Finite Group Databasebeta

← #16834952

Subgroups — #16834952

Order 3712.

264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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#14272186C211yesmaximal, characteristic, complemented
2C4×#90796C211yesmaximal, characteristic, complemented
3#14272019C212yesmaximal, complemented
4#14272018C212yesmaximal, complemented
5#124×D29C211yesmaximal, characteristic
6C2×Q8×D29C411yescharacteristic
7C2×D4×D29C411yescharacteristic
8C2×#90796—21no—
9C29×#124C411yescharacteristic
10#11745309C2211yescharacteristic
11#11745298C2211yescharacteristic
12#11745247—21no—
13#11745247—21no—
14C22⋊C4×D29—21no—
15C22⋊C4×D29—21no—
16#11745237C411yescharacteristic
17C42×D29C2211yescharacteristic
18#11745220—21no—
19#11745219—21no—
20#11745218C2212yescomplemented
21#11745218C2212yescomplemented
22C4×#6599—21no—
23C23×D29—21no—
24C2×Q8×C29C2×C411yescharacteristic
25C2×D4×C29C2×C411yescharacteristic
26C2×C22⋊D29—21no—
27Q8×D29—42no—
28D4×D29—42no—
29C2×D116C2×C411yescharacteristic
30C2×C4×D29—21no—
31C2×C4×D29C2×C411yescharacteristic
32C2×C4×D29D411yescharacteristic
33C2×C4×D29D411yescharacteristic
34C2×Dic58—21no—
35C2×Dic58C2×C411yescharacteristic
36C2×#6599—22no—
37C2×#6599—22no—
38#90796—24no—
39C22⋊C4×C29—21no—
40C22⋊C4×C29—21no—
41C42×C29C2×C411yescharacteristic
42C22⋊Dic29—21no—
43C22⋊Dic29—21no—
44#90781—21no—
45#90781—21no—
46#90781—21no—
47#90781—21no—
48C4×Dic29D411yescharacteristic
49C4×Dic29D411yescharacteristic
50C4×Dic29C2311yescharacteristic
51C23×C29—21no—
52C22×D29—21no—
53C22×D29—42no—
54C22×D29—42no—
55C22×D29—42no—
56C22×D29C22⋊C411yescharacteristic
57Q8×C29—41no—
58D4×C29—41no—
59C2×C4×C29—21no—
60C2×C4×C29C22⋊C411yescharacteristic
61C2×C4×C29C22⋊C411yescharacteristic
62C2×C4×C29C22×C411yescharacteristic
63C22⋊D29—42no—
64C2×Dic29—21no—
65C2×Dic29C22⋊C411yescharacteristic
66C2×Dic29C2×D411yescharacteristic
67C2×Dic29C2×D411yescharacteristic
68D116—41no—
69C4×D29—22no—
70C4×D29—22no—
71C4×D29—41no—
72C4×D29—42no—
73Dic58—42no—
74Dic58—41no—
75#6599—24no—
76#6599—42no—
77#1527—291nomaximal, Sylow
78C22×C29—41no—
79C22×C29—41no—
80C22×C29—41no—
81C22×C29C2×C22⋊C411yescharacteristic
82C2×D29—21no—
83C2×D29—21no—
84C2×D29—41no—
85C2×D29—41no—
86C2×D29—41no—
87C2×D29—84no—
88C2×D29#10412yes—
89C4×C29—21no—
90C4×C29—21no—
91C4×C29—21no—
92C4×C29—41no—
93Dic29—21no—
94Dic29—21no—
95Dic29—41no—
96Dic29#10012yes—
97C2×#124—291no—
98#432—291no—
99C4×M16—291no—
100#329—292no—
101#329—292no—
102C2×C29—81no—
103C2×C29C2×#10011yescharacteristic
104C2×C29C2×#10411yescharacteristic
105C2×C29#42111yescharacteristic
106D29—22no—
107D29—81no—
108C22×Q8—291no—
109C22×D4—291no—
110C2×M16—581no—
111#124—291no—
112#124—291no—
113#124—291no—
114#124—581no—
115#124—581no—
116#124#118111yescharacteristic
117C2×C22⋊C4—581no—
118C2×C22⋊C4—581no—
119C2×C42—291no—
120C4⋊C8—581no—
121C22⋊C8—581no—
122#97—292no—
123#97—292no—
124C4×C8—581no—
125C29#152711yescharacteristic, complemented, Sylow
126C24—581no—
127C2×Q8—291no—
128C2×Q8—581no—
129C2×Q8—1162no—
130C2×Q8C2×#118111yescharacteristic
131C2×D4—291no—
132C2×D4—581no—
133C2×D4—1162no—
134C2×D4C2×#118111yescharacteristic
135C22×C4—291no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—581no—
139M16—584no—
140C2×C8—582no—
141C2×C8—582no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—581no—
145C22⋊C4—581no—
146C22⋊C4—581no—
147C22⋊C4—581no—
148C22⋊C4—581no—
149C22⋊C4—581no—
150C42—291no—
151C42—291no—
152C42—291no—
153C42C2×#118111yescharacteristic
154C23—21no—
155C23—291no—
156C23—581no—
157C23—1162no—
158C23—1162no—
159C23—1162no—
160Q8—41no—
161Q8—1161no—
162Q8—1162no—
163D4—41no—
164D4—1161no—
165D4—1162no—
166C2×C4—21no—
167C2×C4—291no—
168C2×C4—291no—
169C2×C4—291no—
170C2×C4—582no—
171C2×C4—582no—
172C2×C4—581no—
173C2×C4—1161no—
174C2×C4—1162no—
175C2×C4C22⋊#118111yescharacteristic
176C2×C4C22⋊#118111yescharacteristic
177C2×C4C22×#118111yescharacteristic
178C8—584no—
179C8—1162no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—292no—
184C22—581no—
185C22—581no—
186C22—1161no—
187C22—1161no—
188C22—1161no—
189C22—2324no—
190C22C2×C22⋊#118111yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—292no—
196C4—581no—
197C4—581no—
198C4—1161no—
199C2—81no—
200C2—582no—
201C2—2321no—
202C2D29⋊#10011yescharacteristic
203C2D29⋊#10411yescharacteristic
204C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#124C4
socleC22×C29C2×C22⋊C4
prime radicalC2×D4×D29C4
cosocleC4×Dic29C23
hypercenter#124#1181
hypocenterC29#1527
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14272186C2semidirect
2. C4×#90796C2semidirect
3. #14272019C2semidirect
4. #14272018C2semidirect
20. #11745218C22semidirect
21. #11745218C22semidirect
125. C29#1527semidirect

Maximal subgroups

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

subgroupindex
#142721862
C4×#907962
#142720192
#142720182
#124×D292
#152729