Finite Group Databasebeta

← #16818430

Subgroups — #16818430

Order 3712.

266 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 51 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#14271792C211yesmaximal, characteristic, complemented
2#14271314C211yesmaximal, characteristic
3#14271077C211yesmaximal, characteristic
4#14270901C211yesmaximal, characteristic, complemented
5#14270900C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#450C211yesmaximal, characteristic
8C22×D4×C29C2211yescharacteristic
9C2×SD16×C29—21no—
10C29×C22⋊Q8C2211yescharacteristic
11C2×C22⋊Dic29—21no—
12C2×C22⋊Dic29—21no—
13#11745306—21no—
14C2×#90783—21no—
15#11745286C2211yescharacteristic
16C2×#90779C2211yescharacteristic
17#11745251—21no—
18#11745251—21no—
19#11745250—21no—
20#11745240—21no—
21#11745239—21no—
22C29×#102—21no—
23C29×C22⋊C8C2211yescharacteristic
24#11745180—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C24×C29—21no—
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29—42no—
32C22×C4×C29C2311yescharacteristic
33C22×Dic29—21no—
34C22×Dic29D411yescharacteristic
35C22×Dic29D411yescharacteristic
36C2×Dic58—21no—
37C2×Dic58D411yescharacteristic
38SD16×C29—42no—
39C2×C8×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29D411yescharacteristic
42C22⋊C4×C29—21no—
43C22⋊Dic29—21no—
44C22⋊Dic29—42no—
45C22⋊Dic29—42no—
46#90783—42no—
47C4⋊Dic29—21no—
48C4⋊Dic29D411yescharacteristic
49#90779—21no—
50#90779—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—21no—
55#90779—21no—
56C4×Dic29—21no—
57C4×Dic29—21no—
58C2×#6597—21no—
59C23×C29—22no—
60C23×C29—41no—
61C23×C29—41no—
62C23×C29—41no—
63C23×C29—41no—
64C23×C29—41no—
65C23×C29—41no—
66C23×C29C2×D411yescharacteristic
67Q8×C29—41no—
68D4×C29—22no—
69D4×C29—22no—
70D4×C29—41no—
71D4×C29—41no—
72C2×C4×C29—21no—
73C2×C4×C29—21no—
74C2×C4×C29—41no—
75C2×C4×C29C2×D411yescharacteristic
76C2×C4×C29C2×D411yescharacteristic
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29—41no—
83C2×Dic29—41no—
84C2×Dic29—41no—
85C2×Dic29—41no—
86C2×Dic29SD1612yescomplemented
87Dic58—41no—
88Dic58—81no—
89C8×C29—41no—
90#6597—41no—
91#1599—291nomaximal, Sylow
92C22×C29—21no—
93C22×C29—21no—
94C22×C29—42no—
95C22×C29—42no—
96C22×C29—42no—
97C22×C29—81no—
98C22×C29—81no—
99C22×C29—81no—
100C22×C29—81no—
101C22×C29#12011yescharacteristic
102C22×C29C2×SD1611yescharacteristic
103C22×C29#13711yescharacteristic
104C4×C29—21no—
105C4×C29—21no—
106C4×C29—41no—
107C4×C29—41no—
108Dic29—22no—
109Dic29—41no—
110Dic29—41no—
111Dic29—41no—
112Dic29—81no—
113#544—291no—
114#450—291no—
115#450D2911yescharacteristic
116#394—291no—
117#328—291no—
118#328—291no—
119#324—291no—
120C2×C29—21no—
121C2×C29—21no—
122C2×C29—82no—
123C2×C29#44811yescharacteristic
124C2×C29#45411yescharacteristic
125C2×C29B(4,𝔽2)11yescharacteristic
126C22×D4C2×D2911yescharacteristic
127C2×SD16—21no—
128C2×SD16—581no—
129C4⋊Q8—581no—
130C4⋊Q8—581no—
131#125—581no—
132#125—581no—
133C22⋊Q8—291no—
134C22⋊Q8—581no—
135C22⋊Q8C2×D2911yescharacteristic
136#117—581no—
137C2×C4⋊C4—291no—
138C2×C22⋊C4—581no—
139C2×C22⋊C4—581no—
140#102—21no—
141#102—581no—
142C22⋊C8—291no—
143C22⋊C8C2×D2911yescharacteristic
144#95—291no—
145C29#159911yescharacteristic, complemented, Sylow
146C24—21no—
147C2×Q8—291no—
148C2×Q8—581no—
149C2×Q8C22⋊D2911yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C22×C4—291no—
154C22×C4—291no—
155C22×C4—581no—
156C22×C4C22×D2911yescharacteristic
157SD16—42no—
158SD16—1162no—
159C2×C8—21no—
160C2×C8—581no—
161C4⋊C4—21no—
162C4⋊C4—291no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—581no—
167C4⋊C4—581no—
168C4⋊C4—581no—
169C4⋊C4—581no—
170C4⋊C4—581no—
171C4⋊C4C22⋊D2911yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—581no—
174C22⋊C4—1162no—
175C22⋊C4—1162no—
176C42—581no—
177C42—581no—
178C23—22no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23D4×D2911yescharacteristic
186Q8—41no—
187Q8—1161no—
188Q8—2321no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—292no—
197C2×C4—581no—
198C2×C4—581no—
199C2×C4—581no—
200C2×C4—581no—
201C2×C4—581no—
202C2×C4—1161no—
203C2×C4—1161no—
204C2×C4—1161no—
205C2×C4—1161no—
206C2×C4D4×D2911yescharacteristic
207C2×C4C2×C22⋊D2911yescharacteristic
208C8—41no—
209C8—1161no—
210C22—21no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—81no—
216C22—81no—
217C22—81no—
218C22—81no—
219C22SD16×D2911yescharacteristic
220C22#1174527711yescharacteristic
221C22#1174529911yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—582no—
227C4—1161no—
228C4—1161no—
229C4—1161no—
230C4—2321no—
231C2—21no—
232C2—21no—
233C2—82no—
234C2#1427130011yescharacteristic
235C2#1427133411yescharacteristic
236C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#450C2
socleC22×C29#120
prime radicalC22×D4×C29C22
hypercenter#450D29
hypocenterC29#1599
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14271792C2semidirect
4. #14270901C2semidirect
5. #14270900C2semidirect
6. #14270888C2semidirect
86. C2×Dic29SD16semidirect
145. C29#1599semidirect

Maximal subgroups

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

subgroupindex
#142717922
#142713142
#142710772
#142709012
#142709002
#142708882
C29×#4502
#159929