Finite Group Databasebeta

← #16821499

Subgroups — #16821499

Order 3712.

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

normal subgroups only

This group has 260 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, complemented
3#14271330C211yesmaximal, characteristic, complemented
4#14270956C211yesmaximal, characteristic, complemented
5#14270953C211yesmaximal, characteristic, complemented
6#14270950C211yesmaximal, characteristic, complemented
7C29×#560C211yesmaximal, characteristic, complemented
8#11745359C2211yescharacteristic
9C29×#127C2211yescharacteristic
10C29×#126—21no—
11C29×#123—21no—
12C29×#123C2211yescharacteristic
13C29×#121—21no—
14C29×#121—21no—
15C29×#121—21no—
16C29×#120—21no—
17C29×#120C2211yescharacteristic
18#11745315—21no—
19#11745294—21no—
20#11745291—21no—
21#11745182C2211yescharacteristic
22#11745182C2211yescharacteristic
23#11745181C2211yescharacteristic
24#11745154—21no—
25#11745154—21no—
26#11745153—21no—
27C24×C29D411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29—21no—
32C2×D4×C29—21no—
33C2×D4×C29D411yescharacteristic, complemented
34C2×D4×C29C2311yescharacteristic
35C22×C4×C29—21no—
36C22×C4×C29D411yescharacteristic, complemented
37C2×C22⋊D29—21no—
38C2×C22⋊D29—21no—
39C2×C22⋊D29—41no—
40#90807—41no—
41D4×D29—41no—
42#90805—21no—
43C4⋊C4×C29—21no—
44C4⋊C4×C29—21no—
45C4⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C22⋊C4×C29—21no—
50C22⋊C4×C29—21no—
51C22⋊C4×C29D411yescharacteristic
52C22⋊C4×C29D411yescharacteristic, complemented
53C42×C29D411yescharacteristic, complemented
54C22⋊Dic29—21no—
55C22⋊Dic29—21no—
56C22⋊Dic29—41no—
57#90783—41no—
58#90782—41no—
59#90781—41no—
60#90779—41no—
61#90777—21no—
62C23×C29—21no—
63C23×C29—21no—
64C23×C29—41no—
65C23×C29—81no—
66C23×C29C2×D411yescharacteristic
67C23×C29C2×D411yescharacteristic
68C22×D29—21no—
69C22×D29—21no—
70D4×C29—41no—
71D4×C29—41no—
72D4×C29—81no—
73D4×C29—81no—
74D4×C29—81no—
75D4×C29—81no—
76D4×C29—81no—
77C2×C4×C29—21no—
78C2×C4×C29—21no—
79C2×C4×C29—21no—
80C2×C4×C29—21no—
81C2×C4×C29—41no—
82C2×C4×C29—81no—
83C2×C4×C29C2×D411yescharacteristic
84C22⋊D29—41no—
85C22⋊D29—41no—
86C22⋊D29—41no—
87C22⋊D29—82no—
88C2×Dic29—21no—
89C2×Dic29—21no—
90C2×Dic29—41no—
91C2×Dic29—41no—
92D116—21no—
93C4×D29—41no—
94Dic58—21no—
95#6597—41no—
96#2200—291nomaximal, Sylow
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29—41no—
103C22×C29—41no—
104C22×C29—41no—
105C22×C29—42no—
106C22×C29—41no—
107C22×C29—41no—
108C22×C29—81no—
109C22×C29#12011yescharacteristic
110C2×D29—41no—
111C2×D29—81no—
112C2×D29—81no—
113C4×C29—21no—
114C4×C29—41no—
115C4×C29—41no—
116C4×C29—41no—
117C4×C29—41no—
118Dic29—41no—
119Dic29—81no—
120Dic29—81no—
121#560D2911yescharacteristic, complemented
122#458—291no—
123B(4,𝔽2)—291no—
124#453—291no—
125#353—291no—
126#352—291no—
127AΣL(1,𝔽16)—291no—
128C2×C29—21no—
129C2×C29—41no—
130C2×C29—41no—
131C2×C29—81no—
132C2×C29—81no—
133C2×C29B(4,𝔽2)11yescharacteristic
134D29—81no—
135H(5,𝔽2)—291no—
136AGL(1,ℤ/8)—581no—
137#127C2×D2911yescharacteristic
138#126—21no—
139#123—21no—
140#123—581no—
141#123C2×D2911yescharacteristic
142#121—21no—
143#121—21no—
144#121—21no—
145#120—21no—
146#120—581no—
147#120C2×D2911yescharacteristic
148#104—581no—
149#100—291no—
150#99—291no—
151#99—291no—
152#99—581no—
153#99—581no—
154C29#220011yescharacteristic, complemented, Sylow
155C24C22⋊D2911yescharacteristic
156#41—581no—
157#41—1161no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—581no—
164C2×D4—581no—
165C2×D4—1161no—
166C2×D4—1161no—
167C2×D4C22⋊D2911yescharacteristic, complemented
168C2×D4C22×D2911yescharacteristic
169C22×C4—21no—
170C22×C4C22⋊D2911yescharacteristic, complemented
171SD16—1161no—
172D8—1161no—
173M16—581no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—1161no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—581no—
184C22⋊C4—581no—
185C22⋊C4—1161no—
186C22⋊C4—1161no—
187C22⋊C4C22⋊D2911yescharacteristic
188C22⋊C4C22⋊D2911yescharacteristic, complemented
189C42C22⋊D2911yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—41no—
193C23—81no—
194C23—581no—
195C23—581no—
196C23C2×C22⋊D2911yescharacteristic
197C23C2×C22⋊D2911yescharacteristic
198Q8—581no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—81no—
204D4—81no—
205D4—81no—
206D4—581no—
207D4—1161no—
208D4—1161no—
209D4—1161no—
210D4—2322no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—581no—
218C2×C4—581no—
219C2×C4—1161no—
220C2×C4—1161no—
221C2×C4—1161no—
222C2×C4C2×C22⋊D2911yescharacteristic
223C8—1161no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22—81no—
236C22—1161no—
237C22—2321no—
238C22—2321no—
239C22#1174531511yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—1161no—
246C4—2321no—
247C4—2321no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—2321no—
254C2#1427135011yescharacteristic
subgroupG/H
centerC2#14271350
commutator, cosocleC2×D4×C29C23
FrattiniC2×D4C22×D29
FittingC29×#560C2
socleC2×C29B(4,𝔽2)
hypercenter#560D29
hypocenterC29#2200
LCSG ▷ C2×D4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #560

Complements

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

NH ≅ G/Ntype
1. #14271352C2semidirect
2. #14271349C2semidirect
3. #14271330C2semidirect
4. #14270956C2semidirect
5. #14270953C2semidirect
6. #14270950C2semidirect
7. C29×#560C2semidirect
33. C2×D4×C29D4semidirect
36. C22×C4×C29D4semidirect
52. C22⋊C4×C29D4semidirect
53. C42×C29D4semidirect
121. #560D29semidirect
154. C29#2200semidirect
167. C2×D4C22⋊D29semidirect
170. C22×C4C22⋊D29semidirect
188. C22⋊C4C22⋊D29semidirect
189. C42C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142713522
#142713492
#142713302
#142709562
#142709532
#142709502
C29×#5602
#220029