Finite Group Databasebeta

← #16818516

Subgroups — #16818516

Order 3712.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271789C211yesmaximal, characteristic
2#14271498C212yesmaximal, complemented
3#14270899C212yesmaximal, complemented
4#14270887C211yesmaximal, characteristic
5C29×#399C211yesmaximal, characteristic
6C2×C4⋊C4×C29—21no—
7C2×C4⋊C4×C29C2211yescharacteristic
8C2×C22⋊C4×C29—21no—
9C2×C22⋊C4×C29C2211yescharacteristic
10C2×C22⋊Dic29—21no—
11#11745286—21no—
12#11745286C2212yes—
13#11745240—22no—
14#11745240—22no—
15C29×#95C2211yescharacteristic
16C22⋊#6597C2212yes—
17#11745158—22no—
18#11745155—22no—
19C24×C29D411yescharacteristic
20C22×C4×C29—21no—
21C22×C4×C29—21no—
22C22×C4×C29D411yescharacteristic
23C22×C4×C29C2311yescharacteristic
24C22×Dic29—21no—
25C22×Dic29—21no—
26C2×Dic58—21no—
27C2×Dic58D412yes—
28C4⋊C4×C29—22no—
29C4⋊C4×C29—42no—
30C22⋊C4×C29—22no—
31C22⋊C4×C29—42no—
32C22⋊Dic29—22no—
33C22⋊Dic29—22no—
34C4⋊Dic29—21no—
35C4⋊Dic29D412yes—
36#90779—22no—
37#90779—22no—
38C2×#6597—22no—
39C23×C29—21no—
40C23×C29—21no—
41C23×C29—41no—
42C23×C29—41no—
43C23×C29Q1612yes—
44C23×C29C2×D411yescharacteristic
45C2×C4×C29—22no—
46C2×C4×C29—21no—
47C2×C4×C29—41no—
48C2×C4×C29—41no—
49C2×C4×C29—41no—
50C2×C4×C29—41no—
51C2×C4×C29—41no—
52C2×C4×C29—41no—
53C2×C4×C29—41no—
54C2×C4×C29C2×D412yes—
55C2×Dic29—22no—
56C2×Dic29—22no—
57C2×Dic29—81no—
58C2×Dic29—81no—
59Dic58—42no—
60Dic58—81no—
61#6597—42no—
62#1614—291nomaximal, Sylow
63C22×C29—21no—
64C22×C29—21no—
65C22×C29—22no—
66C22×C29—42no—
67C22×C29—41no—
68C22×C29—41no—
69C22×C29—81no—
70C22×C29#12011yescharacteristic
71C22×C29C2×Q1611yescharacteristic
72C22×C29#13711yescharacteristic
73C4×C29—22no—
74C4×C29—42no—
75C4×C29—41no—
76C4×C29—81no—
77Dic29—42no—
78Dic29—42no—
79#543—291no—
80#484—292no—
81#399D2911yescharacteristic
82#328—292no—
83#323—291no—
84C2×C29—21no—
85C2×C29—21no—
86C2×C29—42no—
87C2×C29#45111yescharacteristic
88C2×C29#45311yescharacteristic
89C2×C29#45811yescharacteristic
90C22⋊Q8—292no—
91C22⋊Q8—582no—
92C22⋊Q8—582no—
93C22⋊Q8—581no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4C2×D2911yescharacteristic
96C2×C22⋊C4—21no—
97C2×C22⋊C4—581no—
98C2×C22⋊C4C2×D2911yescharacteristic
99#107—582no—
100#103—582no—
101C22⋊C8—292no—
102#95C2×D2911yescharacteristic
103C29#161411yescharacteristic, complemented, Sylow
104C24C22⋊D2911yescharacteristic
105C2×Q8—292no—
106C2×Q8—581no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—581no—
110C22×C4—581no—
111C22×C4C22⋊D2911yescharacteristic
112C22×C4C22×D2911yescharacteristic
113C2×C8—582no—
114C4⋊C4—22no—
115C4⋊C4—42no—
116C4⋊C4—292no—
117C4⋊C4—582no—
118C4⋊C4—581no—
119C4⋊C4—582no—
120C22⋊C4—22no—
121C22⋊C4—42no—
122C22⋊C4—582no—
123C22⋊C4—582no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#9078512yes—
129C23C2×C22⋊D2911yescharacteristic
130Q8—1162no—
131Q8—2321no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—582no—
142C2×C4—582no—
143C2×C4—2321no—
144C2×C4—2321no—
145C2×C4D4×D2912yes—
146C8—1162no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1174529911yescharacteristic
155C22C2×#9078511yescharacteristic
156C22#1174531311yescharacteristic
157C4—22no—
158C4—42no—
159C4—41no—
160C4—81no—
161C4—1162no—
162C4—1162no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1427131811yescharacteristic
167C2#1427133011yescharacteristic
168C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#399C2
socleC22×C29#120
prime radicalC24×C29D4
hypercenter#399D29
hypocenterC29#1614
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #14271498C2semidirect
3. #14270899C2semidirect
103. C29#1614semidirect

Maximal subgroups

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

subgroupindex
#142717892
#142714982
#142708992
#142708872
C29×#3992
#161429