Finite Group Databasebeta

← #16818538

Subgroups — #16818538

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#14271751C211yesmaximal, characteristic
2#14271498C211yesmaximal, characteristic, complemented
3#14271481C211yesmaximal, characteristic, complemented
4#14270899C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic, complemented
6#14270887C211yesmaximal, characteristic, complemented
7C29×#399C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C29—21no—
9C2×C4⋊C4×C29C2211yescharacteristic
10C2×C22⋊C4×C29—21no—
11C2×C22⋊C4×C29C2211yescharacteristic
12#11745315—21no—
13#11745292C2211yescharacteristic
14C4×C22⋊D29—21no—
15#11745286C2211yescharacteristic
16#11745247—21no—
17#11745246—21no—
18#11745245—21no—
19#11745241—21no—
20C29×#95C2211yescharacteristic
21C22⋊#6597C2211yescharacteristic
22C22⋊#6597C2211yescharacteristic
23#11745158—21no—
24#11745157—21no—
25#11745156—21no—
26#11745155—21no—
27C24×C29D411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29—21no—
30C22×C4×C29D411yescharacteristic
31C22×C4×C29C2311yescharacteristic
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C2×D116D411yescharacteristic
36C2×C4×D29—21no—
37C2×Dic58D411yescharacteristic
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—42no—
41C22⋊C4×C29—21no—
42C22⋊C4×C29—21no—
43C22⋊C4×C29—42no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46C22⋊Dic29—21no—
47#90781—21no—
48#90781—21no—
49C4⋊Dic29D411yescharacteristic
50C4⋊Dic29D411yescharacteristic
51#90779—21no—
52#90779—21no—
53C4×Dic29—21no—
54C2×#6597—21no—
55C2×#6597—21no—
56C23×C29—21no—
57C23×C29—21no—
58C23×C29—21no—
59C23×C29—41no—
60C23×C29—41no—
61C23×C29C2×D411yescharacteristic
62C22×D29—21no—
63C2×C4×C29—22no—
64C2×C4×C29—21no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C22⋊D29—41no—
75C22⋊D29—41no—
76C22⋊D29—81no—
77C22⋊D29—81no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81D116—41no—
82C4×D29—81no—
83Dic58—41no—
84#6597—41no—
85#6597—41no—
86#1618—291nomaximal, Sylow
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—42no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29—81no—
94C22×C29#12011yescharacteristic
95C22×C29#13511yescharacteristic
96C22×C29#13711yescharacteristic
97C2×D29—41no—
98C2×D29—41no—
99C2×D29—41no—
100C4×C29—21no—
101C4×C29—21no—
102C4×C29—42no—
103C4×C29—41no—
104C4×C29—81no—
105Dic29—41no—
106Dic29—41no—
107Dic29—41no—
108#538—291no—
109#484—291no—
110#481—291no—
111#399D2911yescharacteristic, complemented
112#328—291no—
113#327—291no—
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—291no—
127#121—581no—
128#120—581no—
129C4×D4—581no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4C2×D2911yescharacteristic
132C2×C22⋊C4—21no—
133C2×C22⋊C4C2×D2911yescharacteristic
134#107—581no—
135#106—581no—
136#103—581no—
137#102—581no—
138C22⋊C8—291no—
139C22⋊C8—291no—
140#95C2×D2911yescharacteristic
141C29#161811yescharacteristic, complemented, Sylow
142C24C22⋊D2911yescharacteristic
143C2×Q8—291no—
144C2×D4—291no—
145C2×D4—581no—
146C2×D4—581no—
147C2×D4—581no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—581no—
151C22×C4C22⋊D2911yescharacteristic
152C22×C4C22×D2911yescharacteristic
153C2×C8—581no—
154C2×C8—581no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—291no—
159C4⋊C4—291no—
160C4⋊C4—581no—
161C4⋊C4—581no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—42no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C22⋊C4—581no—
170C42—581no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23—581no—
177C23C2×C22⋊D2911yescharacteristic
178Q8—1161no—
179D4—1161no—
180D4—1161no—
181D4—1161no—
182D4—2321no—
183D4—2321no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—581no—
194C2×C4—581no—
195C2×C4—581no—
196C2×C4—2321no—
197C2×C4D4×D2911yescharacteristic
198C2×C4D4×D2911yescharacteristic
199C8—1161no—
200C8—1161no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—1161no—
209C22—1161no—
210C22—1161no—
211C22#1174529911yescharacteristic
212C22#1174530411yescharacteristic
213C22#1174531211yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—81no—
219C4—1161no—
220C4—1161no—
221C4—1161no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—2321no—
226C2#1427132311yescharacteristic
227C2#1427133011yescharacteristic
228C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#399C2
socleC22×C29#120
prime radical#14271751C2
hypercenter#399D29
hypocenterC29#1618
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #14271498C2semidirect
3. #14271481C2semidirect
4. #14270899C2semidirect
5. #14270896C2semidirect
6. #14270887C2semidirect
7. C29×#399C2semidirect
111. #399D29semidirect
141. C29#1618semidirect

Maximal subgroups

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

subgroupindex
#142717512
#142714982
#142714812
#142708992
#142708962
#142708872
C29×#3992
#161829