Finite Group Databasebeta

← #16819705

Subgroups — #16819705

Order 3712.

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

normal subgroups only

This group has 272 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
1#14271640C211yesmaximal, characteristic
2#14271203C211yesmaximal, characteristic
3C2×#11745172C211yesmaximal, characteristic
4#14271068C211yesmaximal, characteristic
5#14270924C211yesmaximal, characteristic
6#14270922C211yesmaximal, characteristic
7C29×#428C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C2×M16×C29C2211yescharacteristic
10C29×#117C2211yescharacteristic
11C2×C4⋊C4×C29C2211yescharacteristic
12#11745288C2211yescharacteristic
13C2×C4×Dic29C2211yescharacteristic
14C2×#90777C2211yescharacteristic
15#11745249—21no—
16#11745249—21no—
17#11745239—22no—
18C4×Dic58—21no—
19C4×Dic58—21no—
20C29×#107—21no—
21C29×#106—21no—
22#11745179—22no—
23#11745172C414yescomplemented
24#11745156—21no—
25#11745155—21no—
26C22×C4×C29—21no—
27C22×C4×C29C2311yescharacteristic
28C22×Dic29—21no—
29C22×Dic29D412yes—
30C2×Dic58—21no—
31C2×Dic58—21no—
32C2×Dic58—21no—
33C2×Dic58—21no—
34C2×Dic58C2×C412yes—
35C2×Dic58Q812yes—
36M16×C29—21no—
37M16×C29C2×C412yes—
38C2×C8×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29D411yescharacteristic
42C4⋊C4×C29D411yescharacteristic
43C22⋊C4×C29—21no—
44C42×C29—21no—
45C22⋊Dic29—21no—
46C4⋊Dic29D411yescharacteristic
47C4⋊Dic29D411yescharacteristic
48#90779—22no—
49#90779—22no—
50C4×Dic29—22no—
51C4×Dic29—22no—
52C4×Dic29—21no—
53C4×Dic29—21no—
54C4×Dic29—21no—
55#90777—21no—
56#90777C2×C412yes—
57C2×#6597—21no—
58C23×C29C2×D411yescharacteristic
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—42no—
62C2×C4×C29—41no—
63C2×C4×C29C22×C411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C2×C4×C29C2×Q811yescharacteristic
67C2×C4×C29#4111yescharacteristic
68C2×C4×C29#4111yescharacteristic
69C2×Dic29—22no—
70C2×Dic29—22no—
71C2×Dic29—22no—
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29C4⋊C414yes—
77Dic58—22no—
78Dic58—22no—
79Dic58—22no—
80Dic58—22no—
81C8×C29—22no—
82#6597—22no—
83#1857—291nomaximal, Sylow
84C22×C29—21no—
85C22×C29—21no—
86C22×C29C2×C4⋊C411yescharacteristic
87C22×C29#12011yescharacteristic
88C22×C29#12311yescharacteristic
89C4×C29—41no—
90C4×C29—41no—
91C4×C29—81no—
92C4×C29C4×D411yescharacteristic
93C4×C29C4×D411yescharacteristic
94C4×C29C22⋊Q811yescharacteristic
95C4×C29C22⋊Q811yescharacteristic
96Dic29—24no—
97Dic29—42no—
98Dic29—41no—
99Dic29—41no—
100#519—291no—
101#428—291no—
102#428D2911yescharacteristic
103C2×#101—291no—
104#391—291no—
105#339—291no—
106#339—291no—
107C2×C29—21no—
108C2×C29—21no—
109C2×C29#38511yescharacteristic
110C2×C29#45411yescharacteristic
111C2×C29#45611yescharacteristic
112C22×Q8—291no—
113C2×M16—291no—
114C2×M16C2×D2911yescharacteristic
115C4×Q8—581no—
116C4×Q8—581no—
117C4×Q8—581no—
118C4×Q8—581no—
119#117—291no—
120#117—582no—
121#117C2×D2911yescharacteristic
122C2×C4⋊C4C2×D2911yescharacteristic
123C2×C42—291no—
124#107—21no—
125#107—581no—
126#106—21no—
127#106—581no—
128#101—294no—
129#95—582no—
130C29#185711yescharacteristic, complemented, Sylow
131C2×Q8—292no—
132C2×Q8—292no—
133C2×Q8—581no—
134C2×Q8—581no—
135C2×Q8—581no—
136C2×Q8—581no—
137C22×C4—21no—
138C22×C4—292no—
139C22×C4—581no—
140C22×C4C22×D2911yescharacteristic
141M16—21no—
142M16—292no—
143M16—581no—
144M16C4×D2912yes—
145C2×C8—21no—
146C2×C8—581no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—291no—
150C4⋊C4—291no—
151C4⋊C4—582no—
152C4⋊C4—582no—
153C4⋊C4C22⋊D2911yescharacteristic
154C4⋊C4C22⋊D2911yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—581no—
157C42—21no—
158C42—582no—
159C42—582no—
160C42—581no—
161C42—581no—
162C42—581no—
163C23D4×D2911yescharacteristic
164Q8—582no—
165Q8—582no—
166Q8—582no—
167Q8—582no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—294no—
173C2×C4—582no—
174C2×C4—582no—
175C2×C4—582no—
176C2×C4—581no—
177C2×C4—581no—
178C2×C4—1161no—
179C2×C4—1161no—
180C2×C4C2×C4×D2911yescharacteristic
181C2×C4#9080511yescharacteristic
182C2×C4D4×D2911yescharacteristic
183C2×C4Q8×D2911yescharacteristic
184C2×C4#9080911yescharacteristic
185C2×C4C2×C22⋊D2911yescharacteristic
186C8—22no—
187C8—582no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D2911yescharacteristic
191C22#1174525611yescharacteristic
192C22#1174529911yescharacteristic
193C4—41no—
194C4—41no—
195C4—81no—
196C4—584no—
197C4—1162no—
198C4—1161no—
199C4—1161no—
200C4#1174525511yescharacteristic
201C4#1174525811yescharacteristic
202C4C4×C22⋊D2911yescharacteristic
203C4#1174530811yescharacteristic
204C2—21no—
205C2—21no—
206C2#1427103411yescharacteristic
207C2#1427133411yescharacteristic
208C2#1427134411yescharacteristic
subgroupG/H
centerC22#11745299
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#428C2
socleC22×C29#120
prime radicalC23×C29C2×D4
cosocleC22×C4×C29C23
hypercenter#428D29
hypocenterC29#1857
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
23. #11745172C4semidirect
130. C29#1857semidirect

Maximal subgroups

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

subgroupindex
#142716402
#142712032
C2×#117451722
#142710682
#142709242
#142709222
C29×#4282
#185729