Finite Group Databasebeta

← #16830962

Subgroups — #16830962

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#14271780C212yesmaximal, complemented
2#14271451C212yesmaximal, complemented
3#14271447C212yesmaximal, complemented
4#14271421C211yesmaximal, characteristic, complemented
5#14271390C212yesmaximal, complemented
6#14271384C212yesmaximal, complemented
7#14271376C212yesmaximal, complemented
8#14271191C211yesmaximal, characteristic, complemented
9C29×#469C211yesmaximal, characteristic
10C2×D8×C29C2211yescharacteristic
11C2×M16×C29C2211yescharacteristic
12C29×#121C2212yes—
13#11745298—22no—
14#11745298C2212yes—
15#11745297—22no—
16D4×Dic29C2212yes—
17C2×#90783C2212yes—
18#11745288C2211yescharacteristic
19#11745286C2212yes—
20C22×#6597C2211yescharacteristic
21C2×Dic116C2211yescharacteristic
22#11745250C2212yes—
23#11745249C2212yes—
24#11745241—22no—
25#11745240—22no—
26C29×#106C2211yescharacteristic
27C29×#102C2212yes—
28#11745180C2212yes—
29#11745165C2211yescharacteristic
30#11745164C2212yes—
31#11745162C2212yes—
32#11745162C2212yes—
33#11745158C2212yes—
34#11745156C2212yes—
35C2×D4×C29—22no—
36C2×D4×C29C2312yes—
37C22×C4×C29C2311yescharacteristic
38C22×Dic29—22no—
39C2×Dic58—22no—
40C2×Dic58C2312yes—
41D8×C29—41no—
42M16×C29—41no—
43C2×C8×C29C2311yescharacteristic
44C2×C8×C29C2311yescharacteristic
45C4⋊C4×C29C2312yes—
46C22⋊C4×C29—22no—
47C22⋊Dic29—22no—
48C22⋊Dic29—22no—
49C22⋊Dic29—22no—
50C22⋊Dic29—22no—
51C22⋊Dic29D411yescharacteristic
52C22⋊Dic29D411yescharacteristic
53#90783—42no—
54C4⋊Dic29D412yes—
55C4⋊Dic29C2312yes—
56#90779—22no—
57#90779—22no—
58#90779—22no—
59C4×Dic29—22no—
60C4×Dic29C2312yes—
61C2×#6597—41no—
62C2×#6597C2312yes—
63Dic116—41no—
64C23×C29—22no—
65C23×C29C2×D411yescharacteristic
66D4×C29—22no—
67D4×C29—22no—
68D4×C29—82no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—22no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2411yescharacteristic
74C2×Dic29—22no—
75C2×Dic29—22no—
76C2×Dic29—82no—
77C2×Dic29C2×D412yes—
78C2×Dic29C2×D412yes—
79Dic58—22no—
80Dic58—22no—
81Dic58—82no—
82C8×C29—21no—
83C8×C29—21no—
84#6597—22no—
85#3263—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—22no—
88C22×C29—42no—
89C22×C29—42no—
90C22×C29—42no—
91C22×C29C22×D411yescharacteristic
92C4×C29—21no—
93C4×C29—42no—
94C4×C29H(5,𝔽2)11yescharacteristic
95C4×C292−1+411yescharacteristic
96Dic29—22no—
97Dic29—22no—
98Dic29—42no—
99Dic29—42no—
100#542—292no—
101#476—292no—
102#475—292no—
103#470—291no—
104#469D2911yescharacteristic
105#465—292no—
106#464—292no—
107#463—292no—
108#424—291no—
109C2×C29—41no—
110C2×C29—82no—
111C2×C29#53711yescharacteristic
112C2×C29#57712yes—
113C2×Q16—291no—
114C2×SD16—292no—
115C2×D8C2×D2911yescharacteristic
116C2×M16C2×D2911yescharacteristic
117C22×C8—291no—
118C4⋊Q8—292no—
119#126—582no—
120#124—292no—
121#124—582no—
122#123—582no—
123C22⋊Q8—292no—
124C22⋊Q8—582no—
125#121C2×D2912yes—
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#103—292no—
136#102—292no—
137#102C2×D2912yes—
138C29#326311yescharacteristic, complemented, Sylow
139C2×Q8—292no—
140C2×Q8—582no—
141C2×D4—22no—
142C2×D4C22×D2912yes—
143C22×C4—582no—
144C22×C4C22×D2911yescharacteristic
145Q16—1161no—
146SD16—1162no—
147D8—41no—
148M16—41no—
149C2×C8—292no—
150C2×C8—1161no—
151C2×C8C22×D2911yescharacteristic
152C2×C8C22×D2911yescharacteristic
153C4⋊C4—292no—
154C4⋊C4—292no—
155C4⋊C4—582no—
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—22no—
169C23D4×D2911yescharacteristic
170Q8—582no—
171Q8—582no—
172Q8—2322no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—292no—
180C2×C4—292no—
181C2×C4—582no—
182C2×C4—582no—
183C2×C4—2322no—
184C2×C4D4×D2911yescharacteristic
185C2×C4C23×D2911yescharacteristic
186C8—21no—
187C8—21no—
188C8—582no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D2911yescharacteristic
195C4—21no—
196C4—42no—
197C4—582no—
198C4—582no—
199C4—1162no—
200C4—1162no—
201C4#1174535911yescharacteristic
202C4#1174536511yescharacteristic
203C2—41no—
204C2—82no—
205C2#1427174011yescharacteristic
206C2#1427197312yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#469C2
socleC22×C29C22×D4
hypercenter#469D29
hypocenterC29#3263
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14271780C2semidirect
2. #14271451C2semidirect
3. #14271447C2semidirect
4. #14271421C2semidirect
5. #14271390C2semidirect
6. #14271384C2semidirect
7. #14271376C2semidirect
8. #14271191C2semidirect
138. C29#3263semidirect

Maximal subgroups

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

subgroupindex
#142717802
#142714512
#142714472
#142714212
#142713902
#142713842
#142713762
#142711912
C29×#4692
#326329