Finite Group Databasebeta

← #16817937

Subgroups — #16817937

Order 3712.

252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×Q8×D29C211yesmaximal, characteristic
2#14271219C211yesmaximal, characteristic
3C4×#90772C211yesmaximal, characteristic
4#14270895C211yesmaximal, characteristic, complemented
5Q8⋊#6597C211yesmaximal, characteristic, complemented
6#14270893C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D29C411yescharacteristic
9C4×Q8×C29C2211yescharacteristic
10Q8×Dic29C411yescharacteristic
11C2×#90772—21no—
12C4⋊C4×D29—21no—
13C4⋊C4×D29C411yescharacteristic
14#11745249—21no—
15#11745249C411yescharacteristic
16C42×D29—21no—
17C42×D29C2211yescharacteristic
18C4×Dic58—21no—
19C4×Dic58C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C4×C8×C29C2211yescharacteristic
22#11745168—21no—
23#11745163—21no—
24#11745163—21no—
25C4⋊#6597C2211yescharacteristic
26C4×#6597C2211yescharacteristic
27C2×Q8×C29C2×C411yescharacteristic
28Q8×D29—22no—
29Q8×D29—22no—
30C2×C4×D29—21no—
31C2×C4×D29—21no—
32C2×C4×D29C2×C411yescharacteristic
33C2×C4×D29D411yescharacteristic
34C2×C4×D29D411yescharacteristic
35C2×Dic58—21no—
36C2×Dic58C2×C411yescharacteristic
37C2×C8×C29—21no—
38C2×C8×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29C2×C411yescharacteristic
41C42×C29—21no—
42C42×C29C2311yescharacteristic
43C4⋊Dic29—21no—
44C4⋊Dic29C2×C411yescharacteristic
45#90779—21no—
46#90779—21no—
47#90779—21no—
48C4×Dic29—21no—
49C4×Dic29—21no—
50C4×Dic29—21no—
51C4×Dic29C2×C411yescharacteristic
52C4×Dic29D411yescharacteristic
53C4×Dic29D411yescharacteristic
54C2×#6597—21no—
55C2×#6597—21no—
56#90772—24no—
57C22×D29C22⋊C411yescharacteristic
58Q8×C29—21no—
59Q8×C29M1612yescomplemented
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29C22×C411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29C22⋊C411yescharacteristic
68C2×Dic29C22⋊C411yescharacteristic
69C2×Dic29C22⋊C411yescharacteristic
70C4×D29—24no—
71C4×D29—22no—
72C4×D29—21no—
73C4×D29—21no—
74C4×D29—21no—
75C4×D29—21no—
76C4×D29—42no—
77Dic58—24no—
78Dic58—21no—
79Dic58M1612yescomplemented
80C8×C29—22no—
81C8×C29—41no—
82#6597—22no—
83#6597—41no—
84#1491—291nomaximal, Sylow
85C22×C29C2×C22⋊C411yescharacteristic
86C2×D29—21no—
87C2×D29—21no—
88C2×D29#10412yes—
89C4×C29—22no—
90C4×C29—21no—
91C4×C29—41no—
92C4×C29C2×M1611yescharacteristic
93C4×C29C2×M1611yescharacteristic
94C4×C29#13711yescharacteristic
95C4×C29#13711yescharacteristic
96Dic29—21no—
97Dic29—22no—
98Dic29—21no—
99Dic29—21no—
100Dic29—41no—
101C2×C4×Q8—291no—
102#432—291no—
103C4×M16—291no—
104Q8⋊C8—291no—
105Q8⋊C8—291no—
106Q8⋊C8—291no—
107Q8⋊C8D2911yescharacteristic, complemented
108C2×C29#40711yescharacteristic
109C2×C29#41911yescharacteristic
110C2×C29C2×#10411yescharacteristic
111D29—22no—
112C22×Q8—291no—
113C2×M16—581no—
114C4×Q8—291no—
115C4×Q8—291no—
116C4×Q8—291no—
117C4×Q8—581no—
118C4×Q8—581no—
119C4×Q8C2×D2911yescharacteristic
120C2×C4⋊C4—291no—
121C2×C4⋊C4—581no—
122C2×C42—291no—
123C2×C42—581no—
124C4⋊C8—291no—
125C4⋊C8C2×D2911yescharacteristic
126C22⋊C8—581no—
127#97—581no—
128#97—581no—
129C4×C8—291no—
130C4×C8C2×D2911yescharacteristic
131C29#149111yescharacteristic, complemented, Sylow
132C2×Q8—291no—
133C2×Q8—581no—
134C2×Q8—582no—
135C2×Q8—582no—
136C2×Q8C4×D2911yescharacteristic
137C22×C4—291no—
138C22×C4—291no—
139C22×C4—291no—
140C22×C4—581no—
141C22×C4—581no—
142M16—584no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—581no—
146C2×C8—581no—
147C4⋊C4—21no—
148C4⋊C4—291no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4C4×D2911yescharacteristic
154C42—21no—
155C42—291no—
156C42—291no—
157C42—291no—
158C42—581no—
159C42—581no—
160C42—581no—
161C42C22×D2911yescharacteristic
162C23—291no—
163Q8—21no—
164Q8—292no—
165Q8—584no—
166Q8—581no—
167Q8#9077212yescomplemented
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—291no—
171C2×C4—291no—
172C2×C4—291no—
173C2×C4—582no—
174C2×C4—584no—
175C2×C4—581no—
176C2×C4—581no—
177C2×C4—581no—
178C2×C4—581no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—1162no—
182C2×C4C2×C4×D2911yescharacteristic
183C2×C4D4×D2911yescharacteristic
184C2×C4D4×D2911yescharacteristic
185C8—22no—
186C8—41no—
187C8—582no—
188C8—1161no—
189C22—292no—
190C22—581no—
191C22—581no—
192C22C22⋊C4×D2911yescharacteristic
193C4—22no—
194C4—21no—
195C4—41no—
196C4—581no—
197C4—582no—
198C4—581no—
199C4—581no—
200C4—1161no—
201C4C2×#9077211yescharacteristic
202C4M16×D2911yescharacteristic
203C4#1174527711yescharacteristic
204C4#1174528011yescharacteristic
205C2—582no—
206C2#1427112511yescharacteristic
207C2#1427117011yescharacteristic
208C2#104×D2911yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29C2×C22⋊C4
prime radicalC22×D29C22⋊C4
cosocleC42×C29C23
hypercenterQ8⋊C8D29
hypocenterC29#1491
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #14270895C2semidirect
5. Q8⋊#6597C2semidirect
6. #14270893C2semidirect
7. C29×Q8⋊C8C2semidirect
59. Q8×C29M16semidirect
79. Dic58M16semidirect
107. Q8⋊C8D29semidirect
131. C29#1491semidirect
167. Q8#90772semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D292
#142712192
C4×#907722
#142708952
Q8⋊#65972
#142708932
C29×Q8⋊C82
#149129