Finite Group Databasebeta

← #16818811

Subgroups — #16818811

Order 3712.

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

normal subgroups only

This group has 208 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#14271911C211yesmaximal, characteristic
2#14271573C211yesmaximal, characteristic, complemented
3#14271557C211yesmaximal, characteristic, complemented
4#14271523C211yesmaximal, characteristic, complemented
5#14270902C211yesmaximal, characteristic, complemented
6#14270902C211yesmaximal, characteristic, complemented
7C29×#330C211yesmaximal, characteristic, complemented
8C29×#125C2211yescharacteristic
9C2×Dic116—21no—
10C2×#90773—21no—
11#11745258—21no—
12#11745258—21no—
13#11745257—21no—
14#11745257—21no—
15#11745256—21no—
16#11745256—21no—
17#11745237C2211yescharacteristic
18#11745237C2211yescharacteristic
19#11745231C2211yescharacteristic
20C29×#97C2211yescharacteristic
21C29×#97C2211yescharacteristic
22#11745169—21no—
23#11745164—21no—
24#11745156—21no—
25#11745155—21no—
26#11745151C2211yescharacteristic
27C2×D116—21no—
28C2×D116—21no—
29C2×D116D411yescharacteristic
30C2×D116D411yescharacteristic
31C2×C4×D29—21no—
32C2×C4×D29—21no—
33C2×Dic58—21no—
34C2×Dic58D411yescharacteristic
35C2×Dic58D411yescharacteristic
36C2×C8×C29—21no—
37C2×C8×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C4⋊C4×C29D411yescharacteristic
42C42×C29C2311yescharacteristic
43#90781—21no—
44#90781—21no—
45#90781—21no—
46#90781—21no—
47#90781—21no—
48#90781—21no—
49C4⋊Dic29—21no—
50C4⋊Dic29—21no—
51#90779—21no—
52#90779—21no—
53C2×#6597—21no—
54Dic116—42no—
55#90773—42no—
56C22×D29—21no—
57C22×D29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C2×Dic29—21no—
64C2×Dic29—21no—
65C2×Dic29—41no—
66D116—41no—
67D116—41no—
68D116—81no—
69D116—81no—
70C4×D29—81no—
71C4×D29—81no—
72Dic58—41no—
73Dic58—41no—
74Dic58—41no—
75Dic58—41no—
76C8×C29—22no—
77C8×C29—41no—
78#6597—22no—
79#1661—291nomaximal, Sylow
80C22×C29#12011yescharacteristic
81C2×D29—41no—
82C2×D29—41no—
83C2×D29—41no—
84C2×D29—41no—
85C2×D29—41no—
86C2×D29—41no—
87C4×C29—21no—
88C4×C29—21no—
89C4×C29—21no—
90C4×C29—41no—
91C4×C29—41no—
92Dic29—41no—
93Dic29—41no—
94Dic29—81no—
95#562—291no—
96#501—291no—
97#497—291no—
98#489—291no—
99#330D2911yescharacteristic, complemented
100#329—291no—
101#329—291no—
102C2×C29#45311yescharacteristic
103C2×C29#45511yescharacteristic
104C2×C29#45611yescharacteristic
105D29—81no—
106D29—81no—
107C2×Q16—581no—
108C2×SD16—581no—
109C4⋊Q8—291no—
110#125C2×D2911yescharacteristic
111#124—291no—
112#124—291no—
113#123—581no—
114#123—581no—
115C22⋊Q8—581no—
116C22⋊Q8—581no—
117#121—581no—
118#121—581no—
119#107—581no—
120#106—581no—
121#103—581no—
122#102—581no—
123#97—291no—
124#97C2×D2911yescharacteristic
125#97C2×D2911yescharacteristic
126C29#166111yescharacteristic, complemented, Sylow
127C2×Q8—291no—
128C2×Q8—291no—
129C2×Q8—581no—
130C2×D4—291no—
131C2×D4—291no—
132C2×D4—581no—
133C2×D4—581no—
134C22×C4—581no—
135C22×C4—581no—
136Q16—1162no—
137SD16—1162no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—581no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—581no—
144C4⋊C4—581no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4D11611yescharacteristic
148C4⋊C4D11611yescharacteristic
149C22⋊C4—581no—
150C22⋊C4—581no—
151C22⋊C4—581no—
152C22⋊C4—581no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C42C22×D2911yescharacteristic
156C23—581no—
157C23—581no—
158Q8—1161no—
159Q8—1161no—
160Q8—1161no—
161Q8—1161no—
162D4—1161no—
163D4—1161no—
164D4—2321no—
165D4—2321no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—581no—
169C2×C4—581no—
170C2×C4—1161no—
171C2×C4—2321no—
172C2×C4—2321no—
173C2×C4C2×D11611yescharacteristic
174C2×C4D4×D2911yescharacteristic
175C2×C4D4×D2911yescharacteristic
176C8—22no—
177C8—41no—
178C8—582no—
179C22—1161no—
180C22—1161no—
181C22—1161no—
182C22—1161no—
183C22—1161no—
184C22—1161no—
185C22#1174524411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—1161no—
192C4—1161no—
193C4—2321no—
194C2—2321no—
195C2—2321no—
196C2#1427133211yescharacteristic
197C2#1427134211yescharacteristic
198C2#1427134811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#330C2
socleC22×C29#120
prime radical#14271911C2
hypercenter#330D29
hypocenterC29#1661
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14271573C2semidirect
3. #14271557C2semidirect
4. #14271523C2semidirect
5. #14270902C2semidirect
6. #14270902C2semidirect
7. C29×#330C2semidirect
99. #330D29semidirect
126. C29#1661semidirect

Maximal subgroups

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

subgroupindex
#142719112
#142715732
#142715572
#142715232
#142709022
C29×#3302
#166129