Finite Group Databasebeta

← #16817928

Subgroups — #16817928

Order 3712.

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

normal subgroups only

This group has 266 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×#90807C211yesmaximal, characteristic
2#14271185C211yesmaximal, characteristic, complemented
3C4×#90772C211yesmaximal, characteristic, complemented
4#14270895C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#90807C411yescharacteristic
9C4×D4×C29C2211yescharacteristic
10D4×Dic29C411yescharacteristic
11C4×C22⋊D29—21no—
12C2×C4×Dic29—21no—
13C2×#90772—21no—
14C2×#90772—21no—
15#11745254C411yescharacteristic
16#11745249C411yescharacteristic
17#11745243—21no—
18#11745239—21no—
19C42×D29C2211yescharacteristic
20C4×Dic58C2211yescharacteristic
21C29×C4⋊C8C2211yescharacteristic
22C4×C8×C29C2211yescharacteristic
23#11745163—21no—
24#11745162—21no—
25C4⋊#6597C2211yescharacteristic
26C4×#6597C2211yescharacteristic
27C2×D4×C29C2×C411yescharacteristic
28C22×C4×C29—21no—
29C2×C22⋊D29—21no—
30C22×Dic29—21no—
31C22×Dic29—21no—
32#90807—22no—
33#90807—22no—
34C2×C4×D29C2×C411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×Dic58C2×C411yescharacteristic
38C2×C8×C29—21no—
39C2×C8×C29—21no—
40C4⋊C4×C29C2×C411yescharacteristic
41C22⋊C4×C29—21no—
42C42×C29C2311yescharacteristic
43C22⋊Dic29—21no—
44#90781—21no—
45C4⋊Dic29C2×C411yescharacteristic
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—
57#90772—42no—
58C23×C29—21no—
59C22×D29C22⋊C411yescharacteristic
60D4×C29—21no—
61D4×C29M1612yescomplemented
62C2×C4×C29—21no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29C22×C411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D411yescharacteristic
68C22⋊D29—24no—
69C2×Dic29—24no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—42no—
73C2×Dic29C22⋊C411yescharacteristic
74C2×Dic29C22⋊C411yescharacteristic
75C2×Dic29C22⋊C411yescharacteristic
76C4×D29—21no—
77C4×D29—21no—
78C4×D29—21no—
79C4×D29—21no—
80C4×D29—22no—
81Dic58—21no—
82Dic58M1612yescomplemented
83C8×C29—22no—
84C8×C29—41no—
85#6597—22no—
86#6597—41no—
87#1489—291nomaximal, Sylow
88C22×C29—22no—
89C22×C29—41no—
90C22×C29—41no—
91C22×C29C2×C22⋊C411yescharacteristic
92C2×D29—21no—
93C2×D29—21no—
94C2×D29—21no—
95C4×C29—21no—
96C4×C29—41no—
97C4×C29C2×M1611yescharacteristic
98C4×C29C2×M1611yescharacteristic
99C4×C29AGL(1,ℤ/8)11yescharacteristic
100C4×C29#13711yescharacteristic
101Dic29—22no—
102Dic29—21no—
103Dic29—21no—
104Dic29—41no—
105Dic29#10412yes—
106C4×#41—291no—
107#423—291no—
108C4×M16—291no—
109Q8⋊C8—291no—
110Q8⋊C8—291no—
111D4⋊C8—291no—
112D4⋊C8D2911yescharacteristic, complemented
113C2×C29—42no—
114C2×C29#40711yescharacteristic
115C2×C29#41711yescharacteristic
116C2×C29C2×#10411yescharacteristic
117D29—41no—
118C2×#41—291no—
119C2×M16—581no—
120C2×M16—581no—
121C4×Q8—291no—
122C4×Q8—291no—
123C4×D4—291no—
124C4×D4—581no—
125C4×D4—581no—
126C4×D4C2×D2911yescharacteristic
127#117—291no—
128#117—581no—
129C2×C42—291no—
130C2×C42—581no—
131C4⋊C8—291no—
132C4⋊C8—581no—
133C4⋊C8C2×D2911yescharacteristic
134#97—581no—
135C4×C8—291no—
136C4×C8C2×D2911yescharacteristic
137C29#148911yescharacteristic, complemented, Sylow
138#41—582no—
139#41—582no—
140C2×Q8—291no—
141C2×D4—581no—
142C2×D4C4×D2911yescharacteristic
143C22×C4—21no—
144C22×C4—291no—
145C22×C4—291no—
146C22×C4—291no—
147C22×C4—581no—
148C22×C4—581no—
149M16—584no—
150M16—1162no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—581no—
154C2×C8—581no—
155C4⋊C4—291no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4C4×D2911yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C42—291no—
163C42—291no—
164C42—291no—
165C42—581no—
166C42—581no—
167C42—581no—
168C42C22×D2911yescharacteristic
169C23—21no—
170C23—291no—
171Q8—292no—
172Q8—581no—
173D4—21no—
174D4—584no—
175D4#9077212yescomplemented
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—291no—
180C2×C4—291no—
181C2×C4—291no—
182C2×C4—582no—
183C2×C4—584no—
184C2×C4—581no—
185C2×C4—581no—
186C2×C4—581no—
187C2×C4—581no—
188C2×C4—581no—
189C2×C4—581no—
190C2×C4—1162no—
191C2×C4C2×C4×D2911yescharacteristic
192C2×C4D4×D2911yescharacteristic
193C2×C4D4×D2911yescharacteristic
194C8—22no—
195C8—41no—
196C8—582no—
197C8—1161no—
198C22—22no—
199C22—41no—
200C22—41no—
201C22—581no—
202C22—581no—
203C22—581no—
204C22C22⋊C4×D2911yescharacteristic
205C4—21no—
206C4—41no—
207C4—292no—
208C4—581no—
209C4—582no—
210C4—581no—
211C4—1161no—
212C4C2×#9077211yescharacteristic
213C4M16×D2911yescharacteristic
214C4#1174527311yescharacteristic
215C4#1174527711yescharacteristic
216C2—42no—
217C2—1161no—
218C2#1427112511yescharacteristic
219C2#1427116111yescharacteristic
220C2#104×D2911yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29C2×C22⋊C4
prime radicalC2×#90807C4
cosocleC42×C29C23
hypercenterD4⋊C8D29
hypocenterC29#1489
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14271185C2semidirect
3. C4×#90772C2semidirect
4. #14270895C2semidirect
5. #14270893C2semidirect
6. D4⋊#6597C2semidirect
7. C29×D4⋊C8C2semidirect
61. D4×C29M16semidirect
82. Dic58M16semidirect
112. D4⋊C8D29semidirect
137. C29#1489semidirect
175. D4#90772semidirect

Maximal subgroups

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

subgroupindex
C4×#908072
#142711852
C4×#907722
#142708952
#142708932
D4⋊#65972
C29×D4⋊C82
#148929