Finite Group Databasebeta

← #16830953

Subgroups — #16830953

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#14271784C212yesmaximal, complemented
2#14271459C212yesmaximal, complemented
3#14271444C212yesmaximal, complemented
4#14271409C212yesmaximal, complemented
5#14271404C211yesmaximal, characteristic, complemented
6#14271399C211yesmaximal, characteristic
7#14271386C212yesmaximal, complemented
8#14271379C212yesmaximal, complemented
9C29×#424C211yesmaximal, characteristic, complemented
10C2×M16×C29C2211yescharacteristic
11C22×C8×C29C2211yescharacteristic
12C29×#117C2211yescharacteristic
13#11745292C2212yes—
14#11745286C2212yes—
15C2×Dic116C2211yescharacteristic
16C2×D232C2211yescharacteristic
17C2×#90773C2212yes—
18#11745260—22no—
19#11745258—22no—
20#11745247—22no—
21#11745245—22no—
22#11745237C2212yes—
23C4×D116C2212yes—
24#11745231C2212yes—
25C4×Dic58C2212yes—
26C29×C4⋊C8C2212yes—
27C29×C4⋊C8C2212yes—
28#11745169C2212yes—
29#11745169C2212yes—
30#11745166C2211yescharacteristic
31#11745166C2211yescharacteristic
32#11745166C2212yes—
33#11745164C2212yes—
34#11745164C2212yes—
35C22×C4×C29C2311yescharacteristic
36C2×C22⋊D29—22no—
37C2×D116C2312yes—
38C2×C4×D29—22no—
39C2×Dic58—22no—
40C2×Dic58C2312yes—
41M16×C29—41no—
42C2×C8×C29—41no—
43C2×C8×C29C2311yescharacteristic
44C2×C8×C29C2311yescharacteristic
45C2×C8×C29C2312yes—
46C4⋊C4×C29D411yescharacteristic
47C4⋊C4×C29D411yescharacteristic
48C22⋊C4×C29D412yes—
49C42×C29C2312yes—
50C22⋊Dic29—22no—
51#90781—22no—
52#90781—22no—
53#90781—22no—
54#90781—22no—
55C4⋊Dic29—22no—
56C4⋊Dic29C2312yes—
57C4⋊Dic29C2312yes—
58#90779—22no—
59#90779—22no—
60C4×Dic29—22no—
61Dic116—41no—
62D232—41no—
63#90773—42no—
64C23×C29C2×D411yescharacteristic
65C22×D29—22no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29C2×D412yes—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D412yes—
71C2×C4×C29C2411yescharacteristic
72C22⋊D29—82no—
73C2×Dic29—22no—
74C2×Dic29—22no—
75C2×Dic29—22no—
76D116—22no—
77D116—22no—
78C4×D29—82no—
79Dic58—22no—
80Dic58—22no—
81Dic58—82no—
82C8×C29—22no—
83C8×C29—21no—
84C8×C29—21no—
85#3262—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29C22×D411yescharacteristic
90C2×D29—42no—
91C2×D29—42no—
92C2×D29—42no—
93C4×C29—21no—
94C4×C29—22no—
95C4×C29—22no—
96C4×C29H(5,𝔽2)11yescharacteristic
97C4×C292−1+411yescharacteristic
98Dic29—42no—
99Dic29—42no—
100Dic29—42no—
101#542—292no—
102#477—292no—
103#474—292no—
104#468—292no—
105#467—291no—
106#466—291no—
107#464—292no—
108#463—292no—
109#424D2911yescharacteristic, complemented
110C2×C29—41no—
111C2×C29#53711yescharacteristic
112C2×C29#57611yescharacteristic
113C2×C29#57811yescharacteristic
114D29—82no—
115C2×Q16—291no—
116C2×SD16—292no—
117C2×D8—291no—
118C2×M16C2×D2911yescharacteristic
119C22×C8C2×D2911yescharacteristic
120C4⋊Q8—292no—
121#126—582no—
122#124—292no—
123#124—582no—
124#123—582no—
125C22⋊Q8—292no—
126C22⋊Q8—582no—
127#121—292no—
128C4×Q8—292no—
129C4×D4—292no—
130#117C2×D2911yescharacteristic
131#107—291no—
132#107—291no—
133#107—292no—
134C4⋊C8C2×D2912yes—
135C4⋊C8C2×D2912yes—
136#103—292no—
137#103—292no—
138#102—292no—
139#102—292no—
140C29#326211yescharacteristic, complemented, Sylow
141C2×Q8—292no—
142C2×Q8—582no—
143C2×D4—292no—
144C2×D4—582no—
145C22×C4—582no—
146C22×C4C22×D2911yescharacteristic
147Q16—1161no—
148SD16—1162no—
149D8—1161no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D2911yescharacteristic
153C2×C8C22×D2912yes—
154C2×C8C22×D2911yescharacteristic
155C4⋊C4—292no—
156C4⋊C4—292no—
157C4⋊C4—582no—
158C4⋊C4—582no—
159C4⋊C4—582no—
160C4⋊C4D11611yescharacteristic
161C4⋊C4D11611yescharacteristic
162C22⋊C4—582no—
163C22⋊C4—582no—
164C22⋊C4—582no—
165C22⋊C4—582no—
166C22⋊C4—582no—
167C22⋊C4D11612yes—
168C42—582no—
169C42C22×D2912yes—
170C23—582no—
171C23C2×D11611yescharacteristic
172Q8—582no—
173Q8—582no—
174Q8—2322no—
175D4—582no—
176D4—582no—
177D4—2322no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—582no—
181C2×C4—582no—
182C2×C4—582no—
183C2×C4—2322no—
184C2×C4C2×D11612yes—
185C2×C4C2×D11612yes—
186C2×C4C2×D11611yescharacteristic
187C2×C4C23×D2911yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—1162no—
195C22—1162no—
196C22—1162no—
197C22C22×D11611yescharacteristic
198C4—21no—
199C4—22no—
200C4—22no—
201C4—1162no—
202C4—1162no—
203C4—1162no—
204C4#1174535911yescharacteristic
205C4#1174536211yescharacteristic
206C2—41no—
207C2—2322no—
208C2#1427174411yescharacteristic
209C2#1427196811yescharacteristic
210C2#1427198011yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#424C2
socleC22×C29C22×D4
prime radical#14271399C2
hypercenter#424D29
hypocenterC29#3262
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. #14271784C2semidirect
2. #14271459C2semidirect
3. #14271444C2semidirect
4. #14271409C2semidirect
5. #14271404C2semidirect
7. #14271386C2semidirect
8. #14271379C2semidirect
9. C29×#424C2semidirect
109. #424D29semidirect
140. C29#3262semidirect

Maximal subgroups

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

subgroupindex
#142717842
#142714592
#142714442
#142714092
#142714042
#142713992
#142713862
#142713792
C29×#4242
#326229