Finite Group Databasebeta

← #16820642

Subgroups — #16820642

Order 3712.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11745252C211yesmaximal, characteristic
2C2×#11745164C211yesmaximal, characteristic
3C2×#11745158C211yesmaximal, characteristic
4#14271068C211yesmaximal, characteristic
5#14270925C211yesmaximal, characteristic
6#14270917C211yesmaximal, characteristic
7C29×#340C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C22×C8×C29C2211yescharacteristic
10C2×C4⋊C4×C29C2211yescharacteristic
11C2×C4⋊C4×C29C2211yescharacteristic
12C2×C4⋊Dic29—21no—
13C2×C4⋊Dic29C2211yescharacteristic
14C2×#90779—21no—
15C2×C4×Dic29C2211yescharacteristic
16C22×#6597C2211yescharacteristic
17#11745252—22no—
18#11745252—22no—
19#11745179—21no—
20#11745179—21no—
21#11745164—22no—
22#11745158—22no—
23C22×C4×C29—21no—
24C22×C4×C29—21no—
25C22×C4×C29C2311yescharacteristic
26C22×Dic29—21no—
27C22×Dic29—21no—
28C22×Dic29D411yescharacteristic
29C22×Dic29D411yescharacteristic
30C2×Dic58—21no—
31C2×Dic58—21no—
32C2×Dic58—21no—
33C2×Dic58—21no—
34C2×Dic58—21no—
35C2×Dic58Q812yes—
36C2×C8×C29—21no—
37C2×C8×C29—21no—
38C2×C8×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29D412yes—
43C4⋊Dic29—24no—
44C4⋊Dic29—21no—
45C4⋊Dic29D412yes—
46#90779—24no—
47C4×Dic29—21no—
48C4×Dic29—21no—
49C2×#6597—21no—
50C2×#6597—21no—
51C2×#6597—21no—
52C23×C29C2×D411yescharacteristic
53C2×C4×C29—22no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×Q811yescharacteristic
62C2×C4×C29#4111yescharacteristic
63C2×C4×C29#4111yescharacteristic
64C2×C4×C29#4111yescharacteristic
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29—22no—
68C2×Dic29—22no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—41no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77Dic58—22no—
78Dic58—22no—
79Dic58—41no—
80Dic58—41no—
81C8×C29—41no—
82#6597—41no—
83#2026—291nomaximal, Sylow
84C22×C29#12011yescharacteristic
85C22×C29C22⋊Q811yescharacteristic
86C22×C29#12411yescharacteristic
87C22×C29#13511yescharacteristic
88C22×C29#13511yescharacteristic
89C22×C29#13711yescharacteristic
90C22×C29#13711yescharacteristic
91C4×C29—42no—
92C4×C29—81no—
93C4×C29C22⋊Q811yescharacteristic
94C4×C29C22⋊Q811yescharacteristic
95C4×C29#12411yescharacteristic
96C4×C29#12411yescharacteristic
97Dic29—42no—
98Dic29—41no—
99Dic29—41no—
100Dic29—42no—
101C2×#125—291no—
102C2×#103—291no—
103C2×#103—291no—
104#391—291no—
105#340—291no—
106#340D2911yescharacteristic
107#336—291no—
108C2×C29#39311yescharacteristic
109C2×C29#45211yescharacteristic
110C2×C29#45211yescharacteristic
111C2×C29#47911yescharacteristic
112C2×C29#47911yescharacteristic
113C2×C29#48811yescharacteristic
114C2×C29#49111yescharacteristic
115C22×Q8—291no—
116C22×C8—291no—
117C22×C8C2×D2911yescharacteristic
118#125—582no—
119#125—582no—
120C2×C4⋊C4—291no—
121C2×C4⋊C4—581no—
122C2×C4⋊C4—581no—
123C2×C4⋊C4C2×D2911yescharacteristic
124C2×C4⋊C4C2×D2911yescharacteristic
125C2×C42—291no—
126#103—582no—
127#103—582no—
128#95—581no—
129#95—581no—
130C29#202611yescharacteristic, complemented, Sylow
131C2×Q8—292no—
132C2×Q8—581no—
133C2×Q8—581no—
134C2×Q8—581no—
135C2×Q8—581no—
136C2×Q8—581no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—291no—
140C22×C4—291no—
141C22×C4—581no—
142C22×C4—581no—
143C22×C4C22×D2911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—581no—
148C2×C8—581no—
149C2×C8—581no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—292no—
154C4⋊C4—584no—
155C4⋊C4—584no—
156C4⋊C4—581no—
157C4⋊C4D11612yes—
158C42—581no—
159C42—581no—
160C23D4×D2911yescharacteristic
161Q8—582no—
162Q8—582no—
163Q8—1161no—
164Q8—1161no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—581no—
172C2×C4—581no—
173C2×C4—581no—
174C2×C4—582no—
175C2×C4—582no—
176C2×C4—581no—
177C2×C4—581no—
178C2×C4—581no—
179C2×C4—1161no—
180C2×C4—1161no—
181C2×C4—1161no—
182C2×C4—1161no—
183C2×C4C2×D11611yescharacteristic
184C2×C4#9080511yescharacteristic
185C2×C4#9080511yescharacteristic
186C2×C4D4×D2911yescharacteristic
187C2×C4#9080711yescharacteristic
188C2×C4Q8×D2911yescharacteristic
189C8—41no—
190C8—1161no—
191C22#1174524411yescharacteristic
192C22#1174524711yescharacteristic
193C22#1174525811yescharacteristic
194C22#1174527411yescharacteristic
195C22#1174527711yescharacteristic
196C22#1174527811yescharacteristic
197C22#1174528011yescharacteristic
198C4—42no—
199C4—81no—
200C4—1161no—
201C4—1161no—
202C4—1162no—
203C4—1162no—
204C4#1174523711yescharacteristic
205C4#1174524711yescharacteristic
206C4#1174525811yescharacteristic
207C4#1174525911yescharacteristic
208C2#1427107611yescharacteristic
209C2#1427132611yescharacteristic
210C2#1427132811yescharacteristic
211C2#1427146911yescharacteristic
212C2#1427147311yescharacteristic
213C2#1427151611yescharacteristic
214C2#1427153011yescharacteristic
subgroupG/H
centerC23D4×D29
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#340C2
socle, prime radicalC23×C29C2×D4
hypercenter#340D29
hypocenterC29#2026
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
130. C29#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#117452522
C2×#117451642
C2×#117451582
#142710682
#142709252
#142709172
C29×#3402
#202629