Finite Group Databasebeta

← #16832214

Subgroups — #16832214

Order 3712.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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#14271887C211yesmaximal, characteristic, complemented
2D4×Dic58C211yesmaximal, characteristic, complemented
3#14271524C212yesmaximal, complemented
4#14271513C211yesmaximal, characteristic, complemented
5#14271456C212yesmaximal, complemented
6#14271444C211yesmaximal, characteristic, complemented
7#14271380C212yesmaximal
8#14271290C211yesmaximal, characteristic, complemented
9#14271264C212yesmaximal, complemented
10C4×#90782C211yesmaximal, characteristic
11C29×#461C211yesmaximal, characteristic, complemented
12C22×Dic58—21no—
13C2×SD16×C29C2212yes—
14C29×C4⋊Q8C2211yescharacteristic
15C4×D4×C29C2211yescharacteristic
16#11745309C2212yes—
17Q8×Dic29C2212yes—
18D4×Dic29C2212yes—
19C2×#90782C2211yescharacteristic
20#11745286—21no—
21#11745260—22no—
22#11745259—21no—
23#11745254—21no—
24#11745250C2212yes—
25#11745240—22no—
26C4×D116C2211yescharacteristic
27#11745231C2211yescharacteristic
28C4×Dic58C2211yescharacteristic
29C29×C4⋊C8C2211yescharacteristic
30C29×#103C2212yes—
31#11745183C2212yes—
32#11745183C2212yes—
33#11745180C2211yescharacteristic
34#11745169C2212yes—
35#11745166C2212yes—
36#11745163C2212yes—
37#11745162C2212yes—
38#11745157C2211yescharacteristic
39#11745155C2211yescharacteristic
40C4×#6597C2211yescharacteristic
41C2×Q8×C29C2312yes—
42C2×D4×C29C2311yescharacteristic
43C22×C4×C29—21no—
44C22×Dic29—22no—
45C2×D116C2311yescharacteristic
46C2×C4×D29—21no—
47C2×Dic58—21no—
48C2×Dic58—22no—
49C2×Dic58—44no—
50C2×Dic58D411yescharacteristic
51SD16×C29—24no—
52C2×C8×C29C2312yes—
53C4⋊C4×C29—21no—
54C4⋊C4×C29—21no—
55C4⋊C4×C29C2311yescharacteristic
56C22⋊C4×C29—21no—
57C42×C29C2311yescharacteristic
58C22⋊Dic29—22no—
59#90782—22no—
60#90781—21no—
61#90781—22no—
62#90781—22no—
63C4⋊Dic29—21no—
64C4⋊Dic29—22no—
65C4⋊Dic29D411yescharacteristic
66C4⋊Dic29C2312yes—
67C4⋊Dic29C2311yescharacteristic
68#90779—22no—
69#90779D412yes—
70C4×Dic29—22no—
71C4×Dic29C2312yes—
72C2×#6597C2311yescharacteristic
73C2×#6597C2311yescharacteristic
74C23×C29—21no—
75C22×D29—21no—
76Q8×C29—22no—
77Q8×C29—22no—
78D4×C29—21no—
79D4×C29#4112yes—
80C2×C4×C29—22no—
81C2×C4×C29—21no—
82C2×C4×C29—42no—
83C2×C4×C29C2×D411yescharacteristic
84C2×C4×C29C2×D411yescharacteristic
85C2×C4×C29C2411yescharacteristic
86C2×Dic29—21no—
87C2×Dic29—22no—
88C2×Dic29—44no—
89C2×Dic29C2×D412yes—
90C2×Dic29C2×D412yes—
91D116—21no—
92D116—21no—
93C4×D29—42no—
94Dic58—22no—
95Dic58—44no—
96Dic58—42no—
97C8×C29—22no—
98#6597—21no—
99#6597—21no—
100#3367—291nomaximal, Sylow
101C22×C29—22no—
102C22×C29—41no—
103C22×C29—41no—
104C22×C29C22×D411yescharacteristic
105C2×D29—41no—
106C2×D29—41no—
107C2×D29—41no—
108C4×C29—21no—
109C4×C29—42no—
110C4×C29—41no—
111C4×C29AGL(1,ℤ/8)12yes—
112C4×C29C2×#4111yescharacteristic
113C4×C292−1+411yescharacteristic
114Dic29—22no—
115Dic29—22no—
116Dic29—42no—
117Dic29—41no—
118#556—291no—
119D4×Q8—291no—
