Finite Group Databasebeta

← #16818484

Subgroups — #16818484

Order 3712.

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

normal subgroups only

This group has 228 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#14271494C211yesmaximal, characteristic, complemented
3#14271491C211yesmaximal, characteristic, complemented
4#14271090C211yesmaximal, characteristic
5#14270899C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic
7C29×#328C211yesmaximal, characteristic, complemented
8C29×C22⋊Q8C2211yescharacteristic
9#11745308—21no—
10C2×#90781—21no—
11C2×#90781C2211yescharacteristic
12C2×C4⋊Dic29C2211yescharacteristic
13#11745286C2211yescharacteristic
14#11745259—21no—
15#11745258—21no—
16#11745258—21no—
17C22⋊C4×D29—21no—
18#11745240—21no—
19C29×C22⋊C8C2211yescharacteristic
20C29×#95C2211yescharacteristic
21#11745183—21no—
22#11745179—21no—
23C22⋊#6597C2211yescharacteristic
24#11745165—21no—
25#11745164—21no—
26#11745156—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×Dic58D411yescharacteristic
37C2×C8×C29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29D411yescharacteristic
40C22⋊C4×C29—21no—
41C22⋊Dic29—21no—
42#90781—21no—
43#90781—21no—
44#90781—21no—
45#90781—21no—
46#90781—42no—
47C4⋊Dic29—21no—
48C4⋊Dic29—21no—
49C4⋊Dic29—21no—
50C4⋊Dic29D411yescharacteristic
51#90779—21no—
52#90779—21no—
53#90779—21no—
54C2×#6597—21no—
55C23×C29C2×D411yescharacteristic
56C22×D29—21no—
57C22×D29—21no—
58C22×D29—41no—
59C22×D29—41no—
60C22×D29SD1612yes—
61Q8×C29—41no—
62C2×C4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29C2×D411yescharacteristic
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—41no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C4×D29—81no—
78C4×D29—81no—
79Dic58—41no—
80Dic58—81no—
81C8×C29—41no—
82#6597—41no—
83#1608—291nomaximal, Sylow
84C22×C29—21no—
85C22×C29—21no—
86C22×C29#12011yescharacteristic
87C22×C29C2×SD1611yescharacteristic
88C22×C29#13711yescharacteristic
89C2×D29—22no—
90C2×D29—41no—
91C2×D29—41no—
92C2×D29—42no—
93C2×D29—81no—
94C4×C29—21no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29—41no—
98C4×C29—81no—
99Dic29—41no—
100Dic29—41no—
101Dic29—41no—
102Dic29—81no—
103#543—291no—
104#483—291no—
105#483—291no—
106#397—291no—
107#328—291no—
108#328D2911yescharacteristic, complemented
109#323—291no—
110C2×C29—21no—
111C2×C29—21no—
112C2×C29#44811yescharacteristic
113C2×C29#45511yescharacteristic
114C2×C29#45811yescharacteristic
115D29—42no—
116C22⋊Q8—291no—
117C22⋊Q8—581no—
118C22⋊Q8—581no—
119C22⋊Q8—581no—
120C22⋊Q8—581no—
121C22⋊Q8—581no—
122C22⋊Q8C2×D2911yescharacteristic
123C2×C4⋊C4—291no—
124C2×C22⋊C4—291no—
125C2×C22⋊C4—581no—
126C2×C22⋊C4—581no—
127#106—581no—
128#106—581no—
129#103—581no—
130#103—581no—
131C22⋊C8—291no—
132C22⋊C8C2×D2911yescharacteristic
133#95—581no—
134#95C2×D2911yescharacteristic
135C29#160811yescharacteristic, complemented, Sylow
136C24—291no—
137C2×Q8—291no—
138C2×Q8—581no—
139C2×Q8D11611yescharacteristic
140C22×C4—21no—
141C22×C4—291no—
142C22×C4—581no—
143C22×C4—581no—
144C22×C4—581no—
145C22×C4C22×D2911yescharacteristic
146C2×C8—21no—
147C2×C8—581no—
148C4⋊C4—21no—
149C4⋊C4—291no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4—581no—
154C4⋊C4—581no—
155C4⋊C4—581no—
156C4⋊C4D11611yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—581no—
159C22⋊C4—581no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C22⋊C4—581no—
163C22⋊C4—1162no—
164C23—292no—
165C23—581no—
166C23—581no—
167C23—1161no—
168C23—1161no—
169C23D4×D2911yescharacteristic
170Q8—41no—
171Q8—1161no—
172Q8—2321no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—1161no—
183C2×C4—1161no—
184C2×C4—1161no—
185C2×C4—1161no—
186C2×C4—2321no—
187C2×C4—2321no—
188C2×C4C2×D11611yescharacteristic
189C2×C4D4×D2911yescharacteristic
190C8—41no—
191C8—1161no—
192C22—21no—
193C22—21no—
194C22—582no—
195C22—1162no—
196C22—1161no—
197C22—1161no—
198C22—2321no—
199C22#1174524411yescharacteristic
200C22SD16×D2911yescharacteristic
201C22#1174528011yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—1161no—
208C4—1161no—
209C4—1161no—
210C4—2321no—
211C2—21no—
212C2—21no—
213C2—1162no—
214C2#1427130311yescharacteristic
215C2#1427134211yescharacteristic
216C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29#120
prime radicalC23×D29D4
hypercenter#328D29
hypocenterC29#1608
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. #14271494C2semidirect
3. #14271491C2semidirect
5. #14270899C2semidirect
7. C29×#328C2semidirect
108. #328D29semidirect
135. C29#1608semidirect

Maximal subgroups

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

subgroupindex
#142717882
#142714942
#142714912
#142710902
#142708992
#142708862
C29×#3282
#160829