Finite Group Databasebeta

← #16832209

Subgroups — #16832209

Order 3712.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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#14271883C211yesmaximal, characteristic, complemented
2#14271828C211yesmaximal, characteristic, complemented
3#14271521C212yesmaximal, complemented
4#14271515C211yesmaximal, characteristic, complemented
5#14271457C212yesmaximal, complemented
6#14271377C212yesmaximal
7#14271369C211yesmaximal, characteristic, complemented
8#14271290C211yesmaximal, characteristic, complemented
9#14271262C212yesmaximal, complemented
10C4×#90782C211yesmaximal, characteristic
11C29×#474C211yesmaximal, characteristic, complemented
12C2×Q8×D29—21no—
13C29×C4⋊Q8C2211yescharacteristic
14C4×D4×C29C2211yescharacteristic
15#11745308—21no—
16#11745298C2212yes—
17C2×#90782C2211yescharacteristic
18#11745288—21no—
19#11745286—21no—
20C2×#90773C2212yes—
21#11745258—22no—
22#11745255C2212yes—
23#11745250C2212yes—
24#11745249C2212yes—
25#11745241—22no—
26C4×D116C2211yescharacteristic
27#11745231C2211yescharacteristic
28C4×Dic58C2211yescharacteristic
29C29×#107C2212yes—
30C29×C4⋊C8C2211yescharacteristic
31C29×#102C2212yes—
32#11745180C2211yescharacteristic
33#11745164C2212yes—
34#11745163C2212yes—
35#11745162C2212yes—
36#11745158C2212yes—
37#11745158C2212yes—
38#11745157C2211yescharacteristic
39#11745155C2211yescharacteristic
40C4×#6597C2211yescharacteristic
41C2×Q8×C29—21no—
42C2×D4×C29C2311yescharacteristic
43C22×C4×C29—21no—
44Q8×D29—44no—
45C2×D116C2311yescharacteristic
46C2×C4×D29—21no—
47C2×C4×D29—22no—
48C2×Dic58—22no—
49C2×Dic58D411yescharacteristic
50C2×Dic58C2312yes—
51C2×C8×C29C2312yes—
52C4⋊C4×C29—21no—
53C4⋊C4×C29C2311yescharacteristic
54C4⋊C4×C29C2312yes—
55C22⋊C4×C29—21no—
56C42×C29C2311yescharacteristic
57C22⋊Dic29—22no—
58C22⋊Dic29—22no—
59#90782—22no—
60#90781—21no—
61#90781—22no—
62C4⋊Dic29—21no—
63C4⋊Dic29—21no—
64C4⋊Dic29D411yescharacteristic
65C4⋊Dic29C2311yescharacteristic
66#90779—22no—
67#90779—22no—
68#90779D412yes—
69C4×Dic29—22no—
70C4×Dic29C2312yes—
71C2×#6597C2311yescharacteristic
72C2×#6597C2311yescharacteristic
73#90773—24no—
74C23×C29—21no—
75C22×D29—21no—
76Q8×C29—42no—
77D4×C29—21no—
78D4×C29—21no—
79C2×C4×C29—21no—
80C2×C4×C29—22no—
81C2×C4×C29—42no—
82C2×C4×C29C2×D411yescharacteristic
83C2×C4×C29C2×D411yescharacteristic
84C2×C4×C29C2411yescharacteristic
85C2×Dic29—22no—
86C2×Dic29—21no—
87C2×Dic29C2×D412yes—
88C2×Dic29C2×D412yes—
89D116—21no—
90D116#4112yes—
91C4×D29—44no—
92C4×D29—42no—
93Dic58—22no—
94Dic58—22no—
95Dic58—22no—
96Dic58—44no—
97C8×C29—22no—
98#6597—21no—
99#6597—21no—
100#3367—291nomaximal, Sylow
101C22×C29—41no—
102C22×C29—41no—
103C22×C29—41no—
104C22×C29C22×D411yescharacteristic
105C2×D29—22no—
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#474D2911yescharacteristic, complemented
124#463—292no—
125#461—291no—
126#446—291no—
127#440—292no—
128C4×D8—291no—
129C2×C29—81no—
130C2×C29#54811yescharacteristic
131C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C29#57811yescharacteristic
133D29—42no—
134C22×Q8—581no—
135C2×SD16—292no—
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—291no—
152#107C2×D2912yes—
153C4⋊C8—292no—
154C4⋊C8C2×D2911yescharacteristic
155#103—292no—
156#103—292no—
157#103—292no—
158#102—291no—
159#102—291no—
160#102C2×D2912yes—
161#97—292no—
162C4×C8—291no—
163C29#336711yescharacteristic, complemented, Sylow
164C2×Q8—21no—
165C2×Q8—291no—
166C2×Q8—292no—
167C2×Q8—582no—
168C2×Q8—1164no—
169C2×D4—291no—
170C2×D4C22×D2911yescharacteristic
171C22×C4—21no—
172C22×C4—582no—
173C22×C4—581no—
174SD16—584no—
175D8—582no—
176C2×C8—291no—
177C2×C8—291no—
178C2×C8C22×D2912yes—
179C4⋊C4—21no—
180C4⋊C4—291no—
181C4⋊C4—292no—
182C4⋊C4—291no—
183C4⋊C4—582no—
184C4⋊C4—582no—
185C4⋊C4—581no—
186C4⋊C4—581no—
187C4⋊C4C22×D2911yescharacteristic
188C4⋊C4C22×D2912yes—
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—42no—
200Q8—582no—
201Q8—582no—
202Q8—582no—
203Q8—1164no—
204D4—21no—
205D4—21no—
206D4—292no—
207D4—581no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—292no—
212C2×C4—292no—
213C2×C4—582no—
214C2×C4—581no—
215C2×C4—1164no—
216C2×C4—1162no—
217C2×C4D4×D2911yescharacteristic
218C2×C4D4×D2911yescharacteristic
219C2×C4C23×D2911yescharacteristic
220C8—22no—
221C8—581no—
222C8—581no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—582no—
227C22—1161no—
228C22—1161no—
229C22C2×D4×D2911yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—582no—
234C4—582no—
235C4—1162no—
236C4—1161no—
237C4#1174527312yes—
238C4#1174536211yescharacteristic
239C4#41×D2911yescharacteristic
240C2—81no—
241C2—1162no—
242C2#1427182311yescharacteristic
243C2C2×#1174527311yescharacteristic
244C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#474C2
socleC22×C29C22×D4
prime radicalC2×#90782C22
hypercenter#474D29
hypocenterC29#3367
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14271883C2semidirect
2. #14271828C2semidirect
3. #14271521C2semidirect
4. #14271515C2semidirect
5. #14271457C2semidirect
7. #14271369C2semidirect
8. #14271290C2semidirect
9. #14271262C2semidirect
11. C29×#474C2semidirect
123. #474D29semidirect
163. C29#3367semidirect

Maximal subgroups

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

subgroupindex
#142718832
#142718282
#142715212
#142715152
#142714572
#142713772
#142713692
#142712902
#142712622
C4×#907822
C29×#4742
#336729