Finite Group Databasebeta

← #16835537

Subgroups — #16835537

Order 3712.

362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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#14272230C211yesmaximal, characteristic, complemented
2#14272162C212yesmaximal, complemented
3D29⋊#100C211yesmaximal, characteristic, complemented
4#14272030C212yesmaximal, complemented
5#14271731C211yesmaximal, characteristic
6C2×#90809C2211yescharacteristic
7C2×D4×D29C2211yescharacteristic
8C2×C22⋊#1181—22no—
9D4×#1181—24no—
10#11745345C2212yes—
11D29⋊M16C2212yes—
12C29×#124C411yescharacteristic, complemented
13#11745309C411yescharacteristic, complemented
14#11745302C411yescharacteristic, complemented
15#11745246—22no—
16#11745244—22no—
17#11745236C411yescharacteristic, complemented
18#11745234C2211yescharacteristic
19#11745229—22no—
20#11745226—24no—
21C23×D29D412yes—
22C22×#1181—24no—
23C2×Q8×C29C2×C411yescharacteristic, complemented
24C2×D4×C29C2×C411yescharacteristic
25C2×C22⋊D29—22no—
26C2×C22⋊D29D412yes—
27#90809—22no—
28#90809—22no—
29D4×D29—22no—
30D4×D29—22no—
31C2×D116—21no—
32C2×D116—22no—
33C2×D116C2×C411yescharacteristic
34C2×D116C2×C411yescharacteristic, complemented
35C2×C4×D29—21no—
36C2×C4×D29C2311yescharacteristic
37C22⋊#1181—24no—
38C22⋊#1181—22no—
39#90800—22no—
40C4⋊#1181—22no—
41C4×#1181D414yescomplemented
42#90796—22no—
43D29⋊C8—22no—
44C22⋊C4×C29—22no—
45C42×C29C2×C411yescharacteristic, complemented
46#90781—22no—
47#90781—21no—
48#90779—21no—
49C4×Dic29C2×C411yescharacteristic, complemented
50C23×C29C22⋊C412yes—
51C22×D29—22no—
52C22×D29—22no—
53C22×D29—21no—
54C22×D29—82no—
55C22×D29C22⋊C412yes—
56C22×D29C2×D411yescharacteristic
57C2×#1181—24no—
58C2×#1181—84no—
59Q8×C29—22no—
60D4×C29—22no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29C22×C411yescharacteristic
64C22⋊D29—24no—
65C22⋊D29—82no—
66C2×Dic29—21no—
67C2×Dic29C2×D411yescharacteristic
68D116—22no—
69D116—22no—
70D116—41no—
71D116—41no—
72D116—82no—
73C4×D29—42no—
74C4×D29C2×D412yes—
75C4×D29#4112yes—
76#6599—42no—
77#1911—291nomaximal, Sylow
78C22×C29—22no—
79C22×C29—42no—
80C22×C29C2×C22⋊C411yescharacteristic
81C2×D29—22no—
82C2×D29—41no—
83C2×D29—44no—
84C2×D29—42no—
85C2×D29—42no—
86C2×D29—41no—
87C2×D29—82no—
88C2×D29#12011yescharacteristic
89C2×D29#12311yescharacteristic
90#1181—44no—
91C4×C29—41no—
92C4×C29—41no—
93C4×C29C4×D412yes—
94Dic29—41no—
95Dic29#12112yes—
96#535—291no—
97#518—291no—
98#421—292no—
99C2×#100—291no—
100H(3,ℤ/4)—292no—
101C2×C29—21no—
102C2×C29—42no—
103C2×C29#38611yescharacteristic
104D29—21no—
105D29—21no—
106D29—42no—
107D29—81no—
108C2×#41—291no—
109C22×D4—291no—
110C2×M16—292no—
111#127—291no—
112#127—291no—
113#124—291no—
114#124#118111yescharacteristic, complemented
115#121—582no—
116#120—582no—
117C4×D4—584no—
118#117—292no—
119#117—291no—
120C2×C22⋊C4—582no—
121#104—584no—
122#100—582no—
123C29#191111yescharacteristic, complemented, Sylow
124C24—292no—
125#41—582no—
126#41—582no—
127C2×Q8C2×#118111yescharacteristic, complemented
128C2×D4—292no—
129C2×D4—291no—
130C2×D4—291no—
131C2×D4—581no—
132C2×D4—582no—
133C2×D4—582no—
134C2×D4—582no—
135C2×D4—582no—
136C2×D4C2×#118111yescharacteristic
137C22×C4—291no—
138C22×C4—581no—
139C22×C4—584no—
140M16—582no—
141M16—582no—
142C2×C8—582no—
143C4⋊C4—581no—
144C4⋊C4—582no—
145C22⋊C4—22no—
146C22⋊C4—581no—
147C22⋊C4—582no—
148C22⋊C4—582no—
149C22⋊C4—584no—
150C42—294no—
151C42—291no—
152C42C2×#118111yescharacteristic, complemented
153C23—291no—
154C23—292no—
155C23—582no—
156C23—582no—
157C23—581no—
158C23—2322no—
159C23C22⋊#118112yes—
160Q8—22no—
161D4—22no—
162D4—584no—
163D4—582no—
164D4—582no—
165D4—1161no—
166D4—1161no—
167D4—2322no—
168D4—2322no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—291no—
172C2×C4—292no—
173C2×C4—292no—
174C2×C4—584no—
175C2×C4—581no—
176C2×C4—1162no—
177C2×C4—2324no—
178C2×C4C22×#118111yescharacteristic
179C8—1162no—
180C22—22no—
181C22—42no—
182C22—291no—
183C22—291no—
184C22—582no—
185C22—1161no—
186C22—1162no—
187C22—1162no—
188C22—1164no—
189C22—1161no—
190C22—2322no—
191C22C2×C22⋊#118111yescharacteristic
192C4—41no—
193C4—41no—
194C4—292no—
195C4—1161no—
196C4—1164no—
197C4D4×#118112yes—
198C2—21no—
199C2—42no—
200C2—581no—
201C2—581no—
202C2—1162no—
203C2—2321no—
204C2#1427211111yescharacteristic
subgroupG/H
centerC2#14272111
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#124C4
socleC2×C29#386
prime radical#14271731C2
cosocleC2×C4×D29C23
hypercenter#124#1181
hypocenterC29#1911
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14272230C2semidirect
2. #14272162C2semidirect
3. D29⋊#100C2semidirect
4. #14272030C2semidirect
12. C29×#124C4semidirect
13. #11745309C4semidirect
14. #11745302C4semidirect
17. #11745236C4semidirect
23. C2×Q8×C29C2×C4semidirect
34. C2×D116C2×C4semidirect
41. C4×#1181D4semidirect
45. C42×C29C2×C4semidirect
49. C4×Dic29C2×C4semidirect
114. #124#1181semidirect
123. C29#1911semidirect
127. C2×Q8C2×#1181semidirect
152. C42C2×#1181semidirect

Maximal subgroups

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

subgroupindex
#142722302
#142721622
D29⋊#1002
#142720302
#142717312
#191129