Finite Group Databasebeta

← #16821482

Subgroups — #16821482

Order 3712.

258 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 45 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#14271352C211yesmaximal, characteristic, complemented
2#14271349C211yesmaximal, characteristic
3#14271340C211yesmaximal, characteristic, complemented
4#14270958C211yesmaximal, characteristic, complemented
5#14270953C211yesmaximal, characteristic, complemented
6#14270950C211yesmaximal, characteristic, complemented
7C29×#551C211yesmaximal, characteristic, complemented
8#11745359C2211yescharacteristic
9C29×#126—21no—
10C29×#124C2211yescharacteristic
11C29×#123—21no—
12C29×#123C2211yescharacteristic
13C29×C22⋊Q8—21no—
14C29×#120C2211yescharacteristic
15C4×D4×C29—21no—
16C29×#117—21no—
17C2×C22⋊C4×C29—21no—
18#11745315—21no—
19#11745304—21no—
20#11745291—21no—
21#11745182C2211yescharacteristic
22#11745182C2211yescharacteristic
23#11745181C2211yescharacteristic
24#11745154—21no—
25#11745154—21no—
26#11745153—21no—
27C24×C29D411yescharacteristic
28C2×Q8×C29D411yescharacteristic, complemented
29C2×D4×C29—21no—
30C2×D4×C29C2311yescharacteristic
31C22×C4×C29—21no—
32C22×C4×C29—21no—
33C22×C4×C29D411yescharacteristic, complemented
34C2×C22⋊D29—21no—
35C2×C22⋊D29—21no—
36C2×C22⋊D29—41no—
37#90807—41no—
38D4×D29—41no—
39#90805—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29—21no—
44C22⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C22⋊C4×C29—21no—
50C22⋊C4×C29D411yescharacteristic
51C22⋊C4×C29D411yescharacteristic, complemented
52C42×C29—21no—
53C42×C29D411yescharacteristic, complemented
54C22⋊Dic29—21no—
55C22⋊Dic29—21no—
56C22⋊Dic29—41no—
57#90785—41no—
58#90784—41no—
59#90781—41no—
60#90779—41no—
61#90777—21no—
62C23×C29—21no—
63C23×C29—41no—
64C23×C29—42no—
65C23×C29C2×D411yescharacteristic
66C23×C29C2×D411yescharacteristic
67C22×D29—21no—
68C22×D29—21no—
69Q8×C29—41no—
70D4×C29—41no—
71D4×C29—42no—
72C2×C4×C29—21no—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29—21no—
76C2×C4×C29—21no—
77C2×C4×C29—42no—
78C2×C4×C29—41no—
79C2×C4×C29—81no—
80C2×C4×C29C2×D411yescharacteristic
81C22⋊D29—41no—
82C22⋊D29—41no—
83C22⋊D29—41no—
84C22⋊D29—82no—
85C2×Dic29—21no—
86C2×Dic29—21no—
87C2×Dic29—41no—
88C2×Dic29—41no—
89D116—21no—
90C4×D29—41no—
91Dic58—21no—
92#6597—41no—
93#2197—291nomaximal, Sylow
94C22×C29—22no—
95C22×C29—21no—
96C22×C29—21no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29—41no—
100C22×C29—42no—
101C22×C29—41no—
102C22×C29—81no—
103C22×C29#12011yescharacteristic
104C2×D29—41no—
105C2×D29—81no—
106C2×D29—81no—
107C4×C29—21no—
108C4×C29—41no—
109C4×C29—41no—
110C4×C29—41no—
111C4×C29—41no—
112C4×C29—41no—
113Dic29—41no—
114Dic29—81no—
115Dic29—81no—
116#551D2911yescharacteristic, complemented
117#458—291no—
118B(4,𝔽2)—291no—
119#455—291no—
120#354—291no—
121#352—291no—
122AΣL(1,𝔽16)—291no—
123C2×C29—21no—
124C2×C29—41no—
125C2×C29—41no—
126C2×C29—42no—
127C2×C29B(4,𝔽2)11yescharacteristic
128D29—81no—
129H(5,𝔽2)—291no—
130#137—581no—
131#126—21no—
132#124C2×D2911yescharacteristic
133#123—21no—
134#123—581no—
135#123C2×D2911yescharacteristic
136C22⋊Q8—21no—
137#120—581no—
138#120C2×D2911yescharacteristic
139C4×D4—21no—
140#117—21no—
141C2×C22⋊C4—21no—
142#104—581no—
143#100—291no—
144#99—291no—
145#99—291no—
146#99—581no—
147#99—581no—
148C29#219711yescharacteristic, complemented, Sylow
149C24C22⋊D2911yescharacteristic
150#41—581no—
151#41—1161no—
152C2×Q8C22⋊D2911yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—581no—
155C2×D4—581no—
156C2×D4—1161no—
157C2×D4—1161no—
158C2×D4C22×D2911yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4C22⋊D2911yescharacteristic, complemented
162Q16—1161no—
163SD16—1161no—
164M16—581no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—1161no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—581no—
177C22⋊C4—581no—
178C22⋊C4—1161no—
179C22⋊C4—1161no—
180C22⋊C4C22⋊D2911yescharacteristic
181C22⋊C4C22⋊D2911yescharacteristic, complemented
182C42—21no—
183C42C22⋊D2911yescharacteristic, complemented
184C23—21no—
185C23—41no—
186C23—42no—
187C23—581no—
188C23—581no—
189C23C2×C22⋊D2911yescharacteristic
190C23C2×C22⋊D2911yescharacteristic
191Q8—41no—
192Q8—581no—
193D4—41no—
194D4—42no—
195D4—581no—
196D4—1161no—
197D4—1161no—
198D4—1161no—
199D4—2322no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—581no—
209C2×C4—581no—
210C2×C4—1161no—
211C2×C4—1161no—
212C2×C4—1161no—
213C2×C4C2×C22⋊D2911yescharacteristic
214C8—1161no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22—1161no—
225C22—2321no—
226C22—2321no—
227C22#1174531511yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—1161no—
235C4—2321no—
236C4—2321no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—2321no—
242C2#1427135011yescharacteristic
subgroupG/H
centerC2#14271350
commutator, cosocleC2×D4×C29C23
FrattiniC2×D4C22×D29
FittingC29×#551C2
socleC2×C29B(4,𝔽2)
prime radical#14271349C2
hypercenter#551D29
hypocenterC29#2197
LCSG ▷ C2×D4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #551

Complements

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

NH ≅ G/Ntype
1. #14271352C2semidirect
3. #14271340C2semidirect
4. #14270958C2semidirect
5. #14270953C2semidirect
6. #14270950C2semidirect
7. C29×#551C2semidirect
28. C2×Q8×C29D4semidirect
33. C22×C4×C29D4semidirect
51. C22⋊C4×C29D4semidirect
53. C42×C29D4semidirect
116. #551D29semidirect
148. C29#2197semidirect
152. C2×Q8C22⋊D29semidirect
161. C22×C4C22⋊D29semidirect
181. C22⋊C4C22⋊D29semidirect
183. C42C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142713522
#142713492
#142713402
#142709582
#142709532
#142709502
C29×#5512
#219729