Finite Group Databasebeta

← #16818450

Subgroups — #16818450

Order 3712.

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

normal subgroups only

This group has 256 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#14271788C211yesmaximal, characteristic
2#14271321C211yesmaximal, characteristic, complemented
3#14271318C211yesmaximal, characteristic, complemented
4#14271076C211yesmaximal, characteristic
5#14270899C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic
7C29×#328C211yesmaximal, characteristic, complemented
8C22×Dic58C2211yescharacteristic
9C29×C22⋊Q8C2211yescharacteristic
10#11745308—21no—
11C2×#90785—21no—
12C2×#90781—21no—
13C2×#90781C2211yescharacteristic
14#11745286C2211yescharacteristic
15C2×Dic116—21no—
16#11745259—21no—
17#11745258—21no—
18#11745258—21no—
19C22⋊C4×D29—21no—
20#11745240—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179—21no—
24C22⋊#6597C2211yescharacteristic
25#11745164—21no—
26#11745158—21no—
27C23×D29D411yescharacteristic
28C2×Q8×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C22×Dic29—21no—
32C22×Dic29D411yescharacteristic
33C2×C4×D29—21no—
34C2×C4×D29—21no—
35C2×Dic58—21no—
36C2×Dic58—21no—
37C2×Dic58—21no—
38C2×Dic58—42no—
39C2×Dic58D411yescharacteristic
40C2×C8×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29D411yescharacteristic
43C22⋊C4×C29—21no—
44C22⋊Dic29—21no—
45#90785—42no—
46#90781—21no—
47#90781—21no—
48#90781—21no—
49#90781—21no—
50#90781—42no—
51C4⋊Dic29—21no—
52C4⋊Dic29D411yescharacteristic
53#90779—21no—
54#90779—21no—
55#90779—21no—
56C2×#6597—21no—
57Dic116—42no—
58C23×C29C2×D411yescharacteristic
59C22×D29—21no—
60C22×D29—21no—
61C22×D29—41no—
62C22×D29—41no—
63C22×D29Q1612yescomplemented
64Q8×C29—41no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29—41no—
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C2×Dic29—22no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C4×D29—81no—
81C4×D29—81no—
82Dic58—22no—
83Dic58—22no—
84Dic58—41no—
85Dic58—41no—
86Dic58—41no—
87Dic58—81no—
88C8×C29—41no—
89#6597—41no—
90#1602—291nomaximal, Sylow
91C22×C29—21no—
92C22×C29—21no—
93C22×C29#12011yescharacteristic
94C22×C29C2×Q1611yescharacteristic
95C22×C29#13711yescharacteristic
96C2×D29—22no—
97C2×D29—41no—
98C2×D29—41no—
99C2×D29—42no—
100C2×D29—81no—
101C4×C29—21no—
102C4×C29—21no—
103C4×C29—41no—
104C4×C29—41no—
105C4×C29—81no—
106Dic29—41no—
107Dic29—41no—
108Dic29—42no—
109Dic29—41no—
110#543—291no—
111#451—291no—
112#451—291no—
113#393—291no—
114#328—291no—
115#328D2911yescharacteristic, complemented
116#323—291no—
117C2×C29—21no—
118C2×C29—21no—
119C2×C29#45111yescharacteristic
120C2×C29#45511yescharacteristic
121C2×C29B(4,𝔽2)11yescharacteristic
122D29—42no—
123C22×Q8—291no—
124C2×Q16—581no—
125C2×Q16—581no—
126C22⋊Q8—291no—
127C22⋊Q8—581no—
128C22⋊Q8—581no—
129C22⋊Q8—581no—
130C22⋊Q8—581no—
131C22⋊Q8—581no—
132C22⋊Q8C2×D2911yescharacteristic
133C2×C22⋊C4—291no—
134C2×C22⋊C4—581no—
135C2×C22⋊C4—581no—
136#103—581no—
137#103—581no—
138C22⋊C8—291no—
139C22⋊C8C2×D2911yescharacteristic
140#95—581no—
141#95C2×D2911yescharacteristic
142C29#160211yescharacteristic, complemented, Sylow
143C24—291no—
144C2×Q8—291no—
145C2×Q8—581no—
146C2×Q8—581no—
147C2×Q8—581no—
148C2×Q8—1162no—
149C2×Q8D11611yescharacteristic
150C22×C4—21no—
151C22×C4—291no—
152C22×C4—581no—
153C22×C4—581no—
154C22×C4—581no—
155C22×C4C22×D2911yescharacteristic
156Q16—1162no—
157Q16—1162no—
158C2×C8—21no—
159C2×C8—581no—
160C4⋊C4—21no—
161C4⋊C4—291no—
162C4⋊C4—581no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4D11611yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—581no—
169C22⋊C4—581no—
170C22⋊C4—581no—
171C22⋊C4—581no—
172C22⋊C4—581no—
173C22⋊C4—1162no—
174C23—292no—
175C23—581no—
176C23—581no—
177C23—1161no—
178C23—1161no—
179C23D4×D2911yescharacteristic
180Q8—41no—
181Q8—582no—
182Q8—582no—
183Q8—1161no—
184Q8—1161no—
185Q8—1161no—
186Q8—2321no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—582no—
194C2×C4—581no—
195C2×C4—581no—
196C2×C4—581no—
197C2×C4—1161no—
198C2×C4—1161no—
199C2×C4—1161no—
200C2×C4—2321no—
201C2×C4—2321no—
202C2×C4C2×D11611yescharacteristic
203C2×C4D4×D2911yescharacteristic
204C8—41no—
205C8—1161no—
206C22—21no—
207C22—21no—
208C22—582no—
209C22—1162no—
210C22—1161no—
211C22—1161no—
212C22—2321no—
213C22#1174524411yescharacteristic
214C22#1174527711yescharacteristic
215C22Q16×D2911yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—81no—
221C4—1161no—
222C4—1161no—
223C4—1162no—
224C4—1161no—
225C2—21no—
226C2—21no—
227C2—1162no—
228C2#1427132011yescharacteristic
229C2#1427134211yescharacteristic
230C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29#120
prime radicalC23×D29D4
hypercenter#328D29
hypocenterC29#1602
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14271321C2semidirect
3. #14271318C2semidirect
5. #14270899C2semidirect
7. C29×#328C2semidirect
63. C22×D29Q16semidirect
115. #328D29semidirect
142. C29#1602semidirect

Maximal subgroups

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

subgroupindex
#142717882
#142713212
#142713182
#142710762
#142708992
#142708862
C29×#3282
#160229