Finite Group Databasebeta

← #16835255

Subgroups — #16835255

Order 3712.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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×#11745224C212yesmaximal
2C4×#90796C211yesmaximal, characteristic, complemented
3#14272099C211yesmaximal, characteristic, complemented
4#14272033C212yesmaximal, complemented
5C4×#90807C211yesmaximal, characteristic
6C2×#90807C2211yescharacteristic
7C2×C4×#1181C2212yes—
8C2×#90796C2212yes—
9C4×D4×C29C411yescharacteristic, complemented
10D4×Dic29C411yescharacteristic, complemented
11C4×C22⋊D29—21no—
12C2×C4×Dic29—21no—
13#11745254C2211yescharacteristic
14#11745249C411yescharacteristic, complemented
15#11745243—21no—
16#11745239—21no—
17C42×D29C2211yescharacteristic
18C4×Dic58C411yescharacteristic, complemented
19#11745224C418yescomplemented
20(C2×#1181)⋊C4—21no—
21(C2×#1181)⋊C4—21no—
22#11745218—21no—
23C4×#6599—21no—
24C22×#1181—22no—
25C2×D4×C29C2×C411yescharacteristic
26C22×C4×C29—21no—
27C2×C22⋊D29—21no—
28C22×Dic29—21no—
29C22×Dic29—21no—
30#90807—22no—
31#90807C2×C414yes—
32C2×C4×D29D411yescharacteristic
33C2×C4×D29D411yescharacteristic
34C2×C4×D29C2311yescharacteristic
35C2×Dic58C2×C411yescharacteristic
36C2×#6599—22no—
37C4×#1181—22no—
38C4×#1181C2×C414yescomplemented
39#90796—22no—
40#90796C2×C414yescomplemented
41C4⋊C4×C29C2×C411yescharacteristic
42C22⋊C4×C29—21no—
43C42×C29C2×C411yescharacteristic
44C22⋊Dic29—21no—
45#90781—21no—
46C4⋊Dic29C2×C411yescharacteristic
47#90779—21no—
48#90779—21no—
49C4×Dic29—21no—
50C4×Dic29—21no—
51C4×Dic29—21no—
52C4×Dic29C2×C411yescharacteristic
53C4×Dic29D411yescharacteristic
54C4×Dic29D411yescharacteristic
55C23×C29—21no—
56C22×D29C2×D411yescharacteristic
57C2×#1181—24no—
58C2×#1181—42no—
59C2×#1181—42no—
60D4×C29—21no—
61D4×C29C4212yes—
62C2×C4×C29—21no—
63C2×C4×C29—42no—
64C2×C4×C29C22⋊C411yescharacteristic
65C2×C4×C29C22⋊C411yescharacteristic
66C2×C4×C29C22×C411yescharacteristic
67C22⋊D29—24no—
68C2×Dic29—21no—
69C2×Dic29—24no—
70C2×Dic29—21no—
71C2×Dic29—42no—
72C2×Dic29C22⋊C411yescharacteristic
73C2×Dic29C22⋊C411yescharacteristic
74C2×Dic29C2×D411yescharacteristic
75C4×D29—41no—
76C4×D29—41no—
77C4×D29C22×C412yes—
78C4×D29#4112yes—
79Dic58—21no—
80Dic58C4212yes—
81#6599—24no—
82#1759—291nomaximal, Sylow
83C22×C29—22no—
84C22×C29—41no—
85C22×C29—41no—
86C22×C29C2×C22⋊C411yescharacteristic
87C2×D29—21no—
88C2×D29—21no—
89C2×D29C4×D412yes—
90#1181—44no—
91C4×C29—21no—
92C4×C29—21no—
93C4×C29—41no—
94C4×C29C2×C4211yescharacteristic
95C4×C29#11711yescharacteristic
96Dic29—22no—
97Dic29—21no—
98Dic29—21no—
99Dic29—41no—
100Dic29C4×D412yes—
101C4×#41—291no—
102C2×#104—292no—
103C4×M16—291no—
104#376—291no—
105#339—292no—
106C2×C29—42no—
107C2×C29C4×C22⋊C411yescharacteristic
108C2×C29#42111yescharacteristic
109C2×C29#42111yescharacteristic
110D29—22no—
111C2×#41—291no—
112C2×M16—292no—
113C4×Q8—291no—
114C4×Q8—291no—
115C4×D4—291no—
116C4×D4—581no—
117C4×D4—581no—
118C4×D4#118111yescharacteristic, complemented
119#117—291no—
120#117—581no—
121C2×C42—291no—
122C2×C42—292no—
123C2×C42—581no—
124#104—298no—
125#97—581no—
126C4×C8—581no—
127#95—581no—
128#95—581no—
129C29#175911yescharacteristic, complemented, Sylow
130#41—294no—
131#41—582no—
132C2×Q8—291no—
133C2×D4—581no—
134C2×D4C2×#118111yescharacteristic
135C22×C4—21no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—291no—
139C22×C4—581no—
140C22×C4—581no—
141C22×C4—582no—
142M16—294no—
143M16—582no—
144C2×C8—582no—
145C4⋊C4—291no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4C2×#118111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—581no—
151C22⋊C4—581no—
152C42—291no—
153C42—291no—
154C42—291no—
155C42—294no—
156C42—581no—
157C42—581no—
158C42—582no—
159C42—581no—
160C42C2×#118111yescharacteristic
161C23—21no—
162C23—291no—
163Q8—292no—
164Q8—581no—
165D4—21no—
166D4—584no—
167D4C4×#118112yes—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—291no—
171C2×C4—292no—
172C2×C4—292no—
173C2×C4—291no—
174C2×C4—291no—
175C2×C4—584no—
176C2×C4—581no—
177C2×C4—584no—
178C2×C4—581no—
179C2×C4—1161no—
180C2×C4—1161no—
181C2×C4—1162no—
182C2×C4—1162no—
183C2×C4—1162no—
184C2×C4C22⋊#118111yescharacteristic
185C2×C4C22⋊#118111yescharacteristic
186C2×C4C22×#118111yescharacteristic
187C8—584no—
188C22—22no—
189C22—41no—
190C22—41no—
191C22—292no—
192C22—581no—
193C22—581no—
194C22C2×C22⋊#118111yescharacteristic
195C4—21no—
196C4—21no—
197C4—41no—
198C4—292no—
199C4—582no—
200C4—581no—
201C4—581no—
202C4—1164no—
203C4—1161no—
204C4C2×C4×#118111yescharacteristic
205C4#1174534511yescharacteristic
206C2—42no—
207C2—582no—
208C2C4×C22⋊#118111yescharacteristic
209C2#1427216011yescharacteristic
210C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC4×C29C2×C42
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#90807C22
cosocleC2×C4×D29C23
hypercenterC4×D4#1181
hypocenterC29#1759
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#90796C2semidirect
3. #14272099C2semidirect
4. #14272033C2semidirect
9. C4×D4×C29C4semidirect
10. D4×Dic29C4semidirect
14. #11745249C4semidirect
18. C4×Dic58C4semidirect
19. #11745224C4semidirect
38. C4×#1181C2×C4semidirect
40. #90796C2×C4semidirect
118. C4×D4#1181semidirect
129. C29#1759semidirect

Maximal subgroups

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

subgroupindex
C2×#117452242
C4×#907962
#142720992
#142720332
C4×#908072
#175929