Finite Group Databasebeta

← #16835464

Subgroups — #16835464

Order 3712.

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

normal subgroups only

This group has 260 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#14272241C211yesmaximal, characteristic
2#14272169C212yesmaximal, complemented
3#14272136C211yesmaximal, characteristic
4#14272044C212yesmaximal, complemented
5#14271135C211yesmaximal, characteristic
6C2×#90807C2211yescharacteristic
7C2×#90800—21no—
8C2×#90800C2211yescharacteristic
9C2×#90800C2212yes—
10C22×#6599C2211yescharacteristic
11#11745346—22no—
12#11745346—22no—
13D29⋊M16—21no—
14#11745239C2212yes—
15C22⋊#6599—21no—
16#11745220—22no—
17#11745219—21no—
18C4⋊#6599—22no—
19C29×#99C411yescharacteristic
20#11745182C411yescharacteristic
21#11745154C412yes—
22C2×D4×C29C2×C411yescharacteristic
23C2×C22⋊D29C2×C411yescharacteristic
24C2×C22⋊D29Q811yescharacteristic
25C22×Dic29D411yescharacteristic
26C22×Dic29C2311yescharacteristic
27#90807—22no—
28#90807—22no—
29C2×C4×D29D411yescharacteristic
30C2×Dic58Q811yescharacteristic
31#90800—22no—
32#90800—22no—
33#90800—22no—
34#90800—22no—
35C2×#6599—21no—
36C2×#6599—21no—
37C2×#6599—22no—
38C2×#6599—21no—
39C2×#6599—21no—
40C2×#6599D412yes—
41C2×#6599D412yes—
42#90796—21no—
43#90796—21no—
44D29⋊C8—22no—
45C22⋊C4×C29C2×C412yes—
46C22⋊Dic29C2×C412yes—
47#90779—22no—
48C4×Dic29—22no—
49C23×C29C4⋊C411yescharacteristic
50C23×C29C22×C411yescharacteristic
51C22×D29C4⋊C411yescharacteristic
52D4×C29—22no—
53C2×C4×C29—22no—
54C2×C4×C29C4⋊C411yescharacteristic
55C22⋊D29—22no—
56C22⋊D29—22no—
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—22no—
60C2×Dic29C4⋊C411yescharacteristic
61C2×Dic29C2×D412yes—
62C2×Dic29C2×D411yescharacteristic
63C2×Dic29C2×Q811yescharacteristic
64C2×Dic29#4112yes—
65C4×D29—21no—
66C4×D29—21no—
67Dic58—22no—
68#6599—22no—
69#6599—22no—
70#6599—41no—
71#6599—41no—
72#1868—291nomaximal, Sylow
73C22×C29—21no—
74C22×C29—41no—
75C22×C29—41no—
76C22×C29C2×C4⋊C411yescharacteristic
77C22×C29C4×D412yes—
78C2×D29—21no—
79C2×D29—41no—
80C4×C29—21no—
81C4×C29—42no—
82Dic29—21no—
83Dic29—42no—
84Dic29#12011yescharacteristic
85Dic29C22⋊Q812yes—
86Dic29#12311yescharacteristic
87#568—291no—
88#424—292no—
89#410—291no—
90#408—291no—
91#344—292no—
92C2×C29—22no—
93C2×C29—21no—
94C2×C29—41no—
95C2×C29#38511yescharacteristic
96D29—41no—
97C2×#41—291no—
98#131—582no—
99#131—582no—
100C2×M16—292no—
101C2×M16—291no—
102C2×M16—581no—
103C2×M16—581no—
104C22×C8—291no—
105#117—292no—
106C4⋊C8—582no—
107C4⋊C8—582no—
108#99—291no—
109#99—292no—
110#99#118111yescharacteristic
111C22⋊C8—581no—
112C22⋊C8—581no—
113C29#186811yescharacteristic, complemented, Sylow
114#41—582no—
115#41—582no—
116C2×Q8—291no—
117C2×D4—291no—
118C2×D4—291no—
119C2×D4C2×#118111yescharacteristic
120C22×C4—291no—
121C22×C4—291no—
122C22×C4—291no—
123M16—582no—
124M16—582no—
125M16—581no—
126M16—581no—
127M16—582no—
128M16—582no—
129C2×C8—292no—
130C2×C8—292no—
131C2×C8—582no—
132C2×C8—581no—
133C2×C8—581no—
134C2×C8—581no—
135C2×C8—581no—
136C2×C8—582no—
137C4⋊C4—582no—
138C22⋊C4—292no—
139C22⋊C4C2×#118112yes—
140C42—582no—
141C23—291no—
142C23C4⋊#118111yescharacteristic
143C23C22×#118111yescharacteristic
144Q8—582no—
145D4—22no—
146D4—582no—
147D4—582no—
148C2×C4—22no—
149C2×C4—291no—
150C2×C4—291no—
151C2×C4—292no—
152C2×C4—292no—
153C2×C4—291no—
154C2×C4—581no—
155C2×C4—581no—
156C2×C4—581no—
157C2×C4—581no—
158C2×C4—582no—
159C2×C4C4⋊#118111yescharacteristic
160C8—582no—
161C8—582no—
162C8—1161no—
163C8—1161no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—581no—
168C22—1161no—
169C22C2×C4⋊#118111yescharacteristic
170C22D4×#118112yes—
171C4—21no—
172C4—42no—
173C4—291no—
174C4—291no—
175C4—292no—
176C4—581no—
177C4—1162no—
178C2—22no—
179C2—21no—
180C2—41no—
181C2—1161no—
182C2#1427211011yescharacteristic
subgroupG/H
centerC2#14272110
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#99C4
socleC2×C29#385
prime radicalC2×#90807C22
cosocleC22×Dic29C23
hypercenter#99#1181
hypocenterC29#1868
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #14272169C2semidirect
4. #14272044C2semidirect
113. C29#1868semidirect

Maximal subgroups

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

subgroupindex
#142722412
#142721692
#142721362
#142720442
#142711352
#186829