Finite Group Databasebeta

← #16834967

Subgroups — #16834967

Order 3712.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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
2#14272122C211yesmaximal, characteristic, complemented
3#14272020C212yesmaximal, complemented
4#14272018C212yesmaximal, complemented
5#14271695C211yesmaximal, characteristic
6C2×D29⋊C8—21no—
7C4×D4×C29C411yescharacteristic
8#11745300C411yescharacteristic
9#11745298C2211yescharacteristic
10C4×C22⋊D29—21no—
11#11745288—21no—
12#11745259C411yescharacteristic
13#11745252C2211yescharacteristic
14#11745245—21no—
15#11745241—21no—
16C42×D29C2211yescharacteristic
17C4×Dic58C411yescharacteristic
18#11745220—21no—
19#11745219—21no—
20#11745218—21no—
21#11745218C2212yes—
22#11745218C2212yes—
23C2×D4×C29C2×C411yescharacteristic
24C22×C4×C29—21no—
25C2×C22⋊D29—21no—
26C2×C4×D29C2×C411yescharacteristic
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×Dic58C2×C411yescharacteristic
30C2×#6599—22no—
31C2×#6599—22no—
32D29⋊C8—24no—
33C4⋊C4×C29C2×C411yescharacteristic
34C22⋊C4×C29—21no—
35C42×C29C2×C411yescharacteristic
36C22⋊Dic29—21no—
37C22⋊Dic29—21no—
38C22⋊Dic29—21no—
39#90781—21no—
40C4⋊Dic29—21no—
41C4⋊Dic29—21no—
42C4⋊Dic29C2×C411yescharacteristic
43#90779—21no—
44#90779—21no—
45C4×Dic29—21no—
46C4×Dic29D411yescharacteristic
47C4×Dic29D411yescharacteristic
48C4×Dic29C2311yescharacteristic
49C23×C29—21no—
50C22×D29C22⋊C411yescharacteristic
51D4×C29—41no—
52C2×C4×C29—21no—
53C2×C4×C29—42no—
54C2×C4×C29C22⋊C411yescharacteristic
55C2×C4×C29C22⋊C411yescharacteristic
56C2×C4×C29C22×C411yescharacteristic
57C22⋊D29—42no—
58C2×Dic29—21no—
59C2×Dic29—21no—
60C2×Dic29C22⋊C411yescharacteristic
61C2×Dic29C2×D411yescharacteristic
62C2×Dic29C2×D411yescharacteristic
63C4×D29—22no—
64C4×D29—41no—
65C4×D29—41no—
66Dic58—41no—
67#6599—24no—
68#6599—42no—
69#1532—291nomaximal, Sylow
70C22×C29—41no—
71C22×C29—41no—
72C22×C29—41no—
73C22×C29C2×C22⋊C411yescharacteristic
74C2×D29—21no—
75C2×D29—21no—
76C2×D29#10412yes—
77C4×C29—21no—
78C4×C29—21no—
79C4×C29—21no—
80C4×C29—41no—
81Dic29—21no—
82Dic29—21no—
83Dic29—21no—
84Dic29—41no—
85Dic29—41no—
86#529—291no—
87#432—291no—
88C2×#97—291no—
89#330—292no—
90#329—292no—
91C2×C29—81no—
92C2×C29#41311yescharacteristic
93C2×C29C2×#10411yescharacteristic
94C2×C29#42111yescharacteristic
95D29—22no—
96C22×C8—581no—
97#126—581no—
98#125—291no—
99#124—291no—
100#123—581no—
101C22⋊Q8—291no—
102#121—291no—
103C4×Q8—291no—
104C4×D4—581no—
105C4×D4#118111yescharacteristic
106#117—581no—
107C2×C42—291no—
108C4⋊C8—581no—
109C22⋊C8—581no—
110#97—292no—
111#97—292no—
112#97—581no—
113C29#153211yescharacteristic, complemented, Sylow
114C2×Q8—291no—
115C2×D4—581no—
116C2×D4C2×#118111yescharacteristic
117C22×C4—21no—
118C22×C4—291no—
119C22×C4—291no—
120C22×C4—291no—
121C2×C8—582no—
122C2×C8—584no—
123C2×C8—582no—
124C4⋊C4—291no—
125C4⋊C4—581no—
126C4⋊C4—581no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4C2×#118111yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—581no—
132C22⋊C4—581no—
133C22⋊C4—581no—
134C22⋊C4—581no—
135C42—291no—
136C42—291no—
137C42—291no—
138C42—581no—
139C42C2×#118111yescharacteristic
140C23—21no—
141C23—291no—
142Q8—1161no—
143D4—41no—
144D4—1162no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—291no—
148C2×C4—291no—
149C2×C4—291no—
150C2×C4—582no—
151C2×C4—581no—
152C2×C4—581no—
153C2×C4—1161no—
154C2×C4—1161no—
155C2×C4C22⋊#118111yescharacteristic
156C2×C4C22⋊#118111yescharacteristic
157C2×C4C22×#118111yescharacteristic
158C8—584no—
159C8—1162no—
160C22—41no—
161C22—41no—
162C22—41no—
163C22—292no—
164C22—581no—
165C22—581no—
166C22C2×C22⋊#118111yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—41no—
171C4—581no—
172C4—581no—
173C4—581no—
174C4—1161no—
175C4—1161no—
176C2—81no—
177C2—582no—
178C2#1427214911yescharacteristic
179C2D29⋊#10411yescharacteristic
180C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radical#11745300C4
cosocleC4×Dic29C23
hypercenterC4×D4#1181
hypocenterC29#1532
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14272186C2semidirect
2. #14272122C2semidirect
3. #14272020C2semidirect
4. #14272018C2semidirect
113. C29#1532semidirect

Maximal subgroups

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

subgroupindex
#142721862
#142721222
#142720202
#142720182
#142716952
#153229