Finite Group Databasebeta

← #16834810

Subgroups — #16834810

Order 3712.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D29⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×#90796C211yesmaximal, characteristic, complemented
3#14272013C212yesmaximal, complemented
4#14272011C212yesmaximal, complemented
5#14271698C211yesmaximal, characteristic
6C2×#90796—21no—
7C2×D29⋊C8—21no—
8C29×#125C411yescharacteristic
9#11745260—21no—
10#11745259C411yescharacteristic
11#11745257C411yescharacteristic
12#11745256—21no—
13#11745255—21no—
14#11745255C2211yescharacteristic
15#11745254—21no—
16#11745249C2211yescharacteristic
17#11745237C411yescharacteristic
18C42×D29C2211yescharacteristic
19#11745220—21no—
20#11745218—21no—
21C4⋊#6599C2212yes—
22C4×#6599C2212yes—
23C2×D116—21no—
24C2×D116C2×C411yescharacteristic
25C2×C4×D29—21no—
26C2×C4×D29C2×C411yescharacteristic
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×Dic58C2×C411yescharacteristic
30C2×#6599—22no—
31C2×#6599—22no—
32#90796—24no—
33D29⋊C8—42no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29C2×C411yescharacteristic
37C4⋊C4×C29C2×C411yescharacteristic
38C42×C29C2×C411yescharacteristic
39#90781—21no—
40#90781—21no—
41#90781—21no—
42#90781—21no—
43#90781—21no—
44C4⋊Dic29—21no—
45#90779—21no—
46C4×Dic29—21no—
47C4×Dic29D411yescharacteristic
48C4×Dic29D411yescharacteristic
49C4×Dic29C2311yescharacteristic
50C22×D29—21no—
51C22×D29C22⋊C411yescharacteristic
52C2×C4×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29C22⋊C411yescharacteristic
55C2×C4×C29C22⋊C411yescharacteristic
56C2×C4×C29C22×C411yescharacteristic
57C2×Dic29—21no—
58C2×Dic29C22⋊C411yescharacteristic
59C2×Dic29C2×D411yescharacteristic
60C2×Dic29C2×D411yescharacteristic
61D116—22no—
62D116—42no—
63C4×D29—22no—
64C4×D29—22no—
65C4×D29—21no—
66C4×D29—21no—
67C4×D29—41no—
68C4×D29—41no—
69Dic58—22no—
70#6599—24no—
71#6599—42no—
72#1483—291nomaximal, Sylow
73C22×C29C2×C22⋊C411yescharacteristic
74C2×D29—21no—
75C2×D29—21no—
76C2×D29—41no—
77C2×D29—41no—
78C2×D29—41no—
79C2×D29#10412yes—
80C4×C29—21no—
81C4×C29—21no—
82C4×C29—41no—
83C4×C29—41no—
84C4×C29#13112yes—
85Dic29—21no—
86Dic29—21no—
87Dic29—41no—
88Dic29AGL(1,ℤ/8)11yescharacteristic
89Dic29#13711yescharacteristic
90#529—291no—
91C2×C4⋊C8—291no—
92C4×M16—291no—
93Q8⋊C8—292no—
94D4⋊C8—292no—
95C2×C29#40811yescharacteristic
96C2×C29#41711yescharacteristic
97C2×C29C2×#10411yescharacteristic
98D29—22no—
99D29—81no—
100C2×M16—581no—
101C22×C8—581no—
102#126—581no—
103#125#118111yescharacteristic
104#124—291no—
105#123—581no—
106C22⋊Q8—291no—
107#121—291no—
108C4×Q8—291no—
109C4×D4—291no—
110C4×D4—581no—
111#117—581no—
112C2×C42—291no—
113C4⋊C8—292no—
114C4⋊C8—581no—
115#97—581no—
116C4×C8—292no—
117C29#148311yescharacteristic, complemented, Sylow
118C2×Q8—291no—
119C2×D4—291no—
120C2×D4—581no—
121C22×C4—291no—
122C22×C4—291no—
123C22×C4—291no—
124C22×C4—581no—
125M16—584no—
126C2×C8—582no—
127C2×C8—582no—
128C2×C8—1162no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—581no—
132C4⋊C4—581no—
133C4⋊C4C2×#118111yescharacteristic
134C4⋊C4C2×#118111yescharacteristic
135C22⋊C4—581no—
136C22⋊C4—581no—
137C22⋊C4—581no—
138C22⋊C4—581no—
139C22⋊C4—581no—
140C42—291no—
141C42—291no—
142C42—291no—
143C42—581no—
144C42C2×#118111yescharacteristic
145C23—291no—
146C23—581no—
147Q8—582no—
148D4—582no—
149D4—1162no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—291no—
153C2×C4—291no—
154C2×C4—291no—
155C2×C4—581no—
156C2×C4—581no—
157C2×C4—582no—
158C2×C4—582no—
159C2×C4—581no—
160C2×C4—1161no—
161C2×C4—1161no—
162C2×C4C22⋊#118111yescharacteristic
163C2×C4C22⋊#118111yescharacteristic
164C2×C4C22×#118111yescharacteristic
165C8—584no—
166C8—1162no—
167C22—292no—
168C22—581no—
169C22—581no—
170C22—1161no—
171C22—1161no—
172C22—1161no—
173C22C2×C22⋊#118111yescharacteristic
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—291no—
179C4—291no—
180C4—581no—
181C4—581no—
182C4—1161no—
183C4#1174534812yes—
184C2—582no—
185C2—2321no—
186C2#1427213811yescharacteristic
187C2#1427215411yescharacteristic
188C2D29⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#125C4
socleC22×C29C2×C22⋊C4
prime radical#11745257C4
cosocleC4×Dic29C23
hypercenter#125#1181
hypocenterC29#1483
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. D29⋊(C4⋊C8)C2semidirect
2. C4×#90796C2semidirect
3. #14272013C2semidirect
4. #14272011C2semidirect
117. C29#1483semidirect

Maximal subgroups

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

subgroupindex
D29⋊(C4⋊C8)2
C4×#907962
#142720132
#142720112
#142716982
#148329