Finite Group Databasebeta

← #16832141

Subgroups — #16832141

Order 3712.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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#14271886C211yesmaximal, characteristic, complemented
2#14271520C212yesmaximal, complemented
3#14271515C211yesmaximal, characteristic, complemented
4#14271467C212yesmaximal, complemented
5#14271450C211yesmaximal, characteristic, complemented
6#14271378C212yesmaximal
7#14271368C211yesmaximal, characteristic, complemented
8Q8×#6597C211yesmaximal, characteristic, complemented
9C4×#90783C212yesmaximal, complemented
10C4×#90782C211yesmaximal, characteristic
11C29×#554C211yesmaximal, characteristic, complemented
12C29×C4⋊Q8C2211yescharacteristic
13C29×#125C2212yes—
14C29×C22⋊Q8—21no—
15C29×C22⋊Q8—22no—
16C4×Q8×C29C2211yescharacteristic
17C4×D4×C29C2211yescharacteristic
18C4×D4×C29C2212yes—
19C2×C4⋊C4×C29—21no—
20#11745308—21no—
21C2×#90783C2212yes—
22C2×#90782C2211yescharacteristic
23#11745260—22no—
24#11745254—21no—
25#11745237C2212yes—
26C4×D116C2211yescharacteristic
27#11745231C2211yescharacteristic
28C4×Dic58C2212yes—
29#11745180C2211yescharacteristic
30#11745158C2212yes—
31#11745158C2212yes—
32#11745158C2212yes—
33#11745157C2211yescharacteristic
34#11745157C2212yes—
35#11745156C2212yes—
36#11745155C2211yescharacteristic
37C4⋊#6597C2211yescharacteristic
38C4⋊#6597C2212yes—
39C4×#6597C2211yescharacteristic
40C4×#6597C2212yes—
41C2×Q8×C29—21no—
42C2×Q8×C29D411yescharacteristic
43C2×D4×C29C2311yescharacteristic
44C22×C4×C29—21no—
45C22×C4×C29—22no—
46C2×D116C2311yescharacteristic
47C2×C4×D29—21no—
48C2×Dic58C2312yes—
49C4⋊C4×C29—22no—
50C4⋊C4×C29—21no—
51C4⋊C4×C29—22no—
52C4⋊C4×C29D411yescharacteristic
53C4⋊C4×C29D412yes—
54C4⋊C4×C29C2311yescharacteristic
55C4⋊C4×C29C2312yes—
56C22⋊C4×C29—21no—
57C22⋊C4×C29—22no—
58C42×C29C2312yes—
59C42×C29C2311yescharacteristic
60#90783—24no—
61#90782—22no—
62#90781—22no—
63#90781—21no—
64#90781—22no—
65C4⋊Dic29—21no—
66C4⋊Dic29—21no—
67C4⋊Dic29C2311yescharacteristic
68#90779—22no—
69C4×Dic29—22no—
70C2×#6597C2311yescharacteristic
71C2×#6597C2312yes—
72C2×#6597C2311yescharacteristic
73C23×C29—21no—
74C22×D29—21no—
75Q8×C29—22no—
76Q8×C29—81no—
77D4×C29—21no—
78D4×C29#4112yes—
79C2×C4×C29—21no—
80C2×C4×C29—22no—
81C2×C4×C29—42no—
82C2×C4×C29—82no—
83C2×C4×C29C2×D412yes—
84C2×C4×C29C2×D412yes—
85C2×C4×C29C2×D411yescharacteristic
86C2×C4×C29C2×D411yescharacteristic
87C2×C4×C29C2411yescharacteristic
88C2×Dic29—21no—
89C2×Dic29—22no—
90D116—21no—
91D116—21no—
92C4×D29—42no—
93Dic58—22no—
94Dic58—22no—
95#6597—21no—
96#6597—22no—
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—22no—
107C4×C29—22no—
108C4×C29—21no—
109C4×C29—41no—
110C4×C29—42no—
111C4×C29#13512yes—
112C4×C29C2×#4111yescharacteristic
113C4×C292−1+411yescharacteristic
114Dic29—42no—
115Dic29—41no—
116#556—291no—
117#554D2911yescharacteristic, complemented
118#488—292no—
119#487—291no—
120#479—292no—
121#476—291no—
