Finite Group Databasebeta

← #16829778

Subgroups — #16829778

Order 3712.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#14271640C211yesmaximal, characteristic, complemented
2#14271484C212yesmaximal, complemented
3#14271467C212yesmaximal, complemented
4#14271360C212yesmaximal, complemented
5#14271301C212yesmaximal, complemented
6#14271263C212yesmaximal, complemented
7C4×#90783C212yesmaximal, complemented
8#14271224C211yesmaximal, characteristic, complemented
9C29×#540C211yesmaximal, characteristic
10C22×Dic58C2211yescharacteristic
11C29×#127C2211yescharacteristic
12C29×#125C2211yescharacteristic
13C29×#123—22no—
14C29×#121—22no—
15C29×#121C2212yes—
16C4×D4×C29C2212yes—
17C29×#117C2211yescharacteristic
18C2×#90783C2212yes—
19C2×#90783C2212yes—
20#11745288C2211yescharacteristic
21#11745249—22no—
22#11745239—22no—
23C4×Dic58C2212yes—
24C4×Dic58C2212yes—
25#11745180C2212yes—
26#11745180C2212yes—
27C22⋊#6597C2212yes—
28#11745158C2212yes—
29#11745158C2212yes—
30#11745156C2212yes—
31#11745155C2212yes—
32C4⋊#6597C2212yes—
33#11745151C2211yescharacteristic
34C4×#6597C2211yescharacteristic
35C2×D4×C29—22no—
36C2×D4×C29—22no—
37C2×D4×C29C2312yes—
38C22×C4×C29—22no—
39C22×C4×C29C2311yescharacteristic
40C22×Dic29—21no—
41C2×Dic58—21no—
42C2×Dic58—24no—
43C2×Dic58C2312yes—
44C4⋊C4×C29—22no—
45C4⋊C4×C29D412yes—
46C4⋊C4×C29C2312yes—
47C22⋊C4×C29—22no—
48C22⋊C4×C29—22no—
49C22⋊C4×C29D412yes—
50C42×C29C2311yescharacteristic
51C42×C29C2311yescharacteristic
52C22⋊Dic29—21no—
53#90783—24no—
54#90783—24no—
55C4⋊Dic29C2312yes—
56#90779—22no—
57#90779—22no—
58C4×Dic29—21no—
59C4×Dic29—22no—
60C4×Dic29—22no—
61C2×#6597C2312yes—
62C2×#6597C2312yes—
63C23×C29—22no—
64C23×C29C2×D411yescharacteristic
65D4×C29—22no—
66D4×C29—22no—
67D4×C29—82no—
68D4×C29—82no—
69C2×C4×C29—22no—
70C2×C4×C29—22no—
71C2×C4×C29—82no—
72C2×C4×C29C2×D412yes—
73C2×C4×C29C2×D412yes—
74C2×C4×C29C2×D411yescharacteristic
75C2×C4×C29C2411yescharacteristic
76C2×Dic29—24no—
77C2×Dic29—22no—
78C2×Dic29—22no—
79Dic58—24no—
80Dic58—22no—
81Dic58#4114yes—
82#6597—22no—
83#6597—22no—
84#3126—291nomaximal, Sylow
85C22×C29—21no—
86C22×C29—22no—
87C22×C29—42no—
88C22×C29—42no—
89C22×C29—42no—
90C22×C29C22×D411yescharacteristic
91C4×C29—21no—
92C4×C29—22no—
93C4×C29—22no—
94C4×C29—42no—
95C4×C29C2×#4112yes—
96Dic29—24no—
97Dic29—42no—
98#540D2911yescharacteristic
99#519—291no—
100#482—292no—
101#479—292no—
102#460—292no—
103#448—292no—
104#440—292no—
105C4×SD16—292no—
106#433—291no—
107C2×C29—41no—
108C2×C29—82no—
109C2×C29#52511yescharacteristic
110C2×C29#57712yes—
111C22×Q8—291no—
112C2×SD16—292no—
113C2×SD16—292no—
114#127C2×D2911yescharacteristic
115#125C2×D2911yescharacteristic
116#123—22no—
117#121—22no—
118#121C2×D2912yes—
119C4×Q8—292no—
120C4×Q8—292no—
121C4×Q8—582no—
122C4×D4C2×D2912yes—
123#117—291no—
124#117—582no—
125#117C2×D2911yescharacteristic
126#107—292no—
127#106—292no—
128C4⋊C8—292no—
129#103—292no—
130#103—292no—
131#102—292no—
132#102—292no—
133C22⋊C8—292no—
134#97—291no—
135C4×C8—291no—
136C29#312611yescharacteristic, complemented, Sylow
137C2×Q8—292no—
138C2×Q8—584no—
139C2×Q8—581no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D2912yes—
143C22×C4—22no—
144C22×C4—581no—
145C22×C4C22×D2911yescharacteristic
146SD16—584no—
147SD16—584no—
148C2×C8—292no—
149C2×C8—292no—
150C4⋊C4—22no—
151C4⋊C4—292no—
152C4⋊C4—582no—
153C4⋊C4—582no—
154C4⋊C4C22⋊D2912yes—
155C4⋊C4C22×D2912yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—581no—
159C22⋊C4C22⋊D2912yes—
160C42—581no—
161C42—582no—
162C42—582no—
163C42C22×D2911yescharacteristic
164C42C22×D2911yescharacteristic
165C23—22no—
166C23C2×C22⋊D2911yescharacteristic
167Q8—294no—
168Q8—584no—
169Q8—582no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—584no—
178C2×C4—582no—
179C2×C4—582no—
180C2×C4C2×C22⋊D2912yes—
181C2×C4C2×C22⋊D2912yes—
182C2×C4C2×C22⋊D2911yescharacteristic
183C2×C4C23×D2911yescharacteristic
184C8—582no—
185C8—582no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D2911yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—584no—
197C4—1162no—
198C4#41×D2912yes—
199C2—41no—
200C2—82no—
201C2#1427167011yescharacteristic
202C2#1427197412yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#540C2
socleC22×C29C22×D4
hypercenter#540D29
hypocenterC29#3126
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14271640C2semidirect
2. #14271484C2semidirect
3. #14271467C2semidirect
4. #14271360C2semidirect
5. #14271301C2semidirect
6. #14271263C2semidirect
7. C4×#90783C2semidirect
8. #14271224C2semidirect
136. C29#3126semidirect

Maximal subgroups

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

subgroupindex
#142716402
#142714842
#142714672
#142713602
#142713012
#142712632
C4×#907832
#142712242
C29×#5402
#312629