Finite Group Databasebeta

← #16832140

Subgroups — #16832140

Order 3712.

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

normal subgroups only

This group has 350 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#14271874C211yesmaximal, characteristic, complemented
3#14271516C212yesmaximal, complemented
4#14271515C211yesmaximal, characteristic, complemented
5#14271473C212yesmaximal, complemented
6#14271377C212yesmaximal
7#14271369C211yesmaximal, characteristic, complemented
8#14271287C211yesmaximal, characteristic, complemented
9#14271250C212yesmaximal, complemented
10C4×#90782C211yesmaximal, characteristic
11C29×#476C211yesmaximal, characteristic, complemented
12C29×C4⋊Q8C2211yescharacteristic
13C4×D4×C29C2211yescharacteristic
14#11745308—22no—
15#11745298C2212yes—
16C2×#90782C2211yescharacteristic
17#11745288—21no—
18#11745286—21no—
19C2×#90773C2212yes—
20#11745259—21no—
21#11745255C2212yes—
22C4⋊C4×D29—21no—
23#11745252C2212yes—
24#11745249C2212yes—
25#11745241—22no—
26C4×D116C2211yescharacteristic
27#11745231C2211yescharacteristic
28C4×Dic58C2211yescharacteristic
29C29×#106C2212yes—
30C29×C4⋊C8C2211yescharacteristic
31C29×#102C2212yes—
32#11745180C2211yescharacteristic
33#11745164C2212yes—
34#11745162C2212yes—
35C8×Dic29C2212yes—
36#11745158C2212yes—
37#11745158C2212yes—
38#11745157C2211yescharacteristic
39#11745155C2211yescharacteristic
40C4×#6597C2211yescharacteristic
41C2×Q8×C29—21no—
42C2×D4×C29C2311yescharacteristic
43C22×C4×C29—21no—
44C2×D116C2311yescharacteristic
45C2×C4×D29—21no—
46C2×C4×D29—22no—
47C2×Dic58D411yescharacteristic
48C2×Dic58C2312yes—
49C2×C8×C29C2312yes—
50C4⋊C4×C29—21no—
51C4⋊C4×C29C2311yescharacteristic
52C4⋊C4×C29C2312yes—
53C22⋊C4×C29—21no—
54C42×C29C2311yescharacteristic
55C22⋊Dic29—22no—
56C22⋊Dic29—22no—
57#90782—22no—
58#90781—21no—
59#90781—22no—
60C4⋊Dic29—21no—
61C4⋊Dic29—21no—
62C4⋊Dic29—22no—
63C4⋊Dic29D411yescharacteristic
64C4⋊Dic29C2311yescharacteristic
65#90779—22no—
66#90779—22no—
67#90779D412yes—
68C4×Dic29—22no—
69C4×Dic29C2312yes—
70C2×#6597C2311yescharacteristic
71C2×#6597C2311yescharacteristic
72#90773—24no—
73C23×C29—21no—
74C22×D29—21no—
75Q8×C29—81no—
76D4×C29—21no—
77D4×C29—21no—
78C2×C4×C29—21no—
79C2×C4×C29—22no—
80C2×C4×C29—42no—
81C2×C4×C29C2×D411yescharacteristic
82C2×C4×C29C2×D411yescharacteristic
83C2×C4×C29C2411yescharacteristic
84C2×Dic29—22no—
85C2×Dic29—21no—
86C2×Dic29C2×D412yes—
87C2×Dic29C2×D412yes—
88D116—21no—
89D116#4112yes—
90C4×D29—42no—
91C4×D29—82no—
92Dic58—22no—
93Dic58—22no—
94Dic58—22no—
95C8×C29—22no—
96#6597—21no—
97#6597—21no—
98#3360—291nomaximal, Sylow
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29C22×D411yescharacteristic
103C2×D29—22no—
104C2×D29—41no—
105C2×D29—41no—
106C4×C29—21no—
107C4×C29—41no—
108C4×C29—42no—
109C4×C29#13512yes—
110C4×C29C2×#4111yescharacteristic
111C4×C292−1+411yescharacteristic
112Dic29—22no—
113Dic29—22no—
114Dic29—42no—
115Dic29—41no—
116#556—291no—
117#554—291no—
