Finite Group Databasebeta

← #16818574

Subgroups — #16818574

Order 3712.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271878C211yesmaximal, characteristic, complemented
2#14271535C211yesmaximal, characteristic, complemented
3#14271355C211yesmaximal, characteristic, complemented
4#14270911C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#459C211yesmaximal, characteristic, complemented
8C2×D8×C29—21no—
9C29×#127C2211yescharacteristic
10C4×D4×C29C2211yescharacteristic
11#11745300—21no—
12C2×#90783—22no—
13C2×#90782—21no—
14#11745292—21no—
15#11745288—21no—
16#11745254—21no—
17#11745247—22no—
18C4×D116C2211yescharacteristic
19#11745231C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C29×#102—21no—
22#11745180—21no—
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×D4×C29—21no—
26C2×D4×C29—21no—
27C2×D4×C29—21no—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29—21no—
30C2×C22⋊D29—22no—
31C2×D116D411yescharacteristic
32C2×C4×D29—21no—
33C2×Dic58D412yes—
34D8×C29—42no—
35C2×C8×C29—21no—
36C4⋊C4×C29D411yescharacteristic
37C22⋊C4×C29—21no—
38C42×C29C2311yescharacteristic
39C22⋊Dic29—22no—
40#90783—44no—
41#90782—42no—
42#90781—22no—
43#90781—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29D411yescharacteristic
47C4×Dic29—22no—
48C2×#6597—21no—
49C2×#6597—21no—
50C23×C29—21no—
51C23×C29—41no—
52C22×D29—21no—
53D4×C29—21no—
54D4×C29—21no—
55D4×C29—42no—
56D4×C29—41no—
57D4×C29—41no—
58D4×C29—41no—
59D4×C29—41no—
60C2×C4×C29—21no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C22⋊D29—82no—
67C2×Dic29—21no—
68C2×Dic29—22no—
69D116—21no—
70D116—21no—
71C4×D29—41no—
72C4×D29—41no—
73Dic58—42no—
74C8×C29—41no—
75#6597—22no—
76#6597—41no—
77#1624—291nomaximal, Sylow
78C22×C29—41no—
79C22×C29—41no—
80C22×C29—41no—
81C22×C29—81no—
82C22×C29—81no—
83C22×C29—81no—
84C22×C29#12011yescharacteristic
85C2×D29—41no—
86C2×D29—41no—
87C2×D29—41no—
88C4×C29—21no—
89C4×C29—41no—
90C4×C29#13511yescharacteristic
91C4×C29#13511yescharacteristic
92C4×C29AGL(1,ℤ/8)11yescharacteristic
93C4×C29AGL(1,ℤ/8)11yescharacteristic
94Dic29—41no—
95Dic29—42no—
96#555—291no—
97#492—291no—
98#459—291no—
99#459D2911yescharacteristic, complemented
100#333—291no—
101D4⋊C8—291no—
102D4⋊C8—291no—
103C2×C29—81no—
104C2×C29—161no—
105C2×C29#44911yescharacteristic
106C2×C29#44911yescharacteristic
107C2×C29#45311yescharacteristic
108D29—81no—
109C2×SD16—582no—
110C2×D8—21no—
111C2×D8—581no—
112C4⋊Q8—291no—
113#127C2×D2911yescharacteristic
114#124—582no—
115#121—581no—
116#121—581no—
117C4×D4—291no—
118C4×D4C2×D2911yescharacteristic
119#117—581no—
120#117—581no—
121C4⋊C8—291no—
122C4⋊C8C2×D2911yescharacteristic
123#102—21no—
124#102—581no—
125C4×C8—291no—
126C29#162411yescharacteristic, complemented, Sylow
127C2×Q8—292no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—291no—
132C2×D4—582no—
133C2×D4C22⋊D2911yescharacteristic
134C22×C4—21no—
135C22×C4—581no—
136SD16—1164no—
137D8—42no—
138D8—1162no—
139C2×C8—21no—
140C2×C8—581no—
141C2×C8—581no—
142C4⋊C4—291no—
143C4⋊C4—581no—
144C4⋊C4—581no—
145C4⋊C4C22⋊D2911yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—582no—
148C22⋊C4—582no—
149C22⋊C4—581no—
150C42—582no—
151C42C22×D2911yescharacteristic
152C23—21no—
153C23—41no—
154C23—581no—
155Q8—1162no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—581no—
164D4—581no—
165D4—2322no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—581no—
170C2×C4—582no—
171C2×C4—1161no—
172C2×C4—1161no—
173C2×C4D4×D2911yescharacteristic
174C2×C4D4×D2911yescharacteristic
175C2×C4C2×C22⋊D2911yescharacteristic
176C8—41no—
177C8—582no—
178C8—1161no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—1161no—
186C22—1161no—
187C22—1161no—
188C22#1174529911yescharacteristic
189C4—21no—
190C4—41no—
191C4—1161no—
192C4—1162no—
193C4#1174527311yescharacteristic
194C4#1174527411yescharacteristic
195C4#1174529411yescharacteristic
196C4#1174531211yescharacteristic
197C2—81no—
198C2—161no—
199C2—2321no—
200C2#1427130511yescharacteristic
201C2#1427130611yescharacteristic
202C2#1427132911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#459C2
socleC22×C29#120
hypercenter#459D29
hypocenterC29#1624
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14271878C2semidirect
2. #14271535C2semidirect
3. #14271355C2semidirect
4. #14270911C2semidirect
5. D4⋊#6597C2semidirect
6. #14270890C2semidirect
7. C29×#459C2semidirect
99. #459D29semidirect
126. C29#1624semidirect

Maximal subgroups

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

subgroupindex
#142718782
#142715352
#142713552
#142709112
D4⋊#65972
#142708902
C29×#4592
#162429