Finite Group Databasebeta

← #16818495

Subgroups — #16818495

Order 3712.

254 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271474C212yesmaximal, complemented
2#14271093C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#537C211yesmaximal, characteristic
6C2×#41×C29—21no—
7C29×C22⋊Q8—22no—
8C29×#121—22no—
9C29×#121—21no—
10C29×#121C2212yes—
11C2×C4⋊C4×C29C2211yescharacteristic
12C2×C4⋊Dic29C2211yescharacteristic
13C2×#90779—21no—
14#11745180—22no—
15#11745179—21no—
16#11745179C2211yescharacteristic
17C22⋊#6597C2212yes—
18#11745155—22no—
19#41×C29—42no—
20#41×C29—42no—
21C2×Q8×C29—21no—
22C2×D4×C29—21no—
23C2×D4×C29—22no—
24C2×D4×C29—21no—
25C2×D4×C29D412yes—
26C22×C4×C29—22no—
27C22×C4×C29D411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29—22no—
34C4⋊C4×C29D412yes—
35C22⋊C4×C29—22no—
36C22⋊C4×C29—22no—
37C4⋊Dic29—22no—
38#90779—42no—
39C2×#6597—22no—
40C23×C29—22no—
41C23×C29C2×D411yescharacteristic
42Q8×C29—42no—
43D4×C29—42no—
44D4×C29—42no—
45D4×C29—42no—
46D4×C29—42no—
47D4×C29—81no—
48C2×C4×C29—21no—
49C2×C4×C29—21no—
50C2×C4×C29—21no—
51C2×C4×C29—22no—
52C2×C4×C29—41no—
53C2×C4×C29—44no—
54C2×C4×C29—41no—
55C2×C4×C29D812yes—
56C2×C4×C29C2×D412yes—
57C2×Dic29—22no—
58C2×Dic29—41no—
59C2×Dic29—41no—
60C2×Dic29—41no—
61C2×Dic29—41no—
62C2×Dic29—41no—
63#6597—42no—
64#1610—291nomaximal, Sylow
65C22×C29—21no—
66C22×C29—21no—
67C22×C29—42no—
68C22×C29—42no—
69C22×C29—42no—
70C22×C29#12011yescharacteristic
71C22×C29C2×D811yescharacteristic
72C22×C29AGL(1,ℤ/8)11yescharacteristic
73C4×C29—22no—
74C4×C29—22no—
75C4×C29—42no—
76C4×C29—41no—
77Dic29—42no—
78Dic29—81no—
79#537D2911yescharacteristic
80#480—292no—
81#398—291no—
82#327—292no—
83#324—291no—
84C2×C29—21no—
85C2×C29—21no—
86C2×C29—82no—
87C2×C29#44711yescharacteristic
88C2×C29#45611yescharacteristic
89C2×C29#45811yescharacteristic
90C2×#41—21no—
91C22⋊Q8—22no—
92#121—22no—
93#121—21no—
94#121C2×D2912yes—
95C2×C4⋊C4—291no—
96C2×C4⋊C4—581no—
97C2×C4⋊C4C2×D2911yescharacteristic
98#107—582no—
99#102—582no—
100C22⋊C8—292no—
101#95—291no—
102#95—581no—
103C29#161011yescharacteristic, complemented, Sylow
104#41—42no—
105#41—42no—
106C2×Q8—21no—
107C2×D4—21no—
108C2×D4—22no—
109C2×D4—21no—
110C2×D4C22⋊D2912yes—
111C22×C4—22no—
112C22×C4—581no—
113C22×C4—581no—
114C22×C4C22⋊D2911yescharacteristic
115C22×C4C22⋊D2911yescharacteristic
116C22×C4C22×D2911yescharacteristic
117C2×C8—582no—
118C4⋊C4—21no—
119C4⋊C4—22no—
120C4⋊C4—582no—
121C4⋊C4—1162no—
122C4⋊C4C22⋊D2912yes—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C23—22no—
126C23C2×C22⋊D2911yescharacteristic
127Q8—42no—
128D4—42no—
129D4—42no—
130D4—42no—
131D4—42no—
132D4—81no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—44no—
139C2×C4—41no—
140C2×C4—582no—
141C2×C4—1161no—
142C2×C4—1161no—
143C2×C4—1161no—
144C2×C4—1161no—
145C2×C4—1161no—
146C2×C4#9078212yes—
147C2×C4C2×C22⋊D2912yes—
148C8—1162no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22C2×#9078211yescharacteristic
155C22#1174529411yescharacteristic
156C22#1174531511yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—1162no—
162C4—2321no—
163C2—21no—
164C2—21no—
165C2—82no—
166C2#1427129711yescharacteristic
167C2#1427134611yescharacteristic
168C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#537C2
socleC22×C29#120
hypercenter#537D29
hypocenterC29#1610
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14271474C2semidirect
2. #14271093C2semidirect
3. #14270897C2semidirect
4. #14270889C2semidirect
103. C29#1610semidirect

Maximal subgroups

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

subgroupindex
#142714742
#142710932
#142708972
#142708892
C29×#5372
#161029