Finite Group Databasebeta

← #16819884

Subgroups — #16819884

Order 3712.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#11745231C211yesmaximal, characteristic
2#14271640C211yesmaximal, characteristic
3#14271173C211yesmaximal, characteristic
4#14271171C211yesmaximal, characteristic
5C2×#11745172C211yesmaximal, characteristic
6#14270923C211yesmaximal, characteristic
7C29×#339C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C22×Dic58C2211yescharacteristic
10C2×M16×C29C2211yescharacteristic
11C29×#117C2211yescharacteristic
12C2×C42×C29C2211yescharacteristic
13#11745288C2211yescharacteristic
14C2×C4⋊Dic29—22no—
15C2×#90777C2211yescharacteristic
16#11745249—22no—
17#11745239—22no—
18#11745231—22no—
19#11745231C414yescomplemented
20C4×Dic58—22no—
21#11745172—22no—
22#11745164—22no—
23#11745158—22no—
24C22×C4×C29—21no—
25C22×C4×C29C2311yescharacteristic
26C22×Dic29—21no—
27C22×Dic29D412yes—
28C2×Dic58—21no—
29C2×Dic58—21no—
30C2×Dic58—21no—
31C2×Dic58—21no—
32C2×Dic58—21no—
33C2×Dic58—21no—
34C2×Dic58—21no—
35C2×Dic58—21no—
36C2×Dic58—21no—
37C2×Dic58C2×C412yes—
38C2×Dic58C2×C412yes—
39C2×Dic58D412yes—
40M16×C29—21no—
41M16×C29—21no—
42C2×C8×C29—21no—
43C4⋊C4×C29D412yes—
44C22⋊C4×C29—21no—
45C42×C29—21no—
46C42×C29—21no—
47C42×C29C2×C412yes—
48C22⋊Dic29—21no—
49C4⋊Dic29—28no—
50C4⋊Dic29D412yes—
51#90779—24no—
52C4×Dic29—24no—
53C4×Dic29—21no—
54#90777—21no—
55#90777—21no—
56C2×#6597—21no—
57C23×C29C2×D411yescharacteristic
58C2×C4×C29—24no—
59C2×C4×C29—22no—
60C2×C4×C29—22no—
61C2×C4×C29C22×C411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29#4111yescharacteristic
66C2×C4×C29#4111yescharacteristic
67C2×Dic29—22no—
68C2×Dic29—22no—
69C2×Dic29—22no—
70C2×Dic29—22no—
71C2×Dic29—41no—
72C2×Dic29—41no—
73C2×Dic29C22⋊C414yes—
74Dic58—22no—
75Dic58—22no—
76Dic58—22no—
77Dic58—22no—
78Dic58—22no—
79Dic58—22no—
80Dic58—41no—
81Dic58—41no—
82C8×C29—41no—
83#6597—41no—
84#1886—291nomaximal, Sylow
85C22×C29—22no—
86C22×C29C2×C22⋊C411yescharacteristic
87C22×C29#12011yescharacteristic
88C22×C29#12311yescharacteristic
89C4×C29—24no—
90C4×C29—42no—
91C4×C29C4×D411yescharacteristic
92C4×C29C4×D411yescharacteristic
93C4×C29#12111yescharacteristic
94C4×C29#12111yescharacteristic
95Dic29—24no—
96Dic29—42no—
97Dic29—42no—
98C2×C4⋊Q8—291no—
99#519—291no—
100#419—291no—
101#419—291no—
102C2×#101—291no—
103#339—291no—
104#339D2911yescharacteristic
105C2×C29—21no—
106C2×C29—21no—
107C2×C29#38611yescharacteristic
108C2×C29#45612yes—
109C22×Q8—291no—
110C22×Q8—291no—
111C2×M16—291no—
112C2×M16C2×D2911yescharacteristic
113C4⋊Q8—294no—
114C4⋊Q8—582no—
115C4×Q8—582no—
116C4×Q8—582no—
117#117—291no—
118#117—582no—
119#117C2×D2911yescharacteristic
120C2×C4⋊C4—582no—
121C2×C42C2×D2911yescharacteristic
122#103—582no—
123#103—582no—
124#101—582no—
125C29#188611yescharacteristic, complemented, Sylow
126C2×Q8—292no—
127C2×Q8—292no—
128C2×Q8—292no—
129C2×Q8—581no—
130C2×Q8—581no—
131C2×Q8—581no—
132C2×Q8—581no—
133C2×Q8—581no—
134C2×Q8—581no—
135C2×Q8—581no—
136C2×Q8—581no—
137C2×Q8—581no—
138C22×C4—21no—
139C22×C4—292no—
140C22×C4—581no—
141C22×C4C22×D2911yescharacteristic
142M16—21no—
143M16—21no—
144M16—581no—
145M16—581no—
146C2×C8—21no—
147C2×C8—581no—
148C4⋊C4—292no—
149C4⋊C4—588no—
150C4⋊C4—584no—
151C4⋊C4D11612yes—
152C22⋊C4—21no—
153C22⋊C4—581no—
154C42—21no—
155C42—21no—
156C42—584no—
157C42—581no—
158C42C4×D2912yes—
159C23D4×D2911yescharacteristic
160Q8—582no—
161Q8—582no—
162Q8—582no—
163Q8—582no—
164Q8—582no—
165Q8—582no—
166Q8—1161no—
167Q8—1161no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—294no—
172C2×C4—582no—
173C2×C4—582no—
174C2×C4—582no—
175C2×C4—582no—
176C2×C4—1161no—
177C2×C4—1161no—
178C2×C4C2×C4×D2911yescharacteristic
179C2×C4C2×D11611yescharacteristic
180C2×C4#9080511yescharacteristic
181C2×C4D4×D2911yescharacteristic
182C2×C4D4×D2911yescharacteristic
183C2×C4#9080911yescharacteristic
184C8—41no—
185C8—1161no—
186C22—22no—
187C22C22⋊C4×D2911yescharacteristic
188C22#1174524411yescharacteristic
189C22#1174525611yescharacteristic
190C4—24no—
191C4—42no—
192C4—584no—
193C4—1162no—
194C4—1162no—
195C4C4×D11611yescharacteristic
196C4#1174524611yescharacteristic
197C4#1174525511yescharacteristic
198C4#1174525711yescharacteristic
199C2—21no—
200C2—21no—
201C2#1427104111yescharacteristic
202C2#1427134712yes—
subgroupG/H
centerC22#11745244
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#339C2
socleC22×C29#120
prime radicalC23×C29C2×D4
cosocleC22×C4×C29C23
hypercenter#339D29
hypocenterC29#1886
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
19. #11745231C4semidirect
125. C29#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#117452312
#142716402
#142711732
#142711712
C2×#117451722
#142709232
C29×#3392
#188629