Finite Group Databasebeta

← #16835752

Subgroups — #16835752

Order 3712.

266 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 52 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#14272150C211yesmaximal, characteristic, complemented
2#14272143C211yesmaximal, characteristic, complemented
3#14272064C212yesmaximal, complemented
4#14272063C212yesmaximal, complemented
5#14271728C211yesmaximal, characteristic
6C22×C22⋊D29C411yescharacteristic, complemented
7C2×#90807C2211yescharacteristic
8C2×#90800—21no—
9#11745345—21no—
10C29×#120C411yescharacteristic, complemented
11#11745315C2211yescharacteristic
12#11745302—21no—
13#11745301—21no—
14#11745299C411yescharacteristic, complemented
15#11745247—21no—
16#11745246—21no—
17#11745244C2211yescharacteristic
18#11745239C411yescharacteristic, complemented
19#11745229C2212yes—
20#11745227—21no—
21#11745227C2212yes—
22#11745221—21no—
23C24×C29C2×C411yescharacteristic
24C23×D29C2×C411yescharacteristic
25C2×D4×C29—21no—
26C2×D4×C29C2×C411yescharacteristic
27C2×C22⋊D29—21no—
28C2×C22⋊D29—21no—
29C2×C22⋊D29—21no—
30C2×C22⋊D29—21no—
31C2×C22⋊D29—41no—
32C2×C22⋊D29—41no—
33C2×C22⋊D29D411yescharacteristic
34C2×C22⋊D29C2311yescharacteristic
35C22×Dic29C2×C411yescharacteristic
36C22×Dic29D411yescharacteristic
37#90807—41no—
38#90807—41no—
39C2×D116—21no—
40C2×C4×D29D411yescharacteristic
41C2×Dic58D411yescharacteristic
42C22⋊#1181—22no—
43#90800—22no—
44#90800—41no—
45C2×#6599—41no—
46C4⋊#1181—41no—
47C4×#1181—41no—
48C22⋊C4×C29—21no—
49C22⋊C4×C29C2×C411yescharacteristic
50C22⋊Dic29—21no—
51C22⋊Dic29C2×C411yescharacteristic
52#90781—21no—
53#90781—21no—
54#90779—21no—
55C4×Dic29—21no—
56C23×C29—21no—
57C23×C29—41no—
58C23×C29—81no—
59C23×C29C22⋊C411yescharacteristic
60C23×C29C22×C411yescharacteristic
61C22×D29—21no—
62C22×D29—41no—
63C22×D29—81no—
64C22×D29C2×D411yescharacteristic
65C2×#1181—42no—
66D4×C29—41no—
67D4×C29—81no—
68C2×C4×C29—21no—
69C2×C4×C29C22⋊C411yescharacteristic
70C22⋊D29—41no—
71C22⋊D29—41no—
72C22⋊D29—42no—
73C22⋊D29—41no—
74C22⋊D29—41no—
75C22⋊D29—81no—
76C22⋊D29—81no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29C22⋊C411yescharacteristic
83C2×Dic29C22⋊C411yescharacteristic
84C2×Dic29C2×D411yescharacteristic
85D116—81no—
86C4×D29—21no—
87C4×D29—21no—
88Dic58—41no—
89#6599—42no—
90#2122—291nomaximal, Sylow
91C22×C29—21no—
92C22×C29—21no—
93C22×C29—41no—
94C22×C29—41no—
95C22×C29—41no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29—82no—
99C22×C29C2×C22⋊C411yescharacteristic
100C2×D29—21no—
101C2×D29—41no—
102C2×D29—41no—
103C2×D29—41no—
104C2×D29—41no—
105C2×D29—82no—
106#1181—82no—
107C4×C29—21no—
108C4×C29—41no—
109Dic29—21no—
110Dic29—21no—
111Dic29—41no—
112Dic29#9911yescharacteristic
113Dic29#9911yescharacteristic
114#535—291no—
115#413—291no—
116#410—291no—
117AΣL(1,𝔽16)—292no—
118AΣL(1,𝔽16)—292no—
119C2×C29—21no—
120C2×C29—41no—
121C2×C29—41no—
122C2×C29—81no—
123C2×C29C2×#9911yescharacteristic
124D29—41no—
125D29—81no—
126C2×#41—291no—
127C22×D4—291no—
128C2×M16—581no—
129#127—581no—
130#124—581no—
131#121—581no—
132#121—581no—
133#120—291no—
134#120—291no—
135#120—291no—
136#120#118111yescharacteristic, complemented
137#117—291no—
138#117—581no—
139#101—581no—
140#100—292no—
141#99—292no—
142#99—581no—
143C29#212211yescharacteristic, complemented, Sylow
144C24—291no—
145C24C2×#118111yescharacteristic
146#41—1161no—
147#41—1161no—
148C2×Q8—291no—
149C2×D4—21no—
150C2×D4—291no—
151C2×D4—291no—
152C2×D4—581no—
153C2×D4—581no—
154C2×D4—581no—
155C2×D4—581no—
156C2×D4—581no—
157C2×D4—1161no—
158C2×D4—1161no—
159C2×D4C2×#118111yescharacteristic
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163M16—582no—
164M16—1161no—
165C2×C8—1161no—
166C4⋊C4—581no—
167C4⋊C4—1161no—
168C22⋊C4—21no—
169C22⋊C4—291no—
170C22⋊C4—581no—
171C22⋊C4—581no—
172C22⋊C4—581no—
173C22⋊C4—582no—
174C22⋊C4C2×#118111yescharacteristic
175C42—581no—
176C42—1161no—
177C23—21no—
178C23—41no—
179C23—81no—
180C23—291no—
181C23—581no—
182C23—1161no—
183C23—2321no—
184C23C22⋊#118111yescharacteristic
185C23C22×#118111yescharacteristic
186Q8—1161no—
187D4—41no—
188D4—81no—
189D4—1161no—
190D4—1161no—
191D4—1161no—
192D4—1161no—
193D4—1162no—
194D4—2321no—
195D4—2321no—
196D4—2321no—
197C2×C4—21no—
198C2×C4—291no—
199C2×C4—291no—
200C2×C4—291no—
201C2×C4—581no—
202C2×C4—581no—
203C2×C4—581no—
204C2×C4—581no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—581no—
208C2×C4—1162no—
209C2×C4C22⋊#118111yescharacteristic
210C8—1162no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—82no—
219C22—581no—
220C22—1161no—
221C22—1161no—
222C22—1161no—
223C22—1161no—
224C22—2322no—
225C22C2×C22⋊#118111yescharacteristic
226C4—21no—
227C4—41no—
228C4—291no—
229C4—291no—
230C4—581no—
231C4—581no—
232C4—1161no—
233C4—2322no—
234C2—21no—
235C2—41no—
236C2—41no—
237C2—81no—
238C2—1161no—
239C2—2321no—
240C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#120C4
socleC2×C29C2×#99
prime radical#14271728C2
cosocleC2×C22⋊D29C23
hypercenter#120#1181
hypocenterC29#2122
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #14272150C2semidirect
2. #14272143C2semidirect
3. #14272064C2semidirect
4. #14272063C2semidirect
6. C22×C22⋊D29C4semidirect
10. C29×#120C4semidirect
14. #11745299C4semidirect
18. #11745239C4semidirect
136. #120#1181semidirect
143. C29#2122semidirect

Maximal subgroups

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

subgroupindex
#142721502
#142721432
#142720642
#142720632
#142717282
#212229