Finite Group Databasebeta

← #16835544

Subgroups — #16835544

Order 3712.

308 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 66 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#14272241C211yesmaximal, characteristic
2#14272150C211yesmaximal, characteristic
3C2×#11745221C212yesmaximal, complemented
4#14272044C212yesmaximal, complemented
5#14271735C211yesmaximal, characteristic
6C2×#90807C2211yescharacteristic
7C22×Dic58C2211yescharacteristic
8C2×#90800—21no—
9C2×#90800C2212yes—
10C2×#90800C2212yes—
11#11745346—24no—
12D29⋊M16—21no—
13C29×#123C411yescharacteristic
14#11745297C411yescharacteristic
15#11745291C411yescharacteristic
16#11745258—21no—
17#11745250—21no—
18#11745248C411yescharacteristic
19#11745247—21no—
20#11745240—21no—
21#11745239C2211yescharacteristic
22#11745229—21no—
23#11745221—21no—
24#11745221—24no—
25C2×D4×C29C2×C411yescharacteristic
26C22×C4×C29C2×C411yescharacteristic
27C2×C22⋊D29C2×C411yescharacteristic
28C2×C22⋊D29D411yescharacteristic
29C22×Dic29C2×C411yescharacteristic
30C22×Dic29D411yescharacteristic
31C22×Dic29C2311yescharacteristic
32#90807—22no—
33#90807—22no—
34C2×C4×D29D411yescharacteristic
35C2×Dic58—22no—
36C2×Dic58—21no—
37C2×Dic58—21no—
38C2×Dic58—22no—
39C2×Dic58D411yescharacteristic
40#90800—22no—
41#90800—22no—
42#90800—22no—
43#90800—22no—
44#90800D414yes—
45C2×#6599—22no—
46C2×#6599—22no—
47C2×#6599—22no—
48#90796—22no—
49D29⋊C8—22no—
50C4⋊C4×C29—21no—
51C22⋊C4×C29—21no—
52C22⋊C4×C29C2×C411yescharacteristic
53C22⋊Dic29—21no—
54C22⋊Dic29C2×C411yescharacteristic
55#90781—21no—
56#90781—21no—
57C4⋊Dic29—21no—
58#90779—21no—
59#90779—21no—
60#90779—21no—
61C4×Dic29—21no—
62C23×C29C22⋊C411yescharacteristic
63C23×C29C22×C411yescharacteristic
64C22×D29C22⋊C411yescharacteristic
65D4×C29—22no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—22no—
69C2×C4×C29C22⋊C411yescharacteristic
70C22⋊D29—22no—
71C22⋊D29—22no—
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—22no—
77C2×Dic29C22⋊C411yescharacteristic
78C2×Dic29C2×D412yes—
79C2×Dic29C2×D411yescharacteristic
80C2×Dic29C2×D411yescharacteristic
81C2×Dic29#4112yes—
82C4×D29—21no—
83C4×D29—21no—
84Dic58—22no—
85Dic58—41no—
86Dic58—42no—
87Dic58—41no—
88#6599—24no—
89#6599—42no—
90#1915—291nomaximal, Sylow
91C22×C29—21no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29C2×C22⋊C411yescharacteristic
95C22×C29C4×D412yes—
96C2×D29—21no—
97C2×D29—41no—
98C4×C29—21no—
99C4×C29—41no—
100C4×C29—41no—
101Dic29—21no—
102Dic29—41no—
103Dic29—41no—
104Dic29#12011yescharacteristic
105Dic29#12112yes—
106Dic29#12311yescharacteristic
107#568—291no—
108#536—291no—
109#413—291no—
110C2×#101—292no—
111#344—292no—
112C2×C29—21no—
113C2×C29—22no—
114C2×C29—41no—
115C2×C29#38611yescharacteristic
116D29—41no—
117C2×#41—291no—
118C22×Q8—291no—
119#131—584no—
120C2×M16—292no—
121C2×M16—292no—
122C2×M16—581no—
123C2×M16—581no—
124C4⋊Q8—581no—
125#124—581no—
126#123—291no—
127#123—291no—
128#123—291no—
129#123#118111yescharacteristic
130C22⋊Q8—581no—
131C22⋊Q8—581no—
132#117—291no—
133#101—584no—
134#101—581no—
135#100—581no—
136C29#191511yescharacteristic, complemented, Sylow
137#41—582no—
138#41—582no—
139C2×Q8—291no—
140C2×Q8—582no—
141C2×Q8—581no—
142C2×Q8—581no—
143C2×Q8—582no—
144C2×D4—291no—
145C2×D4—291no—
146C2×D4C2×#118111yescharacteristic
147C22×C4—291no—
148C22×C4—291no—
149C22×C4—291no—
150C22×C4—291no—
151C22×C4C2×#118111yescharacteristic
152M16—294no—
153M16—582no—
154M16—582no—
155M16—582no—
156M16—582no—
157M16—582no—
158C2×C8—582no—
159C2×C8—582no—
160C2×C8—582no—
161C2×C8—582no—
162C4⋊C4—21no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—581no—
167C22⋊C4—21no—
168C22⋊C4—291no—
169C22⋊C4—581no—
170C22⋊C4—581no—
171C22⋊C4—581no—
172C22⋊C4C2×#118111yescharacteristic
173C42—581no—
174C23—291no—
175C23C22⋊#118111yescharacteristic
176C23C22×#118111yescharacteristic
177Q8—582no—
178Q8—1161no—
179Q8—1162no—
180Q8—1161no—
181D4—22no—
182D4—582no—
183D4—582no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—292no—
188C2×C4—292no—
189C2×C4—291no—
190C2×C4—291no—
191C2×C4—291no—
192C2×C4—581no—
193C2×C4—581no—
194C2×C4—581no—
195C2×C4—581no—
196C2×C4—582no—
197C2×C4—581no—
198C2×C4—581no—
199C2×C4C22⋊#118111yescharacteristic
200C8—584no—
201C8—1162no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—581no—
206C22—1161no—
207C22D4×#118112yes—
208C22C2×C22⋊#118111yescharacteristic
209C4—21no—
210C4—41no—
211C4—41no—
212C4—291no—
213C4—292no—
214C4—291no—
215C4—581no—
216C4—1161no—
217C4—1161no—
218C2—21no—
219C2—22no—
220C2—41no—
221C2—1161no—
222C2#1427211111yescharacteristic
subgroupG/H
centerC2#14272111
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#123C4
socleC2×C29#386
prime radicalC2×#90807C22
cosocleC22×Dic29C23
hypercenter#123#1181
hypocenterC29#1915
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
3. C2×#11745221C2semidirect
4. #14272044C2semidirect
136. C29#1915semidirect

Maximal subgroups

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

subgroupindex
#142722412
#142721502
C2×#117452212
#142720442
#142717352
#191529