Finite Group Databasebeta

← #16835756

Subgroups — #16835756

Order 3712.

234 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 54 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#14272149C211yesmaximal, characteristic
2#14272142C211yesmaximal, characteristic
3#14272066C214yesmaximal, complemented
4#14271739C211yesmaximal, characteristic
5C2×#90805C2211yescharacteristic
6C22×Dic58C411yescharacteristic, complemented
7#11745345—21no—
8D29⋊M16—21no—
9C29×#117C411yescharacteristic, complemented
10#11745259—21no—
11#11745259—21no—
12#11745248C412yescomplemented
13#11745248C2212yes—
14#11745237—21no—
15#11745231—21no—
16#11745229C2212yes—
17#11745227C2212yes—
18#11745221—21no—
19#11745215—21no—
20C22×C4×C29C2×C411yescharacteristic
21C2×C22⋊D29C2×C411yescharacteristic
22C2×C22⋊D29C2311yescharacteristic
23C22×Dic29C2×C412yes—
24#90805—41no—
25#90805—41no—
26C2×D116D411yescharacteristic
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×Dic58—21no—
30C2×Dic58—21no—
31C2×Dic58—41no—
32C2×Dic58—41no—
33C2×Dic58D411yescharacteristic
34C22⋊#1181—22no—
35#90800—22no—
36C4⋊#1181—41no—
37C4×#1181—41no—
38#90796—41no—
39D29⋊C8—41no—
40C4⋊C4×C29—21no—
41C22⋊C4×C29C2×C412yes—
42C42×C29—21no—
43#90781—22no—
44#90781—22no—
45C4⋊Dic29—22no—
46C4⋊Dic29—22no—
47C23×C29C22×C411yescharacteristic
48C22×D29C22⋊C411yescharacteristic
49C22×D29C2×D411yescharacteristic
50C2×#1181—42no—
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29—22no—
54C2×C4×C29C22⋊C411yescharacteristic
55C2×C4×C29C22⋊C411yescharacteristic
56C22⋊D29—41no—
57C22⋊D29—41no—
58C2×Dic29—22no—
59C2×Dic29—42no—
60C2×Dic29C22⋊C411yescharacteristic
61C2×Dic29C2×D411yescharacteristic
62D116—41no—
63C4×D29—21no—
64C4×D29—21no—
65C4×D29—21no—
66C4×D29—21no—
67Dic58—41no—
68Dic58—42no—
69Dic58—41no—
70Dic58—41no—
71#6599—42no—
72#2123—291nomaximal, Sylow
73C22×C29—21no—
74C22×C29—41no—
75C22×C29C2×C22⋊C411yescharacteristic
76C2×D29—21no—
77C2×D29—21no—
78C2×D29—41no—
79C2×D29—41no—
80#1181—82no—
81C4×C29—21no—
82C4×C29—42no—
83C4×C29#9911yescharacteristic
84C4×C29#9911yescharacteristic
85Dic29—21no—
86Dic29—21no—
87Dic29—42no—
88#536—291no—
89#413—291no—
90#410—291no—
91#352—294no—
92C2×C29—21no—
93C2×C29—41no—
94C2×C29C2×#9911yescharacteristic
95D29—41no—
96D29—41no—
97C2×#41—291no—
98C22×Q8—291no—
99C2×M16—581no—
100C4⋊Q8—581no—
101#124—581no—
102#123—292no—
103#123—292no—
104C22⋊Q8—581no—
105C22⋊Q8—581no—
106#117—581no—
107#117#118111yescharacteristic, complemented
108#101—581no—
109#100—292no—
110#99—292no—
111#99—581no—
112C29#212311yescharacteristic, complemented, Sylow
113#41—1161no—
114#41—1161no—
115C2×Q8—291no—
116C2×Q8—581no—
117C2×Q8—581no—
118C2×Q8—1161no—
119C2×Q8—1161no—
120C2×D4—291no—
121C2×D4—291no—
122C2×D4—291no—
123C22×C4—291no—
124C22×C4—291no—
125C22×C4—292no—
126C22×C4C2×#118111yescharacteristic
127M16—582no—
128M16—1161no—
129C2×C8—1161no—
130C4⋊C4—21no—
131C4⋊C4—582no—
132C4⋊C4—582no—
133C4⋊C4—1161no—
134C22⋊C4—582no—
135C22⋊C4—582no—
136C22⋊C4—582no—
137C22⋊C4C2×#118112yes—
138C42—21no—
139C42—1161no—
140C23—291no—
141C23—291no—
142C23C22×#118111yescharacteristic
143Q8—1161no—
144Q8—1162no—
145Q8—1161no—
146Q8—1161no—
147D4—1161no—
148D4—1161no—
149D4—1161no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—291no—
154C2×C4—291no—
155C2×C4—581no—
156C2×C4—581no—
157C2×C4—581no—
158C2×C4—581no—
159C2×C4—582no—
160C2×C4—1162no—
161C2×C4—1162no—
162C2×C4C22⋊#118111yescharacteristic
163C2×C4C22⋊#118111yescharacteristic
164C8—1162no—
165C22—21no—
166C22—41no—
167C22—581no—
168C22—581no—
169C22—1161no—
170C22—1161no—
171C22C2×C22⋊#118111yescharacteristic
172C4—21no—
173C4—42no—
174C4—581no—
175C4—581no—
176C4—1162no—
177C4—2322no—
178C4#1174521511yescharacteristic
179C4#1174521511yescharacteristic
180C2—21no—
181C2—41no—
182C2—1161no—
183C2—1161no—
184C2C2×#1174521511yescharacteristic
subgroupG/H
centerC2C2×#11745215
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#117C4
socleC2×C29C2×#99
prime radicalC2×#90805C22
cosocleC2×C22⋊D29C23
hypercenter#117#1181
hypocenterC29#2123
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #14272066C2semidirect
6. C22×Dic58C4semidirect
9. C29×#117C4semidirect
12. #11745248C4semidirect
107. #117#1181semidirect
112. C29#2123semidirect

Maximal subgroups

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

subgroupindex
#142721492
#142721422
#142720662
#142717392
#212329