118#488—292no—
119#487—291no—
120#479—292no—
121#476D2911yescharacteristic, complemented
122#463—292no—
123#461—291no—
124C8×Q8—291no—
125C4×SD16—292no—
126C4×D8—291no—
127C2×C29—81no—
128C2×C29#54811yescharacteristic
129C2×C29C2×#13511yescharacteristic
130C2×C29#57711yescharacteristic
131D29—42no—
132C2×SD16—292no—
133C2×D8—291no—
134C4⋊Q8—291no—
135C4⋊Q8C2×D2911yescharacteristic
136#126—582no—
137#125—292no—
138#124—292no—
139C22⋊Q8—581no—
140C22⋊Q8—582no—
141C22⋊Q8—581no—
142C4×Q8—291no—
143C4×Q8—292no—
144C4×D4—292no—
145C4×D4—291no—
146C4×D4C2×D2911yescharacteristic
147#117—581no—
148C2×C4⋊C4—581no—
149#107—291no—
150#106C2×D2912yes—
151C4⋊C8—292no—
152C4⋊C8C2×D2911yescharacteristic
153#103—292no—
154#103—292no—
155#103—292no—
156#102—291no—
157#102—291no—
158#102C2×D2912yes—
159C4×C8—292no—
160C4×C8—291no—
161C29#336011yescharacteristic, complemented, Sylow
162C2×Q8—21no—
163C2×Q8—291no—
164C2×Q8—292no—
165C2×D4—291no—
166C2×D4C22×D2911yescharacteristic
167C22×C4—21no—
168C22×C4—582no—
169C22×C4—581no—
170SD16—584no—
171D8—582no—
172C2×C8—291no—
173C2×C8—291no—
174C2×C8C22×D2912yes—
175C4⋊C4—21no—
176C4⋊C4—291no—
177C4⋊C4—292no—
178C4⋊C4—291no—
179C4⋊C4—582no—
180C4⋊C4—582no—
181C4⋊C4—582no—
182C4⋊C4—581no—
183C4⋊C4—581no—
184C4⋊C4C22×D2911yescharacteristic
185C4⋊C4C22×D2912yes—
186C22⋊C4—21no—
187C22⋊C4—582no—
188C22⋊C4—582no—
189C22⋊C4—582no—
190C22⋊C4—581no—
191C42—292no—
192C42—582no—
193C42C22×D2911yescharacteristic
194C23—21no—
195C23—581no—
196Q8—81no—
197Q8—582no—
198Q8—582no—
199Q8—582no—
200D4—21no—
201D4—21no—
202D4—292no—
203D4—581no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—292no—
208C2×C4—292no—
209C2×C4—582no—
210C2×C4—581no—
211C2×C4—1162no—
212C2×C4—2322no—
213C2×C4D4×D2911yescharacteristic
214C2×C4D4×D2911yescharacteristic
215C2×C4C23×D2911yescharacteristic
216C8—22no—
217C8—581no—
218C8—581no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—582no—
223C22—1161no—
224C22—1161no—
225C22C2×D4×D2911yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—582no—
230C4—582no—
231C4—1162no—
232C4—1161no—
233C4#1174527812yes—
234C4#1174536211yescharacteristic
235C4#41×D2911yescharacteristic
236C2—81no—
237C2—1162no—
238C2#1427182311yescharacteristic
239C2C2×#1174527811yescharacteristic
240C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#476C2
socleC22×C29C22×D4
prime radicalC2×#90782C22
hypercenter#476D29
hypocenterC29#3360
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #14271883C2semidirect
2. #14271874C2semidirect
3. #14271516C2semidirect
4. #14271515C2semidirect
5. #14271473C2semidirect
7. #14271369C2semidirect
8. #14271287C2semidirect
9. #14271250C2semidirect
11. C29×#476C2semidirect
121. #476D29semidirect
161. C29#3360semidirect

Maximal subgroups

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

subgroupindex
#142718832
#142718742
#142715162
#142715152
#142714732
#142713772
#142713692
#142712872
#142712502
C4×#907822
C29×#4762
#336029