Finite Group Databasebeta

← #16835636

Subgroups — #16835636

Order 3712.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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#14272166C211yesmaximal, characteristic, complemented
2C2×#11745221C212yesmaximal, complemented
3C2×#11745229C212yesmaximal
4C4×#90800C211yesmaximal, characteristic, complemented
5C2×#11745247C211yesmaximal, characteristic
6C22×C22⋊D29C2211yescharacteristic
7C22×Dic58C2211yescharacteristic
8C2×#90800C2212yes—
9C2×#90800C2212yes—
10C2×C22⋊C4×C29C411yescharacteristic
11C2×C22⋊Dic29C411yescharacteristic
12C2×#90781C411yescharacteristic
13C2×#90781C411yescharacteristic
14C2×C4×Dic29C2211yescharacteristic
15#11745247—21no—
16#11745247—21no—
17#11745247—21no—
18#11745247—21no—
19#11745229—24no—
20#11745221—24no—
21#11745220—21no—
22#11745218—21no—
23C4⋊#6599—21no—
24C4×#6599—21no—
25C24×C29C2×C411yescharacteristic
26C23×D29C2×C411yescharacteristic
27C22×C4×C29C2×C411yescharacteristic
28C22×C4×C29C2×C411yescharacteristic
29C2×C22⋊D29—22no—
30C2×C22⋊D29—21no—
31C2×C22⋊D29—21no—
32C2×C22⋊D29—22no—
33C22×Dic29C2×C411yescharacteristic
34C22×Dic29C2×C411yescharacteristic
35C22×Dic29C2311yescharacteristic
36C2×Dic58—22no—
37C2×Dic58—21no—
38C2×Dic58—21no—
39C2×Dic58—22no—
40#90800—22no—
41#90800—22no—
42#90800—22no—
43#90800D414yes—
44C2×#6599—22no—
45C2×#6599—22no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊Dic29—21no—
49C22⋊Dic29—21no—
50#90781—21no—
51#90781—21no—
52#90781—21no—
53#90781—21no—
54C4×Dic29D411yescharacteristic
55C4×Dic29D411yescharacteristic
56C4×Dic29D411yescharacteristic
57C4×Dic29D411yescharacteristic
58C23×C29—21no—
59C23×C29—22no—
60C23×C29—41no—
61C23×C29—41no—
62C23×C29C22×C411yescharacteristic
63C22×D29—21no—
64C22×D29—22no—
65C22×D29—41no—
66C22×D29—41no—
67C2×C4×C29—21no—
68C2×C4×C29—22no—
69C2×C4×C29—41no—
70C2×C4×C29C22⋊C411yescharacteristic
71C2×C4×C29C22⋊C411yescharacteristic
72C22⋊D29—42no—
73C22⋊D29—41no—
74C22⋊D29—41no—
75C2×Dic29—21no—
76C2×Dic29—22no—
77C2×Dic29—41no—
78C2×Dic29C22⋊C411yescharacteristic
79C2×Dic29C22⋊C411yescharacteristic
80C2×Dic29C2×D411yescharacteristic
81C2×Dic29C2×D412yes—
82C2×Dic29C2×D411yescharacteristic
83C2×Dic29#4112yes—
84Dic58—42no—
85Dic58—41no—
86Dic58—41no—
87#6599—24no—
88#6599—42no—
89#1967—291nomaximal, Sylow
90C22×C29—21no—
91C22×C29—21no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29—41no—
95C22×C29—82no—
96C22×C29C2×C22⋊C411yescharacteristic
97C22×C29C4×D412yes—
98C2×D29—41no—
99C2×D29—41no—
100C2×D29—41no—
101C2×D29—82no—
102C4×C29—21no—
103C4×C29—21no—
104C4×C29—41no—
105Dic29—21no—
106Dic29—21no—
107Dic29—41no—
108Dic29#12112yes—
109Dic29#12411yescharacteristic
110Dic29#12711yescharacteristic
111C2×#124—291no—
112#423—291no—
113C2×#101—292no—
114C2×#100—292no—
115C4×M16—291no—
116C2×C29—22no—
117C2×C29—81no—
118C2×C29#39011yescharacteristic
119C2×C29#41311yescharacteristic
120C2×C29#41311yescharacteristic
121D29—81no—
122C22×Q8—291no—
123C22×D4—291no—
124C2×M16—292no—
125C2×M16—292no—
126#124—581no—
127#124—581no—
128#124—581no—
129#124—581no—
130C2×C22⋊C4—291no—
131C2×C22⋊C4—291no—
132C2×C22⋊C4—291no—
133C2×C22⋊C4#118111yescharacteristic
134C2×C42—291no—
135C4⋊C8—581no—
136C4⋊C8—581no—
137#101—584no—
138#100—584no—
139#97—581no—
140C4×C8—581no—
141C29#196711yescharacteristic, complemented, Sylow
142C24—291no—
143C24C2×#118111yescharacteristic
144C2×Q8—582no—
145C2×Q8—581no—
146C2×Q8—581no—
147C2×Q8—582no—
148C2×D4—582no—
149C2×D4—581no—
150C2×D4—581no—
151C2×D4—582no—
152C22×C4—291no—
153C22×C4—291no—
154C22×C4—291no—
155C22×C4C2×#118111yescharacteristic
156C22×C4C2×#118111yescharacteristic
157M16—294no—
158M16—582no—
159M16—582no—
160M16—582no—
161C2×C8—582no—
162C2×C8—582no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C22⋊C4—581no—
170C22⋊C4—581no—
171C42—291no—
172C42—291no—
173C42—291no—
174C42—291no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—581no—
180C23—582no—
181C23—1161no—
182C23—1161no—
183C23C22×#118111yescharacteristic
184Q8—1162no—
185Q8—1161no—
186Q8—1161no—
187D4—1162no—
188D4—1161no—
189D4—1161no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—292no—
194C2×C4—292no—
195C2×C4—291no—
196C2×C4—291no—
197C2×C4—291no—
198C2×C4—291no—
199C2×C4—582no—
200C2×C4—581no—
201C2×C4—1161no—
202C2×C4C22⋊#118111yescharacteristic
203C2×C4C22⋊#118111yescharacteristic
204C8—584no—
205C8—1162no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—1161no—
213C22—1161no—
214C22—1161no—
215C22—2322no—
216C22D4×#118112yes—
217C22C2×C22⋊#118111yescharacteristic
218C4—21no—
219C4—21no—
220C4—41no—
221C4—292no—
222C4—291no—
223C4—291no—
224C4—581no—
225C4—581no—
226C4—1161no—
227C2—22no—
228C2—81no—
229C2—2321no—
230C2#1427211511yescharacteristic
231C2#1427214911yescharacteristic
232C2#1427215011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×C22⋊D29C22
cosocleC22×Dic29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29#1967
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14272166C2semidirect
2. C2×#11745221C2semidirect
4. C4×#90800C2semidirect
141. C29#1967semidirect

Maximal subgroups

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

subgroupindex
#142721662
C2×#117452212
C2×#117452292
C4×#908002
C2×#117452472
#196729