Finite Group Databasebeta

← #16819911

Subgroups — #16819911

Order 3712.

342 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 93 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#14271930C211yesmaximal, characteristic, complemented
2#14271147C211yesmaximal, characteristic, complemented
3#14271127C212yesmaximal, complemented
4#14270933C212yesmaximal, complemented
5C29×#525C211yesmaximal, characteristic
6C2×#41×C29C2211yescharacteristic
7C23×C4×C29C2211yescharacteristic
8C29×#123C412yes—
9C29×C22⋊Q8—21no—
10C29×#121—21no—
11C29×#120C412yes—
12C4×D4×C29—22no—
13C29×#117C2211yescharacteristic
14#11745310—24no—
15C2×#90777—22no—
16C2×#90777C2212yes—
17C2×#90777C2212yes—
18#11745184—21no—
19#11745181—21no—
20C22⋊#6597—24no—
21C24×C29C2×C411yescharacteristic
22#41×C29—22no—
23#41×C29—22no—
24C2×Q8×C29D411yescharacteristic
25C2×D4×C29—22no—
26C2×D4×C29C2×C412yes—
27C2×D4×C29D411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29—21no—
30C22×C4×C29—22no—
31C22×C4×C29—22no—
32C22×C4×C29C2×C411yescharacteristic
33C22×C4×C29D412yes—
34C22×C4×C29C2311yescharacteristic
35C4⋊C4×C29—22no—
36C4⋊C4×C29—21no—
37C22⋊C4×C29—22no—
38C22⋊C4×C29—22no—
39C22⋊C4×C29C2×C412yes—
40C42×C29—21no—
41#90777—24no—
42#90777—22no—
43#90777—22no—
44#90777—22no—
45#90777—22no—
46C2×#6597—24no—
47C2×#6597—22no—
48C2×#6597D414yescomplemented
49C23×C29—21no—
50C23×C29—22no—
51C23×C29—42no—
52C23×C29C22⋊C412yes—
53C23×C29C22×C411yescharacteristic
54Q8×C29—22no—
55D4×C29—24no—
56D4×C29—22no—
57D4×C29—44no—
58C2×C4×C29—22no—
59C2×C4×C29—22no—
60C2×C4×C29—22no—
61C2×C4×C29—21no—
62C2×C4×C29—22no—
63C2×C4×C29—41no—
64C2×C4×C29—42no—
65C2×C4×C29—41no—
66C2×C4×C29C22⋊C412yes—
67C2×C4×C29C2×D412yes—
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29#4112yes—
71#6597—24no—
72#6597—42no—
73#1891—291nomaximal, Sylow
74C22×C29—22no—
75C22×C29—24no—
76C22×C29—22no—
77C22×C29—41no—
78C22×C29—42no—
79C22×C29—41no—
80C22×C29—42no—
81C22×C29—41no—
82C22×C29C2×C22⋊C411yescharacteristic
83C22×C29C4×D412yes—
84C4×C29—22no—
85C4×C29—42no—
86C4×C29—41no—
87C4×C29#12011yescharacteristic
88C4×C29#12112yes—
89C4×C29#12311yescharacteristic
90#568—291no—
91#525D2911yescharacteristic
92#413—291no—
93#407—292no—
94#344—292no—
95C2×C29—21no—
96C2×C29—22no—
97C2×C29—42no—
98C2×C29—42no—
99C2×C29#38611yescharacteristic
100C2×#41C2×D2911yescharacteristic
101C23×C4C2×D2911yescharacteristic
102#131—584no—
103C2×M16—292no—
104C2×M16—292no—
105C2×M16—582no—
106#123Dic2912yes—
107C22⋊Q8—21no—
108#121—21no—
109#120Dic2912yes—
110C4×D4—22no—
111#117C2×D2911yescharacteristic
112#101—581no—
113#100—581no—
114C22⋊C8—584no—
115C29#189111yescharacteristic, complemented, Sylow
116C24C2×Dic2911yescharacteristic
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D2911yescharacteristic
120C2×D4—22no—
121C2×D4C2×Dic2912yes—
122C2×D4C22⋊D2911yescharacteristic
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4C2×Dic2911yescharacteristic
128C22×C4C22⋊D2912yes—
129C22×C4C22×D2911yescharacteristic
130M16—584no—
131M16—582no—
132M16—582no—
133M16—582no—
134M16—582no—
135C2×C8—294no—
136C2×C8—584no—
137C2×C8—582no—
138C4⋊C4—22no—
139C4⋊C4—21no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4C2×Dic2912yes—
143C42—21no—
144C23—22no—
145C23—21no—
146C23—42no—
147C23C22⋊Dic2912yes—
148C23C22×Dic2911yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4C22⋊Dic2912yes—
162C2×C4D4×D2912yes—
163C2×C4#9080712yes—
164C2×C4C2×C22⋊D2911yescharacteristic
165C2×C4C2×C22⋊D2911yescharacteristic
166C8—584no—
167C8—1162no—
168C22—22no—
169C22—24no—
170C22—22no—
171C22—41no—
172C22—42no—
173C22—41no—
174C22—42no—
175C22—41no—
176C22D4×Dic2912yes—
177C22C2×C22⋊Dic2911yescharacteristic
178C4—22no—
179C4—42no—
180C4—41no—
181C4#1174529711yescharacteristic
182C4#1174529911yescharacteristic
183C4#1174530112yes—
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2#1427104311yescharacteristic
subgroupG/H
centerC4#11745299
commutatorC23×C29C22×C4
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#525C2
socleC2×C29#386
cosocleC22×C4×C29C23
hypercenter#525D29
hypocenterC29#1891
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14271930C2semidirect
2. #14271147C2semidirect
3. #14271127C2semidirect
4. #14270933C2semidirect
48. C2×#6597D4semidirect
115. C29#1891semidirect

Maximal subgroups

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

subgroupindex
#142719302
#142711472
#142711272
#142709332
C29×#5252
#189129