Finite Group Databasebeta

← #16830939

Subgroups — #16830939

Order 3712.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#14271775C211yesmaximal, characteristic, complemented
2#14271768C211yesmaximal, characteristic
3#14271471C212yesmaximal, complemented
4#14271464C212yesmaximal, complemented
5#14271409C212yesmaximal, complemented
6#14271392C212yesmaximal, complemented
7#14271369C212yesmaximal, complemented
8#14271364C212yesmaximal, complemented
9C29×#424C211yesmaximal, characteristic, complemented
10C2×M16×C29C2211yescharacteristic
11C22×C8×C29C2211yescharacteristic
12C29×#117C2211yescharacteristic
13#11745292C2212yes—
14#11745286C2212yes—
15C2×#90773C2212yes—
16C2×#90773C2212yes—
17#11745256—22no—
18#11745251—22no—
19#11745246—22no—
20#11745241—22no—
21#11745236C2211yescharacteristic
22C4×D116C2212yes—
23#11745232C2211yescharacteristic
24#11745232C2211yescharacteristic
25#11745231C2211yescharacteristic
26C4×Dic58C2212yes—
27C29×C4⋊C8C2212yes—
28C29×C4⋊C8C2212yes—
29#11745169C2212yes—
30#11745169C2212yes—
31#11745166C2212yes—
32#11745165C2212yes—
33#11745164C2212yes—
34#11745164C2212yes—
35C22×C4×C29C2311yescharacteristic
36C2×C22⋊D29—22no—
37C2×D116—22no—
38C2×D116C2312yes—
39C2×C4×D29—22no—
40C2×Dic58C2312yes—
41M16×C29—41no—
42C2×C8×C29—41no—
43C2×C8×C29C2312yes—
44C2×C8×C29C2312yes—
45C4⋊C4×C29D412yes—
46C22⋊C4×C29D412yes—
47C42×C29C2311yescharacteristic
48C42×C29C2311yescharacteristic
49C22⋊Dic29—22no—
50#90781—22no—
51#90781—22no—
52C4⋊Dic29—22no—
53C4⋊Dic29C2312yes—
54C4⋊Dic29C2312yes—
55#90779—22no—
56#90779—22no—
57#90779—22no—
58#90779—22no—
59C4×Dic29—22no—
60#90773—42no—
61#90773—42no—
62C23×C29C2×D411yescharacteristic
63C22×D29—22no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29C2×D412yes—
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29C2×D412yes—
69C2×C4×C29C2411yescharacteristic
70C22⋊D29—82no—
71C2×Dic29—22no—
72C2×Dic29—22no—
73C2×Dic29—22no—
74D116—22no—
75D116—22no—
76D116—82no—
77C4×D29—82no—
78Dic58—22no—
79Dic58—22no—
80C8×C29—22no—
81C8×C29—22no—
82#3260—291nomaximal, Sylow
83C22×C29—21no—
84C22×C29—22no—
85C22×C29C22×D411yescharacteristic
86C2×D29—42no—
87C2×D29—42no—
88C2×D29—42no—
89C4×C29—21no—
90C4×C29—22no—
91C4×C29—22no—
92C4×C29H(5,𝔽2)11yescharacteristic
93C4×C292−1+411yescharacteristic
94Dic29—42no—
95Dic29—42no—
96Dic29—42no—
97#541—291no—
98#540—291no—
99#479—292no—
100#478—292no—
101#468—292no—
102#465—292no—
103#461—292no—
104#460—292no—
105#424D2911yescharacteristic, complemented
106C2×C29—41no—
107C2×C29#53711yescharacteristic
108C2×C29#57712yes—
109D29—82no—
110C2×SD16—292no—
111C2×SD16—292no—
112C2×M16C2×D2911yescharacteristic
113C22×C8C2×D2911yescharacteristic
114C4⋊Q8—291no—
115#127—291no—
116#126—582no—
117#125—291no—
118#125—291no—
119#125—582no—
120#123—582no—
121C22⋊Q8—292no—
122#121—292no—
123#121—582no—
124C4×Q8—292no—
125C4×D4—292no—
126#117C2×D2911yescharacteristic
127#107—292no—
128#106—292no—
129C4⋊C8C2×D2912yes—
130C4⋊C8C2×D2912yes—
131#103—292no—
132#103—292no—
133#102—292no—
134#102—292no—
135C29#326011yescharacteristic, complemented, Sylow
136C2×Q8—292no—
137C2×D4—292no—
138C2×D4—582no—
139C2×D4—582no—
140C22×C4—582no—
141C22×C4C22×D2911yescharacteristic
142SD16—1162no—
143SD16—1162no—
144M16—41no—
145C2×C8—41no—
146C2×C8C22×D2912yes—
147C2×C8C22×D2912yes—
148C4⋊C4—292no—
149C4⋊C4—292no—
150C4⋊C4—582no—
151C4⋊C4—582no—
152C4⋊C4—582no—
153C4⋊C4—582no—
154C4⋊C4—582no—
155C4⋊C4D11612yes—
156C22⋊C4—582no—
157C22⋊C4—582no—
158C22⋊C4—582no—
159C22⋊C4D11612yes—
160C42—582no—
161C42C22×D2911yescharacteristic
162C42C22×D2911yescharacteristic
163C23—582no—
164C23C2×D11611yescharacteristic
165Q8—582no—
166Q8—582no—
167D4—582no—
168D4—582no—
169D4—2322no—
170D4—2322no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—582no—
174C2×C4—582no—
175C2×C4—582no—
176C2×C4—2322no—
177C2×C4C2×D11612yes—
178C2×C4C2×D11612yes—
179C2×C4C2×D11611yescharacteristic
180C2×C4C23×D2911yescharacteristic
181C8—22no—
182C8—22no—
183C22—21no—
184C22—22no—
185C22—1162no—
186C22—1162no—
187C22—1162no—
188C22C22×D11611yescharacteristic
189C4—21no—
190C4—22no—
191C4—22no—
192C4—1162no—
193C4—1162no—
194C4—1162no—
195C4#1174535911yescharacteristic
196C4#1174536211yescharacteristic
197C2—41no—
198C2—2322no—
199C2#1427174411yescharacteristic
200C2#1427197512yes—
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#424C2
socleC22×C29C22×D4
prime radical#14271768C2
hypercenter#424D29
hypocenterC29#3260
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #14271775C2semidirect
3. #14271471C2semidirect
4. #14271464C2semidirect
5. #14271409C2semidirect
6. #14271392C2semidirect
7. #14271369C2semidirect
8. #14271364C2semidirect
9. C29×#424C2semidirect
105. #424D29semidirect
135. C29#3260semidirect

Maximal subgroups

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

subgroupindex
#142717752
#142717682
#142714712
#142714642
#142714092
#142713922
#142713692
#142713642
C29×#4242
#326029