Finite Group Databasebeta

← #16818498

Subgroups — #16818498

Order 3712.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#14271792C211yesmaximal, characteristic
2#14271493C211yesmaximal, characteristic
3#14271094C211yesmaximal, characteristic
4#14270901C211yesmaximal, characteristic
5#14270900C211yesmaximal, characteristic
6#14270888C211yesmaximal, characteristic
7C29×#483C211yesmaximal, characteristic
8C29×C22⋊Q8C2211yescharacteristic
9C2×C4⋊C4×C29C2211yescharacteristic
10#11745306—21no—
11#11745286C2211yescharacteristic
12C2×#90779—21no—
13C2×#90779C2211yescharacteristic
14#11745251—21no—
15#11745251—21no—
16#11745250—21no—
17#11745240—21no—
18#11745239—21no—
19C29×#106—21no—
20C29×#103—21no—
21C29×C22⋊C8C2211yescharacteristic
22#11745179—21no—
23#11745179C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745158—21no—
26#11745156—21no—
27C2×Q8×C29D411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29D411yescharacteristic
32C22×Dic29D411yescharacteristic
33C2×Dic58—21no—
34C2×Dic58D411yescharacteristic
35C2×C8×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29D411yescharacteristic
40C22⋊C4×C29—21no—
41C22⋊Dic29—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29D411yescharacteristic
44#90779—21no—
45#90779—21no—
46#90779—21no—
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—42no—
52C4×Dic29—21no—
53C4×Dic29—21no—
54C2×#6597—21no—
55C23×C29C2×D411yescharacteristic
56Q8×C29—41no—
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29—22no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—41no—
72C2×Dic29—41no—
73C2×Dic29—41no—
74C2×Dic29SD1612yes—
75Dic58—41no—
76Dic58—81no—
77C8×C29—41no—
78#6597—41no—
79#1611—291nomaximal, Sylow
80C22×C29—21no—
81C22×C29—21no—
82C22×C29#12011yescharacteristic
83C22×C29C2×SD1611yescharacteristic
84C22×C29#13711yescharacteristic
85C4×C29—21no—
86C4×C29—21no—
87C4×C29—41no—
88C4×C29—41no—
89C4×C29—81no—
90Dic29—22no—
91Dic29—42no—
92Dic29—41no—
93Dic29—41no—
94Dic29—41no—
95#544—291no—
96#483—291no—
97#483D2911yescharacteristic
98#398—291no—
99#328—291no—
100#328—291no—
101#324—291no—
102C2×C29—21no—
103C2×C29—21no—
104C2×C29#44811yescharacteristic
105C2×C29#45611yescharacteristic
106C2×C29#45811yescharacteristic
107C4⋊Q8—581no—
108C4⋊Q8—581no—
109#125—581no—
110#125—581no—
111C22⋊Q8—291no—
112C22⋊Q8—581no—
113C22⋊Q8C2×D2911yescharacteristic
114#117—581no—
115C2×C4⋊C4—291no—
116C2×C4⋊C4—581no—
117C2×C4⋊C4C2×D2911yescharacteristic
118#106—21no—
119#106—581no—
120#103—21no—
121#103—581no—
122C22⋊C8—291no—
123C22⋊C8C2×D2911yescharacteristic
124#95—291no—
125#95—581no—
126C29#161111yescharacteristic, complemented, Sylow
127C2×Q8—291no—
128C2×Q8—581no—
129C2×Q8C22⋊D2911yescharacteristic
130C22×C4—21no—
131C22×C4—291no—
132C22×C4—291no—
133C22×C4—581no—
134C22×C4C22×D2911yescharacteristic
135C2×C8—21no—
136C2×C8—581no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—291no—
141C4⋊C4—581no—
142C4⋊C4—581no—
143C4⋊C4—581no—
144C4⋊C4—581no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4—581no—
149C4⋊C4—1162no—
150C4⋊C4C22⋊D2911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—581no—
153C42—581no—
154C42—581no—
155C23D4×D2911yescharacteristic
156Q8—41no—
157Q8—1161no—
158Q8—2321no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—292no—
166C2×C4—581no—
167C2×C4—581no—
168C2×C4—582no—
169C2×C4—581no—
170C2×C4—581no—
171C2×C4—581no—
172C2×C4—1161no—
173C2×C4—1161no—
174C2×C4—1161no—
175C2×C4D4×D2911yescharacteristic
176C2×C4C2×C22⋊D2911yescharacteristic
177C8—41no—
178C8—1161no—
179C22—21no—
180C22—21no—
181C22SD16×D2911yescharacteristic
182C22#1174527711yescharacteristic
183C22#1174529911yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—582no—
190C4—1162no—
191C4—1161no—
192C4—1161no—
193C4—1161no—
194C2—21no—
195C2—21no—
196C2#1427130011yescharacteristic
197C2#1427134411yescharacteristic
198C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#483C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#483D29
hypocenterC29#1611
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
126. C29#1611semidirect

Maximal subgroups

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

subgroupindex
#142717922
#142714932
#142710942
#142709012
#142709002
#142708882
C29×#4832
#161129