Finite Group Databasebeta

← #16821130

Subgroups — #16821130

Order 3712.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271669C211yesmaximal, characteristic
2#14271144C211yesmaximal, characteristic, complemented
3#14271135C211yesmaximal, characteristic, complemented
4#14270954C211yesmaximal, characteristic, complemented
5#14270952C211yesmaximal, characteristic, complemented
6#14270950C211yesmaximal, characteristic, complemented
7C29×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C23×Dic29C411yescharacteristic, complemented
9C2×#90807C2211yescharacteristic
10C29×#120C2211yescharacteristic
11#11745315C411yescharacteristic, complemented
12#11745301—21no—
13#11745297C2211yescharacteristic
14D4×Dic29—21no—
15M16×D29—21no—
16#11745248C411yescharacteristic, complemented
17#11745243—21no—
18#11745240—21no—
19#11745239—21no—
20#11745239C411yescharacteristic, complemented
21C29×#100C2211yescharacteristic
22C29×#99C2211yescharacteristic
23#11745182C2211yescharacteristic
24#11745181C2211yescharacteristic
25#11745172—21no—
26#11745154—21no—
27C24×C29C2×C411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29C2311yescharacteristic
30C2×C22⋊D29—21no—
31C2×C22⋊D29C2×C411yescharacteristic
32C2×C22⋊D29D411yescharacteristic
33C22×Dic29—21no—
34C22×Dic29—21no—
35C22×Dic29—41no—
36C22×Dic29—41no—
37C22×Dic29C2×C411yescharacteristic
38C22×Dic29C2×C411yescharacteristic
39C22×Dic29D411yescharacteristic
40#90807—41no—
41#90807—41no—
42C2×C4×D29D411yescharacteristic
43C2×Dic58D411yescharacteristic
44M16×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29C2×C411yescharacteristic
48C22⋊Dic29—21no—
49C22⋊Dic29—21no—
50C22⋊Dic29—21no—
51C22⋊Dic29C2×C411yescharacteristic
52#90781—21no—
53C4⋊Dic29—21no—
54#90779—21no—
55#90779—21no—
56#90779—41no—
57C4×Dic29—21no—
58C4×Dic29—41no—
59#90777—21no—
60#90772—41no—
61C8×D29—41no—
62C23×C29—21no—
63C23×C29—41no—
64C23×C29—42no—
65C23×C29C22×C411yescharacteristic
66C23×C29C2×D411yescharacteristic
67C22×D29C22⋊C411yescharacteristic
68D4×C29—41no—
69D4×C29—42no—
70C2×C4×C29—21no—
71C2×C4×C29—41no—
72C2×C4×C29C2×D411yescharacteristic
73C22⋊D29—41no—
74C22⋊D29—41no—
75C22⋊D29—42no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29—42no—
83C2×Dic29—41no—
84C2×Dic29—41no—
85C2×Dic29—41no—
86C2×Dic29—41no—
87C2×Dic29C22⋊C411yescharacteristic
88C2×Dic29C22⋊C411yescharacteristic
89C2×Dic29C22⋊C411yescharacteristic
90C4×D29—21no—
91C4×D29—21no—
92Dic58—41no—
93C8×C29—41no—
94#6597—41no—
95#2120—291nomaximal, Sylow
96C22×C29—22no—
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29—42no—
103C22×C29—42no—
104C22×C29—41no—
105C22×C29C2×C22⋊C411yescharacteristic
106C2×D29—21no—
107C2×D29—41no—
108C4×C29—21no—
109C4×C29—41no—
110C4×C29—81no—
111Dic29—21no—
112Dic29—21no—
113Dic29—41no—
114Dic29—41no—
115Dic29—81no—
116Dic29#9911yescharacteristic
117Dic29#9911yescharacteristic
118#525—291no—
119#413—291no—
120#410—291no—
121#352—291no—
122#352—291no—
123AΣL(1,𝔽16)—291no—
124AΣL(1,𝔽16)D2911yescharacteristic, complemented
125C2×C29—21no—
126C2×C29—41no—
127C2×C29—42no—
128C2×C29—41no—
129C2×C29C2×#9911yescharacteristic
130D29—41no—
131C2×#41—291no—
132C23×C4—291no—
133C2×M16—581no—
134#123—291no—
135#123—291no—
136C22⋊Q8—581no—
137#121—581no—
138#120—291no—
139#120C2×D2911yescharacteristic
140C4×D4—581no—
141C4×D4—581no—
142#117—291no—
143#117—581no—
144#101—581no—
145#100—291no—
146#100C2×D2911yescharacteristic
147#99—291no—
148#99—581no—
149#99C2×D2911yescharacteristic
150C29#212011yescharacteristic, complemented, Sylow
151C24C4×D2911yescharacteristic
152#41—1161no—
153#41—1161no—
154C2×Q8—291no—
155C2×D4—21no—
156C2×D4—291no—
157C2×D4—291no—
158C2×D4—581no—
159C2×D4C22×D2911yescharacteristic
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163C22×C4—291no—
164C22×C4—581no—
165C22×C4—581no—
166C22×C4—1161no—
167C22×C4—1161no—
168M16—21no—
169M16—581no—
170M16—1161no—
171C2×C8—1161no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C4⋊C4—581no—
175C4⋊C4—1161no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—291no—
179C22⋊C4—581no—
180C22⋊C4—581no—
181C22⋊C4—581no—
182C22⋊C4—581no—
183C22⋊C4C4×D2911yescharacteristic
184C42—581no—
185C42—1161no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23—291no—
190C23C2×C4×D2911yescharacteristic
191C23D4×D2911yescharacteristic
192Q8—1161no—
193D4—41no—
194D4—42no—
195D4—1161no—
196D4—1161no—
197D4—1162no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—291no—
201C2×C4—291no—
202C2×C4—291no—
203C2×C4—581no—
204C2×C4—581no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—581no—
208C2×C4—581no—
209C2×C4—581no—
210C2×C4—581no—
211C2×C4—1161no—
212C2×C4—1161no—
213C2×C4—1162no—
214C2×C4—1161no—
215C2×C4—1161no—
216C2×C4D4×D2911yescharacteristic
217C8—41no—
218C8—1161no—
219C22—22no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—581no—
229C22—1161no—
230C22C22⋊C4×D2911yescharacteristic
231C4—21no—
232C4—41no—
233C4—81no—
234C4—291no—
235C4—291no—
236C4—581no—
237C4—581no—
238C4—1161no—
239C4—1161no—
240C4—2321no—
241C2—21no—
242C2—41no—
243C2—42no—
244C2—41no—
245C2—1161no—
246C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC23×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×AΣL(1,𝔽16)C2
socleC2×C29C2×#99
prime radical#14271669C2
cosocleC2×D4×C29C23
hypercenterAΣL(1,𝔽16)D29
hypocenterC29#2120
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #14271144C2semidirect
3. #14271135C2semidirect
4. #14270954C2semidirect
5. #14270952C2semidirect
6. #14270950C2semidirect
7. C29×AΣL(1,𝔽16)C2semidirect
8. C23×Dic29C4semidirect
11. #11745315C4semidirect
16. #11745248C4semidirect
20. #11745239C4semidirect
124. AΣL(1,𝔽16)D29semidirect
150. C29#2120semidirect

Maximal subgroups

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

subgroupindex
#142716692
#142711442
#142711352
#142709542
#142709522
#142709502
C29×AΣL(1,𝔽16)2
#212029