Finite Group Databasebeta

← #16834922

Subgroups — #16834922

Order 3712.

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

normal subgroups only

This group has 264 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#14272182C211yesmaximal, characteristic, complemented
2#14272107C211yesmaximal, characteristic, complemented
3#14272015C212yesmaximal, complemented
4#14272014C212yesmaximal, complemented
5#14271710C211yesmaximal, characteristic
6C2×#90805—21no—
7C2×C4⋊#1181—21no—
8C4×D4×C29C411yescharacteristic, complemented
9#11745302C411yescharacteristic, complemented
10#11745300C2211yescharacteristic
11C4×C22⋊D29—21no—
12#11745257C2211yescharacteristic
13#11745250C411yescharacteristic, complemented
14#11745247—21no—
15#11745246—21no—
16C4×D116C411yescharacteristic, complemented
17C42×D29C2211yescharacteristic
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4C2212yes—
20#11745219C2212yes—
21C4⋊#6599—21no—
22C4×#6599—21no—
23C22×#1181—22no—
24C2×D4×C29C2×C411yescharacteristic
25C22×C4×C29—21no—
26C2×C22⋊D29—21no—
27C2×C22⋊D29—21no—
28C2×C22⋊D29—21no—
29#90805—42no—
30#90805—42no—
31C2×D116—21no—
32C2×D116C2×C411yescharacteristic
33C2×C4×D29—21no—
34C2×C4×D29D411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29C2311yescharacteristic
37C2×Dic58—21no—
38C2×#6599—22no—
39C4⋊#1181—42no—
40C4⋊C4×C29C2×C411yescharacteristic
41C22⋊C4×C29—21no—
42C42×C29C2×C411yescharacteristic
43C22⋊Dic29—21no—
44#90781—21no—
45#90781—21no—
46C4⋊Dic29C2×C411yescharacteristic
47#90779—21no—
48C4×Dic29C2×C411yescharacteristic
49C4×Dic29D411yescharacteristic
50C4×Dic29D411yescharacteristic
51C23×C29—21no—
52C22×D29—21no—
53C22×D29C2×D411yescharacteristic
54C2×#1181—42no—
55C2×#1181—42no—
56C2×#1181—42no—
57D4×C29—41no—
58C2×C4×C29—21no—
59C2×C4×C29—42no—
60C2×C4×C29C22⋊C411yescharacteristic
61C2×C4×C29C22⋊C411yescharacteristic
62C2×C4×C29C22×C411yescharacteristic
63C22⋊D29—42no—
64C22⋊D29—41no—
65C22⋊D29—41no—
66C22⋊D29—42no—
67C2×Dic29—21no—
68C2×Dic29C22⋊C411yescharacteristic
69C2×Dic29C22⋊C411yescharacteristic
70C2×Dic29C2×D411yescharacteristic
71D116—41no—
72D116—41no—
73D116—41no—
74C4×D29—41no—
75C4×D29—41no—
76C4×D29—42no—
77C4×D29D812yes—
78C4×D29SD1612yes—
79Dic58—42no—
80#6599—42no—
81#1517—291nomaximal, Sylow
82C22×C29—41no—
83C22×C29—41no—
84C22×C29—41no—
85C22×C29C2×C22⋊C411yescharacteristic
86C2×D29—21no—
87C2×D29—21no—
88C2×D29—41no—
89C2×D29—41no—
90C2×D29—41no—
91C2×D29C2×D811yescharacteristic
92C2×D29C2×SD1611yescharacteristic
93#1181—82no—
94C4×C29—21no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29#10212yes—
98Dic29—21no—
99Dic29—21no—
100Dic29—41no—
101Dic29#10212yes—
102#532—291no—
103#431—291no—
104#382—291no—
105#327—292no—
106#327—292no—
107C2×C29—81no—
108C2×C29#41011yescharacteristic
109C2×C29C2×#10211yescharacteristic
110C2×C29#42111yescharacteristic
111D29—21no—
112D29—21no—
113D29—81no—
114C2×#41—581no—
115C4⋊Q8—291no—
116#127—291no—
117#124—581no—
118#121—291no—
119#121—291no—
120#121—581no—
121C4×D4—291no—
122C4×D4—581no—
123C4×D4#118111yescharacteristic, complemented
124C2×C4⋊C4—581no—
125C2×C42—291no—
126C4⋊C8—581no—
127C22⋊C8—292no—
128C4×C8—581no—
129#95—292no—
130#95—581no—
131C29#151711yescharacteristic, complemented, Sylow
132#41—1162no—
133#41—1162no—
134C2×Q8—581no—
135C2×D4—291no—
136C2×D4—581no—
137C2×D4—581no—
138C2×D4—581no—
139C2×D4—581no—
140C2×D4C2×#118111yescharacteristic
141C22×C4—21no—
142C22×C4—291no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—581no—
146C22×C4—582no—
147C2×C8—582no—
148C4⋊C4—291no—
149C4⋊C4—581no—
150C4⋊C4—1162no—
151C4⋊C4C2×#118111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C42—291no—
157C42—291no—
158C42—291no—
159C42C2×#118111yescharacteristic
160C23—21no—
161C23—291no—
162C23—581no—
163Q8—1162no—
164D4—41no—
165D4—1161no—
166D4—1161no—
167D4—1161no—
168D4—1162no—
169D4—1162no—
170D4—1161no—
171D4—1161no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—291no—
175C2×C4—292no—
176C2×C4—292no—
177C2×C4—291no—
178C2×C4—291no—
179C2×C4—581no—
180C2×C4—1161no—
181C2×C4—1161no—
182C2×C4—1162no—
183C2×C4—1162no—
184C2×C4—1162no—
185C2×C4—1162no—
186C2×C4C22⋊#118111yescharacteristic
187C2×C4C22⋊#118111yescharacteristic
188C2×C4C22×#118111yescharacteristic
189C8—1162no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—291no—
194C22—291no—
195C22—581no—
196C22—581no—
197C22—1161no—
198C22—1161no—
199C22—1161no—
200C22C2×C22⋊#118111yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—292no—
205C4—581no—
206C4—581no—
207C4—1161no—
208C4—2322no—
209C4#1174522312yes—
210C2—81no—
211C2—581no—
212C2—581no—
213C2—2321no—
214C2#1427214211yescharacteristic
215C2C2×#1174522311yescharacteristic
216C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radical#14271710C2
cosocleC2×C4×D29C23
hypercenterC4×D4#1181
hypocenterC29#1517
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14272182C2semidirect
2. #14272107C2semidirect
3. #14272015C2semidirect
4. #14272014C2semidirect
8. C4×D4×C29C4semidirect
9. #11745302C4semidirect
13. #11745250C4semidirect
16. C4×D116C4semidirect
123. C4×D4#1181semidirect
131. C29#1517semidirect

Maximal subgroups

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

subgroupindex
#142721822
#142721072
#142720152
#142720142
#142717102
#151729