Finite Group Databasebeta

← #16818496

Subgroups — #16818496

Order 3712.

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

normal subgroups only

This group has 254 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#14271740C211yesmaximal, characteristic
2#14271477C211yesmaximal, characteristic, complemented
3#14271474C211yesmaximal, characteristic, complemented
4#14271095C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C2×#90807—21no—
9C29×#121C2211yescharacteristic
10#11745301—21no—
11#11745301—21no—
12#11745292C2211yescharacteristic
13C2×C4⋊Dic29—21no—
14C2×C4⋊Dic29C2211yescharacteristic
15C2×#90779C2211yescharacteristic
16#11745258—21no—
17#11745246—21no—
18#11745240—21no—
19C29×C22⋊C8C2211yescharacteristic
20C29×#95C2211yescharacteristic
21#11745180—21no—
22#11745179—21no—
23C22⋊#6597C2211yescharacteristic
24#11745169—21no—
25#11745166—21no—
26#11745155—21no—
27C2×D4×C29—21no—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—21no—
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C22×Dic29—21no—
35C22×Dic29—21no—
36C22×Dic29D411yescharacteristic
37C22×Dic29D411yescharacteristic
38#90807—42no—
39#90807—42no—
40C2×D116D411yescharacteristic
41C2×C4×D29—21no—
42C2×Dic58—21no—
43C2×C8×C29—21no—
44C4⋊C4×C29D411yescharacteristic
45C22⋊C4×C29—21no—
46C22⋊Dic29—21no—
47#90781—21no—
48#90781—21no—
49C4⋊Dic29—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29—42no—
52C4⋊Dic29D411yescharacteristic
53#90779—21no—
54#90779—21no—
55#90779—21no—
56C2×#6597—21no—
57C23×C29—21no—
58C23×C29C2×D411yescharacteristic
59C22×D29—21no—
60D4×C29—41no—
61D4×C29—41no—
62D4×C29—41no—
63C2×C4×C29—22no—
64C2×C4×C29—21no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29C2×D411yescharacteristic
70C22⋊D29—42no—
71C22⋊D29—41no—
72C22⋊D29—41no—
73C22⋊D29—81no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—42no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29—41no—
82C2×Dic29—41no—
83C2×Dic29D812yes—
84D116—41no—
85C4×D29—42no—
86Dic58—42no—
87C8×C29—41no—
88#6597—41no—
89#1610—291nomaximal, Sylow
90C22×C29—21no—
91C22×C29—21no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29—41no—
95C22×C29#12011yescharacteristic
96C22×C29C2×D811yescharacteristic
97C22×C29AGL(1,ℤ/8)11yescharacteristic
98C2×D29—41no—
99C2×D29—41no—
100C2×D29—41no—
101C4×C29—21no—
102C4×C29—21no—
103C4×C29—42no—
104C4×C29—41no—
105Dic29—22no—
106Dic29—41no—
107Dic29—41no—
108Dic29—81no—
109#537—291no—
110#480—291no—
111#480—291no—
112#398—291no—
113#327—291no—
114#327D2911yescharacteristic, complemented
115#324—291no—
116C2×C29—21no—
117C2×C29—21no—
118C2×C29—81no—
119C2×C29#44711yescharacteristic
120C2×C29#45611yescharacteristic
121C2×C29#45811yescharacteristic
122D29—81no—
123C2×#41—581no—
124C22⋊Q8—581no—
125C22⋊Q8—581no—
126#121—291no—
127#121—581no—
128#121—581no—
129#121—581no—
130#121C2×D2911yescharacteristic
131C2×C4⋊C4—291no—
132C2×C4⋊C4—291no—
133C2×C4⋊C4—581no—
134#107—581no—
135#107—581no—
136#102—581no—
137#102—581no—
138C22⋊C8—291no—
139C22⋊C8C2×D2911yescharacteristic
140#95—581no—
141#95C2×D2911yescharacteristic
142C29#161011yescharacteristic, complemented, Sylow
143#41—1162no—
144#41—1162no—
145C2×Q8—581no—
146C2×D4—21no—
147C2×D4—291no—
148C2×D4—581no—
149C2×D4—581no—
150C2×D4—581no—
151C2×D4D11611yescharacteristic
152C22×C4—21no—
153C22×C4—291no—
154C22×C4—291no—
155C22×C4—581no—
156C22×C4—581no—
157C22×C4—581no—
158C22×C4C22×D2911yescharacteristic
159C2×C8—21no—
160C2×C8—581no—
161C4⋊C4—291no—
162C4⋊C4—581no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—581no—
167C4⋊C4—1162no—
168C4⋊C4D11611yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—581no—
171C22⋊C4—581no—
172C22⋊C4—581no—
173C23—21no—
174C23—581no—
175C23D4×D2911yescharacteristic
176Q8—1162no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—1161no—
181D4—1162no—
182D4—1161no—
183D4—1161no—
184D4—2321no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—292no—
191C2×C4—581no—
192C2×C4—581no—
193C2×C4—581no—
194C2×C4—581no—
195C2×C4—1162no—
196C2×C4—1162no—
197C2×C4—1161no—
198C2×C4—1161no—
199C2×C4—1161no—
200C2×C4—1161no—
201C2×C4C2×D11611yescharacteristic
202C2×C4D4×D2911yescharacteristic
203C8—41no—
204C8—1161no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—1161no—
211C22—1161no—
212C22—1161no—
213C22#1174524411yescharacteristic
214C22D8×D2911yescharacteristic
215C22#1174527611yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—582no—
221C4—1161no—
222C4—1161no—
223C4—2321no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—2321no—
228C2#1427129811yescharacteristic
229C2#1427134711yescharacteristic
230C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radical#14271740C2
hypercenter#327D29
hypocenterC29#1610
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. #14271477C2semidirect
3. #14271474C2semidirect
4. #14271095C2semidirect
5. #14270896C2semidirect
6. #14270888C2semidirect
7. C29×#327C2semidirect
114. #327D29semidirect
142. C29#1610semidirect

Maximal subgroups

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

subgroupindex
#142717402
#142714772
#142714742
#142710952
#142708962
#142708882
C29×#3272
#161029