120#489—292no—
121#487—291no—
122#477—292no—
123#474—291no—
124#463—292no—
125#461D2911yescharacteristic, complemented
126#446—291no—
127#440—292no—
128C4×D8—291no—
129C2×C29—42no—
130C2×C29#54811yescharacteristic
131C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C29#57811yescharacteristic
133D29—81no—
134C22×Q8—581no—
135C2×SD16C2×D2912yes—
136C2×D8—291no—
137C4⋊Q8—292no—
138C4⋊Q8—291no—
139C4⋊Q8C2×D2911yescharacteristic
140#126—582no—
141#124—292no—
142C22⋊Q8—582no—
143C22⋊Q8—581no—
144C22⋊Q8—581no—
145C4×Q8—291no—
146C4×Q8—292no—
147C4×D4—292no—
148C4×D4—291no—
149C4×D4C2×D2911yescharacteristic
150#117—581no—
151#107—292no—
152#107—291no—
153C4⋊C8—292no—
154C4⋊C8C2×D2911yescharacteristic
155#103—292no—
156#103—292no—
157#103C2×D2912yes—
158#102—291no—
159#102—292no—
160#102—291no—
161#97—292no—
162C4×C8—291no—
163C29#336711yescharacteristic, complemented, Sylow
164C2×Q8—291no—
165C2×Q8—582no—
166C2×Q8—581no—
167C2×Q8—1164no—
168C2×Q8C22×D2912yes—
169C2×D4—291no—
170C2×D4C22×D2911yescharacteristic
171C22×C4—21no—
172C22×C4—582no—
173C22×C4—581no—
174SD16—24no—
175D8—582no—
176C2×C8—291no—
177C2×C8—291no—
178C2×C8C22×D2912yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—291no—
182C4⋊C4—292no—
183C4⋊C4—292no—
184C4⋊C4—291no—
185C4⋊C4—582no—
186C4⋊C4—582no—
187C4⋊C4—581no—
188C4⋊C4C22×D2911yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—582no—
191C22⋊C4—582no—
192C22⋊C4—582no—
193C22⋊C4—581no—
194C42—292no—
195C42—582no—
196C42C22×D2911yescharacteristic
197C23—21no—
198C23—581no—
199Q8—22no—
200Q8—22no—
201Q8—582no—
202Q8—1164no—
203Q8—1162no—
204D4—21no—
205D4—581no—
206D4—581no—
207D4#9080712yes—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—292no—
212C2×C4—292no—
213C2×C4—581no—
214C2×C4—582no—
215C2×C4—1164no—
216C2×C4—1162no—
217C2×C4D4×D2911yescharacteristic
218C2×C4D4×D2911yescharacteristic
219C2×C4C23×D2911yescharacteristic
220C8—22no—
221C8—581no—
222C8—581no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—1161no—
227C22—1161no—
228C22—1161no—
229C22C2×D4×D2911yescharacteristic
230C4—21no—
231C4—42no—
232C4—41no—
233C4—582no—
234C4—582no—
235C4—1162no—
236C4—1161no—
237C4#1174527612yes—
238C4C2×#9080711yescharacteristic
239C4#1174536511yescharacteristic
240C2—42no—
241C2—2321no—
242C2#1427181911yescharacteristic
243C2C2×#1174527611yescharacteristic
244C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#461C2
socleC22×C29C22×D4
prime radicalC2×#90782C22
hypercenter#461D29
hypocenterC29#3367
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #14271887C2semidirect
2. D4×Dic58C2semidirect
3. #14271524C2semidirect
4. #14271513C2semidirect
5. #14271456C2semidirect
6. #14271444C2semidirect
8. #14271290C2semidirect
9. #14271264C2semidirect
11. C29×#461C2semidirect
125. #461D29semidirect
163. C29#3367semidirect

Maximal subgroups

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

subgroupindex
#142718872
D4×Dic582
#142715242
#142715132
#142714562
#142714442
#142713802
#142712902
#142712642
C4×#907822
C29×#4612
#336729