Finite Group Databasebeta

← #16835753

Subgroups — #16835753

Order 3712.

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

normal subgroups only

This group has 266 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, complemented
2#14272142C211yesmaximal, characteristic, complemented
3#14272064C214yesmaximal, complemented
4#14271732C211yesmaximal, characteristic
5C2×#90805C2211yescharacteristic
6C22×D116C411yescharacteristic, complemented
7#11745345—21no—
8D29⋊M16—21no—
9C29×#117C411yescharacteristic, complemented
10#11745257—21no—
11#11745257—21no—
12#11745244C412yescomplemented
13#11745244C2212yes—
14#11745237—21no—
15#11745236—21no—
16#11745229C2212yes—
17#11745227C2212yes—
18#11745221—21no—
19#11745215—21no—
20C23×D29C2×C412yes—
21C22×C4×C29C2×C411yescharacteristic
22C2×C22⋊D29C2×C411yescharacteristic
23C2×C22⋊D29C2311yescharacteristic
24#90805—41no—
25#90805—41no—
26C2×D116—21no—
27C2×D116—21no—
28C2×D116—22no—
29C2×D116—22no—
30C2×D116—41no—
31C2×D116—41no—
32C2×D116D411yescharacteristic
33C2×C4×D29D411yescharacteristic
34C2×C4×D29D411yescharacteristic
35C2×Dic58D411yescharacteristic
36C22⋊#1181—22no—
37#90800—22no—
38C4⋊#1181—41no—
39C4×#1181—41no—
40#90796—41no—
41D29⋊C8—41no—
42C4⋊C4×C29—21no—
43C22⋊C4×C29C2×C412yes—
44C42×C29—21no—
45#90781—22no—
46#90781—22no—
47C23×C29C22×C411yescharacteristic
48C22×D29—22no—
49C22×D29—42no—
50C22×D29—82no—
51C22×D29C22⋊C411yescharacteristic
52C22×D29C2×D411yescharacteristic
53C2×#1181—42no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29—22no—
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22⋊C411yescharacteristic
59C22⋊D29—41no—
60C22⋊D29—41no—
61C2×Dic29C22⋊C411yescharacteristic
62C2×Dic29C2×D411yescharacteristic
63D116—41no—
64D116—42no—
65D116—41no—
66D116—41no—
67D116—82no—
68D116—82no—
69C4×D29—21no—
70C4×D29—21no—
71C4×D29—21no—
72C4×D29—21no—
73Dic58—41no—
74#6599—42no—
75#2122—291nomaximal, Sylow
76C22×C29—21no—
77C22×C29—41no—
78C22×C29C2×C22⋊C411yescharacteristic
79C2×D29—21no—
80C2×D29—21no—
81C2×D29—41no—
82C2×D29—41no—
83C2×D29—42no—
84C2×D29—42no—
85C2×D29—42no—
86C2×D29—84no—
87#1181—82no—
88C4×C29—21no—
89C4×C29—42no—
90C4×C29#9911yescharacteristic
91C4×C29#9911yescharacteristic
92Dic29—21no—
93Dic29—21no—
94#535—291no—
95#413—291no—
96#410—291no—
97AΣL(1,𝔽16)—294no—
98C2×C29—21no—
99C2×C29—41no—
100C2×C29C2×#9911yescharacteristic
101D29—41no—
102D29—41no—
103D29—82no—
104C2×#41—291no—
105C22×D4—291no—
106C2×M16—581no—
107#127—581no—
108#124—581no—
109#121—581no—
110#121—581no—
111#120—292no—
112#120—292no—
113#117—581no—
114#117#118111yescharacteristic, complemented
115#101—581no—
116#100—292no—
117#99—292no—
118#99—581no—
119C29#212211yescharacteristic, complemented, Sylow
120C24—292no—
121#41—1161no—
122#41—1161no—
123C2×Q8—291no—
124C2×D4—291no—
125C2×D4—291no—
126C2×D4—291no—
127C2×D4—582no—
128C2×D4—582no—
129C2×D4—581no—
130C2×D4—581no—
131C2×D4—1161no—
132C2×D4—1161no—
133C22×C4—291no—
134C22×C4—291no—
135C22×C4C2×#118111yescharacteristic
136M16—582no—
137M16—1161no—
138C2×C8—1161no—
139C4⋊C4—21no—
140C4⋊C4—1161no—
141C22⋊C4—582no—
142C22⋊C4—582no—
143C22⋊C4—582no—
144C22⋊C4C2×#118112yes—
145C42—21no—
146C42—1161no—
147C23—291no—
148C23—291no—
149C23—582no—
150C23—1162no—
151C23—2322no—
152C23C22×#118111yescharacteristic
153Q8—1161no—
154D4—1161no—
155D4—1162no—
156D4—1161no—
157D4—1161no—
158D4—1161no—
159D4—1161no—
160D4—2322no—
161D4—2322no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—291no—
166C2×C4—291no—
167C2×C4—581no—
168C2×C4—581no—
169C2×C4—581no—
170C2×C4—581no—
171C2×C4—1162no—
172C2×C4C22⋊#118111yescharacteristic
173C2×C4C22⋊#118111yescharacteristic
174C8—1162no—
175C22—21no—
176C22—41no—
177C22—581no—
178C22—581no—
179C22—1161no—
180C22—1161no—
181C22—1162no—
182C22—1162no—
183C22—1162no—
184C22—2324no—
185C22C2×C22⋊#118111yescharacteristic
186C4—21no—
187C4—42no—
188C4—581no—
189C4—581no—
190C4—2322no—
191C4#1174521511yescharacteristic
192C4#1174521511yescharacteristic
193C2—21no—
194C2—41no—
195C2—1161no—
196C2—1161no—
197C2—2322no—
198C2C2×#1174521511yescharacteristic
subgroupG/H
centerC2C2×#11745215
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#117C4
socleC2×C29C2×#99
prime radical#14271732C2
cosocleC2×C22⋊D29C23
hypercenter#117#1181
hypocenterC29#2122
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
1. #14272149C2semidirect
2. #14272142C2semidirect
3. #14272064C2semidirect
6. C22×D116C4semidirect
9. C29×#117C4semidirect
12. #11745244C4semidirect
114. #117#1181semidirect
119. C29#2122semidirect

Maximal subgroups

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

subgroupindex
#142721492
#142721422
#142720642
#142717322
#212229