Finite Group Databasebeta

← #16834828

Subgroups — #16834828

Order 3712.

266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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#14272167C211yesmaximal, characteristic, complemented
2C4×#90796C211yesmaximal, characteristic, complemented
3#14272013C212yesmaximal, complemented
4D4⋊#6599C212yesmaximal, complemented
5C4×#90807C211yesmaximal, characteristic
6C2×#90807C411yescharacteristic
7C2×#90796—21no—
8C2×#90796—21no—
9C4×D4×C29C411yescharacteristic
10D4×Dic29C2211yescharacteristic
11C4×C22⋊D29—21no—
12C2×C4×Dic29—21no—
13#11745254C411yescharacteristic
14#11745249C2211yescharacteristic
15#11745243—21no—
16#11745239—21no—
17C42×D29C2211yescharacteristic
18C4×Dic58C411yescharacteristic
19#11745218—21no—
20C4⋊#6599—21no—
21C4⋊#6599C2212yes—
22C4×#6599C2212yes—
23C2×D4×C29C2×C411yescharacteristic
24C22×C4×C29—21no—
25C2×C22⋊D29—21no—
26C22×Dic29—21no—
27C22×Dic29—21no—
28#90807—22no—
29#90807—22no—
30C2×C4×D29C2×C411yescharacteristic
31C2×C4×D29D411yescharacteristic
32C2×C4×D29D411yescharacteristic
33C2×Dic58C2×C411yescharacteristic
34C2×#6599—22no—
35C2×#6599—22no—
36#90796—24no—
37#90796—42no—
38C4⋊C4×C29C2×C411yescharacteristic
39C22⋊C4×C29—21no—
40C42×C29C2×C411yescharacteristic
41C22⋊Dic29—21no—
42#90781—21no—
43C4⋊Dic29C2×C411yescharacteristic
44#90779—21no—
45#90779—21no—
46C4×Dic29—21no—
47C4×Dic29—21no—
48C4×Dic29—21no—
49C4×Dic29D411yescharacteristic
50C4×Dic29D411yescharacteristic
51C4×Dic29C2311yescharacteristic
52C23×C29—21no—
53C22×D29C22⋊C411yescharacteristic
54D4×C29—21no—
55D4×C29M1612yescomplemented
56C2×C4×C29—21no—
57C2×C4×C29—42no—
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22⋊C411yescharacteristic
60C2×C4×C29C22×C411yescharacteristic
61C22⋊D29—24no—
62C2×Dic29—24no—
63C2×Dic29—21no—
64C2×Dic29—21no—
65C2×Dic29—41no—
66C2×Dic29—41no—
67C2×Dic29C22⋊C411yescharacteristic
68C2×Dic29C2×D411yescharacteristic
69C2×Dic29C2×D411yescharacteristic
70C4×D29—22no—
71C4×D29—21no—
72C4×D29—21no—
73C4×D29—21no—
74C4×D29—21no—
75Dic58—21no—
76Dic58M1612yescomplemented
77#6599—24no—
78#6599—42no—
79#1489—291nomaximal, Sylow
80C22×C29—22no—
81C22×C29—41no—
82C22×C29—41no—
83C22×C29C2×C22⋊C411yescharacteristic
84C2×D29—21no—
85C2×D29—21no—
86C2×D29—21no—
87C4×C29—21no—
88C4×C29—41no—
89C4×C29#10412yes—
90C4×C29C2×M1611yescharacteristic
91C4×C29C2×M1611yescharacteristic
92Dic29—22no—
93Dic29—21no—
94Dic29—21no—
95Dic29—41no—
96Dic29AGL(1,ℤ/8)11yescharacteristic
97Dic29#13711yescharacteristic
98C4×#41—291no—
99#423—291no—
100C4×M16—291no—
101Q8⋊C8—292no—
102D4⋊C8—292no—
103C2×C29—42no—
104C2×C29#40711yescharacteristic
105C2×C29#41711yescharacteristic
106C2×C29C2×#10411yescharacteristic
107D29—41no—
108C2×#41—291no—
109C2×M16—581no—
110C2×M16—581no—
111C4×Q8—291no—
112C4×Q8—291no—
113C4×D4—291no—
114C4×D4—581no—
115C4×D4—581no—
116C4×D4#118111yescharacteristic
117#117—291no—
118#117—581no—
119C2×C42—291no—
120C2×C42—581no—
121C4⋊C8—292no—
122C4⋊C8—581no—
123#97—581no—
124C4×C8—292no—
125C29#148911yescharacteristic, complemented, Sylow
126#41—582no—
127#41—582no—
128C2×Q8—291no—
129C2×D4—581no—
130C2×D4C2×#118111yescharacteristic
131C22×C4—21no—
132C22×C4—291no—
133C22×C4—291no—
134C22×C4—291no—
135C22×C4—581no—
136C22×C4—581no—
137M16—584no—
138M16—1162no—
139C2×C8—582no—
140C2×C8—582no—
141C4⋊C4—291no—
142C4⋊C4—581no—
143C4⋊C4—581no—
144C4⋊C4C2×#118111yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—581no—
147C22⋊C4—581no—
148C42—291no—
149C42—291no—
150C42—291no—
151C42—581no—
152C42—581no—
153C42—581no—
154C42C2×#118111yescharacteristic
155C23—21no—
156C23—291no—
157Q8—292no—
158Q8—581no—
159D4—21no—
160D4—584no—
161D4#9079612yescomplemented
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—291no—
165C2×C4—291no—
166C2×C4—291no—
167C2×C4—581no—
168C2×C4—581no—
169C2×C4—584no—
170C2×C4—581no—
171C2×C4—581no—
172C2×C4—581no—
173C2×C4—582no—
174C2×C4—581no—
175C2×C4—1161no—
176C2×C4—1161no—
177C2×C4C22⋊#118111yescharacteristic
178C2×C4C22⋊#118111yescharacteristic
179C2×C4C22×#118111yescharacteristic
180C8—584no—
181C8—1162no—
182C22—22no—
183C22—41no—
184C22—41no—
185C22—581no—
186C22—581no—
187C22—581no—
188C22C2×C22⋊#118111yescharacteristic
189C4—21no—
190C4—41no—
191C4—291no—
192C4—291no—
193C4—581no—
194C4—582no—
195C4—581no—
196C4—1161no—
197C4#1174522412yes—
198C4C2×#9079611yescharacteristic
199C4D29⋊M1611yescharacteristic
200C2—42no—
201C2—1161no—
202C2#1427213411yescharacteristic
203C2#1427215411yescharacteristic
204C2C2×#1174522411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#90807C4
cosocleC4×Dic29C23
hypercenterC4×D4#1181
hypocenterC29#1489
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14272167C2semidirect
2. C4×#90796C2semidirect
3. #14272013C2semidirect
4. D4⋊#6599C2semidirect
55. D4×C29M16semidirect
76. Dic58M16semidirect
125. C29#1489semidirect
161. D4#90796semidirect

Maximal subgroups

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

subgroupindex
#142721672
C4×#907962
#142720132
D4⋊#65992
C4×#908072
#148929