Finite Group Databasebeta

← #16818541

Subgroups — #16818541

Order 3712.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271750C211yesmaximal, characteristic
2#14271499C211yesmaximal, characteristic, complemented
3#14271479C211yesmaximal, characteristic, complemented
4#14271100C211yesmaximal, characteristic, complemented
5#14270899C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C29×#121C2211yescharacteristic
9#11745301—21no—
10#11745299—21no—
11D4×Dic29—21no—
12C2×#90781—21no—
13C2×#90781C2211yescharacteristic
14C2×C4⋊Dic29—21no—
15C2×C4⋊Dic29C2211yescharacteristic
16#11745286C2211yescharacteristic
17#11745260—21no—
18#11745248—21no—
19#11745247—21no—
20C29×C22⋊C8C2211yescharacteristic
21C29×#95C2211yescharacteristic
22#11745180—21no—
23C22⋊#6597C2211yescharacteristic
24#11745166—21no—
25#11745164—21no—
26#11745156—21no—
27C23×D29D411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29D411yescharacteristic
30C22×C4×C29—21no—
31C22×C4×C29C2311yescharacteristic
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C22×Dic29—21no—
35C22×Dic29—21no—
36C22×Dic29D411yescharacteristic
37C2×Dic58D411yescharacteristic
38C2×C8×C29—21no—
39C4⋊C4×C29D411yescharacteristic
40C22⋊C4×C29—21no—
41C22⋊Dic29—21no—
42C22⋊Dic29—21no—
43#90781—21no—
44#90781—21no—
45#90781—21no—
46#90781—21no—
47#90781—42no—
48C4⋊Dic29—21no—
49C4⋊Dic29—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29—42no—
52C4⋊Dic29D411yescharacteristic
53#90779—21no—
54C4×Dic29—21no—
55C2×#6597—21no—
56C23×C29—21no—
57C23×C29C2×D411yescharacteristic
58C22×D29—21no—
59C22×D29—21no—
60C22×D29—21no—
61C22×D29—41no—
62C22×D29—41no—
63D4×C29—41no—
64D4×C29—41no—
65D4×C29—41no—
66C2×C4×C29—22no—
67C2×C4×C29—21no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29—41no—
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C22⋊D29—81no—
74C22⋊D29—81no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29—41no—
82C2×Dic29—81no—
83Dic58—41no—
84C8×C29—41no—
85#6597—41no—
86#1618—291nomaximal, Sylow
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—41no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29#12011yescharacteristic
93C22×C29#13511yescharacteristic
94C22×C29#13711yescharacteristic
95C2×D29—42no—
96C2×D29—41no—
97C2×D29—41no—
98C2×D29—41no—
99C2×D29—81no—
100C4×C29—21no—
101C4×C29—21no—
102C4×C29—42no—
103C4×C29—41no—
104Dic29—41no—
105Dic29—41no—
106Dic29—41no—
107Dic29—81no—
108#538—291no—
109#484—291no—
110#481—291no—
111#399—291no—
112#328—291no—
113#327D2911yescharacteristic, complemented
114#323—291no—
115C2×C29—21no—
116C2×C29—21no—
117C2×C29—81no—
118C2×C29#45211yescharacteristic
119C2×C29#45311yescharacteristic
120C2×C29#45811yescharacteristic
121D29—81no—
122#126—581no—
123#124—581no—
124#123—581no—
125C22⋊Q8—291no—
126#121—581no—
127#121C2×D2911yescharacteristic
128#120—581no—
129C4×D4—581no—
130C2×C4⋊C4—291no—
131C2×C4⋊C4—581no—
132C2×C22⋊C4—291no—
133C2×C22⋊C4—581no—
134#107—581no—
135#106—581no—
136#103—581no—
137#102—581no—
138C22⋊C8—291no—
139C22⋊C8C2×D2911yescharacteristic
140#95C2×D2911yescharacteristic
141C29#161811yescharacteristic, complemented, Sylow
142C24—291no—
143C2×Q8—291no—
144C2×D4—21no—
145C2×D4—581no—
146C2×D4—581no—
147C2×D4D11611yescharacteristic
148C22×C4—21no—
149C22×C4—291no—
150C22×C4—581no—
151C22×C4—581no—
152C22×C4C22×D2911yescharacteristic
153C2×C8—21no—
154C2×C8—581no—
155C4⋊C4—291no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4—581no—
159C4⋊C4—581no—
160C4⋊C4—1162no—
161C4⋊C4D11611yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—581no—
164C22⋊C4—581no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C22⋊C4—1162no—
170C42—581no—
171C23—21no—
172C23—581no—
173C23—581no—
174C23—581no—
175C23—1161no—
176C23—1161no—
177C23D4×D2911yescharacteristic
178Q8—1161no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—2321no—
183D4—2321no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4—2321no—
197C2×C4C2×D11611yescharacteristic
198C2×C4D4×D2911yescharacteristic
199C8—41no—
200C8—1161no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—1162no—
207C22—1161no—
208C22—1161no—
209C22—1161no—
210C22—2321no—
211C22#1174524411yescharacteristic
212C22#1174527411yescharacteristic
213C22#1174527711yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—1161no—
219C4—1161no—
220C4—1161no—
221C4—2321no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—2321no—
226C2#1427132611yescharacteristic
227C2#1427133211yescharacteristic
228C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radical#14271750C2
hypercenter#327D29
hypocenterC29#1618
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14271499C2semidirect
3. #14271479C2semidirect
4. #14271100C2semidirect
5. #14270899C2semidirect
6. #14270886C2semidirect
7. C29×#327C2semidirect
113. #327D29semidirect
141. C29#1618semidirect

Maximal subgroups

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

subgroupindex
#142717502
#142714992
#142714792
#142711002
#142708992
#142708862
C29×#3272
#161829