Finite Group Databasebeta

← #16834829

Subgroups — #16834829

Order 3712.

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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#14272166C211yesmaximal, characteristic, complemented
2C4×#90800C211yesmaximal, characteristic, complemented
3#14272013C212yesmaximal, complemented
4#14272011C212yesmaximal, complemented
5#14271631C211yesmaximal, characteristic
6C2×#90805C411yescharacteristic
7C2×#90800—21no—
8C2×#90800—21no—
9C29×#117C411yescharacteristic
10C2×C4×Dic29C2211yescharacteristic
11#11745255C411yescharacteristic
12#11745255C2211yescharacteristic
13#11745249C411yescharacteristic
14#11745249C2211yescharacteristic
15#11745243—21no—
16#11745243—21no—
17#11745234—21no—
18C42×D29—21no—
19#11745220—21no—
20#11745218—21no—
21C4⋊#6599C2212yes—
22C4×#6599C2212yes—
23C22×C4×C29C2×C411yescharacteristic
24C2×C22⋊D29—21no—
25C22×Dic29D411yescharacteristic
26C22×Dic29D411yescharacteristic
27#90805—22no—
28#90805—22no—
29C2×D116C2×C411yescharacteristic
30C2×C4×D29—21no—
31C2×C4×D29—21no—
32C2×C4×D29—21no—
33C2×Dic58C2×C411yescharacteristic
34#90800—24no—
35#90800—42no—
36C2×#6599—22no—
37C2×#6599—22no—
38C4⋊C4×C29C2×C411yescharacteristic
39C4⋊C4×C29C2×C411yescharacteristic
40C22⋊C4×C29—21no—
41C42×C29—21no—
42#90781—21no—
43#90781—21no—
44#90779—21no—
45#90779—21no—
46C4×Dic29—21no—
47C4×Dic29—21no—
48C4×Dic29C2×C411yescharacteristic
49C4×Dic29D411yescharacteristic
50C4×Dic29D411yescharacteristic
51C4×Dic29C2311yescharacteristic
52C23×C29C22⋊C411yescharacteristic
53C22×D29—21no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22×C411yescharacteristic
60C22⋊D29—24no—
61C2×Dic29—21no—
62C2×Dic29—22no—
63C2×Dic29—21no—
64C2×Dic29—21no—
65C2×Dic29C22⋊C411yescharacteristic
66C2×Dic29C22⋊C411yescharacteristic
67C2×Dic29C2×D411yescharacteristic
68C2×Dic29C2×D411yescharacteristic
69D116—21no—
70D116M1612yescomplemented
71C4×D29—24no—
72C4×D29—42no—
73C4×D29—41no—
74C4×D29—41no—
75Dic58—21no—
76Dic58M1612yescomplemented
77#6599—24no—
78#6599—42no—
79#1489—291nomaximal, Sylow
80C22×C29—21no—
81C22×C29—21no—
82C22×C29—21no—
83C22×C29C2×C22⋊C411yescharacteristic
84C2×D29—22no—
85C2×D29—41no—
86C2×D29—41no—
87C4×C29—21no—
88C4×C29—41no—
89C4×C29—41no—
90C4×C29C2×M1611yescharacteristic
91C4×C29C2×M1611yescharacteristic
92Dic29—22no—
93Dic29—21no—
94Dic29—21no—
95Dic29#10412yes—
96Dic29AGL(1,ℤ/8)11yescharacteristic
97Dic29#13711yescharacteristic
98C4×#41—291no—
99#423—291no—
100C4×M16—291no—
101Q8⋊C8—292no—
102D4⋊C8—292no—
103C2×C29—41no—
104C2×C29#40711yescharacteristic
105C2×C29#41711yescharacteristic
106C2×C29C2×#10411yescharacteristic
107D29—42no—
108C2×#41—291no—
109C2×M16—581no—
110C2×M16—581no—
111C4×Q8—291no—
112C4×Q8—291no—
113C4×D4—291no—
114C4×D4—291no—
115C4×D4—581no—
116C4×D4—581no—
117#117—581no—
118#117#118111yescharacteristic
119C2×C42—291no—
120C2×C42—581no—
121C4⋊C8—292no—
122C4⋊C8—581no—
123#97—581no—
124C4×C8—292no—
125C29#148911yescharacteristic, complemented, Sylow
126#41—582no—
127#41—582no—
128C2×Q8—291no—
129C2×D4—291no—
130C2×D4—581no—
131C22×C4—291no—
132C22×C4—291no—
133C22×C4—581no—
134C22×C4—581no—
135C22×C4—581no—
136C22×C4C2×#118111yescharacteristic
137M16—584no—
138M16—1162no—
139C2×C8—582no—
140C2×C8—582no—
141C4⋊C4—581no—
142C4⋊C4—581no—
143C4⋊C4C2×#118111yescharacteristic
144C4⋊C4C2×#118111yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—581no—
147C22⋊C4—581no—
148C42—21no—
149C42—291no—
150C42—291no—
151C42—291no—
152C42—291no—
153C42—581no—
154C42—581no—
155C23—581no—
156C23C22⋊#118111yescharacteristic
157Q8—292no—
158Q8—581no—
159D4—292no—
160D4—584no—
161D4—581no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—291no—
167C2×C4—291no—
168C2×C4—291no—
169C2×C4—291no—
170C2×C4—584no—
171C2×C4—582no—
172C2×C4—581no—
173C2×C4—581no—
174C2×C4—581no—
175C2×C4—1161no—
176C2×C4—1161no—
177C2×C4—1162no—
178C2×C4C22⋊#118111yescharacteristic
179C2×C4C22×#118111yescharacteristic
180C8—584no—
181C8—1162no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—582no—
186C22—1161no—
187C22—1161no—
188C22C2×C22⋊#118111yescharacteristic
189C4—21no—
190C4—41no—
191C4—41no—
192C4—291no—
193C4—291no—
194C4—292no—
195C4—582no—
196C4—581no—
197C4—581no—
198C4D29⋊M1611yescharacteristic
199C4D29⋊M1611yescharacteristic
200C2—41no—
201C2—1162no—
202C2#1427213511yescharacteristic
203C2#1427215411yescharacteristic
204C2D29⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#117C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#90805C4
cosocleC4×Dic29C23
hypercenter#117#1181
hypocenterC29#1489
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #14272166C2semidirect
2. C4×#90800C2semidirect
3. #14272013C2semidirect
4. #14272011C2semidirect
70. D116M16semidirect
76. Dic58M16semidirect
125. C29#1489semidirect

Maximal subgroups

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

subgroupindex
#142721662
C4×#908002
#142720132
#142720112
#142716312
#148929