—292no—
107#413—291no—
108#410—291no—
109C2×C29—22no—
110C2×C29—21no—
111C2×C29—42no—
112C2×C29—42no—
113C2×C29#37911yescharacteristic
1142−1+4—24no—
1152−1+4—24no—
116C2×#41—21no—
117C2×#41—22no—
118C2×#41Dic2912yescomplemented
119C2×#41C2×D2911yescharacteristic
120C2×#41C2×D2911yescharacteristic
121C22×Q8—21no—
122C22×Q8Dic2912yescomplemented
123C22×Q8C2×D2911yescharacteristic
124C2×M16—292no—
125#117—292no—
126#104—584no—
127#103—584no—
128#101—581no—
129#100—581no—
130#99—582no—
131C29#179611yescharacteristic, complemented, Sylow
132#41—216no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—22no—
137#41—22no—
138#41—22no—
139#41C22⋊D2914yes—
140C2×Q8—28no—
141C2×Q8—24no—
142C2×Q8—24no—
143C2×Q8—22no—
144C2×Q8—21no—
145C2×Q8—22no—
146C2×Q8C2×Dic2911yescharacteristic
147C2×Q8C2×Dic2912yes—
148C2×Q8C22⋊D2914yes—
149C2×Q8C22⋊D2911yescharacteristic
150C2×D4—22no—
151C2×D4—21no—
152C2×D4C2×Dic2911yescharacteristic
153C2×D4C22⋊D2912yes—
154C2×D4C22⋊D2911yescharacteristic
155C22×C4—22no—
156C22×C4—21no—
157C22×C4—22no—
158C22×C4—21no—
159C22×C4C2×Dic2912yes—
160C22×C4C22×D2911yescharacteristic
161M16—582no—
162M16—582no—
163C2×C8—582no—
164C4⋊C4—582no—
165C22⋊C4—582no—
166C42—582no—
167C23—21no—
168C23C22⋊Dic2912yes—
169C23C2×C22⋊D2911yescharacteristic
170Q8—28no—
171Q8—21no—
172Q8—22no—
173Q8—24no—
174Q8—22no—
175Q8C22⋊Dic2912yes—
176Q8C22⋊Dic2914yes—
177D4—28no—
178D4—24no—
179D4—24no—
180D4—21no—
181D4—22no—
182D4C22⋊Dic2912yes—
183C2×C4—28no—
184C2×C4—28no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—1162no—
192C2×C4C22⋊Dic2912yes—
193C2×C4C22×Dic2911yescharacteristic
194C2×C4C2×C22⋊D2912yes—
195C2×C4C2×C22⋊D2912yes—
196C2×C4C2×C22⋊D2911yescharacteristic
197C8—1162no—
198C22—22no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22C2×C22⋊Dic2911yescharacteristic
204C22#1174531512yes—
205C4—24no—
206C4—22no—
207C4—22no—
208C4—2322no—
209C4C2×C22⋊Dic2911yescharacteristic
210C4C2×C22⋊Dic2911yescharacteristic
211C4#1174531512yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—42no—
216C2#1427101911yescharacteristic
subgroupG/H
centerC2#14271019
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
Fitting, prime radicalC2×C29×2−1+4C2
socleC2×C29#379
cosocleC22×C4×C29C23
hypercenterC2×2−1+4D29
hypocenterC29#1796
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #14271180C2semidirect
2. #14271172C2semidirect
3. #14271147C2semidirect
4. #14271137C2semidirect
10. C2×#41×C29C4semidirect
14. C22×Q8×C29C4semidirect
118. C2×#41Dic29semidirect
122. C22×Q8Dic29semidirect
131. C29#1796semidirect

Maximal subgroups

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

subgroupindex
#142711802
#142711722
#142711472
#142711372
C2×C29×2−1+42
#179629