Finite Group Databasebeta

← #16830958

Subgroups — #16830958

Order 3712.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#14271786C212yesmaximal, complemented
2#14271452C212yesmaximal, complemented
3#14271446C212yesmaximal, complemented
4#14271416C211yesmaximal, characteristic
5#14271394C212yesmaximal, complemented
6#14271387C212yesmaximal, complemented
7#14271381C212yesmaximal, complemented
8#14271191C211yesmaximal, characteristic, complemented
9C29×#470C211yesmaximal, characteristic, complemented
10C2×Q16×C29C2211yescharacteristic
11C2×M16×C29C2211yescharacteristic
12C29×C22⋊Q8C2212yes—
13#11745309C2212yes—
14Q8×Dic29C2212yes—
15C2×#90784C2212yes—
16#11745292C2212yes—
17#11745288C2211yescharacteristic
18C22×#6597C2211yescharacteristic
19C2×D232C2211yescharacteristic
20#11745260—22no—
21#11745259—22no—
22#11745255C2212yes—
23#11745250C2212yes—
24#11745247—22no—
25#11745245—22no—
26C29×#106C2211yescharacteristic
27C29×#103C2212yes—
28#11745183C2212yes—
29#11745169C2212yes—
30#11745165C2211yescharacteristic
31#11745162C2212yes—
32#11745162C2212yes—
33#11745157C2212yes—
34#11745156C2212yes—
35C2×Q8×C29C2312yes—
36C22×C4×C29C2311yescharacteristic
37C2×C22⋊D29—22no—
38C2×D116C2312yes—
39C2×C4×D29—22no—
40C2×Dic58—22no—
41Q16×C29—41no—
42M16×C29—41no—
43C2×C8×C29C2311yescharacteristic
44C2×C8×C29C2311yescharacteristic
45C4⋊C4×C29—22no—
46C4⋊C4×C29C2312yes—
47C22⋊C4×C29—22no—
48C22⋊Dic29D411yescharacteristic
49C22⋊Dic29D411yescharacteristic
50#90784—42no—
51#90781—22no—
52#90781—22no—
53#90781—22no—
54#90781—22no—
55C4⋊Dic29—22no—
56C4⋊Dic29D412yes—
57C4⋊Dic29C2312yes—
58#90779—22no—
59C4×Dic29—22no—
60C4×Dic29C2312yes—
61C2×#6597—41no—
62C2×#6597C2312yes—
63D232—41no—
64C23×C29C2×D411yescharacteristic
65C22×D29—22no—
66Q8×C29—22no—
67Q8×C29—22no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—22no—
71C2×C4×C29—22no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2411yescharacteristic
74C22⋊D29—82no—
75C2×Dic29—22no—
76C2×Dic29C2×D412yes—
77C2×Dic29C2×D412yes—
78D116—22no—
79D116—22no—
80C4×D29—82no—
81Dic58—82no—
82C8×C29—21no—
83C8×C29—21no—
84#6597—22no—
85#3263—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—22no—
88C22×C29C22×D411yescharacteristic
89C2×D29—42no—
90C2×D29—42no—
91C2×D29—42no—
92C4×C29—21no—
93C4×C29—42no—
94C4×C29—42no—
95C4×C29H(5,𝔽2)11yescharacteristic
96C4×C292−1+411yescharacteristic
97Dic29—22no—
98Dic29—22no—
99Dic29—42no—
100#542—292no—
101#476—292no—
102#475—292no—
103#470D2911yescharacteristic, complemented
104#469—291no—
105#465—292no—
106#464—292no—
107#463—292no—
108#424—291no—
109C2×C29—41no—
110C2×C29#53711yescharacteristic
111C2×C29#57712yes—
112D29—82no—
113C2×Q16C2×D2911yescharacteristic
114C2×SD16—292no—
115C2×D8—291no—
116C2×M16C2×D2911yescharacteristic
117C22×C8—291no—
118C4⋊Q8—292no—
119#126—582no—
120#124—292no—
121#124—582no—
122#123—582no—
123C22⋊Q8—582no—
124C22⋊Q8C2×D2912yes—
125#121—292no—
126C4×Q8—292no—
127C4×D4—292no—
128#117—291no—
129#106—291no—
130#106—292no—
131#106C2×D2911yescharacteristic
132C4⋊C8—292no—
133C4⋊C8—292no—
134#103—292no—
135#103C2×D2912yes—
136#102—292no—
137#102—292no—
138C29#326311yescharacteristic, complemented, Sylow
139C2×Q8—582no—
140C2×Q8C22×D2912yes—
141C2×D4—292no—
142C2×D4—582no—
143C22×C4—582no—
144C22×C4C22×D2911yescharacteristic
145Q16—41no—
146SD16—1162no—
147D8—1161no—
148M16—41no—
149C2×C8—292no—
150C2×C8—1161no—
151C2×C8C22×D2911yescharacteristic
152C2×C8C22×D2911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—292no—
155C4⋊C4—292no—
156C4⋊C4—582no—
157C4⋊C4—582no—
158C4⋊C4C22×D2912yes—
159C22⋊C4—22no—
160C22⋊C4—291no—
161C22⋊C4—291no—
162C22⋊C4—582no—
163C22⋊C4—582no—
164C22⋊C4—582no—
165C22⋊C4—582no—
166C42—292no—
167C42—582no—
168C23—582no—
169C23D4×D2911yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—2322no—
173D4—582no—
174D4—582no—
175D4—2322no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—292no—
181C2×C4—292no—
182C2×C4—582no—
183C2×C4—2322no—
184C2×C4D4×D2911yescharacteristic
185C2×C4C23×D2911yescharacteristic
186C8—21no—
187C8—21no—
188C8—582no—
189C22—22no—
190C22—21no—
191C22—1162no—
192C22—1162no—
193C22—1162no—
194C22C2×D4×D2911yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—582no—
199C4—582no—
200C4—1162no—
201C4#1174535911yescharacteristic
202C4#1174536511yescharacteristic
203C2—41no—
204C2—2322no—
205C2#1427174011yescharacteristic
206C2#1427197212yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#470C2
socleC22×C29C22×D4
prime radical#14271416C2
hypercenter#470D29
hypocenterC29#3263
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #14271786C2semidirect
2. #14271452C2semidirect
3. #14271446C2semidirect
5. #14271394C2semidirect
6. #14271387C2semidirect
7. #14271381C2semidirect
8. #14271191C2semidirect
9. C29×#470C2semidirect
103. #470D29semidirect
138. C29#3263semidirect

Maximal subgroups

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

subgroupindex
#142717862
#142714522
#142714462
#142714162
#142713942
#142713872
#142713812
#142711912
C29×#4702
#326329