122#463—292no—
123#461—291no—
124C8×Q8—291no—
125C4×SD16—292no—
126C4×D8—291no—
127C2×C29—42no—
128C2×C29#54811yescharacteristic
129C2×C29C2×#13511yescharacteristic
130C2×C29#57711yescharacteristic
131D29—81no—
132C2×SD16—292no—
133C2×D8—291no—
134C4⋊Q8—291no—
135C4⋊Q8C2×D2911yescharacteristic
136#126—582no—
137#125C2×D2912yes—
138#124—292no—
139C22⋊Q8—21no—
140C22⋊Q8—22no—
141C22⋊Q8—581no—
142C4×Q8—292no—
143C4×Q8C2×D2911yescharacteristic
144C4×D4—291no—
145C4×D4C2×D2911yescharacteristic
146C4×D4C2×D2912yes—
147#117—581no—
148C2×C4⋊C4—21no—
149#107—291no—
150#106—292no—
151C4⋊C8—291no—
152C4⋊C8—292no—
153#103—292no—
154#103—292no—
155#103—292no—
156#102—291no—
157#102—291no—
158#102—292no—
159C4×C8—291no—
160C4×C8—292no—
161C29#336011yescharacteristic, complemented, Sylow
162C2×Q8—21no—
163C2×Q8—292no—
164C2×Q8C22⋊D2911yescharacteristic
165C2×D4—291no—
166C2×D4C22×D2911yescharacteristic
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—581no—
170SD16—584no—
171D8—582no—
172C2×C8—291no—
173C2×C8—292no—
174C2×C8—291no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—291no—
179C4⋊C4—581no—
180C4⋊C4—582no—
181C4⋊C4—581no—
182C4⋊C4C22⋊D2911yescharacteristic
183C4⋊C4C22⋊D2912yes—
184C4⋊C4C22×D2912yes—
185C4⋊C4C22×D2911yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—22no—
188C22⋊C4—582no—
189C22⋊C4—581no—
190C22⋊C4—582no—
191C42—582no—
192C42C22×D2911yescharacteristic
193C42C22×D2912yes—
194C23—21no—
195C23—581no—
196Q8—22no—
197Q8—81no—
198Q8—582no—
199Q8—582no—
200D4—21no—
201D4—581no—
202D4—581no—
203D4#9080912yes—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4—581no—
209C2×C4—582no—
210C2×C4—1162no—
211C2×C4C2×C22⋊D2912yes—
212C2×C4C2×C22⋊D2912yes—
213C2×C4C2×C22⋊D2911yescharacteristic
214C2×C4C2×C22⋊D2911yescharacteristic
215C2×C4C23×D2911yescharacteristic
216C8—581no—
217C8—582no—
218C8—581no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—1161no—
223C22—1161no—
224C22—1161no—
225C22C22×C22⋊D2911yescharacteristic
226C4—22no—
227C4—22no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—1162no—
232C4—1161no—
233C4#1174531212yes—
234C4C2×#9080911yescharacteristic
235C4#1174536211yescharacteristic
236C2—42no—
237C2—2321no—
238C2#1427182411yescharacteristic
239C2C2×#1174531211yescharacteristic
240C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#554C2
socleC22×C29C22×D4
prime radicalC2×#90782C22
hypercenter#554D29
hypocenterC29#3360
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #14271886C2semidirect
2. #14271520C2semidirect
3. #14271515C2semidirect
4. #14271467C2semidirect
5. #14271450C2semidirect
7. #14271368C2semidirect
8. Q8×#6597C2semidirect
9. C4×#90783C2semidirect
11. C29×#554C2semidirect
117. #554D29semidirect
161. C29#3360semidirect

Maximal subgroups

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

subgroupindex
#142718862
#142715202
#142715152
#142714672
#142714502
#142713782
#142713682
Q8×#65972
C4×#907832
C4×#907822
C29×#5542
#336029