Finite Group Databasebeta

← #16832145

Subgroups — #16832145

Order 3712.

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

normal subgroups only

This group has 350 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
2#14271870C211yesmaximal, characteristic, complemented
3#14271519C212yesmaximal, complemented
4#14271513C211yesmaximal, characteristic, complemented
5#14271468C212yesmaximal, complemented
6#14271454C211yesmaximal, characteristic, complemented
7#14271380C212yesmaximal
8#14271287C211yesmaximal, characteristic, complemented
9SD16×Dic29C212yesmaximal, complemented
10C4×#90782C211yesmaximal, characteristic
11C29×#461C211yesmaximal, characteristic, complemented
12C2×SD16×C29C2212yes—
13C29×C4⋊Q8C2211yescharacteristic
14C4×D4×C29C2211yescharacteristic
15#11745309C2212yes—
16Q8×Dic29C2212yes—
17D4×Dic29C2212yes—
18C2×#90782C2211yescharacteristic
19C2×C4⋊Dic29—21no—
20#11745286—21no—
21#11745260—22no—
22#11745259—21no—
23#11745254—21no—
24#11745252C2212yes—
25#11745240—22no—
26C4×D116C2211yescharacteristic
27#11745231C2211yescharacteristic
28C4×Dic58C2211yescharacteristic
29C29×C4⋊C8C2211yescharacteristic
30C29×#103C2212yes—
31#11745183C2212yes—
32#11745183C2212yes—
33#11745180C2211yescharacteristic
34#11745169C2212yes—
35#11745165C2212yes—
36#11745162C2212yes—
37C8×Dic29C2212yes—
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×Dic58D411yescharacteristic
49SD16×C29—24no—
50C2×C8×C29C2312yes—
51C4⋊C4×C29—21no—
52C4⋊C4×C29—21no—
53C4⋊C4×C29C2311yescharacteristic
54C22⋊C4×C29—21no—
55C42×C29C2311yescharacteristic
56C22⋊Dic29—22no—
57#90782—22no—
58#90781—21no—
59#90781—22no—
60#90781—22no—
61C4⋊Dic29—21no—
62C4⋊Dic29—22no—
63C4⋊Dic29—22no—
64C4⋊Dic29D411yescharacteristic
65C4⋊Dic29C2312yes—
66C4⋊Dic29C2311yescharacteristic
67#90779—22no—
68#90779D412yes—
69C4×Dic29—22no—
70C4×Dic29C2312yes—
71C2×#6597C2311yescharacteristic
72C2×#6597C2311yescharacteristic
73C23×C29—21no—
74C22×D29—21no—
75Q8×C29—22no—
76Q8×C29—22no—
77D4×C29—21no—
78D4×C29#4112yes—
79C2×C4×C29—22no—
80C2×C4×C29—21no—
81C2×C4×C29—42no—
82C2×C4×C29C2×D411yescharacteristic
83C2×C4×C29C2×D411yescharacteristic
84C2×C4×C29C2411yescharacteristic
85C2×Dic29—21no—
86C2×Dic29—22no—
87C2×Dic29—82no—
88C2×Dic29C2×D412yes—
89C2×Dic29C2×D412yes—
90D116—21no—
91D116—21no—
92C4×D29—42no—
93Dic58—22no—
94Dic58—81no—
95C8×C29—22no—
96#6597—21no—
97#6597—21no—
98#3360—291nomaximal, Sylow
99C22×C29—22no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29C22×D411yescharacteristic
103C2×D29—41no—
104C2×D29—41no—
105C2×D29—41no—
106C4×C29—21no—
107C4×C29—42no—
108C4×C29—41no—
109C4×C29#13512yes—
110C4×C29C2×#4111yescharacteristic
111C4×C292−1+411yescharacteristic
112Dic29—22no—
113Dic29—22no—
114Dic29—41no—
115Dic29—42no—
116#556—291no—
117#554—291no—
118#488—292no—
119#487—291no—
120#479—292no—
121#476—291no—
122#463—292no—
123#461D2911yescharacteristic, complemented
124C8×Q8—291no—
125C4×SD16—292no—
126C4×D8—291no—
127C2×C29—42no—
128C2×C29#54811yescharacteristic
129C2×C29C2×#13511yescharacteristic
130C2×C29#57711yescharacteristic
131D29—81no—
132C2×SD16C2×D2912yes—
133C2×D8—291no—
134C4⋊Q8—291no—
135C4⋊Q8C2×D2911yescharacteristic
136#126—582no—
137#125—292no—
138#124—292no—
139C22⋊Q8—582no—
140C22⋊Q8—581no—
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#106—292no—
151C4⋊C8—292no—
152C4⋊C8C2×D2911yescharacteristic
153#103—292no—
154#103—292no—
155#103C2×D2912yes—
156#102—291no—
157#102—292no—
158#102—291no—
159C4×C8—292no—
160C4×C8—291no—
161C29#336011yescharacteristic, complemented, Sylow
162C2×Q8—291no—
163C2×Q8—581no—
164C2×Q8C22×D2912yes—
165C2×D4—291no—
166C2×D4C22×D2911yescharacteristic
167C22×C4—21no—
168C22×C4—582no—
169C22×C4—581no—
170SD16—24no—
171D8—582no—
172C2×C8—291no—
173C2×C8—291no—
174C2×C8C22×D2912yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—291no—
178C4⋊C4—292no—
179C4⋊C4—292no—
180C4⋊C4—291no—
181C4⋊C4—582no—
182C4⋊C4—582no—
183C4⋊C4—582no—
184C4⋊C4—581no—
185C4⋊C4C22×D2911yescharacteristic
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—22no—
197Q8—22no—
198Q8—582no—
199Q8—2321no—
200D4—21no—
201D4—581no—
202D4—581no—
203D4#9080712yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—292no—
208C2×C4—292no—
209C2×C4—581no—
210C2×C4—582no—
211C2×C4—1162no—
212C2×C4—2322no—
213C2×C4D4×D2911yescharacteristic
214C2×C4D4×D2911yescharacteristic
215C2×C4C23×D2911yescharacteristic
216C8—22no—
217C8—581no—
218C8—581no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—1161no—
223C22—1161no—
224C22—1161no—
225C22C2×D4×D2911yescharacteristic
226C4—21no—
227C4—42no—
228C4—41no—
229C4—582no—
230C4—582no—
231C4—1161no—
232C4—1162no—
233C4#1174527812yes—
234C4C2×#9080711yescharacteristic
235C4#1174536511yescharacteristic
236C2—42no—
237C2—2321no—
238C2#1427181911yescharacteristic
239C2C2×#1174527811yescharacteristic
240C2#1427197211yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#461C2
socleC22×C29C22×D4
prime radicalC2×#90782C22
hypercenter#461D29
hypocenterC29#3360
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. #14271870C2semidirect
3. #14271519C2semidirect
4. #14271513C2semidirect
5. #14271468C2semidirect
6. #14271454C2semidirect
8. #14271287C2semidirect
9. SD16×Dic29C2semidirect
11. C29×#461C2semidirect
123. #461D29semidirect
161. C29#3360semidirect

Maximal subgroups

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

subgroupindex
#142718872
#142718702
#142715192
#142715132
#142714682
#142714542
#142713802
#142712872
SD16×Dic292
C4×#907822
C29×#4612
#336029