Finite Group Databasebeta

← #16820300

Subgroups — #16820300

Order 3712.

336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#11745309C211yesmaximal, characteristic
2C2×#11745183C211yesmaximal, characteristic, complemented
3C2×#11745169C211yesmaximal, characteristic
4C2×#11745157C211yesmaximal, characteristic
5C2×C8×Dic29C211yesmaximal, characteristic, complemented
6#14271028C211yesmaximal, characteristic, complemented
7C2×C29×#103C211yesmaximal, characteristic, complemented
8C22×Q8×C29C2211yescharacteristic
9C22×D116C2211yescharacteristic
10C22×C8×C29C2211yescharacteristic
11C2×C4⋊C4×C29C2211yescharacteristic
12#11745309—22no—
13#11745309C414yescomplemented
14C2×#90781—22no—
15C2×C4⋊Dic29C2211yescharacteristic
16C2×C4×Dic29C2211yescharacteristic
17C22×#6597C2211yescharacteristic
18C29×#103—22no—
19#11745183—22no—
20#11745179—22no—
21#11745169—22no—
22C8×Dic29—22no—
23#11745157—22no—
24C23×D29—21no—
25C2×Q8×C29—21no—
26C2×Q8×C29—21no—
27C2×Q8×C29—21no—
28C2×Q8×C29—21no—
29C2×Q8×C29—21no—
30C2×Q8×C29C2×C412yes—
31C22×C4×C29—21no—
32C22×C4×C29—21no—
33C22×C4×C29C2311yescharacteristic
34C22×Dic29—21no—
35C22×Dic29D412yes—
36C2×D116—21no—
37C2×D116—21no—
38C2×D116—21no—
39C2×D116—21no—
40C2×D116—21no—
41C2×D116C2×C412yes—
42C2×C8×C29—21no—
43C2×C8×C29—21no—
44C2×C8×C29D412yes—
45C4⋊C4×C29—21no—
46C4⋊C4×C29—21no—
47#90781—28no—
48C4⋊Dic29—21no—
49C4⋊Dic29—21no—
50C4×Dic29C2×C412yes—
51C4×Dic29D412yes—
52C2×#6597—21no—
53C2×#6597—21no—
54C2×#6597D412yes—
55C23×C29C2×D411yescharacteristic
56C22×D29—22no—
57C22×D29—41no—
58C22×D29—41no—
59C22×D29—42no—
60C22×D29—42no—
61Q8×C29—22no—
62Q8×C29—22no—
63Q8×C29—41no—
64Q8×C29—41no—
65C2×C4×C29—22no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29—42no—
70C2×C4×C29C22×C411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29#4111yescharacteristic
75C2×C4×C29#4111yescharacteristic
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—41no—
79C2×Dic29—42no—
80C2×Dic29C22⋊C414yes—
81D116—22no—
82D116—22no—
83D116—41no—
84D116—41no—
85C8×C29—22no—
86#6597—22no—
87#1958—291nomaximal, Sylow
88C22×C29C2×C22⋊C411yescharacteristic
89C22×C29#12411yescharacteristic
90C22×C29#12711yescharacteristic
91C22×C29#13512yes—
92C22×C29#13512yes—
93C2×D29—42no—
94C2×D29—44no—
95C2×D29—82no—
96C2×D29—81no—
97C2×D29—81no—
98C4×C29—42no—
99C4×C29—81no—
100C4×C29C4×D411yescharacteristic
101C4×C29C4×D411yescharacteristic
102C4×C29#12111yescharacteristic
103C4×C29#12111yescharacteristic
104Dic29—24no—
105Dic29—81no—
106C2×#124—291no—
107C2×#103—291no—
108C2×#103D2911yescharacteristic, complemented
109C2×#102—291no—
110C2×#102—291no—
111C2×C4×C8—291no—
112#382—291no—
113C2×C29#39011yescharacteristic
114C2×C29#41612yes—
115C2×C29#48812yes—
116C2×C29#49511yescharacteristic
117C2×C29#49511yescharacteristic
118D29—82no—
119C22×Q8C2×D2911yescharacteristic
120C22×D4—291no—
121C22×C8—291no—
122C22×C8C2×D2911yescharacteristic
123#124—294no—
124#124—582no—
125C2×C4⋊C4—291no—
126C2×C4⋊C4C2×D2911yescharacteristic
127C2×C22⋊C4—582no—
128C2×C42—291no—
129#103—22no—
130#103—582no—
131#102—582no—
132#102—582no—
133C4×C8—582no—
134#95—582no—
135C29#195811yescharacteristic, complemented, Sylow
136C24—581no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C4×D2912yes—
143C2×D4—292no—
144C2×D4—581no—
145C2×D4—581no—
146C2×D4—581no—
147C2×D4—581no—
148C2×D4—581no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—292no—
152C22×C4—581no—
153C22×C4C22×D2911yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—292no—
157C2×C8—581no—
158C2×C8—581no—
159C2×C8C22⋊D2912yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—581no—
163C4⋊C4—581no—
164C22⋊C4—588no—
165C42—292no—
166C42—292no—
167C23—582no—
168C23—1162no—
169C23—1161no—
170C23—1161no—
171C23—1162no—
172C23D4×D2911yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—41no—
176Q8—41no—
177D4—582no—
178D4—582no—
179D4—1161no—
180D4—1161no—
181C2×C4—22no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—294no—
187C2×C4—582no—
188C2×C4—582no—
189C2×C4—1162no—
190C2×C4—1161no—
191C2×C4C2×C4×D2911yescharacteristic
192C2×C4#9080511yescharacteristic
193C2×C4D4×D2911yescharacteristic
194C2×C4D4×D2911yescharacteristic
195C2×C4#9080711yescharacteristic
196C2×C4C2×C22⋊D2911yescharacteristic
197C8—22no—
198C8—582no—
199C22—1162no—
200C22—1164no—
201C22—2322no—
202C22—2321no—
203C22—2321no—
204C22C22⋊C4×D2911yescharacteristic
205C22#1174524711yescharacteristic
206C22#1174527812yes—
207C22#1174528112yes—
208C22#1174530211yescharacteristic
209C4—42no—
210C4—81no—
211C4—584no—
212C4—2321no—
213C4#1174524311yescharacteristic
214C4#1174524611yescharacteristic
215C4C4×C22⋊D2911yescharacteristic
216C4#1174530111yescharacteristic
217C2—2322no—
218C2#1427106311yescharacteristic
219C2#1427115812yes—
220C2#1427151912yes—
221C2#1427154411yescharacteristic
222C2#1427154811yescharacteristic
subgroupG/H
centerC23D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC2×C29×#103C2
socleC23×C29C2×D4
prime radicalC22×D116C22
cosocleC22×C4×C29C23
hypercenterC2×#103D29
hypocenterC29#1958
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#11745183C2semidirect
5. C2×C8×Dic29C2semidirect
6. #14271028C2semidirect
7. C2×C29×#103C2semidirect
13. #11745309C4semidirect
108. C2×#103D29semidirect
135. C29#1958semidirect

Maximal subgroups

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

subgroupindex
C2×#117453092
C2×#117451832
C2×#117451692
C2×#117451572
C2×C8×Dic292
#142710282
C2×C29×#1032
#195829