Finite Group Databasebeta

← #16818518

Subgroups — #16818518

Order 3712.

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

normal subgroups only

This group has 236 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#14271499C211yesmaximal, characteristic, complemented
3#14271496C211yesmaximal, characteristic, complemented
4#14271100C211yesmaximal, 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⋊Dic29—21no—
13C2×C4⋊Dic29C2211yescharacteristic
14#11745286C2211yescharacteristic
15#11745259—21no—
16#11745258—21no—
17#11745258—21no—
18C22⋊C4×D29—21no—
19#11745240—21no—
20C29×C22⋊C8C2211yescharacteristic
21C29×#95C2211yescharacteristic
22#11745183—21no—
23C22⋊#6597C2211yescharacteristic
24#11745166—21no—
25#11745164—21no—
26#11745155—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⋊Dic29—42no—
51C4⋊Dic29D411yescharacteristic
52#90779—21no—
53#90779—21no—
54#90779—21no—
55C2×#6597—21no—
56C23×C29C2×D411yescharacteristic
57C22×D29—21no—
58C22×D29—21no—
59C22×D29—41no—
60C22×D29—41no—
61C22×D29Q1612yes—
62Q8×C29—41no—
63C2×C4×C29—22no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D411yescharacteristic
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29—41no—
78C4×D29—81no—
79C4×D29—81no—
80Dic58—41no—
81Dic58—81no—
82C8×C29—41no—
83#6597—41no—
84#1614—291nomaximal, Sylow
85C22×C29—21no—
86C22×C29—21no—
87C22×C29#12011yescharacteristic
88C22×C29C2×Q1611yescharacteristic
89C22×C29#13711yescharacteristic
90C2×D29—22no—
91C2×D29—41no—
92C2×D29—41no—
93C2×D29—42no—
94C2×D29—81no—
95C4×C29—21no—
96C4×C29—21no—
97C4×C29—42no—
98C4×C29—41no—
99C4×C29—41no—
100Dic29—41no—
101Dic29—41no—
102Dic29—41no—
103Dic29—81no—
104#543—291no—
105#484—291no—
106#484—291no—
107#399—291no—
108#328—291no—
109#328D2911yescharacteristic, complemented
110#323—291no—
111C2×C29—21no—
112C2×C29—21no—
113C2×C29#45111yescharacteristic
114C2×C29#45311yescharacteristic
115C2×C29#45811yescharacteristic
116D29—42no—
117C22⋊Q8—291no—
118C22⋊Q8—581no—
119C22⋊Q8—581no—
120C22⋊Q8—581no—
121C22⋊Q8—581no—
122C22⋊Q8—581no—
123C22⋊Q8C2×D2911yescharacteristic
124C2×C4⋊C4—291no—
125C2×C4⋊C4—581no—
126C2×C22⋊C4—291no—
127C2×C22⋊C4—581no—
128C2×C22⋊C4—581no—
129#107—581no—
130#107—581no—
131#103—581no—
132#103—581no—
133C22⋊C8—291no—
134C22⋊C8C2×D2911yescharacteristic
135#95C2×D2911yescharacteristic
136C29#161411yescharacteristic, complemented, Sylow
137C24—291no—
138C2×Q8—291no—
139C2×Q8—581no—
140C2×Q8D11611yescharacteristic
141C22×C4—21no—
142C22×C4—291no—
143C22×C4—581no—
144C22×C4—581no—
145C22×C4—581no—
146C22×C4C22×D2911yescharacteristic
147C2×C8—21no—
148C2×C8—581no—
149C4⋊C4—21no—
150C4⋊C4—291no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4—581no—
154C4⋊C4—581no—
155C4⋊C4—581no—
156C4⋊C4—581no—
157C4⋊C4—1162no—
158C4⋊C4D11611yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C22⋊C4—581no—
163C22⋊C4—581no—
164C22⋊C4—581no—
165C22⋊C4—1162no—
166C23—292no—
167C23—581no—
168C23—581no—
169C23—1161no—
170C23—1161no—
171C23D4×D2911yescharacteristic
172Q8—41no—
173Q8—1161no—
174Q8—2321no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—581no—
182C2×C4—581no—
183C2×C4—581no—
184C2×C4—1161no—
185C2×C4—1161no—
186C2×C4—1161no—
187C2×C4—1161no—
188C2×C4—2321no—
189C2×C4—2321no—
190C2×C4C2×D11611yescharacteristic
191C2×C4D4×D2911yescharacteristic
192C8—41no—
193C8—1161no—
194C22—21no—
195C22—21no—
196C22—582no—
197C22—1162no—
198C22—1161no—
199C22—1161no—
200C22—2321no—
201C22#1174524411yescharacteristic
202C22#1174527711yescharacteristic
203C22Q16×D2911yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—1161no—
210C4—1161no—
211C4—1161no—
212C4—2321no—
213C2—21no—
214C2—21no—
215C2—1162no—
216C2#1427132011yescharacteristic
217C2#1427133211yescharacteristic
218C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29#120
prime radicalC23×D29D4
hypercenter#328D29
hypocenterC29#1614
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. #14271499C2semidirect
3. #14271496C2semidirect
5. #14270899C2semidirect
7. C29×#328C2semidirect
109. #328D29semidirect
136. C29#1614semidirect

Maximal subgroups

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

subgroupindex
#142717882
#142714992
#142714962
#142711002
#142708992
#142708862
C29×#3282
#161429