Finite Group Databasebeta

← #16818783

Subgroups — #16818783

Order 3712.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#14271907C211yesmaximal, characteristic, complemented
2#14271550C211yesmaximal, characteristic, complemented
3#14271527C211yesmaximal, characteristic, complemented
4#14270904C211yesmaximal, characteristic, complemented
5#14270903C211yesmaximal, characteristic, complemented
6#14270902C211yesmaximal, characteristic, complemented
7C29×#496C211yesmaximal, characteristic, complemented
8C2×SD16×C29—21no—
9C2×D8×C29—21no—
10C29×#127C2211yescharacteristic
11C29×#124C2211yescharacteristic
12#11745308—21no—
13#11745301—21no—
14C2×#90783—21no—
15C2×#90782—21no—
16#11745248—21no—
17#11745246—21no—
18#11745245—21no—
19#11745240—21no—
20#11745237C2211yescharacteristic
21#11745232C2211yescharacteristic
22C29×#97C2211yescharacteristic
23#11745180—21no—
24#11745180—21no—
25#11745151C2211yescharacteristic
26#11745151C2211yescharacteristic
27C2×Q8×C29D411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29D411yescharacteristic
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C22×Dic29—21no—
35C2×D116D411yescharacteristic
36C2×C4×D29—21no—
37C2×Dic58D411yescharacteristic
38SD16×C29—42no—
39D8×C29—42no—
40C2×C8×C29—21no—
41C22⋊C4×C29—21no—
42C22⋊C4×C29—21no—
43C42×C29C2311yescharacteristic
44C22⋊Dic29—21no—
45#90783—42no—
46#90782—42no—
47#90781—21no—
48#90781—21no—
49#90781—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29D411yescharacteristic
52C4⋊Dic29D411yescharacteristic
53#90779—21no—
54#90779—21no—
55#90779—21no—
56C2×#6597—21no—
57C2×#6597—21no—
58C23×C29—21no—
59C23×C29—41no—
60C22×D29—21no—
61Q8×C29—41no—
62D4×C29—41no—
63D4×C29—41no—
64D4×C29—41no—
65D4×C29—41no—
66D4×C29—41no—
67D4×C29—42no—
68C2×C4×C29—21no—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C22⋊D29—81no—
73C22⋊D29—81no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—81no—
78D116—41no—
79C4×D29—81no—
80Dic58—41no—
81C8×C29—22no—
82#6597—22no—
83#6597—41no—
84#1656—291nomaximal, Sylow
85C22×C29—41no—
86C22×C29—41no—
87C22×C29—41no—
88C22×C29—81no—
89C22×C29—81no—
90C22×C29—81no—
91C22×C29#12011yescharacteristic
92C2×D29—41no—
93C2×D29—41no—
94C2×D29—41no—
95C4×C29—21no—
96C4×C29—21no—
97C4×C29—21no—
98C4×C29—41no—
99Dic29—41no—
100Dic29—41no—
101Dic29—41no—
102#562—291no—
103#496—291no—
104#496D2911yescharacteristic, complemented
105#490—291no—
106#330—291no—
107#329—291no—
108#329—291no—
109C2×C29—81no—
110C2×C29—161no—
111C2×C29#45311yescharacteristic
112C2×C29#45311yescharacteristic
113C2×C29#45411yescharacteristic
114D29—81no—
115C2×SD16—21no—
116C2×SD16—581no—
117C2×D8—21no—
118C2×D8—581no—
119#127C2×D2911yescharacteristic
120#125—291no—
121#124—291no—
122#124C2×D2911yescharacteristic
123#123—581no—
124#123—581no—
125C22⋊Q8—581no—
126C22⋊Q8—581no—
127#121—581no—
128#121—581no—
129#102—581no—
130#102—581no—
131#97—291no—
132#97—291no—
133#97C2×D2911yescharacteristic
134C29#165611yescharacteristic, complemented, Sylow
135C2×Q8—291no—
136C2×Q8C22⋊D2911yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—291no—
141C2×D4—581no—
142C2×D4—581no—
143C2×D4C22⋊D2911yescharacteristic
144C22×C4—581no—
145C22×C4—581no—
146SD16—42no—
147SD16—1162no—
148D8—42no—
149D8—1162no—
150C2×C8—21no—
151C2×C8—581no—
152C2×C8—581no—
153C4⋊C4—291no—
154C4⋊C4—291no—
155C4⋊C4—581no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4—581no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—581no—
162C22⋊C4—581no—
163C22⋊C4—581no—
164C22⋊C4—581no—
165C42C22×D2911yescharacteristic
166C23—21no—
167C23—41no—
168C23—581no—
169Q8—41no—
170Q8—1161no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—41no—
176D4—42no—
177D4—1161no—
178D4—2321no—
179D4—2321no—
180C2×C4—21no—
181C2×C4—581no—
182C2×C4—581no—
183C2×C4—581no—
184C2×C4—2321no—
185C2×C4—2321no—
186C2×C4D4×D2911yescharacteristic
187C2×C4D4×D2911yescharacteristic
188C2×C4C2×C22⋊D2911yescharacteristic
189C8—22no—
190C8—582no—
191C8—1161no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22—81no—
197C22—81no—
198C22—1161no—
199C22—1161no—
200C22—1161no—
201C22#1174529911yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—1161no—
207C4—1161no—
208C4—1161no—
209C2—81no—
210C2—161no—
211C2—2321no—
212C2#1427132911yescharacteristic
213C2#1427133011yescharacteristic
214C2#1427133411yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#496C2
socleC22×C29#120
hypercenter#496D29
hypocenterC29#1656
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14271907C2semidirect
2. #14271550C2semidirect
3. #14271527C2semidirect
4. #14270904C2semidirect
5. #14270903C2semidirect
6. #14270902C2semidirect
7. C29×#496C2semidirect
104. #496D29semidirect
134. C29#1656semidirect

Maximal subgroups

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

subgroupindex
#142719072
#142715502
#142715272
#142709042
#142709032
#142709022
C29×#4962
#165629